UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Bayesian Belief network approach to slope management in British Columbia open pits Nunoo, Samuel 2016

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
24-ubc_2016_May_Nunoo_Samuel.pdf [ 5.08MB ]
Metadata
JSON: 24-1.0300348.json
JSON-LD: 24-1.0300348-ld.json
RDF/XML (Pretty): 24-1.0300348-rdf.xml
RDF/JSON: 24-1.0300348-rdf.json
Turtle: 24-1.0300348-turtle.txt
N-Triples: 24-1.0300348-rdf-ntriples.txt
Original Record: 24-1.0300348-source.json
Full Text
24-1.0300348-fulltext.txt
Citation
24-1.0300348.ris

Full Text

 BAYESIAN BELIEF NETWORK APPROACH TO SLOPE MANAGEMENT IN BRITISH COLUMBIA OPEN PITS  by  Samuel Nunoo  B.Sc., University of Mines and Technology, 2004 M.Sc., New Mexico Institute of Mining and Technology, 2009   A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF  THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  in  THE COLLEGE OF GRADUATE STUDIES  (CIVIL ENGINEERING) THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan)   April 2016  © Samuel Nunoo The undersigned certify that they have read, and recommend to the College of Graduate Studies for acceptance, a thesis entitled:   Bayesian Belief Network Approach to Slope Management in British Columbia Open Pits Submitted by  Samuel Nunoo  in partial fulfillment of the requirements of The degree of   Doctor of Philosophy  . Dr. Dwayne D. Tannant, School of Engineering Supervisor, Professor (please print name and faculty/school above the line) Dr. Solomon Tesfamariam, School of Engineering Supervisory Committee Member, Professor (please print name and faculty/school in the line above) Dr. Sumi Siddiqua, School of Engineering Supervisory Committee Member, Professor (please print name and faculty/school in the line above) Dr. Davide Elmo, NBK Institute of Mining Engineering University Examiner, Professor (please print name and faculty/school in the line above) Dr. John P. Harrison, W.M. Keck Chair of Engineering Rock Mechanics, Lassonde Institute of Mining, Dept. of Civil Engineering, University of Toronto External Examiner, Professor (please print name and university in the line above) April 21, 2016 (Date submitted to Grad Studies) Abstract The stability of rock slopes is a major safety issue in open pit mining. It is important for rock engineers and mine operators to be knowledgeable about their pit wall behaviour, and, more specifically, to recognize appropriate conditions that trigger the need to issue warnings or stop work orders. With the current increase in the number of open pit mines in British Columbia and the deepening of existing pits, there is a need for rational, scientifically based decisions in response to measured pit wall performance. The main objective of this research was to develop and establish a Bayesian Belief Network (BBN) model and outline appropriate operational responses to manage slopes in large open pit porphyry mines.  The BBN model can be tailored to specific geotechnical conditions and pit wall configurations. The research integrated available geotechnical engineering data and knowledge, including expert knowledge, ground water conditions, slope geometry, mining activity (blast damage), and consequences of failure, into one platform that can establish appropriate operational responses. A range of pre-defined actions ranging from normal pit operations to orders to stop work and evacuate the pit were defined in this research as operational responses or pit management decisions. These operational responses were linked in the BBN model to predicted states of pit wall movement and estimates of the consequences of these movements. A new relationship was proposed to estimate the travel distance from a wide range of pit slope failure debris volumes. The relationship accounts for a potential rockslide transforming into a rock avalanche. The BBN model was used to retroactively predict the appropriate operational response at four mines to using data from past slope instabilities. The results indicate that equipment damage as well as production losses could have been minimized or prevented had the BBN model been used by the mine operators at the time of each slope instability. The methodology described in the thesis provides the foundation for an innovative tool for the selection of appropriate operational responses linked to measured slope velocity, potential rockslide debris volume, and potential travel distance of the debris. iii Preface This research was conducted under the supervision of Dr. Dwayne D. Tannant. No lab experiment was performed. All data collected were based on visits to BC mine operations, interviews conducted, mine incident reports, consulting reports, and completed questionnaires obtained from mine operators. The thesis is the independent work of the author, Mr. Samuel Nunoo. A workshop was also organised as a means to gather expert knowledge and available data. The questionnaire involved in the study and the workshop were approved by the UBCO Behavioural Research Ethics Board (BREB) with a BREB certificate number of H13-00908. The following are papers published during the PhD study: • Nunoo, S., Tannant, D. D., & Newcomen, H. W. 2015. Slope monitoring practices at open pit porphyry mines in British Columbia, Canada. International Journal of Mining, Reclamation and Environment, 30(3), 245-256. http://doi.org/10.1080/17480930.2015.1038865 • Zheng, W., Zhuang, X., Tannant, D. D., Cai, Y., & Nunoo, S. 2014. Unified continuum/discontinuum modeling framework for slope stability assessment. Engineering Geology, 179, 90–101. doi:10.1016/j.enggeo.2014.06.014 • Nunoo, S., Tannant, D. D., & Newcomen, W. 2014. Current practices for slope monitoring at British Columbia’s open pit porphyry mines. In CIM 2014 Convention. Vancouver, Canada: CIM. iv Table of Contents Abstract .......................................................................................................................................... iii Preface............................................................................................................................................ iv Table of Contents ............................................................................................................................ v List of Tables ................................................................................................................................. ix List of Figures ............................................................................................................................... xii Acknowledgement ....................................................................................................................... xvi Dedication ................................................................................................................................... xvii Chapter 1: Introduction ............................................................................................................... 1 1.1 Motivation ........................................................................................................................ 1 1.2 Research objectives .......................................................................................................... 5 1.3 Research approach............................................................................................................ 6 1.4 Contribution and originality ............................................................................................. 7 1.5 Limitations of the research ............................................................................................... 8 Chapter 2: Open Pit Porphyry Mines in BC ............................................................................. 10 2.1 Copper/molybdenum mines in BC ................................................................................. 10 2.2 Porphyry ore deposits ..................................................................................................... 11 2.3 Pit wall and bench geometry .......................................................................................... 12 2.4 Lessons learnt from open pit instabilities ....................................................................... 14 2.5 Pit wall displacement monitoring ................................................................................... 16 Chapter 3: Risk Assessment Methods Related to Open Pit Slope Management ...................... 19 3.1 Overview of risk ............................................................................................................. 19 3.2 Risk assessment methods ............................................................................................... 21 3.2.1 Fault tree analysis ................................................................................................... 21 3.2.2 Event tree analysis .................................................................................................. 22 3.2.3 Failure mode and effect analysis............................................................................. 22 3.2.4 Bayesian Belief Network ........................................................................................ 23 3.2.4.1 Bayesian Belief Networks used in other disciplines ....................................... 29 3.2.4.2 Bayesian Belief Network software packages .................................................. 31 3.3 Proposed Bayesian Belief Network................................................................................ 34 3.3.1 Data analysis ........................................................................................................... 35 3.3.1.1 Data used for conditional probability tables .................................................... 38 Chapter 4: Geotechnical Properties and Slope Geometry ........................................................ 44 v 4.1 Rock unit weight ............................................................................................................ 44 4.2 Vertical in situ stress ...................................................................................................... 44 4.3 Horizontal to vertical stress ratio ................................................................................... 46 4.3.1 Stress associated with open pit rock slopes ............................................................ 47 4.4 Ground water .................................................................................................................. 49 4.5 Uniaxial compressive strength ....................................................................................... 52 4.6 Rock quality designation ................................................................................................ 53 4.7 Discontinuity spacing ..................................................................................................... 54 4.8 Discontinuity conditions ................................................................................................ 55 4.9 Shear strength of critical discontinuities ........................................................................ 56 4.10 Geological Strength Index (GSI) ................................................................................ 57 4.11 Blast damage............................................................................................................... 60 4.12 Rock mass strength ..................................................................................................... 61 4.13 Rock mass modulus .................................................................................................. 65 4.14 Slope geometry ........................................................................................................... 67 4.14.1 Slope height ............................................................................................................ 67 4.14.2 Overall slope angle ................................................................................................. 68 4.14.3 Pit wall shape .......................................................................................................... 69 Chapter 5: Pit Wall Failure Modes and Travel Distance/Reach ............................................... 70 5.1 Plane sliding ................................................................................................................... 71 5.2 Wedge sliding ................................................................................................................. 73 5.3 Toppling ......................................................................................................................... 75 5.4 Rotational failure ............................................................................................................ 76 5.5 Potential failure and debris volumes .............................................................................. 77 5.6 Slope velocity ................................................................................................................. 80 5.6.1 Strain ....................................................................................................................... 85 5.7 Travel distance / reach.................................................................................................... 86 5.7.1 Rock bulking and spreading.................................................................................... 87 5.7.1.1 Estimation of travel distance angle via reach .................................................. 90 5.7.2 Rock avalanches...................................................................................................... 92 5.7.3 Proposed relationship for travel distance angle ...................................................... 95 Chapter 6: Consequences of Pit Wall Failure ........................................................................... 99 6.1 Harm to personnel (HTP) ............................................................................................... 99 vi 6.2 Equipment damage (ED) .............................................................................................. 102 6.3 Production loss (PL) ..................................................................................................... 105 Chapter 7: Sensitivity Analysis, Operational Response and Scenario Analysis .................... 108 7.1 Sensitivity analysis ....................................................................................................... 108 7.2 Operational Responses and Scenario Analysis ............................................................ 115 7.2.1 Operational response for normal pit production ................................................... 116 7.2.2 Operational response for work with caution ......................................................... 117 7.2.3 Operational response for minimize work and plan evacuation ............................. 119 7.2.4 Operational response for stop work and evacuate ................................................ 119 7.3 Decision node with scenario analysis........................................................................... 120 7.3.1 Decision node........................................................................................................ 120 7.3.2 BBN model scenario analysis ............................................................................... 122 Chapter 8: Case Studies .......................................................................................................... 127 8.1 Overview ...................................................................................................................... 127 8.2 Case 1 – HVC mine ...................................................................................................... 127 8.3 Case 2 – Endako mine .................................................................................................. 132 8.4 Case 3 – Huckleberry mine .......................................................................................... 138 8.5 Case 4 – Copper Mountain mine .................................................................................. 143 8.6 Case 5 – Gibraltar mine ................................................................................................ 146 Chapter 9: Conclusions and Recommendations ..................................................................... 148 9.1 Summary ...................................................................................................................... 148 9.2 Ground water ................................................................................................................ 150 9.3 Travel distance ............................................................................................................. 151 9.4 Slope velocity ............................................................................................................... 152 9.5 Consequence of failure ................................................................................................. 152 9.6 Operational response .................................................................................................... 153 9.7 Recommendations ........................................................................................................ 154 References ................................................................................................................................... 155 Appendix A: Pit wall management questionnaire ........................................................ 177 Appendix B: Conditional probability table .................................................................. 183 Appendix C: Mining conditions at open pit mines in BC ............................................ 186 C.1 Copper Mountain mine .................................................................................. 186 C.2 Huckleberry mine .......................................................................................... 188 vii C.3 Endako mine .................................................................................................. 189 C.4 Mount Polley mine ........................................................................................ 191 C.5 Highland Valley Copper ................................................................................ 193 C.6 Gibraltar mine ................................................................................................ 197 Appendix D: Open pit instability case histories ........................................................... 200 D.1 Kemess South mine ....................................................................................... 200 D.2 Brenda mine ................................................................................................... 201 D.3 Afton mine ..................................................................................................... 202 D.4 Highland Valley Copper mine ....................................................................... 203 D.5 Copper Mountain mine .................................................................................. 204 D.6 Endako mine .................................................................................................. 205 D.7 Gibraltar mine ................................................................................................ 206 Appendix E: BBN analysis results ............................................................................... 209 Appendix F: Results obtained from the case studies ................................................... 213 viii List of Tables Table 2-1. General pit geometries as of 2013 (Nunoo et al. 2015) ............................................... 11 Table 2-2. Data summary of case histories presented in Appendix D .......................................... 15 Table 2-3. Monitoring frequency for typically used instrumentation (Nunoo et al. 2015) .......... 18 Table 3-1. Geotechnical properties and slope geometry parameters ............................................ 37 Table 3-2. Pit wall instability characteristics ................................................................................ 37 Table 3-3. Consequences of failure .............................................................................................. 38 Table 3-4. CPT for “Vertical in situ stress” node ......................................................................... 40 Table 3-5. CPT for “Equipment damage” node ............................................................................ 42 Table 4-1. Rock unit weight states ................................................................................................ 44 Table 4-2. Vertical in situ stress states .......................................................................................... 45 Table 4-3. Snap shot of CPT for "Vertical in situ stress" node .................................................... 46 Table 4-4. Stress ratio states ......................................................................................................... 47 Table 4-5. Ground water condition states ..................................................................................... 50 Table 4-6. UCS states (ISRM 1981) ............................................................................................. 52 Table 4-7. RQD states (Deere 1968)............................................................................................. 54 Table 4-8. Discontinuity spacing states (Bieniawski 1976) .......................................................... 55 Table 4-9. Discontinuity condition states (Bieniawski 1976) ....................................................... 56 Table 4-10. Friction angle states ................................................................................................... 57 Table 4-11. GSI and RMR states .................................................................................................. 58 Table 4-12. Estimating disturbance factor D (Hoek 2002; Hoek et al. 2002) .............................. 61 Table 4-13. Material property, s states.......................................................................................... 62 Table 4-14. Snap shot of CPT for “Material property, s” node .................................................... 63 Table 4-15. Material property, a states ......................................................................................... 63 Table 4-16. CPT for “Material property, a” node ......................................................................... 64 Table 4-17. RMS states ................................................................................................................. 64 Table 4-18. Snap shot of CPT for “RMS” node ........................................................................... 65 Table 4-19. Rock mass modulus states ......................................................................................... 66 Table 4-20. CPT for “Rock mass modulus” node......................................................................... 67 Table 4-21. Slope height states ..................................................................................................... 68 Table 4-22. Slope angle states ...................................................................................................... 68 Table 5-1. Snap shot of CPT for “Plane sliding” node ................................................................. 73 ix Table 5-2. Snap shot of CPT for “Wedge sliding” node ............................................................... 74 Table 5-3. Snap shot of CPT for “Rotational failure” node .......................................................... 77 Table 5-4. Rockslide debris volume states ................................................................................... 79 Table 5-5. CPT for “Debris volume” node ................................................................................... 79 Table 5-6. Slope velocity states .................................................................................................... 82 Table 5-7. Snap shot of CPT for “Slope velocity” node ............................................................... 84 Table 5-8. CPT for “Prism data” node .......................................................................................... 85 Table 5-9. Strain states .................................................................................................................. 86 Table 5-10. Snap shot of CPT for “Strain” node .......................................................................... 86 Table 5-11. Volume generated (plunge of 40°) to estimate Reach and travel distance angle ...... 90 Table 5-12. Volume generated (plunge of 49°) to estimate Reach and travel distance ................ 90 Table 5-13. Vertical to horizontal distance ratio (Travel distance) .............................................. 97 Table 5-14. CPT for "Travel distance" node ................................................................................ 98 Table 5-15. Range of debris volumes used for the respective pit depths ..................................... 98 Table 6-1. States and description used for harm to personnel (MABC and Worksafe BC 2015) ....................................................................................................................... 100 Table 6-2. CPT for “Equipment operator” node ......................................................................... 101 Table 6-3. CPT for “Non-equipment operator” node ................................................................. 101 Table 6-4. Snap shot of CPT for “Harm to personnel” node ...................................................... 102 Table 6-5. States and description used for equipment damage ................................................... 104 Table 6-6. Equipment incident information extracted from BC chief inspector of mines ......... 104 Table 6-7. Snap shot of “Equipment damage” node ................................................................... 105 Table 6-8. States and description used for production loss ........................................................ 106 Table 6-9. Snap shot of CPT for “Production loss” node ........................................................... 107 Table 7-1. Node states for scenario analysis for the proposed model ........................................ 124 Table 8-1. Summary of Nov. 22, 2012 instability at the SE wall of the Valley pit .................... 129 Table 8-2. Summary of failure event at the southeast wall in 2007 ........................................... 132 Table 8-3. Summary of details of June 2007 event at the east zone north wall .......................... 140 Table 8-4. Summary of November 4, 2011 failure event at the Stage 2 east wall ..................... 143 Table A-1. Location, geometry, size and impact on operations ................................................. 181 Table A-2. Movement rate thresholds and failure size ............................................................... 181 Table A-3. Geomechanical information ..................................................................................... 181 Table A-4. Conditional probability table used to determine RMR in the BBN model .............. 183 x Table A-5. Description of geologic structures ............................................................................ 189 Table A-6. Blasting techniques ................................................................................................... 198 Table A-7. Bench geometry ........................................................................................................ 199 Table A-8. Sensitivity analysis data of Harm to personnel node ................................................ 209 Table A-9. Sensitivity analysis data of Equipment damage node .............................................. 210 Table A-10. Sensitivity analysis data of Production loss node ................................................... 211 Table A-11. Sensitivity analysis data of Slope velocity node .................................................... 212 Table A-12. HVC mine case study results with respective probabilities (Beliefs) .................... 213 Table A-13. Endako mine case study results with respective probabilities (Beliefs) ................. 215 Table A-14. Huckleberry mine case study results with respective probabilities (Beliefs) ......... 217 Table A-15. Copper Mountain mine case study results with respective probabilities (Beliefs). 219 Table A-16. Gibraltar mine case study results with respective probabilities (Beliefs) .............. 221  xi List of Figures Figure 1-1. Components used in the research to define the appropriate operational responses ..... 8 Figure 2-1. Operating open pit copper/molybdenum mines in BC (Nunoo et al. 2015) .............. 10 Figure 2-2.Geometry of an open pit slope .................................................................................... 13 Figure 3-1. Simple BBN framework (modified from Cockburn and Tesfamariam (2012)) ........ 27 Figure 3-2. BBN operation flow chart .......................................................................................... 28 Figure 3-3. Bayesian Network example ........................................................................................ 29 Figure 3-4. Graphic user interface of Netica ................................................................................ 32 Figure 3-5. Proposed Bayesian Belief Network model framework to manage open pit slopes ... 43 Figure 4-1. Factors used to determine vertical stress in the BBN ................................................ 45 Figure 4-2. 2D relaxed zone within open pit walls resulted from mining .................................... 48 Figure 4-3. Moist to saturated ground water condition at Highland Valley Copper mine (photo taken 2013) .................................................................................................... 51 Figure 4-4. Dry ground water condition at Copper Mountain mine (photo taken 2013) .............. 51 Figure 4-5. Strength grades (Golder Associates 2007, 2009a) ..................................................... 53 Figure 4-6. RQD data obtained from Gibraltar and Endako mines (Golder Associates 2007, 2009a) ........................................................................................................................ 54 Figure 4-7. Factors used to determine RMR in the BBN ............................................................. 58 Figure 4-8. Predicted GSI based on RMR for BC mines .............................................................. 59 Figure 4-9. CPT data of RMR with no data from parent node ..................................................... 60 Figure 4-10. Factors used to determine rock mass strength in the BBN ...................................... 61 Figure 4-11. Factors used to determine rock mass modulus in the BBN ..................................... 66 Figure 4-12. Plan view of an open pit showing the various pit wall shapes ................................. 69 Figure 5-1. Failure modes in open pit mines: (a) large-scale wedge failure, (b) large-scale plane failure, (c) bench-scale wedge failure, (d) circular failure of intensely fractured and weathered rock along major fault zones - revised from Deere & Patton (1971) by (Gayer et al. 1995) ......................................................................... 70 Figure 5-2. Multi-bench plane sliding at Endako mine (photo taken in 2013) ............................. 72 Figure 5-3. Factors used to determine plane sliding in the BBN .................................................. 72 Figure 5-4. Factors used to determine wedge sliding in the BBN ................................................ 73 Figure 5-5. Multi-bench wedge sliding at Copper Mountain mine Pit 3 west wall with wedge failures outlined in red (photo taken in 2013) ........................................................... 74 Figure 5-6. Large scale toppling at Highland Valley Copper mine Lornex Pit west wall (photo taken in 2013) ................................................................................................ 75 xii Figure 5-7. Rotational failure (Hoek and Bray 1981) ................................................................... 76 Figure 5-8. Factors used to determine rotational failure in the BBN............................................ 76 Figure 5-9. Pit wall used to create a wall profile to generate volumes of failed rock mass ......... 78 Figure 5-10. Factors used to determine potential debris volumes in the BBN ............................. 79 Figure 5-11. Factors used to determine the slope velocity in the BBN ........................................ 81 Figure 5-12. Factor used to determine prism data ........................................................................ 83 Figure 5-13 Factors used to determine strain in the BBN ............................................................ 85 Figure 5-14. Geometry of the failed rock mass (after Gibson et al. 2006) ................................... 88 Figure 5-15. Symmetric wedges plotted on an equal-angle stereonet .......................................... 89 Figure 5-16. Shape of a wedge obtained from two joints ............................................................. 89 Figure 5-17. Estimating travel distance angle using reach (drawn to scale) ................................ 91 Figure 5-18. Rock avalanche that occurred at the Bingham Canyon mine, showing elevation of the crest and toe of the slide, and the extent to which the failed volume traveled (modified from Pankow et al. 2014) ........................................................... 93 Figure 5-19. Schematic diagram used to estimate the travel distance of the failed rock mass ..... 94 Figure 5-20. Data used to establish a relationship for estimating travel distance angle as a function of deposit volume; comparison of the Bingham Canyon rock avalanche (green and red circles, and black triangle) with reported landslide events from Bourrier et al. (2013) ................................................................................................. 96 Figure 5-21. Factor used to determine travel distance in the BBN ............................................... 97 Figure 5-22. Travel distance versus volume based on proposed relationship for different pit depths ........................................................................................................................ 98 Figure 6-1. Factors used to determine harm to personnel (HTP) in the BBN ............................ 100 Figure 6-2. Factors used to determine equipment damage in the BBN ...................................... 104 Figure 6-3. Factors used to determine production loss in the BBN ............................................ 106 Figure 7-1. Proposed BBN model framework with trained data ................................................ 109 Figure 7-2. Sensitivity analysis conducted for “Harm to personnel” node with respect to other nodes in the BBN model ......................................................................................... 112 Figure 7-3. Sensitivity analysis conducted for “Equipment damage” node with respect to other nodes in the BBN model ................................................................................ 112 Figure 7-4. Sensitivity analysis conducted for “Production loss” node with respect to other nodes in the BBN model ......................................................................................... 113 Figure 7-5. Sensitivity analysis conducted for “Slope velocity” node with respect to other nodes (excluding Consequences of Pit Wall Failure nodes) ................................... 113 Figure 7-6. Proposed model framework with decision node (Operational response) ................. 121 xiii Figure 7-7. Results of poor conditions leading to an operational response node in the BBN model ....................................................................................................................... 122 Figure 7-8. Results of typical dry conditions of nodes leading to an operational response node in the BBN model ................................................................................................... 123 Figure 7-9. Results of typical wet conditions of nodes leading to an operational response node in the BBN model ........................................................................................... 123 Figure 7-10. Results of typical good conditions to an operational response node in the BBN model ....................................................................................................................... 126 Figure 8-1. Front view of toppling instability with debris outlined in black (Highland Valley Copper 2013). The red dash line is the approximate location of the vertical cross section shown in Figure 8-2 .................................................................................... 128 Figure 8-2. Approximate profile of the Valley pit east wall used to measure travel distance (drawn to scale) ....................................................................................................... 128 Figure 8-3. BBN model framework with inputted data for incident at HVC mine in 2012 ....... 131 Figure 8-4. Location of multiple bench failure outlined in red at Endako mine (photo taken in 2013); black dashed line is the approximate location of the cross section shown in Figure 8-7 ............................................................................................................ 133 Figure 8-5. Equipment damaged during the incident (Wojdak 2008) ........................................ 133 Figure 8-6. Approximate area of instability outlined in red (July 2007 image obtained from Google Earth) .......................................................................................................... 134 Figure 8-7. Approximate profile of the southeast pit wall used to measure travel distance (drawn to scale) ....................................................................................................... 135 Figure 8-8. BBN model famework with inputted data for 2007 incident at Endako mine ......... 137 Figure 8-9. East zone wall failure outlined in yellow at the Huckleberry mine (photo taken on June 22, 2007); red dash line is the approximate location of the cross section shown in Figure 8-12 .............................................................................................. 138 Figure 8-10. East zone wall failure at Huckleberry mine (side view) (Wojdak 2008) ............... 139 Figure 8-11. Approximate area of instability and the horizontal distance outlined in red (2015 image obtained from Google Earth); note the lower part of the debris has been buried in tailings or waste rock in this image ......................................................... 139 Figure 8-12. Approximate profile of the northwall used to measure travel distance (triple bench and drawn to scale) ....................................................................................... 141 Figure 8-13. BBN model framework with inputted data for 2007 incident at Huckleberry mine ......................................................................................................................... 142 Figure 8-14. Aproximate profile of Stage 2 east pit wall used to measure the travel distance (drawn to scale) ....................................................................................................... 144 Figure 8-15. BBN model famework with inputted data for November 4, 2011 incident at Copper Mountain mine ........................................................................................... 145 xiv Figure 8-16. Predicting operational response using data obtained after a daily routine check for the Gibraltar mine .............................................................................................. 147 xv Acknowledgement I would like to express my sincere appreciation to Dr. Dwayne D. Tannant for providing guidance, insight, and support throughout the course of this research. Additionally, I specially thank him for the opportunity he gave to study and believing in my abilities. His constructive comments and suggestions throughout my research studies have made a significant contribution to the success of this research. I offer my enduring gratitude to the faculty, and staff at the UBC Okanagan Campus School of Engineering. I would also like to acknowledge Natural Sciences and Engineering Research Council of Canada (NSERC)’s support for this research work. I owe particular thanks to Mr. Warren H. Newcomen of BGC Engineering, whose invaluable suggestions and mentorship gave me broad understanding of my research. Special thank you to my advisory committee, Drs. Solomon Tesfamariam and Sumi Siddiqua for the insight and suggestions provided on this research. I also want to express my gratitude to Wenbo Zheng and Dr. H.Q. Zhang (visiting professor from China) who encouraged, as well as guided me in different ways that I cannot fathom. Special thanks are owed to my wife, children and parents for all their love, patience, and encouragement. They are the key source of inspiration for all my achievements. I am also thankful to those who indirectly contributed in this research, your kindness means a lot to me. xvi Dedication This thesis is dedicated to God Almighty for making it possible to complete my PhD degree program. “It is not of him that wills or of him that runs but it is the Lord the shows mercy”, Romans 9:16. I also dedicate this degree my lovely wife Mrs. Josephine Nunoo and children, my parents Maxwell Nunoo and Dora Nunoo, my brothers Moses Nunoo and Joshua Ahenakwah Nunoo and my one and only sister Mrs. Mary Otoo.  xvii Chapter 1: Introduction 1.1 Motivation The process of excavating a deep open pit induces rock mass movements in the pit walls. The stability of rock slopes (i.e. pit walls) is a major safety issue in open pit mining. If pit wall slope movements are monitored appropriately and interpreted correctly, it is often possible to predict impending large-scale pit wall failures. The prediction can prevent loss of equipment, mineable ore, and loss of life incidence (Brox and Newcomen 2004; Osasan and Afeni 2010). The magnitude of pit wall movements generated during mining is often a function of the pit geometry, rock mass quality, pore pressures in the rock mass, and the in situ stresses. It is important for rock engineers and mine operators to be knowledgeable about their pit wall behaviour, and, more specifically, to recognize appropriate operational response that trigger the need to issue warnings or stop work orders. With the current increase in the number of open pit mines in British Columbia (BC) and the deepening of existing pits, there is a need for rational, scientifically-based decisions in response to measured or predicted pit wall performance. Monitoring pit wall movements in open pit mines yields data that can be used to assure production and management officials on issues regarding slope stability of the pit walls; it also aids in identifying areas of the pit that are unstable (Osasan and Afeni 2010). The surveying and monitoring techniques used to measure slope movements have improved steadily over the past few decades. The data collected can help practitioners resolve and mitigate slope stability issues (Jarosz and Wanke 2003). Unfortunately, decision makers at the mines often have difficulty interpreting the significance of measured deformations. The challenge is to interpret the trends and magnitudes of the measured displacements in such a way that meaningful decisions are made and appropriate and timely operational responses are implemented that will minimize production disruptions while ensuring the safety of the workplace. Mistakes in the interpretation of pit wall displacements can be costly (tens of millions of dollars) and can create the potential for loss of life. Moreover, during harsh conditions (e.g. fog), monitoring instruments cannot get accurate readings from the routine daily shots of the pit wall taken by the instruments. Therefore, during such conditions most mines do not use their instrumentation to monitor the performance of the slope. Engineers and other personnel responsible for checking and informing mine management about the pit wall performance do not conduct any slope monitoring during harsh weather. 1 However, frequent routine checks are done by driving into the pit to see how the pit walls are doing. The research methodology presented in this research will provide firsthand information about the pit wall to engineers or personnel responsible, even, giving mine management appropriate recommendations when the sites are experiencing harsh conditions.  Pit walls failures have occurred where pit production and management personnel did not receive any appropriate warning. This might have resulted from faulty data reading by instrumentation or from lack of pit wall monitoring pit operations. In addition, earlier pit wall movements may not have been measured, or measured movements might have been ignored or misinterpreted. Due to these issues, rock engineers and researchers worldwide have been investigating cost effective and accurate ways to help minimize open pit slope failures that lead to production loss, damage to equipment and/or harm to personnel. Researchers have explored techniques to gain a better understanding of the ground movements in open pits and the usefulness of predictions made from monitored movements. Often the research focused on identifying changes in the movement behaviour; for example, acceleration in movements (Voight 1988, 1989; Cruden and Masoumzadeh 1987). Attempts have been made to relate movements to the size of the pit wall and rock mass quality (Brox and Newcomen 2004). Prediction of the failure time is often the main goal once a potential volume of unstable rock mass has been identified and various interpretation techniques have been proposed. Examples of  the techniques are inverse-velocity method (Fukuzono 1985; Rose and Hungr 2007), slope (gradient) method (Mufundirwa et al. 2010), and the percent deformation method (Dick et al. 2014). None of the researchers has considered the mining activity in the pit as a factor that also influences the slope velocity as well as the operational responses. Although these previous works have been helpful, lack of understanding in the interactions and consequences of geotechnical properties, environmental factors, and mining activities has limited the effectiveness of these previous studies and their conclusions. The definition of slope failure is very crucial for risk assessment in open pit mining as it varies from one pit operation to the other. Therefore, mining engineers, geotechnical engineers, geological engineers, pit bosses, and operators in the pit should all be part of developing the criteria for defining slope failure. Slope failure as defined by O’Bryan et al. (2011) is any alteration in the pit wall geometry that causes conditions in the pit to become too dangerous for 2 mining to continue. Hoek & Pentz (1968) implied that a displacement rate around the surrounding rock mass of the pit wall that causes recovery of ore to become uneconomical constitutes a slope failure. Hoek & Pentz (1968) definition refers only to the ore. When a slope fails, pit operations usually stop because the appropriate authority will require an investigation. Call (1982) suggests a definition of open pit failure as when the displacement rates of the rock mass are greater than the rate at which the loose material can be mined safely and economically without an interruption of pit operations, or when movement rate creates unacceptable loss to equipment, personnel, or production. For the purpose of this research, an open pit slope failure is defined as a condition when mining operations in the pit are stopped because pit wall velocities or movement rates are accelerating. It is important to state that the slope movement models developed by other researchers do not have an associated operational response linked to the velocity the pit walls exhibit at a particular time. Operational response is defined as activities that mine personnel should conduct in line with different stages of the slope behaviour during mining operations Open pit mine operations in the pit are governed by: • geotechnical properties, • pit geometry, • influence of blasting, • ground water conditions, and • consequence of failure. The factors listed above indicate the complexity of slope stability assessment. These factors also help in determining the modes of failure. Understanding the failure mode is an important concern for rock slope engineers, as it is somewhat governed by the geological structures and the geometry of the slope. Broadbent & Zavodni (1981) categorize large-scale rock slope failures into three distinctive types. This categorization depends on the shear strength and orientation of discontinuities, and how they relate to the expected displacement behaviour. There are conventional and numerical modeling techniques used for rock slope stability analysis. The conventional methods are categorized into kinematic and limit equilibrium techniques. The kinematic analysis methods consider the orientation of the joints while ignoring some other 3 important geometrical parameters such as spacing (Eberhardt 2003).  