Transcript No Slide Title

Use of numerical modelling to
estimate shotcrete requirements
using a Ground Reaction Curve
approach
Kevin Le Bron (Golder)
Tony Leach (Itasca Africa)
William Joughin (SRK)
Introduction
 Simrac Project SIM 040204
Numerical modelling to investigate:
 Shotcrete/rockmass interaction
 Load/deformation performance requirements of
shotcrete under a range of geotechnical conditions
Modelling requirements
 Modelled rock mass needs to fragment
 Effect of discontinuities on lining – local loading
 Identify deformations under various geotechnical
conditions – rock type, GSI, field stress
Model design – ‘laboratories’
Generic tunnel (voronoi tesselation)
Realistic tunnel in bedded strata
JOB TITLE : Bedded rock mass model - Field stress 80 MPa
JOB TITLE : Voronoi tesselation model - Field stress 100 MPa
UDEC (Version 4.00)
UDEC (Version 4.00)
4.000
Wedge Ejection
LEGEND
LEGEND
22-Aug-07 12:00
SF
F
S F
S F
S F
S F
S F
S F
S F
S F
S F
S F
S F
S F
S F
S F
S F
S F
cycle F 11000
block plot
F
F plot
boundary
velocity Fvectors
F
maximum
= 7.463E-03
F
F
F
0
2E -2
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
Itasca Africa
(Pty) Ltd
F
Johannesburg
F
FF F F F F F F F F F F F F F F F F

0.750
22-Aug-07 10:59
cycle 53080
block plot
boundary plot
2.000
4.000
2.000
2.000
1.500
0.000
0.000
1.000
-2.000
-2.000
0.500
-4.000
-4.000
Itasca Africa (Pty) Ltd
Johannesburg
0.000 -4.000
-2.000
0.000
2.000
4.000
0.100
0.300
0.500
(*10^1)
0.700
0.900
1.100
Various experiments to examine shotcrete loading due to discontinuities using UDEC
1.250
1.750
2.250
2.750
Objectives
 Derive magnitude of rock movements under a range of
geotechnical conditions in SA mines
 Interpret movements applied to shotcrete
 Derive Ground reaction curves
 Assess effect of stress change on movement
 Assess effect of excavation size on movement
 Assess effect of bolting, shotcrete bond strength, etc.
Generic Tunnel Model




