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Runout exceedance prediction for open pit slope failures Whittall, John Russell 2015

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RUNOUT EXCEEDANCE PREDICTION FOR OPEN PIT SLOPE FAILURES  by  John Russell Whittall  B.Sc.E., Queen’s University, 2009  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Geological Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  August 2015  © John Russell Whittall, 2015 ii  Abstract Consequences from recent large open pit slope failures have increased industry and regulatory interest in establishing exclusion zones beneath an impending slope failure.   Damaged infrastructure, equipment, and fatalities have resulted despite geotechnical staff effectively identifying the hazard and predicting the timing of the failure.  Creating exclusion zones is a common response to reduce risk, however uncertainty remains as to how far they should extend.    Advances in natural landslide research have created useful tools for landslide risk management.  These tools have clear applications to pit slopes but most have not been tested or validated.  This thesis validates empirical runout tools to a dataset of 105 pit slope failures and provides design charts to explicitly account for runout and runout exceedance in emergency response procedures.    Results from the analysis presented demonstrate that Fahrböschung angle vs. volume, Fahrböschung angle vs. slope angle, and inundation area vs. volume relationships follow the general trend of established natural landslide models with similar scatter.  However differences in liquefiable substrate, topographic confinement, and a clear dependence on material properties and slope angle necessitate a tool calibrated to open pits.  Open pit specific linear regressions are provided and a new mobility index is proposed to accommodate the geometric and material constraints affecting mobility.  A design tool is provided to map the inundation area back from the estimated deposit toe. These tools are best applied in a probabilistic framework to scale runout to the mine’s tolerable risk level.  Runout exceedance probability charts and simple equations are provided to estimate exclusion zones and integrate runout into the mine’s risk management plan.   iii  Preface This thesis is original work by the author, John Whittall.    A preliminary dataset and observations were presented at the 2014 Canadian Geotechnical Society conference in Regina, Canada.  This work involved a conference paper and presentation titled “Empirical Runout Prediction for Open Pit Slope Failures”, co-authored by John Whittall, Erik Eberhardt, Derek Kinakin, and Oldrich Hungr.  As lead author, John Whittall built the dataset, carried out the analysis, and wrote the text.  The manuscript was reviewed by Erik Eberhardt, Derek Kinakin, and Oldrich Hungr.   A conference paper is in review for the 2015 Slope Stability conference in Cape Town, South Africa.  This paper is a synthesis of Chapter 4, 5, and 6, titled “Runout of open pit slope failures: using and abusing the Fahrböschung method”, co-authored by John Whittall, Erik Eberhardt, Oldrich Hungr, and Doug Stead.  As lead author, John Whittall built the dataset, carried out the analysis, and wrote the text.  The manuscript was reviewed by Erik Eberhardt, Oldrich Hungr, and Doug Stead.    iv  Table of contents Abstract .......................................................................................................................................... ii Preface ........................................................................................................................................... iii Table of contents .......................................................................................................................... iv List of tables.................................................................................................................................. xi List of figures ............................................................................................................................... xii Acknowledgements ................................................................................................................... xvii Chapter 1: Introduction ................................................................................................................1 1.1  Problem statement ........................................................................................................... 1 1.2  Research objectives ......................................................................................................... 1 1.3  Thesis terminology.......................................................................................................... 2 1.4  Thesis organization ......................................................................................................... 4 Chapter 2: Literature review ........................................................................................................5 2.1  What is landslide runout?................................................................................................ 5 2.2  Runout prediction: Established empirical relationships ................................................. 5 2.2.1  Fahrböschung angle vs. volume .................................................................................. 5 2.2.1.1  Stratified Fahrböschung angle vs. volume .......................................................... 7 2.2.2  Fahrböschung angle vs. slope angle ............................................................................ 9 2.2.3  Travel angle ................................................................................................................ 9 2.2.4  Runout length vs. volume ......................................................................................... 10 2.2.5  Excessive travel distance vs. volume ........................................................................ 11 2.2.6  Normalized excessive travel distance vs. volume ..................................................... 12 2.2.7  Constant volume ....................................................................................................... 13 v  2.2.8  Inundation area vs. volume ....................................................................................... 14 2.2.9  Fahrböschung angle vs. potential energy .................................................................. 15 2.2.10  Length vs. potential energy ................................................................................... 16 2.2.11  Inundation area vs. potential energy ..................................................................... 17 2.2.12  Dimensionless runout............................................................................................ 19 2.2.13  Volume balance .................................................................................................... 20 2.2.14  Channeled flow ..................................................................................................... 21 2.2.15  Granular temperature ............................................................................................ 22 2.3  Runout prediction: Established dynamic runout models .............................................. 22 2.4  Trigger action response plans ....................................................................................... 24 2.5  Landslide risk management .......................................................................................... 25 2.5.1  Individual risk ........................................................................................................... 26 2.5.2  Societal risk ............................................................................................................... 27 2.5.2.1  F-N curves ......................................................................................................... 27 2.5.2.2  Risk intervals .................................................................................................... 29 2.5.3  Acceptability ............................................................................................................. 30 2.5.3.1  Industrial risk criteria ........................................................................................ 30 Chapter 3: Methodology, database development and data attributes ....................................32 3.1  Scope and data sources ................................................................................................. 32 3.2  Data reliability .............................................................................................................. 33 3.2.1  Availability ............................................................................................................... 33 3.2.2  Bias ........................................................................................................................... 34 3.3  Data population: Failure description ............................................................................. 36 vi  3.3.1  Volume ...................................................................................................................... 36 3.3.2  Failure mechanism and landslide classification ........................................................ 39 3.3.3  Trigger....................................................................................................................... 40 3.3.4  Number of failures .................................................................................................... 41 3.4  Data distribution: Material attributes ............................................................................ 42 3.4.1  Lithology ................................................................................................................... 42 3.4.2  Fabric ........................................................................................................................ 43 3.4.3  Strength ..................................................................................................................... 44 3.4.4  Rock mass rating ....................................................................................................... 45 3.5  Data attributes: Slope configuration ............................................................................. 46 3.5.1  Slope angle ................................................................................................................ 46 3.5.2  Path morphology ....................................................................................................... 47 3.5.3  Wall shape ................................................................................................................. 48 3.6  Data attributes: Runout ................................................................................................. 49 3.6.1  Fall height ................................................................................................................. 49 3.6.2  Runout length ............................................................................................................ 50 3.6.3  Deposit thickness and inundation area ...................................................................... 51 3.6.4  Deposit shape ............................................................................................................ 52 3.6.4.1  Aspect ratio ....................................................................................................... 54 3.6.4.2  Spreading .......................................................................................................... 55 3.7  Data limitations ............................................................................................................. 56 3.7.1  Error .......................................................................................................................... 56 3.7.2  Incomplete observations ........................................................................................... 56 vii  Chapter 4: Empirical analysis of data .......................................................................................57 4.1  Introduction ................................................................................................................... 57 4.1.1  Relationships analyzed .............................................................................................. 57 4.1.2  Validation procedure ................................................................................................. 58 4.2  Volume models ............................................................................................................. 59 4.2.1  Fahrböschung angle .................................................................................................. 59 4.2.1.1  Stratified Fahrböschung angle .......................................................................... 61 4.2.2  Excessive travel distance .......................................................................................... 66 4.2.3  Normalized excessive travel distance ....................................................................... 69 4.2.4  Runout length ............................................................................................................ 71 4.2.5  Inundation area .......................................................................................................... 74 4.3  Slope angle models ....................................................................................................... 78 4.3.1  Fahrböschung angle .................................................................................................. 78 4.3.2  Runout length ............................................................................................................ 80 4.3.3  Normalized excessive travel distance ....................................................................... 81 4.4  Potential energy models ................................................................................................ 83 4.4.1  Fahrböschung angle .................................................................................................. 83 4.4.2  Runout length ............................................................................................................ 85 4.4.3  Inundation area .......................................................................................................... 87 4.5  Dimensionless model .................................................................................................... 89 4.6  Optimized mobility index ............................................................................................. 91 4.7  Parametric analysis ....................................................................................................... 95 4.7.1  Sensitivity ................................................................................................................. 95 viii  4.7.1.1  Volume .............................................................................................................. 95 4.7.1.2  Slope angle ........................................................................................................ 98 4.7.1.3  Fall height ....................................................................................................... 101 4.7.2  Covariance .............................................................................................................. 103 4.7.2.1  Slope angle and volume .................................................................................. 103 4.7.2.2  Slope angle and material type ......................................................................... 104 4.7.2.3  Fall height and slope angle ............................................................................. 105 4.7.2.4  Fall height and volume.................................................................................... 106 4.8  Mobility index comparison ......................................................................................... 107 Chapter 5: Performance of empirical runout relationships ..................................................111 5.1  Introduction ................................................................................................................. 111 5.2  Spread ......................................................................................................................... 111 5.3  Influence of material properties .................................................................................. 112 5.3.1  Poorly cemented granular materials ........................................................................ 113 5.3.2  Clay-bearing fault zones ......................................................................................... 