The kinematic methods can be used with probability techniques to determine the probability of failure of a rock slope and the corresponding failure volume (Stead et al. 2001). Therefore, this method depends on the detailed evaluation of the rock mass structure and the orientation and geometry of existing discontinuity sets that will lead to a particular mode of failure. Limit equilibrium methods focus on how certain types of slope failure mechanisms occur on distinct failure surfaces. Limit equilibrium methods investigate the equilibrium of a soil or rock mass under the influence of gravity and other forces. Limit equilibrium techniques are used to provide the safety factor, or by means of back analysis, determine the range of shear strength parameters at failure (Stead et al. 2001; Eberhardt 2003). Limit equilibrium methods are limited to a rigid body assumption. The strength reduction method is computationally expensive and has convergence issues due to the non-linear iterative computations (Zheng et al. 2014). Rock slope stability problems are very complex and these conventional methods are sometimes unable to capture all the details needed.  Therefore, advanced numerical methods are used in conjunction to these conventional methods to provide better insight to slope stability problems (Stead et al. 2001; Eberhardt 2003). Because of the complexities relating to rock slope geometry, material properties, in situ stresses coupled with pore pressures, numerical modelling methods become useful in analysis of such problems. Numerical methods can be grouped into continuum modeling, discontinuum modeling, and hybrid modeling (Stead et al. 2001; Eberhardt 2003). Many researchers have implemented numerical modeling methods to resolve complex slope stability (Jing 2003; Zheng et al. 2014; Hart 1991; Benko and Stead 1998; Wheel 1996).  Although the above conventional and numerical methods are helpful in resolving slope stability issues, information used in the application of these techniques are site specific.  Therefore, lots of time is needed to build numerical models for each specific location to analyze slope stability issues. The processes involved in numerical modeling can be very time consuming and computation of results can be slow and expensive.  Due to the limitations with the conventional and numerical methods, it is expedient to define a framework that will be able to use prior information (historical data) to make good decisions.  As locations change and data are obtained, the framework can be updated to make better-informed decisions unlike numerical modelling method that discards previous data and uses new data. The proposed framework of this research allows mine operators to consider information that is not physically measured. Additionally, this framework is a generic 4 model can be applied to multiple locations unlike the numerical modelling techniques that restricts this application. As more data becomes available from different locations with the same geotechnical conditions and pit wall configurations, the proposed model can be updated.  The proposed model does not predict the factor of safety, instead it estimates the movement velocity of a rock slope based on current geotechnical conditions and pit wall conditions. Additionally, the focus of the research is to predict unusual slope behavior to minimize the consequences of slope failure. The technique used to develop the proposed model is a powerful tool that models cause and effect relationships under uncertainty, and it is an effective tool for risk analysis. The technique used to develop the proposed model is discussed in subsequent chapters. Most operating mines have passive guidelines to help mine operations conduct mine activities in a safe manner. However, there is often no rationale behind the magnitudes of the movement criteria. Moreover, to fulfill permit conditions, mines in BC are required by the BC Ministry of Mines and Energy to establish movement criteria to manage risk in their pit operations (Warnock 2013). Incorporating the factors that influence the pit wall performance and establishing slope velocity movement criteria for pit walls is challenging because most open pit mines use past incidents to establish movement criteria without knowing which governing factors should be considered. Since the decision-making process for predicting movement limits for pit walls can be challenging, most mine operators use expert knowledge and experience to do so. In consideration of all these factors, this research combines into one platform (1) expert judgement, (2) geotechnical and geological information, and (3) mining planning and operation information to enable good decision-making backed by a scientific rationale. 1.2 Research objectives The overall goals of this research are to (1) develop a Bayesian Belief Network model framework to manage open pit slope tailored to specific geotechnical conditions and pit wall configurations, and (2) outline appropriate operational responses to measured or predicted slope movements. The research investigated that factors need to be considered to define an appropriate operational response when facing changes in geotechnical parameters, slope geometry, and climatic changes. The research tasks are listed below. 5 • Collect qualitative and quantitative data related to pit wall geometry, slope monitoring data, mechanical properties of the rock mass, and other relevant data in open pit porphyry mines in BC using published literature, unpublished consulting reports, questionnaires, and a workshop. • Understand current mining operations in BC and investigate the similarities and differences among them. • Develop a Bayesian Belief Network model (BBN) incorporating geotechnical and operational parameters and their influence on open pit slope management. • Proposed a relationship to estimate travel distance of rock from a pit slope failure. • Conduct a sensitivity analysis for the developed model to determine the important factors that affect slope movement. • Outline operational responses associated with different states of pit wall movement. • Incorporate a decision node in the proposed model to link all the parameters considered in the model to an appropriate operational response that mine operations can use. • Conduct scenario analyses using the proposed model and apply the model to case studies to validate the model. 1.3 Research approach To study and develop slope movement criteria and establish operational responses for each movement criterion, a review of various important pit wall failures in BC mines was done. The review also examined slope monitoring practices and general pit operations. The review was intentionally broad yet still achievable within the limits of time and financial resources available. The approach adopted in this thesis involved the gathering and analysis of data obtained from BC mines. Due to lack of field data regarding rock slope stability, a questionnaire was developed to collect information about geology, pit geometry, and geotechnical engineering properties of the pit walls for each BC mine operation (Appendix A). A workshop was also organised as a means to gather expert knowledge and available data. The questionnaire involved in the study and the workshop were approved by the UBCO Behavioural Research Ethics Board (BREB) with a BREB certificate number of H13-00908. 6 The research focuses on multiple bench-height pit walls. Pit wall failures were studied to understand the cause-effect relationship as well as the mitigation measures implemented by mine operations. Due to insufficient measured data, the research used a methodology (probabilistic based approach) that can handle scarce data. The probabilistic approach gives the opportunity to incorporate both expert knowledge and measured data available into the analysis and decision making process. Data obtained from consulting reports, mine geotechnical databases, and interviews conducted with BC mine operators were used to construct the proposed model. In addition, empirical and analytical equations were incorporated for some variables where possible for further inference. Knowledge was obtained through interviews conducted during site visits and in one-on-one consultation with an industrial partner. 1.4 Contribution and originality For the first time, this research brings geotechnical engineering data and knowledge, mining operations, expert knowledge, environmental and climatic data together into a Bayesian Belief Network platform for decision-making. The Bayesian Belief Network technique links and appropriately weighs multiple factors affecting slope instability. Even though the BBN technique is used in other fields of engineering, the concept has not been applied to operations decision-making in response to pit wall movements. This research allows mines to make better decisions in terms of their operational responses to predicted or measured slope movements. Figure 1-1 shows the various components that were used to establish the critical slope velocities linked with an appropriate operational response. Multiple variables within each component interact with each other, giving rise to complex cause-and-effect relationships. This research is the first time that all these factors plus human and equipment influences have been linked together in a single platform to make decisions. The consequence of failure is another component that will influence the operational responses because human lives, equipment, and mining economics are involved. As such, this component is embedded in the network to evaluate elements at risk in case an incident occurs. The research aim was to predict the appropriate operational response that should be taken at any point in time when slope movement becomes a concern to management. The operational responses are linked to movement rates. 7  Figure 1-1. Components used in the research to define the appropriate operational responses Because each mine operation is unique, and the geotechnical and environmental conditions vary from one location to another, the relative importance of factors affecting slope stability also vary from one mine to another. This work provides a rational framework for developing a site-specific and calibrated prediction and decision-support tool. The BBN incorporates knowledge and identifies the most influential factors contributing to slope instabilities. Caldwell (2013) stated that Bayesian methods have not been applied to solve difficult issues in the mining industry. He also challenged the mining industry and its practitioners, consultants, and academicians to read and learn about Bayesian methods and show the industry how to apply these methods to solve mining problems. Therefore, for the first time, this methodology has been applied to pit slope management in this thesis in an effort to help the mining industry. Implementation of the research should save money and time that have, in the past, cost some operations millions of dollars. 1.5 Limitations of the research The objectives of the research were achieved through a comprehensive analysis of historical data obtained from mining companies in BC. To validate the proposed model, only mine sites that provided quality data for the work were used as case studies, which limited the quantity of data that were available. The proposed model has numerous parameters that are not physically measured in the field by the mining operations and are primarily assessed by expert judgement (i.e. data based on knowledge or experienced). Incorporating a combination of measured values and expert Pit Wall Failure Modes and Travel Distance/ReachGeotechnical propertiesSlope geometry Blast damageConsequences of Pit Wall FailureOperational response associated with level of consequence of pit wall failure using slope velocity8 judgement was useful in developing the proposed model.  However, it will be important to conduct additional calibration of the model with field data, primarily acquired from well-documented case histories.  Thus, the model in its current state is probably not sufficiently reliable for replacement of current pit management practices.  The calibration process will take years, largely because significant pit slope failures are fortunately not a frequent occurrence despite the significant risk they present to a mining operation. It is important to note that from previous experience, porphyry rock masses will experience considerable deformation before ultimate failure of a pit wall occurs.  Thus, pit wall movement monitoring is highly useful to pit wall management.  In contrast, other rock types (e.g., steeply dipping sedimentary rocks) may behave in a more brittle manner giving less warning of impending failure (Sullivan 2007).  Application of the proposed BBN model, which is calibrated to manage open pit slopes in porphyry rock masses, should be used with caution in these rock masses. 9 Chapter 2: Open Pit Porphyry Mines in BC 2.1 Copper/molybdenum mines in BC Figure 2-1 shows the location of the major copper/ molybdenum mines in BC. They are located in a north trending band between the coastal mountains and the Rocky Mountains.  Figure 2-1. Operating open pit copper/molybdenum mines in BC (Nunoo et al. 2015) A questionnaire (Appendix A) with 50 questions was designed to collect data about mining conditions and pit wall monitoring practices in BC’s copper/ molybdenum mines. The questionnaire was sent to the six operating mines in the summer of 2013. All six mines returned questionnaires, although the results varied in terms of their level of detail and completeness. Follow-up site visits to the four of the mines (Highland Valley Copper, Gibraltar, Endako, and Copper Mountain) were conducted to validate the data provided and to inspect the pit walls and slope monitoring systems. The data from the questionnaire were used to understand each mine’s operations and to investigate the similarities and differences between their slope management Copper MountainVancouverHighland Valley CopperMt. PolleyGibraltarHuckleberryEndakoMt. MilliganKelownaPrince GeorgeKamloopsB R I T I S H  C O LU M B I A10 systems. Findings from the survey were presented in a workshop associated with the CIM Maintenance Engineering / Mine Operators Conference in Kamloops in September 2013. The pit geometry and rock mass conditions in the BC mines are summarized in Table 2-1. Table 2-1. General pit geometries as of 2013 (Nunoo et al. 2015) Mine Pit Slope (°) Depth (m) Length (m) Width (m) RMR76 (approx.) Copper Mountain  Pit 2 Pit 3 44–51 37–55 90 75 1,000 900 300 800 60 Endako Denak 39 350 1,940 830 60–80 above SBF 25–45 beside SBF 40–60 below SBF 65–75 at depth Gibraltar Granite 37–43 245 1,830 765 60 HVC  Valley Lornex Highmont 39–42 34–40 40–45 800 530 155 2,800 2,400 1,000 2,300 1,400 400 65 40–50 75 Huckleberry  top bottom 39 125 1,000 400 800 200 60 Mount Polley unknown 43–49 270 1,000 600 60 SBF-South Basalt Fault  Appendix C gives an overview of all the open pit porphyry operations in BC including production rate, slope-stabilizing techniques used, bench configurations, blasting techniques and monitoring techniques used by individual mines. It is important to state that rock mass quality for Copper Mountain, Endako and Gibraltar pit walls increases with depth. However, Huckleberry and HVC mines shows no change of rock mass quality with depth and at the Mount Polley mine, pit wall rock mass quality decreases with depth. 2.2 Porphyry ore deposits Porphyry ore bodies consists of various igneous rocks that have large grain crystals. Some of the crystals are quartz, distributed in a fine grain feldspathic rock mass. This type of deposit is formed when column of rising magma undergoes two cooling stages. During the first stage, the 11 magma is cooled gradually deeply in the earth crust forming large crystal grains with 2 mm diameter or more. The final process involves the magma cooling rapidly at relatively shallow depth forming small grains that are usually invisible to the eye (McMillan and Panteleyev 1988; Sinclair 2007). Porphyry deposits are large, relatively low-grade, epigenetic deposits that are structurally controlled. They are spatially and genetically related to intrusive igneous rocks that are epizonal and invariably porphyritic. Furthermore, igneous rocks associated with this deposit consist of diorite-granodiorite to high-silica granite. They are often differentiated from other intrusive deposits like skarns, by their large size and structural control (McMillan and Panteleyev 1988; Sinclair 2007). Porphyry deposits are the world's most important source of copper (60% – 70% of world production) and molybdenum (more than 95% of world production), and are major sources of gold and silver. They typically contain hundreds of millions of tonnes of ore, even though they vary in size from tens of millions to a billion tonnes. For porphyry copper deposits, the copper grade varies from 0.2% to more than 1% and in porphyry molybdenum deposits, the molybdenum grades varies from 0.07% to 0.3% (Sinclair 2007). 2.3 Pit wall and bench geometry Figure 2-2 shows the geometry of an open pit slope, where the overall pit slope angle (i.e. slope crest to slope toe), the inter-ramp angles (i.e. bench toe to bench toe) and the bench face angle are the key features of an open-pit slope (Wyllie and Mah 2004). The overall pit slope includes inter-ramp areas, haulage roads and benches (which is sometimes steeper in competent rocks than in weak rocks) with varying slope angles within the same mine. The bench geometry that results from the bench face angle and bench width will end up dictating the inter-ramp slope angle. Hence, the inter-ramp angle is a function of the bench face angle, the bench height and width, and these are governed by the geomechanical properties of the rock mass and operational factors. 12  Figure 2-2.Geometry of an open pit slope Benches are designed and constructed based on the following reasons. • Practicality (drilling and loading) – Most often, the shovel size dictates the height of a bench. Benches usually have flat area to provide room for equipment access for haulage of materials and to enable shovels to excavate and load fragmented rocks. Additionally, during progressive pushback, it is imperative to work on multiple benches as compared to conventional pushback (Darling 2011; Hartman et al. 1992). • To satisfy safe and stable slope – Pit slopes are cut into benches to aid stability and contain any small-scale slope instabilities. The bench face angle is carefully chosen in a way as to lessen, to an acceptable level, the amount of material that will likely fall from the face or crest (Hartman et al. 1992; Miller et al. 2000). • To catch falling rocks and debris – For safety reasons, benches aid to catch falling rocks from the top of the pit. The bench width is sized (around 10 m) to prevent small wedges and blocks from the bench faces falling down the slope and potentially causing fatality to personnel and equipment (Darling 2011; Hartman et al. 1992). Overall slope angle Bench faceInter-ramp slope angleBench angleRampwidthOverall slope height Bench height Floor / working bench Bench widthFuture working bench13 The overall slope angle is a function of the bench angles and width, and inter-ramp angle and width (Sjöberg 1999). The overall slope angle is usually flatter than the maximum inter-ramp angle because of the presence of haulage ramps. Other factors influencing the design of the overall slope angle are rock mass strength, ground water pressures, blasting vibrations, stress conditions, and mine equipment requirements. 2.4 Lessons learnt from open pit instabilities Case histories for pit wall slope failures were collected for porphyry deposit mines in BC. In order to understand the similarities/or differences in slope failures in BC, both active and inactive case histories of open pit BC mine operation were collected (Table 2-2). The first three mines presented in Table 2-2 are for inactive BC mines. Four case histories from active mines were used to validate the proposed BBN model in the case studies section of this thesis.  These case histories were for recent slope failure events and there were some data available, which were supplemented by interviews conducted with mine personnel and site visits. Other case histories obtained only provided vague information and could not be used for the BBN model validation. The information for these case histories were collected from literature reviews, mine operation incident reports, and consulting reports. Nothing is presented for Mount Polley mine because no records of instabilities could be found for this mine. Appendix D presents the background information collected for the seven case histories. The case histories reveal cause-effect relationships leading to slope failure with groundwater pressures being one important factor affecting slope stability (Hudson and Harrison 2005). Periods of high rainfall and the spring runoff are two important and common factors that could lead to slope failure. Poor blasting practices can also affect the slope stability, especially at the bench scale.  The case histories presented in Appendix D indicates that both active and inactive BC mines have similar factors leading to slope failures. These factors are: • steep slope angle, • high slope height, • poor rock mass quality, • weathering, • low rock strength, 14 • high ground water levels, • poor blasting practices, • low shear strength on discontinuities, • unfavourable orientation of discontinuities, and • in situ stresses. These factors are used to create the proposed BBN. The travel distance angle presented in Table 2-2 is calculated using an equation presented by Li (1983). This equation is discussed later in the thesis. Table 2-2. Data summary of case histories presented in Appendix D Mine / Pit Year Pit height at failure (m) Size of failure (1000 x m3) Consequence of failure Slope angle (°) Travel distance angle (°) Slope velocity (mm/day) Afton 1984 - 566   Production loss 40 ~31 2880  1985-1986 300 (170 involved) ~2,832  - ~25 - Brenda 1978 - - - 45 - >150  Kemess south 2004 100  ~4,248  Production loss > 40 ~24 150  Copper mountain /Pit 3 2011 80  ~14  Equipment damage & Production loss > 40 ~47 - Endako 1994; 2001; 2003 - - Production loss - - - Huckleberry 2007 - - - - - - HVC/ Highmont 1983 110  ~500 - 1,000  Production loss - ~29- 31 -  The case histories indicate that irrespective of the operation and the instability involved, operations in the pit were somewhat affected. Both active and inactive BC mines used similar operational responses to help manage their pit walls. Some of these similarities include changing the mine plan by redesigning slope angles, constructing buttresses of waste rock, closing access 15 ramps, and stopping mining activity near an instability. Additionally, all of the mines used horizontal drains to reduce the ground water levels affecting the stability of the slope. It is important for pit operations to have an operational response system that can be used to manage slope instabilities. Some mines have successfully mined out instabilities that could have led to catastrophic failures. 2.5 Pit wall displacement monitoring Open pit mining induces movements in the pit walls, which are routinely monitored to evaluate their performance.  Excessive or accelerating pit wall movements must be identified as they may be a precursor to slope instability.  There are a variety of monitoring technologies and associated monitoring practices used by mines to measure movements of the pit wall. Slope monitoring systems for open pit operations can be divided into three categories: 1) visual inspection, 2) surface measurements, and 3) subsurface measurements (Nunoo et al. 2015). All BC mines routinely use visual inspections.  The Health, Safety and Reclamation Code for Mines in BC (BC Ministry of Mines and Energy, 2008) places a requirement upon operating mines that all work shall be carried out without undue risk to the health or safety of any person (Section 1.1.2 of the Code).  Clearly, pit wall monitoring by visual inspection can be used to mitigate risk to people working in mines.  Section 6.5.1 of the Code states that no work shall be carried on, at, or below a face or wall of a surface mine until that face or wall has been examined and declared safe by the shift boss.  At a minimum, visual monitoring of the pit walls is implied by this statement.  Section 6.23.2 of the Code states that loose rock and soil shall not be allowed to accumulate on a bench or catchment berm in a manner that endangers any person working on a lower bench.  Again, visual monitoring is needed as a minimum to assess the accumulation of rock and soil on a bench (Nunoo et al. 2015). Surface techniques used to measure the rock slope geometry and/or rock movements include total stations and prisms, radar, laser scanners (LiDAR*), and wire-line extensometers.  Satellite Synthetic Aperture Radar Interferometry (inSAR), aerial LiDAR, and photogrammetric mapping * Light Detection And Ranging 16                                                   are other technologies that can be used, but a survey of current practices shows that these techniques are not being routinely used in any of the BC open pit porphyry mines.  Some terrestrial photogrammetry has been performed. The use of a total station and prisms for slope monitoring is the most frequently used measurement technique in BC mines. To minimize the manual effort of reading the prism coordinates and to improve the frequency and the accuracy of the measurements, Highland Valley Copper uses robotic total stations operating from within climate-controlled huts. Only the Huckleberry and Highland Valley Copper (HVC) mines use slope stability radar.  Wire-line extensometers are frequently used to measure changes in tension crack widths in active areas of instability. Usually a steel peg is driven into the ground on the downslope side of an observed crack.  A thin steel wire is attached to the peg and is extended to another pin or pulley attached to a tripod and connected to a hanging weight.  Changes in the crack width are visually measured from the position of the hanging weight relative to a ruler/tape measure fixed to the second peg. All BC mine operators use wire-line extensometers (Nunoo et al. 2015). Subsurface measurements typically involved some form of instrumentation placed within a borehole.  A wide range of instrumentation is available including time domain reflectometry (TDR) cables, inclinometers, micro seismic sensors, and borehole extensometers (Dunnicliff 1993; Girard 2001; Jarosz & Wanke 2003; Severin et al. 2009; Osasan & Afeni 2010). Highland Valley Copper mine is the only mine using TDR to monitoring subsurface movements.  They also use inclinometers and borehole extensometers to collect subsurface measurements. Mines in Table 2-2 uses total stations and prisms for pit slope monitoring. Table 2-3 shows a summary to the current state of slope monitoring techniques and frequency of monitoring by BC porphyry mines. 17 Table 2-3. Monitoring frequency for typically used instrumentation (Nunoo et al. 2015) Mine Slope monitoring techniques and frequency of monitoring Visual Total station and prisms Radar Wire-line extensometer Piezometers Copper Mountain  weekly daily -- daily to weekly -- Endako weekly 3 times per week -- -- monthly Gibraltar weekly daily -- daily to weekly weekly to monthly HVC weekly hourly every 10 minutes daily to weekly weekly to monthly Huckleberry weekly daily hourly daily to weekly weekly to monthly Mount Polley weekly daily -- daily to weekly weekly to monthly  Keeping records of the behaviour of pit walls in response to mining activities helps the mine operation to understand slope movement rates and enact responsive measures if possible. As part of managing risk pertaining to slope failures, most mines depend on experience to make decisions regarding the movement rate of the pit wall. Even though there are many variables that lead to high movement rates or instabilities, little attention has been given to the factors involved. 18 Chapter 3: Risk Assessment Methods Related to Open Pit Slope Management 3.1 Overview of risk The term ‘risk’ has a variety of meanings. In a comprehensive way, risk is determined as the product of probability of occurrence of an hazardous event and its related consequence(s) (Baecher and Christian 2003). In assessing risk, it is important to incorporate quantitative or qualitative knowledge. It is possible to conduct risk assessment by explicitly focusing on quantitative data. There are a number of quantitatively based risk assessment methods such as Failure Mode and Effects Analysis (FMEA), Event Tree Analysis (ETA), Fault Tree Analysis (FTA), bowtie diagrams, etc. (Aven 2008). Alternatively, some of the qualitative risk assessment methods are Hazard Assessment Critical Control Points (HACCP), Hazard and Operability Analysis (HAZOP), what-if analysis, etc. These quantitative and qualitative risk methods have been applied in the field of engineering. Most organizational and human risk analyses are usually modeled with qualitative rather than quantitative data (Aven 2008). In assessing risk associated with open pit slope failures, the stochastic behaviour of the pit wall slope has to be modeled to take into consideration the uncertainties associated with geotechnical properties of the rock mass; pit geometry; ground water; effect of blasting; travel distance associated with failure volume of the rock mass; the consequence of failure. Open pit risk assessment can be complex as qualitative data is integrated with quantitative data, with factors associated with open pit slope having multiple states as well as showing dependencies between the factors.  Risk assessment techniques most often model the dependencies between events like occurrence of failure and uncertainties involved. Uncertainties are inevitable when dealing with real world cases. It is important for engineers to identify the major sources of uncertainty in their field of work before making decisions. Many authors attempt to subdivide uncertainty into specific types (Casti 1993; Helton 1994; Hoffman and Hammonds 1994; Hofer 1996). The drive for such divisions occurs because there are things that are inherently unknowable until they are realised. Another reason might be that systems are not 100% accurate because they do not capture every important detail needed. For the purpose of this work, sources of uncertainty can be categorised into two broad types namely aleatory 19 (irreducible) and epistemic (reducible) types of uncertainty (Ang and Tang 1975; Oberkampf et al. 2002; Parry 1996). Ang & Tang (1975) and Oberkampf et al. (2002) have described aleatory uncertainty as intrinsic variability, or just variability. Engineers often deal with randomness associated with aleatory uncertainty where the outcomes are unpredictable to some extent. For example, field or experimental data usually have significant variability reflecting the natural randomness of an underlying process. Aleatory uncertainty is usually associated with database uncertainty that includes basic information that is part of the real world beyond our control except to observe and describe. Measurements taken from one observed experiment may differ from other experiments. In addition, when a range of measured values is obtained by observation or experimental results, certain values may occur more frequently than others. This inherent variability is statistical in nature and hence finding a specific value or range of values will involve using probability. Expert knowledge and supplementary data cannot be used to decrease aleatory uncertainty although they may be effective in quantifying aleatory uncertainty (Conroy and Peterson 2013). Therefore, most practitioners have recommended the use of probability (e.g. BBN) to model this kind of uncertainty (Ang and Tang 1975). In engineering, we depend on ideal models to represent real world cases and use these to make predictions and decisions. These ideal models can be mathematical formulas, numerical algorithms, computer programs, or laboratory models, which usually misrepresent real world cases. These kinds of models produce results that are somewhat inaccurate (with some level of unknown error) and thus contain uncertainty. Epistemic uncertainty is associated with this type of uncertainty. It is caused by lack of knowledge on the side of the decision maker rather than system under analysis. It is necessary to seek advice from experts in the field of interest when making important decisions. These experts or consultants base their advice on collected knowledge, experience or observations and other information related to the field of their expertise (Jensen and Nielsen 2007). Rock slope researchers have based their recommendations regarding slope movement criteria using the behaviour of rock under stress conditions (Stacey et al. 2003), the time-dependant behaviour of rock (Martin 1993; Mercer 2006), slope displacement data (Rose and 20 Hungr 2007; Szwedzicki 2003), history of slope failures, and other factors to establish movement criteria for a mine. There is uncertainty about geotechnical parameters and geologic conditions. Thus, judgment is used to handle uncertainty in engineering geology (Einstein and Baecher 1983). The uncertainty related to slope movements depends on the complexity of the geology and pit geometry. The classical reliability (i.e. safety, dependability, availability, integrity) analysis methods can incorporate parameter variability and uncertainty. Examples include FTA (Baecher and Christian 2003; Bobbio et al. 1999), Stochastic Petri Networks (SPNs) or Petri nets (PN) (Balakrishnan and Trivedi 1996; Wakefield et al. 1998; Wakefield and Sears 1997), FMEA (Abdelgawad and Fayek 2012), Markov chains (Yi et al. 2011), and Bayesian Belief Networks (BBN) (Bensi et al. 2009; Ismail et al. 2011; Liu et al. 2012; Liu et al. 2013). The research presented in this thesis uses a risk assessment method to analyse cause and effect relationships between components of the system so that mine operators can manage open pit slope by minimizing consequences of an undesired event.  With an understanding and the objectives of the research, the next section discusses the most commonly adopted risk assessment techniques used to solve related engineering problems. Among these risk assessment techniques, the best technique to achieve the research objectives is shown. 3.2 Risk assessment methods 3.2.1 Fault tree analysis Fault tree (FT) analysis is a top to down, logical failure analysis whereby Boolean logic is combined with a series of low-level events to analyze the cause of an undesired state of a system. It is a common method used for risk and reliability analysis. The undesired event is usually the top event of the system, which is the starting point when conducting FT analysis. The different components of the system include all the possible events that directly cause the top event (Aven 2008). FT analysis is a deductive kind of modeling risk (i.e. backward looking at the causes). According to Bobbio et al. (1999), during FT analysis, the probability of failure of a system or event can exactly be known. However, it is challenging to estimate exact probability of failure of the components of the system due to insufficient data or indefinite characteristic of the events. Therefore, in the absence of accurate data, it is essential to work with rough estimates of probabilities. The probability of failure are treated as stochastic variables with known probability 21 distributions. Moreover, FT has a problem in dealing with multiple failures of components that lead to numerous consequences on the system (Weber et al. 2012). This problem is common in risk and reliability analysis where components need to be represented by multiple state variables, which FT cannot handle. Additionally, FT models lack the flexibility of incorporating prior and posterior evidences. FT is limited to only one top event. It is therefore impossible to utilize this risk assessment technique to model factors with multiple states and assessment of several output variables in the same model, which is critical in risk associated with open pit slope stability. In addition, prior and posterior evidences are needed to model risk in open pit slope in order to make well-informed decisions. 3.2.2 Event tree analysis Event tree analysis (ET) is used to study the consequences of an event in a bow tie diagram. Thus, ET shows whether an event has or has not occurred or a component in the system has or has not failed and analyzes the consequences rising from the undesired event. ET shows a graphical representation of a logic model by identifying and quantifying possible outcomes following an initiation event. This risk assessment technique can be used for qualitative risk assessment as it provides a picture of potential scenarios; and for quantitative analysis as probability of occurrence are assigned to the respective event and their consequences (Aven 2008).  Like FT, ET is limited to only one event. Therefore, multiple ET analysis is required to assess the consequence of multiple events.  Due to the limitation of both ET and FT analysis, it is impossible to utilize them to achieve the objectives of this research. 3.2.3 Failure mode and effect analysis Failure mode and effect analysis (FMEA) is a simple risk assessment technique used to reveal potential failures and to predict the effects of failure on the whole system (Aven 2008). FMEA represents a systematic method for assessing the way a system might fail and evaluate the relative impact of different failures; in order to identify the parts of the system that are most in need of replacement and maintenance. FMEA are used to identify prospective failure modes, assess the risk associated with those failure modes, and rank the problems in terms of importance, identify, and perform actions to address the most critical concerns (Lee 2001). This technique is also an inductive method that investigates what happens when a component in the 22 system fails. One component of the system is considered at a time as the other components in the system are assumed to work well. Therefore, this technique is not appropriate for showing critical combinations of component failures. The analysis conducted using FMEA can be a good starting point for a FT analysis or an ET analysis (Aven 2008). The concept of conditional probabilities is not considered in FMEA. FMEA is not suitable for doing posterior inference for fault related symptoms (Yang et al. 2009). Although FMEA is a powerful tool, its capabilities restrict its application in achieving the objectives of the research. 3.2.4 Bayesian Belief Network A Bayesian Belief Network (BBN) is another risk assessment technique that provides a probabilistic method of reasoning under uncertainty (Bobbio et al. 1999). BBN consist of events (nodes) and arrows. The arcs (arrows) connecting two nodes denotes a link indicating the probabilistic cause-effect relationship between the variables (Cooper 1989; Neapolitan 1990; Pearl 1988; Robinson 1977).  The nodes represented in BBN can have multiple states depending on the risk analyst. Thus, BBN is not restricted to one or two states (Aven 2008). Conditional probabilities of nodes with multiple states given the causal relationship can be determined during a quantitative analysis (Aven 2008).  BBN allows the user to incorporate both quantitative and qualitative information as well as deal with uncertainties. A limitation with BBN is that the computation can be highly demanding when the BBN is densely connected (Bensi et al. 2011). Another limitation of BBN is that the risk analyst needs to have a good understanding of the situation being modeled. Despite these limitations, the research objectives can be achieved with a BBN because it allows multiple states for nodes, conditional probabilities for nodes, and incorporates quantitative and qualitative data. A BBN has many capabilities that makes it well suited for the risk assessment of open pit slopes. A BBN is a finite, directed, acyclic graphic model that permits probabilistic connection within a set of variables (Cooper 1989;Neapolitan 1990; Pearl 1988; Robinson 1977). A BBN is also termed a Bayesian Net, Causal Net, Probabilistic Cause-Effect Model, or a Probabilistic Causal Network. Variables used in BBN can either be discrete or continuous (Shachter and Kenley 1989). Recent literature shows an increasing number of applications of BBN because of its effectiveness in risk assessment of complex systems (Boudali and Dugan 2005; Langseth and 23 Portinale 2007). BBN has been successfully applied in a variety of practical problems and numerous researchers have found it suitable for risk assessment purposes (Bensi et al. 2009; Cockburn and Tesfamariam 2012; Ismail et al. 2011; Liu et al. 2012). The process of estimating the value of an uncertain quantity using data or expert judgement is usually referred to as statistical inference. Two types of statistical inference are commonly used: the Bayesian approach and the Frequentist approach (Gill 2007). The Bayesian approach determines the conditional probability of an unknown quantity using assumptions and available observations. The approach uses assumptions established by expert opinion, engineering judgement, or physical models. Bayesian prediction models can be updated continuously as new information becomes available because the model represents the probabilistic modeling of an accumulation of data (Congdon 2003). As more data become available, decisions based on Bayesian analysis will converge towards results obtained using a Frequentist approach because the impact of prior assumptions reduces. The Frequentist approach focuses on the frequency concept of probability. This approach explicitly states that the probability of an event is the limit of its corresponding frequency of occurrence as the number of events tested becomes large, hypothetically unlimited. As a result, it is an empirical approach for calculating probabilities. Unknown factors are treated as fixed deterministic values for assessment by the Frequentist method instead of treating the factors as random variables (Gill 2007). Models like Artificial Neural Networks (ANN) can be used to establish the relationships between input and output variables with related uncertainties from learning data if significant historical data are available. For analysis of slope stability where sufficient data for the various factors controlling the slope failures are difficult to obtain, a Bayesian Belief Network is more suitable because of its robustness in situations that lack data (Koop 2003). The BBN uses factors as random variables and then represents the uncertainty under reasoning as a probability distribution that shows the relative likelihoods of outcomes. One of the features of a BBN is that as new data become available, the model can update the probabilities based on the new data. This intuitive nature is very useful for different stakeholders. It easily captures top-down inferences, considering cause and effect relationships, and it deduces 24 the possible effects and vice versa (Jensen and Nielsen 2007; Pearl 1988). Therefore, the developed BBN model is able to resolve the problems of scarcity of measured data availability by combining qualitative data (expert knowledge) and empirical equations. Moreover, the developed BBN model demonstrates the ability to investigate the interdependency of factors such as geotechnical properties, ground water, slope geometry, mining activity, and the consequences of failure parameters and their effects on open pit slope. The development of the proposed BBN will help operating mines and new mines to decide which operational response is required to a given situation of slope movements. This task is similar to studies in other fields that utilize the BBN approach to combine diverse sources of data and intelligence in making meaningful decisions. As no model is ideal, uncertainties related to the BBN model are defined through subjective probability (Cooper 1989; Pearl 1988). Advantages of BBN are that it can: • handle incomplete data sets, • give the user the chance to learn about causal networks, • help in permutation of knowledge and data, and • use an efficient and principled approach to avoid the over-fitting of data (Cooper and Herskovits 1992; Jensen and Nielsen 2007; Pearl 1988). The relationships between the variables used in BBN are described in terms of a parent-child relationship and vice versa. For example, a variable X is said to be the parent (or cause) of C if the link goes from X to C or C is the child (or effect) of X in the same context. For a BBN to be valid, the set of variables used in the network should be mutually exclusive and exhaustive. Conditional probabilities are assigned for each set of parent variables with directed links between the variables. Where a variable has no parent, an unconditional probability is used for that variable. For a number n of mutually exclusive sets of variables with hypothesis Bj, j = 1, 2, …, n, given data or an evidence of A, Bayes’ Theorem states that: ( ) ),(P)(P|P BABBA =  (1) Where P (A, B) is the probability of joint event A and B. Because ( ) )(P)|(P)(P|P AABBBA = , Bayes’ Theorem can be expressed as: 25 ( ) ( ) ( ))(PP|P|PABBAAB ×= (2) Expressed in words, the posterior probability of B given the new information A, is equal to the likelihood of the new information A, given B multiplied by the prior probability of B. Here, P (B|A) = belief for B upon observing A (posterior probability), P (B) = probability that B is true (prior probability), P (A|B) = likelihood that A is observed if B is true. For instance, if P (A) and P (B) are conditional on C, Equation 1 will become: ( ) )|,(P)|(P,|P CBACBCBA =  (3) Hence Bayes’ Theorem conditioned on C is: ( ) ( ) ( ))|(P|P,|P,|PCACBCBACAB ×= (4) By the law of total probability, Equation 2 and Equation 4 can be formulated as: ( ) ( ) ( )∑ =×= nj jjiiiBBABBAAB1)(P)|(PP|P|P (5) ( ) ( ) ( )∑ =×= nj jjiiiCBCBACBCBACAB1)|(P),|(P|P,|P,|P (6) A Bayesian Belief Network can be built using expert knowledge or historical data if available. The available data permits variables and their respective states to be determined, as well as their probability in creating the network. The generic way to construct a BBN is as follows: • Choose the relevant variables and order them. As a suggestion, dependant variables are considered first in the order so when the variables are graphed it is easier to construct the dependency relationships between them. • Define the relationship between variables. No cycles or feedback loops are allowed in BBN. • Determine all the possible condition or states of each variable. For this research, variables with a defined number of conditions are used. Each set of possible conditions of a discrete variable is called a state. Alternatively, when a continuous variable is used, predetermined ranges are used to define states for the variable. Additionally, states in BBN are considered as all the possible conditions or ways that a variable can be configured. For instance, the 26 engine of an automobile can be running well or giving troubles; or the automobile can have a flat or inflated tire; a person can be dead, alive, or sick; and so forth. • For each variable, create conditional probability that shows the probability of the variable states for each combination of states with the given parent-child relationship. These probabilities (i.e. unconditional or conditional) are assessed from historical data, expert judgment, or combination of both. In summary, a BBN can be formulated as shown in Figure 3-1.  Figure 3-1. Simple BBN framework (modified from Cockburn and Tesfamariam (2012)) Figure 3-2 is a flow chart showing the basic steps for manually creating and using a BBN. Variable A ProbabilityA1 P(A=A1)A2 P(A=A2)Variable B ProbabilityB1 P(B=B1)B2 P(B=B2)Unconditional Probability (UP)Unconditional Probability (UP)Variable AVariableBVariable CProbabilityC1 C2 C3A1B1 P(C11= C1|A1, B1) P(C22= C2|A1, B1) P(C33= C3|A1, B1)B2 P(C11= C1|A1, B2) P(C22= C2|A1, B2) P(C33= C3|A1, B2)A2B1 P(C11= C1|A2, B1) P(C22= C2|A2, B1) P(C33= C3|A2, B1)B2 P(C11= C1|A2, B2) P(C22= C2|A2, B2) P(C33= C3|A2, B2)Conditional Probability Table (CPT)A BC27  Figure 3-2. BBN operation flow chart For example, Figure 3-3 is an example of a Bayesian network with three variables: A, B, and C. Nodes are used to express variables in this network. The arrows denote dependencies or causal influences between the parent variables A and B, and the child variable C. The links allow us to show the dependence relationships among variables; the strength of each relationship is expressed by forward conditional probabilities, for example, the conditional probability of event C given that A and B occurred is P (C|A, B). The conditional probability table for node C, must list the values of P (C|A, B) for each possible combination of parent nodes. In this example, all the nodes are taken as binary variables with states “Yes” and “No” and the probability outcome for node C is shown in Figure 3-3. The values of nodes A (P (A = 0.9, P (A = 0.1)) and B (P (B = 0.7), P (B = 0.3)) can be obtained by either data collected or by expert judgement. Based on the available data and the states assigned for the nodes, the probability of occurrence for each node and the respective state was established. In this instance, expert judgement was used. For each possible combination of nodes A and B, node C was calculated based on Bayes’ theorem based on the relationships node C has with nodes A and B. Define relevant variablesSpecify causal links between variablesDefine conditional & prior probabilitiesAdd evidence/data to networkSelect posterior beliefs28  Figure 3-3. Bayesian Network example It is noteworthy that a conditional probability configuration reduces to unconditional probability if a variable does not have a parent node. Most computational methods have limitations including BBN. One limitation of BBN is that the calculations can become computationally demanding when the network in the model is heavily connected. 