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Rock Slope Stability Investigations In ThreeDimensions For A Part Of An Open Pit Mine In USA
Item Type text; Electronic Dissertation
Authors Shu, Biao
Publisher The University of Arizona.
Rights Copyright © is held by the author. Digital access to this materialis made possible by the University Libraries, University of Arizona.Further transmission, reproduction or presentation (such aspublic display or performance) of protected items is prohibitedexcept with permission of the author.
Download date 20/06/2018 00:12:27
Link to Item http://hdl.handle.net/10150/338701
ROCK SLOPE STABILITY INVESTIGATIONS IN THREE DIMENSIONS
FOR A PART OF AN OPEN PIT MINE IN USA
by
Biao Shu
__________________________ Copyright © Biao Shu 2014
A Dissertation Submitted to the Faculty of the
DEPARTMENT OF MINING, GEOLOGICAL, AND GEOPHYSICAL
ENGINEERING
In Partial Fulfillment of the Requirements
For the Degree of
DOCTOR OF PHILOSOPHY
In the Graduate College
THE UNIVERSITY OF ARIZONA
2014
2
THE UNIVERSITY OF ARIZONA
GRADUATE COLLEGE
As members of the Dissertation Committee, we certify that we have read the dissertation
prepared by Biao Shu, titled “Rock Slope Stability Investigations in Three Dimensions for
a Part of an Open Pit Mine in USA” and recommend that it be accepted as fulfilling the
dissertation requirement for the Degree of Doctor of Philosophy.
_______________________________________________________________________ Date: (December 2, 2014)
Pinnaduwa H. S. W. Kulatilake
_______________________________________________________________________ Date: (December 2, 2014)
Ben K. Sternberg
_______________________________________________________________________ Date: (December 2, 2014)
Jinhong Zhang
_______________________________________________________________________ Date: (December 2, 2014)
Kwangmin Kim
Final approval and acceptance of this dissertation is contingent upon the candidate’s
submission of the final copies of the dissertation to the Graduate College.
I hereby certify that I have read this dissertation prepared under my direction and
recommend that it be accepted as fulfilling the dissertation requirement.
________________________________________________ Date: (December 2, 2014)
Dissertation Director: Pinnaduwa H. S. W. Kulatilake
3
STATEMENT BY AUTHOR
This dissertation has been submitted in partial fulfillment of the requirements for
an advanced degree at the University of Arizona and is deposited in the University Library
to be made available to borrowers under rules of the Library.
Brief quotations from this dissertation are allowable without special permission,
provided that an accurate acknowledgement of the source is made. Requests for permission
for extended quotation from or reproduction of this manuscript in whole or in part may be
granted by the copyright holder.
SIGNED: Biao Shu
4
ACKNOWLEDGMENTS
I would like to greatly appreciate my committee members Prof. Pinnaduwa H. S. W.
Kulatilake, Prof. Ben K. Sternberg, Dr. Jinhong Zhang, and Dr. Kwangmin Kim for serving
in my dissertation committee and spending time in reviewing this dissertation. Special
thanks should be given to my advisor, Prof. Pinnaduwa H. S. W. Kulatilake, for his
guidance on my dissertation research, and the time and effort he spent on editing this
dissertation. He has been continually supporting my study and research throughout my Ph.
D. program. Thanks are also extended for Taghi Sherizadeh’s help with the field fracture
mapping and Jun Zheng’s help with fracture data processing.
I would like to acknowledge the financial support I received as a graduate research
assistantship throughout my Ph.D. study period at the University of Arizona from the
research contract, having the contract No. 200-2011-39886, Professor Pinnaduwa H. S. W.
Kulatilake received from the National Institute for Occupational Safety and Health
(NIOSH) of Centers for Disease Control and Prevention. Thanks are also extended to Jorge
Armstrong, Megan Ransom, Justin Hnatiuk, and Burke from the mining company for their
help given to us during the visits to the mine site and in providing many essential data used
for the conducted research.
I am most grateful to my family for their unconditional support and love provided to me
throughout my Ph.D. study period.
5
TABLE OF CONTENTS
LIST OF FIGURES ............................................................................................................ 9
LIST OF TABLES ............................................................................................................ 17
ABSTRACT ...................................................................................................................... 19
CHAPTER 1 INTRODUCTION ...................................................................................... 22
1.1 Motivation ................................................................................................................... 22
1.2 Background and Problem Statement ........................................................................... 23
1.3 Contributions............................................................................................................... 28
1.4 Dissertation Outline .................................................................................................... 30
CHAPTER 2 LITERATURE REVIEW ........................................................................... 34
2.1 Introduction ................................................................................................................. 34
2.2 Discontinuity Mapping Methods ................................................................................ 34
2.2.1 Scan line mapping ................................................................................................ 35
2.2.2 Window mapping ................................................................................................. 36
2.2.3 Core drilling ......................................................................................................... 37
2.2.4 LiDAR.................................................................................................................. 39
2.2.5 Photogrammetry ................................................................................................... 41
2.2.6 Summary .............................................................................................................. 42
2.3 Rock Slope Stability Computational Methods ............................................................ 43
2.3.1 Kinematic analysis ............................................................................................... 44
2.3.2 Block theory ......................................................................................................... 45
2.3.3 Limit equilibrium method .................................................................................... 46
2.3.4 Continuum numerical methods ............................................................................ 47
2.3.5 Discontinuum numerical methods ....................................................................... 49
2.4 Current Status on Numerical Modeling Study of Open Pit Rock Slope Stability ...... 51
2.4.1 Finite element method.......................................................................................... 51
2.4.2 Finite difference method ...................................................................................... 52
2.4.3 Two dimensional discrete element method .......................................................... 52
2.4.4 Consideration about three dimensional analysis .................................................. 53
6
TABLE OF CONTENTS-Continued
2.4.5 Three dimensional discrete element method ........................................................ 54
2.4.6 Consideration of rock excavation ........................................................................ 55
2.4.7 Summary .............................................................................................................. 55
2.5 Conclusions ................................................................................................................. 56
CHAPTER 3 CONDUCTED LABORATORY TESTS AND RESULTS ...................... 57
3.1 Collection and Preparation of Rock Test Samples ..................................................... 57
3.2 Procedures Used for Laboratory Tests ........................................................................ 58
3.2.1 Brazilian tension test ............................................................................................ 58
3.2.2 Uniaxial compression test .................................................................................... 61
3.2.3 Uniaxial compression test with strain gages ........................................................ 62
3.2.4 Triaxial compression test ..................................................................................... 65
3.3 Laboratory Tests for Rock Joints ................................................................................ 70
3.3.1 Uniaxial compression test with a horizontal joint................................................ 70
3.3.2 Joint direct shear test ............................................................................................ 75
3.4 Summary ..................................................................................................................... 85
CHAPTER 4 FRACTURE MAPPING AND ROCK MASS PROPERTIES .................. 87
4.1 Introduction ................................................................................................................. 87
4.2 The Used Remote Fracture Mapping Procedure to Collect Fracture Data ................. 88
4.3 Laser Scanning Data Extraction Method .................................................................... 92
4.3.1 Fracture orientation .............................................................................................. 92
4.3.2 Fracture size ......................................................................................................... 97
4.3.3 Fracture intensity in one-dimension (1-D) and three-dimensions (3-D) ........... 101
4.4 Results Obtained from Mapped Fractures ................................................................ 103
4.4.1 Joint orientation ................................................................................................. 103
4.4.2 Joint size............................................................................................................. 107
4.4.3 Joint intensity ..................................................................................................... 107
4.5 Rock Mass Properties ............................................................................................... 108
4.5.1 GSI rock mass classification system .................................................................. 108
7
TABLE OF CONTENTS-Continued
4.5.2 Rock mass strength properties ........................................................................... 115
4.5.3 Rock mass deformation properties ..................................................................... 119
4.5.4 Properties of DRC-DP contact and faults .......................................................... 121
CHAPTER 5 BUILDING OF THE GEOLOGICAL MODEL ...................................... 124
5.1 Introduction ............................................................................................................... 124
5.2 Topographies of the Mine Site .................................................................................. 125
5.3 Construction of Topographies Using 3DEC Software .............................................. 128
5.4 Construction of the Fault System .............................................................................. 131
5.5 Construction of the Rock Layers .............................................................................. 146
5.6 Integrated Geological Model .................................................................................... 149
5.7 Summary ................................................................................................................... 150
CHAPTER 6 NUMERICAL MODELING AND COMPARISON WITH FIELD
MONITORING DATA ................................................................................................... 152
6.1 Introduction ............................................................................................................... 152
6.2 Constitutive Models and Material Properties ........................................................... 152
6.3 Numerical Modeling Stages ...................................................................................... 156
6.4 Insitu Stress and Boundary Conditions ..................................................................... 160
6.5 Numerical Modeling Results .................................................................................... 168
6.5.1 Validation of basic results .................................................................................. 168
6.5.2 Effect of boundary condition ............................................................................. 171
6.5.3 Effect of the faults .............................................................................................. 174
6.5.4 Effect of the k0 ................................................................................................... 177
6.6 Field Monitoring Results and Comparison with Numerical Predictions .................. 181
CHAPTER 7 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS ............ 189
7.1 Summary and Conclusions ....................................................................................... 189
7.2 Recommendations ..................................................................................................... 198
APPENDIX A – JOINT NORMAL STIFFNESS .......................................................... 200
8
TABLE OF CONTENTS-Continued
APPENDIX B – JOINT SHEAR STIFFNESS .............................................................. 228
APPENDIX C – FIELD MONITORING DISPLACEMENT ....................................... 244
REFERENCES ............................................................................................................... 251
9
LIST OF FIGURES
Figure 1.1 Typical open pit slope geometry (Wyllie and Mah, 2004). ............................. 24
Figure 1.2 Google map of the mine topography (Google Earth). ..................................... 26
Figure 1.3 Slope failure occurred in the south wall of the open pit mine. ........................ 28
Figure 1.4 Flow chart. ....................................................................................................... 31
Figure 2.1 Use of geological compass to measure joint orientation. ................................ 35
Figure 2.2 Four types of failure modes (Hoek and Bray, 1981). ...................................... 44
Figure 2.3 A simple example of the limit equilibrium analysis (Hoek and Bray, 1981). . 47
Figure 3.1 Collected rock blocks from the open pit mine site. ......................................... 58
Figure 3.2 Rock cores drilled out of a rock block. ............................................................ 58
Figure 3.3 Brazilian tension test setup. ............................................................................. 59
Figure 3.4 Some of the tested Brazilian tension test samples. .......................................... 60
Figure 3.5 Part of the tested uniaxial compression test samples....................................... 62
Figure 3.6 Preparation of rock samples with strain gages. ............................................... 63
Figure 3.7 Uniaxial compression test with strain gages. .................................................. 63
Figure 3.8 A sample prepared for the triaxial test. ........................................................... 66
Figure 3.9 Performed linear regression to calculate the Mohr-Coulomb parameters. ...... 67
Figure 3.10 A typical sample set up for uniaxial compression test with a horizontal joint.
........................................................................................................................................... 70
Figure 3.11 Total deformation and intact rock deformation. ............................................ 72
Figure 3.12 Joint deformation vs. Normal stress. ............................................................. 72
Figure 3.13 The fitted exponential regression curve for the experimental joint
deformation data. .............................................................................................................. 73
Figure 3.14 JKN vs. Normal stress curve. ........................................................................ 73
Figure 3.15 Some of the prepared samples for joint direct shear test. .............................. 76
Figure 3.16 Joint direct shear test equipment. .................................................................. 76
Figure 3.17 Fitted linear regression line for JKS vs. normal stress data. .......................... 80
10
LIST OF FIGURES-Continued
Figure 4.1 Set up of the laser scanner of the instrument and the north direction. ............ 89
Figure 4.2 Laser scanner set up in front of a bench face. ................................................. 90
Figure 4.3 A remote fracture mapping picture of DRC rocks. ......................................... 91
Figure 4.4 A remote fracture mapping picture of DP rocks. ............................................ 91
Figure 4.5 A typical image constructed from remote fracture mapping. .......................... 92
Figure 4.6 Three fracture sets of DRC rocks. ................................................................... 93
Figure 4.7 Three fracture sets of DP rocks. ...................................................................... 93
Figure 4.8 Rocks under different status. ........................................................................... 94
Figure 4.9 Three scanned points on a fracture surface. .................................................... 95
Figure 4.10 Calculation of the directional cosines of the unit normal vector to the
discontinuity. ..................................................................................................................... 96
Figure 4.11 Diagram used to explain calculation of fracture area. ................................... 97
Figure 4.12 The vectors used to calculate the area of the triangle. ................................... 98
Figure 4.13 The triangles associated with the calculation of the total fracture area A2
using AutoCAD. ............................................................................................................... 99
Figure 4.14 Lines used to calculate the trace length. ...................................................... 100
Figure 4.15 Converting the square fracture to an equivalent circular fracture. .............. 101
Figure 4.16 Horizontal and vertical survey lines used to calculate fracture intensities. . 102
Figure 4.17 The diagram connected with calculation of 1-D intensity of fractures. ...... 102
Figure 4.18 Orientation distributions of fracture sets for DRC rocks. ........................... 105
Figure 4.19 Orientation distributions of fracture sets for DP rocks. ............................... 106
Figure 4.20 Original GSI chart (Hoek, 2007) ................................................................. 109
Figure 4.21 Quantification of GSI chart (Cai et al., 2004) ............................................. 110
Figure 5.1 Elevation contour map from the USGS (USGS). .......................................... 126
Figure 5.2 Original topography of the research area before mining activities. .............. 126
Figure 5.3 Topography of the research area in the pit in 2001. ...................................... 127
Figure 5.4 Topography of the research area in the pit in July 2011. .............................. 127
11
LIST OF FIGURES-Continued
Figure 5.5 Topography of the research area in the pit in July 2012. .............................. 128
Figure 5.6 One slope failure from the researched open pit mine. ................................... 129
Figure 5.7 Simplified model of initial topography. ........................................................ 130
Figure 5.8 Simplified model of July 2011. ..................................................................... 130
Figure 5.9 Simplified model of July 2012. ..................................................................... 131
Figure 5.10 Some faults that exist in the open pit mine.................................................. 132
Figure 5.11 Original three-dimensional plot of the faults............................................... 133
Figure 5.12 How an irregular fault surface was simplified to a planar surface. ............. 134
Figure 5.13 A fault simplified by trimming and extending. ........................................... 135
Figure 5.14 Plot of the simplified fault system built using 3DEC. ................................. 136
Figure 5.15 Locations of the vertical cross sections used to compare between the
simulated faults using the 3DEC package and the fault cross sectional maps provided by
the mining company. ....................................................................................................... 139
Figure 5.16 Comparison of fault maps on cross section 1. ............................................. 140
Figure 5.17 Comparison of fault maps on cross section 2. ............................................. 141
Figure 5.18 Comparison of fault maps on cross section 3. ............................................. 142
Figure 5.19 Comparison of fault maps on cross section 4. ............................................. 143
Figure 5.20 Comparison of fault maps on cross section 5. ............................................. 144
Figure 5.21 Comparison of fault maps on cross section 6. ............................................. 145
Figure 5.22 Comparison of fault maps on cross section 7. ............................................. 146
Figure 5.23 Stratigraphy of the mine. ............................................................................. 147
Figure 5.24 The natural and simplified contact surfaces between the DRC and DP rocks.
......................................................................................................................................... 148
Figure 5.25 Two rock layer system built using the 3DEC software package. ................ 148
Figure 5.26 The built integrated geological model. ........................................................ 149
Figure 5.27 The meshed integrated geological model. ................................................... 150
Figure 6.1 Mohr-Coulomb failure criterion used in 3DEC............................................. 154
Figure 6.2 Three regions. ................................................................................................ 157
12
LIST OF FIGURES-Continued
Figure 6.3 Three modeling stages performed. ................................................................ 159
Figure 6.4 Locations of selected monitoring points in the set up 3DEC model. ............ 160
Figure 6.5 Zero velocity boundary condition. ................................................................ 162
Figure 6.6 (a) Stress boundary condition type 1, (b) Stress boundary condition type 2. 162
Figure 6.7 Forces applied on the two boundaries are equal to each other in stage 1. ..... 164
Figure 6.8 Forces applied on the two boundaries are not equal in stage 2. .................... 164
Figure 6.9 Whole model is under unbalanced forces. ..................................................... 164
Figure 6.10 x-displacement contours under unbalanced forces (indicate block rotation).
......................................................................................................................................... 165
Figure 6.11 Whole model moves along y-axis under unbalanced forces. ...................... 166
Figure 6.12 Stress contours for case 1(a) in stage 1. ...................................................... 169
Figure 6.13 Stress contours for case 3(a) in stage 1. ...................................................... 170
Figure 6.14 Comparison of the total displacement between case 3(a) and case 8. ......... 172
Figure 6.15 Displacement contours for case 1(a) in stage 3. .......................................... 176
Figure 6.16 Displacement contours for case 3(a) in stage 3. .......................................... 177
Figure 6.17 Model collapsed in stage 1 under boundary stress with k0=0.3. .................. 178
Figure 6.18 Large failure occurred in stage 2 under boundary stress with k0=0.8 ......... 178
Figure 6.19 Comparison of total displacement among cases 3(a), 3(b), 4(a), 4(b), 9(a),
and 9(b). .......................................................................................................................... 180
Figure 6.20 Locations of the robotic total station and the survey targets. ...................... 181
Figure 6.21 Shelter for robotic total station at a mine site (Thomas, 2011). .................. 182
Figure 6.22 A survey target installed on a bench wall (Thomas, 2011). ........................ 182
Figure 6.23 Principle of distance monitoring of a target. ............................................... 183
Figure 6.24 True displacement and measured displacement. ......................................... 184
Figure 6.25 Slope distance of target #1. ......................................................................... 185
Figure 6.26 Measured displacement of target #1. ........................................................... 185
Figure 6.27 x, y, and z displacement components of monitoring point #1. .................... 186
13
LIST OF FIGURES-Continued
Figure A.1 Total deformation and intact rock deformation (DRC-J1). .......................... 200
Figure A.2 Joint deformation vs. Normal stress (DRC-J1). ........................................... 200
Figure A.3 The fitted exponential regression curve for the experimental joint deformation
data (DRC-J1). ................................................................................................................ 201
Figure A.4 JKN vs. Normal stress curve (DRC-J1). ....................................................... 201
Figure A.5 Total deformation and intact rock deformation (DRC-J2). .......................... 202
Figure A.6 Joint deformation vs. Normal stress (DRC-J2) ............................................ 202
Figure A.7 The fitted exponential regression curve for the experimental joint deformation
data (DRC-J2). ................................................................................................................ 203
Figure A.8 JKN vs. Normal stress curve (DRC-J2). ....................................................... 203
Figure A.9 Total deformation and intact rock deformation (DRC-J3). .......................... 204
Figure A.10 Joint deformation vs. Normal stress (DRC-J3). ......................................... 204
Figure A.11 The fitted exponential regression curve for the experimental joint
deformation data (DRC-J3). ............................................................................................ 205
Figure A.12 JKN vs. Normal stress curve (DRC-J3). ..................................................... 205
Figure A.13 Total deformation and intact rock deformation (DRC-J4). ........................ 206
Figure A.14 Joint deformation vs. Normal stress (DRC-J4). ......................................... 206
Figure A.15 The fitted exponential regression curve for the experimental joint
deformation data (DRC-J4). ............................................................................................ 207
Figure A.16 JKN vs. Normal stress curve (DRC-J4). ..................................................... 207
Figure A.17 Total deformation and intact rock deformation (DP-J1). ........................... 208
Figure A.18 Joint deformation vs. Normal stress (DP-J1).............................................. 208
Figure A.19 The fitted exponential regression curve for the experimental joint
deformation data (DP-J1). ............................................................................................... 209
Figure A.20 JKN vs. Normal stress curve (DP-J1). ........................................................ 209
Figure A.21 Total deformation and intact rock deformation (DP-J2). ........................... 210
Figure A.22 Joint deformation vs. Normal stress (DP-J2).............................................. 210
14
LIST OF FIGURES-Continued
Figure A.23 The fitted exponential regression curve for the experimental joint
deformation data (DP-J2). ............................................................................................... 211
Figure A.24 JKN vs. Normal stress curve (DP-J2). ........................................................ 211
Figure A.25 Total deformation and intact rock deformation (DP-J3). ........................... 212
Figure A.26 Joint deformation vs. Normal stress (DP-J3).............................................. 212
Figure A.27 The fitted exponential regression curve for the experimental joint
deformation data (DP-J3). ............................................................................................... 213
Figure A.28 JKN vs. Normal stress curve (DP-J3). ........................................................ 213
Figure A.29 Total deformation and intact rock deformation (DP-J4). ........................... 214
Figure A.30 Joint deformation vs. Normal stress (DP-J4).............................................. 214
Figure A.31 The fitted exponential regression curve for the experimental joint
deformation data (DP-J4). ............................................................................................... 215
Figure A.32 JKN vs. Normal stress curve (DP-J4). ........................................................ 215
Figure A.33 Total deformation and intact rock deformation (DP-J5). ........................... 216
Figure A.34 Joint deformation vs. Normal stress (DP-J5).............................................. 216
Figure A.35 The fitted exponential regression curve for the experimental joint
deformation data (DP-J5). ............................................................................................... 217
Figure A.36 JKN vs. Normal stress curve (DP-J5). ........................................................ 217
Figure A.37 Total deformation and intact rock deformation (DP-J6). ........................... 218
Figure A.38 Joint deformation vs. Normal stress (DP-J6).............................................. 218
Figure A.39 The fitted exponential regression curve for the experimental joint
deformation data (DP-J6). ............................................................................................... 219
Figure A.40 JKN vs. Normal stress curve (DP-J6). ........................................................ 219
Figure A.41 Total deformation and intact rock deformation (DRC-DP-J1). .................. 220
Figure A.42 Joint deformation vs. Normal stress (DRC-DP-J1). ................................... 220
Figure A.43 The fitted exponential regression curve for the experimental joint
deformation data (DRC-DP-J1). ..................................................................................... 221
Figure A.44 JKN vs. Normal stress curve (DRC-DP-J1). .............................................. 221
15
LIST OF FIGURES-Continued
Figure A.45 Total deformation and intact rock deformation (DRC-DP-J2). .................. 222
Figure A.46 Joint deformation vs. Normal stress (DRC-DP-J2). ................................... 222
Figure A.47 The fitted exponential regression curve for the experimental joint
deformation data (DRC-DP-J2). ..................................................................................... 223
Figure A.48 JKN vs. Normal stress curve (DRC-DP-J2). .............................................. 223
Figure A.49 Total deformation and intact rock deformation (DRC-DP-J3). .................. 224
Figure A.50 Joint deformation vs. Normal stress (DRC-DP-J3). ................................... 224
Figure A.51 The fitted exponential regression curve for the experimental joint
deformation data (DRC-DP-J3). ..................................................................................... 225
Figure A.52 JKN vs. Normal stress curve (DRC-DP-J3). .............................................. 225
Figure A.53 Total deformation and intact rock deformation (DRC-DP-J4). .................. 226
Figure A.54 Joint deformation vs. Normal stress (DRC-DP-J4). ................................... 226
Figure A.55 The fitted exponential regression curve for the experimental joint
deformation data (DRC-DP-J4). ..................................................................................... 227
Figure A.56 JKN vs. Normal stress curve (DRC-DP-J4). .............................................. 227
Figure B.1 Fitted linear regression line for JKS vs. normal stress data (DRC #1). ........ 228
Figure B.2 Fitted linear regression line for JKS vs. normal stress data (DRC #2). ........ 228
Figure B.3 Fitted linear regression line for JKS vs. normal stress data (DRC #3). ........ 229
Figure B.4 Fitted linear regression line for JKS vs. normal stress data (DRC #4). ........ 229
Figure B.5 Fitted linear regression line for JKS vs. normal stress data (DRC #5). ........ 230
Figure B.6 Fitted linear regression line for JKS vs. normal stress data (DRC #6). ........ 230
Figure B.7 Fitted linear regression line for JKS vs. normal stress data (DRC #7). ........ 231
Figure B.8 Fitted linear regression line for JKS vs. normal stress data (DRC #8). ........ 231
Figure B.9 Fitted linear regression line for JKS vs. normal stress data (DRC #9). ........ 232
Figure B.10 Fitted linear regression line for JKS vs. normal stress data (DRC #10). .... 232
Figure B.11 Fitted linear regression line for JKS vs. normal stress data (DRC #11). .... 233
Figure B.12 Fitted linear regression line for JKS vs. normal stress data (DRC #12). .... 233
16
LIST OF FIGURES-Continued
Figure B.13 Fitted linear regression line for JKS vs. normal stress data (DRC #13). .... 234
Figure B.14 Fitted linear regression line for JKS vs. normal stress data (DRC #14). .... 234
Figure B.15 Fitted linear regression line for JKS vs. normal stress data (DP #1). ......... 235
Figure B.16 Fitted linear regression line for JKS vs. normal stress data (DP #2). ......... 235
Figure B.17 Fitted linear regression line for JKS vs. normal stress data (DP #3). ......... 236
Figure B.18 Fitted linear regression line for JKS vs. normal stress data (DP #4). ......... 236
Figure B.19 Fitted linear regression line for JKS vs. normal stress data (DP #5). ......... 237
Figure B.20 Fitted linear regression line for JKS vs. normal stress data (DP #6). ......... 237
Figure B.21 Fitted linear regression line for JKS vs. normal stress data (DP #7). ......... 238
Figure B.22 Fitted linear regression line for JKS vs. normal stress data (DP #8). ......... 238
Figure B.23 Fitted linear regression line for JKS vs. normal stress data (DP #9). ......... 239
Figure B.24 Fitted linear regression line for JKS vs. normal stress data (DP #10). ....... 239
Figure B.25 Fitted linear regression line for JKS vs. normal stress data (DP #11). ....... 240
Figure B.26 Fitted linear regression line for JKS vs. normal stress data (DP #12). ....... 240
Figure B.27 Fitted linear regression line for JKS vs. normal stress data (DP #13). ....... 241
Figure B.28 Fitted linear regression line for JKS vs. normal stress data (DRC-DP #1). 241
Figure B.29 Fitted linear regression line for JKS vs. normal stress data (DRC-DP #2). 242
Figure B.30 Fitted linear regression line for JKS vs. normal stress data (DRC-DP #3). 242
Figure B.31 Fitted linear regression line for JKS vs. normal stress data (DRC-DP #4). 243
Figure B.32 Fitted linear regression line for JKS vs. normal stress data (DRC-DP #5). 243
Figure C.1 Displacements of field mentoring point 1..................................................... 244
Figure C.2 Displacements of field mentoring point 2..................................................... 245
Figure C.3 Displacements of field mentoring point 3..................................................... 246
Figure C.4 Displacements of field mentoring point 4..................................................... 247
Figure C.5 Displacements of field mentoring point 5..................................................... 248
Figure C.6 Displacements of field mentoring point 6..................................................... 249
Figure C.7 Displacements of field mentoring point 7..................................................... 250
17
LIST OF TABLES
Table 1.1 Lithology of the research area .......................................................................... 27
Table 3.1 Brazilian tension test results for DRC rocks ..................................................... 60
Table 3.2 Brazilian tension test results for DP rocks ........................................................ 61
Table 3.3 Uniaxial compression test results for DRC rocks ............................................. 64
Table 3.4 Uniaxial compression test results for DP rocks ................................................ 65
Table 3.5 Strength parameters calculated for DRC rocks ................................................. 68
Table 3.6 Strength parameters calculated for DP rocks .................................................... 69
Table 3.7 Obtained joint normal stiffness results for DRC and DP rock joints and
interfaces ........................................................................................................................... 74
Table 3.8 Obtained joint friction angle and joint cohesion for DRC rocks ...................... 77
Table 3.9 Obtained joint friction angle and joint cohesion for DP rocks ......................... 78
Table 3.10 Obtained joint friction angle and joint cohesion for interfaces between DP and
DRC rocks ......................................................................................................................... 79
Table 3.11 Obtained joint shear stiffness values for DRC rock joints.............................. 81
Table 3.12 Obtained joint shear stiffness values for DP rock joints ................................. 83
Table 3.13 Obtained joint shear stiffness values for interfaces between DRC and DP
rocks .................................................................................................................................. 85
Table 4.1 Joint orientation results ................................................................................... 104
Table 4.2 Joint size results .............................................................................................. 107
Table 4.3 Joint intensity results ...................................................................................... 108
Table 4.4 Calculated block size values ........................................................................... 111
Table 4.5 Terms to describe large-scale waviness (Palmstrom, 1995) ........................... 112
Table 4.6 Terms to describle small-scale smoothness (Palmstrom, 1995) ..................... 113
Table 4.7 Rating for the joint alteration factor JA (Cai et al., 2004) ............................... 114
Table 4.8 Estimated GSI values for rock masses ............................................................ 115
Table 4.9 Estimated Hoek-Brown rock mass failure criterion constants........................ 116
18
LIST OF TABLES-Continued
Table 4.10 Estimated values for rock mass cohesion, friction angle and tensile strength
......................................................................................................................................... 119
Table 4.11 Estimated values for rock mass deformation parameters ............................. 121
Table 4.12 Estimated property values of DRC-DP contact ............................................ 122
Table 4.13 Estimated property values of faults .............................................................. 123
Table 5.1 List of all the faults included in the 3DEC model .......................................... 137
Table 6.1 3DEC joint constitutive models (Itasca, 2007) ............................................... 155
Table 6.2 Rock mass material properties used for numerical modeling ......................... 156
Table 6.3 Joint properties used for numerical modeling................................................. 156
Table 6.4 Boundary condition combinations .................................................................. 167
Table 6.5 Comparison of displacement values between case 3(a) and case 8 ................ 173
Table 6.6 Comparison of displacement values between case 1(a) and case 7 ................ 174
Table 6.7 Displacement comparison between case 1(a) and case 3(a) ........................... 175
Table 6.8 Displacement comparison between case 2(a) and case 4(a) ........................... 176
Table 6.9 Comparison of displacements under different k0 - A ...................................... 179
Table 6.10 Comparison of displacements under different k0 - B .................................... 179
Table 6.11 Estimated values of displacements in x, y, and z directions. ........................ 187
Table 7.1 Comparison of current limitations and Contributions .................................... 197
19
ABSTRACT
Traditional slope stability analysis and design methods, such as limit equilibrium method
and continuum numerical methods have limitations in investigating three dimensional large
scale rock slope stability problems in open pit mines associated with stress concentrations
and deformations arising due to intersection of many complex major discontinuity
structures and irregular topographies. Analytical methods are limited to investigating
kinematics and limit equilibrium conditions based on rigid body analyses. Continuum
numerical methods fail to simulate the detachment of rock blocks and large displacements
and rotations. Therefore, there is an urgent need to try some new methods to have a deeper
understanding of the open pit mine rock slope stability problems.
