rock slope stability investigations in...

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.

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Link to Item http://hdl.handle.net/10150/338701

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


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


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


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 5.23 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


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


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.6 Joint deformation vs. Normal stress (DRC-J2) ............................................ 202


data (DRC-J2). ................................................................................................................ 203

Figure A.8 JKN vs. Normal stress curve (DRC-J2). ....................................................... 203


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


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


deformation data (DP-J1). ............................................................................................... 209

Figure A.20 JKN vs. Normal stress curve (DP-J1). ........................................................ 209



14

























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


deformation data (DRC-DP-J1). ..................................................................................... 221

Figure A.44 JKN vs. Normal stress curve (DRC-DP-J1). .............................................. 221

15

















Figure B.1 Fitted linear regression line for JKS vs. normal stress data (DRC #1). ........ 228









Figure B.10 Fitted linear regression line for JKS vs. normal stress data (DRC #10). .... 232



16




Figure B.15 Fitted linear regression line for JKS vs. normal stress data (DP #1). ......... 235









Figure B.24 Fitted linear regression line for JKS vs. normal stress data (DP #10). ....... 239




Figure B.28 Fitted linear regression line for JKS vs. normal stress data (DRC-DP #1). 241





Figure C.1 Displacements of field mentoring point 1..................................................... 244







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

http://apps.webofknowledge.com.ezproxy2.library.arizona.edu/OneClickSearch.do?product=UA&search_mode=OneClickSearch&excludeEventConfig=ExcludeIfFromFullRecPage&SID=2COq2uhxQJiYbM1Jn86&field=AU&value=Azizabadi,%20HRM

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


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


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


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


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


85

Table 3.13 Obtained joint shear stiffness values for interfaces between DRC and DP

rocks


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


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


Manual 157 67 244


Manual 371 16 39

DP-set 1 Remote 87 65 182

Manual 106 68 165


Manual 213 68 253


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):

121

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

122

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)

123

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

124

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.

125

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.

126

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

127

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.

128

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.

131

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.

132

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.

134

(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.

137

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

139

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




142




143




144




145




146




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.

150

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.

152

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.

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(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

163

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

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Table 6.6 Comparison of displacement values between case 1(a) and case 7

Monitoring

point


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


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


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 #


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.


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


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


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


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


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.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


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


data (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


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


204



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


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


deformation data (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


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


206



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


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


deformation data (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


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


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


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


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


JKN = 15.571∙σn

0

20

40

60

80

100

120

140

160

180

0 2 4 6 8 10

JKN

, M

Pa/

mm


210



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


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




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


JKN = 11.221∙σn

0

20

40

60

80

100

120

0 2 4 6 8 10

JKN

, M

Pa/

mm


212



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


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




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


JKN = 14.278σn

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10

JKN

, M

Pa/

mm


214



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


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




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


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


216



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


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




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


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


218



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


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




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


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


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


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


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


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


222



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


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




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


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


224



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


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




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


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


226



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


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




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


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


228

APPENDIX B – JOINT SHEAR STIFFNESS

Figure B.1 Fitted linear regression line for JKS vs. normal stress data (DRC #1).


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


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


229



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


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


230



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


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


231



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


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


232



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


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


233



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


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


234



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


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


235

Figure B.15 Fitted linear regression line for JKS vs. normal stress data (DP #1).


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


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


236



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


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


237



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


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


238



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


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


239



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


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


240



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


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


241


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


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


242



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


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


243



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


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


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


-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


-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


-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


-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


-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

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

250


-0.16

-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

-0.18

-0.16

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

y-d

isp

lace

men

t, m

Date

Original data

Average line

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

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lace

men

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Original data

Average line

251

REFERENCES

ASTM, 2008a. ASTM D2113-08 Standard Practice for Rock Core Drilling and Sampling

of Rock for Site Investigation, ASTM International, West Conshohocken, PA.

ASTM, 2008b. ASTM D3967-08 Standard Test Method for Splitting Tensile Strength of

Intact Rock Core Specimens, ASTM International, West Conshohocken, PA.