3.2.4.1 Bayesian Belief Networks used in other disciplines Over the past two decades, BBN has become a popular tool for modeling several forms of stochastic problems. There has been growing interest in applying BBN in areas such as reliability and risk analysis, forecasting, classifying, causal analysis, diagnostic analysis, etc. The environmental, health, military, electrical, and medical sectors have used the BBN approach (Das et al. 2002; Dawsey et al. 2006; Franzen 1999; Hayes et al. 2000; Jansen et al. 2003; Jones et al. 1998; Lucas 2004; Maglogiannis et al. 2006; Marcot et al. 2001; Pulliam and Dunning 1995; Ramoni et al. 2001; Stiber et al. 1999, 2004; Stow et al. 2003; Tesfamariam and Martín-Pérez 2008; Therrien 2002). Some specific applications include battlefield strategy, fault detection, and optical recognition (Fox et al. 2003; Karlsson et al. 2002; Liu and Zhang 2002). Bayesian Belief Networks have been used in tunneling. The uncertainties associated with various parameters affecting tunnel excavation can be evaluated and used to make better construction A ProbabilityYes P(A=0.9)No P(A=0.1)A BCB ProbabilityYes P(B=0.85)No P(B=0.15)Parent node CA BProbabilityYes NoYes Yes 0.8 0.2No 0.4 0.6No Yes 0.5 0.5No 0.2 0.8P(A) P(B)P(C|A,B)29 decisions. The ability to capture the uncertainties leads to more accurate schedule and cost predictions during tunnelling projects (Chung et al. 2006). Haas & Einstein (2002) used a Bayesian updating method in the computer code called Decision Aids for Tunneling (DAT) to help reduce tunnelling uncertainty. The geologic and geotechnical factors can be updated using Bayesian updating. The concept of Bayesian updating can help a tunnelling contractor reduce uncertainties related to prediction of construction cost and schedule while tunneling is in progress as new data becomes available (Haas and Einstein 2002). Dynamic Bayesian Network that is another form of BBN used to predict the performance of tunnel construction. A random variable (human factor) can be introduced in the model to handle influences from external and organisational factors. A Dynamic Bayesian Network developed by (Špačková and Straub 2013) was applied to estimate the excavation time of a 610 m long tunnel. The model showed its agility to capture the uncertainties estimated during the construction of the tunnel. Both observed data combined with expert knowledge were used in the model. Bayesian Belief Networks have been used in the field of slope stability analysis to verify the factor of safety. The factor of safety usually obtained from a slope stability analysis is often based on tests conducted to estimate the soil strength parameters and pore water pressures. Cao & Wang (2013) and Wang et al. (2013) used a BBN approach to better characterize site conditions measured with cone penetration tests. The factor of safety value for a slope is usually a presented as a deterministic value even though there is variability in the input parameters. In practice, many geotechnical engineers believe slopes with the same factor of safety also have the same probability of failure. However, this notion is not correct because the probability of a slope failing can be influenced by the uncertainty in ground conditions. Tang & Cheung (2000) used a BBN approach to evaluate the reliability of a soil slope. The BBN approach was used to calibrate the reliability index of the slope. Knowledge of prior probabilities is significant in calibrating the reliability index. Liu et al. (2013) used a Bayesian network to evaluate the stability of an open pit slope but their simple approach ignored many important variables such as in situ stress, slope height, rock mass quality, rock mass modulus, and pit wall shape that contribute to slope failures. The research approach in this thesis will include all the factors that Liu et al. (2013) used (i.e. orientation of discontinuities, blast damage, slope angle, and ground water) as well as  in situ stress, slope 30 height, rock mass quality, rock mass modulus, and pit wall shape. Additionally, the research approach goes beyond slope stability because the consequence of failure associated with slope instability is also addressed. The results presented in this thesis are the first rigorous application of the BBN approach in mining geotechnics for open pit slope management. 3.2.4.2 Bayesian Belief Network software packages There are numerous commercial and free software packages available to construct and implement a BBN. GeNIe (dslpitt 2014), AgenaRisk (Agena 2014), Netica software (Norsys Software Corp. 2014), and Microsoft Bayesian Network Editor and tool kit (MSBNx) (Microsoft Research 2014) are some software used for BBN. For this research, Netica was used to develop the proposed model. Additionally, Netica has flexibility for dynamic linking with Microsoft Excel. Thus, the developed model has the capability of being integrated into Microsoft Excel using the Visual Basic programming language to read and write from-to Microsoft Excel. Figure 3-4 shows a typical graphic user interface upon opening Netica software. There are three types of nodes: utility, decision, and nature nodes (Figure 3-4). A decision node is a node in a decision network that denotes a variable (or option) controllable by the decision maker. When the net is resolved, a decision rule is found for the node that augments the expected utility. A utility node is a node in a decision net whose expected value is to be optimized during reasoning for the best decision rule for individual decision nodes. Most often, the utility, decision, and nature nodes are used to create the decision network. It is important to note that a sensitivity analysis cannot be conducted for decision network. A nature node denotes the variable of interest. Nature nodes sometimes appear in a decision network and when that happens, a variable might be under the control of the decision maker. Thus, it is determined by nature. Additionally, when a nature node has a functional relationship with its parents, it is termed as deterministic node. Furthermore, if the relationship of the nature node with its parents is probabilistic, it is termed as a chance node (Norsys Software Corp. 2014). 31  Figure 3-4. Graphic user interface of Netica The following are the steps used to create a network using Netica. i. Click File on the menu bar and then click on New Network. Netica opens an empty network window to construct the network. ii. After determining the variables to be modeled in the network, create one node per variable and place them wherever you want in the window. If there is a causal or functional relationship between nodes, the generic way is to position the causing node (parent) above the caused node (child). To create a node, you can click the nature, utility or decision node depending on what is been modeled. Most often, problems being modeled are nature based. As such, nature node is clicked in this instance to model the problem. Depending on the number of variables to be modeled, you create the same number of nodes by clicking the nature node and dropping the node in the network window by a click in the open window. Once the node has been created and placed in the open net window, it can be moved anywhere within the network by clicking and dragging the node. iii. Once the node has been created, the properties of the node must be defined. Double-clicking on the node will open a node dialog box to enable the properties of the node to be defined (Figure 3-4). Each created node mush be uniquely named and the names are restricted to at most 30 characters. Characters used to name the node can include letters and Nature nodeDecision nodeUtility nodeArc (arrow) Input the name of the nodeOption to choose if node is discrete or continuousThis is box is used to describe the node or write an equation  for a node when necessaryMultipurpose boxClicking the table, gives the user the opportunity to input probabilities or verify the probabilities linked to the nodeUsed to define the states for the nodeDouble clicking a node opens this dialog box for the user to describe or define the node32 digits but the first character of the node must be a letter. Additionally, names must not have spaces. The name given to the node can be modified by double-clicking on the node. Unlike the name, the Title shown in the node dialog box has no character limitations in naming the title of the node and can include any character. iv. The node can either be a continuous indicating an inexhaustible range of possible values (i.e. 0 – 5, 5 – 8, etc.) or discrete indicating inexhaustible number of possible values (i.e. sick/alive/dead, tall/short, cold/hot, etc.). The opened node dialog box has a selector with continuous and discrete option that allows choosing whether the node can be represented as discrete or continuous. Depending on the type of variable, you choose the right one. v. After determining whether the node is discrete or continuous, the states of the node must be given using the space provided in the node dialog box for naming the states. The New button in the node dialog box must be clicked each time states are added to the node. The delete option in the node dialog box is used to delete states when not needed. vi. After the nodes have been created and the properties defined, the arrow is clicked to link the relationship between nodes (Norsys Software Corp. 2014). For more details about how to use Netica and how it works, refer to the Norsys Software Corp website. The website gives a detailed description of how to use the software. Case files are created to store data extracted from case histories. A single file was created in Excel to accommodate all the data collected for this thesis. The file was structured such that each column contained the case (i.e. data relevant) to a specific node. The excel file was converted into a text file before importing to Netica. The data imported to Netica by means of a case file, or inputted through expert knowledge are synthesized by Netica software to develop the conditional probability tables for all child nodes. Netica display the results in probabilities that can be shown in different ways including bar graphs and meters. Nature nodes are used to create the proposed mode. Utility and decision nodes are later incorporated into the proposed model to help decision-making. Where data are not available, expert knowledge, empirical and analytical equations are used. 33 3.3 Proposed Bayesian Belief Network Unexpected movements of pit walls can affect mine operations. An acceleration of movement rates leading to an open pit slope failure typically results in loss of production in the pit, and if the unstable rock moves quickly, it can harm personnel or damage equipment. This research establishes a rigorous way of making decisions based on the measured/predicted pit wall velocity leading up to a pit wall failure as well as the size and travel distance of the failure. Depending on the observed and predicted conditions leading up to a pit wall instability, the proposed BBN is designed to recommend appropriate operational responses to minimize production losses and equipment damage, and to save lives. Many variables need to be considered when determining pit wall movements that trigger an operational response. Interviews conducted with BC mine operators as a follow up of the completed questionnaire indicated that the BC mines depend on experience in defining pit wall movements that trigger warnings or stop-work orders. It is necessary not only to consider individual factors such as in situ stress, slope height, slope angle, ground water conditions, rock mass quality, etc. but also how they interact together. As a means of linking the geomechanics and ground water conditions to the mining activities, it is appropriate to consider how such interactions can be characterised to help determine the influence of pit wall movement on the consequence of failure for an open pit mining operation. Before developing a model using a BBN, it is important to develop the cause-and-effect network of all the important factors leading to potential pit wall failures and the resulting consequences of these failures. Factors that affect rock slope stability in open pit mines were considered having in mind the factors BC porphyry mines use to manage their pit walls. The factors used in this research are grouped into geotechnical properties, pit geometry, influence of blasting, and consequence of failure. These factors are used to predict the probability of occurrence of consequences and responses to unusual slope movement during daily pit operation. Rock slope stability is typically analysed by means of calculating the safety factor.  In contrast, the approach used here estimates different ranges of expected slope movement (velocity), where larger velocities are linked to higher probabilities for adverse consequences to a mining operation. Factors that are intrinsically embedded within other factors were also discounted to 34 avoid bias. For instance, the degree of weathering is captured in the uniaxial compressive strength and the discontinuity conditions of the rock mass and as such, it is not included as a factor in the BBN model. Although the proposed model shows the cause and effect relationship between factors, data available on the child node (i.e. effect) can inform decision makers the state of the parent node (i.e. cause). Thus, there is a two-way flow of knowledge instead of a conventional one-way flow of knowledge. One of the challenges of this work was the lack of quantitative data.  However, a BBN is a good tool to use because the developed model can be easily updated as more data are obtained. The data obtained are populated into the BBN as an unconditional probability (UP) and/or conditional probability table (CPT) assigned to each variable showing a parent-child relationship. The parent-child relationships used for the proposed BBN were based on field observations, empirical and analytical equations, and expert judgement. The states used for each parent and child node were also based on conditions or states already in use by researchers and engineers. Nodes with data reflected what was observed in the field. Each node has predefined states with typically a range of values for each state. For this research, both unconditional and conditional probabilities for the states are expressed in percentage. Child nodes with conditional probability tables based on analytical or empirical equations are also used in this research. 3.3.1 Data analysis The first step in analysing the data obtained from the BC porphyry mines was to use the data as it is. The second step adjusted the data set obtained from the mines to correspond to conditions observed during site visits to the mines. For both steps, the data were fine–tuned using an algorithm in the Netica program to see the differences in the final outputs of the nodes in the proposed model. During the fine-tuning process, the algorithm learns from the data provided to the model. The expectation-maximization (EM) and gradient descent are the most preferred techniques used in Netica algorithms to learn CPTs obtained through given data. The EM provides good results in a comprehensive range of conditions, even though the process can be slower than using the gradient descent algorithm with its faster processing time. The EM technique takes a Bayes net and repetitively finds a better Bayes net by performing expectation and maximization steps. 35 During the expectation process, the technique uses a consistent Bayes net inference with the current Bayes net to calculate the expected value of all missing data. Thus, the expectation process is the step at which the missing values of the observed data are estimated. After the expectation  process, the maximization process finds the maximum likelihood given by the original data, plus the expected value of the missing data (Korb and Nicholson 2010; Neapolitan 2003; Norsys Software Corp. 2014; Russell and Norvig 2009). The research implemented the expected-maximization technique to fine-tuned the CPTs of the nodes given the quantitative data. Quantitative data available for this research were used for parent nodes in the proposed BBN model. Child nodes that had empirical or analytical relationships were conditioned based on these equations as discussed in the subsequent chapters. Nodes with equations were converted to CPTs during the training of the proposed model.  Qualitative data in the form of expert judgement was used to create CPT for nodes with no quantitative data. The factors used in the model are grouped into geotechnical properties, blast damage, pit wall instability characteristics, ground water conditions, slope geometry, and consequence of failure factors (Tables 3-1 to 3-3). 36 Table 3-1. Geotechnical properties and slope geometry parameters Node Type of data Probability Rock unit weight Measured data Unconditional Vertical in situ stress Measured data Conditional Horizontal to vertical stress ratio Expert judgement  Unconditional Ground water conditions Expert judgement Unconditional UCS Measured data Unconditional RQD Measured data Unconditional Discontinuity spacing Measured data Unconditional Discontinuity orientations Measured data Unconditional Discontinuity shear strength Measured data Unconditional GSI Measured data Conditional Blast damage Expert judgement Unconditional Rock mass strength Measured data Conditional Rock mass modulus Measured data Conditional Slope angle Measured data Unconditional Pit wall shape Expert judgement Unconditional Slope height Measured data Unconditional  Table 3-2. Pit wall instability characteristics Node Type of data Probability Plane sliding Measured data Conditional Wedge sliding Measured data Conditional Toppling Measured data Conditional Rotational failure Measured data Conditional Slope velocity Expert judgement Conditional Strain Measured data Conditional Potential rockslide debris volume Expert judgement Conditional Travel distance of failed rock mass Measured data Conditional  37 Table 3-3. Consequences of failure Node Type of data Probability Harm to personnel Expert judgement  Conditional Equipment damage Expert judgement  Conditional Production loss Expert judgement  Conditional  Figure 3-5 shows the proposed BBN model to manage open pit slopes. In Figure 3-5, the nodes (e.g., RMR, GSI, RQD, etc.) show the multiple states of the nodes. The numbers beside the states of each node are the probability of occurrence of each state in the node corresponding to the horizontal black bars. This probability of occurrence sums up to 100%. Some of the nodes in the proposed BBN model are colour-coded to help the user understand the BBN structure. The pink colored nodes are the most critical nodes that determine the consequences of pit wall failures on open pit activities. As shown in Figure 3-5, these pink colored nodes are linked to the red colored nodes (i.e. consequence of failure). A mine can use the states within the pink and red colored nodes to make decisions regarding mining activities in the pit. The light green colored nodes are parent nodes with UPs. The light brown colored nodes are child nodes with CPTs and these nodes are parent nodes leading to the pink and red colored nodes. The light purple nodes are child nodes with CPTs. Chapters 4 to 6 discuss the factors used in the BBN model.  Quantitative data obtained from Gibraltar, HVC, and Endako mines are used construct and training the proposed model. Qualitative data obtained from all six mines were also used. 3.3.1.1 Data used for conditional probability tables Conditional probability tables are key aspects of a BBN.  These tables establish the relationships between two linked nodes.  There are different techniques that can be used to establish a CPT.  The techniques include using an equation between two nodes to create a CPT; using available data for parent and child nodes to complete the CPT for the child node to establish the link between the nodes; and using expert judgement to establish the relationship between parent and child nodes thereby completing the CPT for child nodes. 38 The first technique uses nodes linked by an equation to create CPTs. For this research, nodes with equations (i.e. Vertical in situ stress; Rock mass modulus; Rock mass strength; Travel distance; Material property, a; Material property, s; and Strain) are converted to CPTs. In Netica, it is important to discretized parent nodes that have continuous variables before nodes with equations can be converted to CPT. After the node with continuous variable has been discretized, Netica can easily convert the equation to a CPT. For example, the states of node rock unit weight (γ, kN/m3) are 20 – 24; 24 – 28; and 28 – 40 and the states of node slope height (z, metres are 0 – 100; 100 – 250; 250 – 500; 500 – 800; and 800 – 1500.  The states of node vertical in situ stress (σv) are 0 – 20; 20 – 40; and 40 – 60. The states assigned to each node replicates the present conditions in BC porphyry mines.  However, the range for each state were based on expert judgement. It is important to note that the range and states can be changed if needed to reflect conditions of a mine operation. Continuing with this example, the functional relationship between the parent nodes γ and z and the child node is vertical in situ stress (σv) is; 1000/zv γσ =  MPa (7) The conversion process of the above relationship into a CPT in Netica requires the user to specify how many random samples (simulation of random numbers) to make for each cell (i.e. table entry). It is important to note that the larger the number of random samples, the more accurate the results will be.  For this research, every child node having an equation was converted into a CPT was based on 1,000,000 random samples.  After the user has entered the sampling number, Netica decides where within each discretized cell to calculate the equation. Netica randomly selects numbers within the cell and uses the mean of the results obtained.  Thus, depending on the values given by nodes γ and z; node σv is calculated based on the functional relationship and the result is allocated to the cell that has the value of the state in node σv. Netica generates the CPT based on the given number of states of the child node and the number of states of each of its parent nodes (Norsys Software Corp. 2014). Table 3-4 shows the CPT result for σv after completion of the conversion process using the UP of parent nodes. The CPT can be adjusted after it is created to one significant figure as shown in Table 3-4. 39 Table 3-4. CPT for “Vertical in situ stress” node   σv states (%) z states γ  states 0 to 20 20 to 40 40 to 60 Total  0 to 100 0 to 24 100 0 0 100 0 to 100 24 to 27 100 0 0 100 0 to 100 27 to 40 100 0 0 100 100 to 250 0 to 24 100 0 0 100 100 to 250 24 to 27 100 0 0 100 100 to 250 27 to 40 100 0 0 100 250 to 500 0 to 24 100 0 0 100 250 to 500 24 to 27 100 0 0 100 250 to 500 27 to 40 100 0 0 100 500 to 800 0 to 24 100 0 0 100 500 to 800 24 to 27 93.3 6.7 0 100 500 to 800 27 to 40 35 65 0 100 800 to 1500 0 to 24 75 25 0 100 800 to 1500 24 to 27 1 99 0 100 800 to 1500 27 to 40 0 58 42 100  Another technique for creating CPTs is by learning from the collected data for the parent and child nodes. With the link between the parent and child nodes established, if the data collected are a selection from the population that is being modelled, the number of occurrences of values within each state can be used to approximate the desired probabilities. These probabilities can be manually entered into the CPT cell. Thus, for each parent node state, the corresponding data for the child node state can be entered into the CPT table for each row. For each row of the parent and child node states, the probabilities given should sum to 100%. This technique can also be done using Netica software (Norsys Software Corp. 2014). However, for this research, this technique was not used to create a CPT for the child nodes because insufficient data were available for any parent-child links. The last technique is using expert judgment to create the CPT and this technique was used in this research to create CPTs for child nodes with no equation providing a functional link to the parent 40 nodes.  Expert judgement was used to complete the CPT for the child nodes. For example, expert judgement was used to complete the CPT for the equipment damage node. For this research, slope velocity and travel distance are identified as nodes that can affect equipment damage. This is because during high rates of slope movement, equipment in the pit becomes vulnerable to the impending hazard. Additionally, equipment parked near a slope failure are exposed to damage as a failed rock mass volume travels. A table is created showing all possible combination of the child and parent node states.  The probability values in the cells in the table were entered based on expert judgement, knowledge, and experience gained from mine operators during pit activities. For instance, the first row in Table 3-5 shows the equipment damage probabilities when the slope velocity is less than 2 mm/day and travel distance ratio is between 0 – 0.21. As slope velocity is very low, the probability that equipment damage will occur is effectively zero. At that slope velocity, the pit wall movement is normal for pit operations and as such, pit activities will be ongoing. A slowly deforming slope will result in no instability and it is especially unlikely that the moving rock will travel a large distance.  In contrast, for the tenth row in Table 3-5, the slope velocity is between 100 – 300 mm/day and the travel distance ratio is 0 – 0.21. In this case, there is a higher chance that equipment damage can occur. This is because slope failure is imminent and the failed debris volume may travel a considerable distance thus causing equipment damage. Using a similar logic, each row in the table is filled with the approximate probability values. 41 Table 3-5. CPT for “Equipment damage” node   Equipment damage states (%)  Slope velocity states  Travel distance states No damage Minor damage Major damage Complete loss Total 0 to 2 0 to 0.21 95 5 0 0 100 0 to 2 0.21 to 0.42 95 5 0 0 100 0 to 2 0.42 to 0.63 95 5 0 0 100 2 to 5 0 to 0.21 85 15 0 0 100 2 to 5 0.21 to 0.42 85 15 0 0 100 2 to 5 0.42 to 0.63 90 10 0 0 100 5 to 100 0 to 0.21 75 20 5 0 100 5 to 100 0.21 to 0.42 75 20 5 0 100 5 to 100 0.42 to 0.63 80 15 5 0 100 100 to 300 0 to 0.21 0 5 10 85 100 100 to 300 0.21 to 0.42 10 15 30 45 100 100 to 300 0.42 to 0.63 50 30 10 10 100  The subsequent chapters discusses the factors and links between node using in the proposed model. Each node is discussed as well as the UP/CPT assigned to the nodes. 42  Figure 3-5. Proposed Bayesian Belief Network model framework to manage open pit slopes43 Chapter 4: Geotechnical Properties and Slope Geometry This chapter discusses the geotechnical and slope geometry properties used to construct the proposed BBN model. Additionally, data obtained from BC mines are shown as histograms in respective sections. Sections with no histograms indicate no quantitative data were obtained except for expert judgment. Assumptions made through expert judgement were deduced from mine site visits, work experience, engineering judgement, and interviews. 4.1 Rock unit weight The unit weight of the rock affects the stress within the pit walls. Higher rock unit weight is often correlated with higher rock strength. For porphyry mines, the rock unit weight (γ) usually falls within a narrow range of values depending on the geological formation. Porphyry rocks typically have a unit weight of approximately 26 kN/m3 (BGC Engineering, 2012; Golder Associates 2002, 2009a; Graden 2012; West et al. 2001; Yasrebi et al. 2014). Unit weights less than 24 kN/m3 or greater than 28 kN/m3 are not common. This research uses a minimum unit weight of 20 kN/m3 and a maximum greater than 28 kN/m3 based on the inherent variability of the rock mass. Three states are defined for the rock unit weight as shown in Table 4-1. It is important to note that the states used in this research has not been used in any research work. Moreover, the states can be revised based on the needs of the mine operator. Because majority of porphyry rocks have unit weight of 26 kN/m3, the initial UP assigned to the γ node states are low: 5%, normal: 90%, and high: 5%. Table 4-1. Rock unit weight states States γ (kN/m3) Low 20 – 24  Normal 24 – 28 High  28 – 40   4.2 Vertical in situ stress Vertical in situ (σv)stress as expressed by Brown & Hoek (1978)  is used by BC mine operators to estimate the vertical in situ stress. Brown & Hoek (1978) analysed world data on measured in situ stresses and observed that the in situ vertical stress is the approximately equal to the overburden stress. It is assumed that the vertical stress increase with depth due to 44 the overburden weight. Therefore, Equation 7 is used to calculate the vertical in situ stress. There has not been a definition for low, medium or high σv. Therefore, this research defines an interval of 20 for σv with σv greater than 40 MPa considered high. Table 4-2 shows the states and ranges used for the vertical in situ stress (Figure 4-1). These states can be modified based to meet the specific need of a mine.  Figure 4-1. Factors used to determine vertical stress in the BBN Table 4-2. Vertical in situ stress states States σv (MPa) Low 0 – 20 Moderate 20 – 40 High  40 – 60   Equation 7 was converted to CPT using the UP of input variables with Netica software. A snap shot of these probabilities is shown in Table 4-3. 45 Table 4-3. Snap shot of CPT for "Vertical in situ stress" node   Vertical in situ stress states (%) Slope height states Rock unit weight states 0 to 20 20 to 40 40 to 60 Total  0 to 100 20 to 24 100 0 0 100 0 to 100 24 to 28 100 0 0 100 100 to 250 20 to 24 100 0 0 100 ………… ………… ………… ………… ………… ………… 100 to 250 24 to 28 100 0 0 100 100 to 250 28 to 40 100 0 0 100 250 to 500 20 to 24 100 0 0 100 ………… ………… ………… ………… ………… ………… 800 to 1500 28 to 40 0 58 42 100  4.3 Horizontal to vertical stress ratio The excavation-induced stresses in an open pit and the response of the pit walls to the excavated pit are sensitive to the ratio of horizontal to vertical in situ stresses. The horizontal stress can be larger than the vertical stress in regions where the tectonic stresses have created thrust faulting (Fossen 2010; Pollard and Fletcher 2005). In this case, the vertical in situ stress is the minimum principal stress as the stress field becomes compressive (Peng and Zhang 2007). Alternatively, where the faults in a region are dominated by normal faults the horizontal stress is typically less than the vertical stress. In this instance, the vertical in situ is maximum principal stress (Peng and Zhang 2007).The horizontal stress in one direction can differ from the horizontal stress in another direction. The horizontal stress in the direction perpendicular to the pit wall is of relevance to the behaviour of a pit wall. Unlike vertical in situ stress that is easily estimated on the field, horizontal stress measurement are very difficult to estimate. However, measurements of horizontal stresses at civil and mining sites around the world have shown that that the ratio of the average horizontal stress to the vertical in situ stress (i.e. k value) tends to be high at shallow depth and decreases with depth (Hoek and Brown 1980). The ratio of horizontal to vertical in situ stresses is usually less than 0.9 but not greater than 3.0. Therefore, a range starting from 0.3 to 3.0 was used in this research. The interval given for this node was based on the reasoning 46 that between 0.9 to 1, k can be lithostatic. As such, the interval was created around this range from been low k (i.e. less than 0.9) to high k (greater than 1.1). Table 4-4 are the states used to determine the ratio of horizontal to vertical in situ stresses.  The states used are specific for this research but can be revised by mine operators based on their needs. Horizontal to vertical in situ stress ratio is usually high at low slope height but decreases when the pit slope deepens (Brown and Hoek 1978; Şen and Sadagah 2002). Most of the pit slopes in BC are not too deep (Nunoo et al. 2015), therefore the estimated UP for the states of horizontal to vertical in situ stress ratio node states are low: 10%, lithostatic: 25%, and high: 65%. On site interviews conducted during the time of this research reveals that, no BC open pit porphyry mine consider the effect of k on slope velocity. Table 4-4. Stress ratio states States k  Low 0.3 – 0.9  Lithostatic 0.9 – 1.1 High  1.1 – 3   4.3.1 Stress associated with open pit rock slopes It is important to understand the stress state in the rock mass forming the pit wall to be able to comprehend the behaviour of the slope. The stresses acting on the pit wall are important factors affecting the stability of the rock mass. In situ stresses (prior to mining) in the rock mass are a function of gravitational stresses rising from the weight of the overlying rock, tectonic stresses from external tectonic forces. The vertical in situ stress is usually assumed to be due to the weight of the overlying rock mass, whereas the in situ horizontal stress is challenging to predict as tectonic actions come into play. As mining commences, the in situ stresses that were carried by the excavated material are transferred to the remaining intact rock. These stresses are termed induced stresses as they redistribute stresses in the rock mass. The induced stresses cause the rock mass to undergo elastic rebound, relaxation, and/or dilation. Horizontal stress is redistributed and concentrated at the toe of the slope causing the pit wall above to undergo relaxation (Sjöberg 1999). Movement rates from this effect are about 0.1 to 4 mm/day even though much higher sudden 47 movements (velocities) can be experienced at the onset of excavation (Martin 1993; Zavodni 2000).  Figure 4-2. 2D relaxed zone within open pit walls resulted from mining Open pit mines are now reaching a depth of 1000 m. At this depth, stress levels are very high, in particular when the horizontal in situ stresses are greater than the vertical stresses. At this depth, the rock mass is typically strong and unweathered except for fault zones which will have low rock mass quality. Stress distribution can play a major role in the stability of the slope of the pit. Stacey (1970) found that opposite slopes of an open pit do not interact when the floor width of the pit exceeds about 0.8 times the height of the slope. This implies that the large horizontal in situ stress field has a major influence on the stress distributions in slopes and outweighs the influence of any variation in Poisson’s ratio. Valliappan & Evans (1980) and Brown et al. (1980) used non-linear finite element analyses to determine the effect of stress on rock slopes and they found qualitative agreement between calculated results which was mainly the location of tensile stresses and the interpretations of instability. Dowding & Gilbert (1998) did the same analysis but under seismic and blast vibration loading. Others have used a calibration approach to predict slope behaviour taking into account the measured deformations (Board et al. 1996; Coggan and Pine 1996; Hencher et al. 1996). After using both continuum and discontinuum numerical models in their work, Board et al. (1996) discovered that the discontinuum method could model discontinuous rock masses very well. The use of stress analysis methods to determine slope stability have focused on stress and failure aspects with little attention given to strain distributions in slopes (Stacey et al. 2003). In response to the short-comings of previous stress-related research work, Stacey et al. (2003) Relaxed zoneCrestToeIn situ stress conditionσhσhσv48 developed extensive 2D finite element stress analyses of different slope geometries using elastic analyses with fine meshes to enable precise results. The geometry of the pit wall was modeled at intermediate mining stages to help define the effects of stress and strain distribution. The results from Stacey et al. (2003) indicate that for a 2D analysis of tensile stresses, when k is 0.5, the tensile stress is developed under the pit floor at a slope angle of around 30° with 1200 m slope height. However, when k is 1, the tensile stress is developed at the crest of the slope. Also as the slope angle increases and k increases, the tensile stress within the crest also increases. The results and analysis obtained by Stacey et al. (2003) suggest the reason, in some cases, for the existence of tension cracks behind the crest of the slope during an initiation of slope instability. However, Stacey et al. (2003) assumed homogenous, isotropic and elastic material behaviour for open pit slopes, although, in fact, local stress redistribution along pre-existing discontinuities is to be expected on the field. Moreover, assuming the geometry of the pit as two-dimensional was a critical assumption, even though tension cracks behind the slope crest were observed. This is because the curvature of an open pit (i.e. concave, planar or convex) influences the in situ stress redistribution within the open pit walls. Despite the work by Stacey et al. (2003), evaluations and verifications of the total stress state in and around open pits are relatively rare (Sjöberg 1996). Therefore, it is important for mine operators to consider the state of k in determining the pit wall performance. 4.4 Ground water The presence of ground water within the rock mass can affect the stability of the slope by reducing the shear strength of potential failure surfaces. Hassani & Scoble (1981) reviewed 82 slope failures in mines and 51% of the cases showed water as a major contributing factor to the incident. Ground water pressure reduces the shear strength and thus reduces the safety factor of the slope. The ground water pressures originate from rainwater and snowmelt infiltration and flow along discontinuities or fractures (Sjöberg 1999). The amount of ground water present within a slope can vary in response to precipitation, temperature variation, and the orientation of discontinuities within the slope (Brawner 1982; Sjöberg 1999). The highest ground water pressures are typically associated with the spring freshet. This was evident during visits to the BC mines and interviews conducted with the mine operators showed that the spring freshet caused most of their instability problems. It is worth noting 49 that the ground water is one of the parameters used to determine the quality of the rock mass (i.e. RMR). Ground water also influences weathering within the rock mass through mineralogical and chemical alterations. Additionally, ground water reduces the stability of the pit wall and may result in acceleration of slope movements. Ground water conditions can be recorded by means of wells and standpipe piezometers. However, data concerning ground water conditions in open pit mines is often limited or not available. Although mine operators implement drainage systems to reduce water pressure behind the pit wall, there is no database keeping records of amount of water pumped out; or amount of water that should be pumped out. The variation in groundwater levels due to changes in the climatic condition is also unknown. Thus, making decisions about the ground water is difficult to estimate. To account for ground water effects on slope stability, expert judgement is used along with known seasonal variations in the temperature and precipitation. Only three states are used to describe ground water condition because of feedback obtained from discussions with the mines and other experts (Table 4-5). However, all the states used in the RMR classification system (Bieniawski 1976) can be used in the BBN if a higher degree of resolution is desired by a mining operation. Mine operators must assess the current ground water condition taking into consideration seasonal variation. Thus, this parameter can change over time. Table 4-5. Ground water condition states States GWC/Description Dry Slope surface is dry Moist Slope surface has some wet areas; water is not visibly flowing from the surface Saturated Slope surface has many wet areas and water flow  Figure 4-3 show a section of a pit wall at Highland Valley Copper mine. It is evident that this pit wall location has high probability of moist state occurring. Therefore, in the BBN, the UP that this pit wall location has dry, moist, and saturated states is approximated to be 15%, 75%, and 10% respectively. In contrast to Figure 4-3, the pit wall in Figure 4-4 is looks more dry. As such, the approximate UP for Figure 4-4 ground water states is 90%, 10%, and 0% for dry, moist, and saturated states respectively. Usually before a working floor is created in the pit, the ground water behind the pit walls is lowered. The pit walls are usually dry when 50 deeps wells are able to pump the water out thereby reducing the ground water. Sometimes the pit walls will show signs of seepage indicating the ground water is high behind the pit walls. Based on the BC mine visits and interview conducted, the initial UP assigned to the ground water node states are dry: 70%, moist: 20%, and saturated: 10%.  Figure 4-3. Moist to saturated ground water condition at Highland Valley Copper mine (photo taken 2013)  Figure 4-4. Dry ground water condition at Copper Mountain mine (photo taken 2013) 51 4.5 Uniaxial compressive strength The uniaxial compressive strength (UCS) is an important parameter for characterizing rock in geotechnical engineering designs (Basu and Aydin 2006; Hoek and Brown 1997). The rock strength grading system suggested by ISRM (1981) is used to define the UCS states (Table 4-6). This rock strength grading system is commonly used by BC mines (BGC Engineering, 2012). Weathering can reduce the UCS of rock; hence the influence of weathering is implicitly included in the measured UCS. During site visits to four BC mines, majority of the rock masses in the open pits were observed to typically consist of fresh rock to moderately weathered rocks. The typical UCS for porphyry rocks ranges from 25 – 90 MPa (BGC Engineering 2012; Golder Associates 2009a, 2012; Graden 2012; Pishbin and Fathianpour 2014). Most of the BC mines consider this parameter in their slope stability analysis after an incident has occurred. The site visits also shows most of the UCS range from R3 – R4 for open pit porphyry mines in BC. The data shown in Figure 4-5 is a good representation of UCS in the four visited mines in BC. Therefore, the data shown in Figure 4-5  was used to express the UP for UCS node. Table 4-6. UCS states (ISRM 1981) UCS (MPa) Strength Grades Description/State 0.25 – 1 R0 Extremely weak rock 1 – 5 R1 Very weak rock 5 – 25 R2 Weak 25 – 50 R3 Medium strong 50 – 100 R4 Strong 100 – 250 R5 Very Strong  52  Figure 4-5. Strength grades (Golder Associates 2007, 2009a) 4.6 Rock quality designation The parameter called rock quality designation or RQD was introduced by Deere (1964) to quantify the quality of a rock mass by assessing the degree of fragmentation cause by joints and other discontinuities in the rock mass. RQD is defined as the percentage of intact core pieces longer than 100 mm in a total length of a core run. RQD is a more sensitive index of the core quality than the core recovery (Singh and Goel 1999). To estimate RQD, the International Society for Rock Mechanics (ISRM) suggests that a core size of at least NX (~54.7 mm diameter) should be used and that this core should be recovered using a double-tube core barrel via diamond drilling. Often fractures are created during the drilling and recovery process of the core. As a result, ISRM (1981) recommends that in counting the core length for RQD, these fractures should be ignored. The states used for RQD are the same as those proposed by Deere (1968) and are listed in Table 4-7. Very poor RQD (less than 25%) reveals of closely fractured rock mass, while an RQD greater than 90% is an indicates a fairly massive unfractured rock mass. Typical RQD values for porphyry rock masses range from 40% – 100% (BGC Engineering 2012; Rustan et al. 2010). Figure 4-6 shows RQD data obtained in this research. 01020304050601 2 3 4 5 6R0 R1 R2 R3 R4 R5Frequency of occurenceStrength grading system data to estimate UCS53 Table 4-7. RQD states (Deere 1968) States RQD Very poor rock 0 – 25 Poor rock 25 – 50 Fair rock 50 – 75 Good rock 75 – 90 Excellent 90 – 100  The data shown in Figure 4-6 is a good representation of RQD in the four visited mines in BC. Therefore, the data represented in Figure 4-6 was used as the UP for this parameter.  Figure 4-6. RQD data obtained from Gibraltar and Endako mines (Golder Associates 2007, 2009a) 4.7 Discontinuity spacing Discontinuity spacing determines the size and shape of blocks of rocks in a slope and has an influence on the overall rock slope stability (Devkota et al. 2009; Wyllie and Mah 2004). Discontinuities include joints, bedding or foliations, faults, shear zones, or other surfaces of weakness. The discontinuity spacing (DS) is the average distance between two adjacent discontinuities in a discontinuity set, measured perpendicular to the discontinuity plane. The 0204060801001 2 3 4 5RQD statesVery poor rockPoor rockFair rockGood rockExcellentFrequency of occurence54 states and range used for this variable are listed in Table 4-8 and they are the same as those proposed by Bieniawski (1976) for use in the RMR rock mass classification system. A typical range for DS for porphyry deposit at is 500 mm – 2500 mm and 0 – 40 mm for Endako and Gibraltar mines respectively (BGC Engineering 2012; Golder Associates 2007, 2009a). During a site visit to Endako mine, it was evident that the instabilities that had occurred in most of the sections of the pit resulted from the presence of faults. Therefore, there is the strong likelihood that the DS data obtained from Endako mine were collected from sections beside or within fault zones. Generally, the site visits revealed that DS ranges from very close to close spacing conditions for BC mines. Table 4-8. Discontinuity spacing states (Bieniawski 1976) States DS (mm) Very close 0 – 60  Close  60 – 200  Moderate 200 – 600  Wide 600 – 2,000  Very wide 2,000 – 6,000   From field observation and knowledge obtained from field reports (BGC Engineering 2012; Golder Associates 2007, 2009a), the estimated UP for DS  node states for BC open pit porphyry mines used for this research are very close:10%, close: 40%, moderate: 35%, wide: 10%, and very wide: 5%. 