The intact rock properties and discontinuity properties for both DRC and DP rock
formations that exist in the selected open pit mine were determined from tests conducted
on rock samples collected from the mine site. Special survey equipment (Professor
Kulatilake owns) which has a total station, laser scanner and a camera was used to perform
remote fracture mapping in the research area selected at the mine site. From remote fracture
mapping data, the fracture orientation, spacing and density were calculated in a much
refined way in this dissertation compared to what exist in the literature. Discontinuity
orientation distributions obtained through remote fracture mapping agreed very well with
the results of manual fracture mapping conducted by the mining company. This is an
important achievement in this dissertation compared to what exist in the literature. GSI
rock quality system and Hoek-Brown failure criteria were used to estimate the rock mass
20
properties combining the fracture mapping results with laboratory test results of intact rock
samples. Fault properties and the DRC-DP contact properties were estimated based on the
laboratory discontinuity test results. A geological model was built in a 3DEC model
including all the major faults, DRC-DP contact, and two stages of rock excavation. The
built major discontinuity system of 44 faults in 3DEC with their real orientations, locations
and three dimensional extensions were validated successfully using the fault geometry data
provided by the mining company using seven cross sections. This was a major
accomplishment in this dissertation because it was done for the first time in the world.
Numerical modeling was conducted to study the effect of boundary conditions, fault system
and lateral stress ratio on the stability of the considered rock slope. For the considered
section of the rock slope, the displacements obtained through stress boundary conditions
were seemed more realistic than that obtained through zero velocity boundary conditions
(on all four lateral faces). The fault system was found to play an important role with respect
to rock slope stability. Stable deformation distributions were obtained for k0 in the range
of 0.4 to 0.7. Because the studied rock mass is quite stable, it seems that an appropriate
range for k0 for this rock mass is between 0.4 and 0.7.
Seven monitoring points were selected from the deformation monitoring conducted at the
open pit mine site by the mining company using a robotic total station to compare with
numerical predictions. The displacements occurred between July 2011 and July 2012 due
to the nearby rock mass excavation that took place during the same period were compared
between the field monitoring results and the predicted numerical modeling results; a good
agreement was obtained. This is a huge success in this dissertation because such a
comparison was done for the first time in the world. In overall, the successful simulation
21
of the rock excavation during a certain time period indicated the possibility of using the
procedure developed in this dissertation to investigate rock slope stability with respect to
expected future rock excavations in mine planning.
22
CHAPTER 1 INTRODUCTION
1.1 Motivation
Rock excavation has been involved in many different human activities, such as road
construction, railway construction, dam construction, tunneling and mining engineering.
In mining engineering, open pits account for the major portion of the world’s mineral
production (Wyllie and Mah, 2004). Many mining companies spend millions of dollars on
the slope displacement monitoring equipment and technology to deal with rock slope
failure problems, to ensure the safety of people and equipment, and to reduce economical
loss. However, no matter how accurate the monitoring system is, it can only tell people
what is happening at present, but not a complete forecast of what will happen in the future.
One of the largest and deepest open pit mines in the world is Bingham Canyon Mine, which
is located 30 km southwest of Salt Lake City with a width of 4 km and a depth of about 1
km (Hibert et al., 2014). Unfortunately, such a large open pit mine suffered a massive
landslide on April 10, 2013, even under the protection of its 9 layers monitoring system
(Rio Tinto Kennecott, 2013).
Not only in Bingham Canyon Mine, rock slope failures have occurred in many open pits.
This poses the question “Do we use the available technology at the maximum level to
predict the stability of the existing rock slopes”. The open pit mine studied in this
dissertation was also troubled by slope failures. The mining company reported some large
scale slope failures in the south wall of the open pit, which more or less affected the mining
23
activity in that area. When the mining expanded in the north wall of the open pit, there was
a significant concern whether the slope in the north wall would be stable.
The study of rock slope stability with analytical or numerical modeling methods reveals
the movability of rock blocks, the safety factor of the slope and the stress and displacement
of each point in the slope. The traditional methods used in the open pit rock slope study are
the limit equilibrium method and some continuum numerical modeling methods. The limit
equilibrium method is limited to investigating small scale rock slope stability problems and
is not sufficient to investigate large scale open pit mine slope stability problems.
Continuum numerical modeling methods do not have the capability of simulating large
scale displacements and rotations that occur in discontinuous rock masses arising due to
the presence of discontinuities. Therefore, those methods are not sufficient to investigate
the realistic behavior of rock slope stability problems. Therefore, there is an urgent need to
try some new methods to have a deeper understanding of the open pit mine rock slope
stability problems.
1.2 Background and Problem Statement
The stability criteria of rock slopes depend on their applications. A rock slope along a
highway or railway, which will carry high traffic flows, requires a high safety factor.
However, in mining engineering, rock slope stability of open pit mines is mainly required
during the mining activity, and once the mine is closed, the slope stability becomes less
important. Besides, small scale slope failures in open pit mines may be allowed as long as
they do not cause safety problems. Therefore, the rock slope stability requirements and
design methods for civil engineering and mining engineering are different. A slope can be
24
considered to have failed when displacement has reached a level where it is no longer safe
to operate or the intended function cannot be met, e.g. when ramp access across the slope
is no longer possible (Read and Stacey, 2009).
The standard terminology used in North America to describe the geometric arrangement of
open pit mines is shown in Figure 1.1. The bench face angle is the angle between the toe
and crest of each bench; inter-ramp slope angles between the haul roads/ramps are the
angles between the toe and crest of each ramp; overall slope angle is the angle from the toe
of the slope to the pit crest. The overall slope angles for open pits range from near vertical
for shallow pits in good quality rock to flatter than 30◦ for those in very poor quality rock
(Wyllie and Mah, 2004).
Figure 1.1 Typical open pit slope geometry (Wyllie and Mah, 2004).
The slope failure is then categorized into three types by their sizes: bench failure, inter-
ramp failure and overall slope failure. The impacts of these three types of slope failures are
25
different. A bench failure, which may happen in a single bench or across a few benches,
may have little or no impact on the operation of the mine unless the bench failure occurs
on the ramp/haul road. An inter-ramp failure which cuts the haul road will block the access
to the mine, and therefore, the ramp will require repair. The overall failure usually occurs
from the top to the bottom and damages tens of benches and one or more ramps. An overall
slope failure may cost the mining company several months to clean the debris and recover
the copper production. Therefore, mining companies usually allow some bench failures as
long as they do not affect the mining activities, however, inter-ramp and overall slope
failures are not allowed.
A large slope failure in an open pit mine may cause many losses in several aspects:
(1) Direct safety and economical loss, which includes possible loss of life or injury,
loss of equipment, loss of ore, and the cost of cleanup and facility rebuild.
(2) Indirect economical loss, which includes the loss of invest confidence, loss of stock
market and product sales market.
(3) Social and environment loss, which includes the environmental concern from
communities, safety regulation from government departments.
Open pit mine slope design is not only a safety issue, but also an economical issue. The
main economic concern in most open pit mines is to achieve the maximum slope angle and
at the same time to keep an accepted level of slope stability. In a large open pit mine,
steepening a wall by only a few degrees can have a major impact on the return of the
operation through increased ore recovery and/or reduced stripping (Read and Stacey, 2009).
But, the stability of the slope usually decreases with the increase of the slope angle.
26
Therefore, the main purpose of open pit slope design is to find the balance between keeping
the slope stable and maximizing the economic efficiency.
The Google earth map of the large scale open pit mine considered in this dissertation is
shown in Figure 1.2. However, the study area was limited to the dashed rectangular area
shown in Figure 1.2 in the northwest corner of the mine.
Figure 1.2 Google map of the mine topography (Google Earth).
Please note that we are not allowed to provide specific information about the mine in this
dissertation. According to the mining company, the current bench face angles for the
investigated area of the mine range between 60 and 75°. The rocks in the research area are
divided into two rock units: (1) Devonian Rodeo Creek (DRC) Unit, and (2) Devonian
Popovich Formation (DP) as given in Table 1.1.
27
Table 1.1 Lithology of the research area
Geological unit Sub-layer Rock type description
Devonian Rodeo
Creek Unit
(DRC)
Argillite member-AA Limy siltstone, mudstone, and chert
Bazza sand member-BS Limy siltstone, sandstone and
mudstone
Argillite-mudstone
member-AM Limy mudstone and chert (argillite)
Disconformity
Devonian-
Popovich
Formation (DP)
Upper mud member-UM Laminated limy to dolomitic
mudstone
Deformation member-SD Thin bedded limy to dolomitic
mudstone and micritic limestone
Planar member-PL Laminated limy to dolomitic
mudstone
Wispy member-WS Limy to dolomitic mudstone with
wispy laminations
There are no distinct boundaries between the three members of the DRC unit. For DP
formation, even though there are observable boundaries between UM, SD, PL, and WS
members, their rock types are almost the same, which is mudstone. Therefore, the
geological units are simplified to two layers: DRC and DP.
When it comes to the particular mine we are studying, the complex mechanisms governing
these slope failures occurred in the south wall still have not been fully clarified. Figure 1.3
shows a multiple bench failure occurred in the south wall.
28
Figure 1.3 Slope failure occurred in the south wall of the open pit mine.
In the south wall, the slope failure happened between two faults and the contact between
two rock layers known as Devonian Rodeo Creek (DRC) unit and Devonian Papovich (DP)
unit. This means that it was a structural controlled slope failure. The contact between DRC
and DP rocks was found to be a soft weak layer, which may be a potential sliding plane.
There are many faults that exist in the open pit mine. These faults are also the weak planes
and may contribute to slope failures. How to simulate the geometric network of the faults
and the rock excavation, and to investigate the stability of the slope in the north wall is a
very challenging part of this research.
1.3 Contributions
First of all, the special survey equipment that Professor Pinnaduwa Kulatilake owns, which
has a total station, a laser scanner and a camera, was used for the remote fracture mapping
in the open pit mine. Fracture information obtained through this remote fracture mapping
29
was used along with intact rock properties estimated through laboratory testing in
estimating rock mass properties. In open pit mines, it is very dangerous to conduct manual
mapping of discontinuities. Therefore, the application of the said remote fracture mapping
at the open pit mine was a very useful and constructive effort. Even though the laser
scanning technology has been used in the past to do fracture mapping, in this investigation
the used mapping technique as well as the fracture geometry interpretation techniques were
different. Very good agreement was found between the remote fracture mapping data
results and the manual mapping data provided by the mining company on the dip angle and
dip direction of fracture sets. This was an important accomplishment in the dissertation
compared to what exist in the literature. It was very convenient and fast to apply the used
methodology to capture fracture information. This method may be widely used in open pit
mining in the future.
Secondly, the construction of the complex geological model made it possible to simulate
the real situation of the rock slope movement. Research reported in the literature has
simulated faults only incorporating a very few faults using highly simplified assumptions.
This is the first time that a highly complicated fault system was built with their real
locations, orientations, and three-dimensional persistence. Good matches were found when
the fault system built in the 3DEC model was compared with the data obtained from the
mining company. This was a huge accomplishment in this dissertation. It proved that it is
possible to consider complex geological structures in investigating open pit mine rock
slope stability, which is an essential component in structurally controlled rock slope
failures.
30
Finally, the numerical modeling displacement results were compared with field monitoring
data. The numerical modeling simulated the displacements of seven monitoring points
from July 2011 to July 2012, during that period a part of the rock mass was excavated. The
field displacements from these seven monitoring points were also available from robotic
total station survey. Even though the survey noise was high in robotic total station, the
displacement comparison between the numerical modeling results and field monitoring
data were found to be in good agreement. This is another huge accomplishment in the
dissertation because this is the first time such a comparison has been made at the three
dimensional level.
The results obtained from the conducted research showed the possibility of using the
methods presented in this dissertation to study open pit mine rock slope stability under
different rock excavation scenario to predict the status of rock slope stability and to design
future rock slopes.
1.4 Dissertation Outline
The research performed in this dissertation can be illustrated by the following flow chart.
The listed different tasks in Figure 1.4 are covered under different chapters in the
dissertation as given below.
31
Figure 1.4 Flow chart.
The dissertation is divided into seven chapters.
Chapter 1 is the introduction which includes the motivation for research, background and
problem statement, contributions and the dissertation outline.
Chapter 2 reviews the available literature on current research status of open pit mine rock
slope stability. It discusses different fracture mapping methods and rock slope stability
computational methods. The current status of numerical modeling in open pit mine rock
slope stability is also summarized in this chapter. It shows that the use of a remote fracture
mapping technique that combines laser scanning along with photographs and total station
technology is the best choice to collect fracture data. Among the available computational
techniques, the discrete element method is identified as the most appropriate choice to
conduct computational research to investigate rock slope stability.
32
Chapter 3 covers the field and laboratory investigations performed to estimate physical and
mechanical properties for intact rock and rock discontinuities including collecting rock
samples at the mine site. The conducted laboratory tests include Brazilian test, uniaxial
compressive test (with and without strain gauges), triaxial test, direct shear test on
discontinuities and uniaxial compression test with a horizontal joint.
Chapter 4 describes the performed remote fracture mapping, estimation of fracture
geometry parameters and estimation of rock mass and discontinuity properties.
Comparison of joint orientation distribution obtained from remote fracture mapping and
manual fracture mapping (from the mining company) is discussed in this chapter. GSI
was used to estimate rock mass properties by combining the fracture geometry results
estimated from remote fracture mapping data and observed features of rock mass
discontinuities. Then, rock mass properties are calculated using Hoek-Brown criterion
combining the obtained GSI values with the intact rock properties estimated in Chapter 3.
The joint properties of major discontinuities (faults and DRC/DP contact) are estimated
based on the laboratory test results obtained for discontinuities in Chapter 3.
Chapter 5 presents the process of building the complex geological model and its validation.
The fault system, DRC/DP contact, and rock mass excavation regions are built into an
integrated geological model.
Chapter 6 describes the conducted numerical modeling. The rock mass and discontinuity
properties estimated in Chapter 4 are used along with the geological model obtained in
Chapter 5 in performing the numerical modeling under different boundary conditions for
different excavation scenarios. The obtained field monitoring data from the mining
company is analyzed in this chapter. The analyzed field monitoring data of seven
33
monitoring points are compared with the computed displacements of the same seven
monitoring points from numerical modeling under different scenarios. Effect of the
following factors on rock slope stability is evaluated in this chapter: (a) Faults; (b)
Boundary conditions; and (c) lateral stress ratio.
Chapter 7 covers the summary and final conclusions of the conducted research and the
suggestions given for future research on the topic dealt with.
34
CHAPTER 2 LITERATURE REVIEW
2.1 Introduction
In this chapter, the discontinuity mapping methods and rock slope stability computational
methods are reviewed separately. The discontinuity mapping methods mainly include:
scanline mapping, window mapping, core drilling, LiDAR mapping and photogrammetry.
Slope stability computational methods mainly include: kinematic analysis, block theory,
limit equilibrium analysis, continuum numerical methods, and discontinuum numerical
methods. In this literature review, the advantages and disadvantages of each method is
stated and a comparison among different methods is given. In addition, the current status
of numerical modeling of open pit slope stability is discussed, especially the status of using
the three dimensional discrete element method.
2.2 Discontinuity Mapping Methods
It has been widely recognized that the rock slope stability depends on the discontinuity
geometry and strength more than the strength of the intact rocks. Discontinuities usually
include joints (fractures), bedding planes, faults and contacts between two different rock
types. Joints are usually small size discontinuities that control the rock mass properties
when a significantly fractured rock mass in a large open pit mine is concerned. Faults,
bedding planes and contacts are usually large scale discontinuities, and they control the
overall rock slope stability. Joints, bedding planes, faults and contacts are usually seen on
rock outcrops. Igneous and metamorphic rocks may have jointing systems with three or
35
more discontinuity sets (Goodman, 1989). Sedimentary rocks usually has a bedding plane
and at least other two joint sets.
2.2.1 Scan line mapping
In scanline mapping, a measuring tape is usually placed at waist height or some other
appropriate level, nailed to the outcrop at both ends. The surveyor then traverses the line,
recording discontinuity data for every discontinuity that intersects the line (Piteau and
Martin, 1977). The technique has been widely used in mining and civil engineering (Priest
and Hudson, 1981, Kulatilake et al., 1993) and is still the most widely used discontinuity
mapping method because it uses simple tools and is also easy to operate. The measurement
of dip angle and dip direction is conducted by a compass, see Figure 2.1. As the smart
phone has been widely used, some application software packages have been developed for
smart phones to measure discontinuity orientations.
Figure 2.1 Use of geological compass to measure joint orientation.
36
Discontinuity information is recorded in the field using simple data sheets. During a detail
line survey, the following information is recorded for each discontinuity that crosses the
scanline: rock type, structure type, spacing, roughness, dip angle, dip direction, length, and
fillings. Priest (1993) has suggested that 150-350 measurements should be made, with the
lower number sufficient for a rock mass containing three structural sets and the larger
number for a rock mass containing up to six sets. Discontinuity geometry data obtained
through scaline mapping are subject to sampling biases. Kulatilake and Wu (1984a),
Kulatilake et al. (1990) and Wathugala et al. (1990) have suggested corrections for
sampling biases associated with discontinuity orientation data. Priest and Hudson (1981)
have suggested corrections for sampling biases associated with discontinuity trace length
data. Kulatilake et al. (1993) have suggested corrections for sampling biases associated
with discontinuity spacing data.
2.2.2 Window mapping
Window mapping involves collecting all the structural data above a given cut-off size from
a specified area of a rock face. Alternatively, only the attributes of each of the sets
recognized within the window may be recorded, therefore bias may be introduced into the
results. It is suggested that in an open pit mine, a number of windows should be selected at
regular intervals within each of the mapping units recognized along the benches (Read and
Stacey, 2009). As for scanline mapping, discontinuity geometry data obtained through
window mapping are subject to sampling biases. Kulatilake and Wu (1984a), Kulatilake et
al. (1990) and Wathugala et al. (1990) have suggested corrections for sampling biases
37
associated with discontinuity orientation data. Kulatilake and Wu (1984b) and Kulatilake
and Wu (1984c) have suggested corrections for sampling biases associated with
discontinuity trace length and density data, respectively. Kulatilake et al. (1993) have
suggested corrections for sampling biases associated with discontinuity spacing data. Wu
et al. (2011) have shown that rectangular windows are better than circular windows in
applying for sampling bias corrections associated with discontinuity size and intensity.
The scanline mapping covers only the discontinuities that intersect the scanline. On the
other hand, window mapping covers all the discontinuities that exist in the considered
window. Therefore, window mapped data provide better reliability than that of scanline
data. However, the time needed to conduct window mapping through manual techniques is
way higher than that for scanline mapping. Application of both types data to model fracture
systems in 3-D for real world problems are available in Kulatilake et al. (1993, 1996 and
2003).
2.2.3 Core drilling
In many cases, rocks may be covered by alluvium and/or vegetation; in such situations the
rock mass outcrops are not available for fracture mapping. Under such circumstances core
drilling may be used to obtain the discontinuity information. Besides, because the outcrop
mapping can only provide discontinuity information of the surface rocks, core drilling is
the mostly used method to investigate the subsurface geological structure information. It is
necessary to realize that the main purpose of core drilling in an open pit mine is to discover
the locations and thicknesses of ore bodies, and obtain core samples for mineral analysis
and rock strength tests. The additional function of core drilling is to collect fracture
38
information, mainly the orientation and density of discontinuities. The following
information should be recorded in obtaining discontinuity information (Read and Stacey,
2009):
Natural fracture frequency per meter;
Cemented joint frequency per meter, which represents the number of healed or
cemented joints;
Cement type and strength;
Frequency and strength of micro defects;
Number of joint sets;
Typical angle of the individual joint set to the core axis;
Joint conditions for the individual set.
Many problems exist when data from core drilling are used. The core sample is too small
to provide sufficient information about the length, and continuity of discontinuities. The
sampling bias associated with discontinuity orientation is also a problem with core logging,
as the method gives preference to discontinuities with sub-horizontal orientations, while
those with steeper angles are more likely to be omitted (Kulatilake and Wu, 1984a; Park,
1999).
Because the core samples collected by core drilling are disturbed when they are pulled out
of the drill hole, it is difficult to determine the discontinuity orientations. Therefore, the
downhole tele-viewer method can be used to examine in-situ information through the drill
hole. Tele-viewer provides continuous and 360 degree view of the drill hole wall from
which the character, relation and orientation of lithological and structural planar features
are available for geotechnical logging and analysis (Read and Stacey, 2009).
39
2.2.4 LiDAR
LiDAR (Light Detection and Ranging) sensing is an active form of remote sensing, as
opposed to passive forms that detect natural radiation that is reflected or emitted. It utilizes
artificial light to illuminate a surface with lasers. The lasers hit the ground surface and
scatter (Farny, 2012).
Two distinct operating principles for the laser range finder are used in 3-D laser scanners.
The first and most common type is pulsed lasers. A pulsed laser transmitter sends out light
and the backscatter is recorded by an optical telescope receiver, and then turned into
electrical impulses by a photomultiplier tube. The distance to the object is then calculated
using the time taken by the pulse to travel to the target and back:
𝐷 =𝑐 ∙ 𝑡
2 (2.1)
Where D is the distance the pulse traveled, C is the speed of light, and t is the time of flight,
the elapsed time for the pulse to travel to and from the scanned object. (Kemeny and Turner,
2008)
The second type is continuous wave (CW) or phase shift, which uses a continuous laser
signal and the modulated intensity of the laser light for ranging. In continuous wave
scanning, the travel time of the laser pulse is measured using the phase difference of the
received and transmitted sinusoidal signals:
𝑡 =𝑃
2𝜋 ∙ 𝑀 (2.2)
Where P is the phase shift and M is the modulation frequency. The time of flight calculated
is then plugged into Eq. (2.1) to find the distance traveled. (Kemeny and Turner, 2008)
40
Near range LiDAR or ground based LiDAR has been available since 1998 for common use
(Farny, 2012). Ground based LiDAR scanners weigh around 10 to 15 kilograms and
typically have an effective range of up to a kilometer with an accuracy of 3 to 10 mm
(Kemeny and Turner, 2008). To perform the LiDAR mapping, first the scanner needed to
be set in front of the selected rock face and survey control points may be also placed. After
the scan, digital photographs of the scanning area are taken by the embedded camera. The
photographs taken can be utilized for photo draping over the point cloud (Kemeny and
Turner, 2008).
Kemeny et al. (2006) has described a process to identify joint orientations using LiDAR:
(1) The first step in this process is orientating the point cloud based on real world
orientations. This is typically accomplished using the three point registration
method.
(2) Once the point cloud is orientated, a triangulated mesh surface is generated. 3-D
surface reconstruction is done using Delauney triangulation, a polygonal technique.
This creates triangular facets based on three points using interpolation.
(3) After this, fracture “patches” are determined from this triangulated mesh. Patches
are discontinuities, identified by the fact that they are relatively flat. Once the
normal to a flat triangle facet is found in the mesh, the surrounding area is searched
for triangles with similar properties to expand the patch.
The average orientations of these patches or discontinuities can then be used for stereo net
analysis. From these generated patch surfaces, the discontinuity spacing may be determined
as well as the size of individual rock blocks.
41
It is important to note that some of the fracture surfaces appear on a rock outcrop comes
from disturbed rock or debris. In addition, some of the fracture surfaces are results from
blasting. It is important to separate out natural fracture surfaces from the fracture surfaces
caused by blasting. Therefore, fracture surfaces should be carefully chosen before
processing point cloud data to obtain fracture geometry information. This means point
cloud data processing is not a trivial exercise. If it is done not carefully and accurately it
can lead to misleading results on fracture geometry. Such misleading results appear in the
literature.
2.2.5 Photogrammetry
Photogrammetry is the practice of determining the geometric properties of objects from
photographic images, and it takes advantage of the fact that light rays from an object strike
different parts of a camera’s image sensor as the location of the camera changes (Roman
and Johnson, 2011). Prior to taking the photographs, control points may be placed at
various locations in the study area. At least three control points are required to register the
model to a real world coordinate system. Use of more than three control points provides
redundancy, which is useful for estimating the accuracy of the model and ensuring against
bad observations (Roman and Johnson, 2011). After digitizing the survey control points,
and following with a bundle adjustment, a digital terrain model can be generated by a
software program. With the digital terrain model, discontinuity features may be extracted.
Once a 3D digital terrain model is produced, the analysis of the model to extract
geotechnical information is very similar between LiDAR and photogrammetry (Kemeny
et al. 2006). The advantage of photogrammetry is the low cost of equipment compared to
42
LiDAR, but the disadvantage is that the photogrammetry depends on the light available to
take good pictures.
