Transcript Diapositive 1

Modeling Fractured Rocks
with the Finite Element code DISROC
About Disroc
DISROC is a Finite Element code specially conceived for modeling
geotechnical projects in fractured rocks. It is based on more than
20 years of shared experience between an association of
researchers, engineering consultants and experts in numerical
modeling of civil engineering structures, geotechnical and mining
projects in fractured rock formations.
MechaRock International Consultants
www.mecharock.com
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.
Most of geotechnical projects are designed by Finite Element Method, and softwares using
this method are highly appreciated by engineers.
However, in presence of fractures and discontinuities, softwares based on Finite Difference
or Distinct Element methods seems to be needed, even if these methods are less efficient
or pleasant to use (time duration, geometry limitations, outputs…).
2
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 ()=  +ntg 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.
Disroc has solved this problem.
Contact interface
3
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.
Joint : K n , K t ,c , f
 DIScontinuous ROCk
 DIScretization of CRACked media

e

e
4
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
5
Modelling fractured rocks with 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
6
Modelling fractures and bolts
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.
7
Meshing with Discrac®
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)
8
Tunnels 1: Example of a project with rock cutting in a fractured rockmass
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
9
rock bolts are introduced in the model.
Tunnels :1:Modeling
stages
Example
of a project with rock cutting in a fractured rockmass
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.
10
Tunnels 1: Example of a project with rock cutting in a fractured rockmass
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
11
Tunnels 1: Example of a project with rock cutting in a fractured rockmass
Vertical stress (yy) after rock cutting
Vertical displacement details showing fractures opening
Vertical displacement showing uplift after rock cutting
Bolts stresses change when crossing fractures12
and attain a maximum value of 2 T.
Tunnels 2: Case Study
A double line tunnel in a
sedimentary rock mass
13
Tunnels 3: Example of bolting effects on the Safety Factor
14
Tunnels 4: Bloc fall in a tunnel in blocky rockmass
Displacement
14
Tunnels
Non
convergence
12
10
8
6
4
2
0
0.0
Tunnel in a blocky rockmass
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
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
Rock slope stability analysis
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
16
Rock slope stability analysis
The stability of natural rock slopes, rock cuttings and
open pit mines is easily analyzed with DISROC.



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.
Rock slope with two types of fractures
Finite Element mesh created
by DISCRAC® and GID
Shear stress on fractures
Displacement under
17
prescribed load
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
18
(blue in the figure)
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
19
Stability of dams on fractured rock
•
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
20
Effective model for fractured rockmass
A preliminary homogenization allows replacing the fractured rock mass by a continuous media with
adequate 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 (near-field)
and replaced by an effective material (far-field).
Fractures replaced by a continuous effective material
Example : sedimentary bedded rock
1
1
1


E k nD
Ee
Goodman formulae:
s 11 
1
,
E
s12  s13 

,
E
s 33 
1
1

,
E k nD
s 44 
1
1

G ktD
E = 10 GPa,  = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m
 s11

 s12
 r
 s13
s
 16
s12
r
s13
s22
r
s23
r
s23
r
s33
s26
r
s36
s16 

s26 

r 
s36

s66 
22
Homogenization in DISROC
DISROC contains a specific module for determining a continuum equivalent model for a
fractured rock mass.
1
35
36
34
7
2’ 2
3
1
6
33
4
5
5
32
6
4
31
2
7
3
30
8
2
29
9
1
28
0
1’
-68
10
27
11
26
12
25
13
24
14
23
15
22
16
21
Fractures geometry in a sedimentary rock mass
20
exact.:E^0.25
19
18
17
exact:E/150
Equivalent elastic modulus in different
directions determined by homogenization
The geometry and mechanical properties of fractures are introduced in DISROC which
determines equivalent elastic properties of the rock mass by a numerical
homogenization method.
The following slides show different stages of this process.
23
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.
24
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.
yy
zz
xy
12.1 1.6 2.3 2.6 
 1.6 14.2 3.5 2.8 

Cij  
 2.3 3.5 18.4 1.2 


 2.6 2.8 1.2 5.3 
Anisotropic elastic coefficients
for the homogenized behavior
25
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 c12
 11 

 
c22
22
   

 33 

 
 12 

 c11 c12
 11 
c
 
22
    21 c22
 c31 c32
 33 

 
 12 
 c61 c62
 s11
 e11 

e 
22

  

 e33 



 2e12 

c13
c23
c33
c13
c23
c33
c63
s12
s13
s22
s23
s33
c16 
c26 
c36 

c66 
 e11 
e 
 22 
 e33 


 2e12 
c16 
c26 
c36 

c66 
1 
0
 
0
 
0
s16   11 
s26   22 
s36   33 
 
s66   12 
1
2
3
4
5
6
7
8
26
Homogenization : Anisotropic stiffness and compliance tensor calculation
The homogenized stiffness
and compliance tensors lines
are given as a direct result of
calculation.
 c11 c12
 11 
c
 
