Slide 1

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 2

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 3

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 4

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 5

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 6

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 7

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 8

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 9

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 10

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 11

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 12

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 13

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 14

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 15

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 16

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 17

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 18

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 19

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 20

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 21

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 22

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 23

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 24

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 25

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 26

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 27

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 28

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 29

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 30

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 31

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 32

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 33

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 34

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 35

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 36

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 37

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 38

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 39

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 40

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 41

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 42

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43


Slide 43

MechaRock International Consultants

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

About us
MechaRock International Consultants is an association of
engineering consultants and experts around the world sharing
their experience and numerical tools in the field of modelling
and design of civil engineering structures, geotechnical and
mining projects in rock formations and petroleum
geomechanics.

www.mecharock.com

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Main activities: Software development :

DISROC ®

Finite Element Method for modelling engineering structures
Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal
behaviour of engineering structures and is widely used in various softwares as given by the following figures:

Most of geotechnical projects are designed by Finite Element Method, and software using this
method are highly appreciated by engineers if the .
However, in presence of fractures and discontinuities, softwares based on Finite Difference or
Distinct Element methods seems to be needed, even if these methods and software are less efficient
or less pleasant to use (calculation time, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

5

Main activities: Software development :

DISROC ®

Joint Elements for fractures in Finite Element Method
Zero thickness Joint Element was proposed by (Goodman 1976) for
modeling discontinuities in the Finite Element Method.

3

4

1

2

Joint Element (Goodman 1976)
f (  )=  +  n tg   c

Fracture

With appropriate parameters,
joint elements can reproduce
the behavior of fractures,
rockjoints, interfaces and
contact surfaces.



c

A

 n

Rockjoint, Masonry mortar
However, their use in presence of
a great number of discontinuities
or fractures poses the difficulty
of Conform Finite Element mesh
creation.

Contact interface

6

Main activities: Software development :

DISROC ®

Conform Finite Element mesh generation for fractured medium
DISROC® is the first Finite
Element code especially
conceived for fractured rocks.
Its powerful meshing tool
Discrac® allows easily creating a
conform mesh and special Joint
Elements for fractured media.


e
Joint : K n ,
K t ,c , f


e

7

Main activities: Software development :

DISROC ®

GID

DISROC®
Architecture

WinDisroc
Fracture generation
Parameters

GID is a powerful pre and post
processor developed by Cimne:
www.gidhome.com

DisrocFP generates fractured
rock mass

Geometry
Boundary conditions
Mesh

input
file
DISROC®

Discrac

Discrac allows joint
elements creation

DISROC® is the calculation
module

output
file

GID
Post Process
8

Main activities: Software development :

DISROC ®

Functionalities of DISROC® :
Hydro-mechanical behavior of rock masses
DISROC® has the following main functionalities:
• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading
• Incremental multistage excavation of underground openings and rock cuttings
• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties:
Determination of the effective elastic parameters
Determination of equivalent permeability
Simulation of effective stress-strain curve to determine effective strength properties
• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID
(www.gidhome.com) that allows easily defining the geometry and materials model,
generating mesh, and displaying the calculation results in the form of contours and
9
curves, etc.

Main activities: Software development :

DISROC ®

Modelling fractured rocks
with DISROC®
With DISROC® it becomes easy to model geotechnical projects like dams, tunnels,
bridges and rock cuttings in fractured rocks.
Tunnel in fractured rock

Rock Slope
Stability

10

Main activities: Software development :

DISROC ®

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model
when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts
crossing fractures.

Effective elastic properties of fractured rock masses are very often needed for
projects design:
DISROC® has a “Large scale Homogenization” module for determination of effective
parameters of fracture rock masses (deformation modulus, cohesion, angle of
internal friction).

Homogenization of fractured
rock properties

Bolting fractured rock

11

Main activities: Software development :

DISROC ®

Modeling bolts and anchors in DISROC®
Complete models for bolts, anchors and bars are available in Disroc with full
integration of the grout behavior by an elastic-plastic interface model.
41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contact
Nb = 8
Param1 = E (bolt elastic modulus)
Param2 = Kt (bolt/rock contact shear stifness )
Param3 = Kn (bolt/rock contact normal stifness )
Param4 = Knt = Ktn (bolt/rock contact ns stifness )
Param5 = Ys (bolt elastic limit)
Param6 = c (bolt/rock contact cohesion)
Param7 = f (bolt/rock contact friction angle)
Param8 = s0 (bolt pres-stress)

Bolts can cross fractures. The model of intersection allows
discontinuity of rock displacement at the two side of the fracture
with continuity of the bolt rod.
Disroc® is the only Finite Element software allowing this modeling.
12

Main activities: Software development :

DISROC ®

Representing bolt stresses in DISROC®
 Pull out test on a bolt crossing a fracture

F

SL
SL (MN)

FEM mesh for the sample, bolt
and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a local maximum when crossing the fracture.