2.2.6 Summary
Scanline and window mapping require mining engineer to get close to the rock slope to do
the manual measurement of discontinuity and therefore is not safe when the rock slope is
not quite stable, especially for open pit mines where the rocks are highly fractured and
disturbed by blasting and excavation. Manual mapping is very low efficient and high labor
costing to collect enough discontinuity information. Core drilling method is used when
rock mass outcrops are not available on the particular site. It can be used to measure the
dip angle, spacing, and roughness of discontinuities, and also the dip direction when the
downhole tele-viewer technique is used. However, core drilling is quite expensive and time
consuming; its main function is to analyze ore deposits and is only used as a supplemental
method to investigate discontinuities. LiDAR mapping seems to be the best discontinuity
mapping method for open pit slope when good outcrop is exposed by rock excavation. It
can collect much more information rapidly than manual mapping (scanline and window
mapping). The other advantage is that the equipment is set far away from the slope,
therefore, it is safe for people and equipment. The disadvantage of LiDAR is the high cost
of the equipment. Photogrammetry is also as convenient as LiDAR, but it depends more
on the light to take good pictures and its accuracy is not as high as LiDAR.
43
2.3 Rock Slope Stability Computational Methods
Rock slope stability analysis methods can be mainly divided into five different categories:
kinematic analysis, block theory, limit equilibrium methods, continuum numerical methods
and discontinuum numerical methods. The first three methods are analytical methods, and
the latter two are numerical methods. The first three methods are mainly applicable for
hard rocks which show very distinct fracture sets; such fracture sets can produce plane,
wedge and toppling failures. Kinematic analysis and the first step of block theory only
looks into possible movements of blocks only under gravitational loading without
considering the external forces that may act on the blocks. Block theory was developed by
Goodman and Shi (1985) and is a more complicated and powerful method than kinematic
analysis. Because simplifying assumptions are used in the kinematic analysis compared to
the block theory, the results obtained through the kinematic analysis are too conservative;
the results obtained through block theory are closer to the reality. The blocks that are found
to have possible movements through the aforementioned kinematic analysis or block theory
can be subjected to limit equilibrium analysis by incorporating all the forces and resistances
to determine factor of safety of the blocks. Continuum and discontinuum numerical
methods are applicable to investigate more complex type of failures that can occur in large
rock masses through interactions between intact rock and discontinuities. Continuum
numerical methods usually include Finite Element Method (FEM), Boundary Element
Method (BEM), and Finite Difference Method (FDM). Discontinuum numerical methods
include Discontinuous Deformation Analysis (DDA) and Discrete Element Method (DEM).
This chapter will have a review of all these methods and their applications on rock slope
stability studies of open pit mines.
44
2.3.1 Kinematic analysis
Four types of simple failure modes have been widely recognized in rock engineering based
on years of experience; which are: plane failure, wedge failure, toppling and circular failure,
as illustrated in Figure 2.2. It is possible to have more than one failure mode appearing in
a single rock slope.
(a) Plane failure (b) Wedge failure
(c) Toppling (d) Circular failure
Figure 2.2 Four types of failure modes (Hoek and Bray, 1981).
The method to identify the slope failure mode and the sliding direction for a particular
situation, called kinematic analysis, has been developed by Markland (1972) and Hocking
(1976). Discontinuities and the slope face are plotted on a stereo-net plot and test criteria
are used to identify which failure mode may occur. Once the failure mode is identified on
45
the stereo-net, the same plot can also be used to examine the direction in which the block
slides and give an indication of stability conditions. Applications of kinematic analysis to
real world rock masses are given by Um and Kulatilake (2001), and Kulatilake et al. (2003
and 2011).
2.3.2 Block theory
The block theory is not a substitute of the limit equilibrium method; it will allow you to
determine which blocks need to be analyzed with the limit equilibrium methods. The
objective of the block theory is to locate and then provide details of the most critical rock
blocks in the study area. The intersections of numerous joints create blocks of irregular
shape and size in the rock mass; then, when an excavation is made, many new blocks are
created by the excavation face. Some of these blocks will not be able to move into the free
space of the excavation, either by virtue of their shape, size, or orientation, or because they
are prevented from moving by others. A few blocks are immediately in a position to move,
and as soon as they have done so, other blocks that were previously restrained will be
liberated (Goodman and Shi, 1985).
Block theory divides blocks into five categories: (1) infinite blocks; (2) non-removable
blocks; (3) stable even without friction; (4) stable with sufficient friction; and (5) unstable
without support. A key block (unstable without support) is potentially critical to the
stability of an excavation because by definition, it is finite, removable, and potentially
unstable (Goodman and Shi, 1985).
The block theory analysis is usually performed by drawing a stereo-net plot. Goodman and
Shi (1985) have given the principles and methods to distinguish these five types of blocks.
46
The removability is highly related to the location and orientation of the excavation face.
Therefore, the block theory can be used to find the best excavation surface. Block theory
only determines the removability of blocks; but does not provide stresses or strains in the
blocks. Limit equilibrium analysis may be performed to calculate the factor of safety once
key blocks are found with the block theory.
Application of block theory analysis to real world rock masses are given by Um and
Kulatilake (2001), Kulatilake et al. (2003 and 2011), and Zheng et al. (2014).
2.3.3 Limit equilibrium method
The limit equilibrium means when the driving force is exactly equal to the resistant force
(i.e. the limit equilibrium status), the safety factor equals to 1.0. Adding a little more driving
force can trigger the block to slide. The limit equilibrium method calculates the safety
factor by using the magnitudes of the driving forces and the resisting forces acting on the
rock mass as inputs. When the safety factor is larger than 1.0, the block is safe; or else the
block is not safe. A simple example of the limit equilibrium method is shown in Figure 2.3;
its factor of safety can be calculated as follows:
𝐹𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝑆𝑎𝑓𝑒𝑡𝑦 (𝐹𝑆) =𝑅𝑒𝑠𝑖𝑠𝑡𝑖𝑛𝑔 𝐹𝑜𝑟𝑐𝑒𝑠
𝐷𝑟𝑖𝑣𝑖𝑛𝑔 𝐹𝑜𝑟𝑐𝑒𝑠 (2.3)
𝐹𝑆 =𝐶∙𝐴𝑐+𝑊∙𝑐𝑜𝑠𝜓∙𝑡𝑎𝑛𝜑𝑗
𝑊∙𝑠𝑖𝑛𝜓 (2.4)
where C is the cohesion of the discontinuity, Ac is the contact area of the two blocks, W is
the weight of the upper rock block, ψ is the dip angle of the discontinuity, and φj is the
friction angle of the discontinuity.
47
Figure 2.3 A simple example of the limit equilibrium analysis (Hoek and Bray, 1981).
Goodman (1964) and John (1970) have discussed the limit equilibrium method for wedge
failure in their papers. Muller (1968) was the first one to propose the toppling failure mode.
Goodman and Bray (1976) found that there are two types of toppling failure modes: block
and flexural toppling, and each of them should be analyzed by a different method.
Typical applications of limit equilibrium analysis to rock slopes are given by Kulatilake
and Fuenkajorn (1987), and Kulatilake (1988).
2.3.4 Continuum numerical methods
Currently, three continuum numerical methods are used for rock slope stability analysis:
the finite element method (FEM), finite difference method (FDM), and boundary element
method (BEM).
FEM has been used and developed over many decades. The basic steps for using FEM
include (1) domain discretization, (2) local approximation and (3) solution of the assembled
global matrix equation (Yan, 2008). The most widely used FEM software packages are
ANSYS and ABAQUS.
48
Typical FDM software packages used in the rock mechanics area are FLAC and FLAC3D.
For example, FLAC3D is a three-dimensional explicit finite-difference program for
engineering mechanics computation. It simulates the behavior of three-dimensional
structures built of soil, rock or other materials that undergo plastic flow when their yield
limits are reached (Itasca, 2009).
BEM, as its name indicated, only discretizes the boundaries of the model into elements and
leaves the interior unmeshed as an infinite continuum (Yan, 2008). The solution of a BEM
model requires five steps (Jing, 2003): (1) discretization of the boundary with a finite
number of boundary elements; (2) approximation of the solution of functions locally at
boundary elements by trial/shape functions; (3) evaluation of the integrals with point
collocation method by setting the source point at all boundary nodes successively; (4)
incorporation of boundary conditions and solution; (5) evaluation of displacements and
stresses inside the domain.
When a continuum numerical method is used to study rock engineering, joint elements may
be introduced to represent discontinuities in the rock mass; but these joint elements can
only yield to limited deformation without any detachment. The continuum numerical
methods can only calculate the stresses, strains, displacements or velocities of elements or
grid points. The strength reduction method may be used (Jiang, 2009) to find the safety
factor of the rock slope. The strength reduction method is based on the nonlinear finite
element theory and solves the safety factor by reducing the material strength properties
using the following equations until the numerical model reaches the critical convergence
status. The reduction factor at the critical convergence status is therefore the factor of safety.
𝑐𝑟 =𝑐
𝐹 (2.5)
49
𝜑𝑟 = 𝑎𝑟𝑐𝑡𝑎𝑛𝑡𝑎𝑛𝜑
𝐹 (2.6)
where c and cr are the cohesion and reduced cohesion; φ and φr are the friction angle and
the reduced friction angle; F is the reduction factor and also may be used as the safety
factor.
2.3.5 Discontinuum numerical methods
The most well-known and developed discontinuum numerical methods are discrete
element method (DEM) and discontinuous deformation analysis (DDA).
The name discrete element method applies to a computer program only if it (Itasca, 2007):
(1) Allows finite displacements and rotations of discrete bodies, including complete
detachment;
(2) Recognizes new contacts automatically as the calculation progresses.
Without the first attribute, a program cannot reproduce some important mechanisms in a
discontinuous medium. Without the second, the program is limited to small numbers of
bodies for which the interactions are known in advance. The term “distinct element method”
was coined by Cundall and Strack (1979), refers to the particular discrete-element scheme
that uses deformable contacts and an explicit, time-domain solution of the original
equations of motion (not the transformed, modal equations) (Itasca, 2007). Therefore, it
should be kept in mind that DEM is not the acronym of distinct element method but discrete
element method in this study.
DEM was first proposed by Cundall (1971), and further developed by Lemos et al. (1985),
Cundall (1988), and Hart et al. (1988). DEM considers rock mass as an assembly of rigid
or deformable blocks, while the discontinuities are independent boundaries between blocks.
50
Continuum theories are used in the interior of blocks, while at the same time the
relationship between force and acceleration is used to calculate the motion of each block
under unbalanced forces. By considering the interaction between neighboring blocks, this
method can calculate large displacements, large rotations of blocks and discontinuities. The
corresponding commercial software packages of DEM are UDEC and 3DEC, which are
developed by Itasca Consulting Company Inc. The DEM provides the option to solve a
model to determine the factor of safety against general failure or collapse. The technique
uses an automated, iterative strength-reduction method to determine the factor of safety.
The command allows selection of the properties that are used in the strength reduction
process. A typical application of 3DEC for a rock tunnel in a dam site in China is given by
Wu and Kulatilake (2012a).
DDA was proposed for the first time by Shi and Goodman (1985), and then was
continuously developed by Shi (1988, 1990, 1993, 1995, 1996, and 2001). Similar to DEM,
it can also solve large displacement and rotation problems for blocky rocks. DDA uses an
implicit algorithm for simultaneous solution of the equations of equilibrium by minimizing
the total potential energy of the blocky rock mass system. The relation between adjacent
blocks is governed by equations of contact interpenetration and accounts for friction. DDA
adopts a stepwise approach to solve the large displacements which accompany with
discontinuous movements between blocks.
Wu and Chen (2011) studied an earthquake induced landslide using the DDA method in
which the movement of blocks sliding down from a mountain was accurately simulated;
the computational results agreed with the actual post-failure topography very well.
51
2.4 Current Status on Numerical Modeling Study of Open Pit Rock Slope Stability
In this section, the current status of rock slope stability studies with numerical modeling in
mining industry are introduced and summarized.
2.4.1 Finite element method
The finite element software are well developed and widely available. Therefore, there are
many studies conducted with the finite element method on open pit slope stability problems.
For example, Islam and Faruque (2013) used a two dimensional finite element method to
study the slope angle optimization of a coal mine in Bangladesh. Their study estimated the
safety factor under two conditions: without seismic effect, and with seismic effect. The
results show that the studied slope is under high risk of slope failure with its current slope
angle if the mine site is subject to earthquake shaking. Meng et al. (2013) used the finite
element method to study the failure mode of an open pit mine, and the analysis revealed
the internal sliding along the bottom weak layer. A three dimensional finite element method
was used to study slope stability in a mine combining open pit and underground mining
(Ren and Fang, 2010). The finite element method was used by Hu and Kempfert (1999) to
study the buckling failure process of a rock slope in jointed rocks, and the behavior of
discontinuities was simulated using “a joint element”. Silva et al. (2008) studied the failure
mechanisms of a slope failure occurred in 2003, and evaluated the pit stability in 2006 with
another widely used finite element software package, Phase 2.
52
2.4.2 Finite difference method
Many researchers tend to use the finite difference method to study open pit slope problems.
Li et al. (2013) studied the slope stability of an open pit mine in Xinjiang, China, using
FLAC3D. The creeping test results of the sandy mudstone from the open pit mine showed
strength decrease over time. Therefore, when these test results were used in the numerical
modeling, the results showed that the safety factor reduces from 1.59 to 1.15 in 18 years of
service life. A two dimensional finite difference method (FLAC) was used in estimating
glacier ice deformation rates adjacent to a proposed open pit mine when mining was about
to start (Zarnani et al., 2012). Fu and Dong (2010) used FLAC3D to analyze the rock layer
movement and deformation for an open pit mine with underground mining started under
the open pit.
2.4.3 Two dimensional discrete element method
With the recognition of the advantages of the discrete element method in simulating
discontinuities, many research have been conducted with the two dimensional discrete
element method. For example, Azizabadi et al. (2014) studied the maximum displacement
at the crest of an open pit mine due to the influence of blasting with UDEC software, which
is the two-dimensional version of the discrete element method. Vyazmensky et al. (2010)
used a two dimensional finite element/discrete element modeling (FEM/DEM) approach
for a large open pit slope. Using this method, a threshold percentage of critical intact rock
bridges along a step path failure plane was found, and the development of a large slope
failure triggered by an underground caving operation was analyzed. Sjoberg (1999) also
studied the complex mechanisms that governed several large scale slope failures in an open
53
pit mine in Spain using a 2-D finite difference numerical software. The numerical results
were able to explain the failure mechanism in detail. Hencher et al. (1996) used UDEC in
the design of open pit mine slopes under complex geological conditions.
2.4.4 Consideration about three dimensional analysis
Compared with the two dimensional method, three dimensional numerical modeling is
more complicated but can handle more realistic problems. The study conducted by Lorig
(1999) with the finite difference method showed that the geometry of a slope is an
important consideration in open pit mining and can have a significant effect on the slope
stability, and therefore, a three dimensional numerical modeling is preferred to a two
dimensional limit equilibrium analysis. Cala (2007) studied the stability of two
dimensional and three dimensional convex and concave slopes with both the limit
equilibrium and numerical simulation methods. The calculation results showed that the two
dimensional slope stability analyses cannot capture the reality in many cases, and it is
necessary to perform three dimensional numerical calculations to simulate complex
geology and spatial geometry of slopes. Sainsbury et al. (2003) also compared the
difference between two dimensional and three dimensional numerical modeling with
FLAC and FLAC3D, respectively modeling an open pit slope interacting with remnant
underground voids. The research results pointed out that the two-dimensional geometry
assumption used in most open pit mine design is not the condition encountered in practice
most of the time, and three-dimensional numerical models provided a more realistic
representation of the studied problem.
54
2.4.5 Three dimensional discrete element method
Currently, the main three dimensional discrete element software used in rock slope stability
analysis is 3DEC. In the recent past, a few studies have been conducted on rock slope
stability using 3DEC. Brummer et al. (2013) used the 3DEC software package to study an
open pit slope failure when the open pit mine was transited to an underground mine.
However, the 3DEC model they have built for numerical modeling consists only of four
faults and the joints were simply assumed as evenly distributed parallel discontinuities. The
assumption used to build joint sets cannot reflect the reality because no joints are
distributed evenly with the same orientation. Sainsbury et al. (2007) back-analyzed a slope
failure in an open pit mine with 3DEC software and then the model was used to investigate
the slope stability as the mining had progressed. This study also considered only three faults
and two fault zones, while other discontinuities were not built into the model, which
dramatically decreased the difficulty as well as the reliability of the work. Brideau and
Stead (2011) evaluated the influence of discontinuity set orientation and the lateral
kinematic confinement on the slope failure mechanism with 3DEC software. Similar to the
other studies introduced before, this one also considered very simple parallel and equal
spacing joints. Sainsbury et al. (2003) also tried to use 3DEC to conduct three-dimensional
analysis of an open pit mine; but again the model only included a few discontinuities which
means it did not fully use the advantage of 3DEC software. Similar simple 3DEC model
with a few fully persistent discontinuities was also used by Gheibie and Duzgun (2013)
and Firpo et al. (2011) to study rock slope stability.
55
2.4.6 Consideration of rock excavation
Open pit mine slopes are usually continuously excavated and their topographies change all
the time. Therefore, simulation of rock slope excavation becomes another important issue
in investigating rock slope stability. Some studies are reported in the literature on
simulation of excavation with numerical modeling methods. Behbahani et al. (2013) used
PFC2D (particle flow code) to study the sliding behavior of a rock mass in an open pit
mine under several stages of excavation. During the seven stages of unloading, the
maximum displacements and maximum contact forces among the particles were obtained.
Chen et al. (2007) have studied the difference of open pit mine slope stability under loading
and unloading conditions with the finite element method. They have found the
displacements and stresses of the rock mass to be different under these two conditions. The
research indicated that the simulation considering unloading effect of excavations could
properly reflect the real situation of slope stability. Li and Speight (1997) studied the time-
dependent slope failures using a finite difference code. The mine excavation was simulated
in four stages.
2.4.7 Summary
Overall, most of the open pit mine slope stability studies have used either the finite element
method or the finite difference method. As mentioned before, neither of them can simulate
large displacements and rotations. Some simple two dimensional and three dimensional
discrete element modeling studies also appear in the literature. Unfortunately, those studies
were limited to simulating very few simple fully persistent discontinuities, such as evenly
distributed parallel joints or several faults. In reality, no joints or faults are evenly
56
distributed or strictly parallel, but randomly distributed with finite size lengths in rock
masses. It has been shown that the orientation and location of faults can affect the open pit
mine slope stability (Zhao et al., 2014). Therefore, it is important to consider real
orientations, locations, and three dimensional sizes of various discontinuities/faults in a
three dimensional discrete element method study.
2.5 Conclusions
In the literature review, the current status on rock slope engineering is well introduced and
concluded. The technical issues covered in this chapter consist of two parts: discontinuity
mapping and rock slope stability analysis methods. In the discontinuity mapping part, it
was found that in large open pit mines, the most feasible method is the LiDAR mapping
method. The rocks in open pit mines are usually disturbed by the excavation machine
and/or blasting. Therefore, to ensure the accuracy of mapping results, supplemental manual
discontinuity mapping should be performed to verify the LiDAR mapping results.
Among all of the rock slope stability study methods, it is not difficult to see that the three-
dimensional discrete element method is the best choice for rock slope stability study. The
geological conditions (faults, discontinuities) control the stability of slopes. This means
that accurate modeling of the discontinuity network in the rock mass is an essential item in
obtaining realistic results from three-dimensional numerical modeling of rock slopes.
57
CHAPTER 3 CONDUCTED LABORATORY TESTS AND RESULTS
To obtain the physical and mechanical properties of intact rock and rock joints (fractures),
laboratory tests were conducted in the Geomechanics Laboratory at the University of
Arizona. According to the mine stratigraphy two main rock formations exist in the research
area of the mine selected for this study: (a) Devonian Rodeo Creek (DRC) unit and (b)
Devonian Popovich (DP) formation. DRC unit contains argillite, siltstone and sandstone;
DP formation contains mostly mudstone.
3.1 Collection and Preparation of Rock Test Samples
Rock blocks, including both DRC and DP rocks, were carefully selected by the author and
the co-workers from the research area. Figure 3.1 shows the rock blocks collected from the
open pit mine site.
The rock blocks collected from the mine were shipped to the University of Arizona and
then core samples were extracted from them by core drilling (ASTM, 2008a). Figure 3.2
shows the cores with a diameter of 2 inches drilled out of a rock block. Rock samples were
then prepared out of the cores. Long cores were first cut and then prepared into 4-inch, 2-
inch, or 1-inch long rock test samples. Four-inch long samples were prepared for the
uniaxial tests without strain gages, uniaxial tests with strain gages, and triaxial tests. Two-
inch long samples were prepared for the uniaxial tests with a horizontal joint at the midway
of the sample. One-inch samples were prepared for the Brazilian tests and direct shear tests.
58
Figure 3.1 Collected rock blocks from the open pit mine site.
Figure 3.2 Rock cores drilled out of a rock block.
3.2 Procedures Used for Laboratory Tests
3.2.1 Brazilian tension test
Brazilian tension test is used to obtain the tensile strength of rock samples (ASTM, 2008b).
Rock samples used in Brazilian tension test usually have a thickness of approximately 1
inch and a diameter of 2 inches. Each sample was examined to find pre-existing fractures
59
and determine the best orientation for testing. A single layer of paper tape was wrapped
around the edge of the sample to prevent post-testing sample breakup. During loading, the
sample was continuously observed to record the initial failure pattern. The samples were
loaded to failure, and a record was made of the initial failure pattern. Figure 3.3 shows the
Brazilian tension test procedure, and Figure 3.4 shows some of the Brazilian tension test
samples. Rock samples which failed on pre-existing cracks, or not failed in a proper way
were not used to calculate the tensile strength because they did not give correct values. The
Brazilian tension test results are listed in Tables 3.1 and 3.2 for DRC and DP rocks,
respectively.
(a) Before failure (b) After failure
Figure 3.3 Brazilian tension test setup.
60
Figure 3.4 Some of the tested Brazilian tension test samples.
Table 3.1 Brazilian tension test results for DRC rocks
Sample # Tensile strength (MPa) Sample # Tensile strength (MPa)
1 10.8 14 10.96
2 14.32 15 11.28
3 9.99 16 11.79
4 11.33 17 15.62
5 12.04 18 8.87
6 10.24 19 14.95
7 10.85 20 18.32
8 13.4 21 16.71
9 10.81 22 8.31
10 17.78 23 15.43
11 10.42 24 10.21
12 11.74 25 17.44
13 12.96 AVG. 12.9
Maximum
value
18.32 STD. DEV. 3.1
Minimum
value
8.31 C.V. 0.24
Note:AVG.-Average; STD. DEV.-Standard deviation; C.V.-Coefficient of variation.
61
Table 3.2 Brazilian tension test results for DP rocks
Sample # Tensile strength (MPa) Sample # Tensile strength (MPa)
1 8.38 10 4.98
2 7.49 11 6.23
3 5.43 12 6.55
4 5.31 13 4.26
5 5.17 14 5.64
6 7.12 15 6.11
7 6.26 16 5.58
8 7.10 17 5.29
9 10.86 18 3.84
AVG. 6.2
Maximum
value
10.86 STD. DEV. 1.6
Minimum
value
3.84 C.V. 0.26
3.2.2 Uniaxial compression test
Uniaxial compression test is used to measure the uniaxial compressive strength, or
unconfined compressive strength (UCS), of rock samples (ASTM, 2014). Samples
prepared for regular uniaxial compression test are usually 4 inches in length and 2 inches
in diameter. The two ends of each sample were ground down to form a level surface, and
cracks and voids on the surface of samples were filled in with hydrostone. Any pre-existing
joints and fractures were observed and noted. Measurements were taken using digital
calipers. The height and diameter were determined by averaging 6 measurements, two each
at 120 degrees spacing around the core. A layer of black electrical tape was placed around
the top and bottom of the sample to prevent post-testing breakup. Samples were placed in
62
a 150 thousand pounds testing frame, and loaded at a computer controlled rate. Maximum
stress levels, at which point the samples failed, were obtained and recorded by the test
system. Figure 3.5 shows part of the uniaxial compression test samples.
Figure 3.5 Part of the tested uniaxial compression test samples.
3.2.3 Uniaxial compression test with strain gages
In order to estimate the Young’s modulus (E) and Poisson’s ratio (µ), some uniaxial
compression tests were conducted with two strain gages attached on the two sides of the
sample. The samples are prepared in the same way as the samples prepared for regular
uniaxial compression test. To install the strain gages, locations where the strain gages
should be attached on were carefully measured and marked. Then the rock sample surface
at these two locations were slightly sanded with sand paper and treated with a weak acid
cleanser. Strain gages were mounted with glue, and two leads were soldered to each gauge.
Prior to testing, the gage connections were checked to make sure the strain gages installed
on the rock sample work fine. The sample was placed in a 150 thousand pound testing
frame, and loaded at a computer controlled rate. Data were recorded from the strain gauges
and obtained from computer software. Before conducting the uniaxial compression test,
63
the diameter, length, and weight of each sample were measured; therefore the densities of
rock samples were also obtained.
Figure 3.6(a) shows a rock sample with strain gages installed. Figure 3.6(b) shows how the
prepared rock samples finally look like. Figure 3.7 shows a rock sample with strain gages
under uniaxial compression test.
(a) A sample with strain gages installed (b) Some of the prepared samples with
strain gages
Figure 3.6 Preparation of rock samples with strain gages.
Figure 3.7 Uniaxial compression test with strain gages.
64
The results of uniaxial compression tests without strain gages and with strain gages are
listed in Tables 3.3 and 3.4 for DRC and DP rocks, respectively.
Table 3.3 Uniaxial compression test results for DRC rocks
Sample # Young's modulus
(GPa) Poisson's ratio UCS (MPa)
Density
(kg/m3)
DRC1 - - 52.83 2574
DRC2 - - 154.34 2555
DRC3 - - 74.95 2194
DRC4 - - 62.77 2205
DRC5 - - 190.39 2489
DRC6 - - 78.12 2667
DRC7 - - 117.46 2606
DRC8 53.79 0.22 236.14 2649
DRC9 51.57 0.23 210.12 2638
DRC10 40.94 0.28 211.17 2511
DRC11 40.93 0.29 191.9 2511
DRC12 35.76 0.27 95.81 2411
DRC13 44.79 0.23 148.57 2455
DRC14 30.51 0.26 118.45 2426
Maximum 53.79 0.29 236.14 2194
Minimum 30.51 0.22 52.83 2667
AVG. 42.61 0.254 138.79 2492
STD. DEV. 8.26 0.028 61.56 148
C.V. 0.19 0.11 0.44 0.06
65
Table 3.4 Uniaxial compression test results for DP rocks
Sample # Young's modulus
(GPa) Poisson's ratio UCS (MPa)
Density
(kg/m3)
DP1 - - 83.37 2586
DP2 - - 92.45 2395
DP3 - - 58.31 2420
DP4 - - 97.08 2435
DP5 - - 106.40 2432
DP6 - - 60.00 2484
DP7 23.945 0.208 101.83 2392
DP8 44.933 0.203 87.32 2480
DP9 31.557 0.268 88.14 2529
DP10 27.744 0.253 117.65 2446
Maximum 44.933 0.268 117.65 2586
Minimum 23.945 0.203 58.31 2392
AVG. 32.04 0.233 89.26 2460
STD. DEV. 9.13 0.032 18.81 61
C.V. 0.29 0.14 0.21 0.02
3.2.4 Triaxial compression test
Triaxial compression test was used to estimate the strength parameters of intact rocks such
as cohesion and friction angle (ASTM, 2014). The samples were prepared in the same way
as for the uniaxial compression test. Prior to testing, the sample was fitted into a heat-sealed
sleeve and placed into a pressure vessel. Figure 3.8 shows a sample prepared for the triaxial
test. Oil was transferred to the vessel to provide confining pressure. The pressure vessel
assembly was placed in a 150 thousand pound testing frame, and loaded at a predetermined
66
rate. Confining stresses were manually monitored and controlled using a hydraulic system.