ASTM, 2008c. ASTM D5607-08 Standard Test Method for Performing Laboratory Direct

Shear Strength Tests of Rock Specimens Under Constant Normal Force, ASTM

International, West Conshohocken, PA.

ASTM, 2014. ASTM D7012-14 Standard Test Methods for Compressive Strength and

Elastic Moduli of Intact Rock Core Specimens under Varying States of Stress and

Temperatures, ASTM International, West Conshohocken, PA.

Azizabadi, H.R.M., Mansouri, H., and Fouche, O., 2014. Coupling of two methods,

waveform superposition and numerical, to model blast vibration effect on slope stability in

jointed rock masses. Computers and Geotechnics, 61: 42-49.

Behbahani, S.S., Moarefvand, P., Ahangari, K., and Goshtasbi, K., 2013. Measuring

displacement and contact forces among the particles in unloading of slope by PFC2D

(particle flow code). Achives of Mining Sciences, 58(2): 495-504.

Brideau, A.M., and Stead, D., 2011. The influence of three-dimensional kinematic controls

on rock slope stability. Continuum and Distinct Element Numerical Modeling in

Geomechanics-2011, Paper: 04-05, Itasca International Inc., Minneapolis.

Brummer, K.R., Li, H., and Moss, A., 2013. The transition from open pit to underground

mining: an unusual slope failure mechanism at Palabora. International Symposium on

Stability of Rock Slopes in Open Pit Mining and Civil Engineering, The South African

Institute of Mining and Metallurgy.

Cala, M., 2007. Convex and concave slope stability analyses with numerical methods.

Archives of Mining Sciences, 52(1): 75-89.

Cai, M., Kaiser, P.K., Uno, H., Tasaka, Y., and Minami, M., 2004. Estimation of rock mass

deformation modulus and strength of jointed hard rock masses using the GSI system.

International Journal of Rock Mechanics and Mining Sciences, 41: 3-19.

Chen, J.H., Kang, L.X., and Yang, S.S., 2007. Analysis of open pit slope under excavation

unloading. Mine Hazards Prevention and Control Technology, 311-317.

http://apps.webofknowledge.com.ezproxy2.library.arizona.edu/OneClickSearch.do?product=UA&search_mode=OneClickSearch&excludeEventConfig=ExcludeIfFromFullRecPage&SID=2COq2uhxQJiYbM1Jn86&field=AU&value=Mansouri,%20H

http://apps.webofknowledge.com.ezproxy2.library.arizona.edu/OneClickSearch.do?product=UA&search_mode=OneClickSearch&excludeEventConfig=ExcludeIfFromFullRecPage&SID=2COq2uhxQJiYbM1Jn86&field=AU&value=Fouche,%20O

252

Cundall, P.A., 1971. A computer model for simulating progressive large-scale movements

in blocky rock system. Proc. Symp. Int. Rock Mech., 2(8): 129.

Cundall, P. A., and Strack, O. D. L., 1979. A Discrete Numerical Model for Granular

Assemblies. Geotechnique, 29: 47-65.

Cundall, P.A., 1988. Formulation of a three-dimensional distinct element model-Part 1. A

scheme to detect and represent contacts in a system composed of many polyhedral blocks.

Int. J. Rock. Mech. Min. Sci. & Geomech. Abstr., 25: 107-116.

Desai, C.S., 1982. Constitutive modeling and soil-structure interaction. Numerical

Methods in Geomechanics, 103-143.

Farny, N.J., 2012. Field Methods of Measuring Discontinuities for Rock Slope Stability

Analysis on Price Mountain, VA. Master Thesis, Purdue University, West Lafayette.

Firpo, G., Salvini, R., Francioni, M., and Ranjith, G.P., 2011. Use of digital terrestrial

photogrammetry in rocky slope stability analysis by distinct elements numerical methods.

International Journal of Rock Mechanics & Mining Sciences 48 (2011): 1045-1054.

Fu, Y.H., and Dong, L.J., 2010. Range of rock movement in transition from open pit to

underground mining determined by numerical method. Science & Technology Review,

28(4): 74-79.