 Deformation at the roof of a bolted tunnel
SL (MN)

SL

Weight

FEM mesh for the rock,
Bolt and fracture

Axial force SL in the bolt represented in two different ways.
SL passes by a maximum when crossing the fracture.
13

Main activities: Software development :

DISROC ®

Materials models in DISROC®
A great variety of classical constitutive models are available in DISROC for rocks,
fractures, joints and rockbolts.
• Solid materials:
Elastic-plastic behavior:
- Linear isotropic or anisotropic elasticity
- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic
failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces
Joint : K n , K t ,C , f

- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–grout
interface

14

Main activities: Software development :

DISROC ®

Displaying results in DISROC®
A variety of different representations of the results are possible, specially those
concerning rock joints and fractures.
Example: Deformation of the fractured REV
under shear stress xy :
Ux displacement

Stress vectors on rock joints

Normal stress on rock joints

15

MechaRock International Consultants

• About us
• Main activities
Software DISROC®
Consulting services

Consulting services

Tunnels
Slope stablity
Dams
Homogeneization
Masonry structures

Main activities: Consulting services - TUNNELS
I. Tunnels design
Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting
Modeling fractures and bolts with DISROC® is very easy.
The following tunnel/road project includes:
• a rock mass with two sets of fractures (possibly non persistent)
• non persistent fractures (cracks) on the tunnel’s wall,
• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created
by DISROC®.

18

Main activities: Consulting services - TUNNELS
Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com)
is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.
The meshing tool integrates:
• Intersecting fractures (a)
• Non persistent fractures (b)
• Rockbolts passing through fractures (c)

(a)

(c)
(b)

19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS
Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting
The project includes a tunnel and a rock
cutting for a road in a fractured sedimentary
formation. The formation is constituted of
alternate layers of two limestones varieties.
The interfaces between layers are modeled
as fractures (Fracture1). Two faults are
present in the formation (Fracture2).
Modeling passes through the following
stages.

I) The fractures are generated stochastically
(Fracture1)and faults are placed in the model
with their known position (Fracture2) .

road

II) Other lines defining the soil profile, the
tunnel contour, the cutting contour and the rock
21
bolts are introduced in the model.

Main activities: Consulting services - TUNNELS
Tunnels : Modeling stages
III) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt
elements for rockbolts are created automatically. The material properties are assigned to limestone layers,
fractures and rock bolts.
In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are
introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.

22

Main activities: Consulting services - TUNNELS
IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and
boundary conditions, modeling excavation stages, displaying results…

In situ stress (yy) before excavation

Vertical stress (yy) after tunnel excavation
SL

Vertical displacement Uy due to tunnel excavation

Rock bolts are placed (activated) in the model at
this stage with a pre-stress SL = 0.1 T
23

Main activities: Consulting services - TUNNELS

Vertical stress (yy) after rock cutting

Vertical displacement details showing fractures opening

Vertical displacement showing uplift after rock cutting

Bolts stresses change when crossing fractures24
and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS
Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS
Case study 4 - Tunnels in a blocky rockmass
Displacement
14

Tunnels

Non
convergence

12
10
8
6
4
2
0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1.0
Load ratio

Displacement at the roof of the tunnel versus the
excavation ratio
Tunnel in a blocky rockmass

Calculations diverge before total excavation
and can not go beyond the excavation ratio of
0.9.

The displacement field at this stage shows the
existence of instable blocks at the roof of the
tunnel.
Instable blocks at the roof of the tunnel

Main activities: Consulting services – SLOPE STABILITY
II. Rock slope stability
Analysis and stabilization of natural rock slopes, rock cuttings and
open pit mines





Fractures can be introduced in the model by
stochastic distribution laws or in a deterministic
way.
Gravity load can be applied step by step to
determine the safety factor of the slope.
Horizontal and vertical accelerations can be
applied in order to analyze the stability against
seismic loads.

Finite Element mesh created by
DISCRAC® and GID

Shear stress on fractures

Rock slope with two types of fractures

Displacement under
prescribed load

27

Main activities: Consulting services – SLOPE STABILITY
Slope stability under seismic load

A

Rock cut in a blocky
rockmass

Application of gravity forces to
define the initial state of stress

Addition of 1 g horizontal acceleration to
represent seismic load

Displacement

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Load ratio

Displacement of the point A versus seismic load ratio. The
calculations can not go beyond 0.7 g horizontal
acceleration and diverge at this stage.

The displacement field at 0.7g horizontal
acceleration reveals an instable block (blue
28
in the figure)

Main activities: Consulting services – SLOPE STABILITY
Slope design optimization
Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting
design.
If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and
analyze the modified project.

Initial slope design revealed to
be instable

Design modification

Modified model in DISROC
29

Main activities: Consulting services – DAMS
III. Dams

•

Cross section of an
Earth Dam lying on a
rock mass foundation
with two sets of
discontinuities
(DISROC)

•

Rock foundation along
with the dam and the
dam-foundation
interaction are
analyzed in a unique
model enclosing all the
fractures’ sets

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Fracturing model data acquisition
I) For each family of fractures, the fractures’
orientation, length, spacing and mechanical
parameters are specified.