While keeping the confining pressure constant, the axial compressive stress was increased
until the rock sample failed. To calculate the strength values correctly, samples for each
triaxial test group were selected from the same rock block or similar blocks because rock
properties from different blocks have a tendency to vary significantly.
Figure 3.8 A sample prepared for the triaxial test.
There are two frequently used failure criteria in the rock mechanics literature: Mohr-
Coulomb and Hoek-Brown criteria. The Mohr-Coulomb criterion has two strength
parameters, cohesion (c) and friction angle (φ), which can be calculated by the following
regression equation using the triaxial compression test results.
𝜎1 = 2 ∙ 𝑐 ∙ 𝑡𝑎𝑛 (45 +𝜑
2) + 𝜎3 ∙ 𝑡𝑎𝑛2 (45 +
𝜑
2) (3.1)
where σ1 is the axial stress; σ3 is the confining stress; c is the cohesion; and φ is the angle
of internal friction.
67
Figure 3.9 shows a typical linear regression equation used to calculate the cohesion and
friction angle for sample group #5 of DRC rocks.
The Hoek-Brown failure criterion for intact rock is given by (Hoek et al., 2002):
𝜎1 = 𝜎3 + 𝑈𝐶𝑆 (𝑚𝑖
𝜎3
𝑈𝐶𝑆+ 1)
0.5
(3.2)
where mi is the Hoek-Brown material constant for intact rock.
The calculated strength parameters for the five groups of samples tested for DRC rocks are
listed in Table 3.5 for both the Mohr-Coulomb and Hoek-Brown criteria.
Figure 3.9 Performed linear regression to calculate the Mohr-Coulomb parameters.
σ1 = 4.3856σ3 + 115.98
R²= 0.9442
0
20
40
60
80
100
120
140
160
0 1 2 3 4 5 6 7
σ1,
MP
a
σ3, MPa
68
Table 3.5 Strength parameters calculated for DRC rocks
Group # σ3, MPa σ1, MPa c, MPa φ, ° mi
1
0 62.77
14.8 39.9
-
3.10 77.9 8.5
5.86 89.5 8.3
2
0 190.39
30.8 53.5
-
3.45 214.4 12.6
10.34 284.2 19.7
3
0 148.57
23.4 52.4
-
3.45 158.8 4.0
5.52 173.7 7.6
10.34 235.7 18.7
4
0 118.45
24.2 46.1
-
3.45 145.9 15.3
5.52 151.3 11.0
5
0 117.46
27.7 38.9
-
3.45 127.5 3.9
5.86 143.8 7.6
AVG. 24.2 46.2 10.7
STD. DEV. 6.0 6.8 5.4
C.V. 0.25 0.15 0.50
The calculated strength parameters for the seven groups of samples tested for DP rocks are
listed in Table 3.6 for both Mohr-Coulomb and Hoek-Brown criteria.
69
Table 3.6 Strength parameters calculated for DP rocks
Group # σ3, MPa σ1, Mpa c, MPa φ, ° mi
1
0 83.37
18.8 40.9
-
3.45 97.5 6.6
10.34 132.5 9.2
2 0 88.14
19.1 43.2 -
10.34 143.3 10.9
3
0 87.32
15.8 47.6
-
3.45 99.1 5.1
5.52 113.3 8.3
10.34 154.7 14.6
4
0 92.45
21.1 39.9
-
5.52 110.6 4.9
10.34 140.2 8.7
5
0 58.31
12.2 45.6
-
3.45 84.7 15.9
5.52 90.4 11.8
6
0 88.14
18 43.7
-
3.45 97.5 3.5
10.34 142.8 10.7
7
0 106.4
20.4 46.6
-
3.45 124.1 8.8
5.52 129.2 6.8
10.34 172.3 13.6
AVG. 17.9 43.9 9.3
STD. DEV. 3.0 2.9 3.7
C.V. 0.17 0.07 0.40
70
3.3 Laboratory Tests for Rock Joints
3.3.1 Uniaxial compression test with a horizontal joint
Uniaxial compression test with a horizontal joint is a specific test designed to estimate the
joint normal stiffness (JKN) (Personal communication with Professor Pinnaduwa
Kulatilake). Two samples with diameter of 2 inches and height of 2 inches were aligned
coaxial and placed under uniaxial compression test. Each sample was loaded until failure.
Figure 3.10 shows a typical sample set up.
Figure 3.10 A typical sample set up for uniaxial compression test with a horizontal joint.
The procedure used to calculate JKN (personal communication with Professor Pinnaduwa
Kulatilake) is given below:
(1) Use the experimental results to draw the total deformation of intact rock and joint in
the normal stress-deformation plot (see Figure 3.11). Draw a straight line (line 2)
from the origin in Figure 3.11 parallel to the straight part of line 1; line 2 represents
71
the corresponding intact rock behavior of the same sample under the applied uniaxial
stress.
(2) To obtain the deformation of joint solely, simply subtract the deformation value of
line 2 from line 1. The result is shown in Figure 3.12.
(3) Plot the joint deformation and normal stress (σn) with joint deformation (Dj) on the
x axis and normal stress on the y axis. The fitted exponential regression curve for the
experimental results is shown in Figure 3.13. The fitted regression equation is:
σn=0.7295e15.571Dj. The calculation process of JKN is shown below:
𝜎𝑛 = 0.7295𝑒15.571𝐷𝑗 (3.3)
𝑙𝑛𝜎𝑛 = 𝑙𝑛0.7295 + 15.571𝐷𝑗 (3.4)
𝐷𝑗 =𝑙𝑛𝜎𝑛 − 𝑙𝑛0.7295
15.571 (3.5)
𝑑𝐷𝑗
𝑑𝜎𝑛=
1
15.571𝜎𝑛 (3.6)
𝐽𝐾𝑁 =𝑑𝜎𝑛
𝑑𝐷𝑗= 15.571𝜎𝑛 (3.7)
(4) Plot the curve of JKN vs. normal stress σn as shown in Figure 3.14.
72
Figure 3.11 Total deformation and intact rock deformation.
Figure 3.12 Joint deformation vs. Normal stress.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 20 40 60 80
To
tal d
efo
rmat
ion
, m
m
Normal stress, MPa
1
1. Intact rock + joint
2. Intact rock
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0 20 40 60 80
Join
t def
orm
atio
n,
mm
Normal stress, MPa
73
Figure 3.13 The fitted exponential regression curve for the experimental joint
deformation data.
Figure 3.14 JKN vs. Normal stress curve.
𝜎𝑛 = 0.7295e15.571Dj
R² = 0.9621
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Norm
al s
tres
sσ
n, M
Pa
Joint deformation Dj, mm
JKN = 15.571∙σn
0
20
40
60
80
100
120
140
160
180
0 2 4 6 8 10
JKN
, M
Pa/
mm
Normal stress σn, MPa
74
Joints of DRC and DP rocks, and interfaces between DRC and DP rocks were tested and
the results obtained for joint normal stiffness are listed below in Table 3.7. The detailed
results are given in Appendix A.
Table 3.7 Obtained joint normal stiffness results for DRC and DP rock joints and
interfaces
Sample # JKN, MP/mm
DRC-J1 10.272
DRC-J2 11.316
DRC-J3 9.1895
DRC-J4 9.311
AVG. 10.02×σn (MPa)
DP-J1 15.571
DP-J2 11.221
DP-J3 14.278
DP-J4 16.28
DP-J5 14.789
DP-J6 17.117
AVG. 14.876×σn (MPa)
DRC-DP-J1 9.4604
DRC-DP-J2 15.144
DRC-DP-J3 10.339
DRC-DP-J4 11.305
AVG. 11.5621×σn (MPa)
75
3.3.2 Joint direct shear test
Joint direct shear test can be used to measure the joint cohesion, joint friction angle and
joint shear stiffness (JKS) (ASTM, 2008c). Two types of samples were tested: (1) natural
rock joints and (2) saw cut joints. For saw cut joints, first the cylindrical sample was cut
perpendicular to the cylindrical surface to produce approximately two equal halves of
cylindrical samples. For both types of tests, each half of the cylindrical rock joint sample
was securely mounted in hydrostone with the joint surface appearing on the top side, as
shown in Figure 3.15. Both parts were placed in the direct shear testing machine (see Figure
3.16) so that one piece would slide over the joint surface of the other. A calculated weight
was added to provide the normal stress on the sample. The bottom sample was moved at a
computer controlled rate, and the shear stress on the sample was measured. This process
was repeated three more times for each group of samples with increasing normal stress
applied with each repetition.
Joint direct shear test results related to the joint cohesion and joint friction angle for DRC
and DP rock joints, and the interfaces between DRC and DP rocks are listed in Tables 3.8,
3.9 and 3.10, respectively.
76
Figure 3.15 Some of the prepared samples for joint direct shear test.
Figure 3.16 Joint direct shear test equipment.
77
Table 3.8 Obtained joint friction angle and joint cohesion for DRC rocks
Sample number Natural/Saw cut Friction angle, ° Cohesion, kPa
1 N 28.5 3.3259
2 N 31.3 6.8306
3 N 30.5 7.9266
4 N 32.2 1.1422
5 N 32.2 2.9735
6 N 33.6 2.727
7 S 28.5 -
8 S 22.0 -
9 S 28.4 -
10 S 23.2 -
11 S 33.2 -
12 S 24.0 -
13 S 21.8 -
14 S 22.7 -
15 S 25.4 -
16 S 27.1 -
17 S 25.5 -
Maximum 33.6 7.9266
Minimum 22 1.1422
AVG. 26.4 4.45
STD. DEV. 4.4 2.30
C.V. 0.17 0.52
78
Table 3.9 Obtained joint friction angle and joint cohesion for DP rocks
Sample number Natural/Saw cut Friction angle, ° Cohesion, kPa
1 S 31.6 -
2 S 22.9 -
3 S 22.6 -
4 S 20.3 -
5 S 31.5 -
6 S 25.6 -
7 S 23.9 -
8 S 21.5 -
9 S 35.9 -
10 S 33.1 -
11 S 33.9 -
12 S 29.2 -
13 S 38.8 -
Maximum 38.8 -
Minimum 20.3 -
AVG. 28.5 -
STD. DEV. 6.1 -
C.V 0.21 -
79
Table 3.10 Obtained joint friction angle and joint cohesion for interfaces between DP and
DRC rocks
Sample number Natural/Saw cut Friction angle, ° Cohesion
1 S 28.4 -
2 S 19.7 -
3 S 20.2 -
4 S 33.3 -
5 S 30.8 -
AVG. 26.5 -
STD.DEV. 5.6 -
C.V. 0.21 -
The procedure used to calculate JKS is given below using group #1 of DRC rock joints
given in Table 3.11 as an example:
(1) JKS was estimated from the slope of shear stress vs. shear displacement curve
obtained for each normal stress from the experimental results.
(2) A linear regression line was fitted for JKS versus normal stress data as shown in
Figure 3.17.
(3) The obtained linear regression equation was JKS =0.77σn as the estimated relation
between joint shear stiffness and normal stress.
The obtained calculation results of JKS are listed in Tables 3.11, 3.12 and 3.13 for DRC
rock joints, DP rock joints, and the interfaces between DRC and DP rock joints,
respectively. The detailed results are given in Appendix B.
80
Figure 3.17 Fitted linear regression line for JKS vs. normal stress data.
JKS = 0.77σn
R²= 0.9764
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
81
Table 3.11 Obtained joint shear stiffness values for DRC rock joints
Sample # JKS, MPa/mm σn, MPa Linear regression equation
1
1.02 1.37801 JKS = 0.77σn
R² = 0.9764
0.66 0.82807
0.40 0.41404
0.18 0.20544
2
1.87 1.37593 JKS = 1.2641 σn
R² = 0.9467
0.99 0.82852
0.28 0.41426
0.11 0.20713
3
0.89 1.37802 JKS = 0.6624 σn
R² = 0.9395
0.54 0.82775
0.40 0.41388
0.07 0.20694
4
2.13 1.37984 JKS = 1.7072 σn
R² = 0.9037
1.77 0.83040
0.69 0.41208
0.47 0.20604
5
1.87 1.38074 JKS = 1.2972 σn
R² = 0.9858
0.98 0.82844
0.50 0.41140
0.19 0.20852
6
1.40 1.38102 JKS = 0.9246 σn
R² = 0.9343
0.68 0.82625
0.18 0.41312
0.11 0.20853
7
1.28 1.37957 JKS = 0.9276 σn
R² = 0.9602
0.86 0.82912
0.25 0.41284
0.09 0.20642
82
Table 3.11 Obtained joint shear stiffness values for DRC rock joints-Continued
Sample # JKS, MPa/mm σn, MPa Linear regression equation
8
1.52 1.37918 JKS = 0.9346 σn
R² = 0.8644
0.48 0.82751
0.27 0.41375
0.06 0.20688
9
1.31 1.38076 JKS = 0.9573 σn
R² = 0.977
0.86 0.82648
0.36 0.41571
0.08 0.20786
10
1.88 1.37796 JKS = 1.3372 σn
R² = 0.942
1.22 0.82678
0.25 0.41339
0.18 0.20925
11
2.16 1.38168 JKS = 1.5957 σn
R² = 0.9719
1.46 0.82808
0.64 0.41404
0.11 0.20469
12
1.08 1.38092 JKS = 0.705 σn
R² = 0.9294
0.45 0.82936
0.20 0.41468
0.16 0.20533
13
1.01 0.82757 JKS = 1.1497 σn
R² = 0.9473 0.42 0.41379
0.11 0.20390
14
0.73 0.82613 JKS = 0.9424 σn
R² = 0.9212 0.47 0.41450
0.23 0.20725
AVG. JKS = 1.0839 σn
83
Table 3.12 Obtained joint shear stiffness values for DP rock joints
Sample # JKS, MPa/mm σn, MPa Linear regression equation
1
1.38 1.38049 JKS = 1.1472 σn
R² = 0.8473
1.28 0.82829
0.53 0.41181
0.16 0.20590
2
1.79 1.38143 JKS = 1.2732 σn
R² = 0.9926
1.05 0.82886
0.43 0.41443
0.27 0.20483
3
1.27 1.71980 JKS = 0.7869 σn
R² = 0.7988 0.74 0.85990
0.54 0.41275
4
1.34 1.37833 JKS = 0.9736 σn
R² = 0.8441
0.67 0.82700
0.60 0.41350
0.36 0.20675
5
1.35 1.38041 JKS = 1.0541 σn
R² = 0.9365
1.08 0.82825
0.41 0.41152
0.14 0.20836
6
0.88 1.38147 JKS = 0.653 σn
R² = 0.977
0.54 0.82948
0.35 0.41323
0.13 0.20812
7
1.07 1.37952 JKS = 0.8823 σn
R² = 0.7853
0.86 0.82992
0.57 0.41262
0.24 0.20631
84
Table 3.12 Obtained joint shear stiffness values for DP rock joints-Continued
Sample # JKS, MPa/mm σn, MPa Linear regression equation
8
2.15 1.38014 JKS = 1.5963 σn
R² = 0.979
1.47 0.82624
0.61 0.41543
0.19 0.20771
9
1.70 1.37898 JKS = 1.3752 σn
R² = 0.8959
1.44 0.82646
0.59 0.41323
0.34 0.20894
10
1.08 1.37878 JKS = 0.8247 σn
R² = 0.9556
0.80 0.82657
0.51 0.62256
0.09 0.20752
11
1.68 1.37817 JKS = 1.3071 σn
R² = 0.9389
1.21 0.82623
0.73 0.41311
0.18 0.20656
12
0.73 1.38028 JKS = 0.5171 σn
R² = 0.9918
0.40 0.84163
0.23 0.41317
0.11 0.20811
13
1.07 1.37937 JKS = 0.8476 σn
R² = 0.8975
0.92 0.82581
0.27 0.41290
0.12 0.20872
AVG. JKS = 1.018 σn
85
Table 3.13 Obtained joint shear stiffness values for interfaces between DRC and DP
rocks
Sample # JKS, MPa/mm σn, MPa Linear regression equation
1
1.54 1.37871 JKS = 0.88825 σn
R² = 0.9908
0.99 0.82998
0.40 0.41499
0.19 0.20480
2
0.99 1.38025 JKS = 1.3215 σn
R² = 0.9148
0.74 0.82815
0.18 0.41237
0.08 0.20789
3
1.01 0.82757 JKS = 0.85394 σn
R² = 0.9188 0.42 0.41379
0.11 0.20390
4
1.54 1.37971 JKS = 0.88825 σn
R² = 0.9908
0.99 0.82998
0.40 0.41499
0.19 0.20480
5
1.10 1.37822 JKS = 1.211 σn
R² = 0.9884
0.72 0.82693
0.39 0.41176
0.14 0.20758
AVG. JKS = 0.9914 σn
3.4 Summary
Rock formations in the research area were divided into two rock types: DRC and DP rocks
with each rock group having similar properties. Laboratory tests for intact rock and rock
joints were conducted for both DRC and DP rocks. Laboratory tests for intact rock include
86
Brazilian tension test, uniaxial compression test, uniaxial compression test with strain
gages, and triaxial test. Laboratory tests for rock joints include uniaxial compression test
with a horizontal joint and joint direct shear test. From the data, it can be seen that the
strength of DRC rocks is higher than that of DP rocks according to the tensile strength,
UCS, cohesion and friction angle values. The estimated values also show that the DP rocks
are softer than DRC rocks according to the elastic modulus values. It was also found that
the joint normal stiffness and joint shear stiffness increase with normal stress applied on
the joint according to linear relations.
87
CHAPTER 4 FRACTURE MAPPING AND ROCK MASS PROPERTIES
4.1 Introduction
The purpose of fracture mapping is to obtain the number of fracture sets and their locations,
orientations, and sizes. In the literature review, five mostly used fracture mapping methods
were introduced. It shows that the remote fracture mapping with laser scanner and
photographs is the best choice in such a large open pit mine site. Fracture mapping is a
method for geologist to measure the geometry information of rock fractures (joints, or
discontinuities).
There are several advantages of using laser scanner to do remote fracture mapping
compared to using traditional manual fracture mapping methods:
(1) Safety: Manual mapping requires people getting close to the rock face and it is quite
dangerous because minor rock falls happen all the time in open pit mines. For safety,
mining company usually requires people to stay away from the toe of bench walls.
(2) High efficiency: Manual mapping requires measuring joint orientation, joint size,
spacing and so on one by one, while remote mapping using a laser scanner along
with photographs can get the whole picture of a large area of a rock mass surface
in one step. Therefore it is much faster.
(3) High accuracy: Manual mapping depends on the geologist’s operation and the
reliability of tools, which may cause large human bias. To be contrary, a laser
scanner can provide very accurate 3-diamensional coordinates of each scanning
point on the rock surface and leads to a more accurate mapping results.
88
(4) Low cost. Even though the price of a laser scanner is more expensive than a
geological compass and a measuring tape, the labor cost spend on a large volume
of fracture mapping manually for a long duration can be more than using a laser
scanner. Therefore, long term wise, the average cost for laser scanner mapping can
be lower than manual mapping.
(5) Easy Access. Laser scanner can scan rock faces that are very difficult to reach by
human beings; that means it can obtain more comprehensive data and thus reduce
the human bias.
A special equipment Professor Kulatilake owns, which can be used as a total station, laser
scanner and a camera was used in an open pit mine in US to conduct remote fracture
mapping. The survey results were used to process fracture orientation, size, and density.
GSI rock mass classification system and Hoek-Brown rock mass failure criterion were used
to estimate the rock mass strength and deformation properties.
4.2 The Used Remote Fracture Mapping Procedure to Collect Fracture Data
Before performing laser scanning, the instrument needed to be set in front of the bench
wall about 3-5 meters away from the bench toe. To measure the coordinates of scanning
points correctly, it was necessary to fix the location of the laser scanner of the instrument
and the north direction. These were accomplished using the steps given below:
(1) First, a point on the ground was selected to set up the instrument. This point was
marked with red paint as shown in Figure 4.1.
(2) Then, the coordinates of that point on the ground was measured by a handheld GPS
survey instrument. If it is not necessary to express the scanning results according
89
to a global coordinate system, then it is not necessary to measure the coordinates of
the point using a GPS instrument. In such a case a simple coordinate (0, 0, 0) can
be used to represent the marked point on the ground.
(3) The north direction was first approximated using a geological compass (Figure
4.1(a)). It was then accurately calibrated with a GPS survey instrument. The north
direction was marked on the ground. If a GPS survey instrument is not available,
then the accuracy of a geological compass may be acceptable to set up the north
direction.
(4) The center of the laser scanner was aligned with the point marked on the ground
(Figure 4.2(b)) and the height of the laser scanner to the point on the ground was
measured. These measurements allowed calculation of the coordinates of the center
of the laser scanner.
(a) (b)
Figure 4.1 Set up of the laser scanner of the instrument and the north direction.
A rock surface was selected right in front of the instrument and four corner points were
selected as shown by the four yellow points depicted in Figure 4.2 and measured by the
90
total station part of the instrument. Then the laser scanning was conducted to cover only
the area within the red rectangle which is determined by the four corner points. After the
scanning was finished, photos were taken using the built-in-camera of the instrument to
cover the scanned area and the surrounding. The photos and the scanning points were
matched. The said procedure was conducted at different carefully selected locations of the
open pit mine in order to collect the fracture information for both DRC and DP rocks.
Figures 4.3 and 4.4 show two of the obtained maps.
Figure 4.2 Laser scanner set up in front of a bench face.
91
Figure 4.3 A remote fracture mapping picture of DRC rocks.
Figure 4.4 A remote fracture mapping picture of DP rocks.
92
4.3 Laser Scanning Data Extraction Method
Figure 4.5 shows a typical fracture map obtained from remote fracture mapping. The white
scanning points are called point cloud. For each point, x-y-z coordinate values are available.
Those points are used to calculate the fracture orientations (include dip angle and dip
direction), fracture sizes and intensities.
Figure 4.5 A typical image constructed from remote fracture mapping.
4.3.1 Fracture orientation
Three fracture sets are determined for DRC rocks, as well as for DP rocks, as shown in
Figures 4.6 and 4.7, respectively. These three fracture sets can be divided into two sub-
vertical joint sets (joint sets 1 and 2) and one sub-horizontal bedding set (discontinuity set
3). It is necessary to be quite careful when selecting fracture surfaces because the rock mass
has been disturbed by blasting or excavation. As an example, Figure 4.8 shows the rocks
under different status. It is not correct to include disturbed rocks or debris in the estimation
of fracture orientation, size or intensity.
93
Figure 4.6 Three fracture sets of DRC rocks.
Figure 4.7 Three fracture sets of DP rocks.
94
Figure 4.8 Rocks under different status.
Algorithms were developed based on a procedure suggested by Professor Kulatilake
(personal communications) to compute the fracture orientations for fractures belonging to
each set using the aforementioned x-y-z coordinates. The following provides the procedure
of using three scanning points on one fracture to calculate the fracture dip angle and dip
direction. Figure 4.9 shows an example of using three scanning points on a fracture surface.
95
Figure 4.9 Three scanned points on a fracture surface.
It is well known that equation of a plane can be written as: ax+by+cz=d, where a, b, c, and
d are constants. If three points on a fracture plane have coordinates of (x1, y1, z1), (x2, y2,
z2), and (x3, y3, z3), the following can be obtained.
a(𝑥 − x1) + b(𝑦 − y1) + c(𝑧 − z1) = 0 (4.1)
a(𝑥 − x2) + b(𝑦 − y2) + c(𝑧 − z2) = 0 (4.2)
a(𝑥 − x3) + b(𝑦 − y3) + c(𝑧 − z3) = 0 (4.3)
Equations (1), (2) and (3) can be solved to calculate the parameters a, b and c.
The parameter d can be calculated by rearranging equation (4.1) as equation (4.4) given
below and substituting the parameter values of a, b and c to equation (4.4).
d = a𝑥 + b𝑦 + c𝑧 = ax1 + 𝑏y1 + 𝑐𝑧1 (4.4)
Whenever there are more than three scanning points on the fracture plane, the equation of
the average plane can be easily calculated through multiple linear regression analysis.
The parameters a, b and c of the equation of plane can be normalized by dividing each of
them by √𝑎2 + 𝑏2 + 𝑐2 separately:
96
A =𝑎
√𝑎2 + 𝑏2 + 𝑐2 (4.5)
B =𝑏
√𝑎2 + 𝑏2 + 𝑐2 (4.6)
C =𝑐
√𝑎2 + 𝑏2 + 𝑐2 (4.7)
The relation between the equation of the plane and the unit normal vector shown in Figure
4.10 can be given as follows:
𝐴 = sin𝛼 ∙ sin𝛽 (4.8)
𝐵 = sin𝛼 ∙ cos𝛽 (4.9)
𝐶 = cos𝛼 (4.10)
where α is the dip angle, and β is the dip direction of the plane.
Figure 4.10 Calculation of the directional cosines of the unit normal vector to the
discontinuity.
The dip angle and dip direction can be calculated by solving equations (4.8) through (4.10).
97
4.3.2 Fracture size
Three fracture size distributions exist in each of DRC and DP rocks. The areas of fracture
planes from set 1 and set 2 (sub-vertical fractures) were calculated using the measured
scanning points because the fracture planes show up very well on the bench face cut.
However, it was difficult to obtain complete fracture faces from remote fracture mapping
for fracture set 3 (sub-horizontal fractures) because the dip angle of those fractures were
low. Therefore, for fractures of set 3 the trace lengths were calculated based on the
measured scanning points.
For fracture sets 1 and 2, it is necessary to assume that all the fracture surfaces are flat
planes, even though in reality fracture surfaces are more or less rough planes. In the
scanned pictures, for example in Figure 4.11, the red polygon is the total area (A2) of the
fracture plane. However, there are no scanning points located at the edges and corners of
the red polygon. Therefore it is not possible to calculate the area of the fracture plane by
the coordinates of the scanning points directly.
Figure 4.11 Diagram used to explain calculation of fracture area.
98
However, it may be possible to calculate the total fracture area, A2, by the following
procedure:
(1) Use the Realworks software to draw a triangle using three scanning points as shown
in Figure 4.11. The area of the triangle “A1” can be calculated using the coordinates
of these three points P1, P2 and P3 by the following equations. The area is half of the
cross product of the two vectors P1P⃗⃗⃗⃗⃗⃗ 2 and P1P⃗⃗⃗⃗⃗⃗
3 shown in Figure 4.12.
Figure 4.12 The vectors used to calculate the area of the triangle.
𝐴1 =1
2∙ |P1P⃗⃗⃗⃗⃗⃗
2 × P1P⃗⃗⃗⃗⃗⃗ 3| (4.11)
(2) As shown in Figure 4.13, A3 and A4 are the projections of A1 and A2. The area of A3
and A4 can be obtained using AutoCAD. Then the fracture area A2 can be calculated
by the following equation:
𝐴2 = 𝐴1 ∙𝐴4
𝐴3 (4.12)
99
Figure 4.13 The triangles associated with the calculation of the total fracture area A2
using AutoCAD.