Gheibie, S., and Duzgun, S.H.B., 2013. Probabilistic-numerical modeling of stability of a

rock slope in Amasya-Turkey. 47-th US Rock Mechanics/Geomechanics Symposium, San

Francisco, CA, USA.

Goodman, R. E., 1964. The resolution of stresses in rock using stereographic projection.

Int. J. Rock Mech. Mining Sci., 1(1): 93-103.

Goodman, R. E. and Bray, J., 1976. Toppling of rock slopes. ASCE, Proc. Specialty Conf.

on Rock Eng. for Foundations and Slopes, Boulder, CO, 2: 201-34.

Goodman, E. R., and Shi, G.H, 1985. Block Theory and its Application to Rock

Engineering. Prentice-Hall.

Goodman, R., 1989. Introduction to Rock Mechanics. John Wiley & Sons.

Hart, R., Cundall, P.A., and Lemos, J., 1988. Foundation of a three dimensional distinct

element model-Part II. Mechanical calculations for motion and interaction of a system

composed of many polyhedral blocks. Int. J. Rock. Mech. Min. Sci. & Geomech. Abstr.,

25: 117-126.

253

Hencher, S.R., Liao, Q.H., and Monaghan, B.G., 1996. Modelling slope behaviour for

open-pits. Transactions of the Institution of Mining and Metallurgy Section A-Mining

Industry, 105: A37-47.

Hibert, C., Ekstrom, G. and Stark, P. C., 2014. Dynamics of the Bingham Canyon mine

landslides from seismic signal analysis. Geophysical Research Letters. 41(13): 4535-4541.

Hocking, G., 1976. A method for distinguishing between single and double plane sliding

of tetrahedral wedges. Int. J. Rock. Mech. Min. Sci. & Geomech. Abstr., 13(7): 225–226.

Hoek E., Bray, J., 1981. Rock Slope Engineering, Revised third edition. E & FN SPON.

Hoek, E., 1994. Strength of rock and rock masses. ISRM News Journal, 2(2): 4-16.

Hoek, E., Kaiser, P.K. and Bawden. W.F., 1995. Support of Underground Excavations in

Hard Rock. Rotterdam: Balkema.

Hoek E. and Brown E.T., 1997. Practical estimates of rock mass strength. International

Journal of Rock Mechanics and Mining Sciences, 34(8): 1165-1186.

Hoek E., Carranza-Torres, C.T. and Corkum, B., 2002. Hoek-Brown failure criterion-2002

edition. Proceedings of the 5th North American Rock Mechanics Symposium, Toronto,

Canada 1: 267-73.

Hoek, E., 2007. Practical Rock Engineering, Rocscience.

Hu, Y., and Kempfert, G.H., 1999. Numerical simulation of the buckling failure in rock

slopes. Proceedings of the International Symposium on Slope Stability Engineering,

Matsuyama, Shikoku, Japan.

Islam, M.R., and Faruque, M.O., 2013. Optimization of slope angle and its seismic stability:

a case study for the proposed open pit coal mine in Phulbari, NW Bangladesh. Journal of

Mountain Science, 10(6): 976-986.

Itasca, 2007. 3DEC 3 Dimensional Distinct Element Code User’s Guide. Itasca Consulting

Group Inc.

Itasca, 2009. FLAC 3D Fast Lagrangian Analysis of Continua in 3 Dimensions User’s

Guide. Itasca Consulting Group Inc.

Jing, L., 2003. A review of techniques, advances and outstanding issues in numerical

modelling for rock mechanics and rock engineering. Int. J. Rock. Mech. Min. Sci., 40: 283-

353.

Jiang, Q.Q., 2009. Strength reduction method for slope based on a ubiquitous-joint criterion

and its application. Mining Science and Technology, 19(4): 0452-0456.

254

John, K. W., 1970. Engineering analysis of three dimensional stability problems utilizing

the reference hemisphere. Proc. 2nd Int. Cong. Int. Soc. Rock Mech., Belgrade, 2: 314-321.