4.8 Discontinuity conditions The discontinuities in a rock mass affect the rock mass strength and stiffness. The discontinuity conditions (DC) are affected by the roughness of discontinuity surfaces, discontinuity wall separation (aperture), weathering, continuity or persistence, and infilling or gouge material. Weathering affects the discontinuity conditions thereby weakening the rock mass strength (Price and Freitas 2008). Therefore, the effect of weathering is captured in discontinuity conditions. The states used for this variable are listed in Table 4-9 and their descriptions are the same as those proposed by Bieniawski (1976). Although data were not available during site visits to four mines, the rock masses in the open pits were observed to contain fair to good discontinuity conditions. After site visits to all the pits in the four mines 55 and interview conducted with industrial partner, the UP estimated for DC node states are poor: 5%, fair: 40%, moderate: 35%, good: 15%, and very good: 5%. Table 4-9. Discontinuity condition states (Bieniawski 1976) States Description Poor  Discontinuity has gouge less than 5 mm thick Fair Discontinuity wall rock surface separation is 1-5 mm with thick gouge or 1-5 mm wide continuous discontinuity Moderate Discontinuity is slightly rough and moderately to highly weathered; separation is less than 1 mm Good Discontinuity is rough and slightly weathered, wall rock surface separation less than 1 mm Very good Discontinuity has very rough surfaces, has no separation, and it’s not continuous  4.9 Shear strength of critical discontinuities The shear strength of critical discontinuities (e.g. faults, shear zones) is typically assumed to obey a Mohr-Coulomb failure criterion governed by two strength parameters: friction angle (ϕ) and cohesion (c) (Fang 1990; Goodman 1989; Goodman and Bray 1976; Hoek 1983; Wyllie 1999; Wyllie and Mah 2004). A common method for determining the shear strength parameters is a direct shear test. An alternative method to determine the shear strength is to do back analysis of an existing slope failure to determine the shear strength parameters that must have mobilised at the time of failure (Fang 1990; Goodman 1989; Goodman and Bray 1976; Hoek 1983; Wyllie 1999; Wyllie and Mah 2004). Typical values of ϕ for discontinuities in BC porphyry deposits range between 20°– 35° (BGC Engineering 2012; Golder Associates 2007, 2009b). Due to cracks and discontinuities within the rock mass, cohesion is often assumed zero. Therefore, ϕ is the only shear strength parameter used in this research. Due to inherent variability of the rock mass, a range of ϕ from 0° – 50° with an interval of 10° was chosen for the purpose of this research. Table 4-10 shows the different states of ϕ. Based on field observations and quantitative data (BGC Engineering 2012; Golder Associates 2007, 2009b), the UP estimated for ϕ are very low: 10%, low: 20%, moderate: 50%, high: 20%, and very high: 0%. The UP assigned to very high state was 0% because ϕ is not occurring in that state in the BC mines even though it might occur in mines outside BC. 56 Table 4-10. Friction angle states States ϕ (°) Very low 0 – 10 Low 10 – 20 Moderate  20 – 30 High  30 – 40 Very high 40 – 50  4.10 Geological Strength Index (GSI) Various rock mass classification systems have been developed for application to slope stability analyses. All the BC open pit porphyry mines use the rock mass rating (RMR) classification system. The RMR values are converted to Geological Strength Index (GSI) for the purpose of this research. The original definition of RMR was published in 1976 (Bieniawski 1976). It was subsequently revised in 1989 (Bieniawski 1989). These systems are identified by the year using subscripts RMR76 and RMR89. The data obtained from the questionnaire indicates that RMR76 is mostly widely used by mines in BC to quantify the rock mass quality. The RMR values range from less than 20 (very poor rock) to 100 (very good rock). The application of RMR is best performed by dividing the rock mass around an open pit into regions of similar geological and rock mass characteristics. Within each region or structural domain, the rock mass is classified (Bieniawski 1993). However, often the RMR classification is conducted during a geotechnical drilling program before mining even begins using core samples of the rock. This gives the mine a general overview of the rock mass condition around the planned open pit. Five parameters are used to classify a rock mass using the RMR system. They include the uniaxial compressive strength of rock (UCS), rock quality designation (RQD), discontinuity spacing, discontinuity conditions, and ground water conditions. Figure 4-7 shows the factors used to estimate RMR in the model. 57  Figure 4-7. Factors used to determine RMR in the BBN To directly estimate GSI, the intact rock UCS and the groundwater pressure in the rock mass are ignored because GSI is purely a function of the block size (blockiness) of the rock mass and the shear strength characteristics of the joints. However, there is a strong correlation between GSI and RMR that allows for the use of the RMR data routinely collected by the mines to estimate GSI. This thesis uses GSI because it can be used to estimate the strength and modulus of a rock mass (Hoek et al. 2002). Hoek et al. (1995) presented a study of the relationship between RMR76 and GSI. They assumed the rock mass to be dry (assigning ground water rating =10) and retained the rating value assigned to the rock’s UCS. Thus the relationship between GSI and RMR76 is: GSI = RMR76 – (ground water rating) +10 (Hoek et al. 1995) (8) Since the rock mass in most open pit mines in BC is dry or nearly dry, the ground water rating embedded within supplied RMR data is close to 10. This allows the value of RMR76 to be directly substituted for GSI with little error. Therefore, Equation 8 was used to estimate the GSI node in the BBN. Table 4-11 shows the states for GSI and RMR. Table 4-11. GSI and RMR states States RMR/GSI Very poor rock 0 – 20 Poor rock 20 – 40 Fair rock 40 – 60 Good rock 60 – 80 Very good rock 80 – 100   Figure 4-8 shows a histogram of the predicted GSI (obtained via RMR) for BC mines based on UP of parent nodes. The histogram reflect the conditions as seen on the field. Porphyry 58 deposits in BC mines typically have rock mass with RMR values ranging from fair to good (Nunoo et al. 2015).  Figure 4-8. Predicted GSI based on RMR for BC mines Conditional probabilities for RMR based on a parent-child relationship was determined using the rating system developed by (Bieniawski 1976). The rating embedded within each state of the parent nodes were added together to get a rating number assigned to the RMR state. Due to the range of values for the RMR states, the RMR was deterministic as it follows the classification system. Snap shot of the CPT for using the rating system is given in Appendix B. The histogram of the CPT for RMR using Bieniawski (1976) rating system is shown in Figure 4-9. It can be seen from Figure 4-9 that although the five parent nodes are equally occurring to determine RMR, the child node (RMR) does not show uniform distribution of the output states. 0204060801001 2 3 4 5Very poor Poor rock Fair rockGood rockVerygood Frequency of occurenceRMR states59  Figure 4-9. CPT data of RMR with no data from parent node 4.11 Blast damage The mines in BC use controlled blasting near the final pit wall to fragment the rocks for easy excavation, loading, and milling. Controlled blasting methods are used to control adverse impacts. For instance, over-break of the rock mass, ground vibrations, fractures within the intact rock mass, reduction of dilution, etc. are lessened because of controlled blasting. Although control blasting does minimize the ground vibration, blasting in general affects the rock slope stability (Jimeno et al. 1995). Feedback obtained from experts in the field and an overview of hard rock open pit slope instability indicated that ground vibrations from blasting can trigger slope instabilities. Therefore, the blast damage is considered in pit wall movement as well as the failure modes. Additionally, the disturbance factor from blasting is used to determine rock mass strength and Em. Depending on the proximity of blasting to the rock face, the rock slope is disturbed because of this activity. The disturbance factor, D, is used to determine the different effects of blasting on the rock mass. Table 4-12 shows the three states used in the BBN based on Hoek (2002) and Hoek et al. (2002). 0204060801001 2 3 4 5Very poor Poor rock Fair rockGood rockVerygood Frequency of occurenceRMR states60 Table 4-12. Estimating disturbance factor D (Hoek 2002; Hoek et al. 2002) States  D Description Low 0 Blasting results in minimal disturbance to the surrounding rock mass Medium 0.7 Modest blast damage because of blasting High 1 Disturbance due to heavy production blasting and also due to stress relief from overburden removal  It is important to note that data obtained from the completed questionnaires shows that all mines in BC use control blasting techniques to minimize slope stability issues (Appendix C). Therefore, the initial UP for the D node states are low: 10%, medium: 30%, and high: 60%. 4.12 Rock mass strength The strength of a rock mass depends not only on the strength of the intact rock pieces, but also upon the degree of fracturing and the nature of the fracture surface. It is expensive and usually impractical to carry out large-scale field tests to determine the overall strength of a rock mass. Therefore, empirical methods are used to estimate the rock mass strength (RMS). The Hoek et al. (2002) method is commonly used in mining.  Figure 4-10. Factors used to determine rock mass strength in the BBN The  Hoek et al. (2002) method uses and modifies the unconfined compressive strength (UCS) of intact rock to account for the degree and nature of fracturing in the rock mass (Figure 4-10). The rock mass strength, expressed in terms of the principal stresses, is (Hoek et al. 2002): abc sUCSm  +σ′σ+σ′=σ′ 331  (9) 61 Where σ1´and σ3´ are the maximum and minimum effective stress at failure; mb is the value of the Hoek & Brown constant m for the rock mass, s and a are constants that depend upon the characteristics of the rock mass. The parameters s and a are associated with the rock mass rating through the GSI. The focus of the research is to determine the movement on the surface of the pit wall and possibly at the toe of the wall in order to make appropriate operational response decisions. These locations are free surfaces with zero normal stress and one can set σ3´= 0 to calculate the rock mass strength at the pit wall. At the pit wall, Equation 9 becomes (Hoek et al. 2002): ( )asUCS=′1σ  (10) Where s and a are: −−=Ds39100GSIexp (11)  −+=−−32015615.0 eeaGSI (12) Due to the inherent rock mass variability and blast damage effect, material property s was given a range from 0 – 1 having three states for this research work. Typically the material property, s ranges between 0.0002 – 0.006 the rock types associated with porphyry ore bodies in BC. Therefore, in order to take into consideration uncertainties associated with the material property s, ranges outside the normal range (0.0002 – 0.006) were used to establish the states. The states used to estimate the material property s are shown in Table 4-13. Table 4-13. Material property, s states States Material property, s Low 0 – 0.0002 Normal  0.0002 – 0.006 High  0.006 – 1   Equation 11 was converted to CPT using the probabilities of the input nodes (Figure 4-10) with Netica software. A snap shot of these probabilities is shown in Table 4-14. 62 Table 4-14. Snap shot of CPT for “Material property, s” node   Material property, s states (%) GSI states Blast damage states 0 to 0.0002 0.0002 to 0.006 0.006 to 1 Total  0 to 20 0 100 0 0 100 0 to 20 0.7 100 0 0 100 ………… ………… ………… ………… ………… ………… 20 to 40 1 100 0 0 100 40 to 60 1 45 55 0 100 80 to 100 0.7 0 0 100 100 ………… ………… ………… ………… ………… …………  The parameter D is a factor that depends upon the degree of rock mass disturbance caused by blast damage and stress relaxation. It varies from 0 for undisturbed rock masses to 1 for very disturbed rock masses. Since of the rock masses are disturbed, a typical value of s and a for a BC porphyry deposit is 0.0002 and 0.51 respectively (Golder Associates 2009a, 2009b). Typically the material property, a ranges between 0.5 – 0.6 the rock types associated with porphyry ore bodies in BC. Therefore, in order to take into consideration uncertainties associated with the material property a, ranges outside the normal range (0.5 – 0.6) were used to establish the states. The states used to estimate the material property a is shown in Table 4-13. Table 4-15. Material property, a states States Material property, a Common 0.5 – 0.6 Uncommon 0.6 – 0.66  Equation 12 was converted to CPT using the probabilities of the input nodes (Figure 4-10) with Netica software. The CPT for material property a node is shown in Table 4-16. 63 Table 4-16. CPT for “Material property, a” node Material property, a states (%) GSI states 0.5 to 0.6 0.6 to 0.66 Total  0 to 20 62 38 100 20 to 40 99 1 100 40 to 60 99 1 100 60 to 80 99 1 100 80 to 100 99 1 100  There has not been a definition for low, medium or high RMS even though RMS can have values as low 0.001 MPa to as high as 50 MPa for intrusive igneous rocks. This research assumes RMS < 10 MPa is low strength and RMS > 20 MPa is high strength. Additionally, BC mine operators identify with these intervals and states assigned to RMS. The states used for RMS are shown in Table 4-17. RMS is important in decision over pit wall performance that BC mines should always consider. Equation 10 was converted to CPT using the probabilities of the input nodes (Figure 4-10) with Netica software. A snap shot of these probabilities is shown in Table 4-18. Table 4-17. RMS states States RMS (MPa) Low 0 – 10 Medium  10 – 20 High  20 – 70   64 Table 4-18. Snap shot of CPT for “RMS” node    RMS states (%) UCS states a states s states 0 to 10 10 to 20 20 to 70 Total  0.25 to 1 0 to 0.5 5.77775e-8 to 0.0002 100 0 0 100 0.25 to 1 0 to 0.5 0.0002 to 0.006 100 0 0 100 0.25 to 1 0 to 0.5 0.006 to 1 1 1 98 100 ………… ………… ………… ………… ………… ………… ……… 50 to 100 0 to 0.5 0.0002 to 0.006 33 23 44 100 ………… ………… ………… ………… ………… ………… ……… 100 to 250 0.51 to 1 0.0002 to 0.006 97 3 0 100 100 to 250 0.51 to 1 0.006 to 1 0 0 100 100  4.13 Rock mass modulus The rock mass modulus (Em) or in situ modulus of deformation is an important factor that controls the amount of elastic strain and thus deformation that occurs in response to the excavation of an open pit. Empirical techniques are typically used to estimate the deformability of the rock mass and using other input parameters that are typically collected for classifying the quality of a rock mass (Zhang 2005). The presence of discontinuities in a rock mass is an influential factor in its deformability; highly jointed rocks generally experience higher deformations. Thus, it is important to consider the spacing and orientation of the discontinuities when determining the deformation of the rock mass (Zhang 2005). Numerous tests can be used to determine the rock mass deformation modulus. The most common tests carried out are plate bearing, flat jack, pressure chamber, and dilatometer tests. However these tests are time consuming and expensive to perform, and often there are uncertainties associated with the results obtained. Therefore, many researchers have proposed empirical methods to estimate the rock deformation modulus. The most common empirical approaches used to estimate the rock deformation modulus of a rock mass incorporate various rock mass classification schemes such as RMR, RQD, Tunneling Quality Index (Q), and the Geological Strength Index (GSI). These empirical methods used to estimate indirectly the deformation modulus of a rock mass have uncertainties associated with them due to lack of data, variability of the rock type and the heterogeneity of the rock mass. 65 There are over twenty empirical equations for estimating the rock mass modulus but for this research, Equation 13 (Hoek and Diederichs 2006) is used because it uses GSI and D as input values. )]11/)GSI2575exp((1[)2/1(100Em −++−=DD  (13) There has not been a definition for low, medium or high Em. Therefore, this research defines an interval of 20 for Em with Em greater than 40 GPa considered high. The reason for choosing those intervals was that most researchers consider Em of more than 40GPa high. Table 4-19 shows the states and ranges used. These states can be modified based to meet the specific need of a mine. Em is important in decision over pit wall performance that BC mines should always consider.  Figure 4-11. Factors used to determine rock mass modulus in the BBN Table 4-19. Rock mass modulus states States Em (GPa) Low 0 – 20 Medium  20 – 40 High  40 – 100  Equation 13 was converted to CPT using the probabilities of the input nodes (Figure 4-11) with Netica software. The CPT for rock mass modulus node is shown in Table 4-20. 66 Table 4-20. CPT for “Rock mass modulus” node   Rock mass modulus states (%) GSI states Blast damage states 0 to 20 20 to 40 40 to 100 Total  0 to 20 0 100 0 0 100 0 to 20 0.7 100 0 0 100 0 to 20 1 100 0 0 100 20 to 40 0 100 0 0 100 20 to 40 0.7 100 0 0 100 20 to 40 1 100 0 0 100 40 to 60 0 99 1 0 100 40 to 60 0.7 100 0 0 100 40 to 60 1 100 0 0 100 60 to 80 0 0 53 47 100 60 to 80 0.7 100 0 0 100 60 to 80 1 100 0 0 100 80 to 100 0 0 0 100 100 80 to 100 0.7 0 1 99 100 80 to 100 1 0 1 99 100  4.14 Slope geometry 4.14.1 Slope height Slope height (SH) is the vertical distance from the toe of the pit wall to the crest of the pit. Another equivalent definition is that SH is the depth below the surface to the current working floor of the pit. The pit depth or SH influences the strain induced in the pit walls and controls the vertical in situ stress at the pit floor. With the help and discussion with mine operators, slope height names and intervals was established for BC mine. It is important to note that these states are based on the range of slope heights found in BC porphyry mines and what these BC mines consider as very low, low, moderate, high, and very high slope height. Therefore, the proposed states for SH are listed in Table 4-21. The data obtained for BC open pit porphyry mines and mine site visits reveals that most of the slope heights range from low-moderate (Nunoo et al. 2015). Therefore, the UP for the SH node states are very low: 5%; low: 40%; moderate: 40%; high: 10%; and very high: 5%. 67 Table 4-21. Slope height states States SH (m) Very low 0 – 100  Low 100 – 250 Moderate 250 – 500 High  500 – 800 Very high 800 – 1,500  4.14.2 Overall slope angle The overall slope angle (OSA) is illustrated on Figure 2-2. The slope angle is achieved by developing benches as mining progresses. The overall slope angle may change as mining progresses. Knowledge of the overall slope angle is typically available at a mine. Using this knowledge, the corresponding state is determined with Table 4-22. The proposed states for OSA were based on the same rationale used to define the states for SH.  Thus by discussion with BC mine operators and what they consider to be gentle, low, moderate, steep or very steep OSA. Typical slope angles for BC pits range from 37°– 55° (Nunoo et al. 2015). The data obtained for BC open pit porphyry mines and mine site visits reveals that most of the OSA are in the low – moderate state with the moderate state slightly dominating in the BC mines. Therefore, the UP assigned to the OSA node states are gentle: 0%, low: 40%, moderate: 50%, steep: 10%, and very steep: 0%. Table 4-22. Slope angle states States OSA (°) Gentle 0 – 30°  Low 30° – 40° Moderate 40° – 50° Steep  50° – 60° Very steep 60° – 90°   68 4.14.3 Pit wall shape The shape of a section of an open pit wall can range from concave to convex when viewed in plan (Figure 4-12). Convex pit walls (i.e. noses which stick out into the pit) tend to be less stable compared to concave walls (Chowdhury et al. 2009; Zhang et al. 2013). This is mainly due to the differences in stress conditions and freedom for the rock mass to deform into the pit. Concave pit walls (arch shape of the slope) tend to initiate compressive stresses, which can increase stability. Convex shapes on the other hand are prone to relaxation of normal stresses on discontinuities with subsequent decrease of shear strength. The states used for this parameter are convex, planar, and concave. A wall curvature of ±15° defines the range for a planar wall. Even though mine operators agree that pit wall shape affects the pit wall movement, none of them classifies their pit wall shapes. However, most open pits are round (more elliptical) in shape and thus making most sections of a pit wall concave in shape. As such, UP for the pit wall shape node states are convex: 15%, planar: 30%, and concave: 55%.  Figure 4-12. Plan view of an open pit showing the various pit wall shapes Concave pit wall shape (showing 15° out of the slope face)Convex pit wall shape (showing 15° into the slope face)Planar pit wall shape (showing perpendicular to the slope face)69 Chapter 5: Pit Wall Failure Modes and Travel Distance/Reach In any open pit operation, slope instability can vary from bench sloughing to large-scale movement. The research is mainly focused on large-scale, multiple bench instabilities. Sjöberg (1999) defined slope instability as a condition where the consequence of an emerging failure creates an impossible situation for the slope to be mined out. There have been several classifications of slope failure by different authors. One good example is Deere & Patton (1971) classification of slope failure into three categories namely small scale local failure involving a single bench, large-scale wedge failures comprising a intersection of joints along a single or multiple benches and circular failure in sheared/fractured and weathered rock which may involve several benches (Figure 5-1).  Figure 5-1. Failure modes in open pit mines: (a) large-scale wedge failure, (b) large-scale plane failure, (c) bench-scale wedge failure, (d) circular failure of intensely fractured and weathered rock along major fault zones - revised from Deere & Patton (1971) by (Gayer et al. 1995) The orientation of discontinuities in a rock mass can dictate the likely pit wall failure modes (Hoek and Bray 1981; Wyllie and Mah 2004). Wyllie & Mah (2004) categorised slope failures into four major modes namely planar, toppling, wedge, and circular/rotational failure. Rock falls is another minor mode of failure. A slope failure can be considered complex when more than one of the failure modes occur. Sjöberg (2001) studied failure mechanisms of high slopes in rock by simulating five different mechanisms. The simulation showed that there are other potentially unknown or poorly examined mechanisms. These unknown mechanisms may be critical for higher and steeper (a)(c)70 slopes. Based on the conclusions of Sjöberg (2001), Stacey (2006) asked the following questions. • Do the strength parameters used for back analysis represent the strength of the rock slope? • Does failure occur on multiple slip surfaces inside the slope? • Does the selected slip surface create a unique failure mode? • Is consideration given to the 3D geometry of the failure? The four major failure modes classified by Wyllie & Mah (2004) are reviewed and used in the proposed BBN. The failure modes exist in the BBN to give additional information to mine operators the type of failure mode that must be expected in case slope failure occurs. 5.1 Plane sliding Planar sliding or plane failure takes place when a volume of rock slides along a one or more slip surfaces of similar orientation. According to Kliche (1999), movement of the rock block is generally structurally controlled by joints, faults or bedding planes. For this kind of failure mode to occur, the dip direction of the slip surface should be within ± 20° of the dip direction of the slope. The toe of the slip surface must daylight or intersect the face of the excavation above pit floor. In addition, the dip of the slip surface should be greater than the friction angle of the slip surface, and less than the dip of the slope face (Hoek and Bray 1981). Figure 5-2 shows a multiple-bench planar sliding failure that occurred in a pit at Endako mine. The orientations of discontinuities are usually measured by an engineer or geologist by conducting field mapping. The orientation of the slope angle is compared with the orientation of discontinuities and then the possible modes of failure are determined. Based on feedback obtained from interviews of BC mine operators, four variables that affect plane sliding are shown in Figure 5-3. The dip of the dominant discontinuities and their friction angle are usually ranked higher compared to the other variables. Sometimes blast vibrations and ground water conditions contribute to plane sliding. The plane sliding failure mode in the network has states of yes and no. 71  Figure 5-2. Multi-bench plane sliding at Endako mine (photo taken in 2013)  Figure 5-3. Factors used to determine plane sliding in the BBN The CPT for plane sliding was completed based on expert judgement (qualitative data) for current pit conditions in BC mines. Table 5-1 shows a snap shot of the CPT for plane sliding node.  For the first row in Table 5-1, plane sliding is not likely to occur because the friction angle ranges from 0° – 10°; the discontinuity angle is less than slope angle; blast damage is low (D = 0); ground water is in dry state; and the dip direction of the slip surface is not within ± 20° of the dip direction of the slope. A discontinuity dip direction in the No state means that dip direction of the slip surface is greater than ± 20° from the dip direction of the slope. A Yes state occurs when the discontinuity dip direction is within ± 20° of the dip direction of the slope. The same understanding was used to determine the rest of the CPTs. 72 Table 5-1. Snap shot of CPT for “Plane sliding” node      Plane sliding states (%) Friction angle states Discontinuity angle<slope angle states Blast damage states Ground water states Discontinuity dip direction states No Yes Total  0 to 10 No 0 Dry No 95 5 100 ………… ………… ………… ………… ……… … … … 0 to 10 Yes 0.7 Saturated Yes 2 98 100 0 to 10 Yes 1 Dry No 5 95 100 40 to 50 No 1 Moist Yes 90 10 100 ………… ………… ………… ………… ………… … … … 40 to 50 Yes 1 Moist Yes 30 70 100 ………… ………… ………… ………… ………… … … …  5.2 Wedge sliding When two discontinuities strike diagonally through the slope face and their line of intersection daylights in the slope face, a wedge of rock resting on the discontinuities is formed. This wedge may slide along the line of intersection. If the trend of the intersection line is sub-perpendicular to the slope and is significantly steeper than the internal friction angle along the discontinuities, the wedge of rock may slide out of the slope (Hoek and Bray 1981; Kliche 1999). If the plunge of the discontinuity intersection angle is less than the slope angle and the plunge is greater than the friction angle along the discontinuities, wedge sliding is possible. Sometimes blast vibrations and ground water conditions contribute to sliding (Figure 5-4). Wedge sliding node is a discrete variable and has two states (yes and no).  Figure 5-4. Factors used to determine wedge sliding in the BBN Figure 5-5 shows several multi-bench wedge failures that occurred in the west wall of Pit 3 at Copper Mountain mine. During these failures, persons working close by were evacuated as 73 work in that location was suspended. Even though delays in production occurred at this location of the pit wall, no personnel and equipment were affected by the wedge sliding.  Figure 5-5. Multi-bench wedge sliding at Copper Mountain mine Pit 3 west wall with wedge failures outlined in red (photo taken in 2013) The CPT for plane sliding was completed based on expert judgement (qualitative data) for current pit conditions in BC mines.  For the first row in Table 5-2, wedge sliding is likely to occur because the friction angle ranges from 0° – 10°; structure intersection angle is less than the slope angle; ground water is in dry state;  and blast damage is medium (D = 0.7). Table 5-2 shows a snap shot of the CPT for wedge sliding node. Table 5-2. Snap shot of CPT for “Wedge sliding” node     Wedge sliding states (%) Friction angle states Structure intersection angle<slope angle states Ground water states Blast damage states No Yes Total  0 to 10 Yes Dry 0.7 20 80 100 20 to 30 Yes Saturated 0 15 85 100 ………… ………… ………… ………… …. …. …. 20 to 30 Yes Saturated 1 12 88 100 30 to 40 No Dry 1 98 2 100 ………… ………… ………… ………… …. …. ….  74 5.3 Toppling Toppling failure takes place when columns of rock formed by steeply dipping discontinuities overturn (Hoek and Bray 1981). Three different types of toppling failure are block toppling, block-flexure toppling, and flexure toppling (Goodman and Bray 1976). For toppling failure to occur, the existing discontinuities must steeply dip (> 70°) into the slope and the discontinuities must strike sub-parallel to the slope face (± 20°). Figure 5-3 is used to determine whether this failure mode will occur or not. In other words, when there is no plane sliding occurring in Figure 5-3, toppling is occurring and vice versa. Figure 5-6 shows a multiple-bench topple that occurred in the Lornex pit at the Highland Valley Copper mine.  Figure 5-6. Large scale toppling at Highland Valley Copper mine Lornex Pit west wall (photo taken in 2013) East wallWest wallToppling failure  location75 5.4 Rotational failure A rotational failure (Kliche 1999) or a circular failure (Hoek and Bray 1981) is characterized by a mass of rock that slides on a cylindrical or spoon-shaped slip surface (Figure 5-7). In an open pit, this failure mechanism can occur in highly jointed or fractured rock slopes or in highly weathered rock. The size of the failed volume of rock is usually larger than a single bench, into order to incorporate a sufficient number of discontinuities.  Figure 5-7. Rotational failure (Hoek and Bray 1981) Rotational failure occurs when the rock mass blocks are small as compared to the size of the slope. Figure 5-8 shows the variables leading to rotational failure. This node is discrete with yes and no states.  Figure 5-8. Factors used to determine rotational failure in the BBN In current mining practice, engineers or geologists have first-hand information regarding the discontinuity conditions and orientations in their mines. They also conduct daily inspections of the pit slopes. This knowledge can be used as input into the nodes. The CPT for rotational failure was completed based on expert judgement (qualitative data) for current pit conditions in BC mines. The explanation given in the last paragraph of Section 5.2 was used to complete the CPT for this node. Table 5-3 shows a snap shot of the CPT for rotational failure node. 76 Table 5-3. Snap shot of CPT for “Rotational failure” node    Rotational failure states (%) RMS states Ground water states Slope angle states No Yes Total  0 to 10 Dry 0 to 30 50 50 100 0 to 10 Dry 30 to 40 50 50 100 ………… ………… ………… ……… ……… ……… 0 to 10 Dry 50 to 60 50 50 100 0 to 10 Dry 60 to 90 50 50 100 ………… ………… ………… ……… ……… ……… 0 to 10 Moist 40 to 50 60 40 100 0 to 10 Moist 50 to 60 60 40 100 ………… ………… ………… ……… ……… ………  5.5 Potential failure and debris volumes The potential failure volume or the volume of the generated debris becomes very important when the slope velocity moves beyond the normal state. The potential debris volume is estimated in order to calculate the horizontal reach of the debris in case the slope fails. The following steps are a common approach used to estimate the potential failure volume of an impending rock slope failure and then using expected bulking factors, the potential volume of the debris. • Use field observation to inspect cracks at the location of the failure zone and the extent of the cracks into the pit wall. • Determine the orientation of the cracks with respect to the pit wall alignment. • With the help of a computer-aided program, delineate the instability zone with respect to the pit wall; the volume of rock mass in an impending rock mass failure can then be estimated. Figure 5-9 is a photogrammetric model of a pit wall from Gibraltar mine, showing a profile (green line) of the southwest wall of the granite pit. The wall profile was imported to AutoCAD. A polyline was used to trace the imported wall profile and extruded to create bench surfaces. Based on experience obtained from previous slope failures, a section of a sphere was used to create a failure surface (i.e. approximating a rotational failure). With the MASSPROP command in AUTOCAD, the volume of the generated arc that insects the pit 77 wall was estimated. Due to the complex nature of open pit slope failures, different failure surfaces were created at different locations of the pit wall in order to estimate the failure volume. The estimated volumes of hypothetical failures at different locations varied by a few 100 m3 from each other.  Figure 5-9. Pit wall used to create a wall profile to generate volumes of failed rock mass The failure volume generated from different locations on the pit wall profile (Figure 5-9) ranged from 10,000 to 30,000,000 m3. The volume generated by a failed rock mass is influenced by the slope height,  and pit wall shape (Brunetti et al. 2009). For this research, the pit wall shape and slope height parameters (Figure 5-10) are used to estimate the potential debris volumes generated by the pit wall slope failure. The recent Bingham Canyon mine pit wall failure generated one of the largest events that has occurred in an open pit mine, with an estimated debris volume of just under 100,000,000 m3. Conversely much smaller bench-scale wedge failures can generate debris volumes in the order of 100 m3. As such, five states were defined for the debris volume states in terms of their sizes ranging by orders of magnitude. The established states considered less than 10,000 m3 as Vol. 1 and more than 10,000,000 m3 as Vol.5. Table 5-4 shows the volume states used in the proposed model. This node is an important parameter that could lead to production loss, equipment damage, or harm to personnel. This node is considered to be important for the decision making process considering its impact on mine operations. 78 Table 5-4. Rockslide debris volume states States Debris volume (m3) Vol. 1 100 – 10,000  Vol. 2 10,000 – 100,000 Vol. 3 100,000 – 1,000,000 Vol. 4 1,000,000 – 10,000,000 Vol. 5 10,000,000 – 1,000,000,000   Figure 5-10. Factors used to determine potential debris volumes in the BBN Table 5-5. CPT for “Debris volume” node    Debris volume states (%)  Slope height states Pit wall shape states 100 to 10000 10000 to 1e5 1e5 to 1e6 1e6 to 1e7 1e7 to 1e9 Total  0 to 100 Convex 45 45 5 3 2 100 0 to 100 Planar 55 40 3 1 1 100 0 to 100 Concave 60 35 3 2 0 100 100 to 250 Convex 10 35 45 8 2 100 100 to 250 Planar 15 42 34 8 1 100 100 to 250 Concave 15 43 32 9 1 100 250 to 500 Convex 5 20 33 32 10 100 250 to 500 Planar 7 22 31 32 8 100 250 to 500 Concave 8 22 30 30 10 100 500 to 800 Convex 5 20 32 33 10 100 500 to 800 Planar 7 22 31 32 8 100 500 to 800 Concave 8 22 30 30 10 100 800 to 1500 Convex 1 4 10 20 65 100 800 to 1500 Planar 1 6 12 22 59 100 800 to 1500 Concave 0 10 15 25 50 100  79 Table 5-5 shows the conditional probability table for “potential debris volume” node used in the BBN model. The estimated CPT assigned to volume states were based on expert judgement (qualitative data). In Table 5-5, the reason for the given CPT is that a convex pit wall with a slope height between 0 – 100 m has a high chance if creating small debris volumes Vol. 1 (i.e. 100 – 10,000 m3) and Vol. 2 (i.e. 10,000 – 100,000 m3) states with little chance of larger failures. 5.6 Slope velocity As mining progress, a pit slope will deform in responses to the excavation activities. Pit slopes are expected to experience some movement. Mines will watch and monitor for abnormal movements, which might be a precursor to slope failure. Most mines depend on prism data to make decisions related to slope movements. Usually rock slope stability analysis is based on limited site-specific data and knowledge of the rock mass deformation, strength, and ground water conditions. For example, the presence of poor rock mass quality, high ground water pressure, and steep slope angle contributed to the northwest wall failure at Kemess South mine reported by Yang et al. (2011). As a drainage system was implemented and the slope angle was reduced, the movement rate reduced. The same factors caused slope failures at the Brenda mine (Calder and Blackwell 1980; Martin 1990, 1993). Newcomen et al. (2003) noted that ground water pressure and precipitation (rainfall) were factors leading to high movement rates. In 2012 at Highland Valley Copper mine, a slope failure occurred and the factors that contributed to the slope failure were discontinuity conditions (i.e. weathering), slope height, and rock mass quality. As discussed in earlier, the shape of the pit wall affects the stability of the slope. Additionally, after discussion with an industry partner and BC mine operators, the parameters used in the proposed BBN mode for predicting slope movement are rock mass strength and modulus of deformation, slope angle, horizontal to vertical stress ratio, vertical in situ stress, pit wall shape, ground water, and slope angle (Figure 5-11). 80  Figure 5-11. Factors used to determine the slope velocity in the BBN Broadbent & Zavodni (1983) illustrated that the onset of slope failure can be predicted once the movement rate of the slope reaches 3 mm/day. The onset of slope failure is usually termed by some researchers as transitional movement (Broadbent and Zavodni 1983; Glastonbury 2002; Mercer 2006; Wieczorek and Snyder 2009; Zavodni 2000; Zavodni and Broadbent 1978). Usually a slope failure is imminent when the rate of movement of the slope wall exceeds 50 mm/day (Broadbent and Zavodni 1983; Doyle and Reese 2011; Glastonbury 2002; Lee and Hencher 2009; Sullivan 1993, 2007). This kind of movement leading to slope failure is usually termed by some authors as progressive movement (Broadbent and Zavodni 1983; Glastonbury 2002; Mercer 2006; Zavodni 2000; Zavodni and Broadbent 1978). It is important to note that the limit given by these authors for progressive movement does not account for the scale of the failure. Therefore, most operating mines have set movement limits for the slope walls using past experience, help of consultants, and with aid of numerical modeling. The states and intervals used for this node were based on data obtained from the mines and feedback received from BC mine operators after the questionnaire was completed (Table 5-6). The slope velocity range for each state can be changed to conform to the needs of an operating or greenfield mine. 81 Table 5-6. Slope velocity states States Range (mm/day) Normal 0 – 2  Transitional 2 – 5  Progressive 5 – 100 Failure 100 – 300  Most practitioners in the mining industry find it very challenging to determine the possible or expected velocity of the pit walls in response to mining activities. This is because factors needed to determine slope velocity are somewhat overlooked in many situations as observed from visits to BC mine. An attempt to define the possible or expected velocity or behaviour of the pit walls as mining progresses will be a useful support tool for the open pit operations (Sullivan 2007). All mines expect pit walls to experience some movement. The mines hope that the movement velocity will not affect pit operations and they measure pit wall movement and velocities as a primary means to manage pit operations (Nunoo et al. 2015). As a pit wall deteriorates, the probability of pit wall failure increases and the pit wall movement velocity increases. In this thesis, the pit wall velocitiy is assumed to be a parameter that is representative of the probability of instability in the pit wall (Jaboyedoff et al. 2012). A high probability of failure is associated with a high slope velocity (i.e. possibly in transition to progressive states). The normal state used for the “slope velocity” node corresponds to normal movement of the pit wall at the low probability of failure level. The rate of movement of the pit wall dictates if a mine operation should be concerned with a potential debris volume as well as the possible reach of the debris. When slope velocity moves from a normal state to a transition state and then to a progressive state, the level of concern increases and hence the appropriate operational responses change. When the proposed BBN predicts the slope velocity to be in transition to progressive states, the potential debris volume from a slope failure is estimated. Based on the proposed BBN model, even if the potential debris volume cannot be reliably estimated, the slope height and the pit wall shape can provide operators with an indication of the volume of rock mass that may detach in case the movement rate leads to failure. There is no empirical relationship linking expected slope movement and the above-mentioned factors. The CPT for the slope velocity node was completed using expert knowledge and the 82 node is continuous. In the first row of Table 5-7, when slope angle is between 0° – 30°; ground water is in dry state; pit wall shape is convex; k is between 0 – 9; Em is between 0 – 20 GPa; RMS is between 0 – 10 MPa; and vertical in situ stress is between 0 – 20 MPa; there is a high chance that slope velocity is between 0 – 2 mm/day. Thus the given CPT for the first row Table 5-7. With the same rationale, the rest of the CPT for slope velocity was completed. A snap shot of the CPT for slope velocity node is shown in Table 5-7. A prism data node was linked to slope velocity node which can be used to take advantage of monitoring data obtained from measurement from a total station and prisms (Figure 5-12). Based on intrumentational and human errors (Nunoo et al. 2015), the CPT for the prism data node was completed. Therefore, when a total station and prisms are working well, the monitoring data can be used to guide the appropriate operational response and to account for changes in the slope behaviour. For each slope velocity state node, the corresponding prism data state can be known and vice versa.  Figure 5-12. Factor used to determine prism data Table 5-8 shows the CPT for prism data node.  83 Table 5-7. Snap shot of CPT for “Slope velocity” node        Slope velocity states (%) Slope angle states Ground water states Pit wall shape k states Rock mass modulus states RMS states Vertical in situ stress states 0 to 2 2 to 5 5 to 100 100 to 300 Total 0 to 30 Dry Convex 0 to 0.9 0 to 20 0 to 10 0 to 20 93 5 2 0 100 0 to 30 Dry Convex 0 to 0.9 0 to 20 0 to 10 20 to 40 80 15 4 1 100 …………. …………. ………… …… …………. …… …………. … … … … … 40 to 50 Dry Concave 0 to 0.9 40 to 100 10 to 20 40 to 60 72 22 5 1 100 …………. …………. ………… …… …………. …… …………. … … … … … 40 to 50 Dry Concave 0.9 to 1.1 0 to 20 0 to 10 0 to 20 76 17 5 2 100 40 to 50 Dry Concave 0.9 to 1.1 0 to 20 20 to 70 0 to 20 82 14.5 3 0.5 100 50 to 60 Dry Planar 1.1 to 3 0 to 20 10 to 20 20 to 40 36 35 18 11 100 …………. …………. ………… …… …………. …… …………. … … … … … 50 to 60 Dry Planar 1.1 to 3 0 to 20 20 to 70 0 to 20 45 30 15 10 100 …………. …………. ………… …… …………. …… …………. … … … … … 84 Table 5-8. CPT for “Prism data” node  Prism data states (%) Slope velocity states 0 to 2 2 to 5 5 to 100 100 to 300 Total 0 to 2 95 5 0 0 100 2 to 5 5 92 3 0 100 5 to 100 0 5 92 3 100 100 to 300 0 0 5 95 100  5.6.1 Strain The strain (ε) that occurs in a rock mass in response to excavation of the pit is considered important in evaluating the stability performance of an open pit highwall. Strain is usually obtained by linking monitoring data obtained from prisms to the height of the highwall. The strain experienced by a slope wall can be estimated by (Brox and Newcomen 2004): ε = Δx/H × 100% (14) Where Δx is the maximum deformation of the highwall and H is the height of the highwall. The maximum highwall deformation is never known because monitoring of prisms is started after some amount of excavation-induced displacement occurs. However, as an approximation, the pit wall velocity can be used the capture the effect of displacement by converting slope velocity (mm/day) to total displacement (metres). Figure 5-13 shows the factors that can be used to estimate the strain. The states for pit wall strain ε are based on Brox & Newcomen (2004) and are shown in Table 5-9.  Figure 5-13 Factors used to determine strain in the BBN 85 Table 5-9. Strain states States ε (%) Tension crack < 0.1 Progressive movement  0.1 – 0.6 Imminent failure/collapse 0.6 – 2  This node is important in knowing deformation of the pit wall. From the proposed model, the “strain” node (from Brox and Newcomen 2004) also delivers more understanding about the total deformation expected to be experienced by the pit wall. This parameter should be considered in decision-making regarding slope behaviour as this parameter can help mine operators better understand the pit wall conditions. Hence, strain can be used as a confirmation node to verify the performance of the pit wall. Equation 14 was converted to CPT using the UP of input variables with Netica software. A snap shot of these probabilities is shown in Table 5-10. Table 5-10. Snap shot of CPT for “Strain” node   Strain states (%) Slope velocity states Slope height states 0 to 0.1 0.1 to 0.6 0.6 to 2 Total 0 to 2 0 to 100 2.5 12.6 84.9 100 0 to 2 100 to 250 8.7 43.6 47.7 100 0 to 2 250 to 500 18.8 77.1 4.1 100 2 to 5 100 to 250 0 0 100 100 ………… ………… ………… ………… ………… ……... 5 to 100 800 to 1500 0 2 98 100 100 to 300 0 to 100 0 0 100 100 ………… ………… ………… ………… ………… ……... 100 to 300 250 to 500 0 0 100 100 100 to 300 500 to 800 0 0 100 100 ………… ………… ………… ………… ………… ……...  5.7 Travel distance / reach Some pit wall failure modes result in significant displacement of the failed rock. This can cause single or multiple benches or ramps to be lost, as shown in Figure 5-6, taken from the 86 Highland Valley Copper mine. Sometimes, when benches are lost during a failure, the remaining lower catch benches may catch and retain the fallen rock. However, when all the benches are lost and the debris travels to the toe of the pit wall, equipment and/or personnel are exposed to the hazard. This typically results in a disruption to the mining operation. Pit production can resume only after the movement of the pit walls begins to decelerate. Knowing the potential failure volume of a slope failure can be used to estimate the travel distance (Hungr et al. 2005, Jaboyedoff et al. 2012).This section discusses two different approaches that can be used to estimate the horizontal extent that a failed rock mass volume can travel during a slope failure. The first approach developed by Gibson et al. (2006) assumes that a wedge failure spills onto a bench or pit floor and takes into consideration the geometry of the failed rock mass to estimate the horizontal reach of the debris. The second approach applies to a failure mode where the displaced volume of rock becomes a highly mobile rock avalanche and uses an empirical relationship to determine the travel distance angle of the debris. 5.7.1 Rock bulking and spreading The equation developed by Gibson et al. (2006) can be used to estimate the extent that a failed mass of rock will cover a bench or pit floor. This approach was developed for wedge failures although it could be adopted for other failure geometries too. This equation takes into account the volume of the wedge failure, the assumed shape of the debris pile, and the bench face angle (Figure 5-14). The horizontal extent that the failed rock spreads out across the bench or pit floor is defined as the reach of the failure. The equation includes a bulking factor to account for the increase in volume of the fragmented rock and it assumes that the failed rock comes to rest with a geometry defined by the angle of repose of the broken rock. The predicted reach Rp (m) is given by: αφφαtan.tantantanV6R op−×=LK  (15) where, L = length of wedge (m), Vo = failure volume (m3), K = bulking factor (typically ranging from 1.3 to 1.5), α = bench face angle (°), and 87 ϕ = angle of repose of the failed material.  Figure 5-14. Geometry of the failed rock mass (after Gibson et al. 2006) The bulk factor given by Gibson et al. (2006) might be suitable for small failure volumes. A smaller value may be more realistic for larger volumes (i.e. approximately 25% increase in volume (Hungr and Evans 2004 ). The influence of the wedge volume on the reach distance was analysed. The average bench face angle for BC mines is 65° (BGC Engineering 2012) and a typical bench height is 15 m. Different wedge angles for vertically upright symmetric wedges (Figure 5-15) were used in conjunction with different pit wall or wedge heights to calculate the wedge volumes. LRDebris covering a bench or pit floorα88  Figure 5-15. Symmetric wedges plotted on an equal-angle stereonet Figure 5-16 shows a typical wedge shape formed from two joint sets with a wedge angle of 100°. For a range of wedge angles from 100° to 140° (with plunges of 40° or 49°); bench face angle of 65°; bulking factor, K of 1.5; angle of repose, ϕ of 38°; and wedge heights ranging from 15 to 45 m, the calculated wedge volumes range from 150 to 28,000 m3 as shown in Tables 5-11 and 5-12. The generated wedge volume were calculated using Rocscience SWEDGE 6.0 software (Rocscience 2014).  Figure 5-16. Shape of a wedge obtained from two joints 100°120°140°89 Table 5-11. Volume generated (plunge of 40°) to estimate Reach and travel distance angle  Benches involved Wedge angle (°) Vo (m3) L (m) B (m) Rp (m) R2 (m) H/L Travel distance angle (°) 1 100 465 17 11 14.2 32.2 0.91 25.0 120 694 25 14.3 32.3 0.91 24.9 140 1037 38 14.1 32.1 0.91 25.0 2 100 3723 34 22 28.3 64.3 0.91 25.0 120 5552 50 28.5 64.5 0.91 24.9 140 8294 76 28.3 64.3 0.91 25.0 3 100 12566 50 33 42.9 95.9 0.91 25.1 120 18739 75 42.8 95.8 0.91 25.2 140 27992 114 42.4 95.4 0.90 25.3  Table 5-12. Volume generated (plunge of 49°) to estimate Reach and travel distance  Benches involved Wedge angle (°) Vo (m3) L (m) B (m) Rp (m) R2 (m) H/L Travel distance angle (°) 1 100 159 11 6 10.4 23.4 0.84 32.6 120 209 15 10.1 23.1 0.84 33.0 140 376 25 10.5 23.5 0.84 32.6 2 100 1274 21 12 20.9 46.9 0.84 32.6 120 1672 30 20.2 46.2 0.84 33.0 140 3009 50 21.0 47.0 0.84 32.6 3 100 4300 32 18 31.4 69.4 0.84 33.0 120 5644 46 30.0 68.0 0.83 33.5 140 10156 75 31.5 69.5 0.84 32.9  5.7.1.1 Estimation of travel distance angle via reach The predicted reach (Rp) defined by Gibson et al. (2006) was used to determine the travel distance angle for the debris from a wedge failure. Figure 5-17 shows a vertical profile taken through a typical wedge on a single bench. The failed rock is assumed to spread out along the a bench top or pit floor and comes to rest with some debris lying in the volume defined by the original slip surfaces and the outer volume coming to rest at the angle of repose for the rock debris. The debris outline is indicated in Figure 5-17. The travel distance R2 is defined as the 90 horizontal distance of travel from top of the scar to end of deposit. The travel distance angle ω is shown on Figure 5-17.  