The real fractures are irregular shaped. However, in fracture network modeling in 3-D
fractures may be represented by equivalent circular disks in 3-D space. Since the area of
fracture (A2) has been calculated, the equivalent diameter of the fracture can be calculated
as follows:
𝐷𝑒 = √4 ∙ 𝐴2
𝜋 (4.13)
For the sub-horizontal bedding set 3, it is impossible to calculate the area of the fracture
surface directly from scanned measurements because of the low dip angle. First, it is
assumed that all the set 3 fractures are approximate squares. Then the trace length is used
to represent the edge length of the fracture plane. The trace length can be calculated by the
coordinates of two scanning points. In case that there are no scanning points close to the
trace, the following method is used to estimate the trace length.
A1
A2
A3
A4
100
(1) Select two scanning points on the fracture plane and get their coordinates. Draw a
straight line using these two points (L1), and another straight line along the trace as
shown in Figure 4.14.
(2) Use the same method as the one used to calculate the fracture area in Figure 4.13
with the help of AutoCAD software and calculate the trace length L2.
The trace length is assumed to be the edge length of a square fracture plane. Keeping the
area the same, convert the square to an equivalent circle as shown in Figure 4.15. The
following equation can be used to calculate the diameter of the circle.
𝐷𝑒 = √4 ∙ 𝐿2
𝜋 (4.14)
Figure 4.14 Lines used to calculate the trace length.
101
Figure 4.15 Converting the square fracture to an equivalent circular fracture.
4.3.3 Fracture intensity in one-dimension (1-D) and three-dimensions (3-D)
To calculate the linear intensity of fractures, horizontal scan lines and vertical scan lines
were used for joint sets 1 and 2, and joint set 3, respectively. Figure 4.16 shows the drawn
scan lines. The following procedure (Kulatilake et al., 1993, 1996 and 2003) was used in
calculating 1-D fracture intensities.
(1) Count the number (N) of fractures crossing each survey line of length Ls for each set
and calculate 𝐿𝑠
N . Calculate the mean of
L𝑠
N , (
𝐿𝑠
𝑁)
mean, for each fracture set.
(2) Calculate cosθ (see Figure 4.17) using the following equation:
𝑐𝑜𝑠𝜃 =𝑚 × 𝑛
|𝑚| ∙ |𝑛| (4.15)
In the above equation, m is the mean normal vector of the fracture set, n is the
vector of the survey line and θ is the angle between the vectors m and n.
(3) Calculate true mean fracture spacing ds using the following equation:
𝑑𝑠 = (𝐿𝑠
𝑁)𝑚𝑒𝑎𝑛
∙ 𝑐𝑜𝑠𝜃 (4.16)
(4) Calculate the one-dimensional intensity of fractures, λ1, for each fracture set using
the following equation:
102
𝜆1 =1
𝑑𝑠 (4.17)
Figure 4.16 Horizontal and vertical survey lines used to calculate fracture intensities.
Figure 4.17 The diagram connected with calculation of 1-D intensity of fractures.
The 3-dimensional intensity of fractures for each set was calculated by using the following
equation (Kulatilake et al., 1993, 1996 and 2003):
λ𝑣 =4 ∙ λ1
𝜋 ∙ 𝐸(𝐷𝑒2) ∙ 𝐸(𝑙 ∙ 𝑚)
(4.18)
103
where, λ𝑣 is the volumetric fracture frequency (3-D intensity) of the fracture set; λ1 is the
linear frequency of the fracture set along the mean normal vector direction; E(De2) is the
expected value of the fracture diameter; E(l•m)is the expected value of 𝑙 ∙ 𝑚; l is the unit
normal vector of a fracture in the fracture set; and m is the unit mean normal vector of
fracture. The procedure to calculate the joint size was discussed in the previous section.
Thus, E(De2) can be calculated. Three dimensional intensities for each joint set for DRC
and DP rocks were calculated separately using the aforementioned procedure.
4.4 Results Obtained from Mapped Fractures
4.4.1 Joint orientation
The joint orientations were collected and calculated using the method given in Section
4.3.1 above and the obtained results are listed in Table 4.1. The mining company also
provided the manually mapped data for the studied research area collected during the past
many years. The orientation data of each joint set were plotted using DIPS software and
the obtained results are shown in Figures 4.18 and 4.19. The comparisons made between
the results obtained through manual mapping and laser scanner mapping are shown in
Table 4.1 and Figures 4.18 and 4.19. Note that as mentioned earlier, for bedding planes
(DRC-set 3 and DP-set 3) it was difficult to obtain a sufficient number of data through
remote mapping due to low dip angles. So, the values estimated for DRC-set 3 and DP-set
3 based on remote mapping data do not have good reliability. The table shows that the
agreement is very good between the two types of results for joint sets 1 and 2. For joint
sets 1 and 2, the data available from each mapping technique is very high. Therefore the
104
reliability of the results should be high from both methods if the human error part is low
with respect to the manual mapping. To estimate rock mass properties, the results from
remote mapping are used for joint sets 1 and 2. However, for joint set 3 of each rock type,
the data available from the remote mapping is low. Thus, the reliability of the results from
remote mapping is low. Therefore, for joint set 3 of each rock type the results from the
manual mapping should be used.
Table 4.1 Joint orientation results
Joint set
number Mapping type
Number of
data
Mean dip
angle
Mean dip
direction
DRC-set 1 Remote 367 70 149
Manual 209 76 154
DRC-set 2 Remote 137 60 221
Manual 157 67 244
DRC-set 3 Remote 33 16 5
Manual 371 16 39
DP-set 1 Remote 87 65 182
Manual 106 68 165
DP-set 2 Remote 186 60 257
Manual 213 68 253
DP-set 3 Remote 7 35 69
Manual 208 15 25
105
(a) DRC-set1 from laser scanning (b) DRC-set 1 from manual mapping
(c) DRC-set 2 from laser scanning (d) DRC-set 2 from manual mapping
(e) DRC-set 3 from laser scanning (f) DRC-set 3 from manual mapping
Figure 4.18 Orientation distributions of fracture sets for DRC rocks.
106
(a) DP-set 1 from laser scanning (b) DP-set 1 from manual mapping
(c) DP-set 2 from laser scanning (d) DP-set 2 from manual mapping
(e) DP-set 3 from laser scanning (f) DP-set 3 from manual mapping
Figure 4.19 Orientation distributions of fracture sets for DP rocks.
107
4.4.2 Joint size
Joint sizes for each joint set were calculated according to the method explained in section
4.3.2, and the results obtained are listed in Table 4.2. It is clear from the results that the
joint sizes of sets 1 and 2 are much smaller than that of set 3. Intuitively this was expected
because the fracture set 3 for each rock type is a bedding plane.
Table 4.2 Joint size results
Joint set number # of data AVG. joint size, m STD.DEV., m
DRC set 1 64 0.1352 0.0756
DRC set 2 50 0.1049 0.0551
DRC set 3 118 1.939 0.982
DP set 1 50 0.116 0.035
DP set 2 56 0.1429 0.0473
DP set 3 51 2.7886 1.3180
4.4.3 Joint intensity
The procedures given in Section 4.3.3 were used to calculate the 1-D fracture intensities
and and 3-D fracture intensities. The obtained results are given in Table 4.3.
108
Table 4.3 Joint intensity results
Joint Set Number # of survey lines 1-D intensity, λl,
m-1
3-D intensity, λV,
m-3
DRC set 1 20 4.6 68.8
DRC set 2 20 4.7 106.8
DRC set 3 41 4.2 1.2
DP set 1 14 3.4 99.6
DP set 2 14 3.5 73.8
DP set 3 18 3.2 0.5
4.5 Rock Mass Properties
The strength and deformation properties of rock masses may be estimated by Hoek-Brown
criterion using GSI rock mass classification system.
4.5.1 GSI rock mass classification system
Geological Strength Index (GSI) system was introduced by Hoek and his coworkers (Hoek,
1994; Hoek et al., 1995) to characterize blocky rock masses on the basis of interlocking
and joint conditions, using a range between 0 and 100. The GSI value together with intact
rock properties have been widely used to estimate rock mass strength and deformation
properties. The original GSI chart used to classify rock mass quality is shown in Figure
4.20. It shows that the original GSI chart uses qualitative description to identify conditions
of the structure and rock surface, which relies more on the engineering experience and
professional judgment.
109
Figure 4.20 Original GSI chart (Hoek, 2007)
Cai et al. (2004) proposed a more quantitative method to estimate GSI value (see Figure
4.21). It uses the block volume (Vb) and a joint condition factor (Jc) to replace the structure
and surface condition in the original GSI system.
110
Figure 4.21 Quantification of GSI chart (Cai et al., 2004)
Joint Condition Factor Jc
N/A N/A
12 4.5 1.7 0.67 0.25 0.1
0.1
10
100
1000(1 dm3)
10E+3
100E+3
10E+6
150
100 cm
908070
50
40
30 cm
10 cm
5
3
2
1 cm 1
1E+6
(1 m3)
Joint or Block Wall Condition
GSI
Block Size
60
20
Blo
ck V
olu
me,
Vb
(cm
3 )
Massive - very well interlocked
undisturbed rock mass blocks formed with
very wide joint spacingjoint spacing >100 cm
Blocky - very well interlocked
undisturbed rock mass consisting of
cubical blocks formed by three
orthogonal discontinuity setsJoint spacing 30 - 100 cm
Very Blocky - interlocked, partially
disturbed rock mass with multifaceted
angular blocks formed by four or more
discontinuity setsJoint spacing 10 - 30 cm
Blocky/disturbed - folded and/or faulted
with angular blocks formed by many
intersecting discontinuity setsJoint spacing 3 -10 cm
Disintegrated - poorly interlocked,
heavily broken rock mass with a
mixture or angular and rounded rock
piecesJoint spacing < 3 cm
Foliated/laminated/sheared - thinly
laminated or foliated, tectonically sheared
weak rock; closely spaced schistosity
prevails over any other discontinuity set,
resulting in complete lack of blockinessJoint spacing < 1cm
Ver
y g
ood
Ver
y r
oug
h,
fres
h u
nw
eath
ered
surf
aces
Good
Rou
gh
, sl
ightl
y w
eath
ered
,
iro
n s
tain
ed s
urf
aces
Fai
r
Sm
ooth
, m
od
erat
ely w
eath
ered
or
alte
red
surf
aces
Poor
Sli
cken
sided
, hig
hly
wea
ther
ed s
urf
aces
wit
h
com
pac
t co
atin
g o
r fi
llin
gs
of
angula
r fr
agm
ents
Ver
y p
oor
Sli
cken
sided
, hig
hly
wea
ther
ed s
urf
aces
wit
h
soft
cla
y c
oat
ing
s or
fill
ings
95
90 85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
111
The block size depends on the joint spacing, joint orientation and number of joint sets. For
example, if there are three joint sets in the rock mass, the block volume can be calculated
as follows:
𝑉𝑏 =𝑠1 ∙ 𝑠2 ∙ 𝑠3
𝑠𝑖𝑛𝛾12 ∙ 𝑠𝑖𝑛𝛾23 ∙ 𝑠𝑖𝑛𝛾31 (4.19)
where s1, s2 and s3 are the mean joint spacing of the three joint sets; γ12, γ23, and γ31 are the
intersection angles between each of the two joint set combinations.
The mean joint spacing and the intersection angle between each of the two joint set
combinations can be calculated from the remote fracture mapping results. The mean joint
spacing is the inverse of the one dimensional joint intensity. The mean dip angles/dip
directions of joint sets 1, 2 and 3 for DRC rocks are 70/149, 60/221, and 16/39, respectively.
For DP rocks, the same are 65/182, 60/257, and 15/25, respectively. The calculations of
the block volumes are given below.
𝑉𝑏1 =1
4.6∙
1
4.7∙
1
4.2∙
1
0.91 ∙ 0.97 ∙ 0.97= 12.86 × 10−3 𝑚3 (4.20)
𝑉𝑏2 =1
3.4∙
1
3.5∙
1
3.2∙
1
0.91 ∙ 0.94 ∙ 0.98= 31.33 × 10−3 𝑚3 (4.21)
The results of the block volumes are listed in Table 4.4.
Table 4.4 Calculated block size values
Rock
type
S1
(m)
S2
(m)
S3
(m) γ12 γ 23 γ 31 sinγ12 sinγ23 sinγ31 Vb, m
3
DRC 1/4.6 1/4.7 1/4.2 65 76 76 0.91 0.97 0.97 12.86×10-3
DP 1/3.4 1/3.5 1/3.2 66 70 79 0.91 0.94 0.98 31.33×10-3
112
The joint surface condition is estimated by considering joint roughness, joint weathering
and infilling condition. These parameters are similar to that used in RMi system
(Palmstrom, 1995).
The factors included in the joint condition factor are combined in the following way:
𝐽𝑐 =𝐽𝑤 ∙ 𝐽𝑠
𝐽𝐴 (4.22)
where Jw is the large scale waviness (1-10 m); Js is the small scale smoothness (1-20 cm);
and JA is the joint alteration factor. The guidelines to estimate Jw, Js and JA are given in
Tables 4.5, 4.6 and 4.7, respectively.
Table 4.5 Terms to describe large-scale waviness (Palmstrom, 1995)
Waviness Undulation Rating for waviness Jw
Interlocking (large scale) - 3
Stepped - 2.5
Large undulation >3% 2
Small to moderate undulation 0.3%-3% 1.5
Planar <0.3% 1
Undulation= 𝐷𝑚
𝑙𝑝, Dm-maximum amplitude, lp-length of profile
Dm
lp
113
Table 4.6 Terms to describle small-scale smoothness (Palmstrom, 1995)
Smoothness term Description Ratings for
Smoothness, Js
Very rough Near vertical steps and ridges occur with
interlocking effect on the joint surface. 3
Rough
Some ridge and side-angle steps are evident;
asperities are clearly visible; discontinuity
surface feels very abrasive (rougher than
sandpaper grade 30).
2
Slightly rough
Asperities on the discontinuity surfaces are
distinguishable and can be felt (like
sandpaper grade 30 - 300).
1.5
Smooth Surface appears smooth and feels so to the
touch (smoother than sandpaper grade 300). 1
Polished
Visual evidence of polishing exists. This is
often seen in coatings of chlorite and
specially talc
0.75
Slicken sided
Polished and striated surface that results
from friction along a fault surface or other
movement surface.
0.6-1.5*
*Rating depends on the actual shear in relation to the striations.
114
Table 4.7 Rating for the joint alteration factor JA (Cai et al., 2004)
Term Description JA
Rock wall
contact
Clear joints
Healed or “welded”
joints (unweathered)
Softening, impermeable filling
(quartz, epidote, etc.) 0.75
Fresh rock walls
(unweathered)
No coating and fillings on joint
surface, except for staining. 1
Alteration of joint wall:
slightly to moderately
weathered
The joint surface exhibits one
class high alteration than the
rock
2
Alteration of joint wall:
highly weathered
The joint surface exhibits two
classes high alteration than the
rock
4
Coating or thin filling
Sand, silt, calcite, etc. Coating of friction materials
without clay 3
Clay, chlorite, talc, etc. Coating of softening and
cohesive minerals 4
Filled joints
with partial
or no contact
between the
rock wall
surface
Sand, silt, calcite, etc. Filling of friction materials
without clay 4
Compacted clay
materials
"Hard" filling of softening and
cohesive materials 6
Soft clay materials Medium to low over-
consolidation of filling 8
Swelling clay materials Filling material exhibits clear
swelling properties 8-12
115
The selected Jw, Js, and JA values based on the field investigation for both DRC and DP
rocks and the calculated Jc values are listed in Table 4.8. The estimated Vb and Jc values
were then used to estimate the GSI values using the modified GSI chart given in Figure
4.21. The estimated GSI values are also listed in Table 4.8. The values given in Table 4.8
show that the DRC rocks have better rock mass quality than DP rocks. This was expected
intuitively too through field observations.
Table 4.8 Estimated GSI values for rock masses
Rock type Jw Js JA Jc GSI
DRC 2.5 2 3 1.67 50
DP 1.5 1.5 4 0.56 37
4.5.2 Rock mass strength properties
The Hoek-Brown failure criterion for intact rock was introduced in Chapter 3, and the
strength constant mi was estimated as 10.7 and 9.3 for DRC and DP rocks, respectively.
The generalized Hoek-Brown failure criterion for jointed rock masses is given by (Hoek et
al., 2002):
𝜎1′ = 𝜎3
′ + 𝑈𝐶𝑆 (𝑚𝑏
𝜎3′
𝑈𝐶𝑆+ 𝑠)
𝑎
(4.23)
where σ1΄ and σ3΄ are the maximum and minimum effective principal stresses at failure; mb
is the value of the Hoek-Brown constant for the rock mass; s and a are constants which
depend upon the rock mass characteristics; and UCS is the uniaxial compressive strength
of intact rock.
116
The equations used to calculate mb, s and a are as follows (Hoek et al., 2002):
𝑚𝑏 = 𝑚𝑖 ∙ 𝑒𝐺𝑆𝐼−10028−14𝐷 (4.24)
𝑠 = 𝑒𝐺𝑆𝐼−100
9−3𝐷 (4.25)
𝑎 =1
2+
1
6(𝑒−
𝐺𝑆𝐼15 − 𝑒−
203 ) (4.26)
where D is a factor that depends on the degree of disturbance due to blast damage and stress
relaxation. It varies from 0 for undisturbed in situ rock masses to 1 for very disturbed rock
masses. For example, for excellent controlled blasting, D is zero; but for very large open
pit mine slopes that suffer significant disturbance due to heavy production blasting and also
due to stress relief from removal of overburden, the D is one. However, D only applies to
the blast damaged zone and not for those undisturbed rock masses. The blast damage zone
is usually very thin about 1-2 meters (Hoek, 2007); therefore, the blast damaged zone may
be ignored in this study by assuming that the blast is well controlled with D=0.
The estimated Hoek-Brown rock mass failure criterion constants are shown in Table 4.9.
Table 4.9 Estimated Hoek-Brown rock mass failure criterion constants
Rock type mi D mb s a
DRC 10.7 0 1.79 3.866e-3 0.506
DP 9.3 0 0.98 0.912e-3 0.514
The Mohr-Coulomb failure criterion for rock masses can be expressed using the following
equation:
𝜏 = 𝑐′ + 𝜎 ∙ 𝑡𝑎𝑛𝜑′ (4.27)
117
or, in terms of the major and minor principal stresses as (Hoek et al., 2002):
𝜎1′ =
2 ∙ 𝑐′ ∙ 𝑐𝑜𝑠𝜑′
1 − 𝑠𝑖𝑛𝜑′+
1 + 𝑠𝑖𝑛𝜑′
1 − 𝑠𝑖𝑛𝜑′∙ 𝜎3
′ (4.28)
where c’ and φ’ are the rock mass cohesion and friction angle.
The equivalent parameters for Mohr-Coulomb criterion can be estimated using the Hoek-
Brown parameters as follows (Hoek et al., 2002):
𝜑′ = sin−1 [6 ∙ 𝑎 ∙ 𝑚𝑏 ∙ (𝑠 + 𝑚𝑏𝜎3𝑛
′)𝑎−1
2(1 + 𝑎)(2 + 𝑎) + 6 ∙ 𝑎 ∙ 𝑚𝑏(𝑠 + 𝑚𝑏𝜎3𝑛′)𝑎−1
] (4.29)
𝑐′ =𝜎𝑐𝑖[(1 + 2𝑎)𝑠 + (1 − 𝑎)𝑚𝑏𝜎3𝑛
′] ∙ (𝑠 + 𝑚𝑏𝜎3𝑛′)𝑎−1
(1 + 𝑎)(2 + 𝑎) ∙ √1 +(6𝑎𝑚𝑏(𝑠 + 𝑚𝑏𝜎3𝑛
′)𝑎−1)(1 + 𝑎)(2 + 𝑎)
(4.30)
where
𝜎3𝑛′ =
𝜎3𝑚𝑎𝑥′
𝑈𝐶𝑆 (4.31)
The value of σ3max΄ is the upper limit of confining stress that need to be determined
separately for each case.
For slopes, the relation between σ3max΄ and σcm΄ can be determined by the following
equation (Hoek et al., 2002):
𝜎3𝑚𝑎𝑥′ = 𝜎𝑐𝑚
′ ∙ 0.72 (𝜎𝑐𝑚
′
𝛾 ∙ 𝐻)
−0.91
(4.32)
where γ is the unit weight of the rock mass; H is the height of the slope; and σcm΄ is the rock
mass compressive strength.
The rock mass compressive strength σcm΄ can be calculated using the following equation
(Hoek, 2007):
118
𝜎𝑐𝑚′ = 𝑈𝐶𝑆 ∙
(𝑚𝑏 + 4𝑠 − 𝑎(𝑚𝑏 − 8𝑠)) (𝑚𝑏
4 + 𝑠)𝑎−1
2(1 + 𝑎)(2 + 𝑎) (4.33)
The calculated results of equivalent cohesion and friction angle for the rock masses are
listed in Table 4.10.
Rock mass tensile strength which reflects the interlocking of rock particles when they are
not free to dilate is given by (Hoek and Brown, 1997):
𝜎𝑡𝑚 =𝑈𝐶𝑆
2(√𝑚𝑏
2 + 4𝑠−𝑚𝑏) (4.34)
or (Hoek, 2007)
𝜎𝑡𝑚 =𝑠 ∙ 𝑈𝐶𝑆
𝑚𝑏 (4.35)
The results obtained from these two equations turned out to be almost the same. Therefore
the second equation was used to calculate σtm. The obtained values are given in Table 4.10.
119
Table 4.10 Estimated values for rock mass cohesion, friction angle and tensile strength
DRC DP
UCS, MPa 138.79 89.26
a 0.508 0.514
mb 1.50 0.98
s 2.218×10-3 0.912×10-3
σcm', MPa 24.56 11.13
σ3max', MPa 3.80 6.21
σ3n', MPa 0.027392 0.069596
c', MPa 1.882 1.521
φ', ° 49.0 36.3
σtm, MPa 0.299 0.083
4.5.3 Rock mass deformation properties
The rock mass deformation properties usually include deformation modulus and Poisson’s
ratio. Several methods are available to estimate rock mass deformation modulus as given
below:
(1) For UCS ≤ 100 MPa, the rock mass modulus of deformation is given by (Hoek et
al., 2002):
𝐸𝑚(𝐺𝑃𝑎) = (1 −𝐷
2) ∙ √
𝑈𝐶𝑆
100∙ 10
𝐺𝑆𝐼−1040 (4.36)
For UCS > 100 MPa, the rock mass modulus of deformation is given by:
120
𝐸𝑚(𝐺𝑃𝑎) = (1 −𝐷
2) ∙ 10
𝐺𝑆𝐼−1040 (4.37)
(2) The rock mass modulus of deformation may also be calculated by (Hoek, 2007):
𝐸𝑟𝑚 = 𝐸 ∙ (0.02 +1 −
𝐷2
1 + 𝑒60+15𝐷−𝐺𝑆𝐼
11
) (4.38)
where E is the Young’s modulus of intact rock.
If no reliable intact rock modulus is available, the following equation may be used
(Hoek, 2007) to estimate rock mass modulus:
𝐸𝑟𝑚(𝐺𝑃𝑎) = 100 ∙ (1 −
𝐷2
1 + 𝑒75+25𝐷−𝐺𝑆𝐼
11
) (4.39)
The aforementioned methods (1) and (2) use GSI values and disturbance factor D. However,
the method (1) uses the uniaxial compressive strength (UCS), while method (2) uses intact
rock Young’s modulus. It is more reasonable to relate rock mass deformation modulus to
intact rock Young’s modulus rather than uniaxial compressive strength. Therefore, method
(2) makes more sense and it is used in this study.
There are no available empirical equations to estimate rock mass Poisson’s ratio. However,
the previous research has shown that the Poisson’s ratio increase about 21% from intact
rock to rock mass due to the presence of discontinuities (Kulatilake et al., 2004). Therefore,
the Poisson’s ratio of the rock mass (µr) is assumed to be 1.2 times of that of intact rock in
this study.
In numerical modeling, rock mass bulk modulus (Kr) and shear modulus (Gr) are usually
used instead of the deformation modulus and Poisson’s ratio. Kr and Gr may be calculated
by the following equations (Itasca, 2007):
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𝐾𝑟 =𝐸𝑟
3(1 − 2𝜇𝑟) (4.40)
𝐺𝑟 =𝐸𝑟
2(1 + 𝜇𝑟) (4.41)
The obtained results of the rock mass deformation parameters are listed in Table 4.11.
Table 4.11 Estimated values for rock mass deformation parameters
DRC DP
E, GPa 42.61 32.04
µ 0.254 0.233
GSI 50 37
D 0 0
Er, GPa 13.089 4.165
µr 0.3048 0.2796
Kr, GPa 11.1759 3.1493
Gr, GPa 5.0158 1.6273
4.5.4 Properties of DRC-DP contact and faults
Several slope failures have taken place along the DRC-DP contact in the south wall of the
open pit mine. Investigations revealed that the DRC-DP contact in the south wall is a thin
layer of soft materials that has a low strength. It is not quite sure whether the soft contact
is the reason for failure or is it due to daylighting condition of the contact.
The lab test results are used to estimate the strength and stiffness of the contact between
the DRC and DP rocks. The used friction angle is 26.5° from the direct shear test. The
cohesion and tensile strength of the DRC-DP contact is assumed as 5% of that of the DRC
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and DP rock masses. JKN and JKS are estimated using the laboratory test results and an
average normal stress value as given below:
𝐽𝐾𝑁 = 11.5621 × 𝜎𝑛 (MPa) = 52.439 GPa/m (4.42)
𝐽𝐾𝑆 = 0.9914 × 𝜎𝑛 (MPa) = 4.496 GPa/m (4.43)
where
𝜎𝑛 = 𝜌𝑔ℎ = 2492 × 10 × 182 = 4535440 Pa = 4.53544 MPa (4.44)
σn is the normal stress on the DRC-DP contact, MPa; h is the average thickness of DRC
rocks, m. Because the orientation of DRC-DP contact is almost horizontal (dip angle 5°),
an average thickness of DRC rock is sufficient to calculate JKN and JKS.
The obtained values for DRC-DP contact are listed in Table 4.12.
Table 4.12 Estimated property values of DRC-DP contact
Contact property
JKN,
GPa/m
JKS,
GPa/m
cj, MPa φj, ° σt, MPa
DRC-DP 52.439 4.496 0.0851 26.5 0.0096
The properties of faults are estimated from the laboratory test results of joints in Chapter
3. The relation between normal stress and joint normal and shear stiffness are shown in the
following equations.
For discontinuities of DRC rocks:
𝐽𝐾𝑁 (𝑀𝑃𝑎
𝑚𝑚) = 10.02 × 𝜎𝑛(𝑀𝑃𝑎) (4.45)
𝐽𝐾𝑆 (𝑀𝑃𝑎
𝑚𝑚) = 1.0839 × 𝜎𝑛(𝑀𝑃𝑎) (4.46)
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For discontinuities of DP rocks:
𝐽𝐾𝑁 (𝑀𝑃𝑎
𝑚𝑚) = 14.876 × 𝜎𝑛(𝑀𝑃𝑎) (4.47)
𝐽𝐾𝑆 (𝑀𝑃𝑎
𝑚𝑚) = 1.018 × 𝜎𝑛(𝑀𝑃𝑎) (4.48)
The normal stress σn may be calculated with average depth of DRC and DP rock mass. The
average depth of DRC and DP rocks are 91 m, and 353 m respectively. The calculated joint
normal stiffness and joint shear stiffness are listed in Table 4.13. The cohesion and tensile
strength values are taken as 5% of those of the two rock masses. The friction angles are
estimated from the laboratory test results. Table 4.13 lists all the parameters for faults.