II) Fractures sets are generated stochastically
according to specified parameters.

III) A conform Finite
Element mesh is created by
Discrac® + GID.

31

Main activities: Consulting services - HOMOGENEIZATION
Homogenization in DISROC : Load application on the REV
IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are
applied on the REV’s contour.

Uy displacement under uniaxial
compression yy

Ux displacement under shear
stress xy
xx

V) The average stresses and strains in the REV, taking into
account the fractures opening, are computed for each
loading case and the homogenized elastic properties of
the fractured rock mass are determined from the average
values.

1 2 .1

1 .6
C ij  
 2 .3

 2 .6

yy

zz

xy

1 .6

2 .3

1 4 .2

3 .5

3 .5

1 8 .4

2 .8

 1 .2

2 .6 

2 .8

 1 .2 

5 .3 

Anisotropic elastic coefficients
for the homogenized behavior

32

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The stiffness and compliance tensors lines are computed automatically by imposing boundary
conditions corresponding to macroscopic strain or stress in different directions.
 c11
  11 



 22

  

  33 



  12 

 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61
 s11
 e 11 



e 22

  

 e 33 



 2 e 12 


c12

c13

c 22

c 23
c 33

c12

c13

c 22

c 23

c 32

c 33

c 62

c63

s12

s13

s 22

s 23
s 33

c16 

c 26

c 36 

c 66 

 e 11 


e 22


 e 33 


 2 e 12 

c16 

c 26

c 36 

c66 

1 
 
0
 
0 
 
0 

s16 

s 26

s 36 

s 66 

  11 


 22


  33 


  12 

1
2
3
4

5
6
7
8
33

Main activities: Consulting services - HOMOGENEIZATION
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness and
compliance tensors lines are
given as a direct result of
calculation.
 c11
  11 



c
 22

   21
 c31
  33 



  12 
 c 61

 0.347 E  1

.
C ij  

.

.


c12

c13

c 22

c 23

c 32

c 33

c 62

c63

c16 

c 26

c 36 

c66 

 0.495 E  2

0.353 E  16

.

.

.

.

.

.

1 
 
0
 
0 
 
0 

0. 128 E  0 

.


.

.


34

Main activities: Consulting services - HOMOGENEIZATION
Example : sedimentary bedded rock
1

Goodman formula:
s11 

1
E

,

s12  s13 

E

E

,

s 33 

1
E

e





1



1

E

k nD

,

s 44 

1
k nD

1



G

1
k tD

E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

 s1 1

 s1 2
 r
 s1 3
s
 16

r

s1 2

s1 3

s22

s23

s23

r

s3 3

s26

s3 6

r

r

r

s1 6 

s26 

r 
s3 6 
s 6 6 

35

Main activities: Consulting services - HOMOGENEIZATION
IV. Fractured rock mass replaced by a continuous effective Material
•

•

Accurate calculation of the Homogenized large scale mechanical properties of rock masses:
Equivalent anisotropic mechanical properties: E(MPa), , C (MPa) and f ().
This method replaces the inaccurate empirical classification systems like RMR and Q used by
engineers.

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

36 in different
Equivalent elastic modulus

directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION
Case study 2 - Granitic rock mass : De la Vienne, France

37

Main activities: Consulting services - HOMOGENEIZATION
Case study 3 – General case
A preliminary homogenization allows replacing the fractured rock mass with a continuous media with
effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

?
Fractures and faults modeled individually as discontinuities

Far-field fractures act only by their global
effects, and only in elastic phase.
Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field).

Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION

Rockmass with general configuration of fractures
The effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and
can be introduced as material parameters for modeling the rock mass by its effective properties.

xx
 0 .1

.
C ij  
 .

 .

yy

zz

-0 .2 5

-0 .2 5

0 .2

-0 .2 5

.

0 .1

.

.

xy
0



0

0 

0 .3 2 5 

?

39

Main activities: Consulting services – MASONRY STRUCTURES
V. Masonry structures
Case study 1 – Bridges
Stability assessment for retrofitting purposes

Déformée du pont sous charge concentrée

Pont de Nahr el Kalb-Liban

Evolution de
le pont
Evolution
ofl’état
thed’endommagement
damage state dans
in the
bridge
Ouverture et
Opening
ofdécollement
the
des joints en traction
active fractures

Force (T)

3

Vertical stress maps

Cartographie de la contrainte verticale

2

1
Déplacement (m)

Concentration des contraintes au

Concentrationvoisinage
of stress
near
des fractures
the fractures zone
1

2

3

40

Main activities: Consulting services – MASONRY STRUCTURES
Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the
development of an active fracture due to foundation settlement

Geometry of the masonry bridge

Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress

Horizontal stress

41

Main activities: Consulting services – MASONRY STRUCTURES
Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes

Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

42

For more information:

MechaRock International Consultants
www.mecharock.com

43