114 5.3.3  Weathered materials ................................................................................................ 114 5.3.4  Pore pressure dissipation in clay-rich materials ...................................................... 114 5.3.5  Distinguishing mobility trends ................................................................................ 116 5.4  Travel path obstruction ............................................................................................... 117 5.5  Failure mechanism ...................................................................................................... 118 5.6  Retrogressive failures .................................................................................................. 120 Chapter 6: Implementation of the empirical runout and exclusion zone procedure ..........121 6.1  Introduction ................................................................................................................. 121 ix  6.2  Estimating source volume ........................................................................................... 124 6.3  Selecting a runout model ............................................................................................ 126 6.4  Probabilistic runout estimates: calculating P(S:L) ........................................................ 128 6.5  Implementing the exclusion zone ............................................................................... 133 6.6  Evaluating the risk to the exclusion zone ................................................................... 135 6.6.1  F-N curves for open pit landslides .......................................................................... 137 6.7  Limitations .................................................................................................................. 139 Chapter 7: Recommendations and conclusions ......................................................................141 7.1  Runout observations.................................................................................................... 141 7.2  Appropriate mobility relationships ............................................................................. 141 7.3  Further work................................................................................................................ 142 7.3.1  Local calibration ..................................................................................................... 142 7.3.2  Societal risk to moving elements ............................................................................ 142 7.3.3  Implementation ....................................................................................................... 142 7.3.4  Proactive risk planning ........................................................................................... 143 References ...................................................................................................................................144 Appendices ..................................................................................................................................160 Appendix A Empirical database ............................................................................................. 161 Appendix B Remote sensing observations used to develop empirical database .................... 172 Appendix C Example risk calculation .................................................................................... 195 C.1  Scenario................................................................................................................... 196 C.2  Assumptions ............................................................................................................ 196 C.3  Estimating P(S:L) ...................................................................................................... 197 x  C.4  Estimating P(T:S) ...................................................................................................... 198 C.5  Individual risk ......................................................................................................... 199 C.6  Societal risk ............................................................................................................. 200  xi  List of tables  Table 1. Industrial precedents for acceptable and tolerable landslide risk ................................... 31 Table 2. Mobility index comparison ........................................................................................... 109  xii  List of figures Figure 1. Schematic of open pit mine terminology......................................................................... 3 Figure 2. Schematic of slope failure terminology ........................................................................... 3 Figure 3. Established rock avalanche Fahrböschung angle vs. volume mobility relationships ...... 6 Figure 4. Fahrböschung angle vs. volume mobility relationships after Corominas (1996) grouped by landslide classification (left) and path obstruction (right) ......................................................... 8 Figure 5. Fahrböschung angle vs. downslope angle mobility relationship according to Hunter and Fell (2003) ....................................................................................................................................... 9 Figure 6. Runout length vs. volume mobility relationship after Legros (2002) ........................... 10 Figure 7. Excessive travel distance vs. volume mobility relationship after Hsü (1975) and Hungr (1981) ............................................................................................................................................ 12 Figure 8. Normalized excessive travel distance vs. volume mobility relationship after Nicoletti and Sorriso-Valvo (1991) ............................................................................................................. 13 Figure 9. Inundation area vs. volume mobility relationship after Griswold and Iverson (2008) . 15 Figure 10. Potential energy vs. Fahrböschung angle mobility relationship after Howard (1973) 16 Figure 11. Runout length vs. potential energy mobility relationship after McSaveney (1975) .... 17 Figure 12. Inundation area vs. potential energy mobility relationship after Dade and Huppert (1998) ............................................................................................................................................ 18 Figure 13. Dimensionless mobility relationship after Staron (2008) ............................................ 20 Figure 14. Reproduction of volume balance schematic procedure in Fannin and Wise (2001) ... 21 Figure 15. Example DAN3D output from Strouth and Eberhardt (2009) .................................... 23 Figure 16. Example of F-N curve and criterion line ..................................................................... 28 Figure 17. Example F-N curve with Kendall et al. (1977) tolerance criteria ............................... 29 xiii  Figure 18. Timeline of data source publication ............................................................................ 34 Figure 19. Distribution of mines contributing case histories ........................................................ 36 Figure 20. Distribution of landslide volume, n=105 ..................................................................... 37 Figure 21. Example consequences from small volume landslides. Note truck buried in slide debris ............................................................................................................................................. 38 Figure 22. Distribution of failure mechanism, n=105 .................................................................. 40 Figure 23. Distribution of reported triggering events, n=105 ....................................................... 41 Figure 24. Distribution of events per landslide, n=105 ................................................................ 42 Figure 25. Distribution of simplified material type groupings, n=105 ......................................... 43 Figure 26. Distribution of rock mass fabric orientation, n=105 ................................................... 44 Figure 27. Distribution of strength grade, n=105 ......................................................................... 45 Figure 28. Distribution of rock mass rating, n=105 ...................................................................... 46 Figure 29. Distribution of slope angles, n=105 ............................................................................ 47 Figure 30. Distribution of travel path attributes, n=105 ............................................................... 48 Figure 31. Distribution of wall shape, n=105 ............................................................................... 49 Figure 32. Distribution of fall height, n=105 ................................................................................ 50 Figure 33. Distribution of runout length, n=105 ........................................................................... 51 Figure 34. Distribution of deposit inundation area, n=47 ............................................................. 52 Figure 35. Example deposit morphologies for (a) talus pile and (b) flow-like deposits free to spread or obstructed (c) and (d). Photograph are from cases 4 (Martin, 1990), 38 (Sheets et al., 2014), 86 (Szwedzicki, 2001), and 27 (Sharon, 2011), respectively. ........................................... 53 Figure 36. Map of deposit aspect observations ............................................................................. 54 Figure 37. Degree of spreading in open pit slope failures ............................................................ 55 xiv  Figure 38. Open pit data with Scheidegger (1975), Li (1983), and Davidson (2011) best fit Fahrböschung angle vs. volume regressions ................................................................................. 60 Figure 39. Error distribution for Fahrböschung angle vs. volume mobility index ....................... 61 Figure 40. Tangent of Fahrböschung angle vs. volume trends based on material behaviour ....... 62 Figure 41. Error distribution for stratified Fahrböschung angle vs. volume mobility index ........ 63 Figure 42. Open pit data compared to Corominas (1996) (a) landslide classification and (b) path obstruction Fahrböschung angle vs. volume mobility relationships ............................................. 65 Figure 43. Open pit data with Hsü (1975) and Hungr (1981) excessive travel distance mobility indices ........................................................................................................................................... 67 Figure 44. Error distribution for excessive travel distance mobility index ................................... 68 Figure 45. Open pit data with excessive travel distance normalized to total runout length vs. volume........................................................................................................................................... 70 Figure 46. Error distribution for normalized excessive travel distance mobility index ................ 71 Figure 47. Open pit data with runout length vs. volume mobility index ...................................... 72 Figure 48. Distribution of error for runout length vs. volume mobility index .............................. 73 Figure 49. Comparison of open pit failure fall height to runout length ........................................ 74 Figure 50. Open pit data with Li (1983) and Griswold and Iverson (2008) planimetric deposit area vs. volume relationships ........................................................................................................ 75 Figure 51. Error distribution for inundation area vs. volume mobility index ............................... 76 Figure 52. Demonstration of achievable inundation area prediction quality ................................ 77 Figure 53. Correlation heat map comparing volume, inundation area, and Fahrböschung angle (red=most mobile, green=least mobile) ........................................................................................ 77 Figure 54. Open pit data with Fahrböschung angle vs. slope angle mobility index ..................... 79 xv  Figure 55. Error distribution for Fahrböschung angle vs. slope angle mobility index ................. 80 Figure 56. Open pit data with runout length vs. slope angle mobility index ................................ 81 Figure 57. Open pit data with normalized excessive travel distance vs. slope angle mobility index....................................................................................................................................................... 82 Figure 58. Error distribution for normalized excessive travel distance vs. slope angle mobility index .............................................................................................................................................. 83 Figure 59. Open pit data with Fahrböschung angle vs. potential energy mobility index ............. 84 Figure 60. Error distribution for Fahrböschung angle vs. potential energy mobility index ......... 85 Figure 61. Open pit data with runout length vs. potential energy mobility index ........................ 86 Figure 62. Error distribution for runout length vs. potential energy mobility index .................... 87 Figure 63. Open pit data with inundation area vs. potential energy mobility index ..................... 88 Figure 64. Error distribution for inundation area vs. potential energy mobility index ................. 89 Figure 65. Open pit data with dimensionless mobility index ....................................................... 90 Figure 66. Schematic of optimized mobility index geometry ....................................................... 91 Figure 67. Open pit data with optimized mobility index, as define in Figure 66 ......................... 93 Figure 68. Error distribution optimized mobility index ................................................................ 94 Figure 69. Open pit data with Fahrböschung angle normalized to slope angle ............................ 96 Figure 70. Model sensitivity to volume ........................................................................................ 97 Figure 71. Fahrböschung angle vs. volume mobility index symbolized by slope angle .............. 98 Figure 72. Exaggerated schematic of slope angle’s effect on centripetal acceleration ................ 99 Figure 73. Model sensitivity to slope angle ................................................................................ 100 Figure 74. Model sensitivity to fall height .................................................................................. 102 Figure 75. Volume vs. slope angle correlation heat maps .......................................................... 104 xvi  Figure 76. Material type vs. slope angle correlation heat maps .................................................. 105 Figure 77. Slope angle vs. fall height correlation heat maps ...................................................... 106 Figure 78. Volume vs. fall height correlation heat maps ............................................................ 107 Figure 79. Prediction quality of runout relationships calibrated to open pit landslides ............. 110 Figure 80. Rock mass property mobility trend matrix for use with Figure 40 ........................... 117 Figure 81. Fahrböschung angle vs. volume relationship symbolized by failure mechanism ..... 119 Figure 82. Example workflow to estimate P(S:L) and generate exclusion zones ......................... 123 Figure 83.  Comparison of source deformation surface area and reported volume .................... 125 Figure 84. Comparison of reported and empirically estimated source volumes ......................... 126 Figure 85. Prediction interval design chart for the less mobile (trend 1) Fahrböschung angle vs. volume mobility index ................................................................................................................ 129 Figure 86. Prediction interval design chart for the more mobile (trend 2) Fahrböschung angle vs. volume mobility index ................................................................................................................ 130 Figure 87. Prediction interval design chart for the Fahrböschung angle vs. slope angle mobility index ............................................................................................................................................ 131 Figure 88. Prediction interval design chart for the optimized mobility index ............................ 132 Figure 89. Example application of Fahrböschung angle to defining an exclusion zone ............ 133 Figure 90. Empirical deposit hazard mapping tool ..................................................................... 