Table 4.13 Estimated property values of faults
Property JKN JKS cj, MPa φj, ° σt, MPa
DRC-fault 22.743 2.458 0.0941 26.4 0.015
DP-fault 129.257 8.899 0.0761 28.5 0.00415
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CHAPTER 5 BUILDING OF THE GEOLOGICAL MODEL
5.1 Introduction
The mining company’s survey team usually measures the topography of the open pit mine
to keep track of the topography changes due to blasting and excavation. The topographies
of the open pit mine are available from the mining company during its lifetime. The faults
that exist in the area of the open pit mine also have been surveyed by the mining company
during the life of the mine.
The geological structure is a main factor which influences open pit mine slope stability.
When compared to slope stability problems in civil engineering, such as highways, open
pit mine slope design pay little attention to small scale failures like rock falls compared to
inter-ramp or overall failures. For example, it is not allowed to have any rock fall or slope
failure along a highway slope, but mines may allow small rock falls or part of bench failures
to happen in an open pit mine as far as it does not affect the safety of the traffic, people and
equipment in the mine. Therefore, mining companies focus more on inter-ramp and overall
failures. It is usually known that for large scale failure in hard rock slopes, the control factor
is the geological structure. For example, existence of large faults played the main role with
respect to the massive landslide happened in Bingham Canyon mine, Utah on April 10th,
2013. To perform a realistic numerical study to investigate stability of a rock slope, it is
very important to build an accurate geological model including all the important faults.
This issue has not been addressed properly in previous research conducted on rock slope
stability using three dimensional discrete element numerical modeling.
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The Google earth map of the whole open pit mine considered in this study is shown in
Figure 1.2.
5.2 Topographies of the Mine Site
The earliest topography drawing that the mining company provided was the one in 2001.
In this drawing, part of our research area appears was excavated. Therefore, it is not suitable
to reflect the original topography. Fortunately, it was possible to download an elevation
contour map from the USGS website. The elevation contour map of 1968 version was
found from the USGS website, as shown in Figure 5.1. A three dimensional topography of
the research area was built using this elevation contour map to show how the original
surface looks like (see Figure 5.2). From Figure 5.2, it can be seen that the highest elevation
in this area is 1685 m, and the lowest elevation is around 1600 m in the Rodeo Creek part
of the mine. Because the topography of this area is quite flat without any high mountains
or deep valleys, a flat surface which has an elevation around 1621 m may be assumed to
represent the top surface of the numerical model.
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Figure 5.1 Elevation contour map from the USGS (USGS).
Figure 5.2 Original topography of the research area before mining activities.
The open pit mine was started around year 1976 with small scale mining activities. The
earliest topography drawing that the mining company provided is the one of 2001, which
is shown in Figure 5.3. It shows that only the southeast part of the research area was
excavated prior to 2001, and the rest of the considered research area is similar to that given
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in Figure 5.2. However, after 2001, the mining activities increased in the research area, and
the topographies of July 2011 and July 2012 are shown in Figures 5.4 and 5.5, respectively.
Figure 5.3 Topography of the research area in the pit in 2001.
Figure 5.4 Topography of the research area in the pit in July 2011.
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Figure 5.5 Topography of the research area in the pit in July 2012.
5.3 Construction of Topographies Using 3DEC Software
The topographies of the research area were simplified and then built using the 3DEC
software package. There are two reasons why the topographies were simplified:
(1) First, this research was aimed at studying the large scale slope stability, rather than
small scale instabilities. Large scale failure includes inter-ramp and overall failures,
while small scale failure usually refers to rock fall and a few bench failures. Figure
5.6 shows a slope failure that crosses about 5 benches (around 60 meters high),
however, still it may not get considered as a large failure in the open pit mine. This
means that it may be sufficient only to represent the major topography changes and
not necessary to include all the benches in detail in the 3DEC model.
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Figure 5.6 One slope failure from the researched open pit mine.
(2) Even though there is no technical difficulties for the author to build more detailed
topographies, the calculation time for stress analyses using the 3DEC model
increases dramatically when more geometry details are included in the model. Thus,
the 3DEC manual also suggests that the numerical model should be as simple as
possible (Itasca, 2007).
Two excavations were simulated: (1) the excavation from the initial topography to that of
July 2011, and (2) the excavation from July 2011 to July 2012. The simplified models used
for the initial topography, the topography of July 2011 and the topography of July 2012 are
shown in Figures 5.7, 5.8, and 5.9, respectively.
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Figure 5.7 Simplified model of initial topography.
Figure 5.8 Simplified model of July 2011.
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Figure 5.9 Simplified model of July 2012.
5.4 Construction of the Fault System
Fault is a surface or narrow zone along which one side has moved relative to the other in a
direction parallel to the surface or zone (Twiss and Moores, 1992). Most faults are brittle
shear fractures or zones of closely spaced shear fractures. Figure 5.10 shows several faults
that exist in the research area.
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Figure 5.10 Some faults that exist in the open pit mine.
The approximate locations, orientations and persistence of all the faults that exist in the
research area were provided by the mining company. There are 44 important faults located
within our research area. Faults are formed due to geological movements and therefore
their shape and size are usually irregular. Some of them were fully persistent; some others
terminated on another fault or faults; the remaining terminated on rock. Using the 3DEC
software package, it is very difficult if not impossible to build very complicated fault
patterns that exist in rock masses such as the one shown in Figure 5.11.
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Figure 5.11 Original three-dimensional plot of the faults.
By examining the faults one by one, it was found that the faults can be simplified as follows
to reduce the unnecessary work on the model building and keep the important geological
information at the same time:
(1) All faults were simplified into planar faces. Figure 5.12 shows an irregular fault
surface which was simplified to a planar surface.
(2) Some faults were extended or trimmed in reasonable ranges in order to make them
intersect with other faults. For example in Figure 5.13, the extra part of fault A
beyond fault B was trimmed, while the missing part was extended to terminate fault
B on fault A.
(3) Some minor and unimportant faults were eliminated from the model.
(4) Some faults which were very close to model boundaries were extended to make
them fully persistent faults.
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(a) Before simplification
(b) After simplification
(c) Comparison
Figure 5.12 How an irregular fault surface was simplified to a planar surface.
135
(a) Before simplification
(b) After simplification
Figure 5.13 A fault simplified by trimming and extending.
136
A new procedure was developed for the first time in the world according to a technique
suggested by Professor Pinnaduwa Kulatilake to build a three-dimensional fault system
which consists of the different types of faults mentioned before. The final picture of the
built simplified fault system using 3DEC is shown in Figure 5.14. Table 5.1 lists all the
faults that were included in the numerical model along with their orientations.
Figure 5.14 Plot of the simplified fault system built using 3DEC.
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Table 5.1 List of all the faults included in the 3DEC model
Fault # Dip angle Dip direction
1 53 103
2 75 330
3 71 310
4 65 260
5 70 260
6 65 260
7 62 283
8 61 41
9 51 149
10 75 270
11 63 247
12 65 248
13 67 131
14 61 264
15 47 30
16 28 146
17 44 31
18 59 245
19 53 252
20 55 258
21 59 249
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Table 5.1 List of all the faults included in the 3DEC model-Continued.
Fault # Dip angle Dip direction
22 6 27
23 36 9
24 54 54
25 54 349
26 63 249
27 45 281
28 79 253
29 71 298
30 11 307
31 80 327
32 60 245
33 68 75
34 10 341
35 60 343
36 73 141
37 79 232
38 50 339
39 10 360
40 65 40
41 80 14
42 63 245
43 69 69
44 58 16
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The mining company provided fault maps on several vertical cross sections in the studied
area. Figure 5.15 shows the location of these vertical cross sections. After building the
three-dimensional fault system using the 3DEC software package, cross sections of fault
maps from the 3DEC model were produced along the cross sectional lines shown in Figure
5.15 to compare with the cross sectional maps of faults given by the mining company.
Pretty good agreement was found between them. Figures 5.16 through 5.22 show the
comparisons of fault maps between the 3DEC simulations and maps given by the mining
company on cross sections 1 through 7, respectively.
Figure 5.15 Locations of the vertical cross sections used to compare between the
simulated faults using the 3DEC package and the fault cross sectional maps provided by
the mining company.
140
(a) From the mining company
(b) From the 3DEC model
Figure 5.16 Comparison of fault maps on cross section 1.
141
(a) From the mining company
(b) From the 3DEC model
Figure 5.17 Comparison of fault maps on cross section 2.
142
(a) From the mining company
(b) From the 3DEC model
Figure 5.18 Comparison of fault maps on cross section 3.
143
(a) From the mining company
(b) From the 3DEC model
Figure 5.19 Comparison of fault maps on cross section 4.
144
(a) From the mining company
(b) From the 3DEC model
Figure 5.20 Comparison of fault maps on cross section 5.
145
(a) From the mining company
(b) From the 3DEC model
Figure 5.21 Comparison of fault maps on cross section 6.
146
(a) From the mining company
(b) From the 3DEC model
Figure 5.22 Comparison of fault maps on cross section 7.
5.5 Construction of the Rock Layers
The rocks in the research area are divided into two rock units: (1) Devonian Rodeo Creek
(DRC) unit, and (2) Devonian Popovich (DP) formation as given in Table 1.1.
147
The contact between DRC and DP rocks is a disconformity. A disconformity is a buried
erosional or non-depositional surface separating two rock masses or strata of different ages,
indicating that sediment deposition was not continuous (Kleber and Terhorst, 2013). In
general, the older layer was exposed to erosion for an interval of time before deposition of
the younger. The layer boundaries between the different rock formations and members are
shown in Figure 5.23. The contact between the DRC and DP rocks in a three dimensional
view is shown in Figure 5.24. It shows that the contact is an irregular surface with many
small waviness. However, it may be simplified to a flat plane with a dip angle of 5 degrees
and a dip direction of 345 degrees. The two layer system was built using the 3DEC software
package as shown in Figure 5.25.
Figure 5.23 Stratigraphy of the mine.
DRC
UM
SD
PL
WS
1021.08 m
524.2
56 m
North
148
Figure 5.24 The natural and simplified contact surfaces between the DRC and DP rocks.
Figure 5.25 Two rock layer system built using the 3DEC software package.
149
5.6 Integrated Geological Model
So far, the building of the topography system, the fault system and the stratigraphy system
using the 3DEC software package were explained separately. However, to conduct
numerical modeling, all the geological features, including the three topographies, all the
faults, and the two layers should be built together in one single integrated 3DEC model.
The built integrated geological model is shown in Figure 5.26. Then the integrated
geological model was meshed as shown in Figure 5.27. No cut or geometry changes on
blocks are allowed once the model was meshed.
Figure 5.26 The built integrated geological model.
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Figure 5.27 The meshed integrated geological model.
5.7 Summary
In this chapter, all the geological features, including the topographies, faults and DRC-DP
contact of the research area were investigated and built using the 3DEC software package.
The topographies were simplified eliminating bench details but keeping all the major
geometry features to focus the study on large scale slope stability investigations. The three-
dimensional fault system in the research area is very complicated with 44 irregular shaped
faults having many orientations and different types of intersections. The approximate
orientation and position of each fault were used in building the fault system in three-
dimensions. The fault system was also simplified in order to build a practical three-
dimensional fault system using the 3DEC software package. Comparison of the fault map
cross sections obtained from the mining company with the ones simulated using the 3DEC
model showed that they agree quite well. This proved that the construction of the fault
151
system using the 3DEC model is successful. The DRC-DP contact was simplified as a sub-
horizontal plane. An integrated model which combined all these geological features was
built using 3DEC and meshed successfully.
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CHAPTER 6 NUMERICAL MODELING AND COMPARISON WITH
FIELD MONITORING DATA
6.1 Introduction
The main purpose of this chapter is to develop a methodology to estimate 3-D deformation
resulting from an open pit mine excavation by performing 3-D stress analysis. This chapter
illustrates how such a methodology was developed using the excavations performed for the
mine during the period between July 2011 and July 2012. The needed geological models
to show the methodology were presented in Chapter 5. The material property values that
went into the numerical model were estimated in Chapters 3 and 4. Numerical modeling
was performed under two different boundary conditions: (a) zero velocity boundary
conditions and (b) stress boundary conditions.
6.2 Constitutive Models and Material Properties
Five constitutive models are available in the 3DEC software package to use to represent
the mechanical properties of the rock masses: null, isotropic elastic, anisotropic elastic,
Mohr-Coulomb plasticity model, and bilinear strain-hardening/softening with ubiquitous
joint model. The details of these models are as follows:
(1) Null model: A null model is used to represent material that is removed or excavated
from the model (Itasca, 2007). Once a rock block is excavated, its constitutive
model automatically changes to the null model. However, it can be changed back
to other models using the “Fill” command.
153
(2) Isotropic elastic model: The elastic isotropic model is used to describe the simplest
material behavior with a linear relation between stress and strain.
(3) Anisotropic elastic model: Elastic anisotropic model represents different material
properties in different directions. The orthotropic model, and transversely isotropic
model are two special cases of the anisotropic elastic model.
(4) Mohr-Coulomb plasticity model: The Mohr-Coulomb model is the conventional
model for plasticity in soil and rock mechanics and the failure envelope for the
Mohr-Coulomb model in 3DEC consists of a Mohr-Coulomb criterion with a
tension cutoff (Itasca, 2007). Mohr-Coulomb model assumes a linear relation
between the normal stress and shear stress or between the maximum principal stress
and minimum principal stress as given below:
𝜏 = 𝐶 + 𝜎𝑛 ∙ 𝑡𝑎𝑛𝜑 (6.1)
𝜎1 = 𝑈𝐶𝑆 + 𝜎3 ∙ 𝑡𝑎𝑛2 (45 +𝜑
2) (6.2)
where τ is the shear stress, C is the cohesion, σn is the normal stress, φ is the angle
of internal friction, σ1 is the maximum principal stress, and σ3 is the minimum
principal stress.
Figure 6.1 shows the Mohr-Coulomb failure criterion used in the 3DEC software
package. The predicted tensile strength from the original Mohr-Coulomb criterion,
which is the intersection of the failure line with the σ3 axis, is considered to be much
higher than reality. Therefore, the tensile strength value from the Brazilian test, the
so called tension cutoff, is used in the Mohr-Coulomb failure criterion. The Mohr-
Coulomb is used for most general slope stability and underground excavation
problems.
154
(5) Bilinear strain-hardening/softening with ubiquitous joint model: This model is
applicable for granular materials that exhibit nonlinear material hardening or
softening and/or thinly laminated material exhibiting strength anisotropy (Itasca,
2007). Therefore, this model is usually used to study progressive collapse or pillar
yielding in laminated underground coal mines.
Since there is no unique model applicable for all geological materials under all conditions
(Desai, 1982), the philosophy of selecting a constitutive model depends on the material
parameters that are available and the application of the numerical modeling (Itasca, 2007).
By comparing all the available rock block constitutive models, the Mohr-Coulomb
plasticity model, which is used for general soil and rock mechanics problems, was adopted
in this study.
Figure 6.1 Mohr-Coulomb failure criterion used in 3DEC.
σ1
σ3σt
slope = tan2(45+φ/2)
tension cutoffUCS
155
Two joint (discontinuity) constitutive models are available in the 3DEC software package
to represent discontinuity mechanical properties: (a) joint area contact-Coulomb slip model,
and (b) continuously yielding model (Itasca, 2007). The joint area contact model assumes
a linear relation between joint stiffness and yield limit. Joint stiffness, friction, cohesion
and tensile strength are needed to use joint contact model. Joint area contact model
simulates displacement-weakening of the joint by loss of cohesive and tensile strength
properties while the continuously yielding joint model simulates continuous weakening
behavior as a function of accumulated plastic-shear displacement (Itasca, 2007). The
features of these two model are described in the following table.
Table 6.1 3DEC joint constitutive models (Itasca, 2007)
Model Representative material Example application
Area contact Joints, faults, bedding planes
in rock General rock mechanics
Continuously
yielding
Rock joints displaying
progressive damage and
hysteretic behavior
Cyclic loading and load reversal
with predominant hysteretic
loop; dynamic analysis
The area contact model was used for all the faults and DRC-DP contact in this study.
Intact rock properties and joint properties were estimated in Chapter 3 using the results of
laboratory tests. Intact rock properties were used along with the remote fracture mapping
results to estimate rock mass properties in Chapter 4. The rock mass properties used in the
numerical modeling are summarized and listed in Table 6.2. The discontinuity properties
used in the numerical modeling are listed in Table 6.3.
156
Table 6.2 Rock mass material properties used for numerical modeling
Property DRC DP
Density, kg/m3 2492 2460
Bulk modulus, Kr (GPa) 11.18 3.15
Shear modulus, Gr (GPa) 5.02 1.63
Rock mass cohesion, c' (MPa) 1.88 1.52
Rock mass friction angle, φ' (°) 49.0 36.3
Tensile strength, σtm (MPa) 0.299 0.083
Table 6.3 Joint properties used for numerical modeling
Property Fault-DRC Fault-DP DRC-DP
contact
C, MPa 0.0941 0.0761 0.0851
φ, ° 26.4 28.5 26.5
σt, MPa 0.015 0.00415 0.0096
JKN, GPa/m 22.743 129.257 52.439
JKS, GPa/m 2.458 8.899 4.496
6.3 Numerical Modeling Stages
The excavation of the rock mass was simulated using 3DEC software. As shown in Figure
6.2, the rock mass of the model is divided into three regions: region 1, region 2 and region
3. Region 1 is the top part of the model which needs to be removed from the prismatic
model to obtain the topography of July 2011. The two blocks belonging to region 2 need
removal to simulate the excavation and reach the topography of July 2012. Thus region 3
shows the topography of July 2012.
157
Figure 6.2 Three regions.
To simulate the rock excavation procedure, three stages were simulated as stated below:
(1) First, the initial status of the whole model under gravity was obtained by applying
the boundary conditions to the prismatic body. The stress and displacement values
were checked to make sure the model works correctly under gravity.
(2) The displacements in the rock mass, joint displacements, and velocity of the model
were reset to zero; but the obtained stress distribution was not changed. Then region
1 was excavated to obtain the topography of July 2011. The numerical model was
run monitoring the displacement values until the model reached the equilibrium
again.
(3) The displacements in the rock mass, joint displacements, and velocity were reset
again to zero; but the obtained stress distribution was not changed as before. Then
region 2 was excavated to obtain the topography of July 2012. The numerical model
158
was run again and stopped when the model reached the equilibrium. Displacements,
velocities and stresses were monitored during the numerical modeling.
The purpose of simulating stages 1 and 2 is to get the stress distribution of the rock mass,
while the results of stage 3 is the main focus of this study. The three stages of the numerical
modeling performed are illustrated in Figure 6.3.
159
(a) Stage 1, whole model
(b) Stage 2, July 2011 topography
(c) Stage 3, July 2012 topography
Figure 6.3 Three modeling stages performed.
160
During the numerical simulation, the histories of displacement, stress and velocity were
monitored by setting monitoring points in the numerical model. According to the available
field monitoring data, seven monitoring points (see Figure 6.4) were set in the numerical
model in order to compare with the field monitoring data. Because these monitoring points
were selected outside the excavation area, it was possible to monitor them continuously to
record the displacements of the rock masses due to the performed excavations.
Figure 6.4 Locations of selected monitoring points in the set up 3DEC model.
6.4 Insitu Stress and Boundary Conditions
In-situ stress may be applied in a numerical model before any excavation is conducted. As
discussed above, no in-situ stress data is available for the mine site. The most commonly
used method to calculate in-situ stress is based on the assumption that the vertical stress
161
equals to the overburden soil/rock weight, while horizontal stress equals to the vertical
stress times a lateral stress ratio. This approach is correct only for horizontal layer deposits
having no geological structures or no complicated geology (Tan et al., 2014a). However,
in this study, many geological structures (faults, inclined DRC-DP contact) needed to be
accounted in the numerical model. Those structures definitely affect the distribution of in-
situ stresses (Tan et al., 2014b). Therefore, to obtain the initial status of in-situ stress in the
prismatic block shown in Chapter 5, it is necessary to calculate it by applying the boundary
conditions along with the gravity command in using 3DEC.
Usually two different boundary conditions are used in numerical modeling: (1) zero
velocity boundary condition and (2) stress boundary condition.
(1) Zero velocity boundary condition: Under this condition, the displacement is
restrained in the normal direction to the boundary and may be allowed in the
tangential direction. For example, the vertical displacement of the model bottom is
usually set to zero velocity, however, the displacements in the horizontal directions
may be allowed. For the four lateral boundaries, the displacements are restrained in
the normal directions to the boundaries. The top surface of the model is a free
surface without any displacement restriction. Figure 6.5 shows the zero velocity
boundary conditions.
(2) Stress boundary condition: The boundary stresses applied on the four lateral
boundaries vary with the lateral stress ratio which depends on the in-situ stress.
However, there is no in-situ stress data available for the mine site, and therefore
several different lateral stress ratios may be tried. The lateral stress ratio is defined
as the ratio of lateral stress over the vertical stress as given below:
162
𝐾𝑥 =𝜎𝑥
𝜎𝑧 (6.3)
𝐾𝑦 =𝜎𝑦
𝜎𝑧 (6.4)
where
𝜎𝑧 = 𝜌 ∙ g ∙ ℎ (6.5)
In this study, the lateral stress ratios in the x and y directions were assumed to be
the same. Different lateral stress ratio values were tried in the numerical modeling
and the results were compared. Figure 6.6 shows two stress boundary conditions.
Figure 6.5 Zero velocity boundary condition.
(a) (b)
Figure 6.6 (a) Stress boundary condition type 1, (b) Stress boundary condition type 2.
BoundaryStress
BoundaryStress
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If both boundary stress and boundary velocity conditions should be applied on one surface,
the boundary stress condition should be applied prior to the boundary velocity condition,
or else, the effect of the boundary velocity will be lost (Itasca, 2007). The bottom of the
model was always fixed with zero velocity boundary, and the top of the model was always
set as a free surface. The boundary conditions of the four lateral boundaries may be changed
among boundary stress or boundary velocity in order to study the effect of boundary
conditions. For the considered part of the open pit mine no one knows what boundary
condition is suitable to apply. Therefore, in this study, both boundary conditions were tried.
Boundary condition is one of the most important parts in a numerical modeling study. First,
the stress boundary condition type 1 was tried, as shown in Figure 6.7. In stage 1, forces
applied on the two boundaries are equal to each other, therefore the model is in equilibrium.
However, in stage 2, once the upper rock mass was removed, the total force applied on the
left side boundary is smaller than that on the right side boundary because the sizes of the
two boundaries became different (see Figure 6.8). Then the whole model will move to the
left side. As far as the whole model is concern, the force applied on the left boundary does
not equal to that on the right boundary, and the force applied on the front boundary does
not equal to that on the back boundary (Figure 6.9).
𝐹1 ≠ 𝐹2 (6)
𝐹3 ≠ 𝐹4 (7)
The model may rotate under such boundary stress conditions.
164
Figure 6.7 Forces applied on the two boundaries are equal to each other in stage 1.
Figure 6.8 Forces applied on the two boundaries are not equal in stage 2.
Figure 6.9 Whole model is under unbalanced forces.
165
A trial was conducted to demonstrate the boundary stress condition type 1. Boundary
stresses with k0=0.5 were applied on the four lateral boundaries, with the bottom of the
model fixed in the z direction. After the upper rock mass was removed, the x-displacement
was positive at the back side and negative at the front side; that means the model had rotated
(see Figure 6.10). The y-displacement was around -50 m and the model could not reach
equilibrium; that means the whole model moved towards the opposite direction of y axis
(see Figure 6.11).
Figure 6.10 x-displacement contours under unbalanced forces (indicate block rotation).
166
Figure 6.11 Whole model moves along y-axis under unbalanced forces.
It shows that to use the stress boundary condition for this case study, either the left
boundary or right boundary, and front boundary or back boundary should be fixed to
prevent the movement of the entire model. Therefore, the boundary stress condition type 2
is more applicable in this study. From the topography map (Figure 1.2) shown in Chapter
1, it can be seen that the front boundary of this numerical model is located close to the
west-east center line of the open pit. Therefore, it is reasonable to assume a zero velocity
boundary condition on the front boundary, while applying the boundary stress on the back
side of the model. On the other hand, for left and right boundaries, it is difficult to decide
which side should be applied with zero velocity boundary, and thus it may be better to try
both cases. Table 6.4 shows all the 16 boundary condition cases conducted in this study.
In Table 6.4, V=0 means zero velocity boundary, σ=0 means zero stress boundary, and
k0=0.4 means boundary stress condition with lateral stress ratio of 0.4. Numerical modeling
without faults were also tried to study the effect of faults on slope stability. Left boundary
is the west side; right boundary is the east side; front boundary is the south side; back
boundary is the north side.
167
Table 6.4 Boundary condition combinations
Bottom
boundary
Top
boundary
Left
boundary
Right
boundary
Front
boundary
Back
boundary
Faults
Yes/No
1(a) V=0 σ=0 V=0 k0=0.4 V=0 k0=0.4 No
1(b) V=0 σ=0 k0=0.4 V=0 V=0 k0=0.4 No
2(a) V=0 σ=0 V=0 k0=0.5 V=0 k0=0.5 No
2(b) V=0 σ=0 k0=0.5 V=0 V=0 k0=0.5 No
3(a) V=0 σ=0 V=0 k0=0.4 V=0 k0=0.4 Yes
3(b) V=0 σ=0 k0=0.4 V=0 V=0 k0=0.4 Yes
4(a) V=0 σ=0 V=0 k0=0.5 V=0 k0=0.5 Yes
4(b) V=0 σ=0 k0=0.5 V=0 V=0 k0=0.5 Yes
5 V=0 σ=0 V=0 k0=0.3 V=0 k0=0.3 Yes
6 V=0 σ=0 V=0 k0=1.0 V=0 k0=1.0 Yes
7 V=0 σ=0 V=0 V=0 V=0 V=0 No
8 V=0 σ=0 V=0 V=0 V=0 V=0 Yes
9(a) V=0 σ=0 V=0 k0=0.7 V=0 k0=0.7 Yes
9(b) V=0 σ=0 k0=0.7 V=0 V=0 k0=0.7 Yes
10 V=0 σ=0 V=0 k0=0.8 V=0 k0=0.8 Yes
11 V=0 σ=0 V=0 k0=2.0 V=0 k0=2.0 Yes
168
6.5 Numerical Modeling Results
6.5.1 Validation of basic results
Figure 6.12 shows the z-stress, x-stress and y-stress contours for the whole model for case
1(a) in stage 1. The z-stress at the bottom of the model is close to the gravitational stress
of the rock mass above the bottom, which is approximately 13 MPa. In case 1(a), the k0
value used is 0.4; so the x-stress and y-stress are around 0.4 times of the z-stress, which
agree with the stresses in Figures 6.12 (b) and (c). Please note that the unit in all the stress
contour plots in this dissertation is Pascal (Pa).
When faults are introduced into the numerical model in case 3(a), the stress contours still
agree approximately with the estimated values (see Figure 6.13). These show that the
numerical model works correctly.
169
(a)
(b)
(c)
Figure 6.12 Stress contours for case 1(a) in stage 1.
170
(a)
(b)
(c)
Figure 6.13 Stress contours for case 3(a) in stage 1.