Figure 5-17. Estimating travel distance angle using reach (drawn to scale) Equation 16 is used to calculate the travel distance and uses Rp from Equation 15 where, H – bench height B – distance from bench crest to line of intersection ψi – plunge of line of intersection for two discontinuities forming the wedge. αφφαα tan.tantantanV6tanR o2−×++=LKHB (16) As seen from Tables 6-5 and 6-6, the wider the wedge angle, the larger the wedge volume. Large volumes of failed rock tend to spread farther than small volumes of rock. The average achieved bench width of open pit mines in BC is 9 m (see Appendix D). The values of R calculated indicate that for wedges that are the full bench height in size, some of the failed rock mass will eventually hit a safety berm, cover the whole bench width, or pit ramp at the bottom of a bench. B Rp H/tan (α) ω α ϕ H R2 Debris (V) ψi 91 5.7.2 Rock avalanches According to Hungr et al. (2001), a rock slope failure with more than 10,000 m3 of loose material can be classified as a rock avalanche if it demonstrates extremely rapid movement (>5 m/s, (Cruden and Varnes 1996)). While rock avalanches within open pit mines are not common, they have occurred (Bingham Canyon mine) and they have resulted in loss of life (Grasberg mine). The consequence of a rock avalanche in an open pit mine is extreme given the large volume and high velocity associated with this failure mode. A relevant example of a rock avalanche hazard is the massive slope failure that occurred April 2013 at the Bingham Canyon mine. The slope had been carefully monitored and the failure had been predicted, but the volume of rock from the failure transformed into a rapidly moving rock avalanche (Pankow et al. 2014; Petley 2013). The displaced rock travelled a horizontal distance of over 2000 m as it vertically dropped approximately 850 m as seen in Figure 5-18 (Pankow et al. 2014). Most of the pit floor was covered with displaced rock and some equipment was damaged or buried. During the Bingham Canyon mine incident, a large-scale wedge failure originated along near-planar slip surfaces. As the wedge of rock moved, the rock mass became more fragmented and lost internal shear strength, causing the displaced mass to gain speed as it moved over a steep section of the pit wall. The rock then transitioned into an avalanche as it plummeted to the pit floor (Petley 2013). It is useful to note that as rock disintegrates during a rock avalanche, the volume of the displaced rock increases by approximately 25% (Hungr and Evans 2004). The source volume of the failed rock mass at Bingham Canyon mine was estimated as 55 Mm3, but the final deposit was approximately 60 – 65 Mm3 (Pankow et al. 2014). 92  Figure 5-18. Rock avalanche that occurred at the Bingham Canyon mine, showing elevation of the crest and toe of the slide, and the extent to which the failed volume traveled (modified from Pankow et al. 2014) The distance that rock debris can travel from the pit wall to the working floor during a rock avalanche is defined as the travel distance. Figure 5-19 presents a schematic diagram defining the horizontal travel distance of the displaced rock mass and the vertical distance (drop). The travel distance of a mobile rock avalanche depends on the geometry of the slope and its rock mass properties. Prediction of whether a pit wall failure could escalate into a rock avalanche and an estimation of its travel distance is of paramount importance for risk management in an open pit. Failure to recognize and account for highly mobile failure modes can result in a loss of equipment in the pit, as well as loss of lives. 93  Figure 5-19. Schematic diagram used to estimate the travel distance of the failed rock mass Methods used to predict travel distances for naturally occurring rock avalanches can also be used for open pits. Different researchers have developed ways to predict the travel distance of debris (Corominas 1996; Davies 1982; Finlay et al. 1999; Heim 1932; Hsü 1975; Hungr et al. 2005; Hungr 1995; Hunter and Fell 2003; Li 1983; Nicoletti and Sorriso-Valvo 1991; Scheidegger 1973). Usually the debris travel distance is linked with the failure volume to determine the travel angle that is used in turn to estimate the horizontal travel distance. Hungr et al. (2005) classifies methods for predicting the travel distance of debris into geomorphological based, geometrical approach, and volume change. Once the debris from a slope failure is estimated to be larger than 104 m3, then the travel distance can be calculated using a simple trigonometry equation (Hungr et al. 2005). ωtanHL td =  (17) where, H = vertical distance (drop) (m), ω = travel distance angle (°), and Ltd = horizontal distance of travel from top of the scar to end of deposit (m). The definition for Ltd (Equation 17) is the same as for R2 (Equation 16). Li (1983) established a correlation between rockslide debris volume V and the ratio of the maximum vertical drop H Ltd ω Failure volume (Vo) Debris deposit (V) 94 to the maximum horizontal distance travelled. The empirical relationship established by Li (1983) can be used to estimate the travel distance of a threatening rockslide if the debris volume can be estimated. The equation was revised by converting the logarithmic equation from: 664.0log1529.0)/(log +−= VLH td  (18) to 1529.0664.0 /10)/( VLH td =  (19) Prediction of travel distance (run out) is challenging, even with the help of numerical modeling techniques (Pankow et al. 2014). 5.7.3 Proposed relationship for travel distance angle This research proposes a new relationship to estimate the travel distance angle. This proposed relationship is based on equations presented by Gibson et al. (2006) and Li (1983). The debris volumes for wedge failures that would typically be less than 100,000 m3 were used in the Gibson et al. (2006) predictive equation to estimate the travel distance angle as shown in Tables 5-11 and 5-12. For larger pit wall failures that could result in rock avalanches, the data from Bourrier et al. (2013) was fit to an equation in a similar form to that used by Li (1983). The results are shown Figure 5-20. This research proposes a new two-component relationship for calculating travel distance angle. The first component assumes that if a debris volume is less than 100,000 m3, a debris spreading mechanism is likely to occur and as such, ω is ~32°.  The second component, for debris volumes larger than 100,000 m3, modifies the Li (1983) equation (Equation 19) to: 16.0/4)/(tan VLH td ==ω  (20) Therefore the new proposed relationship is: If V <100,000 m3, ω = ~32°, else ( )16.0/4arctan V=ω  (21) V is always in m3. 95  Figure 5-20. Data used to establish a relationship for estimating travel distance angle as a function of deposit volume; comparison of the Bingham Canyon rock avalanche (green and red circles, and black triangle) with reported landslide events from Bourrier et al. (2013) This relationship fits well with published field data for natural rock avalanches. For the rock avalanche at Bingham Canyon mine, the debris volume was 65 Mm3. This volume was used to estimate the ratio of the vertical drop to the horizontal distance of travel from the top of the scar to end of deposit using Equation 19 (black triangle in Figure 5-20). Estimates of the actual reach and vertical drop of the slide debris were used to plot the red circle on Figure 5-20 using Equation 17. Equation 21 was also used to estimate the travel distance angle for the Bingham Canyon mine event (green circle in Figure 5-20). Although the travel distance angle calculated with the proposed relationship for the Bingham Canyon mine case history (green dot) is lower than the observed angle (red dot), the failure volume would have had a lower travel distance angle if the debris had not been obstructed by the opposite pit wall. If the pit floor had been wider, the travel distance would have been higher, resulting in a lower travel distance angle. 01020304050100 1000 10000 100000 1000000 10000000 10000000 1E+09Traveldistance angle,ω(°)Debris volume, V (m3)reach predictions from Gibson et al. (2006)rock avalanche data from Bourrier et al. (2013)proposeddebris spread rock avalanche49° plunge40° plunge96  Figure 5-21. Factor used to determine travel distance in the BBN Figure 5-21 shows the node used to estimate the travel distance. Even though this parameter/node has been used to estimate travel distance, there has not been any previously defined states for the vertical distance to horizontal distance ratio. Using Figure 5-20, the research established three states of equal interval to define vertical distance to horizontal distance ratio as shown in Table 5-13. The vertical distance to horizontal distance ratio (H/L) states used to determine the travel distance upon calculating the travel distance angle. Table 5-13. Vertical to horizontal distance ratio (Travel distance) States Ratio H/L 1 0 – 0.21 H/L 2 0.21 – 0.42 H/L 3 0.42 – 0.63    Equation 21 was converted to CPT using the probabilities of the input node (Figure 5-21) with Netica software. The CPT for travel distance node is shown in Table 5-14. The pit width for BC mines is usually less than 2500 m (Nunoo et al. 2015) but the pit floor width is usually less than 1 km. It is important to know the distance that the debris can travel during a slope failure. The deeper the pit, the larger the potential debris volume generated. Figure 5-22 plots theoretical travel distance versus volume based on Equation 21 for different pit depths.  Table 5-15 shows the range of the volumes used to calculate the travel distance at different pit depths. 97 Table 5-14. CPT for "Travel distance" node  Travel distance states (%) Debris volume states 0 to 0.21 0.21 to 0.42 0.42 to 0.63 Total 100 to 10000 0 0 100 100 10000 to 10000 0 0 100 100 100000 to 1000000 0 0 100 100 1000000 to 10000000 0 96.5 3.5 100 10000000 to 1000000000 91 9 0 100  Table 5-15. Range of debris volumes used for the respective pit depths Pit depth (m) V (m3) 100 100 – 1,000,000 250 100 – 15,000,000 500 100 – 30,000,000 800 100 – 60,000,0000   Figure 5-22. Travel distance versus volume based on proposed relationship for different pit depths 05001000150020002500100 1000 10000 100000 1000000 10000000 100000000Debris volume, V (m3)Traveldistance,R2or Ltd(m)98 Chapter 6: Consequences of Pit Wall Failure The risk associated with slope failures can be grouped into injury to personnel, damage to equipment, economic impact on production, force majeure, industrial action, and public relations (Steffen et al. 2006, 2008). For this research, the focus is on fatalities and economic aspects. When pit wall instability occurs, a mine is most concerned about impacts to personnel, mine production, and equipment. Movement of pit walls can harm persons working in the pit, damage equipment, and result in production losses. Even when personnel are not harmed or equipment are not damaged, the pit wall movements can cause production losses in the pit because mining operations can be stopped knowing that rock mass behaviour is somewhat unpredictable. Timely and appropriate operational decisions can be made by the mine to minimize the effects of pit wall movements and slope failures. The consequences of a slope failure are influenced by the location of personnel and equipment relative to the failure and the mobility of the failure relative to that of people and/or equipment. The size of the failure and the travel distance or reach of a failure are also important. Therefore, it is important to take into the consideration these factors when accounting for the risk involved. 6.1 Harm to personnel (HTP) In BC, the Chief Inspector of Mines issues an annual report summarizing mining activities and safety statistics. For example, Chief Inspector of Mines (2011-2014) reported work related injuries in BC open pit mines; there was no reported injuries related to slope instability. At the time this research was conducted, the author was not aware of any loss of life in BC porphyry mines because of slope failures during the past three decades although injures have occurred due to small-scale rockfalls. Various personnel that work within an open pit includes equipment and non-equipment operators. The non-equipment operators include labourers working alongside blasters charging the drilled holes, maintenance personnel, engineers doing daily or weekly routine checks in the pit, surveyors, and pit supervisors / pit bosses checking the productivity in the pit. These kinds of personnel are termed as non-equipment operators in this research. During a slope failure, personnel in the open pit may be vulnerable. However, the exposure time and mobility of personnel vary depending on their role and the protection and mobility of the equipment they are in. Equipment operators that spend most of their time working on the pit 99 floor have the greatest exposure. Equipment operators defined in this research include operators of drills, shovels, and haul trucks. The states used for “harm to personnel” node are adopted and modified from A Supervisor’s Guide to Managing Workplace Injuries handbook (MABC and Worksafe BC 2015) (Table 9 1). The handbook defines what to report to Worksafe BC and the states used in the “harm to personnel” node correspond to those definitions in the handbook. Additionally, mine operators are required to report every incident (even if the incident had a potential for causing serious injury to personnel) to Worksafe BC. Reported cases received by Worksafe BC from mine operators is the only way Worksafe BC tracks work related injuries of an operation.  Figure 6-1. Factors used to determine harm to personnel (HTP) in the BBN Table 6-1. States and description used for harm to personnel (MABC and Worksafe BC 2015) States Harm to personnel No injury All person working in the pit are evacuated to a safe zone Minor injury Injuries that cause (or are likely to cause) a person to miss work beyond the day or require modified work beyond the day of injury Moderate injury Injuries that require medical treatment beyond first aid Major injury Injuries that may result in a permanent disability Death One or more person dies  During a normal pit production, equipment and non-equipment operators are in the pit except during blasting hours or lunch breaks. The blasting hours and lunch breaks are negligible compared to the time equipment and non-equipment operators spend in the pit during activities. In addition, the exposure time and the level of vulnerability for equipment and non-equipment operator was assumed the same for the purpose of this research. It is important to note that the presence of equipment and non-equipment operators in the pit are mostly 100 dependable on the slope performance (i.e. high slope velocity leads to the evacuation of equipment and non-equipment operators and vice versa).  For both nodes (i.e. equipment operator and non-equipment operator) two states (No and Yes) are assigned to each with slope velocity determining their presence or absence in the pit. Figure 6-1 shows that slope velocity determines whether equipment and non-equipment operators are in the pit. Table 6-2 and 6-3 shows the CPT for equipment operator and non-equipment nodes completed based on expert judgement (qualitative data). The approximate probability of occurrence implies the frequency these two kinds of personnel are usually in the pit and out of the pit during normal pit production. Figure 6-1 shows the factors used to determine harm to personnel node. Table 6-4 shows a snap shot of CPT for Harm to personnel node completed based on expert judgement (qualitative data) obtained from interviews conducted with BC mine operators and from literature review discussed in Chapter 2 and in Appendix D. Table 6-2. CPT for “Equipment operator” node  Equipment operator states (%) Slope velocity states No Yes Total 0 to 2 0.5 99.5 100 2 to 5 10 90 100 5 to 100 95 5 100 100 to 300 99 1 100  Table 6-3. CPT for “Non-equipment operator” node  Non-equipment operator states (%) Slope velocity states No Yes Total 0 to 2 1.5 98.5 100 2 to 5 10 90 100 5 to 100 95 5 100 100 to 300 99.5 0.5 100  101 Table 6-4. Snap shot of CPT for “Harm to personnel” node     Harm to personnel states (%) Non equipment operator states Equipment operator states Slope velocity states Travel distance states No injury Minor injury Moderate injury Major injury Death Total No No 0 to 2 0 to 0.21 95 5 0 0 0 100 No No 0 to 2 0.21 to 0.42 95 5 0 0 0 100 ……… ……… ……… ……… …. …. …. …. … … No No 2 to 5 0.42 to 0.63 95 5 0 0 0 100 No No 5 to 100 0 to 0.21 95 5 0 0 0 100 ……… ……… ……… ……… …. …. …. …. … … No Yes 5 to 100 0.21 to 0.42 0 5 20 25 50 100 No Yes 5 to 100 0.42 to 0.63 20 20 20 20 20 100 ……… ……… ……… ……… …. …. …. …. … … Yes No 100 to 300 0 to 0.21 0 0 0 0 100 100 Yes No 100 to 300 0.21 to 0.42 0 0 5 15 80 100  For harm to personnel, the proposed model shows that the probability personnel will experience no injury is ~95%. The probability of death is approximately 0.00005%. Morgan et al. (1992) suggested that the annual probability of death of an individual (PDI) accepted by society is less than 1 x10-4. Fell (1994) considered an annual PDI of not greater than 1x10-5 might be acceptable. Ale (1991) has suggested acceptable PDIs of between 10-6 and 10-8. These values correspond to the harm to personnel node as shown in Figure 7-1. 6.2 Equipment damage (ED) The direct costs associated with equipment damage in an open pit can range up to millions of dollars. The definition of equipment used in this context includes haul trucks, shovels, and light vehicles used for daily activities in the pit. Shovels somewhat contribute to the triggering of slope instability when the shovel is working near the bench face or toe of the 102 slope. The vibration caused by mining equipment is not considered to influence slope velocity because the vibrations caused by equipment are negligible compared to blasting vibrations. When a rapid slope failure occurs, slow moving mining equipment such as shovels are more vulnerable to the hazard. Therefore, slope velocity and travel distance nodes are used to estimate the damage to equipment (Figure 6-2). The states used for this variable are based on feedback obtained through interviews conducted as a follow-up to the submitted questionnaires by the mines (Table 6-5). This parameter is a discrete node. The Chief Inspector of Mines (2001-2014) annual reports shows the percentage of total incidents of equipment. The annual reports do not explicitly differentiate equipment damage related to slope instability.  Table 6-6 shows the annual report data for total number of incidents related to equipment. It is important to note that BC chief inspector of mines reports states that the numbers in  Table 6-6 are not intended to add up to 100%, as there may be multiple equipment involved for a single incident (Chief Inspector of Mines 2001-2014). From  Table 6-6, using 365 working days in the pit, there is 0.3% average daily chance that an equipment will experience an incident. Additionally, out the 0.3%, the annual reports does not indicate which state the equipment falls into when the incident occurs. It is obvious that mine operators report equipment incidents to the Ministry of Mines and Energy if the equipment is major to complete loss state. Therefore, based on literature review discussed in Chapter 2 and Appendix D, this research assumed that 0.3% incident can be for the state of major damage state of the equipment because the equipment is bound cause production loss time.  Even though equipment can be completely destroyed by a slope instability, there has not been any reported equipment loss that is related to slope instability in BC open pit mines. From this knowledge, case histories reported about equipment damages related to slope instability in this thesis (Chapter 2 and Appendix D), and the interviews conducted with BC mine operators, the CPT for the equipment damage node was completed. Table 6-7 shows a 103 snap shot of the CPT for equipment damage node used in the BBN model. The equipment damage node in Figure 7-1 shows a probability of occurrence for no damage equipment as ~98% compared to a complete loss of equipment at ~0.001%. The probability values as shown in Figure 7-1 reflects current conditions for daily pit production.  Figure 6-2. Factors used to determine equipment damage in the BBN Table 6-5. States and description used for equipment damage States Equipment damage No damage Equipment evacuated safely without experiencing any damage Minor damage Equipment experiences minor damage (<$5,000) Major damage Equipment experiences major damage (>$5,000) Complete loss Equipment destroyed and beyond repair  Table 6-6. Equipment incident information extracted from BC chief inspector of mines  Equip. % of Total incidents reported annually 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Haul truck 27 37 43 32 27 24 48 28 22 17 26 23 14 14 Grader 1 3 1 0 1 2 0 0 4 1 3 1 2 1 Loader 6 6 4 4 5 7 2 6 5 2 6 4 3 3 Shovel 11 9 7 10 8 6 13 10 8 11 8 5 4 8 Dozer 8 8 8 6 10 4 15 10 6 9 15 9 7 9 Drill surface 5 3 4 3 1 6 2 7 4 6 6 13 4 3 Pickup 7 6 6 5 5 4 7 1 7 7 6 9 5 47 Excavator backhoe 2 3 3 2 1 0 0 6 6 5 5 4 2 3  104 Table 6-7. Snap shot of “Equipment damage” node    Equipment damage states (%)  Slope velocity states  Travel distance states No damage Minor damage Major damage Complete loss Total 0 to 2 0 to 0.21 95 5 0 0 100 ………… ………… ……… ………… ………… ……… … 2 to 5 0.21 to 0.42 85 15 0 0 100 2 to 5 0.42 to 0.63 90 10 0 0 100 5 to 100 0 to 0.21 75 20 5 0 100 5 to 100 0.21 to 0.42 75 20 5 0 100 ………… ………… ……… ………… ………… ………… … 100 to 300 0.21 to 0.42 10 15 30 45 100 ………… ………… ……… ………… ………… ………… …  6.3 Production loss (PL) Slope instability can affect pit production. Each mine has hourly, daily, weekly, and monthly production targets. Production losses can occur if stop-work orders are issues or if personnel and equipment are evacuated from the pit. Damage to the equipment arising from slope instability can also cause production losses. The size of a pit wall failure and the distance it travels will affect the degree of production loss in a pit. Sometimes a pit wall may develop cracks on a haul road that may force alterations to the mining plan and result in production losses. A potential slope failure might need to be mined out or removed to re-establish a safe haul road thus resulting in a loss in production. In the BBN, five parameters are considered to affect production: slope velocity, harm to personnel, equipment, travel distance, and debris volume (Figure 6-3). Production loss has five states depending on the extent of the production loss (Table 6-8). The case histories reported in this thesis (Chapter 2 and Appendix D) shows that BC mine operators have experienced production losses caused by slope instabilities. The production loss has ranged from hours to days but there has not been a production loss that lasted for months in BC open pit mines over the past few decades. However, the slope instability incident that occurred in Bingham Canyon mine caused production loss for months in the pit. Using the observations 105 made from the case histories reported in this thesis and interviews conducted with BC mine operators, expert judgement (qualitative data) was used to complete the CPT for production loss node. The production loss node shows a ~97% probability for no production loss to ~0.008% for production loss for months as shown in Figure 7-1. The probability for production loss as shown in Figure 7-1 reflects reasonable real-world daily pit production activities in BC mine operations. A snap shot of CPT for production loss node is shown in Table 6-9.  Figure 6-3. Factors used to determine production loss in the BBN Table 6-8. States and description used for production loss States Production loss No production loss Pit production/activity is not affected Hours Pit production loss between 1 to 24 hours Days Pit production loss for 1 to 7 days  Weeks Pit production loss for a week or more but less than a month Months Pit production loss for a month or more  106 Table 6-9. Snap shot of CPT for “Production loss” node      Production loss states (%) Slope velocity states Harm to personnel states Equipment damage states Travel distance states Debris volume states No prod. loss Hours Days Weeks Months Total 0 to 2 No injury No damage 0 to 0.21 100 to 10000 99 1 0 0 0 100 0 to 2 No injury No damage 0 to 0.21 10000 to 100000 99 1 0 0 0 100 …… ……. ………….. ………... ……….. … … … … … … 5 to 100 Death Complete loss 0.42 to 0.63 1000000 to 10000000 0 0 3 7 90 100 …… ……. ………….. ………... ……….. … … … … … …  107 Chapter 7: Sensitivity Analysis, Operational Response and Scenario Analysis 7.1 Sensitivity analysis Figure 7-1 shows a presentation of general conditions within BC open pit porphyry mines. Based on the information used to train the proposed model, it is important to conduct a sensitivity analysis to verify which of the parameters are most influential. A sensitivity analysis was performed to determine which factors are most critical to the resulting consequences of pit wall slope movements. There is no common definition of what sensitivity analysis is or ought to be. It is usually a study of how various inputs to a model will influence the resulting model outputs. Sensitivity analysis is conducted to learn how the inference drawn from an evaluation depends on its inputs; it is also used to help direct future empirical studies so that effort is directed into finding better estimates of inputs that will lead to maximum improvement in estimates of the outputs (Ferson and Troy Tucker 2006; Saltelli et al. 2000). Sensitivity analysis methods can be classified into local, or one-at-time (OAT), and global analysis. OAT analyses normally deal individually with uncertain input factors, revealing the range to which the output is determined by any given input. Global analysis incorporates all input factors at the same time, hence addressing dependencies between inputs (Saltelli et al. 2000). Research in engineering has focused on probabilistic sensitivity analysis (Chen et al. 2004; Felli and Hazen 2004; Sobol 2001). Probabilistic sensitivity analysis focuses on identifying the largest contributors to probabilistic effects in the output. This approach attempts to determine the influential parameters in the proposed model with respect to the following nodes: Slope velocity, Harm to personnel, Equipment damage, and Production loss. The probabilistic sensitivity analysis does not explore sensitivity to a lack of information, but rather sensitivity to the physical reality of the problem or process being modeled. This analysis can provide important insights during the design process or decision making, such as indicating that a design process needs improvement so that factors leading to high-risk levels can be reduced to acceptable levels. 108  Figure 7-1. Proposed BBN model framework with trained data109 The output of a BBN normally depends on a priori assigned probabilities. Therefore, it is important to perform sensitivity analysis to identify critical input parameters that will have a major influence on the output results. A BBN sensitivity analysis helps in classifying the important uncertainties for the intention of guiding additional data collection efforts (Laskey 1995). Different methods have been proposed to perform sensitivity analysis in a BBN model (Bednarski et al. 2004; Coupé and Gaag 2002; Laskey 1995; Pearl 1988). For example, entropy reduction (i.e. mutual information), variance reduction, and variance of beliefs estimation are the most common methods used to perform sensitivity analysis in BBN (Norsys Software Corp. 2014; Pearl 1988). As the input parameters that help predict slope movement are both continuous and discrete, a variation reduction is used for this research. This is the first time that a variance reduction method has been used in this field of study, even though this method has been used in other fields of studies (Cockburn and Tesfamariam 2012; Ismail et al. 2011; Tesfamariam and Martín-Pérez 2008). The variance reduction method determines the sensitivity of the BBN model’s output by varying a particular input parameter (Ismail et al. 2011; Jensen 1996; Laskey 1995; Pearl 1988). It is important to note that the variance reduction method is well suited for target nodes that are continuous variables with discretized states. The variance for the real number of node Q given the evidence F is calculated as: 2)]|(EX[)|()V( FQXfqf|Q qq−= ∑  (22) ∑=qqp(q)XEX(Q)  (23) where, q = state of the query node Q, EX (Q) = the expected real value of Q before any new findings, EX(Q|f) = the expected real value of Q after a new finding of f for the node F, f = the state of the varying node, Xq = the numeric real value resulting to state q, and ∑qis the summation of the total states q of Q. On the other hand, entropy reduction (i.e. mutual information) is used to determine the sensitivity between nodes. Mutual information is measured in bits (Norsys Software Corp. 2014). Mutual information can be used with any discrete or discretized nodes (Norsys 110 Software Corp. 2014). Mutual information is given the same value when varying and querying nodes are reversed. Additionally, this technique is useful in measuring the degree to which one varying node can influence a number of different query nodes in an effective way. High mutual information between nodes point to the existence of a parent-child relationship, and low mutual information usually signifies a conditional independence between nodes (Kane et al. 2003; Norsys Software Corp. 2014). Therefore, mutual information I, between two nodes Q and F is: = ∑ )()(),(log),(),(, fpqpfqpfqpFQIfq (24) where Q and F are nodes with it states q and f. Based on the data fed into the proposed model, a sensitivity analysis was conducted for the following nodes: Slope velocity (without considering the consequence of failure), Harm to personnel, Production loss, and Equipment damage. It is important to state that as more data becomes available and CPTs are updated, the sensitivity between the nodes can be affected. Figure 7-2 to 7-5 only include the highly sensitive nodes, due to lack of space. The rest of the data for the sensitivity analysis are attached in Appendix E. 111  Figure 7-2. Sensitivity analysis conducted for “Harm to personnel” node with respect to other nodes in the BBN model  Figure 7-3. Sensitivity analysis conducted for “Equipment damage” node with respect to other nodes in the BBN model 0 20 40 60 80 100Slope velocityProduction lossStrainNon equipment operatorEquipment operatorEquipment damagekTravel distance angleDebris volumeSlope heightVertical in situ stressGround waterPit wall shapeSlope angleRock mass strength% Normalized mutual information0 20 40 60 80 100Slope velocityNon equipment…Equipment operatorProduction lossStrainGround waterSlope angleTravel distance angleDebris volumeHarm to personnelMaterial property,sRock mass strengthGSIkSlope heightVertical in situ stress% Normalized mutual information112  Figure 7-4. Sensitivity analysis conducted for “Production loss” node with respect to other nodes in the BBN model  Figure 7-5. Sensitivity analysis conducted for “Slope velocity” node with respect to other nodes (excluding Consequences of Pit Wall Failure nodes) 0 20 40 60 80 100Slope velocityHarm to personnelStrainNon equipment operatorEquipment operatorEquipment damageGround waterkSlope angleTravel distance angleDebris volumeGSIMaterial property, s% Normalized mutual information0 20 40 60 80 100Ground waterSlope angleGSIRock mass strengthkMaterial property,sMaterial property,aRotational failureRock mass modulusUCSWedge slidingDiscontinuity spacingDiscontinuity condition% Normalized variation reduction113 From the Pearl (1988) perspective, the parameters which have shown the maximum value of variance reduction or high mutual information most often have a major effect on the outcome nodes. The bars shown in Figures 7-2 to 7-5 show the degree of influence the nodes have with the child node. Figure 7-2 shows that slope velocity, production loss, strain, non-equipment operator, equipment operator, equipment damage, k, and travel distance angle highly influence harm to personnel node. Nodes like the vertical in situ stress, rock unit weight, RQD, UCS have less influence on harm to personnel node. Therefore, mine operators should be concern about the significant nodes as changes in those influential nodes can affect the consequence of failure. On the contrary, Figure 7-3 shows that slope velocity, non-equipment operator, equipment operator, production loss, strain, and ground water highly affect equipment damage node. Additionally, Figure 7-4 shows that slope velocity, harm to personnel, strain, non-equipment operator, equipment operator, equipment damage, ground water, and k highly affects production loss node. Slope angle and GSI (via RMR) are the parameters mine operators usually consider in making decisions regarding pit wall velocities. This is evident in the sensitivity analysis in Figure 7-5. Figure 7-5 also shows that slope height has a very low influence on slope velocity but ground water, k, slope angle, and rock mass strength have high influence on slope velocity. The interviews conducted with mine operators revealed that BC mine operators rarely change the slope velocity limits as the slope height increases. Therefore, Figure 7-5 supports the rationale by BC mine operators to keep the same slope movement limits as the pit deepens. Although the travel distance of rockslide debris affects the harm to personnel, production loss, and equipment damage, and it is an important factor to consider by mine operators, the sensitivity analysis conducted shows that it has little impact on the nodes. However, it is important for mine operators not to overlook the reach distance during a slope failure in order to protect lives and equipment. In a mine, ground water and slope angle can affect mining activities as well as the geotechnical properties of the pit walls. The sensitivity analysis in all the four figures proves what mine operators experience on the field. Increasing ground water or steeper slope angles 114 can result in catastrophic events in the pit that can affect production, personnel, and equipment. 7.2 Operational Responses and Scenario Analysis Most mines do not have a strategic response program set up specifically to govern mine operations in the event of usual slope movements. Setting up and executing an operational response program can help to minimize adverse effects on production, equipment, and personnel in the case of an impending slope failure event. There are operational practices and rules used by BC mine operations to govern their activities (BCMME 2008; Canadian Mines Handbook 2011; Hartman et al. 1992). Some of the practices and rules used are listed below. • Personnel are not allowed to park equipment in areas that are known to exhibit signs of instability. • Equipment must not be parked within ~15 m (50 feet) of any pit wall. • When work is conducted in a known active area, spotter(s) must be positioned in the area of the operation, and radio communication should be maintained. • Shovel operators should not work parallel to the face of the wall in known instability areas. • Personnel working in the pit must be aware of pit wall conditions and be able to recognize potential hazards. • Signs of instability in active working areas should be bermed off, and all personnel are to be informed. • Implementation of slope dewatering systems should be used to reduce ground water pressure, thereby improving the stability of the pit walls. •  Bench widths must be frequently cleared of loose rocks. While mines routinely use operational rules, the responses related to occurrences of slope movement are generally poorly defined. Hence, risk management in the open pits can be improved. The implementation of appropriate and practical operational responses is an important step in managing the risk involved in mining activities. The main consequences of failure are harm to personnel, equipment damage, and production loss. The slope velocity usually influences decision making around the consequences of a failure. As the velocity of a slope goes beyond the normal state, operations become more concerned. Moreover, as the 115 velocity of the slope begins to accelerate, the consequences of failure also increase. The recommended operational responses will depend on the consequence of a failure in relation to the slope velocity (Normal, Transitional, Progressive, and Failure). It is important to note that operational responses should be considered in conjunction with the location of a potential pit wall failure, and the size and potential mobility/speed of the failed material. When slope velocity is in a normal state, the probably of a failure occurring is small and hence the consequences are negligible. However, as the slope velocity transitions to a progressive or failure state, the consequence of failure increases. The operational responses discussed in this chapter are based on field experience, consultation with an industrial partner, and modified after Pisters (2005) and Read & Stacey (2009). The results from the BBN can used to support decision made concerning open pit activities of a mine operation. The final output of the BBN model has four alternatives (normal pit production, work with caution, minimize work and plan for an evacuation, and stop work and evacuate) that are associated with the consequence of failure as well as the velocity of the slope. Therefore, based on the level of consequence linked to the slope velocity, the right decisions can be made to avoid false alarms, save lives, and minimize the severity of equipment damage in the pit. The following section describes each alternative of the operational response node. 7.2.1 Operational response for normal pit production The following operation responses for normal pit production should be followed. • Personnel working in the pit, as well as mine operations personnel, should continually watch for signs of pit wall instabilities (i.e. crack on berms, raveling on walls, rock falls, and toe heaves, abnormal water flows). Reports should be made to the appropriate department. • Engineers responsible for monitoring slope performance must constantly maintain lookout for slope instabilities during workdays. Additionally, engineers should inform pit supervisors of any prospective unstable areas. Information regarding instabilities should be recorded in a logbook by the pit shifters’ office. • In cases where personnel in the pits observe instabilities, they should report to engineers for field verification. Engineers are to report back to personnel or pit operations of any restrictions (i.e. working daylight only, working with light during night, or working with 116 spotters), based on field verification. Records of the instability should be logged into the logbook in the shifters’ office. • Engineers responsible must maintain daily monitoring of pit walls using the monitoring equipment (i.e. total station and prisms, or slope stability radar) purchased by operations for slope monitoring. Data obtained from the monitoring equipment should be relayed to all respective bosses and also recorded and posted in the engineering office. In case of any possible instability detected using monitoring equipment, engineers should alert operations and describe any operational limitations: these records should be logged in the logbook located in the shifters’ office. • Mine operations should constantly check installed wire-line extensometers in areas of tension, noting cracks per shift and reporting readings on the daily shift report. • Engineers responsible should check monitoring data obtained from slope monitoring equipment and wireline extensometers at least twice a week to understand the performance of the slope. • There should be frequent monitoring of wells and drainage pipes. 7.2.2 Operational response for work with caution Work with caution is declared when activities in the pit need to go beyond normal levels as wall movement begins to accelerate slightly. At this point, mining operations should start conducting activities to help minimize any risks associated with a further increase in slope movement rates. The operational responses for working under a caution state triggered by measured/observed slope movements are listed below. • Engineers responsible for slope performance should assess the area where data obtained from slope monitoring instrumentation show increasing movement or show any indication of instability. Based on the assessment conducted, engineers should inform mine operations of any limitations regarding operations that need to be implemented, such as reducing truck movement by reducing double traffic haul roads to single lanes, or placing berms the area. Engineers are to make recommendations to mine operations about strategies to reduce the movement rate, such as dumping waste at the toe of the slope, or increasing the dewatering program if it is a water issue. Information regarding assessment of the area, limitations, and recommendations made to mine operations should be recorded in the logbook at the pit shifters’ office. 117 • Based on reports given by mine operations, engineers should verify the instabilities and take pictures of the unstable walls for day-to-day comparison. Engineers should report to mine operations about any restrictions that might affect production (i.e. daylight operation, working with lights, working with spotters). This information should also be recorded in the logbook at the pit shifters’ office. • Equipment working in the area of instability should be minimized. • Limit traffic loads and make sure that two exit routes are clear. Also, there should be no entry to unstable areas without the permission of the engineering department and pit supervisor. In addition, mine operations should clear out a safe working distance and build up safety berms where possible. • The orientation of the pit walls can be flattened slightly in cases where the slope angles are the main cause of the instability. • The frequency of monitoring the pit walls using slope monitoring instrument (i.e. total station and prisms, or slope stability radar) should be increased to two-three times daily. Data obtained from monitoring instruments should be recorded, analysed and posted in the engineering office. In situations where total station and prisms are used for monitoring, engineers should install more prisms in active areas to aid in tracking movement and acceleration. • In areas where wire-line extensometers have been installed, mine operations should take readings every two hours and report the last reading on the daily shift report. The pit supervisor should conduct frequent field tours, checking for tension cracks, raveling, etc. • In areas where high movement is caused by water, engineers or other responsible personnel should make sure the dewatering program is working well to minimize the effect of water in that area. Dewatering wells and horizontal drainage systems should be continuously working to pump water out of the wall and the pit itself. Mining should be stopped during rainfall. Field inspections should be performed after rainfall before mining activities resume. • All personnel should report any unstable signs to the pit supervisor so that alternative working targets can be planned, if necessary. • All vehicles working in the pit should have their engines running and not turned off. • If slope movement decelerates, resume to operational responses for normal movement. 118 7.2.3 Operational response for minimize work and plan evacuation When a pit wall displays progressively accelerating movement even if failure of the pit wall is not yet certain, mine operators should act swiftly to minimize work in the area and plan for a pit evacuation. The following activities should be conducted under these conditions. • All personnel and equipment (if possible) must be evacuated from the unstable area and possibly out of the pit. All pit production should be suspended until a detailed assessment is done and rigorous protection procedures have been applied. • Engineers should define highly dangerous areas and possible failure zones and alert all personnel. • Engineers should make sure that dewatering is working well to minimize the effects of water in that area. Mining should be stopped during periods of rain and inspections conducted and recorded after the rain stops and before production in the pit can resume. • Engineers should frequently review slope monitoring instrument readings and work on protective measures for resuming production in case slope movement starts to decelerate. • Engineers and supervisors should maintain field inspections if it is safe to do so. • As in the case above, if slope movement begins to decelerate, engineers and supervisors should resume activities in the transitional movement state. 7.2.4 Operational response for stop work and evacuate When slope failure is imminent in an open pit wall all work in the area must stop and personnel and equipment should be removed from the area. Being in this stage implies that all previous activities conducted as a result of engineers’ assessments and recommendations to operations did not help to reduce the slope movement velocity. At this stage, mining operations should swiftly conduct activities that will reduce the impending impact on operations. Under this state, the following actions should be taken. • All personnel and equipment must be evacuated from the critical area. • All entries to the defined area must be blocked unless approved otherwise by engineers. • Field inspections should be conducted by engineers when it is safe to do so. • Engineers should assess the significance of the possible failure and loss so that operations can work on alternative mining targets and cleanup plans. 119 7.3 Decision node with scenario analysis 7.3.1 Decision node An influence diagram or a decision net is created once decision and utility nodes are added to a Bayes net. The links that go into a decision node are usually referred to as informational links. The informational links show what will be known at the time the decision is to be made by the decision maker (Norsys Software Corp. 2014). The number beside each decision choice indicates the expected utility (or expected value) of making that choice. The state in the decision node with the maximum expected value is the one that a decision maker should implement (Neapolitan 2003; Norsys Software Corp. 2014). The sum of the expected values in the decision node can sometimes be more than 100 depending on the preference of the designer of the BBN model. As such, values in the decision node are not probability values. The utility node used in the proposed model is called ‘satisfaction’. This node measures the level of the decision maker’s satisfaction of each of the possible worlds represented by the parents (Norsys Software Corp. 2014). Utility nodes are used in a decision net whose expected value is to be maximized while search for the best decision rule in the decision node (Norsys Software Corp. 2014). Most often, utility nodes work together with a decision node. A decision node was incorporated into the proposed model to help make decisions swiftly based on any change in conditions. The difference between Figure 7-1 and Figure 7-6 is the incorporation of the decision and utility node. Decision and utility nodes were incorporated into the proposed model after the sensitivity analysis because currently the sensitivity analysis conducted in Netica works for a Bayes net but for not decision nets. Incorporation of the decision and utility nodes was adopted from the Umbrella example given by Shachter & Peot (2013) as used in the Netica tutorial (Norsys Software Corp. 2014). The decision node used in the proposed model is called ‘operational response’ and it has the following states: normal work production, work with caution, minimize work and plan for evacuation, and stop work and evacuate. For example, in Figure 7-6, the highest expected value in the operational response node (~62) corresponding to normal pit production. Thus, for this case the mine should continue with daily pit activities. 120  Figure 7-6. Proposed model framework with decision node (Operational response) 121 7.3.2 BBN model scenario analysis After building and testing the model as described above, the model was tested to see the behaviour and response of the BBN model to changes in the input parameters. Four scenarios were created to evaluate the performance of the model. These are described as ‘poor conditions’, ‘typical dry conditions’, ‘typical wet conditions’, and ‘good conditions’. The nodes and their states considered for the scenario analysis are listed in Table 7-1.  Figure 7-7. Results of poor conditions leading to an operational response node in the BBN model As shown in Figure 7-7 to 7-10, the results obtained from the proposed model reasonably reproduce the reality of different conditions in the pit. The difference between Figures 7-8 and 7-9 is the change in ground water even though the figures show a typical mining condition. Mine operators indicated during interviews that the aftermath of significant rainfall or precipitation (causing an increase in ground water) could result in slope failure. The difference between Figures 7-8 and 7-9 shows that an increase in ground water increases the likelihood for a slope failure. 