134 Figure 91. Open pit landslide risk event tree analysis ................................................................ 139   xvii  Acknowledgements Thanks to my supervisor, Professor Erik Eberhardt, for just enough leash to chase my academic curiosities while keeping me moving on my path.  Thanks for the opportunities, encouragement, and guidance.   I had the privilege of an extraordinarily helpful supervisory committee.  Thanks to  Professor Oldrich Hungr, who taught me the world takes the simplest route, stop overcomplicating it, and to Professor Doug Stead, who taught me innovation without utility isn’t particularly innovative.  My external examiner, Dr. Scott McDougall, vastly improved this thesis with clear examination of the fundamentals.  I learned a lot, you’re a great teacher.  Thanks for crossing my T’s.    Thanks to Derek Kinakin, Warren Newcomen, and Mike Porter for their patience with my “will this actually work?” type questions.   Financial support from BGC Engineering Inc. and NSERC is gratefully acknowledged.  My GeoEng lab mates made this degree a lot of fun.  Thanks for the good times, both academic and otherwise.      Lastly, thanks to my parents, brother, and best friend Sarah for their support and humour throughout my return to school.    You can, turns out, spend your days dreaming about rocks falling down hills.  1  Chapter 1: Introduction 1.1 Problem statement Recent large open pit slope failures that have caused significant damage to mine infrastructure and equipment demonstrate shortcomings in current practices used to establish exclusion zones for an impending failure.  Objectively forecasting the zone of impact of a potential slope failure, in addition to identifying the failure itself, is a critical component of a mine’s risk management plan.   Empirical models are useful tools to assess the runout component of landslide risk. Their utility has been recognized for open pit slope failures (Rose, 2011) however they were developed solely based on natural landslide case histories and have not been validated for open pit slopes.  Empirical runout models can be useful to perform slope risk assessments and aid decision making in an operating open pit mine. Safety and economic constraints related to personnel withdrawal, equipment, and lost production leave little time for detailed deterministic analyses.  The June 2010 failure at Savage River, for example, occurred only seven minutes after the first radar alert (MacQueen et al., 2013). Treating site specific influences holistically is appropriate when time and geological uncertainty limits the degree of precision that can be expected.  Empirical methods are quick, repeatable, and useful for bracketing site conditions where detailed data is limited.  1.2 Research objectives Using empirical models in a new open pit context requires validation.  This is achieved by building a dataset and evaluating whether it conforms to the constraints of the method. In doing so, several questions arise:  2   Are the model results similar to the field observations?    Will the empirically predicted runout length provide a reasonable match to the observed runout?    If not, do they over (conservative) or under predict runout?    Can we integrate pit slope failure runout into a risk management plan as we do with natural landslides?   In this research, I compare and validate established empirical relationships to a dataset of 105 extremely rapid (>5 m/s) (Cruden and Varnes, 1996) pit slope failures.  A discussion of differences between open pit and natural slope runouts highlights possible limitations to the applications of these models in open pit mining. New empirical relationships and tools are provided to establish open pit exclusion zones and quantify the associated risk.    1.3 Thesis terminology Figure 1 is a schematic of the open pit terminology used throughout this thesis. Benches are horizontal areas between inclined faces used for access and rockfall catchment. A ramp or berm is a wider horizontal area used for access, catchment, instrumentation, or infrastructure.  A bench stack is a group of benches between the ramps/berms.  The toe-to-crest inclination of a bench stack is the bench stack angle.  The overall angle is the toe-to-crest inclination of the entire wall.    Figure 2 is a schematic of the slope failure terminology used throughout this thesis, applied to both open pits and natural landslides.  3   Figure 1. Schematic of open pit mine terminology  Figure 2. Schematic of slope failure terminology  4  1.4 Thesis organization Chapter 2 presents empirical runout relationships and landslide risk management as developed for natural landslides with a discussion of the state-of-practice in open pit mining.  Chapter 3 summarizes the pit slope failure dataset.  Chapter 4 contains the results and sensitivities of applying the established mobility relationships to the mining case histories.  Chapter 5 is a discussion of mobility observations of open pit slope failures. Chapter 6 provides tools for parameter estimation, treating runout statistically, objectively defining exclusion zones, and integrating them into a landslide risk management plan.  Chapter 7 discusses further research into implementation options and proactive risk planning.  The appendices contain case history details, data from remote sensing observations, and an example risk calculation.    5  Chapter 2: Literature review 2.1 What is landslide runout? Runout analysis is the analysis of landslide motion.  Flowing landslides can be extremely rapid (>5 m/s) and reach areas far from their source.  The impact area and intensity of an impending landslide is mapped using runout analysis based on observations of the source, path, and deposit (see Figure 2). Empirical and numerical runout analysis are common tools for land use planning, risk assessment and mitigation strategies (McDougall et al., 2006).     2.2 Runout prediction: Established empirical relationships Empirical runout models for natural landslides have proven to be a useful tool for predicting the runout distance and zone of impact of the landslide material.  Heim (1932) proposed the distance a landslide will travel is proportional to its volume.  Several authors have built on Heim’s work to incorporate path morphology, landslide classification, and obstruction.  Hungr et al. (2004) provide a good synopsis of established empirical relationships.  Each requires an approximation of source location and travel path, however disagreement persists on the importance of other parameters.  The following subsections describe the established empirical runout relationships.  2.2.1 Fahrböschung angle vs. volume A common empirical runout prediction method is the concept of the “Fahrböschung” angle.  Equating energy lost to work done, Heim (1932) postulated the effective friction coefficient of sliding motion should be equal to the ratio of vertical and horizontal displacement. He related the volume (V) of failed material to the ratio of fall height (H) and horizontal runout distance (L) to graphically describe runout as the inclination of the line that connects the crest of the main scarp 6  to the toe of the deposit, as shown in Figure 2.  Subsequent studies by Scheidegger (1973), Li (1983), and more recently Davidson (2011) investigating landslides of various classifications and sizes, establish that landslide mobility is proportional to its volume.  Their Fahrböschung angle relationships are presented in Figure 3 and take the power-law form in Equation 1.   Figure 3. Established rock avalanche Fahrböschung angle vs. volume mobility relationships  log ቀு௅ቁ ൌ െ݈ܽ݋ܸ݃ ൅ ܾ     [1] Parameter a and b are constants and V is the volume. 7  2.2.1.1 Stratified Fahrböschung angle vs. volume Later researchers incorporate differences in landslide classification, path morphology, obstruction, and surficial materials to improve the Fahrböschung-volume correlation.    Nicoletti and Sorriso-Valvo (1991) proposed separating data into three path morphology classes: high mobility channelized by a narrow valley or riding over ice, intermediate mobility where debris is free to spread, and low mobility where debris travels transverse to the channelizing feature.    Corominas (1996) studied the effect of deflection, confinement, and vegetation obstacles for different landslide categories: rockfall/rock avalanche, translational slides, earth flow, and debris flow.  Dividing events into more homogeneous groupings produced distinct trends, Figure 4, and a better correlation than the grouped dataset.  A criticism of this treatment may be the statistical relevance of subdividing an already small dataset (McDougall, 2006).   8   Some datasets show sample stratification even after being separated into homogeneous populations. Pudasaini and Miller (2013) noticed unobstructed natural debris avalanches have separate low and high Fahrböschung angle vs. volume trends despite the similar environment and travel mechanism.  Their data was unified to a single trend by analytically-derived physical and rheological terms in Equation 2.  The dominant terms are fluidization, the ratio of pore pressure at the bed to normal stress, and Coulomb friction. ு௅ ൌ ߤ௘ ൌ ߤ௖ሺ1 െ Λሻܶߛ௏ൈ஺೙షభ஺೟                                           [2]  Parameter μe is a theoretical effective friction coefficient, μc is the Coulomb friction coefficient, Λ is a fluidization term, γ is a volume-inundation area proportionality constant, T is a topographic parameter derived from slope angle and centripetal acceleration, V is the volume, A Figure 4. Fahrböschung angle vs. volume mobility relationships after Corominas (1996) grouped by landslide classification (left) and path obstruction (right)  9  is the deposit inundation area, n is an empirically derived constant, At is the debris covered area at time t.  2.2.2 Fahrböschung angle vs. slope angle Hunter and Fell (2003) found the Fahrböschung angle of flow slides in loose granular fills and waste dumps had almost no dependence on volume or slope height; rather, mobility being proportional to the angle of the substrate below the source area, Figure 5.  Their downslope angle (α) is the average valley inclination.    Figure 5. Fahrböschung angle vs. downslope angle mobility relationship according to Hunter and Fell (2003)  2.2.3 Travel angle The Fahrböschung angle is not, strictly speaking, the frictional angle of the material nor that of the sliding path.  A more physically meaningful parameter is the travel angle, the inclination of the line connecting the centre of gravity of the source and deposit, Figure 2.  Hungr (1981) 10  derived the centre of gravity for 16 natural rock avalanches to find the travel angle is generally similar to the Fahrböschung, minus 2.2°, for most cases.  Notable exceptions are landslides that leave mass behind at topographic constrictions or bends, where the difference was up to 9°.    2.2.4 Runout length vs. volume Legros (2002) and others argue the Fahrböschung angle is physically meaningless and, in a dry cohesionless material, runout distance is a function of volume alone.  Various length-volume power-law regressions exist showing a moderately-strong positive correlation, such as Figure 6.    Figure 6. Runout length vs. volume mobility relationship after Legros (2002) 11   2.2.5 Excessive travel distance vs. volume Shreve (1968), Scheidegger (1973) and others placed caveats on their Fahrböschung regressions asserting only small landslides show mobility corresponding to their effective friction angle.   Above a volume threshold rock avalanches are a flow of disintegrated rock and do not behave as a block sliding down a plane.  Hsü (1975) found landslides smaller than 5,000,000 m3 slide according to Coulombs Law with a basal resistance of tan32°.  Hsü’s excessive travel distance (Le) is the horizontal runout length beyond the distance predicted by simple friction, given in Figure 2 and Equation 3: ݁ܮ ൌ ܮ െ ு௧௔௡ଷଶ°      [3]  Hsü plotted Le against volume in semi-log space and sketched two linear fits for low and high mobility, Figure 7.  Equations are not provided for the fits.  12   Figure 7. Excessive travel distance vs. volume mobility relationship after Hsü (1975) and Hungr (1981)  McSaveney (1975) pointed out excessive travel distance has no theoretical basis and does not provide a convincing correlation.  Hungr (1981) proposed an improvement by plotting a range of curves given by Le~cV1/3, where c varies from 4.4 to 8.8, to better fit the data.  This non-linear correlation shows how flow efficiency increases for larger landslides.     2.2.6 Normalized excessive travel distance vs. volume  Nicoletti and Sorriso-Valvo (1991) found normalizing excessive travel distance by total runout length, Figure 8, creates a mobility index insensitive to fall height and moderately sensitive to volume.  They noted the difficulty in estimating volume a priori and suggested a method with similar scatter but decreased parameter sensitivity provides a better prediction.   13   Figure 8. Normalized excessive travel distance vs. volume mobility relationship after Nicoletti and Sorriso-Valvo (1991)  2.2.7 Constant volume Finlay et al. (1999) compiled a dataset of 1,100 landslides in Hong Kong to study which parameters are most influential on travel distance when volume is kept constant.  Source volumes were typically 1,000 m3 and none exceeded 5,000 m3.  Parameters studied included: slope angle, fall height, deposit thickness, strike length, confinement, and apparent friction coefficient.  Data included cut slopes, fill slopes, retaining walls, and boulder falls.  The cut slope regression, Equation 4, had the tightest correlation and is the closest analogue to open pits.  The study found slope angle (α) and path confinement are the most influential parameters.   logሺܮሻ ൌ 0.109 ൅ 1.010 logሺܪሻ െ 0.506log	ሺߙ݊ܽݐሻ    [4]  14  2.2.8 Inundation area vs. volume Empirical-statistical models are available to estimate the deposit inundation area.  Planimetric deposit area relationships (Li, 1983; Iverson et al., 1998) are useful to characterize the width component and create hazard maps.  The USGS code LAHARZ (Iverson et al., 1998) uses this relationship for automated mapping of lahar hazard zones.  Research has found that this relationship is dependent on landslide classification, distinguishing lahars, rock avalanches, and debris flows, Figure 9.    Power-law fits calibrated by Griswold and Iverson (2008) take the form: ܣ ൌ ܸܿଶ/ଷ      [5]  where the 2/3 fraction is a geometric scaling factor based on the observation that deposit shapes tend to fan into a self-similar arrangement. c is the landslide type dependent y-intercept.    15   Figure 9. Inundation area vs. volume mobility relationship after Griswold and Iverson (2008)  2.2.9 Fahrböschung angle vs. potential energy Howard (1973) noted long runout landslides occur on the moon without air or pore pressure to lubricate the flow.  He reasoned landslide motion as an energy balance independent of lubrication and found a weak positive correlation between potential energy and the tangent of L/H, Figure 10.  He showed long runout landslides only occur if 1020 ergs of potential energy is 16  available to be dissipated and larger events flow proportionally greater distances.   A criticism of this method is that both variables contain fall height.   Figure 10. Potential energy vs. Fahrböschung angle mobility relationship after Howard (1973)  2.2.10 Length vs. potential energy McSaveney (1975) cautions removing fall height from mobility relationships is problematic because it implies the work done to slow the landslide is independent of energy used.  Using Hsü’s (1975) data, McSaveney found a positive power-law relationship (in log space) between horizontal travel distance and potential energy, Figure 11.  This model has the same physical 17  basis as Scheidegger and Heim’s work but suggests height is an independent variable.  The trend and scatter are also similar.     Figure 11. Runout length vs. potential energy mobility relationship after McSaveney (1975)  2.2.11 Inundation area vs. potential energy Dade and Huppert (1998) suggest an approach to estimate a landslide’s inundation area using a fixed yield stress, or purely plastic deformation, rather than a constant friction coefficient.  They argue the y-intercept of area vs. volume models is a function of the shear stress in the mobile debris and the deposit aspect ratio.  A fixed yield stress unifies data into one trend, Figure 12.  18  The x-axis of this approach is potential energy, given by ρgVH, which yields a positive log-log correlation with inundation area.    Figure 12. Inundation area vs. potential energy mobility relationship after Dade and Huppert (1998)  Legros (2002) and Griswold and Iverson (2008) provide two criticisms to the logic of a constant yield stress in an empirical model.   First, if the ability of a material to spread is a function of its yield strength, and if thickness is a result of the degree of spreading, then thickness is a function of yield strength.  