2D model using UDEC
Discontinuous rock mass created using a voronoi
tesselation (0.2m block size)
Simple properties based on UCS, GSI derived using
Rocscience’s Rocklab program.
3.5 x 3.5 tunnel
Vertical Stress Boundary
yy
(*10^1)
JOB TITLE : tunnel shotcrete stability
UDEC (Version 4.00)
1.750
LEGEND
1.250
27-Jan-08 22:28
3000
cy cle
time 5.255E-02 sec
0.750
block plot
0.250
Horizontal
Stress
Boundary
(xx)
-0.250
-0.750
-1.250
-1.750
Lebron REC
Blue Horizon Bay
-1.750
-1.250
-0.750
0.250
-0.250
(*10^1)
Boundary fixed in
vertical direction
0.750
1.250
1.750
Horizontal
Stress
Boundary
(xx)
JOB TITLE : rock mass
UDEC (Version 4.00)
3.500
LEGEND
2.500
12-Feb-09 12:46
cycle 18000
time = 3.683E-01 sec
major principal stress cont
contour interval= 2.000E+07
-1.600E+08 to 0.000E+00
1.500
-1.600E+08
-1.400E+08
-1.200E+08
-1.000E+08
-8.000E+07
-6.000E+07
-4.000E+07
-2.000E+07
0.500
-0.500
-1.500
0.000E+00
joints now at shear limit
joints with FN or SN = 0.0
shear displacement on joint
max shear disp = 3.057E-02
each line thick = 6.115E-03
-2.500
-3.500
Itasca Africa (Pty) Ltd
Johannesburg
-3.500
-2.500
-1.500
-0.500
0.500
1.500
2.500
3.500
JOB TITLE : rock mass
UDEC (Version 4.00)
3.500
LEGEND
2.500
12-Feb-09 12:46
cycle 18000
time = 3.683E-01 sec
X displacement contours
contour interval= 1.000E-02
-2.000E-02 to 4.000E-02
1.500
-2.000E-02
-1.000E-02
0.000E+00
1.000E-02
2.000E-02
3.000E-02
4.000E-02
0.500
-0.500
joints now at shear limit
joints with FN or SN = 0.0
boundary plot
-1.500
-2.500
-3.500
Itasca Africa (Pty) Ltd
Johannesburg
-3.500
-2.500
-1.500
-0.500
0.500
1.500
2.500
3.500
JOB TITLE : rock mass
UDEC (Version 4.00)
4.000
LEGEND
12-Feb-09 16:49
cycle 25000
time = 5.108E-01 sec
boundary plot
Axial Force on Structure
Type # Max. Value
cable 1 -1.051E+05
cable 2 -1.100E+05
cable 3 -1.048E+05
cable 4 -6.021E+04
cable 5 -2.642E+04
cable 6 -2.905E+04
cable 7 -1.087E+05
cable 8 -1.100E+05
cable 9 -8.090E+04
Axial Force on Structure
Type # Max. Value
struct 1
3.808E+06
joints now at shear limit
joints with FN or SN = 0.0
boundary plot
2.000
0.000
-2.000
-4.000
Itasca Africa (Pty) Ltd
Johannesburg
-4.000
-2.000
0.000
2.000
4.000
JOB TITLE : rock mass
UDEC (Version 4.00)
4.000
LEGEND
12-Feb-09 16:49
cycle 25000
time = 5.108E-01 sec
boundary plot
cable reinforcing plotted
X-Disp. on Structure
Type # Max. Value
struct 1
8.765E-02
joints now at shear limit
joints with FN or SN = 0.0
boundary plot
2.000
0.000
-2.000
-4.000
Itasca Africa (Pty) Ltd
Johannesburg
-4.000
-2.000
0.000
2.000
4.000
Limitations of including support

Need hundreds of models to cover support permutations!

Generally in deep mines, support can supply sufficient pressure
to prevent unravelling, but not to prevent failure or limit
deformation prior to final unravelling