Kemeny, J., Turner, K., and Norton, B., 2006. LiDAR for rRock mass characterization:

hardware, software, accuracy and best-practices. Laser and Photogrammetric Methods for

Rock Face Characterization workshop, Golden, CO, American Rock Mechanics

Association, 49-62.

Kemeny, J., and Turner, T., 2008. Ground Based LiDAR Rock Slope Mapping and

Assessment. Lakewood, CO: Central Federal Lands Highway Division, Federal Highway

Administration, U.S. Department of Transportation.

Kleber, A., and Terhorst, B., 2013. Mid-Latitude Slope Deposits (Cover Beds), Elsevier,

Amsterdam, Oxford, Burlington, San Diego.

Kulatilake, P.H.S.W., and Wu, T.H., 1984a. Sampling bias on orientation of discontinuities.

Rock Mechanics and Rock Engineering, 17: 243-254.

Kulatilake, P.H.S.W., and Wu, T.H., 1984b. Estimation of mean trace length of

discontinuities. Rock Mechanics and Rock Engineering, 17: 215-232.

Kulatilake, P.H.S.W., and Wu, T.H., 1984c. The density of discontinuity traces in sampling

windows. Int. Jour. of Rock Mechanics and Mining Sciences, 21: 345-347.

Kulatilake, P.H.S.W., and Fuenkajorn, K., 1987. Factor of safety of tetrahedral wedges: a

probabilistic study. Int. Journal of Surface Mining, 1(2): 147-154.

Kulatilake, P.H.S.W., 1988. Minimum rock bolt force and minimum static acceleration in

tetrahedral wedge stability: a probabilistic study. Int. Journal of Surface Mining, 2(1):19-

26.

Kulatilake, P.H.S.W., Wu, T.H., and Wathugala, D.N., 1990. Probabilistic modeling of

joint orientation. Int. Journal for Numerical and Analytical Methods in Geomechanics,

14:325-350.

Kulatilake, P.H.S.W., Wuthagala, D.N. and Stephansson, O., 1993. Joint network

modelling, including a validation to an area in stripa mine, Sweden. International Journal

of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 30(5): 503-526.

Kulatilake, P.H.S.W., Chen, J., Teng, J., Shufang, X. and Pan, G., 1996. Discontinuity

geometry characterization for the rock mass around a tunnel close to the permanent

shiplock area of the Three Gorges dam site in China. Int. J. Rock Mech. and Min. Sci., 33:

255-277.

255

Kulatilake, P.H.S.W., Um, J., Wang, M., Escandon, R.F., and Narvaiz, J., 2003. Stochastic

fracture geometry modeling in 3-D including validations for a part of arrowhead east tunnel

site, California, USA. Int. Jour. of Engineering Geology, 70(1-2): 131-155.

Kulatilake, P.H.S.W., Park, J., Um, J., 2004. Estimation of rock mass strength and

deformability in 3-D for a 30 m cube at a depth of 485 m at Aspo Hard Rock Laboratory.

Geotechnical and Geological Engineering, 22: 313-330.

Kulatilake, P.H.S.W., Wang, L., Tang, H. and Liang, Y., 2011. Evaluation of rock slope

stability for Yujian river dam site by kinematic and block theory analyses. Computers and

Geotechnics, 38: 846-860.

Lemos, J.V., Hart, R.D., and Cundall, P.A., 1985. A generalized distinct element program

for modeling jointed rock mass. Proc. Symp. On Fundamentals of Rock Joints, Bjorkliden,

Sweden, 335-343.

Li, H., and Speight, H.E., 1997. Analysis of progressive failure of a mine slope in a western

Australian open-pit gold mine. Deformation and Progressive Failure in Geomechanics-IS-

NAGOYA 97, 467-472.

Li, H.Z., Yang, T.H., Xia, D., and Zheng, C., 2013. Slope stability analysis based on soft-

rock rheological characteristics. Journal of Northeastern University, Natural Science, 34(2):

293-296.

Lorig, L., 1999. Lessons learned from slope stability studies. FLAC and Numerical

Modeling in Geomechanics, 17-21.