The positive correlation between thickness and volume (approximately V1/3) implies larger volume landslides have higher strength, for which there is no physical evidence. Second, in a spreading landslide with constant dissipative stress, rather than coefficient of friction, with increased inundation area comes increased force resisting movement.  When numerically modelled this produces impossibly high velocities.  19   2.2.12 Dimensionless runout  Staron (2008) argued a common runout behavior does not exist while disregarding path attributes and basal resistance.  Staron admits incorporating flow dynamics into an empirical model is difficult and made no attempt.  He suggested that rather than pretending we can replicate an energy balance, runout length normalized by lateral spread and plotted against aspect provides just as good a description of deposit geometry.   This dataset has a relatively constant aspect (Section 3.6.4) and does not lend itself well to Staron’s approach.  However in developing his logic, Staron showed a dimensionless, purely geometric, mobility index that may provide an opportunity to estimate deposit thickness, as well as horizontal reach.  Assuming landslide inundation area is proportional to V2/3 implies its average thickness is proportional to V1/3.  Staron plotted runout length normalized to thickness (L/V1/3) against inundation area normalized to volume (A/V2/3) and found a positive correlation in log-log space, Figure 13.   20   Figure 13. Dimensionless mobility relationship after Staron (2008)  2.2.13 Volume balance Some landslides types gain most of their volume by entraining surficial material along the travel path.  Cannon (1993) and Fannin and Wise (2001) developed volume balance relationships using material entrainment and deposition to estimate the distal limit of motion.  These relationships are suited for cases where the path is known a priori (e.g. a channel) and the morphology is well constrained.  They divide the path into segments and assign each as confined, unconfined, or a transition, as in Figure 14.  Confined segments have entrainment, unconfined segments have deposition.  Volume estimates update by dividing the volume entering each segment by the 21  segment length.  The process iterates for each segment and movement continues until the volume is used up.    Figure 14. Reproduction of volume balance schematic procedure in Fannin and Wise (2001)  2.2.14 Channeled flow Debris flow reach is a function of the momentum consuming properties of the travel path.  Assuming the flow exits a channel, toe location can be related to the geometry of the catchment area (Zimmerman et al., 1997), momentum loss in the channel bends (Benda and Cundy, 1990), or the ratio of channel width to gradient (Fannin and Rollerson, 1993).    22  2.2.15 Granular temperature Granular temperature is the degree of agitation of material grains in motion.  Campbell (1989) showed with numerical simulations higher granular temperatures reduce the bulk density of the material and enhance its mobility.  This is analogous to fluid mixing theory where particle collisions and their ability to avoid interlocking indicate bulk properties of the mixture.  Iverson et al. (1998) provide an example application relating vibrational energy to descent height.  Note the authors use this to demonstrate the principle and suggest its place in numerical simulations; neither advocate for it as an empirical approach.  2.3 Runout prediction: Established dynamic runout models Numerical runout models are a useful tool to simulate the bulk behavior of landslides in motion.  Typically they rely on morphology, material properties, and conservation of momentum to time-step the landslide through initiation, motion, and deposition.  They are calibration based models where bulk properties are estimated by matching the model results to observations like runout distance, deposit thickness, and velocity.  Figure 15, for example, is a DAN3D (McDougall and Hungr, 2004) output from Strouth and Eberhardt (2009) showing the runout trimline and velocity contours for the Afternoon Creek rockslide.    23   Figure 15. Example DAN3D output from Strouth and Eberhardt (2009)  Broadly, established models are either a collection of point masses travelling over a prescribed path, or a deformable mass where landslide elements interact with each other.  A benchmarking exercise of established models as of 2007 is summarized in Hungr et al., 2007.  24  Numerical models allow the user to explicitly account for site-specific topography and materials. They are useful for proactive simulations to compare scenarios, assess infrastructure susceptibility, and design protection structures (Hungr et al., 2002).  Model outputs such as flow velocity, flow density, flow depth, erosion depth, and deposit thickness are correlated to landslide intensity, or destructiveness, to provide both the spatial impact and vulnerability of an element at risk.    Inputs for three-dimensional numerical models include a smoothed topography file, the geometry of the rupture surface, an interpretation of the flow rheology, and parameters such as bulk friction angle and a turbulence term derived from back-analyses.  Often these inputs are difficult to estimate a priori and their uncertainties may become lost in a deterministic-looking output.  Also, the vulnerability estimate a numerical model provides is not necessary because a worker impacted by landslide debris is fully vulnerable (V=1).  In many cases, empirical models are better suited to emergency response as they are easy to implement, repeatable, shaped by actual events, and the achievable accuracy is transparent.     2.4 Trigger action response plans An operating open pit mine is required to have a Trigger-Action-Response Plan (TARP) to prescribe emergency response procedures and personnel responsibilities in the event of a slope failure.  TARPs identify a hazard and respond according to its severity. This typically involves using deformation monitoring to estimate time-of-failure and guide evacuation decisions.  Read and Stacey (2009) provide a detailed example.   In several recent pit slope failures, geotechnical staff have effectively identified the impending failure but misjudged the resulting runout (Moore, 25  2003; Pankow et al., 2013; Farina et al., 2013).  Damaged equipment, injuries, and fatalities resulted and emphasize the need to address the consequence of an impending landslide, in addition to the hazard itself.  Although setting exclusion zones are common response to a potential landslide (e.g. Kayesa, 2006), the state-of-practice does not have a validated approach to estimate the zone of influence of a pit slope failure.    2.5 Landslide risk management Decision-making in an operating open pit has moved towards a risk framework.  Balancing geotechnical considerations with many other factors, and tolerating marginally lower factors of safety for economic advantages is acceptable if it poses insignificant consequences.  It provides a transparent framework for designing for uncertainty that is useful in discussion with stakeholders in other disciplines.  Steffen (1997), Terbrugge et al. (2006), and Sullivan (2006) provide strategies for risk-based slope design.  Landslide risk can follow a similar framework.  Researchers studying natural landslides have applied a risk approach to community and infrastructure management (Wise et al., 2004; Fell et al., 2005; Porter and Morgenstern, 2013).  Landslide risk is: ܴ݅݇ݏ ൌ ሺܲ௅ሻ ൈ ሺܲௌ:௅ሻ ൈ ሺ்ܲ:ௌሻ ൈ ܸ ൈ 6]     ܧ]  where P(L) is the frequency of landslide occurrence per year, P(S:L) is the spatial probability a landslide will reach a specific location, P(T:S) is the temporal probability of impact to an element at risk, V is the vulnerability of the element at risk, and E is its worth.    26  In a mining environment, the elements at risk are mine workers, but also equipment, infrastructure, production schedules, ore, etc.  P(L) is the landslide hazard identified through stability analysis and slope monitoring.  Temporal data, P(T:S), is from the production schedule (i.e., drilling a blast pattern below the slope vs. occasional truck traffic).  An individual working in a mine is completely vulnerable to impact (V=1).  Considering the risk to infrastructure will require another estimate of vulnerability.  In this context, the worth of the element at risk is the number of people impacted.  The spatial probability, P(S:L), is delineated with runout analysis.  Potential for loss of life can be either the risk to an individual or society.  Individual risk is to a particular person, typically those most exposed, expressed as the estimated annual probability of death for a given hazard return period.  Societal risk is the number of expected fatalities to the population of a group, quantified using frequency of occurrence vs. number of fatalities statistics.  A proper risk assessment will address both individual and societal risk.  An individual will consider a landslide that kills one person (i.e. themselves) as bad as a landslide that kills numerous.  A society will consider a landslide that kills many people much worse than an event that kills just one.   2.5.1 Individual risk Decision criteria are typically estimated by individual risk if the effects of a landslide are local and specific to a particular individual (Porter and Morgenstern, 2013).  This risk should be insignificant compared to the residual risks incurred in the person’s day-to-day life.  Maximum tolerable risk criteria, such as annual probability of a fatal car accident, are often a benchmark for exposure to individual risk.   27   2.5.2 Societal risk Societal risk is the total potential losses to a community as a whole, or the chances of any person in a community being harmed by an incident.  In addition to the hazard, temporal, and spatial probabilities, societal risk requires an estimate of the number of people in harm’s way and a bench mark to compare its severity.  Societal risk is typically calculated with either an F-N curve or a risk interval.  If exposure varies within a society, the group is subdivided into uniform levels of exposure and results are summed (Porter and Morgenstern, 2013).    2.5.2.1 F-N curves An F-N curve is a log-log plot of cumulative frequency of various accident scenarios against the number of fatalities associated with each event.  An acceptable return interval, say 1 fatality in 10,000 years, is plotted, and a line is projected to the axes at a slope dependent on the number of people at risk (called aversion).  A suite of event frequency vs. number of fatality pairs is superimposed over this criteria line.  If any point on the curve plots above the criteria line, it is an unacceptable risk.  Figure 16 is an example. 28   Figure 16. Example of F-N curve and criterion line  Drawing an F-N curve requires a history of events.  In many applications the data does not exist.  Kendall et al. (1977), for example, developed nuclear power risk tolerance criteria for a single catastrophic event.  Figure 17 is a modification of Kendall et al.’s F-N criteria.  Porter and Morgenstern (2013) and others adopted a similar approach for natural landslides, but caution there is no universally-applicable acceptability criteria.     29   Figure 17. Example F-N curve with Kendall et al. (1977) tolerance criteria  The graph has four regions: unacceptable risk, tolerable risk that is ALARP, risk acceptable to most members of the population, and rare but catastrophic events that require intense scrutiny.  Most residential regulations require natural landslide risk within the ALARP or broadly acceptable regions (e.g., DNV, 2009).  2.5.2.2 Risk intervals Risk intervals are an easy communication tool to summarize the overall level of societal risk, expressed as fatalities per year.  They do not have any relation to decision criteria, but are useful 30  in conjunction with F-N curves to compare landslide risk to relatable events (e.g., risk of a car accident).    Risk intervals are the sum of the F-N pairs: ܴܫ ൌ ∑ܰܨఈ                                            [7]  where α is an aversion factor for the number of fatalities and the slope of the FN criteria line (1 fatality: α=1) (HSE, 2009).  2.5.3 Acceptability Risk acceptability is a group discussion involving all stakeholders.  Ultimately it is the decision of the owner.  An acceptable risk is a loss every stakeholder is prepared to accept.  A wall failure in a completed or evacuated pit may be an example of an acceptable risk.  A tolerable risk is the range of potential losses society can tolerate to obtain a net benefit.  Working below a potential landslide expected to fail in the distant future may be a tolerable risk.  A society may include people exposed to either voluntary or involuntary risk.  A person voluntarily at risk is aware of the situation and receives a benefit, such as a faster commute by driving to work.  A person involuntarily at risk is unaware of the hazard or its consequence.  This may be a homeowner unaware their property is on a flood plain.    2.5.3.1 Industrial risk criteria Choosing a risk criterion is a difficult task.  Whitman (1984) provides an FN curve of societal tolerability for various industries, and places mine slopes at 1:1,000.  Oboni and Oboni (2013) illustrate that risk perception has changed since Whitman’s work and how it is problematic to 31  assign bounds to an entire genre of hazard.  A mine should develop its own unique risk acceptability criteria.  Table 1 is a compilation of industrial landslide risk precedents.    Table 1. Industrial precedents for acceptable and tolerable landslide risk Group at risk Context Description Risk return period1 Source Public Fraser Valley Regional District residential development Tolerable 1:10,000 Berger (1973) British Columbia highways Tolerable 1:10,000 Porter and Morgenstern (2013) Buildings in Hong Kong Tolerable 1:10,000 Reeves et al. (1999) Proposed buildings in Hong Kong Tolerable 1:100,000 Reeves et al. (1999) Buildings in the District of North Vancouver, Canada Tolerable 1:10,000 DNV (2009) Proposed buildings in the District of North Vancouver, Canada Tolerable 1:100,000 DNV (2009) Highway landslide risk in New South Wales Tolerable 1:1,000 Stewart et al. (2001) Established dams Tolerable 1:10,000 BCHYDRO (2003) Established dams Tolerable 1:10,000 ANCOLD (2003) Proposed dams Tolerable 1:100,000 ANCOLD (2003) Engineering projects Not reported 1:100 Whitman (1984) Engineered and natural slopes Tolerable 1:10,000 AGS (2000) Proposed engineered slopes or modifications to natural slopes Tolerable 1:100,000 AGS (2000) Industrial hazard Acceptable 1:10,000 HSE (2001) Established dams Not reported 1:100,000 Wellington and McDonald (1992) Workers  Industrial hazard Tolerable 1:1,000 HSE (2001) Open pit mine Tolerable 1:1,000 -1:10,000 Terbrugge et al. (2006) Railway Tolerable 1:10,000 Bunce and Martin (2011) Notes: 1. Risk return period is for individual risk.  32  Chapter 3: Methodology, database development and data attributes 3.1 Scope and data sources Validating established empirical relationships requires compiling a dataset of open pit slope failures and analyzing their behaviour against established trends.  A comprehensive public-domain literature search returned ninety-six open pit slope failures that included a runout component, involving over fifty mines. Anonymous sources provided another nine case histories. Appendix A presents a detailed accounting of each case.  Primarily, these failures were extremely rapid landslides that meet Hungr et al.’s (2014) description of rock or debris avalanches. One case was rotational with toe runout (case 6).  Low velocity and small volume (<40,000 m3) failures retained by effective slope management measures (e.g., Hamel, 1970; Brawner, 1971; Newcomen and Martin, 1988; Martin and Mehr, 1993; Newcomen et al., 2003) were excluded from the dataset.  Failures where material funneled into collapse features above underground workings related to block caving (e.g., Brummer et al., 2006) are also excluded.  If unspecified, volume estimates are assumed in-place.  Where references provide both in-place and bulked failure volumes, plots use the in-place volume for consistency. Wherever possible, additional geometric estimates are taken from satellite imagery, Appendix B, particularly: Google Earth Pro, NASA earth observatory, UNOSAT, Geoscience Australia, ESRI, and physical aerial photographs.    