Key factor is the deformation that shotcrete will undergo

Adopt a Ground Reaction Curve approach
What is a Ground Reaction Curve?
Support
Pressure
Elastic response
Rock failure initiated
Unravelling
Tunnel wall
deformation
GRC model methodology
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Model tunnel excavated and initially internal rock is
replaced with a high support pressure
Pressure is incrementally reduced to zero
Measure modelled wall deformation
GRC is graph of pressure versus deformation
Example of modelled GRC
1.E+06
9.E+05
Support Pressure (Pa)
8.E+05
7.E+05
6.E+05
5.E+05
4.E+05
300 MPa
3.E+05
250 MPa
2.E+05
1.E+05
0.E+00
0.00
200 MPa
150 MPa
5.00
10.00
15.00
Deformation (mm)
20.00
25.00
30.00
Range in rock mass cases
GSI
Cohesion
Friction Angle
Tensile strength
GSI
Cohesion
Strong Lava
Friction Angle
Tensile strength
GSI
Cohesion
Shale
Friction Angle
Tensile strength
GSI
Cohesion
Pyroxenite
Friction Angle
Tensile strength
GSI
Norite/
Cohesion
Anorthosite Friction Angle
Tensile strength
Siliceous
Quartzite
100
90
80
70
60
50
40
30
20
29
55
10
18
54
4.7
12.4
52
2.2
9.5
50
1
7.8
47
0.5
6.8
44
0.35
6.15
41
0.225
5.75
36
0.125
5.25
30
0.075
100
90
80
70
60
50
40
30
20
37
55
15
22
54
6.9
14.2
52
3.2
10.4
50
1.5
8.2
47
0.7
7.2
44
0.35
6.5
41
0.2
6
36
0.1
5.8
30
0.05
100
90
80
70
60
50
40
30
20
28
46
15
16
45
7.1
10.6
44
3.3
7.7
41
1.6
6.1
39
0.7
5
37
0.35
4.2
34
0.2
3.5
30
0.1
2.9
25
0.05
100
90
80
70
60
50
40
30
20
17
49
6
11.5
47
2.9
8.5
45
1.4
6.8
42
0.7
5.8
39
0.3
5
36
0.2
4.4
31.7
0.15
3.9
26
0.09
3.5
18
0.04
100
90
80
70
60
50
40
30
20
23
54
14.7
52
10.6
50
8.4
48
7
45
6.2
42
5.6
38
5.2
33
5
27
7.5
3.5
1.7
0.8
0.4
0.275
0.2
0.1
0.05
Effect of excavation size
3.5
1 MPa Support Pressure
Sidewall deformation increase factor
3.0
2
y = 0.0673x - 0.5422x + 2.0824
2
R = 0.9976
100 kPa Support Pressure
10 kPa Support Pressure
2.5
Poly. (10 kPa Support
Pressure)
Poly. (100 kPa Support
Pressure)
Poly. (1 MPa Support
Pressure)
2.0
1.5
y = 0.0232x2 - 0.1783x + 1.3381
R2 = 0.9997
1.0
2
0.5
0.0
3.00
y = 0.0474x - 0.387x + 1.7784
2
R = 0.9988
4.00
5.00
6.00
7.00
Excavation Size (m)
8.00
9.00
10.00
Effect of support pressure on
failure envelope
Depth of sidewall instability (% of width of excavation)
Excavation Size
Support Pressure
1 kPa
Support Pressure
10 kPa
Support Pressure
100 kPa
3.5 m wide excavation
37%
37%
37%
5 m wide excavation
32%
32%
32%
7 m wide excavation
22%
22%
22%
Effect of stress change

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
Stress change is the main inducer of deformation in
mining
How to account for stress change with GRC graphs?
GRC graphs developed for static stress cases
Is it reasonable to jump from one graph to the next?
Effect of stress change
Comparison of progressive stress change to static GRC
results - 0.1 MPa support
35
Sidewall deformation (mm)
30
25
20
15
10
Stress change with 0.1 MPa support pressure
Deformation from static GRC curves
5
0
80 MPa initial state
Increase to 100 MPa
Increase to 120 MPa
Reduce to 60 MPa
GRC models versus explicit support
Effect of stress change
60
Sidewall deformation (mm)
50
40
30
20
No support
0.1 MPa support pressure
10
Bolts plus shotcrete
Bolts only
0
80 MPa initial state
Increase to 100 MPa
Increase to 120 MPa
Reduce to 60 MPa
Deformation in 2D and 3D
 How to relate GRCs from 2D models to point of
installation of support relative to face?
 UDEC versus FLAC3D
 Simple tunnel model
3D deformations (mm)
Deformation relative to distance from tunnel face - Quartzite, GSI 70
30
Tunnel sidewall movement (mm)
25
20
60 MPa
80 MPa
15
100 MPa
10
5
0
0
5
10
15
20
Distance from tunnel face (m)
25
30
35
3D deformations (%)
Deformation relative to distance from tunnel face - Quartzite, GSI 70
140
Percentage of final tunnel wall movement (%)
120
100
60 MPa
80
80 MPa
60
100 MPa
40
20
0
0
5
10
15
20
Distance from tunnel face (m)
25
30
35
Conclusions







Deformation applied to support is key
GRC methodology adopted as best means to assess
deformation applied to shotcrete
Limited tendency for shotcrete to bulge between bolts
Layer deflection smoothly distributed over tunnel
height (except where slabs punch through)
Consider bolt spacing as design slab size in assessing
performance
Consider total wall deflection/number of bolts as
shotcrete panel deflection
Permits design using yield line theory