Markland, J. T., 1972. A useful technique for estimating the stability of rock slopes when

the rigid wedge sliding type of failure is expected. Imperial College Rock Mechanics

Research Report No. 19.

Meng, H.D., Xu, Y., and Zang, D.Y., 2013. The failure mode analysis of open pit slope

based on finite element method. Applied Mechanics and Materials, 405-408: 35-39.

Muller, L., 1968. New considerations of the Vaiont slide. Felsmechanik und

engenieurgeologie, 6 (1), 1-91.

Palmstrom A., 1995. RMi-A Rock Mass Characterization System for Rock Engineering

Purposes. PhD thesis, University of Oslo, Norway.

Park, H., 1999. Risk Analysis of Rock Slope Stability and Stochastic Properties of

Discontinuity Parameters in Western North Carolina. PhD. Dissertation, Purdue University,

West Lafayette.

Piteau, D. R., and Martin, D. C., 1977. Detail Line Engineering Geology Mapping Method

Field Manual. West Vancouver, B.C.: D. R. Piteau and Associates Limited.

256

Priest, S. D., and Hudson, J. A., 1981. Estimation of discontinuity spacing and trace length

using scanline surveys. Int. J. of Rock Mechanics and Mining Sciences and Geomechanics

Abstracts, 18 (3): 183-197.

Priest, S. D., 1993. Discontinuity Analysis for Rock Engineering. London: Chapman and

Hall.

Read, J., and Stacey, P., 2009. Guidelines for Open Pit Slope Design. CSIRO Publishing.

Ren, G.F., and Fang, X.K., 2010. Study on the law of the movement and damage to slope

with the combination of underground mining and open-pit mining. Engineering, 2(3): 201-

204.

Rio Tinto Kennecott, 2013. Bingham Canyon Mine-9 layers of protection. Kennecott.com

Roman, M.W., and Johnson, E.R., 2011. Application of Digital Photogrammetry to Rock

Cut Slope Design. Harrisburg, PA.

Sainsbury, D.P., Pierce, M.E., and Lorig, L.J., 2003. Two- and three-dimensional

numerical analysis of the interaction between open pit slope stability and remnant

underground voids. Fifth Large Open Pit Mine Conference: Harnessing Technology by

Managing Data and Information, 2003(7): 251-257.

Sainsbury, D.P., Pothitos, F. Finn, D. and Silva, R., 2007. Three-dimensional discontinuum

analysis of structurally controlled failure mechanism at the Cadia Hill open pit.

Proceedings of International Symposium on Rock Slope Stability in Open Pit Mining and

Civil Engineering, 163-168, Perth, Australian Centre for Geomechanics.

Shi, G.H., and Goodman, R.E., 1985. Two dimensional discontinuous deformation

analysis. International Journal for Numerical and Analytical Methods in

Geomechanics, 9(6): 541-556.

Shi, G.H., 1988. Discontinuous Deformation Analysis---A New Model for the Statics and

Dynamics of Block Systems. Ph. D. thesis, University of California, Berkeley.

Shi, G.H., 1990. Forward and backward discontinuous deformation analysis of rock block

systems. Proceedings of the International Conference on Rock Joints, Loen, Norway, 731-

743. ISRM. Balkema, Rotterdam.

Shi, G.H., 1993. Block System Modeling by Discontinuous Deformation

Analysis. Computation Mechanics Publications, Southampton, UK.

Shi, G.H., 1995. Working Forum on the Manifold Method of Material Analysis. Technical

Report, US Army Corps of Engineers, US Army Corps of Engineers Waterways

Experiment Station, Vicksburg, MS.

257

Shi, G.H., 1996. Discontinuous Deformation Analysis of Block Systems. Technical Report,

US Army Engineer Waterways Experiment Station, 3909 Halls Ferry Road, Vicksburg,

MS 39180.

Shi, G.H., 2001. Three dimensional discontinuous deformation analysis. Proceedings of

the 38th U.S. Rock Mechanics Symposium, American Rock Mechanics Association,

Washington D.C., 1421-1428.