122  Figure 7-8. Results of typical dry conditions of nodes leading to an operational response node in the BBN model  Figure 7-9. Results of typical wet conditions of nodes leading to an operational response node in the BBN model123 Table 7-1. Node states for scenario analysis for the proposed model Node Poor conditions Typical dry conditions Typical wet conditions Good conditions Rock unit weight Low=100% Low=5%; Normal=95%; High=5% Low=5%; Normal=95%; High=5% Moderate=100% Vertical in situ stress High=100% Low=94.3%; Moderate=5.59%; High=0.12% Low=94.3%; Moderate=5.59%; High=0.12% Low=100% Horizontal to vertical stress ratio High=100% Low=10%; Lithostatic=25%; High=65% Low=10%; Lithostatic=25%; High=65% Low=100% Ground water Saturated=100% Dry=70%; Moist=20%; Saturated=10% Dry=10%; Moist=40%; Saturated=50% Dry=100% UCS R1=100% R0=1%; R1=4%; R2=6%; R3=51%; R4=28%; R5=10% R0=1%; R1=4%; R2=6%; R3=51%; R4=28%; R5=10% R5=100% RQD Very poor=100% Very poor=5%; Poor=25%; Fair=50%; Good=15%; Excellent=5% Very poor=5%; Poor=25%; Fair=50%; Good=15%; Excellent=5% Excellent=100% Discontinuity spacing Very close= 100% Very close=10%; Close=40%; Moderate=35%; Wide=10%; Very wide=5%  Very close=10%; Close=40%; Moderate=35%; Wide=10%; Very wide=5%  Very wide=100% Discontinuity conditions Poor=100% Poor=5%; Fair=40%; Moderate=35%; Good=15%; Very good=5% Poor=5%; Fair=40%; Moderate=35%; Good=15%; Very good=5% Very good=100% Friction angle Low=100% Very low=10%; Low=20%; Moderate=50%; High=20%;Very high= 0% Very low=10%; Low=20%; Moderate=50%; High=20%;Very high= 0% High=100% RMR Poor=100% Very poor=0.04%; Poor=5.88%; Fair=50.5%; Good=40.9%; Very good=2.66% Very poor=0.18%; Poor=12.7%; Fair=57.6%; Good=28.4%; Very good=1.13% Good rock=100% 124 Node Poor conditions Typical dry conditions Typical wet conditions Good conditions GSI Poor=100% Very poor=0.18%; Poor=12.7%; Fair=57.6%; Good=28.4%; Very good=1.13% Very poor=0.18%; Poor=12.7%; Fair=57.6%; Good=28.4%; Very good=1.13%  Good rock=100% Blast damage High energy released=100% Low energy released=10%; Medium energy released=30%; High energy released =60% Low energy released=10%; Medium energy released=30%; High energy released =60% Low energy released=100% Rock mass strength Low=100% Low=97.7%; Medium=2.25%; High= 0% Low=97.7%; Medium=2.25%; High= 0% High=100% Modulus of deformation Low =100% Low=96%; Medium=1.57%; High=2.47% Low=96%; Medium=1.57%; High=2.47% High=100% Slope height Very low=5%; Low=40%; Moderate: 40%; High=10%; Very high= 5% Slope angle Steep =100% Gentle=0%; Low=40%; Moderate=50%; Steep=10%; Very steep=0% Gentle=0%; Low=40%; Moderate=50%; Steep=10%; Very steep=0% Moderate=100% Pit wall shape Convex=100% Convex=15%; Planar=30%; Concave=55% Convex=15%; Planar=30%; Concave=55% Concave=100% Structure intersection angle<slope angle Yes=100% Yes=70%; No=30% Yes=70%; No=30% No=100% Discontinuity angle<slope angle Yes=100% Yes=70%; No=30% Yes=70%; No=30% No=100% Discontinuity orientation Yes=100% Yes=70%; No=30% Yes=70%; No=30% No=100% 125  Figure 7-10. Results of typical good conditions to an operational response node in the BBN model The proposed BBN model reveals the importance for mine operators to reduce the impact of rainfall or precipitation on slope instability. Often during a daily routine check of the pit walls, the responsible personnel check for evidence of seepage on the pit wall surface, and tension cracks to make decisions about the performance of the pit walls. 126 Chapter 8: Case Studies 8.1 Overview This section presents four case histories used to validate the BBN model. The data used for the case histories were obtained from the questionnaire, site visit, interviews, consulting reports, and other related literature. The data available for each case history are scant but this chapter shows that even limited data can be used in the proposed BBN model to yield responsible recommendations for an appropriate operational response. In addition, the proposed model provides other useful information such as the possible failure volume and estimates of maximum reach of the debris. Using the obtained data, the proposed model predicted the appropriate operational response for each mine operation even though it may have been contrary to the actual action taken by the mine operation when the actual failure occurred. 8.2 Case 1 – HVC mine Rock ravelling between elevations of 935 to 920 m in Phase 8 of the HVC Valley pit east wall was reported at the end of the day shift on November 18, 2012. Typically, this type of information is communicated to the HVC geotechnical group, but it did not happen on this occasion. During the afternoon of November 22, 2012, Pit Control received geotechnical alarms. At about 4 pm, the pit supervisor contacted a member of the geotechnical group to report a “slough” in Phase 8, based on an observation made by a haul truck driver. A geotechnical expert immediately inspected the area and provided instructions to mine operations by approximately 5 pm the same day. This was not an active mining area. Crews were instructed to stay away from the area. The area of instability corresponded to the same zone “flagged” by one of the pit supervisors a few days before. Typical mild winter weather prevailed up to the day leading to the instability (Figure 8-1). Rock raveling was reported on the morning of November 18, 2012, which intensified the morning of November 22, 2012. 127  Figure 8-1. Front view of toppling instability with debris outlined in black (Highland Valley Copper 2013). The red dash line is the approximate location of the vertical cross section shown in Figure 8-2  Figure 8-2. Approximate profile of the Valley pit east wall used to measure travel distance (drawn to scale) Dump truckω~32°R2 ~145 mα~65°Rp ~48 mH~90 mϕ~38°Pre-failure128 A GroundProbe technician came to the site on November 16, 2012, to repair/adjust the radar system, which was “locking up” during the week preceding the instability (Highland Valley Copper 2013). The technician replaced both the encoder and the onboard camera before leaving the mine site on November 19, 2012. The technician created a new wall folder, but did not bring in the monitoring threshold instructing the system to alarm. A Highland Valley Copper slope monitoring technician returned to the mine on the morning of November 22, 2012, and re-established the slope stability radar alarming capabilities. Table 8-1 gives a summary of the instability. Table 8-1. Summary of Nov. 22, 2012 instability at the SE wall of the Valley pit Term Description Debris volume, V 11,700 m3 Failure mode toppling, structure release Overall height  90 m Overall angle 45° RMR 34 – 36 GSI 34 – 36 UCS 16 – 39 MPa Measured reach (Rm) 18 m (estimated) Friction angle  21°– 34° Impact on operation unknown  With the data provided in Table 8-1, the BBN model was run to verify whether it was possible to predict the situation leading to slope failure. Using the information provided by the engineers, the ground water condition state was assumed to be in moist to saturated states as shown in the BBN model (Figure 8-3). The pit wall shape was convex based on the evidence seen in Figure 8-1. Therefore, the pit wall shape was given the high likelihood to occur in convex state of the node. Additionally, during a reconnaissance visit to the pit, it was evident that most discontinuity orientations were steeper than the pit wall angle. Information about the horizontal to vertical stress ratio was not provided. Based on studies conducted by Brown & Hoek (1978) and Şen & Sadagah (2002), k was kept at ~10%, ~25%, and ~65% for low, lithostatic, and high states respectively. 129 The source volume of the failure was estimated at 9,000 m3. Assuming a bulking factor of 30% from Gibson et al. (2006), the volume of the debris was estimated to be 11,700 m3. The photograph shown in Figure 8-1 was taken after the incident had occurred. Using Figure 8-1, a rough profile of the pit wall before and after the failure was drawn as shown in Figure 8-2. This figure shows a pit wall with six benches with an overall slope angle of 45° before the failure. After the failure, the debris is assumed to have come to rest at the angle of repose (38°) consistent with the uniform slope in the debris seen in Figure 8-1. The maximum reach of the debris should have been governed by a spreading mechanism due to the small debris volume and low pit wall height. Equation 21 would have predicted a travel distance angle of approximately 32°. A reach of 145 m predicted using Equation 21 is also plotted on Figure 8-2. The reach obtained using the proposed relationship is greater than what is seen in Figure 8-1 indicating that a portion of the failed rock mass had been cleaned up or that Equation 21 overestimated the value of Rp for this case. In other to verify if the proposed model could estimate the potential debris volume, the debris volume data was not used. Figure 8-3 shows that the debris volume has a high chance for Vol 1 (0 – 10,000 m3) and Vol 2 (10,000 – 100,000 m3) states with Vol 1 slightly higher, which corresponds to the estimated source volume by the mine operation. Figure 8-3 shows the operational response. The BBN recommends a response of stop work and evacuate all equipment and personnel from the location. In spite of malfunctioning slope monitoring equipment, management could have used this BBN to issue a stop work order in this area. There would have been clarity in the decision to stop the work and there would be no need to interpret pit wall movement data to make this decision. The importance of the ground water condition on the pit wall performance and the resulting predicted state of the slope velocity can be assessed by changing the input of the ground water node from state of moist to dry. If the ground water state is assigned a value of dry, the BBN predicts slope velocity states at 61%, 20%, 12%, and 7% for normal, transitional, progressive, and failure states respectively. As such, the highest expected value for the operational response will have been normal pit production.  When the ground water condition changes from dry to moist state, the operational response changes from normal pit production to stop work and evacuate. This implies that an increase in ground water pressure resulted in the slope failure. Appendix F (Table A-12) presents the tabulated data from this analysis.130  Figure 8-3. BBN model framework with inputted data for incident at HVC mine in 2012131 8.3 Case 2 – Endako mine On November 12, 2007, a pit wall failure occurred that nearly buried a shovel at the southeast wall of the Endako pit at Endako mine. During an interview conducted on a site visit to the mine, the engineer said the slope failure occurred after mining had resumed after a heavy rainfall. At the time of the incident, monitoring of the pit wall location was being conducted weekly, making it difficult for mine operations to capture the detailed sequence of movements leading to the slope failure. From field observations, the RMR for the location ranged from Poor – Fair. For the purpose of this study, RMR was assumed as Fair. The slope angle at the location is moderate (~ 45°). The slope height is around 170 m. Table 8-2 summarize the data for the event. During the site visit, it was observed that the slope failure occurred at a location that had a somewhat convex pit wall shape. Table 8-2. Summary of failure event at the southeast wall in 2007 Term Description Debris volume, V More than 566,000 m3 Failure mode Multi-bench wedge failure Overall height ~170 m Overall angle ~45° RMR 40 – 60 GSI 40 – 60 UCS unknown Measured reach (Rm) ~90 m Friction angle  unknown Impact on operations Shovel nearly got buried and mining was suspended  At the time the photograph in Figure 8-4 was taken, the pit was inactive and water covered the pit floor. When this failure took place, there was a shovel operator working in the area cleaning the bench face. There was also a drill parked in the area. Some of the failed rock damaged the shovel (Figure 8-5). Figure 8-6 shows an aerial view of the failure; this photo was taken a few months before the slope failure occurred. 132  Figure 8-4. Location of multiple bench failure outlined in red at Endako mine (photo taken in 2013); black dashed line is the approximate location of the cross section shown in Figure 8-7  Figure 8-5. Equipment damaged during the incident (Wojdak 2008) Oil spill from impacted shovelPart of shovel buried Drill 133  Figure 8-6. Approximate area of instability outlined in red (July 2007 image obtained from Google Earth) The mine had no pre-determined operational responses when unusual pit wall movements were measured or observed. This situation was still noted during the site visit in June 2013. The ground water condition was assumed to be in moist to saturated states as shown in the BBN model (Figure 8-8). Based on the same reasoning given for the HVC case study, k was kept at ~10%, ~25%, and ~65% for low, lithostatic, and high states respectively. Using observations made in Figures 8-4 and 8-5, a profiles of the pit wall before and after the failure were created as shown in Figure 8-7. The scarp of the failure was assumed to be located approximately 30 m behind the slope crest. The horizontal distance from the scarp of the pit slope to the edge of the debris volume, in Figure 8-7 was measured in the outlined region in Figure 8-6. The pit wall had an overall slope angle of greater than 40°. Without using the debris volume data in the BBN, Figure 8-8 shows that the predicted debris volume has a high chance of occurring between Vol 2 (10,000 – 100,000 m3) and Vol 3 (100,000 – 1,000,000 m3) states with Vol 3 slightly higher, which is similar to the actual failure volume estimated by the mine operation. The volume of the debris was estimated at 566,000 m3. This debris volume was used to estimate the travel distance angle using Equation 21 as shown in Figure 8-8. Using a predicted travel distance angle of approximately 26°, the travel distance Ltd was estimated to be approximately 395 m. 0 545 m 134  Figure 8-7. Approximate profile of the southeast pit wall used to measure travel distance (drawn to scale) In Figure 8-4, the debris appears to be resting at an angle of repose. While pit wall velocities greater than 100 mm/day probably occurred during this failure, the debris does not show evidence that the failing rock mass transformed into a rock avalanche. Thus, it would be expected that Equation 21 would over-predict the travel distance for this debris, and this is seen in Figure 8-7. Based on the scant information about the geotechnical properties and mining activities at this mine, the data used in the proposed model recommended an appropriate operational response in this case. From interviews conducted with personnel at this site, mining activities were going on when the pit wall failure occurred, endangering personnel and equipment. From Figure 8-8, the proposed BBN model recommends that work should have stopped and that all personnel and equipment should have been removed from the area. Although no injuries were not recorded in this instance, people could have been easily injured or killed. The proposed BBN model shows about ~ 20% probability that equipment will experience minor manage to ~8% probability of equipment being completely lost as shown in Figure 8-8. Appendix F (Table A-13) presents the tabulated data from this analysis. Observations made during the mine site visit reveal that irrespective of the rock mass quality, the pit wall angles are all greater than 40°. Therefore, the proposed model could have α~65° ω~26°Rp ~233 mLtd ~395 mPre-failure~245 mRm ~90 mBermH~170 m135 revealed the dangers of creating steep slopes in areas of poor rock mass quality. The proposed model would have revealed the consequences of the slope failure, and provided guidance to evacuate the shovel before the movement of the pit wall accelerated. The mine was unaware of the possibility that the failed rock could travel significant distances from the pit wall (i.e. 90 m from the toe of the upper slope).The volume of the potential failure source could have been estimated through field reconnaissance. The extent of the cracks into the pit wall could have been used to estimate the potential source volume for a rockslide and then the potential debris volume. The potential debris volume could then have been used to determine the travel distance of the rock mass if the debris were to transform into a rock avalanche. Thus, better decisions with respect to moving the shovel and personnel away from the location of the pit wall could have been made. From the BBN model, the predicted travel distance indicates that the debris could travel approximately 233 m from the toe of the pit wall. The model prediction would have been valuable because there was a shovel working close to the pit wall that was hit by the debris. Implementation of the proposed model may have given mine operations a better understanding of the interactions of the geotechnical properties and mining activities. Some of the other factors that were noted for this case history are (1) the effect of the rainfall on ground water was not taken into consideration, and (2) mine operations had no knowledge of the horizontal to vertical stress ratio, thus did not considering the effect of k in the decision making process. Continuous depressurizing the pit walls after the rainfall could have been implemented before resuming mining activities in the mine. Frequent and daily monitoring of the pit walls could have alerted mine operations to a deterioration of the slope performance in response to mining activities.136  Figure 8-8. BBN model famework with inputted data for 2007 incident at Endako mine137 8.4 Case 3 – Huckleberry mine The East pit of Huckleberry mine was abandoned because the entire north wall in the east zone of the pit (presently inactive) failed on June 22, 2007 (Figure 8-9). No injuries were sustained because personnel and equipment were moved to other workplaces when cracks in the highwall were noticed four days before the failure. A large volume of rock from the northern high wall of the East Zone pit moved into the pit over a two-day period. The debris extended across the pit floor and up the opposite pit wall as seen in Figure 8-10. Figure 8-11 shows an aerial view of this area eight years later; part of the pit has been filled with tailing and/or waste rock. The reserve life of this part of the pit was approaching its end and mining was planned to be completed in late July 2007 if the failure had not occurred (Imperial Metals 2007). According to an interview conducted with a mine staff through the follow up section of the completed questionnaire, the failure caused mine production to be suspended. Pit production in that location of the pit was affected as mining in the pit was halted (Christensen et al. 2011).  Figure 8-9. East zone wall failure outlined in yellow at the Huckleberry mine (photo taken on June 22, 2007); red dash line is the approximate location of the cross section shown in Figure 8-12 138  Figure 8-10. East zone wall failure at Huckleberry mine (side view) (Wojdak 2008)  Figure 8-11. Approximate area of instability and the horizontal distance outlined in red (2015 image obtained from Google Earth); note the lower part of the debris has been buried in tailings or waste rock in this image The location of the failure had a slope angle of 51° with a slope height of 250 m. The rock mass quality was very poor, with RMR of 35. The failure occurred in June and there was still remnant snow above the pit that was melting (Figure 8-9). The snowmelt combined with spring rainfall probably increased the groundwater levels (Golder Associates 2007b). Thus 0 705m139 for this case history the ground water node was assigned a moist state. The total volume of the debris was estimated at 2,000,000 m3 (Wojdak 2008). Table 8-3 shows the summary of the event. The limited available information was used to verify the validity of the BBN model. Table 8-3. Summary of details of June 2007 event at the east zone north wall Term Description Debris volume, V 2,000,000 m3 Failure mode Unknown Overall height 250 m Overall angle 51° RMR 35 GSI 35 UCS 146 MPa Measured reach (Rm)  ~223 m Friction angle  Unknown Impact on operations Ore production terminated  An approximate profile of the pit was drawn based on observations made in Figure 8-9 to Figure 8-11. The horizontal distance from the scarp of the pit slope to the edge of the debris volume was measured in the outlined region in Figure 8-11. The opposite pit wall seen in Figure 8-10 obstructed the distal movement of the debris. 140  Figure 8-12. Approximate profile of the northwall used to measure travel distance (triple bench and drawn to scale) Figure 8-13 shows that the potential debris volume has a high chance of occurring between Vol 3 (100,000 – 1,000,000 m3) and Vol 4 (1,000,000 – 10,000,000 m3) states with Vol 4 slightly higher, which corresponds well to the estimated volume by the mine operation (2,000,000 m3). This volume was used estimate the travel distance angle as using Equation 21. Based on the height of the slope, a predicted travel distance angle of 22° resulted in a travel distance Ltd of approximately 636 m as shown in Figure 8-13. While the rockslide showed high rates of movement over a two-day period, it did not generate a rock avalanche. Thus, the predicted reach was larger than the actual reach. From Figure 8-13, the maximum expected value in the “operational response node” corresponds to the state of stop work and evacuate. Additionally, Figure 8-13 shows the proposed model predicted a complex failure mode such as a combination of wedge, rotational and plane sliding. Further confirmation comes from the “strain” node that also indicates an impending slope failure. Although little information was used in the proposed BBN, the network gave some useful insight on the expected performance of the pit wall. Appendix F (Table A-14) presents the tabulated data from this incident.ω~22°α~65°H~250 mLtd ~610mRp ~374 mRm ~220 mPre-failureOpposite pit wall~460m141  Figure 8-13. BBN model framework with inputted data for 2007 incident at Huckleberry mine142 8.5 Case 4 – Copper Mountain mine A multi-bench planar failure occurred on November 4, 2011 along the east wall of Pit 3 burying the front end of an excavator. The excavator lost approximately two weeks of production because it was moved to the workshop for repairs. The failure was characterized by a multi-bench planar rockslide along a continuous, westerly dipping joint that was undercut by the excavator (Golder 2012). After this incidence, the mine reduced the slope angle. Table 8-4 provided further details on the failure event. Table 8-4. Summary of November 4, 2011 failure event at the Stage 2 east wall Term Description Debris volume, V 14158 m3 Failure mode Multi-bench planar failure  Overall height 80 m Overall angle 55° RMR 40 – 60 GSI 40 – 60 UCS 100 – 142 MPa Measured reach (Rm) unknown Friction angle  unknown Impact on operations Shovel lost (equipment damage) for approximately 2 weeks  The available information about the event collected during an interview was used in the proposed model to verify the validity of the model. No photos were available. The estimated volume of the debris was 14,158 m3. Assuming bulking factor of 30% from Gibson et al. (2006), the failure volume was estimated to be 9,910 m3. The BBN model was run without using the estimated debris volume to determine what volume the BBN model would predict. Figure 8-15 shows that the predicted debris volume has a high chance of occurring in Vol 1 (0 – 10,000 m3) state, which corresponds with the failure volume estimated. For this case history, a debris spreading mechanism was predicted by the BBN with a travel distance angle of approximately 32° (Figure 8-14). For the 80 m slope height, a reach of 143 approximately 128 m is predicted using Equation 21. Alternatively, after the failure, the debris could have come to rest at the angle of repose (38°). The actual reach is unknown because the debris was removed before measurements could be taken. Because damage occurred to a shovel, it is clear the shovel working at that location of the pit wall was close to the wall.  Figure 8-14. Aproximate profile of Stage 2 east pit wall used to measure the travel distance (drawn to scale) From Figure 8-15, the highest expected value for the operational response node is for stop work and evacuate. The expected value for normal pit production operational response was low and yet the mining was going on. The proposed BBN model would have alerted the mine operation of the impending danger. Appendix F (Table A-15) presents the tabulated data from this analysis. The importance of the ground water condition on the pit wall performance and the resulting predicted state of the slope velocity can be assessed by changing the input of the groundwater node from state of moist to dry. If the groundwater state is assigned a value of dry, the BBN predicts slope velocity states of approximately 52%, 27%, 13%, and 8% for normal, transitional, progressive, and failure states respectively. As such, the highest expected value for the operational response would be normal pit production. It is clear that the stability of the pit wall is highly sensitive to the ground water.ω~32°α=65°H~80 mR2~128 mRp ~52 mϕ=38°Pre-failure144  Figure 8-15. BBN model famework with inputted data for November 4, 2011 incident at Copper Mountain mine  145 8.6 Case 5 – Gibraltar mine The BBN model was used for the first four case studies to show if the mine operational response was different from what the BBN model would predicted. Although the BBN model predicted operational responses that somewhat different and better than what the mines actually did, it is expedient to show how mine operators can use the BBN model to manage daily pit operation.  Experience from Gibraltar mine was used to collect data after geotechnical engineers conducted a daily routine check. The data for some of the parameters are as follows: RMR is 50; rock unit weight is 26 kN/m3; slope height is 120 m; and slope angle is 40°, blast damage was present (D=1), and no evidence of seepage (ground water state is dry). At a slope height of 150 m, k is usually high (Brown and Hoek 1978; Şen and Sadagah 2002), therefore k is assumed to be was ~10%, ~25%, and ~65% for low, lithostatic, and high states respectively. The discontinuity condition and the discontinuity spacing are easily known. Moreover, the routine check indicates that the orientation of the critical discontinuities is less than the slope angle in some locations of the pit wall. Using these data in the BBN generated the results seen in Figure 8-16. The number beside each decision choice indicates the expected utility of making that choice. The model is able to predict an expected value of ~81, ~18, ~10, and ~5 for normal pit production, work with caution, minimize work and start evacuation, and stop work respectively. Based on these results, clearly the best choice given the available information is to keep working under a normal pit production state. This can assure mine operators that the pit walls have little chance of causing any harm to production or personnel and the results are consistent with the routine operation of mining that was occurring for this case history. In addition, the mine operators are alerted to the possible failure modes that could occur should conditions in the pit deteriorate. The proposed model indicates that mine operators should watch out for possible plane and wedge sliding. However, due to the low rock mass strength exhibited by the pit walls as shown in Figure 8-16, rotational failure could occur if conditions in the pit worsen. Appendix F (Table A-16) presents the tabulated data from this analysis. 146  Figure 8-16. Predicting operational response using data obtained after a daily routine check for the Gibraltar mine 147 Chapter 9: Conclusions and Recommendations 9.1 Summary The main objectives of this research were to develop and establish a Bayesian Belief Network (BBN) model and to outline appropriate operational responses to manage slopes in large open pit porphyry mines.  The research integrated available geotechnical engineering data and knowledge, including expert knowledge, ground water knowledge, slope geometry, mining activity (blast damage), and consequences of failure, into one platform that can establish appropriate operational responses to predicted states of pit wall movement. The proposed model carefully considers and quantifies uncertainty at several levels within each parameter. The characteristics of the BBN model make it very appropriate for application to geomechanical problems, where uncertainty is always present (Miranda et al. 2009). The proposed model captured the uncertainties associated with the different empirical equations and expert judgement. This methodology is equipped to accept conditional probabilities that are developed based on other evidence or data (e.g. historical data, results from analytical and experimental work). Adding quality historical data will help the model make better predictions about the behaviour of rock slopes influenced by mining. Bayesian updating can be used from this point forward as new data become available to enhance the performance of the proposed BBN model. A detailed review was conducted to identify and define the nodes needed to develop the BBN model showing causal relationships and interdependencies among the nodes. The BBN model incorporates a probabilistic characterization of all the important factors affecting slope stability. Using data obtained from questionnaires, interviews conducted with mine operators, and case histories, the BBN model was trained to make better predictions. The methodology described in the thesis provides the foundation for an innovative tool for selection of appropriate operational responses linked to assumed, observed, and measured conditions in an open pit slope. The application of the developed BBN model framework can provide mine operators with a deeper understanding of open pit slope management. Implementation of the proposed BBN model can help reduce the time needed to make decisions, 148 increase safety awareness, maximize productivity, and protect human lives. The BBN model can also help mine operators forecast future pit wall behaviour to help implement short- and long-term planning for the operation. A BBN sensitivity analysis was performed on slope movement and the consequences of pit wall failure nodes to determine the level of influence of geotechnical, ground water, slope geometry, and blast damage parameters. The sensitivity analysis demonstrated the importance of ground water, the effect of k, slope angle, GSI (obtained via RMR), and rock mass strength. The importance of k in the research agrees with the work conducted by Stacey et al. (2003). The sensitivity analysis showed that blasting has less effect than previously thought on the movement of the slope walls. A scenario analysis was conducted using the BBN model to evaluate the capability of the model to handle different pit conditions, including different geotechnical properties, ground water conditions, slope geometries, and consequences of failure parameters, and thus predict the appropriate operational response for each open pit condition. The results obtained from this analysis showed that the model yields reasonable predictions of slope instability volumes, potential reach of the failure debris, and estimates of slope movement velocities. Furthermore, the BBN model for each scenario makes recommendations for operational responses that seem to match best practices in the field. This thesis presents a BBN model that can be used to manage open pit mines in BC. This represents a novel approach to assessing and responding to open pit slope movements, one that integrates knowledge from a range of categories, including geotechnical properties, slope geometry, mining activity (blast damage), ground water, and consequences of failure. The result is a fully updateable probabilistic methodology that goes well beyond the capabilities of existing tools. In addition to demonstrating the value of using BBN for estimating the slope velocity and consequences of failure, the BBN model was structured to provide guidance for making appropriate operational decisions regarding responses to observed or measured performance of the pit walls. The proposed BBN model shows the interaction between various parameters, thereby giving mine operators knowledge, understanding, and guidance in making the correct decisions to prevent catastrophic events and to maximize safety in the pit. 149 The most important conclusions made from this research are: • The proposed BBN model gives a framework that can help open pit slope risk management. • A relationship was proposed to estimate the maximum travel distance from a wide range of debris volumes. • Estimating the travel distance gives mine operators information on whether to evacuate equipment such as shovels and drills from the pit or to move it further from the unstable pit wall. • The proposed model accounts for a potential rockslide transforming into rock avalanche. • The proposed BBN model established links between equipment damage, harm to personnel and production loss in order to predict the level of consequences. • With the help of the BBN model and the recommended operational response arising from data entered into the model, mine operators are provided with a decision-support tool based on current pit conditions. The following sub-sections summarize other important conclusions made from this research. 9.2 Ground water Most pit slope failures, including the case studies discussed in the research, are caused by high ground water levels resulting from periods of precipitation and spring snow melt. The BBN results show the importance of slope dewatering programs, along with monitoring the ground water levels and the amount of water pumped out of a pit wall. Moreover, it is important for operating mines to understand the physical interactions between hydraulic and mechanical processes (Sullivan 2007). All four case studies showed that changes in ground water states contributed to the failure of the slopes. If tension cracks develop because of stress distribution within the rock mass, ground water captured within the tension cracks can trigger slope failure. It is important for mine operators to implement slope depressurization programs to increase the stability of the slope. Although most operating mines have dewatering programs, it is important that dewatering be fully functioning, especially during spring-freshet periods. Reduction in ground water improves stability for all types of failure modes (Brawner 1982). 150 9.3 Travel distance Estimates of the potential travel distance or reach of a slope failure is of significance in mine operations. The proposed methodology explicitly includes an estimate of the maximum likely travel distance, which is a significant improvement over existing approaches for analysing pit wall stability. Different empirical models were used to estimate travel distance using an estimate of the potential debris volume. Mine operators are usually able estimate the potential source volume before a slope failure occurs; however, most mine operators do not use it to assess the travel distance. During interviews conducted with mine operators, none of the BC mine operators considered travel distance in assessing risk related to an impending slope failure. For the first time, this research considers travel distance in the BBN model. With an estimated volume deduced from an impending failure, the proposed model can predict the maximum travel distance. The travel distance predictions assume the process was governed by mechanisms for debris spreading or rock avalanche. Debris volumes greater than 100,000 m3 were assumed capable of converting into a rock avalanche. For both mechanisms, the predicted travel distance is expected to be greater than the actual distance for most cases. For example, rockslides that convert to rock avalanches are fortunately rare in open pits. Nevertheless, it was deemed important to include upper bound estimates of the reach or travel distance as this factor is essential for assessing the consequences of a slope failure and for risk management. The four case histories used to estimate the travel distance of the slope failure indicates that new proposed relationship overestimates the actual travel distance. The angle of repose of the debris influences the predicted travel distance. Nevertheless, the methodology presented for estimating the travel distance is a promising first step. It is recognized that the proposed approach is simple and that estimating the travel distance of a rockslide is a complex area of research that requires further work. The simple approach here can be replaced with a more refined prediction of the travel distance without altering the overall methodology of the BBN model. 151 9.4 Slope velocity Open pit walls are expected to move at a normal rate of deformation during mine operations that would not cause any havoc. The expected normal movement is dependent on the geotechnical parameters and the pit wall geometry. Conversely, the activities conducted in the pit also depend on the performance of the slope in response to mining. Slope monitoring techniques can capture changes in the slope movement as mining progresses, thus identifying transitions to higher rates of movement. The transition stage of movement can be slowed to short-term deceleration if disturbing events external to the pit wall are removed. However, if slope movement accelerates, slope failure can be imminent unless active and effective operational responses are taken. If a mine operates a robust slope monitoring system, any changes in slope performance can be readily detected so that the best response decisions can be made. However, there are multiple reasons why mine operators may not be adequately monitoring their slopes: harsh weather conditions can disable monitoring instrumentation, slope monitoring equipment may be broken, or there may be a lack of competence in using the instrumentation. A node in the BBN was assigned to slope velocity. Seven parameters were used to predict slope velocity of the pit wall. The slope velocity node represents more than just slope velocity. It is also a parameter that reflects the probability for pit wall failure (Jaboyedoff et al. 2012). The proposed BBN model can provide guidance for decision-making even when instrumentation is not providing adequate data. The model also helps mine operators to focus on factors that are most critical to the stability of the pit walls. From experience at Gibraltar mine, during low visibility conditions, no monitoring technique is used aside from daily routine checks to verify the conditions within the pit. Therefore, during bad weather with low visibility, observations collected during daily routine checks can be inputted in the proposed model to predict the expected slope velocity. 9.5 Consequence of failure When a slope failure occurs, a mine is most concerned about harm to personnel, loss of production, and equipment damage. The research therefore considered these three aspects as the relevant consequences of pit wall failure. The proposed BBN model established a link between 152 three important parameters (slope velocity, debris volume, and travel distance) to predict the level of consequences.  In addition, a decision node in the BBN uses the predicted level of consequences to recommend appropriate operational responses. Training of the three consequence nodes used expert opinion and case history data. Since the data were limited, more case history data would help to improve the predictive capability of the consequence section of the BBN model. 9.6 Operational response Although BC mines routinely use operational rules and guidelines for routine daily mining activities, these mines typically have poorly defined plans to deal with unexpected pit wall movements. The proposed BBN model can provide guidance to mine operators to make better operational decisions in response to observed or measured changes in pit wall behaviour. For the purposes of informed decision-making, it is important to link the operational response with the consequence of failure resulting from slope movement velocity as well as the potential debris volume and travel distance of the failure. This allows better decisions to be made which, in turn, will increase the safety of personnel working in the pit, as well as reassure other stakeholders of the mine operation. The BBN model was used to predict the appropriate operational response at four BC mines in response to conditions leading to historical slope instabilities. The results indicate that the appropriate operational response recommended by the BBN model could have been used to avoid or minimize equipment damage as well as production losses at the time of each slope instability. Stakeholders like BC Ministry of Mines and Energy should encourage the use of this tool by BC mine operators. At the same time, the decision nodes implemented in this methodology can enhance the confidence of mine operators when their modus operandi is being assessed by government agencies such as the Ministry of Mines and Energy. 153 9.7 Recommendations Mine operators should cultivate a habit of collecting and documenting field data about pit wall failures as mining progresses, including factors such as geotechnical properties, ground water conditions, and pit wall shape in order to make better decisions. When a failure occurs, it is important to document the geometry of the pit wall before and after the failure, such that parameters like pit depth, slope height, pit wall angle, debris volume, and debris reach can be readily determined. Although the pit wall profiles for pre-failure and post-failure conditions were created for the four case studies, this was challenging because of lack of details at these locations. Therefore, future work should consider using 3D models created from data obtained from laser scans or photogrammetry processing of photographs. Pit walls that are in a state of very rapid motion associated with failures that transform from rockslides to rock avalanches can be catastrophic to mine operations. It would be useful to expand on this aspect in the proposed BBN model. Seismic activity was ignored in the proposed model. Hence, further research should be conducted to understand the effect of earthquakes on slope behaviour so that this aspect can be included. Understanding the influence of seismicity in areas that are prone to earthquakes will enhance the capabilities of the proposed model. The proposed BBN model assumed that the level of vulnerability for equipment and non-equipment operators was equivalent to their exposure time. Future work should improve evaluation of the vulnerabilities for equipment and non-equipment operators.  It would be helpful to differentiate further the exposure and the vulnerability of different categories of personnel working within the open pit. The proposed BBN model in its current state is probably not sufficiently reliable for replacement of current pit management practices. Additional calibration of the BBN model with field data, primarily acquired from well-documented case histories is needed. Bayesian updating can also be implemented during this time to refine the CPT values. 154 References Abdelgawad, M., & Fayek, A. R. (2012). Comprehensive hybrid framework for risk analysis in the construction industry using combined failure mode and effect analysis, fault trees, event trees, and fuzzy logic. Journal of Construction Engineering and Management, 138(5), 642–651. http://doi.org/10.1061/(ASCE)CO.1943-7862.0000471 Agena. (2014). Agena: Bayesian network and simulation software for risk analysis and decision support. Retrieved July 7, 2014, from http://www.agenarisk.com/products/free_download.shtml Ale, B.J.M. (1991). Risk analysis and risk policy in the Netherlands and the EEC. Journal of Loss Prevention in the Process Industries, 4:58–64 Ang, A. H.-S., & Tang, W. H. (1975). Probability concepts in engineering planning and design, volume 1, basic principles. John Wiley & Sons Canada, Ltd. Ash, C. H., Panteleyev, A., MacLennan, K. L., Payne, C. W., & Rydman, M. O. (1999). Geology of the Gibraltar mine area, (NTS 93B/8, 9). BCMEMPR Open File 1999-07, B.C. Ministry of Energy and Mines. Aven, T. (2008). Risk analysis assessing uncertainties beyond expected values and probabilities. Chichester, England; Hoboken, NJ: Wiley. Baecher, G. B., & Christian, J. T. (2003). Reliability and statistics in geotechnical engineering. Wiley. Basu, A., & Aydin, A. (2006). Predictinguniaxial compressive strength by point load test: significance of cone penetration. Rock Mechanics and Rock Engineering, 39(5), 483–490. http://doi.org/10.1007/s00603-006-0082-y BCMME. (2008). Health, safety and reclamation code for mines in BC (p. 356). Victoria, BC: British Columbia Ministry of Energy, Mines and Petroleum Resources Mining and Minerals Division. Retrieved from http://www.empr.gov.bc.ca/Mining/HealthandSafety/Documents/HSRC2008.pdf Bednarski, M., Cholewa, W., & Frid, W. (2004). Identification of sensitivities in Bayesian networks. Engineering Applications of Artificial Intelligence, 17(4), 327–335. http://doi.org/10.1016/j.engappai.2004.03.011 Benko, B., & Stead, D. (1998). The Frank slide: a reexamination of the failure mechanism. Canadian Geotechnical Journal, 35(2), 299–311. http://doi.org/10.1139/t98-005 155 Bensi, M., Kiureghian, A., & Straub, D. (2009). A Bayesian network framework for post-earthquake infrastructure system performance assessment. In TCLEE 2009 (pp. 1–12). American Society of Civil Engineers. BGC Engineering. (2012). Granite open pit slope review (Technical report). Bieniawski, Z. (1976). Rock mass classification in rock engineering. In Exploration for Rock Engineering, Proc. of the Symp (Vol. 1, pp. 97–106). Cape Town,Belkhema South Africa: International Society for Rock Mechanics. Bieniawski, Z. (1979). The Geomechanics classification in rock engineering applications (pp. 41–48). In 4th ISRM Congress, Montreux, Switzerland: International Society for Rock Mechanics. Bieniawski, Z. T. (1989). Engineering rock mass classifications: a complete manual for engineers and geologists in mining, civil, and petroleum engineering. John Wiley & Sons. Bieniawski, Z. T. (1997). Quo vadis rock mass classifications? Felsbau, 15(3), 177–178. Board, M., Chacon, E., Varona, P., & Lorig, L. (1996). Comparative analysis of toppling behaviour at Chuquicamata open-pit mine, Chile. Transactions of the Institution of Mining and Metallurgy Section A-Mining Industry, 105, A11–A21. Bobbio, A., Portinale, L., Minichino, M., & Ciancamerla, E. (1999). Comparing fault trees and Bayesian networks for dependability analysis. In M. Felici & K. Kanoun (Eds.), Computer Safety, Reliability and Security (pp. 310–322). Springer Berlin Heidelberg. Boudali, H., & Dugan, J. B. (2005). A discrete-time Bayesian network reliability modeling and analysis framework. Reliability Engineering & System Safety, 87(3), 337–349. http://doi.org/10.1016/j.ress.2004.06.004 Bourrier, F., Dorren, L., & Hungr, O. (2013). The use of ballistic trajectory and granular flow models in predicting rockfall propagation. Earth Surface Processes and Landforms, 38(4), 435–440. http://doi.org/10.1002/esp.3372 Brawner, C. O. (1982). Control of groundwater in surface mining. International Journal of Mine Water, 1(1), 1–16. http://doi.org/10.1007/BF02504603 Broadbent, C. D., & Zavodni, Z. M. (1983). Influence of rock structures on stability. In Stability in Surface Mining (Vol. 3). Denver, Colorado. 156 Brown, E. T., & Hoek, E. (1978). Trends in relationships between measured in-situ stresses and depth. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 15(4), 211–215. http://doi.org/10.1016/0148-9062(78)91227-5 Brown, I., Hittinger, M., & Goodman, R. (1980). Finite element study of the Nevis Bluff (New Zealand) rock slope failure. Rock Mechanics Felsmechanik Mecanique Des Roches, 12(3-4), 231–245. http://doi.org/10.1007/BF01251027 Brox, D. R., & Newcomen, H. W. (2004). Utilizing strain criteria to predict highwall stability performance. In 2004 SME Annual Meeting and Exhibit February 23– 25, Denver, CO (Vol. Preprint 04–111, p. 5). Denver. Brunetti, M. T., Guzzetti, F., & Rossi, M. (2009). Probability distributions of landslide volumes. Nonlin. Processes Geophys., 16(2), 179–188. http://doi.org/10.5194/npg-16-179-2009 Calder, P. N., & Blackwell, G. (1980). Investigation of a complex rock slope displacement at Brenda Mines. CIM Bulletin, 73(820), 73–82. http://doi.org/10.1016/0148-9062(81)90897-4 Caldwell, J. (2013). Bayesian networks in mining risk assessment and decision analysis. Retrieved December 24, 2013, from http://ithinkmining.com/2013/12/24/bayesian-networks-in-mining-risk-assessment-and-decision-analysis/ Call, R. D. (1982). Monitoring pit slope behavior. In 3rd International Conference on Stability in Surface Mining (pp. 229–248). Vancouver, Canada: New York: Society of Mining Engineers, A.I.M.E. Canadian Mines Handbook. (2011). Canadian mines handbook. Cao, Z., & Wang, Y. (2013). Bayesian approach for probabilistic site characterization using cone penetration tests. Journal of Geotechnical and Geoenvironmental Engineering, 139(2), 267–276. http://doi.org/10.1061/(ASCE)GT.1943-5606.0000765 Casti, J. (1993). Searching for certainty. Abacus. Chief Inspector of Mines (2014). Annual report of the Chief inspector of mines (BC mines Annual report). BC: BC Ministry of Energy and Mines. Chief Inspector of Mines (2013). Annual report of the Chief inspector of mines (BC mines Annual report). BC: BC Ministry of Energy and Mines. Chief Inspector of Mines (2012). Annual report of the Chief inspector of mines (BC mines Annual report). BC: BC Ministry of Energy and Mines. 