171
6.5.2 Effect of boundary condition
It is sometimes difficult to know the type of boundary condition to apply to a particular
surface on the body being modeled (Itasca, 2007); therefore it is necessary to find out the
most applicable boundary condition for the particular case of study. As discussed above,
stress boundary condition type 1 is not applicable, so zero velocity boundary condition and
boundary stress condition type 2 are discussed in this section. By comparing case 3(a) with
case 8, the effect of boundary condition can be evaluated. Case 3(a) studied the boundary
stress condition type 2, while case 8 studied the zero velocity boundary condition. The
displacement values of those seven monitoring points under case 3(a) and case 8 are
compared in Table 6.5. It can be seen from Table 6.5 that the x and y displacements are all
in the millimeter level in case 8, while in the centimeter level in case 3(a) except monitoring
point 2 which had encountered rock block failure. The z displacements are also lower in
case 8 compared to that of case 3(a); however, the difference is not large as for x and y
displacements and both displacements are in the centimeter range. Figure 6.14 shows the
total displacement contours comparison between case 3(a) and case 8. Case 3(a) shows
higher displacements compared to case 8 with significant differences spatially. Similar
situations also occurred when comparing case 1(a) with case 7; in these two cases, the
faults were not included in the model (see Table 6.6). Please note that the unit in all the
displacement contour plots in this dissertation is meter (m).
172
(a) Case 3(a)
(b) Case 8
Figure 6.14 Comparison of the total displacement between case 3(a) and case 8.
Note that cases 7 and 8 restrict the lateral displacements at the applied boundaries. Usually
those boundaries should be placed far from the investigated area so that the effect of the
loading /unloading occurs in the investigated area has almost no effect on the zero velocity
boundaries. If such boundaries are placed far from the investigated area, the displacements
173
obtained between case 3(a) and case 8, and case 1(a) and case 7 most probably would be
comparable. This means the displacements obtained through the stress boundary conditions
(cases 1(a) and 3(a)) for the tackled problem are more realistic than that obtained through
the zero velocity boundary conditions (Cases 7 and 8).
Table 6.5 Comparison of displacement values between case 3(a) and case 8
Monitoring
point
x-displacement, m y-displacement, m z-displacement, m
Case 3(a) Case 8 Case 3(a) Case 8 Case 3(a) Case 8
1 -0.03582 0.00024 -0.06822 -0.0042 0.027865 0.010084
2 -7.27908 0.00055 -5.88426 -0.00112 0.610079 0.008699
3 -0.02671 0.002444 -0.06186 -0.0039 0.050032 0.031853
4 -0.03657 0.001561 -0.06309 -0.00186 0.039552 0.017909
5 -0.03293 0.002554 -0.05996 -0.00176 0.045288 0.025755
6 -0.02286 -0.00219 -0.06348 -0.00292 0.041087 0.027558
7 -0.05086 -0.00087 -0.03046 0.00104 0.012146 0.000336
174
Table 6.6 Comparison of displacement values between case 1(a) and case 7
Monitoring
point
x-displacement, m y-displacement, m z-displacement, m
Case 1(a) Case 7 Case 1(a) Case 7 Case 1(a) Case 7
1 -0.03391 0.000126 -0.06107 0.00096 0.024848 0.01025
2 -0.03629 0.000131 -0.05548 0.00434 0.025278 0.00942
3 -0.02642 -0.00034 -0.05406 0.00786 0.048999 0.03337
4 -0.03401 0.000291 -0.05606 0.00483 0.036122 0.01880
5 -0.03088 0.000369 -0.05429 0.00687 0.043216 0.02672
6 -0.02249 -0.00075 -0.05842 0.00373 0.042198 0.00597
7 -0.05756 -0.00247 -0.02382 0.00388 0.016348 0.00597
6.5.3 Effect of the faults
In this study a lot of time was spent on the construction of the complicated fault system to
simulate the rock mass movements accurately. This study was performed to evaluate the
effect of the fault system on the stability of the slope. From the displacements of those
seven monitoring points, it can be seen that the differences between the cases with faults
and cases without faults is small. Table 6.7 compares case 1(a) with case 3(a). Table 6.8
compares case 2(a) with case 4(a). The y-displacement in cases without faults is slightly
smaller than that in cases with faults. The x-displacement and z-displacements for both
cases are about the same level except for #2 monitoring point. These results do not mean
that the fault has no effect on the displacement of rock blocks and the slope stability. It
indicates that the rock mass parameter values used in the numerical model are comparable
175
to the parameter values used for faults. It is important to note that the rock mass parameter
values used in the numerical model are much less compared to the intact rock parameter
values. When the displacement contours are compared, significant displacement difference
can be found at many locations. Figure 6.15 and Figure 6.16 show the x, y, z, and total
displacements for case 1(a) and case 3(a), respectively. In the case of without faults, no
rock block failures have occurred. However, according to the mine site, local and small
scale failures have occurred close to the right side of the model, which is more consistent
with the case with faults. Please note that the local failures in reality may not be as serious
as that indicated in Figure 6.16, which may be due to the artificial truncation of the rock
blocks at the right boundary.
Table 6.7 Displacement comparison between case 1(a) and case 3(a)
Monitoring
point
x-displacement, m y-displacement, m z-displacement, m
Case 1(a) Case 3(a) Case 1(a) Case 3(a) Case 1(a) Case 3(a)
1 -0.03391 -0.03582 -0.06107 -0.06822 0.024848 0.027865
2 -0.03629 -7.27908 -0.05548 -5.88426 0.025278 0.610079
3 -0.02642 -0.02671 -0.05406 -0.06186 0.048999 0.050032
4 -0.03401 -0.03657 -0.05606 -0.06309 0.036122 0.039552
5 -0.03088 -0.03293 -0.05429 -0.05996 0.043216 0.045288
6 -0.02249 -0.02286 -0.05842 -0.06348 0.042198 0.041087
7 -0.05756 -0.05086 -0.02382 -0.03046 0.016348 0.012146
176
Table 6.8 Displacement comparison between case 2(a) and case 4(a)
Monitoring
point
x-displacement, m y-displacement, m z-displacement, m
Case 2(a) Case 4(a) Case 2(a) Case 4(a) Case 2(a) Case 4(a)
1 -0.04472 -0.04664 -0.07339 -0.0837 0.030147 0.037028
2 -0.04569 -10.3027 -0.06728 -13.1918 0.028972 3.05447
3 -0.03311 -0.0325 -0.06694 -0.08124 0.05043 0.051069
4 -0.0433 -0.04472 -0.06778 -0.08241 0.039521 0.043509
5 -0.03904 -0.04 -0.06622 -0.07877 0.045437 0.04726
6 -0.02639 -0.02689 -0.07747 -0.08524 0.043733 0.04246
7 -0.07008 -0.06554 -0.02983 -0.04133 0.018787 0.017636
(a) (b)
(c) (d)
Figure 6.15 Displacement contours for case 1(a) in stage 3.
177
(a) (b)
(c) (d)
Figure 6.16 Displacement contours for case 3(a) in stage 3.
6.5.4 Effect of the k0
From the above discussion, it is clear that the boundary stress condition type 2 is more
applicable than boundary stress condition type 1 and zero velocity boundary condition and
thus should be used in this study. The lateral stress ratio of the mine site is unknown; so it
is necessary to try several k0 values and evaluate the effect of k0. k0 values of 0.3, 0.4, 0.5,
0.7, 0.8, 1.0 and 2.0 were tried. When k0=0.3, the numerical model fails at stage 1 (see
Figure 6.17); which means that the lateral boundary stress is not high enough to keep the
model stable. This indicates that the k0 value should be larger than 0.3. On the other hand,
178
when k0=2.0, 1.0 and 0.8 were used, the model experienced a large failure under stage 2
and was not able to reach equilibrium (see Figure 6.18).
Figure 6.17 Model collapsed in stage 1 under boundary stress with k0=0.3.
Figure 6.18 Large failure occurred in stage 2 under boundary stress with k0=0.8
Because the k0 should not be less than 0.3 and larger than 0.8, three values (k0=0.4, 0.5 and
0.7) which lie in between 0.3 and 0.8 were tried. Under k0=0.4, 0.5 and 0.7, the model
neither failed at stage 1, nor encountered large failure at stages 2 and 3. The comparison of
displacements under different k0 values are listed in Tables 6.9 and 6.10 for two different
179
boundary conditions, respectively. Figure 6.19 shows the comparison of total displacement
between cases 3(a), 3(b), 4(a), 4(b), 9(a) and 9(b).
Table 6.9 Comparison of displacements under different k0 - A
Displacement,
m
Monitoring point
1 2 3 4 5 6 7
x
Case 3(a) -0.0358 -7.2791 -0.0267 -0.0366 -0.0329 -0.0229 -0.0509
Case 4(a) -0.0466 -10.303 -0.0325 -0.0447 -0.04 -0.0269 -0.0655
Case 9(a) -0.0947 -7.9390 -0.0551 -0.0814 -0.0697 -0.0423 -0.1058
y
Case 3(a) -0.0682 -5.8843 -0.0619 -0.0631 -0.0600 -0.0635 -0.0305
Case 4(a) -0.0837 -13.192 -0.0812 -0.0824 -0.0788 -0.0852 -0.0413
Case 9(a) -0.1530 -13.881 -0.1485 -0.1545 -0.1443 -0.1423 -0.0966
z
Case 3(a) 0.0279 0.6101 0.0500 0.0396 0.0453 0.0411 0.0121
Case 4(a) 0.0370 3.0545 0.0511 0.0435 0.0473 0.0425 0.0176
Case 9(a) 0.0613 1.8432 0.0568 0.0603 0.0550 0.0466 0.0336
Table 6.10 Comparison of displacements under different k0 - B
Displacement,
m
Monitoring point
1 2 3 4 5 6 7
x
Case 3(b) 1.6E-4 4.0E-4 0.0191 0.0067 0.0067 0.0229 -0.0109
Case 4(b) 1.4E-4 2.8E-4 0.0235 0.0081 0.0153 0.0285 -0.0078
Case 9(b) 5.9E-6 -0.0011 0.0197 0.0073 0.0108 0.0184 -0.0127
y
Case 3(b) -0.0530 -0.0489 -0.0588 -0.0535 -0.0536 -0.0648 -0.0238
Case 4(b) -0.0627 -0.0593 -0.0736 -0.0662 -0.067 -0.0845 -0.0297
Case 9(b) -0.1172 -0.1137 -0.1415 -0.1260 -0.1286 -0.1477 -0.0665
z
Case 3(b) 0.0266 0.0236 0.0467 0.0356 0.0410 0.0384 0.0110
Case 4(b) 0.0283 0.0255 0.0478 0.0375 0.0424 0.0393 0.0151
Case 9(b) 0.0578 1.2836 0.0552 0.0576 0.0534 0.0452 0.0304
180
(a) Case 3(a) (b) Case 3(b)
(c) Case 4(a) (d) Case 4(b)
(e) Case 9(a) (f) Case 9(b)
Figure 6.19 Comparison of total displacement among cases 3(a), 3(b), 4(a), 4(b), 9(a),
and 9(b).
In cases 3(a), 4(a) and 9(a), boundary stresses are applied on the right and back sides,
therefore, the x and y displacement values should be negative. These two negative values
increase as the k0 increases from 0.4 to 0.7. In cases 3(b), 4(b) and 9(b), boundary stresses
are applied on the left and back sides, therefore, the x displacement should be positive
181
(except point 1 and 7), while y displacement is still negative. Again the displacement
magnitudes increase with k0.
For cases 3(a) and 3(b), the y-displacement and z-displacement are about the same level no
matter whether the boundary stress is applied on the left or right side. However, the x-
displacement varies very much. It is not sure whether the x-boundary stress should be
applied on the left side boundary or the right side boundary. Therefore, it is difficult to tell
which x-displacement is closer to the reality. Fortunately, the x-displacement is not the
concern of this study. The y-displacement is the important one for the slope stability.
6.6 Field Monitoring Results and Comparison with Numerical Predictions
The field displacement monitoring work of the research area was conducted by the mining
company using a robotic total station. The robotic total station was installed on the crest of
the open pit mine in the southeast corner. Figure 6.20 shows the location of the total station
and the survey targets in the open pit mine. Figures 6.21 and 6.22 show a typical robotic
total station and a monitoring target, respectively.
Figure 6.20 Locations of the robotic total station and the survey targets.
182
Figure 6.21 Shelter for robotic total station at a mine site (Thomas, 2011).
Figure 6.22 A survey target installed on a bench wall (Thomas, 2011).
183
The total station measures the direct distance, called slope distance (DI), from the total
station to each of the targets. The total station can also record the horizontal and vertical
angles of the line between the total station and each target. The principle of measuring the
slope distance, horizontal angle and vertical angle is shown in Figure 6.23.
Figure 6.23 Principle of distance monitoring of a target.
The total station measured each monitoring target every three hours, and all the monitoring
data were stored in a computer. For example, when a target moves from point 1 to point 2
during two measurements as shown in Figure 6.24, the total station measures the slope
distances DI-1 and DI-2 and the corresponding horizontal and vertical angles. The
difference between DI-1 and DI-2 is the measured displacement; however, the true
displacement is very different to the measured displacement in this situation (see Figure
6.24).
North
Elevation
East
monitoring target
total station
slope distance (DI)
vertical angle
horizontal angle
184
Figure 6.24 True displacement and measured displacement.
Figure 6.25 shows the slope distance monitoring data of target #1, and Figure 6.26 shows
the measured displacement of target #1. The field monitoring data are highly fluctuant, so
an average curve was plotted to better reflect the overall trend. The average curve was used
in all other monitoring data. The slope distance from July 2011 to July 2012 has very little
changes, and it is very difficult to estimate the displacement that took place because of the
presence of fluctuations. The accuracy of the total station is at centimeter level for such
long distance measurements; so it is difficult to estimate the small displacement changes
which are less than one centimeter. On the other hand, the x-y-z coordinates of positions 1
and 2 can be calculated using the measured DI, horizontal angle and vertical angle values.
Therefore displacements in x, y, and z directions were calculated. Figure 6.27 shows the
calculated x, y, and z displacements of monitoring target #1.
DI -1
DI-2
total station
1
2
true displacement
measured displacement
185
Figure 6.25 Slope distance of target #1.
Figure 6.26 Measured displacement of target #1.
1679.91
1679.915
1679.92
1679.925
1679.93
1679.935
1679.94
7/1
/20
11
7/1
2/2
01
1
7/2
4/2
01
1
8/5
/20
11
9/1
/20
11
9/1
6/2
01
1
10/4
/201
1
10/1
5/2
011
11/1
/201
1
11/2
1/2
011
12/3
0/2
011
1/2
7/2
01
2
2/7
/20
12
2/1
7/2
01
2
3/1
/20
12
3/1
4/2
01
2
3/2
6/2
01
2
4/6
/20
12
4/1
8/2
01
2
4/2
9/2
01
2
5/1
2/2
01
2
5/2
6/2
01
2
6/1
1/2
01
2
Slo
pe
dis
tan
ce (
DI)
, m
Date
original
monitoring
data
average
value
-0.003
-0.0025
-0.002
-0.0015
-0.001
-0.0005
0
0.0005
0.001
7/1
1/2
01
1
7/2
0/2
01
1
7/3
1/2
01
1
8/1
1/2
01
1
9/6
/20
11
9/1
7/2
01
1
10/4
/201
1
10/1
3/2
011
10/2
5/2
011
11/1
3/2
011
11/2
9/2
011
1/8
/20
12
1/2
8/2
01
2
2/7
/20
12
2/1
5/2
01
2
2/2
6/2
01
2
3/7
/20
12
3/2
0/2
01
2
3/2
8/2
01
2
4/8
/20
12
4/1
8/2
01
2
4/2
7/2
01
2
5/7
/20
12
5/1
9/2
01
2
6/3
/20
12
6/1
5/2
01
2
Dis
pla
cem
ent,
m
Date
186
(a) x-displacement
(b) y-displacement
(c) z-displacement
Figure 6.27 x, y, and z displacement components of monitoring point #1.
-0.16-0.14-0.12-0.1
-0.08-0.06-0.04-0.02
00.020.040.060.080.1
7/1
/201
1
7/1
1/2
011
7/2
0/2
011
7/3
1/2
011
8/1
1/2
011
9/7
/201
1
9/1
7/2
011
10
/4/2
011
10
/13/2
011
10
/25/2
011
11
/13/2
011
12
/2/2
011
1/8
/201
2
1/2
8/2
012
2/7
/201
2
2/1
5/2
012
2/2
6/2
012
3/7
/201
2
3/2
0/2
012
3/2
9/2
012
4/8
/201
2
4/1
8/2
012
4/2
7/2
012
5/7
/201
2
5/2
0/2
012
6/3
/201
2
6/1
5/2
012
x-d
isp
lace
men
t, m
Date
original
data
average
value
-0.07-0.06-0.05-0.04-0.03-0.02-0.01
00.010.020.030.040.05
7/1
/201
1
7/1
1/2
011
7/2
0/2
011
7/3
1/2
011
8/1
1/2
011
9/7
/201
1
9/1
7/2
011
10
/4/2
011
10
/13/2
011
10
/25/2
011
11
/13/2
011
12
/2/2
011
1/8
/201
2
1/2
8/2
012
2/7
/201
2
2/1
5/2
012
2/2
6/2
012
3/7
/201
2
3/2
0/2
012
3/2
9/2
012
4/8
/201
2
4/1
8/2
012
4/2
7/2
012
5/7
/201
2
5/2
0/2
012
6/3
/201
2
6/1
5/2
012
y-d
isp
lace
men
t, m
Date
original
data
average
value
-0.06-0.05-0.04-0.03-0.02-0.01
00.010.020.030.040.050.060.070.080.09
7/1
/201
1
7/1
1/2
011
7/2
0/2
011
7/3
1/2
011
8/1
1/2
011
9/7
/201
1
9/1
7/2
011
10
/4/2
011
10
/13/2
011
10
/25/2
011
11
/13/2
011
12
/2/2
011
1/8
/201
2
1/2
8/2
012
2/7
/201
2
2/1
5/2
012
2/2
6/2
012
3/7
/201
2
3/2
0/2
012
3/2
9/2
012
4/8
/201
2
4/1
8/2
012
4/2
7/2
012
5/7
/201
2
5/2
0/2
012
6/3
/201
2
6/1
5/2
012
z-d
isp
lace
men
t, m
Date
original
data
average
value
187
Estimation of x, y and z displacements have been made based on their field monitoring data.
For example, from Figure 6.27, the estimated value of x-displacement is -0.06 m, y-
displacement is -0.03 m, and z-displacement is 0.02 m. Similar estimations were also made
for other monitoring points (see Appendix C) and all the results are listed in the following
table in comparing with case 3(a) results.
Table 6.11 Estimated values of displacements in x, y, and z directions.
Monitoring
target #
x-displacement, m y-displacement, m z-displacement, m
FM Case 3(a) FM Case 3(a) FM Case 3(a)
1 -0.06 -0.0358 -0.03 -0.068 0.02 0.02787
2 -0.08 -7.2791 -0.03 -5.884 0.05 0.61008
3 -0.04 -0.0267 -0.04 -0.0619 0.01 0.05003
4 -0.03 -0.0366 -0.02 -0.0639 0.02 0.03955
5 -0.05 -0.0329 -0.05 -0.0600 0.03 0.04529
6 -0.05 -0.0229 -0.03 -0.0635 0.02 0.04109
7 -0.04 -0.0509 -0.08 -0.0305 0.03 0.01215
Note:FM-Field monitoring.
Comparison of the values given in the above table with the results from numerical
modeling shows that displacements from both numerical modeling and field monitoring
are in centimeter range. A previous section stated that the computed x displacements are
188
not appropriate to compare with field x displacements due to use of a truncated rock mass
for stress analyses in this study. Because the slope of the study area faces south (opposite
direction to y axis), the important displacements of the rock are in the y and z directions.
Therefore, in the comparison between numerical results and field monitoring results the
focus should be placed on y and z displacements. They seem to agree reasonably well.
189
CHAPTER 7 SUMMARY, CONCLUSIONS AND
RECOMMENDATIONS
Several multiple-bench slope failures had taken place in the south wall of the studied open
pit mine. Therefore, slope stability status in the north wall is a concern where the mining
activities are mainly focused at present and maybe in the future. Under this background, a
comprehensive slope stability study was conducted for a section of this large open pit mine
incorporating field investigations, comprehensive laboratory testing program on intact rock
and discontinuities, remote fracture mapping and estimation of fracture geometry
parameters from the obtained data, estimation of rock mass and fault parameters, building
and validation of a large fault network in 3-D for the first time in the world and performing
numerical modeling in 3-D using a discrete element method and comparing them with
available field monitoring data for the first time in the world.
7.1 Summary and Conclusions
As introduced in the literature review, the traditional analytical methods have the following
main shortcomings and therefore they are not applicable to perform stress and deformation
analysis for large scale investigations of slope stability:
(1) Analytical methods are more suitable to investigate only the kinematics (possible
movement modes) and limit equilibrium conditions (failure or not without any deformation
information) for hard rocks, because both kinematic and block theory analyses are based
on the rigid block assumption.
190
(2) Analytical methods do not have the capability of capturing the deformations resulting
from intersections of a large number of major discontinuities such as faults. The continuum
numerical methods do not have the capability to simulate the detachment of rock blocks
and large displacements and rotations that can occur in discontinuous rock masses.
Therefore, for a rock slope with many major discontinuities, the best choice is to resort to
a discontinuum numerical method. In this study, a three-dimensional (3-D) distinct element
method has been used to investigate the stability of the selected rock slope.
The study of rock slope stability for a large open pit mine with a 3-D discontinuum
numerical method face many challenges as listed below:
(1) Rock mass is composed of intact rocks, minor discontinuities (small scale features) and
major discontinuities (large scale features). It is impossible to simulate all the minor
discontinuities (millions) in a numerical model for a discontinuum rock mass using any
discontinuum numerical method. Therefore, it is necessary to estimate rock mass
mechanical properties combining the effect of intact rock and minor discontinuities. In
doing so, it is necessary to incorporate the effect of minor discontinuity geometry
represented by the number of discontinuity sets, their orientation, size and spacing/intensity
distributions and mechanical properties of intact rock and minor discontinuities. Therefore,
the said rock mass mechanical property estimation is a major challenge.
(2) Major discontinuities, such as faults, control the slope stability of large open pit mines.
Some of these faults terminate on other faults; some others terminate in intact rock.
Therefore, the 3-D fault geometry network is very complex. Due to the difficulty of
building true complicated fault systems in 3DEC software, the previous investigators were
only able to consider very few simple faults or large discontinuities with 3DEC software.
191
Building of complex major discontinuity networks in the 3DEC model and validation of
that is a huge challenge.
(3) It is difficult to determine what boundary conditions should be applied when part of the
open pit mine has been excavated.
(4) Simulation of rock mass excavation with 3DEC software is much more difficult than
with continuum numerical software because model construction capability of 3DEC
software is quite limited.
(5) The user needs to develop an input file as in computer programing (a) to build the
geological system, (b) to assign the appropriate constitutive models and associated material
properties, (c) to apply appropriate boundary conditions, (d) to simulate needed
excavations and (e) to perform stress analyses and collect the needed results in using 3DEC.
Therefore, use of 3DEC is far more difficult than any other software available to perform
stress and deformation analyses.
The rocks in this open pit can be generally divided into Devonian Rodeo Creek (DRC) unit
and Devonian Popovich (DP) formations. DRC unit contains argillite, siltstone and
sandstone; while DP formation contains mostly mud stone. The intact rock properties and
discontinuity properties for both DRC and DP rocks were tested with the rock samples
collected from the mine site. Tensile strength, uniaxial compressive strength, Young’s
modulus, Poisson’s ratio, cohesion, friction angle and Hoek-Brown material constants
were obtained for intact rocks. Joint shear stiffness, joint normal stiffness, cohesion and
friction angle were obtained for joints.
Special survey equipment (Professor Kulatilake owns) which has a total station, laser
scanner and a camera was used to do the remote fracture mapping in the research area.
192
Compared to manual fracture mapping methods, laser scanning method is much efficient,
safe and cost saving when it is used in such a large open pit mine. Manual mapping is not
safe because it requires close contact with bench faces which has rock falls and stability
problems. From field investigations, three discontinuity sets were identified for both DRC
and DP rocks, with two sub-vertical joint sets and one sub-horizontal bedding set. After
comparing the orientation results from laser scanning and manual mapping data provided
by the mining company, it was found that the orientations of the two sub-vertical joint sets
match very well for both DRC and DP rocks. This is an important achievement in this
dissertation compared to what is available in the literature. On the other hand, it was
difficult to obtain a significant number of laser scanning points on sub-horizontal fractures.
Therefore, the field manual mapping results were used for the two sub-horizontal bedding
sets. Joint spacing, joint density and joint size were also calculated using the laser scanning
results in a much refined way in this dissertation compared to what is available in the
literature. .
GSI rock mass quality system was used in this study to estimate the rock mass quality
based on the laser scanning fracture mapping results. Then Hoek-Brown rock mass failure
criterion was adopted here to calculate the rock mass strength parameters using the
estimated GSI values along with the intact rock laboratory test results. Mohr-Coulomb
strength criterion parameters were then calculated based on the estimated Hoek-Brown
failure criterion parameters using several empirical equations. Fault properties and the
DRC-DP contact properties were estimated based on the laboratory discontinuity test
results.
193
A geological model was built in 3DEC model including all the major faults, DRC-DP
contact, and the two stages of rock excavation. The original topography of the mine site,
before any mining activities took place, was obtained from the USGS website. It shows
that the original topography was quit flat with only a small hill and a shallow creek.
Therefore, it was assumed as a flat plane in the numerical modeling. Two excavation stages
were simulated in this study. The first one is the excavation from the original topography
to that of July 2011; the second one is from July 2011 to July 2012. The main purpose of
doing that was to see how the rock slope respond due to the excavation made between July
2011 and July 2012. The original topographies of July 2011 and July 2012 are very
complicated involving more than fifty benches. It was decided that it was not necessary to
simulate the details of all benches because in such a large open pit mine, bench failure may
be allowed as far as it does not block haul roads and threaten mining safety. The main
concern was the inter-ramp failure and over-all failure. Therefore the topographies of July
2011 and July 2012 were simplified. Forty four major faults exist in the research area. Due
to the limited model construction capability of the 3DEC software package, all the faults
were simplified into flat planes and some extension and trimming were made in order to
build them in the 3DEC model. The fault system built in the 3DEC model was compared
with the fault geometry data provided by the mining company using seven cross sections.
Good comparisons were found between them. This was a major accomplishment in this
dissertation because it was done for the first time in the world. The DRC-DP contact is a
quit flat plane, so it was simplified as a flat plane dipping 5 degrees to northwest. Finally,
an integrated numerical model was built with all the faults, topographies, and DRC-DP
contact. Meshes were generated for this integrated model successfully.
194
Numerical modeling was conducted to study the effect of boundary conditions, fault system
and lateral stress ratio on the stability of the considered rock slope. First, it was found that
application of lateral stresses on the four lateral boundaries lead to whole block movement
during unloading stages. Therefore, application of boundary stress condition was modified
to applying a zero velocity boundary on one side and applying boundary stress on the
opposite side. In the y-direction, the front boundary was set to a zero velocity boundary
and stresses were applied on the back boundary. In the x-direction, first, the left boundary
was set to a zero velocity boundary and stresses were applied on the right boundary; as
another option these boundary conditions were switched in the x-direction. Zero velocity
boundary condition was also used for all four lateral boundaries. Under the zero velocity
boundary condition on all four lateral boundaries, the displacements obtained through
numerical modeling were found to be significantly lower than that obtained through field
monitoring data. On the other hand, the stress boundary conditions under the lateral stress
ratios of 0.4 and 0.5 produced displacements comparable to that obtained through field
monitoring data. Therefore, for the considered section of the rock slope, the displacements
obtained through stress boundary conditions were seemed to be more realistic than that
obtained through zero velocity boundary conditions on all four lateral faces.