22
    21 c22
 c31 c32
 33 

 

 12 
 c61 c62
11.0
 0.9
Cij  
 4.0

 0.0
c13
c23
c33
c63
c16 
c26 
c36 

c66 
1 
0
 
0
 
0
0.9 4.0 0.0 
2.8 4.0 0.0 
4.0 12.0 0.0 

0.0 0.0 3.0 
27
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
11.0
 0.9
Cij  
 4.0

 0.0
yy
zz
xy
0.0 
2.8 4.0 0.0 
4.0 12.0 0.0 

0.0 0.0 3.0 
0.9
4.0
? 31200
28
Homogenization of Strength Properties with Disroc
Disroc allows the calculation of stress-strain curve of fractured media with elastic-plastic
behavior. This makes possible determination of the effective cohesion and friction angle
for fractured rockmasses.
Case study - Granitic rockmass of La Vienne, France
29
29
Special model for rockmass with one fracture family
For a fractured rockmass containing a family of parallel and infinite fractures, a special
material model is implemented in Disroc which provides the corresponding effective behavior.
D

x2
x1
E
Kt
Kn
Ktn
D

Numerical homogenization is not needed for this
case: the parameters Cij are computed
automatically based on theoretical relations.
? 31400
30
Masonry Structures
Analysis of masonry structures needs combining discontinuous modeling with
continuous modeling. For instance the vault of masonry bridges are modeled as
assemblage of blocs and walls or fill materials as continuous materials. Disroc allows
easily combining theses two types of models the same process.
Case Study 1: Stability assessment for retrofitting purposes with
bolts
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
31
Masonry Structures
Case study 2 – Temple: Assessment of the temple’s stability for retrofitting purposes
Yanouh Roman temple, Lebanon
Mesh generation in presence of fractures and Stress maps
32
Modeling bolts
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.
33
Representing bolt stresses
 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.
34
Hydraulic module
The hydraulic module of Disroc allows:
- Modeling flow in a fracture network under pressure gradient and gravity forces
- Modeling flow in a porous/fractured rock mass
- Determination of the effective permeability of fractures rock masses
The flow in fractures is modeled by the Poiseuille law, and in the rock matrix by the Darcy’s law,
and fracture/matrix mass exchange are fully taken into account.
The pressure field calculated in fractures can be injected as a pressure load in the mechanical
module in order to take into account its effects on the mechanical stability.
The two types of calculations, on a discrete fracture network and on fractures in a porous matrix,
can be performed on the same geometry and mesh. This makes very easy to estimate the effect
of a matrix permeability.
An example for effective permeability calculation is given in the following page.
35
Hydraulic module :
Effective permeability of fractured rockmass
Effective permeability can be calculated for a discrete fracture network (impervious matrix) or
with taking into account a matrix permeability. The necessary boundary conditions are prescribed
automatically and the effective permeability given as a direct output of the calculation.
Rockmass with two
fracture families
Flow in fractures
Effective
permeability
P
P
1
0
Unit pressure gradient
on the boundary
The average fluid velocity in the
domain calculated automatically
 Effective permeability
Pressure field
27.0 3.0 
Kij  

 2.6 23.7 
36
Materials models
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
- Anisotropic Darcy’s law for hydraulic diffusion
• Discontinuities: fractures, faults, rock joints and interfaces
- Linear or non linear Barton-Bandis elasticity
- Mohr-Coulomb (Cohesion, friction angle) yield criterion
- Poiseuille’s law for flow in fractures
Joint : K n , K t ,C , f
• Rockbolts and cables
- Elastic and plastic limit for steel rod,
- Elastic stiffness, cohesion and friction angle for rock–
grout interface
37
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
38
Architecture
GID
WinDisroc
Fracture generation
Parameters
WinDisroc manages data
acquisition and generates
fractured rockmasses
GID is a powerful pre and
post processor developed by
Cimne: www.gidhome.com
Geometry
Boundary conditions
Mesh
input
file
Disroc
Discrac
Discrac allows joint
elements creation
Disroc is the calculation
module
output
file
GID
Post Process
39
DISROC functionalities
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 acceleration)
• Analysis of block fall down risk in tunnels in blocky rockmasses
• Modeling rock bolts, bars and cables in fractured rock
• Modeling fluid flow in fractured porous rocks or in discrete fracture networks
• Taking into account fluid pressure effects in the mechanical stability analysis
• Homogenization of fractured rock mass mechanical and hydraulic properties:
- determination of the effective elastic parameters
- simulation of effective stress-strain curve to determine effective strength properties
- determination of the effective permeability of fractured rock masses
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 curves, etc.
40
MechaRock International Consultants
www.mecharock.com
For more information, please send an email to:
[email protected]
41