33  3.2 Data reliability  3.2.1 Availability Broadly speaking, the mining industry has an aversion to publishing case histories describing their pit slope failures, although exceptions can be found. Case histories were published in the 1970s or earlier as the industry was building its knowledge base and searching for common stability issues and mitigation strategies. Sharing case histories was promoted to learn from each other’s experiences. In the 1980s, this practice appears to have fallen out of favour presumably in response to legal and public disclosure concerns, but also because mining slope stability conferences became less common. Recently, the past five to ten years have seen the mining geotechnical community returning to the practice of sharing case histories, primarily through the “Slope Stability” proceedings from the International Symposium on Open Pit Mining and Civil Engineering, which has been held approximately every two years since its relaunch in 2006. Nevertheless, the 20 year lull in publishing has left very few case histories, scattered across the public domain.  Those that do exist are mostly written as conference papers, Figure 18, where the details provided are not as thorough as would be typically found in a peer-reviewed journal paper. This sometimes required that more than one source be consulted to obtain the necessary data. Thus, a significant and time consuming contribution of this thesis is the literature review collecting and cataloging the pit slope failures compiled in Appendix A.   34   Figure 18. Timeline of data source publication  3.2.2 Bias An open pit has the advantage, relative to natural landslides, of removing morphological features, vegetation, and liquefiable substrate while controlling travel path angle and roughness.  As such the dataset presented here is a well constrained subset of landslides.  The narrow 35  selection of pre-event characteristics introduces a bias in the sample towards unobstructed rock and debris avalanches running down a uniform slope onto a flat surface.  Also, people tend to publish large, mobile, interesting failures more often than those mitigated by effective slope management.  Building a dataset with greater diversity is desirable but likely only possible with access to mine failure reports.  A further advantage of mine slopes over natural landslides is that most have monitoring instruments and a history of geotechnical study.  Most of the parameters reported in literature and extracted here are tested or measured.    The data are from over 50 mines across the world.  No preference was given to particular regions or operations, however authors at certain mines publish more frequently than others.  Almost one third (31%) of the data comes from four operations: Boron, Goldstrike, Gold Quarry, and various pits in the Warda Valley Coalfield, Figure 19.    Cases from Boron tend to be planar failures in poorly cemented sandstone, but failures at the other three mines occurred in various materials, by various mechanisms, and had a range of runout characteristics.  36   Figure 19. Distribution of mines contributing case histories   3.3 Data population: Failure description 3.3.1 Volume Estimating landslide volume is a difficult task in any context.  Fortunately, parameter uncertainty is perhaps less prominent in this study as volume estimates are derived from comparisons of pre and post event digital elevation models (DEMs) and counting clean-up trucks.   Established runout research tends to focus on exceptional mobility cases involving large landslides.  A common hypothesis is that runout is fundamentally different for small and large landslides, where small landslides behave according to Coulomb’s Law using the kinematics of 37  sliding and do not develop the flow behaviour seen in larger events.  The cutoff for a large natural landslide seems to be between 1,000,000 m3 and 5,000,000 m3 (Hsü, 1975; Davidson, 2011).  A mining context requires a different perspective.  Open pits are rarely deep enough to produce such a large landslide.  The distribution of un-bulked failure volumes, Figure 20, shows the low frequency of events >10,000,000 m3, and no events occur above the 100,000,000 m3 range.     Figure 20. Distribution of landslide volume, n=105  Similarly, the runout of a small natural event may pose no consequence or even go unnoticed.  The 3,300 m3 failure in Figure 21 is a good example of how smaller volume failures are just as dangerous and disruptive as larger ones at an operating mine.   38   Figure 21. Example consequences from small volume landslides. Note truck buried in slide debris  The volume cutoff was chosen in this study by comparing the 105 case histories with others where failure did not involve a runout or were retained by effective slope management (e.g., benches and berms).  It is also important that the volumes selected be in the range used for the established landslide runout methods.  Based on this, the cutoff of how big a failure needs to be to disrupt mine operations and remain relevant to the natural landslide datasets was determined to be 40,000 m3.  Smaller volume failures like in Figure 21 deserve their own risk management plan.  Exclusion from this research is mainly because they are under-reported in the public domain.   39  3.3.2 Failure mechanism and landslide classification Mining and natural geohazard research each have their own preferences for classifying slope instabilities, often confused by local names or language.  For example rotational, rock mass, and slump describe the same failure mechanism.  Words like complex are a catch-all for combinations of mechanisms.    Binning failures into categories might be a simplification but it is preferred to ambiguity.  Hungr et al. (2014) provide an update to the Varnes landslide classification scheme to group failures by movement mechanisms and incorporate geotechnical terminology.  In this system it is up to the user to decide whether the initiation or the motion after detachment is most important.  For example, the Bingham Canyon cases initiate as a rock planar slide, but fall to the pit floor as a rock avalanche.  Nearly all cases travel down the pit wall as rock or debris avalanches.  Figure 22 is the distribution of classification for failure initiation mechanisms of the pit slope failure data set.  40   Figure 22. Distribution of failure mechanism, n=105  3.3.3 Trigger A trigger is an event that initiates slope failure.  Figure 23 illustrates the triggers reported in the literature or inferred from the failure description.  “Long-term weakening” refers to cases where the trigger event occurred long before the failure but initiated the sequence of events.  For example, failure S-09-B at the Goldstrike mine (case 45) initiated by daylighting a structure twenty months prior to slope collapse (Armstrong, 2011).  This led to a coalescence of structures and ultimately resulted in a step-path failure, classified as a rock irregular slide.   41   Figure 23. Distribution of reported triggering events, n=105  3.3.4 Number of failures Eighteen of the pit slope failures involved at least two distinct events.  A continuous series of low volume failures can produce shorter runout lengths than empirical models would estimate based on the total volume.  Figure 24 is the quantity of events in each landslide.  42   Figure 24. Distribution of events per landslide, n=105  3.4 Data distribution: Material attributes 3.4.1 Lithology Source materials include a variety of lithologies from unique ore deposition environments and various degrees of alteration and weathering.  Figure 25 is the distribution of materials grouped into broad classes.  Altered rock zones, fault debris, and saprolite have their own categories because the disturbance history is more important to their behaviour than the regolith. Note seventeen of the sedimentary cases are from just two mines, both with poorly cemented sandstones.   43   Figure 25. Distribution of simplified material type groupings, n=105  3.4.2 Fabric Rock mass fabric represents preferentially oriented planes of weakness within a rock mass.  Typical examples are bedding, schistosity, and foliation.  Figure 26 presents the orientation of the fabric with respect to the pit wall. 44   Figure 26. Distribution of rock mass fabric orientation, n=105   3.4.3 Strength Literature sources provide material strength in a variety of forms: uniaxial compressive strength, Mohr-Coulomb envelopes, bulk and shear moduli, strength grade estimates, and qualitative descriptions.  ISRM’s (1978) strength grade groupings are a useful assimilation because they provide uniaxial compressive strength ranges with qualitative descriptions and field tests.  This provides continuity to group rocks described with various classifications or strength systems.  Figure 27 is the distribution of rock strength grade (R ratings).  Soil strength methods may better describe some cases but for comparison purposes these are reported as R0 here.  This is acceptable because none of the relationships discussed quantitatively rely on material strength.    45   Figure 27. Distribution of strength grade, n=105  3.4.4 Rock mass rating Bieniawski’s (1976) rock mass rating (RMR) is an empirical measure of rock mass quality, incorporating intact strength, degree of fracturing, the condition of the discontinuities separating intact blocks, and groundwater.  Contemporary publications report RMR or GSI (Marinos and Hoek, 2000), the latter being based on RMR, and many older publications have sufficiently detailed qualitative descriptions or photographs to estimate an RMR.  The groupings presented in Figure 28 correspond to Bieniawski’s 1976 version of RMR.  It is ambiguous whether authors account for groundwater in their RMR.  RMR’76 allocates less significance to groundwater and has a direct correlation with GSI.  Potential error is recognized but should be limited by RMR’s broad groupings.  Regardless, none of the relationships discussed rely quantitatively on RMR. 46   Figure 28. Distribution of rock mass rating, n=105  3.5 Data attributes: Slope configuration 3.5.1 Slope angle Open pits have the advantage of a quality-controlled slope angle, in many cases optimized to the geotechnical properties of the slope.   Figure 29 is the distribution of slope angles for the database.  If the source and deposit are contained on a single bench-stack the angle presented is the bench stack angle, otherwise, the overall angle. 47   Figure 29. Distribution of slope angles, n=105  3.5.2 Path morphology Down slope morphology dictates the path shape of a slope failure.  Abele (1974) described four categories of travel paths interacting with morphology: (i) travels down and stops on slope, (ii) travels across narrow valley and runs up opposing wall, (iii) travels across a wide valley or plain, and (iv) travels along a valley.  Figure 30 is the distribution of path morphologies loosely based on Abele’s categories.  Deflections from the landslide striking a valley wall at an oblique angle are also relevant here.  Obstruction or deflection at the opposing pit wall could introduce curvature to the travel path or bulking of the toe.  48  Channeling at corners or along ramps may change the runout shape, however not to the extent that valleys or gullies in natural landscapes would.  Investigation into the effect of deflection and channeling is presented in Section 5.4.   Figure 30. Distribution of travel path attributes, n=105  3.5.3 Wall shape The curvature of the pit wall could provide some confinement to the travel path.  Convex bull nose features typically fail because side constraints are mined away reducing stresses acting on the lateral release planes. Whether these have an effect on mobility or lateral spread is unknown.   Figure 31 provides qualitative descriptions of wall curvature for each case.  49   Figure 31. Distribution of wall shape, n=105  3.6 Data attributes: Runout 3.6.1 Fall height Fall height is the vertical distance from the main scarp crest to the deposit toe.  Figure 32 is the distribution of reported or measured fall heights.  Note approximately a quarter of the dataset has a fall height less than 100 m.  Legros (2002) asserts several empirical runout relationships are inadequate for cases with a large volume and short fall height.   50   Figure 32. Distribution of fall height, n=105  3.6.2 Runout length Runout length is the horizontal distance along the centerline of the travel path from the main scarp to the distal toe of the deposit.  Figure 33 is the distribution of reported or measured runout lengths. The shape of the pit and distance to the opposing wall may limit the achievable runout length.  The relationship between runout length and obstruction (Figure 30) is discussed in Section 5.4.  51   Figure 33. Distribution of runout length, n=105  3.6.3 Deposit thickness and inundation area None of the publications from which the data was extracted provided deposit thickness measurements.  Cross-sections with deposit profiles are available for some, but these appear to be sketched and are of questionable value.    Data could be found on the inundation area in plan. Figure 34 is the distribution of deposit planimetric inundation areas.  Only a subset (47) of cases has sufficient data to measure their surface area.  Note the bin size changes at 100,000 m2.   52   Figure 34. Distribution of deposit inundation area, n=47  3.6.4 Deposit shape Deposit shape in a natural environment conforms to the topography.  A flow may thicken at valley constrictions, super-elevate at bends, and spread in open terrain. Pit slope failures act the same way but are usually constrained by a bowl-shaped topography, where bends and obstructions occur as the opposing wall.  Qualitatively, deposit morphology in photographs appears either as a talus pile sitting below the source (Figure 35a) or as thick flow-like deposits thinning away from the source (Figure 35b).  None appear as discontinuous piles or a thin veneer.  Figure 35c and 33d are typical morphologies for talus pile and flow-like deposits, respectively, obstructed by a berm or opposing wall.  53  Some particularly fluid failures have lobate finger features with concentric transverse ridges as in Figure 35b.    Figure 35. Example deposit morphologies for (a) talus pile and (b) flow-like deposits free to spread or obstructed (c) and (d). Photograph are from cases 4 (Martin, 1990), 38 (Sheets et al., 2014), 86 (Szwedzicki, 2001), and 27 (Sharon, 2011), respectively.   54  3.6.4.1 Aspect ratio There appear to be two common deposit shapes.  Figure 36 depicts deposit width measurements taken at 0%, 10%, 25%, 50%, 75%, 90% and 100% of the deposit length, normalized to deposit length to provide an aspect ratio.    The first shape (black) is a wide talus cone sitting at its angle of repose.  Typically these are an apron hung on or below the source as in Figure 35c.  A more prevalent shape (red) is a long, thin deposit where the width is similar to the source width.   Figure 36. Map of deposit aspect observations   55  3.6.4.2 Spreading Figure 37 is a comparison of the degree of spreading, the ratio of mean source and deposit areas, versus volume, symbolized by broad material categories.  The spread is generally centralized around 1, indicating Areadeposit~Areasource and that this data does not show significant spread.   For context, Abele (1974) found natural rock avalanches in the Alps spread between ratios of 1 and 10 depending on material type, and spread decreased with volume.  A modest negative trend appears in this open pit data and interestingly the weak and weathered rocks appear to spread most.       Figure 37. Degree of spreading in open pit slope failures  56  3.7 Data limitations 3.7.1 Error This study relies on published failure descriptions written from an operations and slope stability perspective.  Only a few of the publications from which the data was extracted explicitly discuss runout.  Plan maps, cross-sections, and satellite imagery depicting failed material were the basis for runout parameter estimates. None of the publications provide velocity, run-up, or super-elevation estimates.  Confirming the reported runout characteristics with mine personnel is beyond the scope of this study, but the potential for error is recognized.    3.7.2 Incomplete observations At a minimum all cases include failure volume, fall height, and centerline runout length.  Not all cases have complete descriptions of the material, failure, or original slope angle.  For example, a paper describing several historic failures may present the current slope angle, but omit the angle at the time of each failure.  Cases with incomplete observations are included if the assessment does not rely on the missing attribute, but are otherwise excluded.  Therefore, different mobility relationships contain different size datasets. 57  Chapter 4: Empirical analysis of data 4.1 Introduction This chapter presents the validation of established empirical mobility relationships developed for natural landslides in comparison to the open pit dataset.  Appropriate models should:  Provide a prediction reasonably similar to the observed behaviour;  Display similar mobility trends;  Rely only on assumptions relevant in an open pit context; and  Minimize sensitivity on difficult to estimate parameters.  