Silva, C.H.C., Lana, M.S., Pereira, L.C., and Lopes, M.D., 2008. Slope stability of

Cachorro Bravo open pit through numerical modeling by finite element method. Rem-

Revista Escola De Minas, 61(3): 323-327.

Sjoberg, J., 1999. Analysis of the Aznalcollar pit slope failures-a case study. FLAC and

Numerical Modeling in Geomechanics, 63-70.

Tan, W.H., Kulatilake, P.H.S.W. and Sun, H., 2014a. Influence of an inclined rock stratum

on in-situ stress state in an open-pit mine. Geotechnical and Geological Engineering, 32

(1): 31-42.

Tan, W.H., Kulatilake, P.H.S.W., Sun, H.B., Sun, Z.H., 2014b. Effect of faults on in-situ

stress state in an open pit mine. Electronic Journal of Geotechnical Engineering, 19: 9597-

9629.

Thomas, Huw Gareth, 2011. Slope Stability Prism Monitoring: A Guide for Practising

Mine Surveyors. Master thesis, University of Witwatersrand, Johannesburg, South Africa.

Twiss R.J. and Moores E.M., 1992. Structural Geology, W.H.Freeman and Company, New

York, NY.

Um, J., and Kulatilake, P.H.S.W., 2001. Kinematic and block theory analyses for shiplock

slopes of the Three Gorges Dam site in China. Int. Jour. Geotechnical and Geological

Engineering, 19: 21-42.

USGS. http://www.usgs.gov/.

Vyazmensky, A., Stead, D., Elmo, D., and Moss, A., 2010. Numerical analysis of block

caving-induced instability in large open pit slopes: a finite element/discrete element

approach. Rock Mechanics and Rock Engineering, 43(1): 21-39.

Wathugala, D.N., Kulatilake, P.H.S.W., Wathugala, G.W., and Stephansson, O., 1990. A

general procedure to correct sampling bias on joint orientation using a vector approach.

Computers and Geotechnics, 10:1-31.

Wu, J.H., and Chen, C.H., 2011. Application of DDA to simulate characteristics of the

Tsaoling landslide. Computers and Geotechnics 38 (5): 741-750.

http://www.usgs.gov/

258

Wu, Q., Kulatilake, P.H.S.W., and Tang H.M., 2011. Comparison of rock discontinuity

mean trace length and density estimation methods using discontinuity data from an outcrop

in Wenchuan area, China. Computers and Geotechnics, 38(2): 258-268.

Wu, Q., and Kulatilake, P.H.S.W., 2012a. Application of equivalent continuum and

discontinuum stress analyses in three-dimensions to investigate stability of a rock tunnel

in a dam site in China. Computers and Geotechnics, 46: 48-68.

Wu, Q. and Kulatilake, P.H.S.W. 2012b. REV and its properties on fracture system and

mechanical properties, and an orthotropic constitutive model for a jointed rock mass in a

dam site in China. Computers and Geotechnics, 43: 124-142.

Wyllie, D. and Mah, C., 2004. Rock Slope Engineering, Civil and mining, 4th edition. Spon

Press, Taylor & Francis Group.

Yan, M., 2008. Numerical Modelling of Brittle Fracture and Step-Path Failure: from

Laboratory to Rock Slope Scale. PhD Dissertation, Simon Fraser University, Canada.

Zarnani, S., Sriskandakumar, S., Arenson, L.U., and Seto, J.C.T., 2012. The use of FLAC

software for assessing deformation rates during ice excavation for open pit mining in

glaciers. Proceedings of the 15th International Specialty Conference on Cold Regions

Engineering, 705-714. ASCE, Quebec City, QC, Canada.

Zhao, H.J., Ma, F.S., Xu, J.M., Guo, J., and Yuan, G.X., 2014. Experimental investigations

of fault reactivation induced by slope excavations in China. Bulletin of Engineering

Geology and the Environment, 73(3): 891-901.

Zheng, J., Kulatilake, P.H.S.W., Shu, B., Sherizadeh, T. and Deng, J., 2014. Probabilistic

block theory analysis for a rock slope at an open pit mine in USA. Computers and

Geotechnics, 61: 254-265.

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