157 Chief Inspector of Mines (2011). Annual report of the Chief inspector of mines (BC mines Annual report). BC: BC Ministry of Energy and Mines. Chief Inspector of Mines (2010). Annual report of the Chief inspector of mines (BC mines Annual report). BC: BC Ministry of Energy and Mines. Chief Inspector of Mines (2009). Annual report of the Chief inspector of mines (BC mines Annual report). BC: BC Ministry of Energy and Mines. Chief Inspector of Mines (2008). Annual report of the Chief inspector of mines (BC mines Annual report). BC: BC Ministry of Energy and Mines. Chief Inspector of Mines (2007). Annual report of the Chief inspector of mines (BC mines Annual report). BC: BC Ministry of Energy and Mines. Chief Inspector of Mines (20006). Annual report of the Chief inspector of mines (BC mines Annual report). BC: BC Ministry of Energy and Mines. Chief Inspector of Mines (2005). Annual report of the Chief inspector of mines (BC mines Annual report). BC: BC Ministry of Energy and Mines. Chief Inspector of Mines (2004). Annual report of the Chief inspector of mines (BC mines Annual report). BC: BC Ministry of Energy and Mines. Chief Inspector of Mines (2003). Annual report of the Chief inspector of mines (BC mines Annual report). BC: BC Ministry of Energy and Mines. Chief Inspector of Mines (2002). Annual report of the Chief inspector of mines (BC mines Annual report). BC: BC Ministry of Energy and Mines. Chief Inspector of Mines (2001). Annual report of the Chief inspector of mines (BC mines Annual report). BC: BC Ministry of Energy and Mines. Chen, G., Yang, Z., & Sun, J. (2010). Safety analysis of complex systems based on bayesian networks. In 2nd Int. Conf. on Industrial Mechatronics and Automation (ICIMA) (Vol. 1, pp. 92–95). http://doi.org/10.1109/ICINDMA.2010.5538083 Chen, W., Jin, R., & Sudjianto, A. (2004). Analytical variance-based global sensitivity analysis in simulation-based design under uncertainty. Journal of Mechanical Design, 127(5), 875–886. http://doi.org/10.1115/1.1904642 Chowdhury, R., Flentje, P., & Bhattacharya, G. (2009). Geotechnical slope analysis. Boca Raton: CRC Press. 158 Christensen, K., Connaughton, G. R., & Ogryzlo, P. (2011). Technical report on the main zone optimization Huckleberry mine Omineca mining division British Columbia, Canada (Technical report). Chung, T., Mohamed, Y., & AbouRizk, S. (2006). Bayesian updating application into simulation in the North Edmonton Sanitary Trunk tunnel project. Journal of Construction Engineering and Management, 132(8), 882–894. http://doi.org/10.1061/(ASCE)0733-9364(2006)132:8(882) Cockburn, G., & Tesfamariam, S. (2012). Earthquake disaster risk index for Canadian cities using Bayesian belief networks. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 6(2), 128–140. http://doi.org/10.1080/17499518.2011.650147 Coggan, J. ., & Pine, R. J. (1996). Application of distinct-element modelling to assess slope stability at Delabole slate quarry, Cornwall, England. Transactions of the Institution of Mining and Metallurgy Section A-Mining Industry, 105, A21–A30. Congdon, P. (2003). Applied Bayesian modelling. Chichester, UK: John Wiley & Sons, Ltd. Conroy, M. J., & Peterson, J. T. (2013). Identifying and reducing uncertainty in decision making. In Decision making in natural resource management: a structured, adaptive approach (pp. 192–231). John Wiley & Sons, Ltd. Cooper, G. F. (1989). Current research directions in the development of expert systems based on belief networks. Applied Stochastic Models and Data Analysis, 5(1), 39–52. http://doi.org/10.1002/asm.3150050106 Cooper, G. F., & Herskovits, E. (1992). A Bayesian method for the induction of probabilistic networks from data. Machine Learning, 9(4), 309–347. http://doi.org/10.1007/BF00994110 Copper Mountain. (2013). Pit wall stability and management. Corominas, J. (1996). The angle of reach as a mobility index for small and large landslides. Canadian Geotechnical Journal, 33(2), 260–271. http://doi.org/10.1139/t96-005 Coupé, V. M. H., & van der Gaag, L. C. (2002). Properties of sensitivity analysis of Bayesian belief networks. Annals of Mathematics and Artificial Intelligence, 36(4), 323–356. http://doi.org/10.1023/A:1016398407857 159 Cruden, D. M., & Masoumzadeh, S. (1987). Accelerating creep of the slopes of a coal mine. Rock Mechanics and Rock Engineering, 20(2), 123–135. http://doi.org/10.1007/BF01410043 Cruden, D. M., & Varnes, D. J. (1996). Landslides: Investigation and mitigation. Chapter 3- Landslide types and processes. Transportation Research Board Special Report, (247), 36–75. Darling, P. (2011). SME mining engineering handbook (3rd edition). Englewood, Colo.: Society for Mining, Metallurgy, and Exploration. Das, S., Grey, R., & Gonsalves, P. (2002). Situation assessment via Bayesian belief networks. In Proc. 5th Int. Conf. on Information Fusion, 2002 (Vol. 1, pp. 664–671 vol.1). http://doi.org/10.1109/ICIF.2002.1021218 Davies, T. R. H. (1982). Spreading of rock avalanche debris by mechanical fluidization. Rock Mechanics, 15(1), 9–24. http://doi.org/10.1007/BF01239474 Dawsey, W. J., Minsker, B. S., & VanBlaricum, V. L. (2006). Bayesian belief networks to integrate monitoring evidence of water distribution system contamination. Journal of Water Resources Planning and Management, 132(4), 234–241. http://doi.org/10.1061/(ASCE)0733-9496(2006)132:4(234) Deere, D. U. (1963). Technical description of rock cores for engineering purposes. Rock Mech Eng Geol, 1(1), 17–22. Deere, D. U., & Patton, F. D. (1971). Slope stability in residual soils (Vols. 1–1). American Society of Civil Engineers. Devkota, K. C., Ham, J.-E., & Kim, G.-W. (2009). Characteristics of discontinuity spacing of Yeongdeok granite. Geosciences Journal, 13(2), 161–165. http://doi.org/10.1007/s12303-009-0015-3 Dick, G. J., Eberhardt, E., Cabrejo-Liévano, A. G., Stead, D., & Rose, N. D. (2014). Development of an early-warning time-of-failure analysis methodology for open-pit mine slopes utilizing ground-based slope stability radar monitoring data. Canadian Geotechnical Journal, 1–15. http://doi.org/10.1139/cgj-2014-0028 Dowding, C. H., & Gilbert, C. (1998). Dynamic stability of rock slopes and high frequency traveling waves. Journal of Geotechnical Engineering, 114, 1069–1088. 160 Doyle, J. B., & Reese, J. D. (2011). Slope monitoring and back analysis of the East Fault failure, Bingham Canyon mine, Utah. In Slope Stability 2011 (p. 10). Vancouver, Canada. dslpitt. (2014). GeNIe & SMILE. Retrieved September 29, 2014, from https://dslpitt.org/genie/index.php/network-repository Dunnicliff, J. (1993). Geotechnical instrumentation for monitoring field performance. John Wiley & Sons Eberhardt, E. (2003). Rock slope stability analysis – utilization of advanced numerical techniques. Vancouver, BC, Canada: Earth and Ocean science, UBC. Fang, H.-Y. (Ed.). (1990). Foundation engineering handbook (2nd edition). New York: Springer. Fell, R. (1994). Landslide risk assessment and acceptable risk. Canadian Geotechnical Journal, 31: 261–272. Felli, J. C., & Hazen, G. B. (2004). Javelin diagrams: a graphical tool for probabilistic sensitivity analysis. Decision Analysis, 1(2), 101–115. http://doi.org/10.1287/deca.1030.0006 Ferson, S., & Troy Tucker, W. (2006). Sensitivity analysis using probability bounding. Reliability Engineering & System Safety, 91(10–11), 1435–1442. http://doi.org/10.1016/j.ress.2005.11.052 Finlay, P. J., Mostyn, G. R., & Fell, R. (1999). Landslide risk assessment: prediction of travel distance. Canadian Geotechnical Journal, 36(3), 556–562. http://doi.org/10.1139/t99-012 Fossen, H. (2010). Structural geology (1st edition). Cambridge University Press. Fox, D., Hightower, J., Liao, L., Schulz, D., & Borriello, G. (2003). Bayesian filtering for location estimation. IEEE Pervasive Computing, 2(3), 24–33. http://doi.org/10.1109/MPRV.2003.1228524 Franzen, D. W. (1999). A Bayesian decision model for battle damage assessment (Master’s thesis). Air Force Inst of Tech Wright-Patterson AFB OH. Gayer, R., Hathaway, T., & Davis, J. (1995). Structural geological factors in open pit coal mine design, with special reference to thrusting: case study from the Ffyndaff sites in the South Wales Coalfield. Geological Society, London, Special Publications, 82(1), 233–249. http://doi.org/10.1144/GSL.SP.1995.082.01.16 Gibson, W., Bruyn, I., & Walter, D. (2006). Considerations in the optimisation of bench face angle and berm width geometries for open pit mines. In Int. Symp. on Stability of Rock 161 Slopes in Open Pit Mining and Civil Engineering, The South African Institute of Mining and Metallurgy (pp. 557–578). Johannesburg. Gill, J. (2007). Bayesian methods: a social and behavioural sciences approach (2nd edition). Boca Raton: Chapman and Hall/CRC. Girard, J. M. (2001). Assessing and monitoring open pit mine highwalls. In 32nd Annual Institute on Mining Health, Safety and Research, Salt Lake City, Utah. Glastonbury, J. P. (2002). The pre- and post-failure deformation behaviour of rock slopes (Ph.D.). University of New South Wales (Australia), Australia. Golder Associates. (2002). A preliminary review of pit slope design parameters for the proposed pushback of the South wall of the Endako pit (Technical report). Endako mine. Golder Associates. (2007a). Granite lake pit - west stage pit expansion (Technical memorandum) (p. 14). Gibraltar Mine. Golder Associates. (2007b). Review of north wall of east zone pit (Technical report). Huckleberry mine. Golder Associates. (2009a). Draft report on geotechnical pit wall stability assessment of the Denak pit (Technical report). Endako mine. Golder Associates. (2009b). Granite lake pit expansion slope stability assessment and design Gibraltar mine ltd. Williams Lake, B.C. (Technical report). Gibraltar mine. Golder Associates. (2011). Site visit report and preliminary recommendations regarding instability of the se wall of the granite lake pit (Technical memorandum) (p. 14). Gibraltar mine. Golder Associates. (2012). Review of pit 3 east wall bench failure (Technical report). Gibraltar mine. Goodman, R. E. (1989). Introduction to rock mechanics. New York: Wiley. Goodman, R. E., & Bray, J. (1976). Toppling of rock slopes. In ASCE, Proc. Specialty Conf. on Rock Eng. for Foundations and Slopes (Vol. 2, pp. 201–234). Boulder, Colorado. Graden, R. (2012). NI 43-101 Technical report Teck Highland Valley Copper (p. 232). Highland Valley Copper. Haas, C., & Einstein, H. H. (2002). Updating the decision aids for tunneling. Journal of Construction Engineering and Management, 128(1), 40–48. http://doi.org/10.1061/(ASCE)0733-9364(2002)128:1(40) 162 Hart, R. D. (1991). General report: an introduction to distinct element modelling for rock engineering. In 7th ISRM Congress, International Society for Rock Mechanics Hartman, H. L., Cummins, A. B., & Seeley, W. (1992). SME mining engineering handbook. SME. Hassani, F. P., & Scoble, M. J. (1981). Properties of weak rocks, with special reference to the shear strength of their discontinuities, as encountered in British Surface Coal Mining. In ISRM Int. Symp., International Society for Rock Mechanics. Hayes, C., Penner, R., Ergan, H., Lu, L., Tu, N., Jones, P., … Wilkins, D. (2000). CoRaven: model-based design of a cognitive tool for real-time intelligence monitoring and analysis. In 2000 IEEE Int. Conf. on Systems, Man, and Cybernetics (Vol. 2, pp. 1117–1122 vol.2). http://doi.org/10.1109/ICSMC.2000.886001 Heim, A. (1932). Bergsturz und menschenleben. (Vol. 77). Zürich: Komm. Beer & Co. Helton, J. C. (1994). Treatment of uncertainty in performance assessments for complex systems. Risk Analysis, 14(4), 483–511. http://doi.org/10.1111/j.1539-6924.1994.tb00266.x Hencher, S. R., Liao, Q. H., & Monaghan, B. G. (1996). Modelling slope behaviour for open-pits. Transactions of the Institution of Mining and Metallurgy Section A-Mining Industry, 105, A37–A47. Highland Valley Copper. (2013). Pit wall stability and management. Hoek, E. (1983). Strength of jointed rock masses. Géotechnique, 33(3), 187–223. http://doi.org/10.1680/geot.1983.33.3.187 Hoek, E. (2002). Blasting damage factor D. Technical note for RocNews, Winter issue. Hoek, E., & Bray, J. D. (1981). Rock slope engineering (3rd edition). London: CRC Press. Hoek, E., & Brown, E. T. (1997). Practical estimates of rock mass strength. International Journal of Rock Mechanics and Mining Sciences, 34(8), 1165–1186. http://doi.org/10.1016/S1365-1609(97)80069-X Hoek, E., & Brown, T. (1980). Underground excavations in rock. London: CRC Press. Hoek, E., Carranza-Torres, C., & Corkum, B. (2002). Hoek-Brown failure criterion-2002 edition. In Proc. of NARMS-TAC (Vol. 1, pp. 267–273). Toronto, Canada. Hoek, E., & Diederichs, M. S. (2006). Empirical estimation of rock mass modulus. International Journal of Rock Mechanics and Mining Sciences, 43(2), 203–215. http://doi.org/10.1016/j.ijrmms.2005.06.005 163 Hoek, E., Kaiser, P. K., & Bawden, W. F. (1995). Support of underground excavations in hard rock (1st edition). New York: CRC Press. Hoek, E., Marinos, P., & Benissi, M. (1998). Applicability of the geological strength index (GSI) classification for very weak and sheared rock masses. The case of the Athens schist formation. Bulletin of Engineering Geology and the Environment, 57(2), 151–160. http://doi.org/10.1007/s100640050031 Hoek, E., & Pentz, D. L. (1968). The stability of open pit mines: a review of the problems and of methods of solution. London: Interdepartmental Rock Mechanics Project, Imperial College of Science and Technology. Hofer, E. (1996). When to separate uncertainties and when not to separate. Reliability Engineering & System Safety, 54(2–3), 113–118. http://doi.org/10.1016/S0951-8320(96)00068-3 Hoffman, F. O., & Hammonds, J. S. (1994). Propagation of uncertainty in risk assessments: the need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability. Risk Analysis, 14(5), 707–712. Hsü, K. J. (1975). Catastrophic debris streams (Sturzstroms) generated by rockfalls. Geological Society of America Bulletin, 86(1), 129–140. http://doi.org/10.1130/0016-7606(1975)86<129:CDSSGB>2.0.CO;2 Hudson, J. A., & Harrison, J. P. (2005). Engineering rock mechanics: an introduction to the principles. Tarrytown, N.Y: Pergamon. Hungr, O. (1995). A model for the runout analysis of rapid flow slides, debris flows, and avalanches. Canadian Geotechnical Journal, 32(4), 610–623. http://doi.org/10.1139/t95-063 Hungr, O., Corominas, J., & Eberhardt, E. (2005). Estimating landslide motion mechanisms, travel distance and velocity. In O. Hungr, R. Fell, R. Couture, & E. Eberthardt (Eds.), Landslide Risk Management (pp. 99–128). London: Taylor and Francis, London. Hungr, O., & Evans, S. G. (2004). Entrainment of debris in rock avalanches: an analysis of a long run-out mechanism. Geological Society of America Bulletin, 116(9-10), 1240–1252. http://doi.org/10.1130/B25362.1 164 Hungr, O., Evans, S. G., Bovis, M. J., & Hutchinson, J. N. (2001). A review of the classification of landslides of the flow type. Environmental & Engineering Geoscience, 7(3), 221–238. http://doi.org/10.2113/gseegeosci.7.3.221 Hunter, G., & Fell, R. (2003). Travel distance angle for “rapid” landslides in constructed and natural soil slopes. Canadian Geotechnical Journal, 40(6), 1123–1141. http://doi.org/10.1139/t03-061 Ian. (2007). All sizes | Pit wall failure | Flickr - Photo Sharing! Retrieved August 19, 2015, from https://www.flickr.com/photos/91997797@N00/593927582/sizes/o/in/photostream/ Imperial Metals. (2007). Imperial reports pit wall failure at Huckleberry mine. Retrieved September 12, 2013, from http://www.imperialmetals.com/s/News_2007.asp?ReportID=561621 Ismail, M. A., Sadiq, R., Soleymani, H. R., & Tesfamariam, S. (2011). Developing a road performance index using a Bayesian belief network model. Journal of the Franklin Institute, 348(9), 2539–2555. http://doi.org/10.1016/j.jfranklin.2011.07.015 ISRM. (1981). Rock characterization testing & monitoring : ISRM suggested methods. (E. T. Brown, Ed.). Pergamon, Oxford. Jansen, R., Yu, H., Greenbaum, D., Kluger, Y., Krogan, N. J., Chung, S., … Gerstein, M. (2003). A Bayesian networks approach for predicting protein-protein interactions from genomic data. Science, 302(5644), 449–453. http://doi.org/10.1126/science.1087361 Jarosz, A., & Wanke, D. (2003). Use of InSAR for monitoring of mining deformations. In FRINGE 2003 Workshop (pp. 1–5). Frascati, Italy. Jaboyedoff, M., Derron, M. H., Pedrazzini, A., Blikra, L., Crosta, G. B., Froese, C., ... & Stead, D. (2012). Fast assessment of susceptibility of massive rock instabilities. Landslides and Engineered Slopes: Protecting Society through Improved Understanding. Taylor and Francis Group, London, 459-465.  Jensen, F., & Nielsen, T. D. (2007). Bayesian networks and decision graphs (2nd edition). New York: Springer Science. Jensen, F. V. (1996). Introduction to Bayesian networks (1st edition). Secaucus, NJ, USA: Springer-Verlag New York, Inc. Jimeno, E. L., Jimino, C. L., & Carcedo, A. (1995). Drilling and blasting of rocks (1st edition). Rotterdam ; Brookfield, VT: CRC Press. 165 Jing, L. (2003). A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering. International Journal of Rock Mechanics and Mining Sciences, 40(3), 283–353. http://doi.org/10.1016/S1365-1609(03)00013-3 Jones, P. M., Hayes, C. C., Wilkins, C., Bargar, R., Sniezek, J., Asaro, P., … Schlabach, M. J. (1998). CoRAVEN: Modeling and design of a multimedia intelligent infrastructure for collaborative intelligence analysis. In 1998 IEEE Int. Conf. on Systems, Man, and Cybernetics, 1998 (Vol. 1, pp. 914–919 vol.1). http://doi.org/10.1109/ICSMC.1998.725532 Kane, M., Sahin, F., & Savakis, A. (2003). A two phase approach to Bayesian network model selection and comparison between the MDL and DGM scoring heuristics. In IEEE Int. Conf. on Systems, Man and Cybernetics, 2003 (Vol. 5, pp. 4601–4606 vol.5). http://doi.org/10.1109/ICSMC.2003.1245709 Karlsson, B., Jarrhed, J.-O., & Wide, P. (2002). A fusion toolbox for sensor data fusion in industrial recycling. IEEE Trans. on Instrumentation and Measurement, 51(1), 144–149. http://doi.org/10.1109/19.989918 Kliche, C. A. (1999). Rock slope stability. SME. Koop, G. (2003). Bayesian econometrics (1st edition). Chichester: Wiley-Interscience. Korb, K. B., & Nicholson, A. E. (2010). Bayesian artificial intelligence (2nd edition). Boca Raton, FL: CRC Press. Langseth, H., & Portinale, L. (2007). Bayesian networks in reliability. Reliability Engineering & System Safety, 92(1), 92–108. http://doi.org/10.1016/j.ress.2005.11.037 Laskey, K. B. (1995). Sensitivity analysis for probability assessments in Bayesian networks. IEEE Transactions on Systems, Man and Cybernetics, 25(6), 901–909. http://doi.org/10.1109/21.384252 Lee, B. H. (2001). Using Bayes belief networks in industrial FMEA modeling and analysis. In Reliability and Maintainability Symp., 2001. Proceedings. Annual (pp. 7–15). IEEE http://doi.org/10.1109/RAMS.2001.902434 Lee, S.-G., & Hencher, S. R. (2009). The repeated failure of a cut-slope despite continuous reassessment and remedial works. Engineering Geology, 107(1–2), 16–41. http://doi.org/10.1016/j.enggeo.2009.03.011 166 Li, T. (1983). A mathematical model for predicting the extent of a major rockfall. Zeitschrift Für Geomorphologie, 24(4), 473–482. Liu, E., & Zhang, D. (2002). Diagnosis of component failures in the space shuttle main engines using Bayesian belief networks: a feasibility study. In 14th IEEE International Conference on Tools with Artificial Intelligence, 2002. (ICTAI 2002). (pp. 181–188). http://doi.org/10.1109/TAI.2002.1180803 Liu, K. F.-R., Lu, C.-F., Chen, C.-W., & Shen, Y.-S. (2012). Applying Bayesian belief networks to health risk assessment. Stochastic Environmental Research and Risk Assessment, 26(3), 451–465. http://doi.org/10.1007/s00477-011-0470-z Liu, W. S., Li, S. B., & Tang, R. (2013). Slope stability evaluation in open pit based on Bayesian networks. In G. Yang (Ed.), Proc. 2012 Int. Conf. on Communication, Electronics and Automation Engineering (pp. 1227–1231). Springer Berlin Heidelberg. Lucas, P. J. F. (2004). Bayesian analysis, pattern analysis and data mining in health care. P. 403. MABC, & Worksafe BC. (2015). A supervisor’s guide to managing workplace injuries. Retrieved June 20, 2015, from http://www.mining.bc.ca/sites/default/files/documents/our-focus/1-a-pdf_backgrounder_-_supervisors_guide_to_managing_workplace_injuries.pdf Maglogiannis, I., Zafiropoulos, E., Platis, A., & Lambrinoudakis, C. (2006). Risk analysis of a patient monitoring system using Bayesian network modeling. Journal of Biomedical Informatics, 39(6), 637–647. http://doi.org/10.1016/j.jbi.2005.10.003 Marcot, B. G., Holthausen, R. S., Raphael, M. G., Rowland, M. M., & Wisdom, M. J. (2001). Using Bayesian belief networks to evaluate fish and wildlife population viability under land management alternatives from an environmental impact statement. Forest Ecology and Management, 153(1–3), 29–42. http://doi.org/10.1016/S0378-1127(01)00452-2 Martin, D. C. (1990). Deformation of open pit mine slopes by deep seated toppling. International Journal of Surface Mining, Reclamation and Environment, 4(4), 153–164. http://doi.org/10.1080/09208119008944183 Martin, D. C. (1993). Time dependent deformation of rock slopes. (Ph.D.). University of London. Mayne, P. W., & Uzielli, M. (2013). Bayesian characterization of transformation uncertainty for strength and stiffness of sands. In Foundation Engineering in the Face of Uncertainty 167 (pp. 368–384). American Society of Civil Engineers. Retrieved from http://ascelibrary.org/doi/abs/10.1061/9780784412763.029 McAndless, P. (2006). Surficial geology of the Mount Polley property: summary of 2005 exploration work (Technical report). Vancouver, Canada. McMillan, W. J., & Panteleyev, A. G. (1988). Porphyry copper deposits. geoscience Canada, (Reprint Series, 3), 45–58. Mercer, K. G. (2006). Investigation into the time dependent deformation behaviour and failure mechanisms of unsupported rock slopes based on the interpretation of observed deformation behaviour (PhD Thesis). University of Witwatersrand, Johannesburg. Microsoft Research. (2014). Microsoft Bayesian network editor. Retrieved September 29, 2014, from http://research.microsoft.com/en-us/um/redmond/groups/adapt/msbnx/ Miller, S. M., Girard, J. M., & McHugh, E. L. (2000). Computer modeling of catch benches to mitigate rockfall hazards in open pit mines. In Proc. 4th North American Rock Mechanics Symp. (pp. 539– 545). Rotterdam: Balkema. Miranda, T., Gomes Correia, A., & Ribeiro e Sousa, L. (2009). Bayesian methodology for updating geomechanical parameters and uncertainty quantification. International Journal of Rock Mechanics and Mining Sciences, 46(7), 1144–1153. http://doi.org/10.1016/j.ijrmms.2009.03.008 Morgan, G.C., Rawlings, G.E., and Sobkowicz, J.C. (1992). Evaluating total risk to communities from large debris flows. In Geotechnique and Natural Hazards. Bi Tech Publishers, Vancouver, B.C., pp. 225–236 Mufundirwa, A., Fujii, Y., & Kodama, J. (2010). A new practical method for prediction of geomechanical failure-time. International Journal of Rock Mechanics and Mining Sciences, 47(7), 1079–1090. http://doi.org/10.1016/j.ijrmms.2010.07.001 Neapolitan, R. E. (1990). Probabilistic reasoning in expert systems: theory and algorithms (1st edition). Wiley-Interscience. Neapolitan, R. E. (2003). Learning Bayesian networks (1st edition). Upper Saddle River, NJ: Prentice Hall. Newcomen, H. W., & Martin, D. C. (1988). Geotechnical assessment of the southeast wall slope failure at Highmont mine, British Columbia. CIM Bulletin, 81(917), 71–76. http://doi.org/10.1016/0148-9062(89)92321-8 168 Newcomen, H. W., Shwydiuk, L., & Maggs, C. S. (2003). Managing pit slope displacements: Highland Valley Copper’s Lornex pit southwest wall. CIM Bulletin, 96(1071), 43–48. Nicoletti, P. G., & Sorriso-Valvo, M. (1991). Geomorphic controls of the shape and mobility of rock avalanches. Geological Society of America Bulletin, 103(10), 1365–1373. http://doi.org/10.1130/0016-7606(1991)103<1365:GCOTSA>2.3.CO;2 Norsys Software Corp. (2014). Netica application. Retrieved June 24, 2014, from http://www.norsys.com/netica.html Nunoo, S., Tannant, D. D., & Newcomen, H. W. (2015). Slope monitoring practices at open pit porphyry mines in British Columbia, Canada. International Journal of Mining, Reclamation and Environment, 1–12. http://doi.org/10.1080/17480930.2015.1038865 Nunoo, S., Tannant, D. D., & Newcomen, W. (2014). Current practices for slope monitoring at British Columbia’s open pit porphyry mines. In CIM 2014 Convention. Vancouver, Canada: CIM. Oberkampf, W. L., DeLand, S. M., Rutherford, B. M., Diegert, K. V., & Alvin, K. F. (2002). Error and uncertainty in modeling and simulation. Reliability Engineering & System Safety, 75(3), 333–357. http://doi.org/10.1016/S0951-8320(01)00120-X O’Bryan, P., Deligeorgoes, E. A., Thompson, A. G., & Hucker, P. (2011). Design, implementation and monitoring of novel rehabilitation measures in an open pit gold mine. In Slope Stability 2011 (p. 13). Vancouver, Canada. Osasan, K., & Afeni, T. (2010). Review of surface mine slope monitoring techniques. Journal of Mining Science, 46(2), 177–186. http://doi.org/10.1007/s10913-010-0023-8 Pankow, K. L., Moore, J. R., Hale, J. M., Koper, K. D., Kubacki, T., Whidden, K. M., & McCarter, M. K. (2014). Massive landslide at Utah copper mine generates wealth of geophysical data. GSA Today, 24(1), 4–9. http://doi.org/10.1130/GSATG191A.1 Parry, G. W. (1996). The characterization of uncertainty in probabilistic risk assessments of complex systems. Reliability Engineering & System Safety, 54(2–3), 119–126. http://doi.org/10.1016/S0951-8320(96)00069-5 Pearl, J. (1988). Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann. 169 Peng, S., & Zhang, J. (2007). In-situ stress and pore pressure. In Engineering Geology for Underground Rocks (pp. 45–74). Springer Berlin Heidelberg. Retrieved from http://link.springer.com/chapter/10.1007/978-3-540-73295-2_3 Petley, D. N. (2013). Analysing the Bingham Canyon mine landslide part 2: the landslide track - The Landslide Blog - AGU Blogosphere. Retrieved June 24, 2013, from http://blogs.agu.org/landslideblog/2013/05/06/analysing-the-bingham-canyon-mine-landslide-part-2-the-landslide-track/ Pishbin, M., & Fathianpour, N. (2014). Assessing the performance of statistical-structural and geostatistical methods in estimating the 3D distribution of the uniaxial compressive strength parameter in the sarcheshmeh porphyry copper deposit. International Journal of Mining & Geo-Engineering, 48(1), 11–30. Pisters, D. (2005). Development of generic guidelines for low wall instability management utilising the slope stability radar – Case studies from the Hunter valley and Bowen basin. In Bowen Basin Symp. 2005 – The Future for coal – fuel for thought (pp. 245 – 252). Yeppoon, QLD, Australia. Pollard, D. D., & Fletcher, R. C. (2005). Fundamentals of structural geology. Cambridge University Press. Price, D. G., & Freitas, M. de. (2008). Engineering geology: principles and practice (1st edition). New York, NY: Springer Pulliam, H. R., & Dunning, J. B. (1995). Spatially explicit population models. Ecological Applications, 5(1), 2. http://doi.org/10.2307/1942044 Ramoni, M., Sebastiani, P., & Cohen, P. (2001). Bayesian clustering by dynamics. Computer Science Department Faculty Publication Series. Retrieved from http://scholarworks.umass.edu/cs_faculty_pubs/158 Read, J., & Stacey, P. (Eds.). (2009). Guidelines for open pit slope design (1st edition). Collingwood, Vic.; Leiden, Netherlands: CRC Press. Read, S. A. L., Richards, L. R., & Perrin, N. D. (1999). Applicability of the Hoek-Brown failure criterion to New Zealand greywacke rocks (Vol. 2, pp. 655–660). In 9th ISRM Congress, Paris, France: International Society for Rock Mechanics. 170 Robinson, R. (1977). Counting unlabeled acyclic digraphs. In C. Little (Ed.), Combinatorial Mathematics V (Vol. 622, pp. 28–43). Springer Berlin Heidelberg. Retrieved from http://dx.doi.org/10.1007/bfb0069178 Rocscience. (2014). Rocscience software products: DIPS V.6, SWEDGE V.6. Toronto, Canada. Rose, N. D., & Hungr, O. (2007). Forecasting potential rock slope failure in open pit mines using the inverse-velocity method. International Journal of Rock Mechanics and Mining Sciences, 44(2), 308–320. http://doi.org/10.1016/j.ijrmms.2006.07.014 Russell, S., & Norvig, P. (2009). Artificial intelligence: a modern approach (3rd edition). Upper Saddle River: Prentice Hall. Rustan, A., Cunningham, C., Fourney, W., Simha, K., & Spathis, A. (Eds.). (2010). Mining and rock construction technology desk reference: rock mechanics, drilling & blasting. CRC Press. Retrieved from http://www.crcnetbase.com/isbn/9780203838198 Saltelli, A., Chan, K., & Scott, E. M. (2000). Sensitivity analysis (1st edition). John Wiley & Sons. Scheidegger, A. E. (1973). On the prediction of the reach and velocity of catastrophic landslides. Rock Mechanics, 5(4), 231–236. http://doi.org/10.1007/BF01301796 Şen, Z., & Sadagah, B. H. (2002). Probabilistic horizontal stress ratios in rock. Mathematical Geology, 34(7), 845–855. http://doi.org/10.1023/A:1020928727867 Severin, J., Eberhardt, E., Ngidi, S., & Stewart, A. (2009). Importance of understanding 3-D kinematic controls in the review of displacement monitoring of deep open pits above underground mass mining operations. Proc. 3rd CAN-US Rock Mechanics Symposium. Toronto, ON. Shachter, R. D., & Kenley, C. R. (1989). Gaussian influence diagrams. Management Science, 35(5), 527–550. http://doi.org/10.1287/mnsc.35.5.527 Shachter, R. D., & Peot, M. A. (2013). Decision making using probabilistic inference methods. arXiv:1303.5428 [cs]. Retrieved from http://arxiv.org/abs/1303.5428 Sinclair, W. D. (2007). Porphyry deposits. In mineral deposits of Canada: A synthesis of major deposit-types, district metallogeny, the evolution of geological provinces, and exploration methods (Vol. 5, pp. 223–243). Geological Association of Canada, Mineral Deposits Division. 171 Singh, B., & Goel, R. K. (1999). Rock mass classification: a practical approach in civil engineering. Elsevier. Sjöberg, J. (1996). Large scale slope stability in open pit mining : a review (Technical report No. 1996:10T) (p. 215). Luleå: Luleå University of Technology. Sjöberg, J. (1999). Analysis of large scale rock slopes (PhD). Luleå University of Technology, Sweden. Sjöberg, J. (2001). Failure mechanisms for high slopes in hard rock. In W. A. Hustrulid, M. K. McCarter, & D. J. A. Van Zyl (Eds.), Slope Stability in Surface Mining (pp. 71–80). Littleton: Society for Mining, Metallurgy, and Exploration, Inc. Sobol, I. M. (2001). Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation, 55(1–3), 271–280. http://doi.org/10.1016/S0378-4754(00)00270-6 Špačková, O., & Straub, D. (2013). Dynamic Bayesian network for probabilistic modeling of tunnel excavation processes. Computer-Aided Civil and Infrastructure Engineering, 28(1), 1–21. http://doi.org/10.1111/j.1467-8667.2012.00759.x Stacey, T. . (2006). Considerations of failure mechanisms associated with rock slope instability and consequences for stability analysis. The Journal of the South African Institute of Mining and Metallurgy, 106(7), 485–494. Stacey, T. R. (1970). The stresses surrounding open pit mine slopes. In P. W. J. van Rensburg (Ed.), Theoretical Background to Planning Open Pit Mines (pp. 199–207). Johannesburg: South African Institute of Mining and Metallurgy. Stacey, T. R., Xianbin, Y., Armstrong, R., & Keyter, G. J. (2003). New slope stability considerations for deep open pit mines. Journal of the South African Institute of Mining and Metallurgy, 103(6), 373 – 389. Stead, D., Eberhardt, E., Coggan, J., & Benko, B. (2001). Advanced numerical techniques in rock slope stability analysis – applications and limitations. In LANDSLIDES – Causes, Impacts and Countermeasures (pp. 615–624). Davos, Switzerland Steffen, O. K. H., Contreras, L. F., Terbrugge, P. J., & Venter, J. (2008). A risk evaluation approach for pit slope design. In Proc. 42nd US Rock Mechanics Symp. and 2nd US–Canada Rock Mechanics Symp. San Francisco, CA, USA: ARMA. 172 Steffen, O. K. H., Terbrugge, P. J., Wesseloo, J., & Venter, J. (2006). A risk evaluation approach for pit slope design. In Proc. Int. Symp. on “Stability of rock slopes in open pit mining and civil engineering” (pp. 81–96). Cape Town, South Africa: SAIMM. Stewart, D. H., & Reid, G. J. (1988). Afton- a geotechnical pot-pourri. CIM Bulletin, 81(917), 77–83. Stiber, N. A., Pantazidou, M., & Small, M. J. (1999). Expert system methodology for evaluating reductive dechlorination at TCE sites. Environmental Science & Technology, 33(17), 3012–3020. http://doi.org/10.1021/es981216s Stiber, N. A., Small, M. J., & Pantazidou, M. (2004). Site-specific updating and aggregation of Bayesian belief network models for multiple experts. Risk Analysis, 24(6), 1529–1538. http://doi.org/10.1111/j.0272-4332.2004.00547.x Stow, C. A., Roessler, C., Borsuk, M. E., Bowen, J. D., & Reckhow, K. H. (2003). Comparison of estuarine water quality models for total maximum daily load development in Neuse river estuary. Journal of Water Resources Planning and Management, 129(4), 307–314. http://doi.org/10.1061/(ASCE)0733-9496(2003)129:4(307) Sullivan, T. D. (1993). Understanding pit slope movements. In Geotechnical Instrumentation and Monitoring in Open Pit and Underground (pp. 435–445). Kalgoorlie, Australia. Sullivan, T. D. (2007). Hydromechanical coupling and pit slope movements. In Proc. of 2007 Int. Symp. on Rock Slope Stability in Open Pit Mining and Civil Engineering (pp. 3–43). Perth, Australia. Szwedzicki, T. (2003). Rock mass behaviour prior to failure. International Journal of Rock Mechanics and Mining Sciences, 40(4), 573–584. http://doi.org/10.1016/S1365-1609(03)00023-6 Tang, W. H., & Cheung, R. W. M. (2000). Bayesian calibration of slope failure probability. In Slope Stability 2000 (pp. 72–85). American Society of Civil Engineers. Retrieved from http://ascelibrary.org/doi/abs/10.1061/40512%28289%296 Tesfamariam, S., & Martín-Pérez, B. (2008). Bayesian belief network to assess carbonation-induced corrosion in reinforced concrete. Journal of Materials in Civil Engineering, 20(11), 707–717. http://doi.org/10.1061/(ASCE)0899-1561(2008)20:11(707) Therrien, S. S. (2002). A Bayesian model to incorporate human factors in Commanders’ decision making. Naval Postgraduate School, Monterey, California. 173 Valliappan, S., & Evans, R. S. (1980). Finite element analysis of a slope at Illawarra escarpment. In 3rd Australia-New Zealand Conf. on Geomechanics (Vol. 2, pp. 241–246). Wellington: Publ Wellington: New Zealand institution of Engineers. http://doi.org/10.1016/0148-9062(82)91571-6 Voight, B. (1988). A method for prediction of volcanic eruptions. Nature, 332(6160), 125–130. http://doi.org/10.1038/332125a0 Voight, B. (1989). A relation to describe rate-dependent material failure. Science, 243(4888), 200–203. Wakefield, R., Damrianant, J. R., & O’Brien, J. B. (1998). A petri net based system for the modeling and computer simulation of automated construction operations. ISARC Proc., 406–414. Wakefield, R., & Sears, G. (1997). Petri nets for simulation and modeling of construction systems. Journal of Construction Engineering and Management, 123(2), 105–112. http://doi.org/10.1061/(ASCE)0733-9364(1997)123:2(105) Wang, Y., Huang, K., & Cao, Z. (2013). Probabilistic identification of underground soil stratification using cone penetration tests. Canadian Geotechnical Journal, 50(7), 766–776. http://doi.org/10.1139/cgj-2013-0004 Warnock, G. (2013). MEMO / CIM open pit monitoring workshop: MEM Perspective. Presented at the MEMO / CIM Open Pit Slope Management Workshop, Kamloops, BC. Weber, P., Medina-Oliva, G., Simon, C., & Iung, B. (2012). Overview on Bayesian networks applications for dependability, risk analysis and maintenance areas. Engineering Applications of Artificial Intelligence, 25(4), 671–682. http://doi.org/10.1016/j.engappai.2010.06.002 West, G., Fookes, P. G., Lay, J., Sims, I., Smith, M. R., & Collis, L. (2001). Aggregates: sand, gravel and crushed rock aggregates for construction purposes (3rd edition). London: Geological Society of London. Wheel, M. A. (1996). A geometrically versatile finite volume formulation for plane elastostatic stress analysis. The Journal of Strain Analysis for Engineering Design, 31(2), 111–116. http://doi.org/10.1243/03093247V312111 174 Wieczorek, G. F., & Snyder, J. B. (2009). Monitoring slope movements. In R. Young & L. Norby (Eds.), Geological monitoring (pp. 245–271). Boulder, Colorado: The Geological Society of America. Wojdak, P. (2008). Northwest region (pp. 1–30). Victoria, BC, Canada: BC Ministry of Energy and Mines. Retrieved September 26, 2014, from http://www.empr.gov.bc.ca/Mining/Geoscience/PublicationsCatalogue/ExplorationinBC/Documents/2007_NW.pdf Wyllie, D. C. (1999). Foundations on rock: engineering practice (2nd edition). London ; New York: CRC Press. Wyllie, D. C., & Mah, C. W. (2004). Rock slope engineering: civil and mining. New York, NY: Spon Press. Yang, D. Y., Mercer, R. A., Brouwer, K. J., & Tomlinson, C. (2011). Managing pit slope stability at the Kemess south mine - changes over time. In Slope Stability 2011 (p. 12). Vancouver, Canada. Yang, S., Lu, M., Liu, B., & Hao, B. (2009). A fault diagnosis model for embedded software based on FMEA/FTA and bayesian network. In 8th Int. Conf. on Reliability, Maintainability and Safety, 2009. ICRMS 2009 (pp. 778–782). http://doi.org/10.1109/ICRMS.2009.5270082 Yasrebi, A. B., Wetherelt, A., Foster, P., Coggan, J., Afzal, P., Agterberg, F., & Kaveh Ahangaran, D. (2014). Application of a density–volume fractal model for rock characterisation of the Kahang porphyry deposit. International Journal of Rock Mechanics and Mining Sciences, 66, 188–193. http://doi.org/10.1016/j.ijrmms.2013.12.022 Yi, H., Jiang, C., Hu, H., Cai, K.-Y., & Mathur, A. P. (2011). Using Markov-Chains to model reliability and QoS for deployed service-based systems. In Computer Software and Applications Conf. Workshops (COMPSACW), 2011 IEEE 35th Annual (pp. 356–361). http://doi.org/10.1109/COMPSACW.2011.66 Zavodni, A. M. (2000). Time-dependent movements on open pit slope. In W. A. Hustrulid, M. K. McCarter, & D. J. A. Van Zyl (Eds.), Slope Stability in Surface Mining (pp. 81–87). Littleton: Society for Mining, Metallurgy, and Exploration, Inc. 175 Zavodni, Z. M., & Broadbent, C. D. (1978). Slope failure kinematics. In 19th U.S. Symp. on Rock Mechanics, May 1 - 3, 1978 , Reno, Nevada (p. 10). American Rock Mechanics Association. http://doi.org/78-0102 Zhang, L. (2005). Engineering properties of rocks. Elsevier. Zhang, Y., Chen, G., Zheng, L., Li, Y., & Zhuang, X. (2013). Effects of geometries on three-dimensional slope stability. Canadian Geotechnical Journal, 50(3), 233–249. http://doi.org/10.1139/cgj-2012-0279 Zheng, W., Zhuang, X., Tannant, D. D., Cai, Y., & Nunoo, S. (2014). Unified continuum/discontinuum modeling framework for slope stability assessment. Engineering Geology, 179, 90–101. http://doi.org/10.1016/j.enggeo.2014.06.014 176 Appendix A: Pit wall management questionnaire General mine Information 1. How many shifts per day does your operation run?  2. What is the operation’s average daily production of ore and waste, respectively? 3. Please provide a plan map of the current pit, if possible. 4. What is the range of the proposed overall pit slope angles and heights for various design sectors/areas of your pit? 5. What is the range of design bench face angles? Are they generally being achieved? 6. What is the range of design bench widths? Are they generally being achieved? 7. Does your operation have a geotechnical department or group? If not, how is geotechnical information collected and interpreted at the mine?  Pit Wall Monitoring/Movement Threshold Information 8. Which of the following techniques do you use to monitor your pit walls? Please check all that apply.  Visual observation  Wireline extensometer  Prisms and total station  Prisms and robotic total station  Ground radar  Other (Please describe) 9. From the answers you have provided in Question 8, how accurate are the monitoring tools? Please specify the estimated accuracy for each system. 177 10. What is the standard time interval between readings for the various monitoring techniques you have indicated in Question 8? 11. If monitoring indicates movement rates for “normal” slope relaxation are being exceeded, how often is monitoring subsequently conducted? 12. Are monitoring data collected analyzed and communicated to other departments in addition to pit operations? Example: 0-4 cm/day: normal expected response (Background or Watch) 4-8 cm/day: mine with caution with monitoring every 4 hours (Caution) 8-12 cm/day: mining should be controlled with monitoring every 2 hours (Alert) >12 cm/day: mining should stop as failure is imminent (Stop Mining, Evacuate) 13. How did the mine develop the threshold limits for the pit walls? 14. If you have more than one geotechnical domain within the pit, are the threshold limits for the slope monitoring different for each geotechnical domain? 15. Have the threshold limits for the pit walls changed over time? 16. What type of displacement/acceleration model, if any, is used to analyze monitoring data? 17. What action is taken when a crack is observed during a visual inspection of the pit? 18. At what displacement rate is mining stopped beneath areas of instability? 19. At what displacement rate is mining allowed to re-commence? Are restrictions placed on the mining (e.g. daylight hours only, rainfall thresholds, etc.)? 20. At what displacement rates will mining be allowed using special monitoring procedures? 21. Has mining been stopped due to false alarms? 22. If movements exceed the ‘stop mining rate’ rate, how often is monitoring subsequently carried out? 23. Which of the techniques listed in Question 8 is most relied upon before an action is taken? 178 24. Are pit wall instabilities associated with rainfall, snow melt, or production blasting? 25. Is the onset of instability typically noticed at the toe or the crest of a slope before a larger instability zone develops? 26. What was the maximum movement rate measured when instabilities occurred? 27. Are there any documentation of slope performance leading up to instabilities and if so, can you provide us with this information? 28. If details on past instabilities have been published, please provide details regarding these publications (or send copies). 29. Are photos of instabilities available and, if so, can you provide them? 30. Do you have monitoring data (displacement or strain) that you would be able to share to further this research? Pit Wall Stabilization Strategies 31. What techniques have you used to stabilize pit wall instability at the mine (e.g. step-outs, push-backs, dewatering, etc.)? 32. Are regular slope depressurization/dewatering efforts being carried out? If yes, what are they and are they successful? 33. Is any controlled blasting being carried out? 34. Are any special measures used to manage slope instability, e.g. free-digging of weak rock, rock support, etc.? 35. Is the open pit in its final phase of mining or are pushbacks currently planned? If the latter, has this affected your slope management strategies? Geological and Geotechnical Information 36. Does the rock mass quality change as the pit goes deeper? 37. Is there evidence that as mining progresses the rock mass conditions deteriorate (i.e. time dependency) and affect the stability of the pit walls? 179 38. Is the quality of the rock mass distinctly affected by major structures? 39. What effect, if any, does the ore body have on the stability of the pit walls (i.e. is alteration from the ore body a factor in the stability)? 40. Briefly describe the dominant geological features (i.e. major faults, foliation, etc.) in the open pit. What role do these features play in the distribution of the ore? 41. What are the orientations (i.e. dip and dip direction) of these geological features? 42. What is the joint stiffness (normal and shear) respectively? 43. What is the average spacing of the major structures? 44. How wide (i.e. true thickness) are the major structures within the pit walls? 45. Have the shear strength properties been determined for the major structures and if so, what are they? How were they determined? 46. How many geotechnical domains or design sectors have been defined in the pit(s)? 47. How were the domain boundaries defined? 48. Were in-situ stresses estimated prior to mining? If so, what were they? 49. Is there any indication that horizontal stress is playing a role in the stability of the pit? The following tables summarize data associated with past pit wall instabilities (failures). In these tables, please ensure that all data provided are consistent. Failure name or identifier for each event should have the same details filled out in the respective tables to help analyze the data.180 Table A-1. Location, geometry, size and impact on operations Name or Identifier Date Size (tonnes) Failure Mechanism Impact on Operations Pit Name Pit Wall Overall Height (m) Overall Angle (°)           Table A-2. Movement rate thresholds and failure size  Movement Rate Thresholds* Failure Size Name or Identifier Background (mm/day) Watch (mm/day) Caution (mm/day) Alert (mm/day) Stop Mining or Max. Measured (mm/day) Bench Interramp Overall slope          * These are sample descriptors for movement rate thresholds; use your own, if they have been developed specifically for your mine  Table A-3. Geomechanical information Name or Identifier Host Rock Primary Rock Type in Failure Mass Slope Angle1 (°) Slope Height1 (m) Rock Mass Quality2 (RMR) GSI  mi3 UCS3 (MPa) Estimated Rock Mass Cohesion4 (kPa) Estimated Rock Mass Friction Angle4 (°)            1. Slope angle and height at time of failure 2. RMR = Rock Mass Rating. If this information is available, please specify version (e.g. 1976, 1989, etc.) 3. Please indicate if the values of mi and UCS are estimated or are from laboratory testing data Filled out by the mine Filled out by the mine Filled out by the mine 181 4. If available from consulting reports. 182 Appendix B: Conditional probability table  Table A-4. Conditional probability table used to determine RMR in the BBN model Nodes with states Nodes with Bieniawski rating assigned to states RMR RMR UCS RQD Spa_dis Dis_cond Grod_water UCS RQD Spa_dis Dis_cond G_water R0 Very poor Very close Poor Dry 0 3 5 0 10 18 Very poor rock R0 Very poor Very close Poor Moist 0 3 5 0 7 15 Very poor rock R0 Very poor Very close Poor Saturated 0 3 5 0 0 8 Very poor rock R0 Very poor Very close Fair Dry 0 3 5 6 10 24 Poor rock R0 Very poor Very close Fair Moist 0 3 5 6 7 21 Poor rock R0 Very poor Very close Fair Saturated 0 3 5 6 0 14 Very poor rock R0 Very poor Very close Moderate Dry 0 3 5 12 10 30 Poor rock R0 Very poor Very close Moderate Moist 0 3 5 12 7 27 Poor rock …… …… …… …… …… …… …… …… …… …… …… …… …… …… …… …… …… …… …… …… …… …… …… …… 183 Nodes with states Nodes with Bieniawski rating assigned to states RMR RMR UCS RQD Spa_dis Dis_cond Grod_water UCS RQD Spa_dis Dis_cond G_water R1 Excellent Very close Poor Dry 1 20 5 0 10 36 Poor rock R1 Excellent Very close Poor Moist 1 20 5 0 7 33 Poor rock R1 Excellent Very close Poor Saturated 1 20 5 0 0 26 Poor rock R1 Excellent Very close Fair Dry 1 20 5 6 10 42 Fair rock R1 Excellent Very close Fair Moist 1 20 5 6 7 39 Poor rock R1 Excellent Very close Fair Saturated 1 20 5 6 0 32 Poor rock R1 Excellent Very close Moderate Dry 1 20 5 12 10 48 Fair rock R1 Excellent Very close Moderate Moist 1 20 5 12 7 45 Fair rock R1 Excellent Very close Moderate Saturated 1 20 5 12 0 38 Poor rock R1 Excellent Very close Good Dry 1 20 5 20 10 56 Fair rock …… …… …… …… …… … … …… …… …… …… …… …… …… …… …… …… … … …… …… …… …… …… 184 Nodes with states Nodes with Bieniawski rating assigned to states RMR RMR UCS RQD Spa_dis Dis_cond Grod_water UCS RQD Spa_dis Dis_cond G_water Excellent R5 Very good Close Saturated 20 15 25 10 0 70 Good rock Excellent R5 Very good Moderate Dry 20 15 25 20 10 90 Very good rock Excellent R5 Very good Moderate Moist 20 15 25 20 7 87 Very good rock Excellent R5 Very good Moderate Saturated 20 15 25 20 0 80 Good rock Excellent R5 Very good Wide Dry 20 15 25 25 10 95 Very good rock Excellent R5 Very good Wide Moist 20 15 25 25 7 92 Very good rock Excellent R5 Very good Wide Saturated 20 15 25 25 0 85 Very good rock Excellent R5 Very good Very wide Dry 20 15 25 30 10 100 Very good rock Excellent R5 Very good Very wide Moist 20 15 25 30 7 97 Very good rock Excellent R5 Very good Very wide Saturated 20 15 25 30 0 90 Very good rock 185 Appendix C: Mining conditions at open pit mines in BC C.1 Copper Mountain mine The ore body is largely located along the contact between the Nicola Group volcanics and the gabbro diorite intrusions of the Copper Mountain Stock. The gabbro-diorite intrusion lies to the west of the north-northwest/south-southeast trending, steeply dipping contact (Figure B-1). Except for the high-mineralized concentrations along the contact, the gabbro-diorite is usually barren of copper mineralization. The volcanic and gabbro-diorite intrusive rocks are and massive. The intrusive rocks are highly fractured.  