The effect of faults on the displacement of the seven monitoring points was found to be
small. Most probably this might have occurred due to using rock mass parameter values
which are comparable to the parameter values of faults in the numerical model. As far as
the whole slope is concerned, the model with faults simulated rock mass displacement
behavior more correctly. Thus, it can be concluded that faults are an essential part of the
geological model. Also, it is important to point out that most of the faults strike
195
approximately in the north-south direction compared to the east-west direction. Due to this
the influence of faults on y-displacements will be low compared to that on x-displacement.
In this slope stability problem, y-displacement is the important one and not the x-
displacement. Also note that the dip direction of the DRC-DP contact is towards the rock
mass and not away from the rock mass. This means it has no chance for daylighting and
causing instability as in the south wall.
It was found that for stability of the rock mass the k0 value should be greater than 0.3 and
less than 0.8; outside of this k0 range, the model may collapse in stage 1 or stage 2. Within
the stable region of k0 (0.4 to 0.7), the magnitude of total displacement increases with k0
value. Because the actual rock mass is quite stable, it seems that an appropriate range for
k0 for this rock mass is between 0.4 and 0.7.
The numerical results were compared with field monitoring data which were collected by
a robotic total station. It is important to note that only a portion of the open pit was
considered in the study. Therefore, it considered only a limited section in the x-direction.
It created difficulty in applying appropriate boundary conditions in the x-direction. In
addition the measured values give x-displacements in a global sense. Therefore, it is no
point of comparing x-displacements between numerical results and field measurements.
Note that the slope is dipping south (opposite to y-direction); therefore, the x-displacement
barely affect the slope stability. The y and z displacements from both the numerical
modeling and field monitoring data were found to be in the centimeter level. This
agreement obtained between the numerical results and field deformation monitoring data
in 3-D is a huge success in this dissertation because such a comparison was done for the
first time in the world. This indicates that the numerical modeling can properly simulate
196
the displacement status of the studied slope. From numerical modeling, no block failure
resulted along the DRC-DP contact, which is different from what happened in the south
wall of the pit. The reason for this is the contact is daylighting on the south wall but non-
daylighting on the north wall.
In summary, it was found that the estimated intact rock and discontinuity properties
through laboratory testing, remote fracture mapping, appropriate estimation of rock mass
and fault parameters, the geological structure building techniques and the discrete element
numerical method used in this research were able to simulate the open pit mine slope
stability problems very well. The successful simulation of the rock excavation during a
certain time period indicated the possibility that it can be used to simulate slope stability
status with the expected rock excavation in mine planning.
In conclusion, the research conducted in this dissertation overcame many difficulties that
appear in the literature with respect to rock slope stability analyses using discontinuum
numerical methods. In addition, a comprehensive methodology was developed in this
dissertation that can be used to study any rock slope stability problem in three dimensions.
The detailed contributions that overcame the current limitations are listed in Table 7.1.
197
Table 7.1 Comparison of current limitations and Contributions
The current limitations Contributions to overcoming the
limitations
Analytical methods:
More suitable to investigate only the
kinematics (possible movement modes)
and limit equilibrium conditions (failure
or not without any deformation
information) for hard rocks.
Using discontinuum numerical method
can calculate the stress and displacement
of all the rock blocks.
Cannot capture the deformations
resulting from intersections of a large
number of major discontinuities such as
faults.
Using discontinuum numerical method
can model the deformation of
discontinuities.
Continuum numerical methods:
Cannot simulate the detachment of rock
blocks and large displacements and
rotations that can occur in discontinuous
rock masses
Using discontinuum numerical method
can simulate the detachments and
rotations that occur in discontinuities.
Current discontinuum numerical methods:
Impossible to simulate all the minor
discontinuities (millions) in a numerical
model.
Estimated rock mass mechanical
properties combining the effect of intact
rock and minor discontinuities.
Unable to build complicated real
discontinuities.
Built a complex major discontinuity
network in the 3DEC model and
validated with seven cross sections.
It is difficult to determine what boundary
conditions should be applied when part
of the open pit mine has been excavated
Found out the most suitable boundary
condition and boundary stress ratio
range.
198
7.2 Recommendations
Even though the numerical simulation results were successful, improvements can be done
by conducting the future research recommended below:
(1) First of all, in the laser scanning part, some automatic data processing techniques
may be developed to save time.
(2) In this study, rock mass properties were estimated using the GSI along with Hoek-
Brown failure criterion. Both the GSI and Hoek-Brown failure criterion are based
on empirical charts and equations. These procedures have limited capability and
accuracy. It is recommended to estimate rock mass properties through numerical
modeling by combining discontinuity geometry parameter estimations obtained
through the fracture mapping results with laboratory determined intact rock and
discontinuity properties. Wu and Kulatilake (2012b) have suggested such a
procedure to estimate rock mass properties combining the intact rock and minor
discontinuities. They have received a Peter Cundall (the main developer of 3DEC
software) award in 2013 for this procedure. However, going through that procedure
is a separate Ph.D. dissertation.
(3) Thirdly, due to the limited capability of building geometry features in 3DEC
software, all the topographies and faults were simplified. It is recommended to
build the complex geometries outside 3DEC software using geo-statistics and
advanced interpolation techniques that are available in the literature. These built
complex geometries then can be imported to 3DEC or other discrete element
software to perform stress analyses.
199
(4) Finally, consideration should be given to increase the accuracy of field
displacement monitoring data. It may be possible to achieve this by using more
advanced ground monitoring equipment such as slope stability radar and IBIS radar
system, which provide sub-millimeter accuracy.
200
APPENDIX A – JOINT NORMAL STIFFNESS
Figure A.1 Total deformation and intact rock deformation (DRC-J1).
Figure A.2 Joint deformation vs. Normal stress (DRC-J1).
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 10 20 30 40 50 60 70
Def
orm
atio
n,
mm
Normal stress, MPa
1
1. Intact rock + joint
2. Intact rock
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0 10 20 30 40 50 60 70
Join
t d
efo
rmat
ion, m
m
Normal stress, MPa
201
Figure A.3 The fitted exponential regression curve for the experimental joint deformation
data (DRC-J1).
Figure A.4 JKN vs. Normal stress curve (DRC-J1).
𝜎𝑛 = 0.3956e10.272Dj
R²= 0.9814
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
0.00 0.10 0.20 0.30 0.40 0.50
No
rmal
str
ess
σn,
MP
a
Joint deformation Dj, mm
JKN = 10.272σn
0
20
40
60
80
100
120
0.00 2.00 4.00 6.00 8.00 10.00
JKN
, M
Pa/
mm
Normal Stress σn, MPa
202
Figure A.5 Total deformation and intact rock deformation (DRC-J2).
Figure A.6 Joint deformation vs. Normal stress (DRC-J2)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 10 20 30 40 50 60 70
Def
orm
atio
n,
mm
Normal stress, MPa
1
1. Intact rock + joint
2. Intact rock
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0 10 20 30 40 50 60 70
Join
t def
orm
atio
n, m
m
Normal stress, MPa
203
Figure A.7 The fitted exponential regression curve for the experimental joint deformation
data (DRC-J2).
Figure A.8 JKN vs. Normal stress curve (DRC-J2).
𝜎𝑛 = 0.3611e11.316Dj
R²= 0.984
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
0.00 0.10 0.20 0.30 0.40 0.50
No
rmal
str
ess
σn,
MP
a
Joint deformation Dj, mm
JKN = 11.316σn
0
20
40
60
80
100
120
0.00 2.00 4.00 6.00 8.00 10.00
JKN
, M
Pa/
mm
Normal stress σn, MPa
204
Figure A.9 Total deformation and intact rock deformation (DRC-J3).
Figure A.10 Joint deformation vs. Normal stress (DRC-J3).
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 10 20 30 40 50 60
Def
orm
atio
n,
mm
Normal stress, MPa
1
1. Intact rock + joint
2. Intact rock
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0 10 20 30 40 50 60
Join
t def
orm
atio
n,
mm
Normal stress, MPa
205
Figure A.11 The fitted exponential regression curve for the experimental joint
deformation data (DRC-J3).
Figure A.12 JKN vs. Normal stress curve (DRC-J3).
y = 0.222e9.1895x
R² = 0.9813
0.00
10.00
20.00
30.00
40.00
50.00
60.00
0.00 0.10 0.20 0.30 0.40 0.50 0.60
No
rmal
str
ess
σn,
MP
a
Joint deformation Dj, mm
JKN = 9.1895σn
0
10
20
30
40
50
60
70
80
90
100
0.00 2.00 4.00 6.00 8.00 10.00
JKN
, M
Pa/
mm
Normal stress σn, MPa
206
Figure A.13 Total deformation and intact rock deformation (DRC-J4).
Figure A.14 Joint deformation vs. Normal stress (DRC-J4).
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 10 20 30 40 50 60
Def
orm
atio
n,
mm
Normal stress, MPa
1
1. Intact rock + joint
2. Intact rock
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0 10 20 30 40 50 60
Join
t def
orm
atio
n, m
m
Normal stress, MPa
207
Figure A.15 The fitted exponential regression curve for the experimental joint
deformation data (DRC-J4).
Figure A.16 JKN vs. Normal stress curve (DRC-J4).
σn = 0.6489e9.311Dj
R² = 0.9907
0.00
10.00
20.00
30.00
40.00
50.00
60.00
0.00 0.10 0.20 0.30 0.40 0.50
No
rmal
str
ess
σn,
MP
a
Joint deformation Dj, mm
JKN = 9.311σn
0
10
20
30
40
50
60
70
80
90
100
0.00 2.00 4.00 6.00 8.00 10.00
JKN
, M
Pa/
mm
Normal stress σn, MPa
208
Figure A.17 Total deformation and intact rock deformation (DP-J1).
Figure A.18 Joint deformation vs. Normal stress (DP-J1).
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 20 40 60 80
To
tal d
efo
rmat
ion
, m
m
Normal stress, MPa
1
1. Intact rock + joint
2. Intact rock
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0 20 40 60 80
Join
t d
eform
atio
n,
mm
Normal stress, MPa
209
Figure A.19 The fitted exponential regression curve for the experimental joint
deformation data (DP-J1).
Figure A.20 JKN vs. Normal stress curve (DP-J1).
𝜎𝑛 = 0.7295e15.571Dj
R² = 0.9621
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
No
rmal
str
ess
σn,
MP
a
Joint deformation Dj, mm
JKN = 15.571∙σn
0
20
40
60
80
100
120
140
160
180
0 2 4 6 8 10
JKN
, M
Pa/
mm
Normal stress σn, MPa
210
Figure A.21 Total deformation and intact rock deformation (DP-J2).
Figure A.22 Joint deformation vs. Normal stress (DP-J2).
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 10 20 30 40 50 60 70
Def
orm
atio
n, m
m
Normal stress, MPa
1
1. Intact rock + joint
2. Intact rock
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0 10 20 30 40 50 60 70
Join
t def
orm
atio
n, m
m
Normal stress, MPa
211
Figure A.23 The fitted exponential regression curve for the experimental joint
deformation data (DP-J2).
Figure A.24 JKN vs. Normal stress curve (DP-J2).
𝜎𝑛 = 0.4751e11.221Dj
R²= 0.9849
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
0.00 0.10 0.20 0.30 0.40 0.50
No
rmal
str
ess
σn,
MP
a
Joint deformation Dj, mm
JKN = 11.221∙σn
0
20
40
60
80
100
120
0 2 4 6 8 10
JKN
, M
Pa/
mm
Normal stress σn, MPa
212
Figure A.25 Total deformation and intact rock deformation (DP-J3).
Figure A.26 Joint deformation vs. Normal stress (DP-J3).
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 20 40 60 80
Def
orm
atio
n, m
m
Normal stress, MPa
1
1. Intact rock + joint
2. Intact rock
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 10 20 30 40 50 60 70 80
Join
t d
efo
rmat
ion
, m
m
Normal stress, MPa
213
Figure A.27 The fitted exponential regression curve for the experimental joint
deformation data (DP-J3).
Figure A.28 JKN vs. Normal stress curve (DP-J3).
𝜎𝑛 = 0.9069e14.278Dj
R² = 0.9622
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
0.00 0.05 0.10 0.15 0.20 0.25 0.30
No
rmal
str
ess
σn,
MP
a
Joint deformation Dj, mm
JKN = 14.278σn
0
20
40
60
80
100
120
140
160
0 2 4 6 8 10
JKN
, M
Pa/
mm
Normal stress σn, MPa
214
Figure A.29 Total deformation and intact rock deformation (DP-J4).
Figure A.30 Joint deformation vs. Normal stress (DP-J4).
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 10 20 30 40 50 60 70 80 90
Def
orm
atio
n, m
m
Normal stress, MPa
1
1. Intact rock + joint
2. Intact rock
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 10 20 30 40 50 60 70 80 90
Join
t def
orm
atio
n, m
m
Normal stress, MPa
215
Figure A.31 The fitted exponential regression curve for the experimental joint
deformation data (DP-J4).
Figure A.32 JKN vs. Normal stress curve (DP-J4).
𝜎𝑛 = 0.7229e16.28Dj
R²= 0.9506
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
0.00 0.05 0.10 0.15 0.20 0.25 0.30
No
rmal
str
ess
σn,
MP
a
Joint deformation Dj, mm
JKN = 16.28σn
0
20
40
60
80
100
120
140
160
180
0.00 2.00 4.00 6.00 8.00 10.00
JKN
, M
Pa/
mm
Normal stress σn, MPa
216
Figure A.33 Total deformation and intact rock deformation (DP-J5).
Figure A.34 Joint deformation vs. Normal stress (DP-J5).
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 10 20 30 40 50 60 70 80
Def
orm
atio
n, m
m
Normal stress, MPa
1
1. Intact rock + joint
2. Intact rock
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 10 20 30 40 50 60 70 80
Join
t def
orm
atio
n, m
m
Normal stress, MPa
217
Figure A.35 The fitted exponential regression curve for the experimental joint
deformation data (DP-J5).
Figure A.36 JKN vs. Normal stress curve (DP-J5).
𝜎𝑛 = 0.8856e14.789Dj
R²= 0.9611
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
0.00 0.05 0.10 0.15 0.20 0.25 0.30
No
rmal
str
ess
σn,
MP
a
Joint deformation Dj, mm
JKN = 14.789σn
0
20
40
60
80
100
120
140
160
0.00 2.00 4.00 6.00 8.00 10.00
JKN
, M
Pa/
mm
Normal stress σn, MPa
218
Figure A.37 Total deformation and intact rock deformation (DP-J6).
Figure A.38 Joint deformation vs. Normal stress (DP-J6).
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 10 20 30 40 50 60 70 80 90
Def
orm
atio
n, m
m
Normal stress, MPa
1
1. Intact rock + joint
2. Intact rock
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 10 20 30 40 50 60 70 80 90
Join
t def
orm
atio
n, m
m
Normal stress, MPa
219
Figure A.39 The fitted exponential regression curve for the experimental joint
deformation data (DP-J6).
Figure A.40 JKN vs. Normal stress curve (DP-J6).
𝜎𝑛 = 0.4895e17.117Dj
R²= 0.9631
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
0.00 0.05 0.10 0.15 0.20 0.25 0.30
No
rmal
str
ess
σn,
MP
a
Joint deformation Dj, mm
JKN = 17.117σn
0
20
40
60
80
100
120
140
160
180
0.00 2.00 4.00 6.00 8.00 10.00
JKN
, M
Pa/
mm
Normal stress σn, MPa
220
Figure A.41 Total deformation and intact rock deformation (DRC-DP-J1).
Figure A.42 Joint deformation vs. Normal stress (DRC-DP-J1).
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 10 20 30 40
Def
orm
atio
n,
mm
Normal stress, MPa
1
1. Intact rock + joint
2. Intact rock
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0 5 10 15 20 25 30 35
Join
t def
orm
atio
n,
mm
Normal stress, MPa
221
Figure A.43 The fitted exponential regression curve for the experimental joint
deformation data (DRC-DP-J1).
Figure A.44 JKN vs. Normal stress curve (DRC-DP-J1).
σn = 0.3638e9.4604Dj
R² = 0.9531
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
0.00 0.10 0.20 0.30 0.40 0.50
No
rmal
str
ess
σn,
MP
a
Joint deformation Dj, mm
JKN = 9.4604σn
0
20
40
60
80
100
120
0.00 2.00 4.00 6.00 8.00 10.00
JKN
, M
Pa/
mm
Normal stress σn, MPa
222
Figure A.45 Total deformation and intact rock deformation (DRC-DP-J2).
Figure A.46 Joint deformation vs. Normal stress (DRC-DP-J2).
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 10 20 30 40 50 60 70 80
Def
orm
atio
n,
mm
Normal stress, MPa
1
1. Intact rock + joint
2. Intact rock
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0 10 20 30 40 50 60 70 80
Join
t def
orm
atio
n, m
m
Normal stress, MPa
223
Figure A.47 The fitted exponential regression curve for the experimental joint
deformation data (DRC-DP-J2).
Figure A.48 JKN vs. Normal stress curve (DRC-DP-J2).
σn = 0.1086e15.144Dj
R²= 0.9856
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
0.00 0.10 0.20 0.30 0.40 0.50
No
rmal
str
ess
σn,
MP
a
Joint deformation Dj, mm
JKN = 15.144σn
0
20
40
60
80
100
120
140
160
0.00 2.00 4.00 6.00 8.00 10.00
JKN
, M
Pa/
mm
Normal stress σn, MPa
224
Figure A.49 Total deformation and intact rock deformation (DRC-DP-J3).
Figure A.50 Joint deformation vs. Normal stress (DRC-DP-J3).
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 10 20 30 40 50
Def
orm
atio
n,
mm
Normal stress, MPa
1
1. Intact rock + joint
2. Intact rock
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0 10 20 30 40 50
Join
t def
orm
atio
n, m
m
Normal stress, MPa
225
Figure A.51 The fitted exponential regression curve for the experimental joint
deformation data (DRC-DP-J3).
Figure A.52 JKN vs. Normal stress curve (DRC-DP-J3).
σn = 0.5587e10.339Dj
R²= 0.9845
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
45.00
0.00 0.10 0.20 0.30 0.40 0.50
No
rmal
str
ess
σn,
MP
a
Joint deformation Dj, mm
JKN = 10.339σn
0
20
40
60
80
100
120
0.00 2.00 4.00 6.00 8.00 10.00
JKN
, M
Pa/
mm
Normal stress σn, MPa
226
Figure A.53 Total deformation and intact rock deformation (DRC-DP-J4).
Figure A.54 Joint deformation vs. Normal stress (DRC-DP-J4).
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 10 20 30 40 50 60
Def
orm
atio
n,
mm
Normal stress, MPa
1
1. Intact rock + joint
2. Intact rock
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0 10 20 30 40 50 60
Join
t def
orm
atio
n, m
m
Normal stress, MPa
227
Figure A.55 The fitted exponential regression curve for the experimental joint
deformation data (DRC-DP-J4).
Figure A.56 JKN vs. Normal stress curve (DRC-DP-J4).
σn = 0.2171e11.305Dj
R² = 0.911
0.00
10.00
20.00
30.00
40.00
50.00
60.00
0.00 0.10 0.20 0.30 0.40 0.50
Norm
al s
tres
s σ
n, M
Pa
Joint deformation Dj, mm
JKN = 11.305σn
0
20
40
60
80
100
120
0.00 2.00 4.00 6.00 8.00 10.00
JKN
, M
Pa/
mm
Normal stress σn, MPa
228
APPENDIX B – JOINT SHEAR STIFFNESS
Figure B.1 Fitted linear regression line for JKS vs. normal stress data (DRC #1).
Figure B.2 Fitted linear regression line for JKS vs. normal stress data (DRC #2).
JKS = 0.77σn
R²= 0.9764
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
JKS = 1.2641σn
R²= 0.9467
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
229
Figure B.3 Fitted linear regression line for JKS vs. normal stress data (DRC #3).
Figure B.4 Fitted linear regression line for JKS vs. normal stress data (DRC #4).
JKS = 0.6624σn
R²= 0.9395
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
JKS = 1.7072σn
R²= 0.9037
0
0.4
0.8
1.2
1.6
2
2.4
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
230
Figure B.5 Fitted linear regression line for JKS vs. normal stress data (DRC #5).
Figure B.6 Fitted linear regression line for JKS vs. normal stress data (DRC #6).
JKS = 1.2972σn
R²= 0.9858
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
JKS = 0.9246σn
R²= 0.9343
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
231
Figure B.7 Fitted linear regression line for JKS vs. normal stress data (DRC #7).
Figure B.8 Fitted linear regression line for JKS vs. normal stress data (DRC #8).
JKS = 0.9276σn
R²= 0.9602
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
JKS = 0.9346σn
R²= 0.8644
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
232
Figure B.9 Fitted linear regression line for JKS vs. normal stress data (DRC #9).
Figure B.10 Fitted linear regression line for JKS vs. normal stress data (DRC #10).
JKS = 0.9573σn
R²= 0.977
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
JKS = 1.3372σn
R²= 0.942
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
233
Figure B.11 Fitted linear regression line for JKS vs. normal stress data (DRC #11).
Figure B.12 Fitted linear regression line for JKS vs. normal stress data (DRC #12).
JKS = 1.5957σn
R²= 0.9719
0
0.5
1
1.5
2
2.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
JKS = 0.705σn
R²= 0.9294
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
234
Figure B.13 Fitted linear regression line for JKS vs. normal stress data (DRC #13).
Figure B.14 Fitted linear regression line for JKS vs. normal stress data (DRC #14).
JKS = 1.1497σn
R²= 0.9473
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1
JKS, M
Pa/
mm
Normal stress σn, MPa
JKS = 0.9424σn
R²= 0.9212
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
JKS, M
Pa/
mm
Normal stress σn, MPa
235
Figure B.15 Fitted linear regression line for JKS vs. normal stress data (DP #1).
Figure B.16 Fitted linear regression line for JKS vs. normal stress data (DP #2).
JKS = 1.1472σn
R²= 0.8473
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
JKS = 1.2732σn
R²= 0.9926
0
0.5
1
1.5
2
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
236
Figure B.17 Fitted linear regression line for JKS vs. normal stress data (DP #3).
Figure B.18 Fitted linear regression line for JKS vs. normal stress data (DP #4).
JKS = 0.7869σn
R²= 0.7988
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
JKS, M
Pa/
mm
Normal stress σn, MPa
JKS = 0.9736σn
R² = 0.8441
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
237
Figure B.19 Fitted linear regression line for JKS vs. normal stress data (DP #5).
Figure B.20 Fitted linear regression line for JKS vs. normal stress data (DP #6).
JKS = 1.0541σn
R² = 0.9365
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
JKS = 0.653σn
R² = 0.977
0
0.5
1
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
238
Figure B.21 Fitted linear regression line for JKS vs. normal stress data (DP #7).
Figure B.22 Fitted linear regression line for JKS vs. normal stress data (DP #8).
JKS = 0.8823σn
R² = 0.7853
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
JKS = 1.5963σn
R² = 0.979
0
0.5
1
1.5
2
2.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
239
Figure B.23 Fitted linear regression line for JKS vs. normal stress data (DP #9).
Figure B.24 Fitted linear regression line for JKS vs. normal stress data (DP #10).
JKS = 1.3752σn
R² = 0.8959
0
0.5
1
1.5
2
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
JKS = 0.8247σn
R² = 0.9556
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
240
Figure B.25 Fitted linear regression line for JKS vs. normal stress data (DP #11).
Figure B.26 Fitted linear regression line for JKS vs. normal stress data (DP #12).
JKS = 1.3071σn
R² = 0.9389
0
0.5
1
1.5
2
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
JKS = 0.5171σn
R² = 0.9918
0
0.5
1
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
241
Figure B.27 Fitted linear regression line for JKS vs. normal stress data (DP #13).
Figure B.28 Fitted linear regression line for JKS vs. normal stress data (DRC-DP #1).
JKS = 0.8476σn
R² = 0.8975
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
JKS = 1.1234σn
R² = 0.9916
0
0.4
0.8
1.2
1.6
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
242
Figure B.29 Fitted linear regression line for JKS vs. normal stress data (DRC-DP #2).
Figure B.30 Fitted linear regression line for JKS vs. normal stress data (DRC-DP #3).
JKS = 0.7382σn
R² = 0.9336
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
JKS = 1.1497σn
R² = 0.9473
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1
JKS, M
Pa/
mm
Normal stress σn, MPa
243
Figure B.31 Fitted linear regression line for JKS vs. normal stress data (DRC-DP #4).
Figure B.32 Fitted linear regression line for JKS vs. normal stress data (DRC-DP #5).
JKS = 1.1228σn
R² = 0.9916
0
0.4
0.8
1.2
1.6
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
JKS = 0.823σn
R² = 0.9879
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4
JKS, M
Pa/
mm
Normal stress σn, MPa
244
APPENDIX C – FIELD MONITORING DISPLACEMENT
Figure C.1 Displacements of field mentoring point 1.
-0.16-0.14-0.12
-0.1-0.08-0.06-0.04-0.02
00.020.040.060.08
0.1
x-d
isp
lace
men
t, m
Date
Original data
Average line
-0.07-0.06-0.05-0.04-0.03-0.02-0.01
00.010.020.030.040.05
y-d
isp
lace
men
t, m
Date
Original data
Average line
-0.06-0.05-0.04-0.03-0.02-0.01
00.010.020.030.040.050.060.070.080.09
z-d
isp
lace
men
t, m
Date
Original data
Average line
245
Figure C.2 Displacements of field mentoring point 2.
-0.15-0.14-0.13-0.12-0.11-0.1
-0.09-0.08-0.07-0.06-0.05-0.04-0.03-0.02-0.01
00.010.020.030.040.050.06
x-d
isp
lace
men
t, m
Date
Original data
Average line
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
y-d
isp
lace
men
t, m
Date
Original data
Average line
-0.04-0.03-0.02-0.01
00.010.020.030.040.050.060.070.080.09
0.10.110.12
z-d
isp
lace
men
t, m
Date
Original data
Average line
246
Figure C.3 Displacements of field mentoring point 3.
-0.12
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
x-d
isp
lace
men
t, m
Date
Original data
Average line
-0.09-0.08-0.07-0.06-0.05-0.04-0.03-0.02-0.01
00.010.020.030.040.050.060.07
y-d
isp
lace
men
t, m
Date
Original data
Average line
-0.08-0.07-0.06-0.05-0.04-0.03-0.02-0.01
00.010.020.030.040.050.060.070.08
z-d
isp
lace
men
t, m
Date
Original data
Average line
247
Figure C.4 Displacements of field mentoring point 4.
-0.12
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
x-d
isp
lace
men
t, m
Date
Original data
Average line
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
y-d
isp
lace
men
t, m
Date
Original data
Average line
-0.06-0.05-0.04-0.03-0.02-0.01
00.010.020.030.040.050.060.070.08
z-d
isp
lace
men
t, m
Date
Original data
Average line
248
Figure C.5 Displacements of field mentoring point 5.
-0.14
-0.12
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
x-d
isp
lace
men
t, m
Date
Original data
Average line
-0.09-0.08-0.07-0.06-0.05-0.04-0.03-0.02-0.01
00.010.020.030.040.05
y-d
isp
lace
men
t, m
Date
Original data
Average line
-0.06-0.05-0.04-0.03-0.02-0.01
00.010.020.030.040.050.060.070.08
z-d
isp
lace
men
t, m
Date
Original data
Average line
249
Figure C.6 Displacements of field mentoring point 6.
-0.14
-0.12
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
x-d
isp
lace
men
t, m
Date
Original data
Average line
-0.09-0.08-0.07-0.06-0.05-0.04-0.03-0.02-0.01
00.010.020.030.040.050.060.07
y-d
isp
lace
men
t, m
Date
Original data
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Figure C.7 Displacements of field mentoring point 7.
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