4.1.1 Relationships analyzed An open pit has the advantage of removing morphological features, vegetation, and liquefiable substrate while controlling travel path angle and roughness.  Methods developed for channeled flow (Benda and Cundy, 1990; Fannin and Rollerson, 1993; Zimmerman, 1997), small volumes involving less than ~1000 m3 (Finlay et al., 1999; Rickenmann, 1999), and volume balance (Cannon, 1993; Fannin and Wise, 2001) landslides do not lend themselves well to a mining context.  The mobility characteristics used in the cited studies incorporate factors not relevant for pit slope failures.  Similarly, relationships describing the centre of mass of the source and deposit are excluded.  Centre of mass is difficult to estimate and inconsequential to a person struck by the leading edge; farthest reach is considered more appropriate here.  Models relying on input parameters that cannot be estimated a priori, like Campbell’s (1989) particle collision angle, are also excluded.    58  Boulder rollout methods are excluded but deserve their own study.  Literature and satellite imagery available for this thesis do not have sufficient detail to describe the boulder rollout.  4.1.2 Validation procedure Validation and parameter sensitivity were assessed using k-fold cross validation (Stone, 1974).  Cases are grouped randomly in k equal sized folds.  Each fold retains a subset of cases as a validation set and the remaining cases are the training set.  The process is repeated k times with each fold having a distinct validation set.  This method is well suited to small datasets that cannot afford to lose data to a validation set. All cases have a role in both training and validation, and each case is used for validation only once.    Root mean square error (RMSE) and normalized index in percent are calculated for each relationship and parameter variance, as in Equations 8 and 9, respectively: ܴܧܵܯ ൌ ට∑ ሺ௑௣௥௘ௗ௜௖௧௘ௗି௑௢௕௦௘௥௩௘ௗሻమ೙భ ௡      [8] ܰ݀݁ݖ݈݅ܽ݉ݎ݋	ݔ݁݀݊ܫ ൌ ௑௣௥௘ௗ௜௖௧௘ௗି௑௢௕௦௘௥௩௘ௗ௑௢௕௦௘௥௩௘ௗ ൈ 100    [9]  Normalization can be positive or negative to observe if the model results in over or under predicting the runout.   A negative normalized index implies the mobility index underestimates runout, and vice versa.  Using RMSE and normalized index together provides context for goodness of fit.  For example, a large landslide with 100 m runout error may in fact only be off by a small percentage.  A small landslide may have a modelled runout off by 50%, but in fact, that distance may be inconsequentially small.   59   4.2 Volume models 4.2.1 Fahrböschung angle The simplest empirical relationships disregard details of underlying mechanisms and model bulk behaviour.  The Fahrböschung angle is the simplest to apply and particularly amenable to rapidly developing scenarios in complex ground.  Figure 38 is the open pit dataset superimposed on established natural rock avalanche Fahrböschung relationship developed by Sheidegger (1975), Li (1983), and Davidson (2011).  All three are an assemblage of rock avalanche datasets with various geology, failure mechanism, geomechanical properties, slope configuration, and path morphology.  The holistic nature of these models captures the inherent complexity of each event.  This, however, leaves significant scatter.    The landslide runout trends in Figure 38 can be seen to generally agree with the open pit data set, although it should be emphasized that the fits are plotted in log-log space.  Scheidegger’s (1975) and Davidson’s (2011) fit reasonably captures the mean trend while Li’s (1983) under predicts a significant number of the cases.    The linear regression for the open pit data has RMSE of 109 m and normalized index of 3.1%.  Error is normally distributed, as can be seen in Figure 39.   60    Figure 38. Open pit data with Scheidegger (1975), Li (1983), and Davidson (2011) best fit Fahrböschung angle vs. volume regressions   61   Figure 39. Error distribution for Fahrböschung angle vs. volume mobility index  4.2.1.1 Stratified Fahrböschung angle Some correlation coefficients for grouped Fahrböschung relationships are too weak to be used for prediction.  Nicoletti and Sorriso-Valvo (1991) and Corominas (1996) divided data into more homogeneous populations to improve the regression equations.  Separating trends based on fundamentally different behaviours (debris flows, for example) should give a better prediction.  Closer interrogation of the material behaviour reveals two trends, as shown in Figure 40.  The mechanisms causing the separate trends are discussed in Section 5.3.  Li’s regression reasonably 62  describes the less mobile trend.  Equations 10 and 11 are best fit least squares regression lines for the two mobility trends, respectively.      Figure 40. Tangent of Fahrböschung angle vs. volume trends based on material behaviour  log ቀு௅ቁ ൌ െ0.138 logሺ݁݉ݑ݈݋ݒሻ െ 0.895     [10] log ቀு௅ቁ ൌ െ0.151 logሺ݁݉ݑ݈݋ݒሻ െ 0.587      [11] 63  Separating the data into two trends improves the correlation, with RMSE 48 m (0.8%) for the less mobile trend and 61 m (1.5%) for the more mobile trend.  Figure 41 is the error distribution.   Figure 41. Error distribution for stratified Fahrböschung angle vs. volume mobility index  The data appears normally distributed but contains tails.  The outlier cases are influenced by obstructions at the opposing wall (less mobile cases) or flow-like behaviour (more mobile cases). These are discussed further in Chapter 5. Other attributes used in previous studies like vegetation and channeling topography do not exist in a mining context.  Nonetheless, narrowing the data to a single mechanism and creating divisions for path deflection may be a useful exercise or identify the cause of the separate trends in Figure 40.    64   Figure 42 compares the open pit dataset with Corominas’ (1996) regressions for landslide classification and path obstruction, respectively.  a)  65  b)  Figure 42. Open pit data compared to Corominas (1996) (a) landslide classification and (b) path obstruction Fahrböschung angle vs. volume mobility relationships    Here the rockfall/rock avalanche regression can be seen to provide the closest fit and intuitively represents the most similar mechanism seen in open pits, but nevertheless over predicts mobility in general. The inverse relation between Fahrböschung angle and volume remains regardless of path attribute.  An inflection appears at 1,000,000 m3 where the data follows more closely Corominas’ deflected regression.  This may indicate a change in mechanism of motion where the 66  mass becomes flow-like, as postulated for natural landslides (Hsü, 1975; Davidson, 2011).  Case 27 (Figure 35d) is a good example of runout forced to bulk and deflect at an opposing wall.  The runout is of course shorter than it could have been.  However, these cases still fall within the scatter of the data and do not stratify themselves into a separate trend.    4.2.2 Excessive travel distance Hsü (1975) observed the runout of small landslides is analogous to a block sliding down an incline, but that larger landslides appeared to flow to surprisingly long distances.  He suggested the change in behaviour is at a volume threshold of 5,000,000 m3.   The inflection in Figure 42 suggests this observation may be relevant to an open pit context.   Figure 43 is a plot of excessive travel distance for pit slope failures.  The trend is flat for smaller landslides, followed by a positive semi-log correlation for larger events.   In his study, Hsü sketched a linear fit and did not provide an equation.  The RMSE and normalized index for the open pit data, assuming a logarithmic fit (data does not approach an asymptote), are 96 m and 6.2%.  Figure 44 shows the error is comparatively wide and lognormally distributed.  Given that Hsü decided to separate his data into two trends (low and high mobility), the single trend is an improvement on the original work.    67   Figure 43. Open pit data with Hsü (1975) and Hungr (1981) excessive travel distance mobility indices  68   Figure 44. Error distribution for excessive travel distance mobility index  McSaveney (1975) pointed out the concept of excessive travel distance has no theoretical basis.  More than a predictive tool, the value here may be Hsü’s qualitative observation that small volume landslides do not develop into a flow.  More large-volume cases are required to assess the suitability of this relationship.  Beyond 10,000,000 m3 it is unclear if the trend continues to be linear or approaches an asymptote.     Hungr (1981) postulated most natural landslides have a gradual bi-linear profile, and typically, the runout material deposits beyond the slope break.  He also noticed that the slope break of many natural landslides is approximately 30°, and therefore the excessive travel distance 69  remaining is simply the length of the deposit.  Dividing the deposit length by its width gives a range of curves given by Le~cV1/3, where c ranges from 4.4 to 8.8.  The fit in Figure 43 adjusted to this dataset is: ݁ܮ ൌ 3.3ܸଵ/ଷ െ 275       [12]  A useful by-product of this analysis is the relationship between volume and deposit thickness.  The poor correlation to this model in a mine is because many deposits do not fully detach from the source and the gradual 30° inflection does not exist.  An open pit has a maintained overall slope angle and an abrupt change to horizontal at the pit floor.  Many deposits drape on the benches below the source and do not separate and flow beyond a 30° reach.   4.2.3 Normalized excessive travel distance In their study of geomorphic controls on landslide runout, Nicoletti and Sorriso-Valvo (1991) found a weak semi-log correlation of excessive travel distance normalized by the total runout length against volume.  They found mobility had no dependence on fall height.  Figure 45 is the open pit data superimposed on this relationship.  There is a positive correlation that can be seen with significant scatter at low volumes.  The RMSE and normalized index for this index are 120 m and 10.6%, respectively with multi-modal, lognormally distributed error (Figure 46).  70   Figure 45. Open pit data with excessive travel distance normalized to total runout length vs. volume  71   Figure 46. Error distribution for normalized excessive travel distance mobility index  4.2.4 Runout length Several researchers (Hsü, 1975; Davies, 1982; Corominas, 1996; Legros, 2002) point to fall height as simply contributing to scatter.  Although its role is clear in analytical methods like a mathematical energy balance, it is less so for physically meaningless proxies like the Fahrböschung angle.  Treating fall height holistically presents the advantage of fewer inputs.  Figure 47 is a horizontal runout length against volume plot for the pit slope failure dataset. 72   Figure 47. Open pit data with runout length vs. volume mobility index  As expected mobility increases with volume.  Several smaller volume cases (e.g., 97, 105) that appeared to have mobility as expected have become outliers.  The RMSE is 116 m and mean normalized index is 13%, with scatter close to 400 m for the low volume cases.  Figure 48 is the lognormal distribution of the error showing a general under prediction.   73   Figure 48. Distribution of error for runout length vs. volume mobility index  Corominas (1996) used a comparison of fall height to horizontal travel length to show that if two identical failures occur from different fall heights, the one with the larger drop will travel farthest.  Figure 49 is a similar plot derived from the open pit data that shows fall height has an influence on runout length. 74   Figure 49. Comparison of open pit failure fall height to runout length  4.2.5 Inundation area Estimating a two-dimensional deposit area is an attractive addition to locating the distal toe.  Established inundation area relationships (Li, 1983; Iverson et al., 1998) have used datasets of various landslide classifications to compare both reach and spread of landslides.  The maximum inundation area of an average flow can be reasonably described in log-log space as A = cV2/3.  75  Griswold and Iverson (2008) compared lahar, debris flow, and rock avalanche cases to show planimetric shape is scale invariant, but different landslide types require unique y-intercepts, c. Figure 50 is the open pit data plotted with Griswold and Iverson’s (2008) and Li’s (1983) regressions.     Figure 50. Open pit data with Li (1983) and Griswold and Iverson (2008) planimetric deposit area vs. volume relationships  76  Open pit landslides show the same self-similar (slope=2/3) deposit shape, but with a less mobile y-intercept (c=6).  Given that no previous dataset included either open pits or landslides flowing into a bowl shaped travel path, the less mobile y-intercept is expected.  Inundation area is only available in 47 (45%) of the cases because it is rarely reported in the literature and high resolution satellite imagery is a recent innovation.  The RMSE and normalized index for this index is 4.6x104 m2 and 10.1%, respectively, uniformly distributed with outliers (Figure 51).     Figure 51. Error distribution for inundation area vs. volume mobility index  Quality of areal predictions are difficult to interpret.  Large (+/- 50%) but uniformly-distributed error provides a misleadingly good average.  Figure 52 is Google Earth images showing full (white) and reduced 50% (red) inundation areas for the two prevalent deposit aspects to contrast the prediction quality.  77    Figure 52. Demonstration of achievable inundation area prediction quality  Predictable, albeit large, error is still useful.  Inundation area combined with other mobility relationships is useful to map a hazard back from the estimated deposit toe.  Figure 53 is a correlation heat map of volume, inundation area, and Fahrböschung angle showing all three increase proportionally to each other.  Figure 53. Correlation heat map comparing volume, inundation area, and Fahrböschung angle (red=most mobile, green=least mobile)  H/LInundation Area(Mm2) <0.10.1 to 0.50.5 to 11 to 55 to 10>10<0.0250.025 to 0.050.05 to 0.10.1 to 0.250.25 to 0.5>0.5Volume (Mm3)78  4.3 Slope angle models 4.3.1 Fahrböschung angle Hunter and Fell (2003) recognised runout of waste dump flow slides is sensitive to path angle and insensitive to volume.  Their dataset included path confinement conditions and volume ranges (103 to 107 m3) similar to those seen with open pit failures.  Figure 54 presents a linear space Fahrböschung angle versus original wall angle plot for the pit slope failure dataset.  Note Hunter and Fell used the angle of the topography, not the waste dump.  Like the waste dumps, the H/L ratio increases with the slope angle without the separate trends seen in the volume dependant relationship, and fits sufficiently well to plot in linear space.    The x-axis of Figure 54 is the bench stack angle if the case was contained to one set of benches, otherwise the overall angle.  The user should recognize volume is implicitly contained in the decision whether the failure will encompass several bench stacks.  More data is required to assess the suitability of this method for slopes steeper than 50°.  Section 4.7.2 shows the failures on the steeper walls are generally smaller.  Mobility may remain relatively constant above an angle threshold, as it appears to do below a certain volume.  Logically, mobility of smaller and steeper failures cannot decrease linearly forever.   These steeper cases illustrate an important limitation of this index and perhaps an additional threshold exists at 50°.  For now, goodness of fit statistics and Equation 13 exclude these cases.   ܮ/ܪ ൌ 0.488 tanሺ݁݌݋݈ݏ	݈ܽ݊݃݁ሻ ൅ 0.117     [13]  79  The remaining data have a RMSE of 87 m and mean normalized index of 1.6% with normally distributed error (Figure 55).     Figure 54. Open pit data with Fahrböschung angle vs. slope angle mobility index  80   Figure 55. Error distribution for Fahrböschung angle vs. slope angle mobility index  4.3.2 Runout length Travel path variability might be the source of scatter in estimating runout length from volume alone.  Figure 56 is the observed runout length plotted against slope angle.  There is no discernable trend and 700 m of scatter, reinforcing the danger of estimating runout length from a single parameter.    81   Figure 56. Open pit data with runout length vs. slope angle mobility index  4.3.3 Normalized excessive travel distance An alternative presentation for Nicoletti and Sorriso-Valvo (1991)’s index is to plot it against slope angle, Figure 57.  Incorporating Hsü’s excessive travel distance accounts for the lower end volume threshold and the deviation from the trend at steeper angles in Figure 54.   82   Figure 57. Open pit data with normalized excessive travel distance vs. slope angle mobility index  Data appears to follow a negative linear trend with RMSE of 96 m and normalized index of 3.1%.  Error is normally distributed but bi-modal (Figure 58), potentially increasing at steeper slope angles.  