Figure B-1. Geologic map of Copper Mountain showing pits and major faults (modified from map obtained from Copper Mountain 2013) 186 Major faults found in Pit 1 are the NW/SE trending Main fault, the Day fault, and the NNE/SSW trending faults (Pratico, Tremblay and Bognar). The Main fault forms the contact is between the volcanics and intrusive rocks. The major fault found in Pit 2 is the steeply dipping and NNE/SE trending Tremblay fault. The major faults found in Pit 3 are the steeply dipping NW/SE trending Main fault, the steeply dipping NNE/SSW trending Tremblay fault, and the steeply dipping ENE/WSW trending mine Break fault (Figure B-1). The mine operates two shifts per day. The mine has two active pits named Pit 2 and Pit 3 with one inactive pit (Pit 1), which will eventually become active as mining progress. As mining progresses, the three pits planned to be connected to form one larger pit. The geotechnical domain for Pit 2 are volcanic and felsite dyke domains. Pit 3 contains volcanics intrusive and felsite dykes. The rock mass quality is found to improve with depth for Pit 2. However, in Pit 3 the rock mass quality in some areas is believed to be low due to previous underground mining operations. Where major faults and dykes occur, evidence of alteration, weathering, and shearing can be seen which results in a strength reduction of the rock mass. The mine uses controlled blasting to ensure no production holes are shot within five rows from the final pit wall until after a presplit blast has been fired. However, the mine is also using high powder factors in their ore production blasts to increase fragmentation as a means to increase the throughput on their mill. The high powder factor releases high energy that might cause slope instabilities even though it is good for the mill. The mine also uses horizontal drain holes to reduce the ground water pressure within the rock mass.      187 C.2 Huckleberry mine Mineralization at Huckleberry mine envelops two Late Cretaceous granodiorite intrusions, the Main Zone Stock and the East Zone Stock. The Main Zone deposit is kidney-shaped in plan, wrapping around the east side of the Main Zone Stock with an arc length of 500 m and a width of 150 m. The ore consists of the minerals chalcopyrite and molybdenite and is contained in fractures and veinlets. The ore is well defined along its southern and eastern edges but remains partly open to expansion on its northern margin. The East Zone deposit was circular in plan view prior to dismemberment by faulting, with a concentric shell of mineralization overlapping the contacts of the East Zone Stock (Christensen et al. 2011). Faulting along the 150 and 105 faults has elongated the deposit to the southeast. The operation at Huckleberry operates two shifts per day. The geotechnical domains formed in the pit are defined by major faults running through the pit, which created three to four domains. The joint conditions are generally quite good with the average spacing between the major structures of tens of metres. Mining activities in the pit do not significantly affect the rock mass condition. Alteration and shearing approximately major structures causes the rock mass strength to reduce near these structures. The bench face angle design of 65° is achieved where the structural geology is favourable. The bench width design of 8 m is also achieved to ±1 m. The mine uses presplit blasting whereby smaller charges are used in blast holes with closer spacing between them. Slope depressurization holes drilled 100 m deep with spacing of 15 m have been successful in helping to stabilise the pit walls.     188 C.3 Endako mine The ore body strikes ESE/WNW for a length of approximately 3 km. The ore body is approximately 365 m wide and extends to a depth of approximately 335 m below the ground surface. The ore body dips to the SSW at an inclination of approximately 45° at the east end of the pit to 55° at the west end. The Endako deposit contains a number of major faults and dykes that control both ore distribution and pit slope stability (Table A-5). The West Pit Fault is exposed in both the south and north walls, near the centre of the pit. A multi-bench scale instability developed along both the north and south wall exposures of the fault. The ground adjacent to the Denak Fault is reported to be highly altered and weak, and instability has occurred in this ground in the past (Golder 2002).  Table A-5. Description of geologic structures Structure Name Description South Basalt Fault Dips south at 50° to 60° South Boundary Fault Dips north at ≈ 60° West Pit Fault Dips ≈ 45° to 50° towards 320° West Basalt fault Dips 45° towards 325°, exposed in the west wall of the pit, and in the ramp Denak fault Dips ≈ 40° to the west; located west of the West Basalt Fault  The operation at Endako operates two shifts per day. Golder (2009) used (International Society for Rock Mechanics) ISRM intact rock estimates developed by (ISRM 1981) to determine the rock mass quality. The analysis conducted by Golder (2009) showed that the unaltered rocks located above the southerly dipping mineralized zone exhibit rock hardness in the order of R4, and the corresponding estimated unconfined compressive strength (UCS) is about 50 to 100 MPa. Highly kaolinite altered envelopes adjacent to the highly mineralized veins within the ore zone exhibit a rock hardness about R1 to R2, with a corresponding UCS of 1 to 25 MPa. 189 The quality of rock mass gets better as the pit gets deeper. Usually near major structures the rock mass quality is degraded, thus reducing the rock strength (Golder 2009). Drain holes are installed to help depressurise the slopes. The mine uses presplit blasting whereby smaller diameter holes at close spacing with smaller charges of explosive are used.                  190 C.4 Mount Polley mine During the time of formation of the deposit, in the Late Triassic, marginally silica-under saturated, shoshonitic arc magmas developed from basaltic to more intermediate compositions. A relatively sodic-alkalic phase of basaltic volcanism apparently marked the transition to more felsic magmatism. Alteration of the rocks is extensive and polyphase, and includes sodic, potassic, magnetite and garnet alteration events. Some potassium feldspathization probably occurred throughout construction of the Mount Polley Complex, consistent with the general potassic geochemical signature of the arc (Figure B-2). Mineralization is generally situated in or adjacent to breccias attributed to hydrothermal and/or volcanoclastic processes (McAndless 2006). The dominant geologic features within the pit walls are also used as structural boundaries. The features are the Polley fault, which dips 70° toward 082° and East Cariboo fault, which dips 84° toward 065°. The mine operates on two shifts per day. The rock mass quality does not improve significantly with depth. However, in areas where major structures occur, the rock mass quality is distinctively degraded. The mine uses presplit and buffer wall control as forms of controlled blasting. 191  Figure B-2. Geologic map of Mount Polley deposit (modified from Jackson 2008)                        192 C.5 Highland Valley Copper The regional geology containing the Highmont, Lornex and Valley deposits is described as the Guichon Creek batholith of upper Triassic age (Figure B-3). The batholith is a composited, concentrically zoned calc-alkaline intrusion that has been emplaced and has metamorphosed the country rock of the Nicola Group. The intrusive is approximately 30 km wide and 65 km long. Gravity surveys have indicated that the intrusive is a flattened, funnel-shaped body whose root zone is found under Highland Valley Copper (Graden 2012).  Figure B-3. Pit locations and the Guichon Creek Batholith (Graden 2012) The Valley deposit is found at the intersection of the northerly striking Lornex Fault and the north-westerly to westerly striking Highland Valley Fault. The deposit is dominated by silicic and potassic alteration in its central core. This alteration zone is encircled by a halo of phyllic and argillic alteration, and this in turn has a fringing propylitic alteration halo (Figure B-4). 193  Figure B-4.  Geology of the Valley deposit (Graden 2012) The Lornex deposit occurs in the Skeena Quartz Diorite, a weakly porphyritic, medium to coarse-grained intrusive. An early quartz porphyry dyke cuts north to northwesterly into the southern end of the Lornex deposit area (Figure B-5). Fracturing controls the mineralization at the Lornex deposit (Graden 2012). The Highmont property contains several low-grade mineralized zones in Skeena quartz diorite. The Gnawed Mountain porphyry dyke, trending west-northwesterly, separates the two ore zones already actively mined. Fractures are concentrated in parallel swarms up to 60 m wide. 194  Figure B-5. Geology of the Lornex deposit (Graden 2012) Mineralization tends to be more concentrated in the swarms. The East Pit has areas of strongly altered rock associated with the fracturing. The predominant economic minerals are chalcopyrite, bornite and molybdenite occurring primarily in veins and fractures with only a small content occurring as disseminations (Graden 2012). The Water Hole fault at the eastern side of the Highmont deposit dips 60° towards 295°. Movement on the fault was largely or wholly post-ore. Fracturing controls the mineralization at the Lornex deposit. A detailed study of the mineralized fracture orientations in the open pit indicates that the following attitudes of the copper-molybdenum veins are predominant; fractures that dip 22° towards 055° are dominant in the northern zone of the deposit; fractures that dip 90° towards 058°are dominant in the south and southeast zones of the deposit; and a third orientation of fractures that dip 64° towards 147° is found throughout the deposit. The dominant faults in the Highland Valley mine are the Lornex fault, Highland Valley fault, Victor fault, and West Hole fault. The Lornex fault dips sub vertically at approximately 85° to the east trending north. The Lornex fault has 30 m to 100 m thick weak shear zone (Graden 2012). 195 The mine operates two shifts per day with an average daily production of 150,000 t/day of ore and 150,000 t/day of waste. The mine has eight design sectors in the Valley pit with 4 sectors in the upper west wall. The domains were determined based on discontinuity orientations, rock mass properties and presence of major structures. The shear strength of the Lornex fault has a friction angle of 21° and cohesion of 50 kPa. The joint stiffness of the Lornex fault zone has a normal of 0.038 GPa and shear of 0.018 GPa. The rock mass quality is distinctly affected by various faults throughout the pit. There is no large variation of rock mass quality with depth in the pit. The average spacing of the major structures is over 100 m with an average thickness of the major structures ranging from approximately 1 to 3 m. Uncontrolled blasting has caused deterioration of the rock mass quality as well as the continuous movement of Lornex fault. The higher grade ore zones are generally more fractured and more altered. Therefore, a shallower inter-ramp angle is used in these areas. The techniques used to stabilize the pit walls include: step out (wider catch benches), buttressing, modifying wall orientations, using catchment berms, dewatering and depressurization of the walls using pumping wells and horizontal drain holes, and rock mesh. The depressurization of the walls using the horizontal drain holes and deep wells has been successful. Trim and buffer blasting which is a form of controlled blasting is implemented. The trim and buffer blasting is implemented during final wall blasts with reduced spacing and powder factor. It usually has patterns of 4 rows, less than 150 holes, with the toe rows lightly charged and little to no stemming (the toe row has tighter spacing). Also free digging of weak rocks is implemented where appropriate to manage the wall stability. During drilling of the rocks, the rocks’ hardness is usually checked by the geologists.     196 C.6 Gibraltar mine The copper-molybdenum deposit is concentrated along hydrothermally altered shear zones contained in the Granite Mountain Batholith along the west slope of Granite Mountain. The other main rock types in the region are metabasalt, limestone, and argillaceous metasediments of the Mississippian to Triassic Cache Creek Group. These are intruded by the dioritic to quartz dioritic Late Triassic Granite Mountain pluton and the Cretaceous Sheridan Creek pluton. Jurassic sedimentary rocks overlap both the Cache Creek and Quesnel terranes to the north and east of the plutons. Older rocks are largely covered by Plateau Basalt of probable Miocene age, to the west. The Granite Mountain pluton has been influenced by regional metamorphism (greenschist facies) and deformation along with the surrounding Cache Creek Group. The core body of the pluton has been deformed. The ore bodies are hosted by the Granite Mountain pluton with ore mineralization almost entirely confined to the mine Phase Tonalite portion of the Granite Mountain pluton. The mine Phase Tonalite appears to form a thin outer shell around the main body of the pluton (Ash et al. 1999). The Granite Pit area, which is the active pit for the mine, is intersected by several well defined and continuous faults including the following: • Early stage, east-west striking, and moderately south dipping thrust fault(s), i.e. the Granite Lake fault zone and associated faults; faults with this strike occasionally dip to the north, and are possibly conjugate structures of the main thrust faults dipping to the south • Late stage, north/south striking and steeply dipping late stage faults, e.g. East Boundary Fault and the Rainbow Fault • Northeasterly striking faults with shallow to moderate-dips to the northwest, e.g. Fault 10 • Westerly to northwesterly striking and shallow to moderate-dipping conjugate faults. The main rock fabric appears to be parallel to the major faults (BGC Engineering 2012). The mine operates two shifts per day with an average daily production of 85,000 t/day of ore and 265,000 t/day of waste. There are four geotechnical domains that have been identified in the active pit. The domain boundaries have been defined by major fault structures. 197 The rock mass quality is distinctly affected by various faults throughout the pit. There is variation of rock mass quality with depth in the pit. The average thickness of the faults varies up to 2 m. The techniques used to stabilize the pit walls include step out, buttressing, dewatering and depressurization of the walls using deep vertical wells. The depressurization of the walls using the deep wells has been successful. Also free digging of weak rocks is implemented where appropriate to manage the wall stability. In summary for all the mines, Tables A-6 and A-7 shows the blasting techniques and bench geometry used by the BC mines.  Table A-6. Blasting techniques Mine Presplit Trim & buffer Powder factor Copper Mountain X  Waste: ~0.2 kg/t Ore: 0.35 kg/t Endako X   Huckleberry X  0.2 - 0.25 kg/t Mount Polley X  0.32 kg/t Highland Valley Copper  X 0.2 kg/t - T&B blast 0.6 kg/t - prdtn blast Gibraltar X  Waste: 0.045 - 0.45 kg/t Ore: 0.54 kg/t  198 Table A-7. Bench geometry Mine Design Bench Face Angle Actual Bench Face Angle Bench Width Copper Mountain 70°-73° 75°<BFA >60° 9.8 - 13.4 m  Endako 70°  Same as design 8 - 24 m Huckleberry 65°  65° if geology favourable 8 m ±1 m Mount Polley 65°-70° Same as design 8.5 - 15 m Highland Valley Copper Valley: 60°-65° Lornex: 56°-60° Highmont: 60°-65°  Varies from same as design to less Valley: 9 - 10 m Lornex: 9 – 13.5 m Highmont: 8 – 9 m Gibraltar 65°-72°  62° 13 m design not achieved 199 Appendix D: Open pit instability case histories D.1 Kemess South mine Kemess South mine is an open pit copper-porphyry mine located in north-central BC. The mine operated from 1996 to 2011 continuously until the end of the mine. It averagely produced 250,000 – 300,000 ounces of gold and 65 – 75 million pounds of copper yearly. The average rock mass quality was in the fair to good range (i.e. RMR = 50 – 60). During the development of the mine, a number of large-scale structural features (faults) were observed. The faults run length across the pit close to the toe of the north wall and another fault running behind the west wall of the pit. The mine experienced a failure of 1.5 million tons of material along the northwest wall at the depth of 100 m during May 2004. This was a multi bench instability and the first among several instability issues along northwest wall. The upper northwest slope kept creeping slowly after the first failure with movement rates of 10 – 150 mm/day during March 2006. This caused operation near the toe of the instability area of the northwest wall to halt. A ground probe SSR was installed and measurements were taken every 3 to 5 minutes and results analyzed instantly. Movement limits were set at 120 mm/day for the North wall and 360 mm/day for the Northwest well. The set limit was based on experience and monitoring data. When slope movement exceeded the limits, an alarm was sounded and visual inspection was conducted to verify the data the system had provided. If the visual inspection backed up the data obtained monitoring instrument, the mine broadcasted evacuation order and all personnel and equipment were taken out of the pit immediately (Yang et al. 2011). The presence of the structural features and the rock mass condition influenced the stability of the pit wall thereby causing instability along the north wall of the pit. In addition, mining activity around the location of the instability might also be a contributing factor in causing the instability at the North wall. In response to the north wall instability, the ground water level was lowered within the northwest corner of the pit with lined ditches above the slope and with horizontal drains as well. In addition to lowering the ground water level, the pit slope angle was reduced causing reduction in the movement rate within the location of the pit slope to 10 mm/day. However, over the cause of time the northwest wall continued to move past the acceptable movement limits along the 200 structural features. The mine carried out a pushback along the northwest corner of the pit and flattened the slope angle to 27° at places where the structural feature was present. The mine also implemented control blasting and horizontal drainage system was setup to depressurize the pit slope. D.2 Brenda mine The Brenda mine is a copper-molybdenum mine located in a rocky region in the southern interior of British Columbia. Several clay gouges run through the mine that influenced the stability of the pit walls. The rock exhibited some schistosity with a reasonably homogeneous quartz diorite ore body that was about 914 m in diameter and 305 m in depth. The overall slope angle of the pit was designed at 45°. The mine was using an advanced electronic distance and angle measurement (EDM) slope monitoring system since 1974 that made it possible to collect displacement data. Blasting practice and heavy precipitation affected the movement rate of the pit walls. During mid-September 1978, an instability that resulted to a failure started in the lower part of the pit, extending from the ramp to the bottom of the pit. The failure, assumed to be structurally controlled by the clay gouges, and the spring runoff was probably the triggering factor. In effect, 0.5 in/day movements or 0.25 in/shift movements would have stopped operations near an instability area. The estimated uniaxial compressive strength of the intact rock for the south wall was more than 150 MPa. The failure was of relatively limited size. During final mining of the south wall, instabilities that were more extensive were clearly apparent. The final cut of the pit wall started in mid-1988 with a design angle at 45° (Martin 1990). The ground water level and rate of mining at the time influenced slope movement rates occurring in excess of 75 – 750 mm/day. These movement rates were recorded after blasting had taken place and during mining of each bench. Flattening the slope angle in the lower portion of the south wall to an overall angle of 40°, and drainage (6 km of drainage holes) kept the failure under control. Measured vertical deformations were significantly larger at the slope crest compared to the lower portions of the slope. The failure mechanism was identified as large scale toppling along the steeply dipping gouge-filled faults in the south wall (Calder & Blackwell 1980; Martin 1990). 201 D.3 Afton mine The Afton copper deposit is located at 13 km west of Kamloops, BC with a pit depth of about 214 m below surface. The ore body occurs in a plutonic diorite with alteration experiences. Geologic mapping of the area indicated that the rock type and geological structures control failures in the pit. Pit wall movement was monitored with a wireline extensometer and EDM. There was variation in the unconfined compressive strengths from 207 MPa for dacite to 3 – 10 MPa for the mudstones. The unconfined compressive strength for the diorite rock mass varied from 2 – 110 MPa. An estimate of 200 kton of material failed on the northwest part of the pit in March 1984. During the event, the overall slope angle for the north wall was 40° with berm with of about 11 m. Furthermore, the rest of the pit wall had a slope angle of 45° with berm width of about 8 m wide. The failure had a minimal impact on production because as failure was about to happen, visual inspection conducted and readings obtained from the extensometer helped to forecast the event. The peak movement rate was 28.8 m/day (Stewart & Reid 1988). Mining in the northeast corner of the pit influenced bench failures. Blasting was noticed to be part of the initiator causing increased movement rates after blasting, hence the failure. The failure caused the north wall slope to be flattened from 40° to 30°. A circular failure of over 1 million tons of overburden and extremely weathered sediments also occurred in the northeast corner of the pit (Stewart & Reid 1988). Failure occurred in 1985-1986 in the south wall because little detail was known about the faults as mining progressed. Approximately 10 kton of material failed on the lower benches of the south wall as the failure mode was believed to be associated with toppling. The overall slope height at the time of failure was just about 300 m but the portion of the slope involved in the failure was approximately 170 m high. Movement rates were around 2 mm/day during the winter season that was good. For the period of 1985 –1986, approximately 3 km of horizontal drain holes were set up, but as the spring-thaw progressed in 1986, movement rates increased to 30 – 60 mm/day. The measured displacements prior to failure were largest at the slope crest (Martin 1990). In early June, a large failure occurred which involved approximately 300 kton of material. After failure, movement rates at the central active area of the slope continued to move at 25 mm/day 202 for a while and movement rates at the edges of the unstable area were 6 – 12 mm/day. It was estimated that the entire area of deep seated toppling involved a total of 7.4 million tons (Martin 1990). D.4 Highland Valley Copper mine This instability occurred in the Highmont pit at Highland Valley Copper mine (HVC). During May 1983, failure at the southeast corner of the east pit began to develop as mining advanced at a depth of about 60 m. Successive mining to a depth of 110 m followed numerous and significant slope movement involving 0.0005 – 0.001 km3 volume of failed rock. A 15 m wide and highly altered quartz diorite with gouge-filled faults intersected the pit striking 20° – 30° towards the east and dipping at 60° to the west. There were varying degrees of alteration all through the mine with intact rock strengths ranging from 1 – 140 MPa. The mine used an AGA Geodimeter 140 to monitor slope movement upon seeing tension cracks behind the crest of the pit near the Waterhole fault. As movement rates increased, monitoring was conducted twice weekly. (Newcomen & Martin 1988). Four distinct pulses were obtained from the monitoring data as mining advanced. The data indicated how the slope is susceptible to precipitation and the mining activity. Based on data obtained from the structural geology, rock engineering properties, management established that failure at the southeast showed a progressive state failure by a combination of sliding alongside structural discontinuities and through poor quality and low strength rock mass in the lower section of the pit. The failure was termed as a deep-seated failure as it was initiated at the toe of the walls and driven by high ground water pressures within the slope. Results from back calculation of the strength parameters for the rock mass showed a friction angle of 33°(Newcomen & Martin 1988). The Lornex pit is presently one of the operational pits of HVC mine. The current Lornex pit design has been broken into eight design sectors with inter-ramp angles ranging from a low of 25°, within the Lornex fault, to a high of 40°.The final southwest wall of the Lornex pit is planned to extend to 500 m high. Hydrothermal alteration has been identified all through the pit which is structurally controlled with some of the zones developed nearby faults and shears (Graden 2012). The major structural feature in the southwest wall is the 80m wide Lornex fault 203 zone which strikes north-south and dips 60°– 80° to west. Three structural domains were assigned to the Lornex pit based on structural data obtained from mapping. The southwest wall of the pit has a long history of slope movements that was first recorded in 1978 immediately after the commencement of mining. The overall pit slope angle was only around 30°. Subsequently, the southwest wall has experienced frequent periods of slope movement linked to precipitation and mining activity. Before 1992, majority of the pit wall movements was managed by scheduling pushbacks on the pit walls that unloads at the crest of the slope. Data collected from prisms for the current wall was put together from early 1997 to August 2001 and assessed. Based on the analysis at least six movement pulses were deduced to have occurred over the period. The pulses were related to contributing factors such as mining activity (blasting), precipitation, and ground water conditions. Movement rates seemed to be structurally controlled. Deep-seated tilting or toppling of the overall slope was proposed to be the key governing mechanism of the movement (Newcomen et al. 2003). D.5 Copper Mountain mine During a night shift on July 17 2013, a shovel was cleaning the wall in Pit 3 when the wall sloughed. At the time of the incident, the shovel was positioned properly for the job and was in the process of backing away from the face. Most of the displaced rock missed the shovel but several rocks still managed to make an impact on the shovel causing damage the left front. The total tonnage of the slough was estimated at 5500 tons (Figure B-1). Geotechnical mapping of the area showed a set of joints steeply dipping into the pit wall and an area of fault shearing. The combination of the two was likely the cause of the rock’s loss in competency and the resulting toppling failure. To the Southwest, the wall changes orientation and this joint set strikes perpendicular to the direction of the wall. To the NE the set appears to terminate with the fault. Both of which indicate that the slough was localized (Figure B-6). 204  Figure B-6. Estimated slough with orientation of the wall and joints (Copper Mountain 2013) Due to past instabilities experienced, the mine has resulted in flattening the bench angles and switching from double bench to single bench pit walls. D.6 Endako mine In 1994, several failures occurred along the continuous northwesterly dipping faults in the Endako pit. A planar failure occurred on the southeast ramp. Wedge failures occurred on the southeast pit wall and the south-central pit wall. These occurred along a majority of the major, continuous northwesterly dipping faults. After the failure, the 3146 ft bench was stepped-in. Furthermore, the bench configuration was modified from the original double bench to a single bench configuration below the 3146 ft bench to reduce the amount of undercutting and failure that was occurring in the double benches exposed adjacent to the West Pit fault (Golder 2002). In 2001, an instability developed on the lower Southeast ramp along the fault in August as mining progressed. It was believed that the low strength and the orientation of the faults resulted to the event (Golder 2002). Top of bench13 m40 m Joint set truncated by faultShearing along fault causing rock to loose  competency and fail along dip of jointNESW205 In March 2002, a planar and wedge failure occurred and it was associated with the northwesterly dipping faults in the upper part slope. The instability in the lower slope appeared to have occurred as the result of sliding along flat lying veins exposed below the South Basalt Fault. The northwesterly dipping faults that caused the planar/wedge instability in the upper slope were very continuous, and had been mapped along the crest of the proposed ultimate pushback slope (Golder 2002). D.7 Gibraltar mine The rock mass near the Granite pit is well fractured and the rock fabric is characterised by joints and faults, with conjugate joint sets being common. Many of these secondary structures are parallel to the major fault systems. The southeast wall of the Granite pit is mainly made up of upper and lower portion separated by a temporary ramp. The upper and lower portion of the southeast wall faces towards an azimuth of approximately 315° and 340° respectively. The southeast wall was excavated at an inter-ramp angle of 37° with a slope height of 137 m. The following structures that are continuous over at least one bench height have been observed in the area of the southeast wall by means of structural mapping: • West-dipping structures oriented approximately 45°/290° (dip/dip-direction). These were seen to be continuous over multiple benches. • Northeast-dipping structures oriented approximately 45°/025°. • Northwest dipping structures oriented approximately 45°/325°. These structures repeatedly unveil clay gouge coatings and slickensides. • West-dipping structures oriented approximately 25°/265°. These were seen to be continuous for up to 31 m, and possibly more. They were observed to be filled with gouge several centimetres thick. • Southwest-dipping structures oriented approximately 40°/220°. • Southeast-dipping structures oriented approximately 45°/165°. These structures were observed to be continuous over up to 31 m, with limited clay coatings. • Southeast-dipping structures oriented approximately 80°/115°. These structures were more widely-spaced and seen to be continuous over multiple bench heights. 206 • Northeast dipping structures dipping 20°/055°. These structures were observed to be isolated and continuous over 3–5 m (Golder 2011). These mapped structures combined to form complex, multi-surface failure mechanism. Early in August 2010, a large crack developed on the crest of the slope. Prisms were installed at the upper portion of the wall to monitor the movement of the wall that showed the southeast wall had been moving. A local structurally controlled wedge instability zone with approximately 3 – 4 benches high developed along the western edge of the larger movement mass in the southeast wall on February 4, 2011. The movement mechanism showed in the local instability zone is similar to the wedge instability that has previously occurred in the central portion of the wall. Slope movement was expected to increase during spring runoff. Therefore, to prevent significant movement rates, it was recommended that the upper portion of the wall be buttressed with waste rock instead of using a drainage system to depressurize the wall. The slope stability performance of the southeast wall was monitored with respect to the location of the buttress. If movement rates increased, the size of the buttress was supposed to be larger but if the movement rate decreased, there was no need to increase the size of the buttress. It is worth noting that irrespective of movement rate been monitored, mining below a moving slope is stopped if the prisms began to show consistent acceleration for three readings or more. Mining is not restarted until prisms exhibited consistent deceleration (Golder 2011). In summary, the following can be concluded for the case histories studied: • When a failure is pending, mine operation should be concerned about the aftermath or consequences of the failure. Mines should be aware that more than one failure could consecutively occur in the same area of a pit. • Sometimes large pit wall movements can be tolerated if the failure location is not above people and equipment. • Rock falls can have significant impact on mining operations when equipment and people are within the range of rock fall trajectories. • Mine operations should use reliable monitoring system to help maximize safety in the pit. Additionally, some failures can be predicted with good monitoring data. 207 • Sometimes when the pit wall is posing stability challenges, mining the area of the wall should be done if possible rather than waiting for failure to occur. • Historical monitoring and rock mass data may perhaps have limited use depending on the type of monitoring technique used, distance of the monitoring station to the pit wall, and the rock material types. • As movement limits used my mine operations are site specific. As such mine operations should have geotechnical and climatic background knowledge at the operations. • Movement limits should always be set to its lowest sensitivities. If an alarm system is used to signal higher movements, the alarms should be distinctive for each area. • Pit slope movements can be slowed down or even stopped by applying appropriate remedial measures. It is important to note that implementing slope remedial measures should be dynamic so that when an action does not help in minimizing the risk of failure, another action can be employed. • Most of the mine operations do not have an idea of the run out distance of the rock mass in case it fails. Therefore, it is important to predict the failure run out distance when failure is pending so that equipment and people will be evacuated from the location of the failure zone 208 Appendix E: BBN analysis results Table A-8. Sensitivity analysis data of Harm to personnel node Node % Normalized Mutual Information Slope velocity 51.23 Production loss 28.13 Strain 7.17 Non equipment operator 6.05 Equipment operator 4.93 Equipment damage 1.11 k 0.96 Travel distance angle 0.11 Debris volume 0.10 Slope height 0.05 Vertical in situ stress 0.04 Ground water 0.03 Pit wall shape 0.03 Slope angle 0.02 Rock mass strength 0.01 Material property, s 0.01 GSI 0.00 UCS 0.00 Rock mass modulus 0.00 Discontinuity spacing 0.00 Discontinuity condition 0.00 Wedge sliding 0.00 RQD 0.00 Rock unit weight 0.00 Blast damage 0.00 Plane sliding 0.00 Rotational failure 0.00 Structure intersection angle<slope angle 0.00 Discontinuity angle<slop angle 0.00 Material property, a 0.00 Friction angle 0.00 209 Table A-9. Sensitivity analysis data of Equipment damage node Node % Normalized Mutual Information Slope velocity 27.21 Non equipment operator 17.92 Equipment operator 17.56 Production loss 10.98 Strain 8.09 Ground water 5.39 Slope angle 2.41 Travel distance angle 2.23 Debris volume 2.13 Harm to personnel 1.09 Material property, s 0.88 Rock mass strength 0.86 GSI 0.86 k 0.81 Slope height 0.55 Vertical in situ stress 0.29 Rotational failure 0.24 Rock mass modulus 0.20 UCS 0.08 Wedge sliding 0.05 Discontinuity condition 0.04 Pit wall shape 0.04 Discontinuity spacing 0.04 Blast damage 0.02 Plane sliding 0.01 RQD 0.00 Material property, a 0.00 Rock unit weight 0.00 Structure intersection angle<slope angle 0.00 Dip direction of discontinuity 0.00 Discontinuity angle<slope angle 0.00 Friction angle 0.00  210 Table A-10. Sensitivity analysis data of Production loss node Node % Normalized Mutual Information Slope velocity 33.27 Harm to personnel 17.41 Strain 13.49 Non equipment operator 9.68 Equipment operator 9.14 Equipment damage 6.88 Ground water 3.60 k 1.55 Slope angle 1.31 Travel distance angle 0.80 Debris volume 0.78 GSI 0.45 Material property, s 0.41 Rock mass strength 0.38 Slope height 0.24 Vertical in situ stress 0.16 Rotational failure 0.14 Rock mass modulus 0.12 Pit wall shape 0.06 Wedge sliding 0.03 UCS 0.03 Discontinuity condition 0.02 Discontinuity spacing 0.02 Blast damage 0.01 Plane sliding 0.01 RQD 0.00 Material property, a 0.00 Rock unit weight 0.00 Structure intersection angle<slope angle 0.00 Dip direction of discontinuity 0.00 Friction angle 0.00 Discontinuity angle<slope angle 0.00   211 Table A-11. Sensitivity analysis data of Slope velocity node Node % Normalized variation reduction Ground water 47.60 Slope angle 17.24 GSI 7.19 Rock mass strength 6.23 k 6.10 Material property, s 5.98 Material property, a 3.23 Rotational failure 2.15 Rock mass modulus 1.63 UCS 0.74 Wedge sliding 0.40 Discontinuity spacing 0.39 Discontinuity condition 0.35 Pit wall shape 0.29 Blast damage 0.23 Vertical in situ stress 0.08 Plane sliding 0.07 Slope height 0.06 RQD 0.03 Rock unit weight 0.00 Friction angle 0.00 Dip direction of discontinuity 0.00 Structure intersection angle<slope angle 0.00 Discontinuity angle<slope angle 0.00 Ground water condition 47.60  212 Appendix F: Results obtained from the case studies Table A-12. HVC mine case study results with respective probabilities (Beliefs) Nodes States  0.25 to 1 1 to 5 5 to 25 25 to 50 50 to 100 100 to 250 UCS 0 0 0 1 0 0  No production loss Hours Days Weeks Months   Production loss 0.48609 0.32537 0.13822 0.042862 0.0074546   Poor Fair Moderate Good Very good  Discontinuity condition 0.20154 0.77109 0.027364 0 0   0 to 10 10 to 20 20 to 30 30 to 40 40 to 50  Friction angle 0 0 1 0 0   0 to 20 20 to 40 40 to 60 60 to 80 80 to 100  GSI 1.00E-04 0.99961 1.00E-04 9.60E-05 9.25E-05  RMR 0 1 0 0 0   0 to 25 25 to 50 50 to 75 75 to 90 90 to 100  RQD 0.28161 0.0018918 0.0034407 0.1508 0.56226   0 to 30 30 to 40 40 to 50 50 to 60 60 to 90  Slope angle 0 0 1 0 0   0 to 60 60 to 200 200 to 600 600 to 2000 2000 to 6000  Discontinuity spacing 0.36391 0.51295 0.12314 0 0   0 to 100 100 to 250 250 to 500 500 to 800 800 to 1500  Slope height 1 0 0 0 0   100 to 10000 10000 to 1E5 1E5 to 1E6 1E6 to 1e7 1E7 to 1E9  Debris volume 0.5146 0.41154 0.039578 0.022039 0.012234   No injury Minor injury Moderate injury Major injury Death  Harm to personnel 0.87914 0.075633 0.030168 0.015032 2.29E-05   No damage Minor damage Major damage Complete loss   Equipment damage 0.63192 0.22245 0.07257 0.073055    0 to 2 2 to 5 5 to 100 100 to 300   213 Nodes States Prism data 0.1269 0.10935 0.16417 0.59958   Slope velocity 0.12809 0.10424 0.14099 0.62669    Convex Planar Concave    Pit wall shape 0.47867 0.27274 0.24858     Dry Moist Saturated    Ground water  0.049307 0.62095 0.32975     0 to 0.21 0.21 to 0.42 0.42 to 0.63    Travel distance angle  0.0112 0.022526 0.96627     0 to 10 10 to 20 20 to 70    Rock mass strength 0.99959 0.00012092 0.00028637     0 to 20 20 to 40 40 to 60    Vertical in situ stress 1 0 0     0 to 20 20 to 40 40 to 100    Rock mass modulus 0.99979 0.00011291 9.23E-05     0 to 24 24 to 27 27 to 40    Rock unit weight 0 1 0     5.8E-8 to 2E-4 2E-4 to 0.006 0.006 to 2    Material property, s 0.99956 0.00020135 0.00023466     4.75E-7 to 0.1 0.1 to 0.6 0.6 to 2.32e6    Strain 0.0033781 0.015389 0.98123     0.3 to 0.9 0.9 to 1.1 1.1 to 3    Hor. to vert. stress ratio 0.096575 0.25097 0.65245     0 0.7 1    Blast damage 0 0 1     No Yes     Disc. angle<slope angle 1 0     Disc. dip direction 0 1     Equipment operator 0.77365 0.22635      0.5 to 0.6 0.6 to 0.66     Material property, a 0.99986 0.00013811     214 Table A-13. Endako mine case study results with respective probabilities (Beliefs) Nodes States  0.25 to 1 1 to 5 5 to 25 25 to 50 50 to 100 100 to 250 UCS 0.0092264 0.038205 0.063402 0.53353 0.26455 0.091092  No production loss Hours Days Weeks Months  Production loss 0.53764 0.28468 0.12993 0.041646 0.0061058   Poor Fair Moderate Good Very good  Discontinuity condition 0.038955 0.42252 0.39611 0.12072 0.021692   0 to 10 10 to 20 20 to 30 30 to 40 40 to 50  Friction angle 0.1 0.2 0.5 0.2 0   0 to 20 20 to 40 40 to 60 60 to 80 80 to 100  GSI 0.0001002 0.0001002 1.00E+00 9.42E-05 8.91E-05  RMR 0 0 1 0 0   0 to 25 25 to 50 50 to 75 75 to 90 90 to 100  RQD 0.16772 0.021287 0.033512 0.068663 0.70882   0 to 30 30 to 40 40 to 50 50 to 60 60 to 90  Slope angle 0 0 1 0 0   0 to 60 60 to 200 200 to 600 600 to 2000 2000 to 6000  Discontinuity spacing 0.080295 0.45329 0.37143 0.073335 0.021651   0 to 100 100 to 250 250 to 500 500 to 800 800 to 1500  Slope height 0 1 0 0 0   0 to 10000 10000 to 1E5 1E5 to 1E6 1E6 to 1E7 1E7 to 1E9  Debris volume 0.13852 0.41956 0.34754 0.079849 0.014528   No injury Minor injury Moderate injury Major injury Death  Harm to personnel 0.91439 0.060246 0.014407 0.01094 1.29E-05   No damage Minor damage Major damage Complete loss   Equipment damage 0.65141 0.20059 0.071446 0.076553    0 to 2 2 to 5 5 to 100 100 to 300   Prism data 0.20267 0.10414 0.16018 0.53302   Slope velocity 0.20837 0.094214 0.14079 0.55663   215 Nodes States  Convex Planar Concave    Pit wall shape 0.47896 0.2728 0.24825     Dry Moist Saturated    Ground water 0.18034 0.58863 0.23103     0 to 0.21 0.21 to 0.42 0.42 to 5.30044    Travel distance angle 0.013205 0.078403 0.90839     0 to 0.5 0.5 to 0.51 0.51 to 0.67    Material property, a 9.51E-06 0.90602 0.09397     0.3 to 0.9 0.9 to 1.1 1.1 to 3    Hor. to vert. stress ratio 0.095933 0.25278 0.65128     0 to 10 10 to 20 20 to 390    Rock mass strength 0.98415 0.015727 0.00012771     0 to 20 20 to 40 40 to 60    Vertical in situ stress 1 0 0     0 to 20 20 to 40 40 to 100    Rock mass modulus 0.99996 2.85E-05 8.87E-06     0 to 24 24 to 27 27 to 40    Rock unit weight 0 1 0     3.73174e-E to 0.1 0.1 to 0.6 0.6 to 1.13858e7    Strain 0.018067 0.090844 0.89109     5.78E-8 to 2E-4 2E-4 to 0.006 0.006 to 2    Material property, s 0.44664 0.55321 0.00014584     0 0.7 1    Blast damage 0 0 1     No Yes     Disc. angle<slope angle 1 0     Disc. dip direction 0 1     Equipment operator 0.70801 0.29199     Non equipment operator 0.7086 0.2914     216 Table A-14. Huckleberry mine case study results with respective probabilities (Beliefs) Nodes States  0.25 to 1 1 to 5 5 to 25 25 to 50 50 to 100 100 to 250 UCS 0 0 0 0 0 1  No production loss Hours Days Weeks Months  Production loss 0.46483 0.27351 0.17618 0.073739 0.011731   Poor Fair Moderate Good Very good  Discontinuity condition 0.34233 0.65767 0 0 0   0 to 10 10 to 20 20 to 30 30 to 40 40 to 50  Friction angle 0.1 0.2 0.5 0.2 0   0 to 20 20 to 40 40 to 60 60 to 80 80 to 100  GSI 0 1 0 0 0  RMR 0 1 0 0 0   0 to 25 25 to 50 50 to 75 75 to 90 90 to 100  RQD 0.7869 0.1066 0.0789 0.00296 0.0247   0 to 30 30 to 40 40 to 50 50 to 60 60 to 90  Slope angle 0 0 0 1 0   0 to 60 60 to 200 200 to 600 600 to 2000 2000 to 6000  Discontinuity spacing 0.526 0.45204 0.02196 0 0.00E+00   No injury Minor injury Moderate injury Major injury Death  Harm to personnel 0.89448 0.061904 0.024773 0.018834 1.25E-05   0 to 100 100 to 250 250 to 500 500 to 800 800 to 1500  Slope height 0 0 1 0 0   0 to 10000 10000 to 1E5 1E5 to 1E6 1E6 to 1E7 1E7 to 1E9  Debris volume 0.072593 0.21741 0.3082 0.30903 0.0928   No damage Minor damage Major damage Complete loss   Equipment damage 0.58013 0.20631 0.087552 0.12601    0 to 2 2 to 5 5 to 100 100 to 300   Prism data 0.13461 0.1128 0.18321 0.56937   Slope velocity 0.1361 0.10634 0.16339 0.59418   217 Nodes States  Convex Planar Concave    Pit wall shape 0.15213 0.29955 0.54831     Dry Moist Saturated    Ground water  0.025752 0.57814 0.39611     0 to 0.21 0.21 to 0.42 0.42 to 0.63    Travel distance angle  0.084193 0.30705 0.60876     0 to 0.9 0.9 to 1.1 1.1 to 3    Hor. to vert. stress ratio 0.098887 0.24625 0.65486     0 to 10 10 to 20 20 to 70    Rock mass strength 1 0 0     0 to 20 20 to 40 40 to 60    Vertical in situ stress 1 0 0     0 to 20 20 to 40 40 to 100    Rock mass modulus 1 0 0     5.778E-8 to 2E-4 2E-4 to 0.006 0.006 to 2    Material property, s 1 0 0     1.4969E-7 to 0.1 0.1 to 0.6 0.6 to 2    Strain 0.0257 0.117 0.857     20 to 24 24 to 27 27 to 40    Rock unit weight 0 1 0     0 0.7 1    Blast damage 0 0 1     No Yes     Disc. angle<slope angle 0.3 0.7     Disc. dip direction 0.3 0.7     Equipment operator 0.76532 0.23468      0.5 to 0.6 0.6 to 0.66     Material property, a 1 0      No Yes     218 Table A-15. Copper Mountain mine case study results with respective probabilities (Beliefs) Nodes States  0.25 to 1 1 to 5 5 to 25 25 to 50 50 to 100 100 to 250 UCS 0 0 0 0 0 1  No production loss Hours Days Weeks Months   Production loss 0.56225 0.2593 0.11171 0.03995 0.02679   Poor Fair Moderate Good Very good  Discontinuity condition 0.11392 0.651 0.187 0.0435 0.00388   0 to 10 10 to 20 20 to 30 30 to 40 40 to 50  Friction angle 0.1 0.2 0.5 0.2 0   0 to 20 20 to 40 40 to 60 60 to 80 80 to 100  GSI 1.00E-04 1.00E-04 0.9996 1.00E-04 1.00E-04  RMR 0 0 1 0 0   0 to 25 25 to 50 50 to 75 75 to 90 90 to 100  RQD 0.33506 0.040913 0.074011 0.081275 0.46874   0 to 30 30 to 40 40 to 50 50 to 60 60 to 90  Slope angle 0 0 0 1 0   0 to 60 60 to 200 200 to 600 600 to 2000 2000 to 6000  Discontinuity spacing 0.17978 0.56191 0.23426 0.021166 0.0028832   0 to 100 100 to 250 250 to 500 500 to 800 800 to 1500  Slope height 1 0 0 0 0   0 to 10000 10000 to 1E5 1E5 to 1E6 1E6 to 1E7 1E7 to 1E9  Debris volume 0.5625 0.38 0.033 0.0185 0.006   No injury Minor injury Moderate injury Major injury Death  Harm to personnel 0.83004 0.089441 0.043862 0.03662 3.46E-05   No damage Minor damage Major damage Complete loss   Equipment damage 0.71994 0.18644 0.045822 0.047796    0 to 2 2 to 5 5 to 100 100 to 300   Prism data 0.19929 0.19919 0.17384 0.42768   Slope velocity 0.1994 0.19707 0.15834 0.44519   219 Nodes States  Convex Planar Concave    Pit wall shape 0.15 0.3 0.55     Dry Moist Saturated    Ground water  0.19186 0.59575 0.21238     0 to 0.21 0.21 to 0.42 0.42 to 0.63    Travel distance angle  0.005469 0.018408 0.97612     0 to 0.9 0.9 to 1.1 1.1 to 3    Hor. to vert. stress ratio 0.1 0.25 0.65     0 to 10 10 to 20 20 to 70    Rock mass strength 0.89444 0.10539 0.00017198     0 to 20 20 to 40 40 to 60    Vertical insitu stress 1 0 0     0 to 20 20 to 40 40 to 100    Rock mass modulus 0.99996 3.23E-05 1.00E-05     3.73174E-8 to 0.1 0.1 to 0.6 0.6 to 2    Strain 0.0050488 0.025082 0.96987     5.77775E-8 to 2E-4 2E-4 to 0.006 0.006 to 2    Material property, s 0.44552 0.55432 0.00016341     20 to 24 24 to 27 27 to 40    Rock unit weight 0 1 0     0 0.7 1    Blast damage 0 0 1     No Yes     Disc. angle<slope angle 0.3 0.7     Disc. dip direction 0.3 0.7     Equipment operator 0.61608 0.38392      0.5 to 0.6 0.6 to 0.66     Material property, a 0.99995 4.81E-05     220 Table A-16. Gibraltar mine case study results with respective probabilities (Beliefs) Nodes States  0.25 to 1 1 to 5 5 to 25 25 to 50 50 to 100 100 to 250 UCS 0.011509 0.044072 0.072168 0.59192 0.22809 0.052246  No production loss Hours Days Weeks Months   Production loss 0.97549 0.021944 0.002491 4.06E-05 2.97E-05   Poor Fair Moderate Good Very good  Discontinuity condition 0.050817 0.49895 0.35776 0.084352 0.008121   0 to 10 10 to 20 20 to 30 30 to 40 40 to 50  Friction angle 0.1 0.2 0.5 0.2 0   0 to 20 20 to 40 40 to 60 60 to 80 80 to 100  GSI 0 0 1 0 0   No injury Minor injury Moderate injury Major injury Death  Harm to personnel 0.9502 0.04703 0.002743 2.28E-05 4.18E-09   0 to 20 20 to 40 40 to 60 60 to 80 80 to 100  RMR 0 0 1 0 0   0 to 25 25 to 50 50 to 75 75 to 90 90 to 100  RQD 0.17804 0.018018 0.029619 0.07462 0.69971   0 to 30 30 to 40 40 to 50 50 to 60 60 to 90  Slope angle 0 0 1 0 0   0 to 60 60 to 200 200 to 600 600 to 2000 2000 to 6000  Discontinuity spacing 0.094514 0.49684 0.34235 0.059847 0.006453   0 to 100 100 to 250 250 to 500 500 to 800 800 to 1500  Slope height 0 1 0 0 0   100 to 10000 10000 to 1E5 1E5 to 1E6 1E6 to 1E7 1E7 to 1E9  Debris volume 0.17143 0.45178 0.28887 0.077518 0.01041   No damage Minor damage Major damage Complete loss   Equipment damage 0.984 0.015618 0.000378 3.66E-06    0 to 2 2 to 5 5 to 100 100 to 300   Prism data 0.75795 0.12915 0.087681 0.025219   221 Nodes States Slope velocity 0.79299 0.092334 0.091008 0.023672    Dry Moist Saturated    Ground water  1 0 0     0 to 0.21 0.21 to 0.42 0.42 to 0.63    Travel distance angle  0.00942 0.075779 0.9148     0 to 10 10 to 20 20 to 70    Rock mass strength 0.98986 0.010134 1.04E-05     0 to 20 20 to 40 40 to 60    Vertical in situ stress 1 0 0     0 to 20 20 to 40 40 to 100    Rock mass modulus 1 0 0     5.77775E-8 to 2E-4 2E-4 to 0.006 0.006 to 2    Material property, s 0 1 0     4.75037E-7 to 0.1 0.1 to 0.6 0.6 to 2    Strain 0.072152 0.3457 0.58214     0.3 to 0.9 0.9 to 1.1 1.1 to 3    Hor. to vert.stress ratio 0.12203 0.27881 0.59916     20 to 24 24 to 28 28 to 40    Rock unit weight 0 1 0     0 0.7 1    Blast damage 0 0 1     Convex Planar Concave    Pit wall shape 0.14407 0.29611 0.55982     No Yes     Disc. angle<slope angle 0 1     Disc. dip direction 0 1     Equipment operator 0.1425 0.8575      0.5 to 0.6 0.6 to 0.66     Material property, a 1 0     222 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.24.1-0300348/manifest

Comment

Related Items