83   Figure 58. Error distribution for normalized excessive travel distance vs. slope angle mobility index  4.4 Potential energy models 4.4.1 Fahrböschung angle Open pit failure mobility observations thus far seem to support Howard’s (1973) hypothesis that there is a lower-bound mobility threshold, and that without accounting for potential energy, other influences may create separate trends.  Figure 59 is the open pit data on Howard’s energy balance approach.  His data and talus slope threshold are plotted for comparison.    84   Figure 59. Open pit data with Fahrböschung angle vs. potential energy mobility index  The open pit data generally agrees with Howard’s observation that lower potential energy (smaller) landslides runout in a similar way and larger failures trend towards increased flow efficiency and longer runout.  The RMSE is 118 m and normalized index is 3.1%.  The error distribution is presented in Figure 60.  Error is normally distributed but multi-modal with tails.  Over and under prediction appear equally likely by up to 40%.     85   Figure 60. Error distribution for Fahrböschung angle vs. potential energy mobility index  4.4.2 Runout length Comparing length to potential energy has the advantage over Fahrböschung angle of limiting fall height to just the independent variable.  McSaveney’s (1975) power-law trendline appears to fit the open pit data well (Figure 61).     86   Figure 61. Open pit data with runout length vs. potential energy mobility index  The RMSE and normalized index are 93 m and 5% respectively, an improved fit over the single parameter runout length relationships discussed previously.  Both Figure 61 and the distribution of error in Figure 62 show under predicted data behaves normally distributed but over predicted cases are more scattered.  Generally it appears this mobility index over predicts runout length by 10 to 30 %.   87   Figure 62. Error distribution for runout length vs. potential energy mobility index  4.4.3 Inundation area Dade and Huppert’s (1998) constant yield stress model relates inundation area to volume (and ρgH) without having to assume self-similar conical deposit shapes or that landslides within a classification have a similar friction coefficient.  Figure 63 is the open pit data superimposed on Dade and Huppert’s (1998) plot.   88   Figure 63. Open pit data with inundation area vs. potential energy mobility index  The trend is less steep than area vs. volume relationships and provides a positive linear (power-law) correlation.  The RMSE and normalized index are 9.1x104 m2 and 3.1%, respectively.  Error appears multi-modal and randomly distributed (Figure 64).  89   Figure 64. Error distribution for inundation area vs. potential energy mobility index  The weaker correlation (worse by 50,000 m2) and unsystematic distribution compared to Iverson et al.’s (1998) index could be that much of the dataset is frictional, not purely plastic, and Iverson’s assumption of self-similar shape works especially well for open pits.    4.5 Dimensionless model Staron’s (2007) dimensionless inundation area to runout length relationship can be a useful comparison of deposit aspect.  Deposits in the bottom left corner of the graph include those that neither ran far nor covered a large area, creating a thick less-mobile deposit.  Cases in the top right corner ran far and spread to form a thin veneer.  Figure 65 is the open pit data fit to Staron’s 90  model with natural landslide cases to show his intended observation.  There is no discernable trend and data tends to cluster to a small range.     Figure 65. Open pit data with dimensionless mobility index  Data clustering at x=6 is encouraging for the A=6V2/3 relationship developed earlier.  A useful by-product is the data is concentrated around the lower left corner of the plot, indicating thicker deposits with similar aspect ratios, and distinctly different behaviour than natural landslides.    91  4.6 Optimized mobility index Purely geometric mobility relationships appear to separate data into trends if they neglect some factor important to the problem’s geometry.  Minimizing inputs is only an advantage if the omitted factor has no influence. Previously discussed relationships show, at minimum, that volume, fall height, and slope angle are important attributes with respect to runout length.  A new mobility index is proposed to incorporate all of these geometric constraints.  Figure 66 is a schematic representation of this optimized mobility index.     Figure 66. Schematic of optimized mobility index geometry  Intersecting the slope angle and Fahrböschung angle gives two triangles.  The upper triangle is within the wall and describes the source.  The lower triangle extends to the pit floor and describes the deposit.  The cumulative cross-sectional area of the triangles is a measure of 92  mobility.  If slope and Fahrböschung angles are equivalent, the slide debris will come to rest on the wall; i.e., it is not particularly mobile.  Debris that reaches a flat surface but only runs a short distance from the toe would have a small difference in angles and a small triangular area.  Debris that runs far from the slope toe would have a larger difference in angle and larger triangular area, indicating more significant mobility.    The area of the upper triangle is a function of the crest back break, the slope angle, and the Fahrböschung angle, given in Equation 14.  If material reaches the pit floor (Fahrböschung angle<slope angle), the second triangle is a function of the slope angle, Fahrböschung angle, and the fall height remaining below where the upper triangle intersects the wall, given in Equation 15.  The areas are normalized to the square of slope height to account for differently shaped triangles with the same area.  Equation 16 is the cumulative cross-sectional area of the two triangles normalized to fall height.  Figure 67 presents the dataset over this mobility index, symbolized by material properties.   ܣ௨௣௣௘௥ ൌ ௖మୱ୧୬ஒୱ୧୬	ሺଵ଼଴ି஑ሻଶୱ୧୬	ሺఈିఉሻ             [14]  ܣ௟௢௪௘௥ ൌ ሾுమା௅మିሺ௖௦௜௡ሺଵ଼଴ିఈሻ ୱ୧୬ሺఈିఉሻ⁄ ሻమሿୱ୧୬ఉୱ୧୬	ሺఈିఉሻଶୱ୧୬	ሺଵ଼଴ିఈሻ    [15]  ܱ݀݁ݖ݅݉݅ݐ݌	ݕݐ݈ܾ݅݅݋݉	ݔ݁݀݊݅ ൌ ஺ೠ೛೛೐ೝା஺೗೚ೢ೐ೝுమ   [16] 93   Figure 67. Open pit data with optimized mobility index, as define in Figure 66  Incorporating slope angle unifies the dataset to one trend by making the material property influence implicit, leaving a purely geometric approach.  Equation 17 is the power-law fit:  ஺ுమ ൌ 0.384ሺ݁݉ݑ݈݋ݒሻ଴.ଶସ଴      [17]  Equation 18 is the runout length beyond the slope toe and Equation 19 is the total runout length.  94  ݋ܮ ൌ ଶሺுమሻ൫଴.ଷ଼ସ௏బ.మరబ൯ି௖మ௧௔௡∝ுି௖௧௔௡∝      [18]  ܮ ൌ ݋ܮ ൅ ு௧௔௡∝      [19]  For this dataset the RMSE is 69 m and the mean normalized index is -4.5%.  The error is close to normally distributed with a tighter range than all the other relationships (Figure 68).     Figure 68. Error distribution optimized mobility index   95  4.7 Parametric analysis 4.7.1 Sensitivity An open pit slope has the advantage of having a well-defined geometry, deformation monitoring, and structural and geotechnical models.  As such, parameter selection is less complicated than for natural landslides.  While uncertainty remains regarding the rupture surface and source volume, a priori estimates of slope angle, crest location, material properties, and failure mechanism are reasonably good.  The model precision discussed above assumes the reported inputs are correct and practitioners can reasonably describe their impending failure.  The following subsections illustrate how sensitive the models are to their inputs, how that contrasts with natural landslide parameter uncertainty, and the certainty required to produce a useful result.   Parameters are varied individually for every case over the range of plausible values, up to 100% of their reported value.  The RMSE and normalized index were calculated for each parameter variance.    4.7.1.1 Volume Most researchers studying natural landslide mobility agree volume has an influence on runout.  However the volume of pit slope failures is a narrow subset of the natural landslide spectrum, biased towards the lower volume end.  The usefulness of established volume-dependent relationships must be tempered by this contextual difference.     96  Figure 69 is the Fahrböschung angle minus the slope angle, as defined in the inset, versus volume.  The horizontal trend infers that mobility for this dataset is only modestly dependent on volume.  This agrees with Finlay et al.’s (1999) work where if volume is held constant slope angle emerges as the next most influential parameter.  Figure 69. Open pit data with Fahrböschung angle normalized to slope angle  Figure 70 summarizes model sensitivity to volume.  Intuitively the single parameter relationships (L vs. V and Le vs. V) are highly sensitive to the volume estimate.  Fahrböschung angle, Le/L, and the optimized mobility index are only modestly dependant on volume.  Note how the 97  optimized mobility index method provides a similar quality prediction that is less sensitive to volume, the hardest parameter to estimate.   Figure 70. Model sensitivity to volume   98  4.7.1.2 Slope angle The separate trends in the Fahrböschung angle vs. volume plot have a clear dependence on original slope angle as shown in Figure 71.   Figure 71. Fahrböschung angle vs. volume mobility index symbolized by slope angle  99  Further interrogation of the dataset shows steeper slopes having shorter runout distances.  Abrupt path angle changes are an obstruction to the travel path and consume energy.  Equation 20 is the sliding resistance (T) to a frictional sliding block.   ܶ ൌ ݄ߩሺ݃ܿߙݏ݋ ൅ ܽ௖ሻ߮݊ܽݐ௕      [20]  When the sliding path is curved, bed-normal stress is a function of centripetal acceleration (ac), shown in Equation 21, which in turn is a function of velocity (v) and radius of curvature (R).   ܽ௖ ൌ ௩మோ        [21]  A shallower slope creates a larger radius, Figure 72, decreasing the centripetal acceleration, and therefore presents less basal resistance or energy consumption.   The same effect occurs with lateral spreading (McDougall, 2006).  If everything else is equal, steeper slopes produce shorter runout lengths and less spread.       Figure 72. Exaggerated schematic of slope angle’s effect on centripetal acceleration  100  The data also indicate that larger volume failures generally occur on flatter overall slope angles as these are more likely to incorporate ramps and berms.  Comparing slope angle to the material groupings provides a similar trend; i.e., slope designs in poorer quality rock require shallower slope angles.  The next section presents this parameter covariance.  Figure 73 summarizes model sensitivity to original slope angle.   Figure 73. Model sensitivity to slope angle 101   Slight (<10%) slope angle deviations from design have minor effect on runout length.  The sensitivity analysis beyond 10% is mainly for comparison with other parameters.  Slope angle can be accurately estimated from as-built surveys.    4.7.1.3 Fall height Fahrböschung angle and excessive travel distance relationships, including the optimized mobility index, have fall height in their equations and are 1:1 sensitive.  Figure 74 shows that all of the remaining mobility relationships are also sensitive to fall height.  This is expected because the length travelled and height dropped for an object traveling down an incline are dependant variables.    102   Figure 74. Model sensitivity to fall height  Runout distance’s sensitivity to fall height shown in Figure 49, Figure 74, and below in Figure 78, contrasts with the opinion of several natural landslide researchers who argue fall height simply creates scatter.  The difference may be the same abrupt change in slope angle discussed above, enhanced by the lack of liquefiable substrate.  A natural landscape typically has a gradual transition from mountain side to a gently inclined overburden-rich valley floor.  The landslide may entrain and rapidly load the valley substrate, producing an undrained condition and 103  contributing to a large increase in L while only modestly increasing H.  These valley conditions are not available in an open pit.  4.7.2 Covariance Identifying parameter relationships can decrease uncertainty in individual parameters.  The plausible range of parameter values is often dependant on other conditions and therefore can be further constrained.  For example, theoretically wall angles can range from 0° to 90°, but rock mass quality substantially narrows the achievable angles.    The following subsections present parameter correlation heat maps for Fahrböschung angle, runout length, inundation area, and average deposit width using a traffic light colour scheme.  Red indicates highest mobility, green indicate lowest mobility, and grey indicates no data.     4.7.2.1 Slope angle and volume Figure 75 is a correlation heat map for slope angle and volume.  There are no larger volume failures on steep walls.  The Fahrböschung angle heat map has a strong correlation between volume and slope angle, where large volume landslides on shallow walls have the highest mobility.  Length, inundation area, and width appear to be insensitive to slope angle (vertical columns) but dependant on volume.    104   Figure 75. Volume vs. slope angle correlation heat maps  4.7.2.2 Slope angle and material type Figure 76 is a slope angle vs. material type correlation heat map.  Rock mass quality increases from left to right.  Except for Bingham Canyon (cases 11 and 12), which has a 29° overall angle and involves igneous rocks, there are no landslides in unaltered igneous or metamorphic rock on shallow slopes.  Similarly no cases with highly to completely weathered materials were mined steeper than 55°.  The Fahrböschung angle heat map has a strong correlation where the most mobile failures occur in poor quality materials on shallow slope angles, and vice versa.  The 105  length, inundation area, and width heat maps show higher quality materials, which are mined steeper, spread least.    Figure 76. Material type vs. slope angle correlation heat maps  4.7.2.3 Fall height and slope angle Figure 77 is a fall height vs. slope angle correlation heat map.  Fahrböschung angle appears more sensitive to slope angle than fall height but with a correlation between them.  A higher wall may contain more ramps, decreasing its angle.  Runout length, inundation area, and deposit width 106  appear to have a weak correlation between slope angle and fall height, where highest mobility occurs on shallow walls with a long drop height.  Short fall height failures seem equally mobile.   Figure 77. Slope angle vs. fall height correlation heat maps  4.7.2.4 Fall height and volume Figure 78 is a fall height vs. volume correlation heat map.  The Fahrböschung angle and width heat maps shows smaller volume failures (<500,000 m3) have similar mobility regardless of fall height, beyond which mobility and spread increase as a function of volume.  Fall height and 107  volume have a strong covariance in horizontal runout length and inundation area, where large failures with greater fall height travel farthest and cover more area.  This observation supports Heim’s original hypothesis that landslide mobility is analogous to an energy balance, where larger landslides falling from greater heights have more potential energy to contribute to motion.     Figure 78. Volume vs. fall height correlation heat maps  4.8 Mobility index comparison Open pit landslides appear to deposit predictably shaped debris aprons that either hang below the source in a 37° talus cone, or flow into a continuous pile thinning away from the source.  108  Compared to natural landslides they form thicker, farther reaching deposits with less lateral spread.     Mobility has a strong sensitivity to (and covariance between) slope angle, material properties, and fall height.  Fahrböschung angle relationships are sensitive to slope angle, material properties, fall height, and modestly to volume.  Runout length relationships are sensitive to volume and fall height, and insensitive to slope angle or material properties.  Deposit area relationships are sensitive to volume and only modestly sensitive to fall height, material properties, or slope angle.  Table 2 is a comparison of the mobility relationships. 109  Table 2. Mobility index comparison Input Mobility index Best fit equation RMSE1 Mean NI (%) Error distribution Parameter sensitivity2 (%) Proponent Volume H/L H/L=0.463V-0.148 109 3.2 Normal 11Heim (1932) H/L  (trend 1) H/L=0.559V-0.150 48 0.8 Normal 11H/L  (trend 2) H/L=0.408V-0.146 61 1.5 Normal 11Le Le=108.3ln(V)+84.4 96 6.2 Lognormal 19 Hsü (1975) Le/L Le/L=0.114ln(V)+0.206 120 10.6 Lognormal 6 Nicoletti and Sorriso-Valvo (1991) L L=321.3V0.383 116 13.0 Lognormal 30 Legros (2002) Inundation area A = 6V2/3 4.6x104 10.1 Uniform 57 Iverson et al. (1998) Optimized  A/H2=0.384V0.240 69 -4.5 Normal 7 Whittall (2015) Dimensionless NO TREND Staron (2008) Slope angle H/L H/L=0.488tan(α)+0.117 87 1.6 Normal 42 Hunter and Fell (2003) L NO TREND - Le/L Le/L=-0.606tan(α)+0.635 96 3.1 Lognormal 31 - Potential energy Area A = 0.13Ep0.0908 9.1x104 9.5 Normal 44 Dade and Huppert (1998) L L=0.0208Ep0.335 93 5.0 Normal 26 McSaveney (1975) L/H L/H=0.218ln(Ep)-3.959 118 3.1 Normal 6 Howard (1973) Notes: 1. RMSE is in metres for distance-based and square metres for area-based relationships. 2. Output response to 100% change in input variable. 110  Figure 79 is a description of the error for each mobility index.  The box is the first and third quartile error bisected by the median error.  The whisker bars contain the 5th and 95th percentile.   Figure 79. Prediction quality of runout relationships calibrated to open pit landslides 111  Chapter 5: Performance of empirical runout relationships 5.1 Introduction Several researchers have searched for trends in natural landslide behaviour and explanations for exceptional cases.  Prominent theories for surprisingly long runout landslides include: interstitial fluids (Iverson, 1997; Wang and Sassa, 2003), air entrapment (Shreve, 1968), mechanical fluidization reducing basal friction (Heim, 1932; McSaveney, 1978; Davies, 1982; Campbell, 1989); air (Kent, 1966) or acoustic (Melosh, 1979) fluidization reducing internal friction; and dynamic fragmentation (Davies and McSaveney, 2002).  Hungr (1990) provides a critical review.  The following subsections discuss mobility trends in the open pit cases and indicators to spot exceptionally mobile behaviour.   5.2 Spread Established runout methods appear to over predict the planimetric deposit area but under predict the location of the distal deposit toe (Figure 50 and Figure 38).  This indicates the deposit is thicker (see Figure 37 and Figure 65), likely a result of a combination of a flat pit bottom stripped of liquefiable substrate and surface water.  Four cases are channeled by the pit geometry, enhancing the effect.    A logical explanation is a pit bottom has finite available space to spread.  An obstruction by the opposing wall will cause toe bulking, rather than spread, reducing the inundation area and perhaps channeling material into a longer runout.  Most cases, however, were not obstructed.   Theoretically spread in landslides without path constrictions is controlled by normal and transverse shear stress, a function of material rigidity, normal stress, and basal shear resistance 112  (McDougall and Hungr, 2004).  A physical justification for the lower inundation area but longer reach of this dataset is the travel path inclination and lack of liquefiable substrate; the same mechanism as in Section 4.7.1.2.  A pit wall transitions abruptly to a flat, rough floor composed of materials of a similar strength, expends centrifugal force, and limits the spread of the landslide.  As such, the landslide may deposit thicker, or the tip may travel farther with less spread.  5.3 Influence of material properties The separate trends in the Fahrböschung angle vs. volume index are partly a consequence of material properties.  Heim’s original Fahrböschung proposition was an energy balance where the friction coefficient is equal to the ratio of vertical and horizontal displacement.  It does not attempt to describe the path or dynamics of the flow.  It is not surprising that materials with different frictional characteristics have different mobility.    In this dataset geology and material properties are generally well known.  The less mobile trend contains failures in fresh, strong rocks and are described well by Li (1983)’s regression.  These rocks failed as dry, cohesionless, frictional materials.  The volume increase resulting from dilation as the rock fails and passes from intact rock to debris removes the possibility of pore pressure increasing in the sliding mass (Hungr and Evans, 2004).  Combined with the lack of liquefiable substrate, the basal friction angle is not mediated by pore pressure and the failures are analogous to a block sliding on a curved path.  Deposits appear granular and sit at approximately 37°. 113  A more mobile Fahrböschung angle vs. volume trend is observed for weathered, clay rich rocks and poorly cemented sedimentary rocks.  Authors often described these materials using soil constitutive models.  A hypothesis for the difference in behaviour is that these materials have a collapsible structure creating undrained strength conditions when sheared.  Hunter and Fell (2003) and Locat and Leroueil (1997) provide natural landslide precedents for different runout behaviour in dilative versus contractive materials.    Many of the literature sources note a significant precipitation event, high or perched water tables, and/or deficiencies in surface water management as contributing to the failures.  Forty-seven of the cases (including all but two of the most mobile cases) assign a precipitation event as the failure trigger, despite pit depressurization measures being in place.  Detailed pore pressure data is not available, however reduced effective stresses in response to elevated pore pressures in the pit walls seem likely given these anecdotes.    5.3.1 Poorly cemented granular materials Poorly cemented sedimentary rocks often have high porosities, either due to the depositional environment (e.g., Boron, cases 13 to 24), alteration (e.g., Gold Quarry, case 38), or mining disturbance (e.g., Grasberg, case 47).  Minor amounts of cohesion hold together a disorganized house of cards clay-rich structure with void space available for contraction.   Hutchinson (2002) and Sassa (2000) proposed such materials crush and contract in shear, generating excess pore pressure at the rupture surface.  When saturated, granular contracting materials subjected to shear at a high strain rate behave undrained, even if initially in a drained condition (Ladd, 1991).    114  Sassa (2000) demonstrated the role of pore pressure in shearing granular materials and coined the term sliding surface liquefaction.  A loose granular material forced to shear will want to contract.  This effect is enhanced if the rock has cohesion to lose.  If the rock is saturated, as the triggering events imply, the volume change cannot occur and pore pressure increases.  In turn, effective stress decreases and pore pressure mediates basal resistance.    5.3.2 Clay-bearing fault zones Sheared discontinuities, and their infill, have a shear strength at or near their residual values.  Any cohesion that existed from previous over-consolidation will be destroyed during shearing. In the case of joint infill, Barton (1974) showed infilling is expected to act in a normally consolidated state.  5.3.3 Weathered materials Saprolite and other residual soils are generally more heterogeneous than sedimentary soils and do not have a stress history.  These weathered materials are not composed of individually deposited discrete particles, rather a degradation of a previously intact block.  The void ratio to effective stress plot, and normal- versus over-consolidated states, are not applicable to residual soils.  Rather, Wesley (2010) showed disturbing or remoulding residual soils causes them to disintegrate and contract much the same as Sassa’s (2000) grain crushing experiment.     5.3.4 Pore pressure dissipation in clay-rich materials Iverson (1997) showed that there is a negative correlation between the rate of pore pressure dissipation (tdiff) and compressibility and permeability of the material (Equation 22).  He shows 115  clay-rich materials with excess pore pressure dissipate their pore pressure orders of magnitude slower than dilative materials, leaving interstitial fluid available to mediate the basal friction:   ݐௗ௜௙௙ ൌ ௒మఓ௞ா        [22]  where Y is a normalizing length term, µ is the viscosity of the fluid, k is the permeability of the material, and E is the stiffness modulus.    Either from the addition of total stress (through redistribution and concentration of stresses during pit excavation) or by decreasing effective stresses (precipitation triggers), clay-rich materials forced to rapidly shear behave in an undrained manner.  Large natural landslides show this effect where fluidization occurs from a relatively small volume of water initially present in the failing mass (Legros, 2002).  The initial failure mass may also load the travel path, increasing the pore pressure and decreasing the shear resistance.  Rapid undrained loading is a common long runout mechanism in natural debris avalanches (Hungr and Evans, 2004).      This mechanism does not dismiss the possibility of other site-specific influences on runout.  A unique combination of material and slope properties are, however, difficult to estimate in an emergency and lead to misguided deterministic use of these empirical relationships.  Pore pressure mediating basal friction provides a reasonable holistic explanation for long runout landslides, agrees with Pudasaini and Miller’s (2013) analytical work, and can be identified using parameters practitioners can map.     116  5.3.5 Distinguishing mobility trends Shear strength and porosity are indicator properties for dilative versus contractive behaviour.  Figure 80 is a design chart to choose the appropriate mobility category (for use with Figure 40) using intact strength (ISRM, 1978), weathering grade (ISRM, 1978), porosity, and disturbance.  The user should apply the properties of the worst 10% of the rock mass.  Pit walls at the boundary between trends may be difficult to place.  Further research is required to suggest testing methods or parameter thresholds to objectively place a wall into a mobility trend.  Until then, any pit wall where the occurrence of instability has decreased its strength or increased its porosity should use the more mobile trend in Figure 40.                 117  Fahrböschung trends: 1 - fresh, strong rocks 2 - weathered, weak rocks High                                 SHEAR STRENGTH                                 Low  strong (>R3)  fresh  strong (>R3)  faintly weathered  medium strong (R2-R3)  slightly to moderately weathered  weak (<R2)  moderate to highly weathered  clay infilled joints  completely weathered  pre-sheared  pervasive clay infill High               STRUCTURE               Low  massive  low porosity            jointed  minor secondary porosity   TREND 1          jointed  ubiquitous primary or secondary porosity            faulted  ubiquitous primary or secondary porosity        TREND 2      confluence of faults  brecciated  ubiquitous porosity  no/poor cementation N/A         Figure 80. Rock mass property mobility trend matrix for use with Figure 40  5.4 Travel path obstruction Obstruction or deflection at the opposing pit wall could introduce curvature to the travel path or bulking of the deposit toe.  Nineteen (18%) of the pit slope failures ran to the opposing wall or a constructed berm.  In the case of a runout length prediction exceeding the available linear 118  distance across the pit floor, an area vs. volume prediction is useful to estimate the degree of spread at the opposing wall.    Channeling at corners or along ramps may change the flow shape, however not to the extent that valleys or gullies in natural landscapes would.  The pit bottom at Pitch (cases 50 and 51) is a good example of confinement in an open pit.  The area available to accept the landslide was narrow and kidney shaped.  The debris struck the opposing (west) wall across the pit floor and channeled to the south into the available space.  The confined pit floor decreased the deposit planimetric area and increased the horizontal runout length.      5.5 Failure mechanism The failure mechanism did not significantly influence mobility because the data is a narrow subset of possible landslide classifications.   Finlay et al. (1999) and Hunter and Fell (2003) also found narrowing the context to small debris flow and mine waste dumps, respectively, removed the variety of mechanisms and limited its effect.    Figure 81 is the Fahrböschung angle vs. volume relationship symbolized by failure mechanism.  The eight toppling failures in this dataset are less mobile than the general trends in Figure 40 but within the scatter of the other cases.  Seventeen of the highly mobile cases are planar failures in poorly cemented sandstones.  It is difficult to determine whether the planar mechanism had a greater influence than the low material strength and collapsible structure.  Planar slides span the scatter of the dataset and the other eleven (of twenty-eight) planar failures occurred in stronger and less porous materials and did not show exceptional mobility characteristics.  Rotational and 119  debris slides occur in the more mobile end of the scatter, which suggests material property has a larger effect on mobility than structural control.     Figure 81. Fahrböschung angle vs. volume relationship symbolized by failure mechanism 120  5.6 Retrogressive failures Eighteen (17%) of the pit slope failures involved at least two distinct events.  The toppling failure at Hogarth (case 49), for example, fell to the pit floor in a piecemeal fashion, resulting in a short runout. Experiences from the 1991 Randa rockslide (Eberhardt et al., 2004) demonstrate simple empirical runout models using the total cumulative volume can over predict mobility.  A continuous series of low volume failures will likely produce a short runout.    Conversely, remobilized debris from previous failures can be more mobile than the virgin material.  Colluvium left with a loose disorganized structure will readily collapse in shear and behave in an undrained manner.  The 2005 La Conchita landslide (Jibson, 2005), for example, remobilized colluvium left by a 1995 event.  Despite being much smaller, the 2005 event exceeded runout expectations and overtopped protection structures designed using experience from the first landslide.  121  Chapter 6: Implementation of the empirical runout and exclusion zone procedure 6.1 Introduction An imminent slope collapse will initiate the Trigger Action Response Plan (TARP) and invoke emergency response measures.  Various methods are established to use slope deformation to define alert thresholds (Brox and Newcomen, 2003) and the time of failure (Rose and Hungr, 2007; Dick et al., 2015).  TARPs rely on these methods to provide important information to safeguard personnel, but they do not address the landslide motion once the slope has collapsed.  Case histories with consequences ranging from expensive (Pankow et al., 2013; Martin and Stacey, 2013) to tragic (Moore, 2003; Farina et al., 2013) highlight the sensitivity of these safeguards to the runout estimate.  Damaged infrastructure, equipment and fatalities have resulted in the past despite geotechnical staff effectively identifying the hazard and predicting its approximate time to failure.  Creating exclusion zones is a common response to remove people and equipment from harm’s way, however uncertainty remains as to how far they should extend.  Empirical mobility relationships calibrated to an open pit context provide reasonable holistic runout estimates.    Empirical mobility relationships are best set in a risk framework.  Iterating this process for each new set of monitoring data will update the risk estimate as the slope deforms.  Figure 82 is a proposed workflow through the empirical process developed in this thesis, from hazard recognition to estimating P(S:L) and calculating risk for an empirically derived exclusion zone.  122  The sub-sections of this chapter present tools to estimate input parameters, set runout in a probabilistic framework, objectively delineate exclusion zones, and quantify the associated risk.  123   Figure 82. Example workflow to estimate P(S:L) and generate exclusion zones124  6.2 Estimating source volume The proposed runout models rely on fall height, slope angle, material properties, and source volume.  All but the latter can be measured.  If a failure is developing with clear, structurally-defined boundaries (such as a wedge), then the volume can be estimated directly.  Also vector solutions such as that of Cruden (1986) can provide reasonable approximations of the rupture surface if a wall has a detailed prism network.  In less instrumented scenarios, natural landslide researchers have proposed various geometrical relationships (Cruden and Varnes, 1996; Marchesini et al., 2009; Nikolaeva et al., 2014), for example assuming the rupture surface is a half-ellipsoid.  Others (Lin et al., 2012) have used remote sensing to measure the source surface area and multiplied this by an average thickness.  Both of these methods rely on an assumption regarding the depth and shape of the rupture surface; an ellipsoid may be a reasonable approximation for a rotational failure and an average thickness may be acceptable for a planar failure.    Another technique is to use the database of pit slope failures compiled for this study to develop empirical relationships comparing measured source surface area and post-failure volume estimates. Figure 83 shows the relationship between reported failure volume and source surface area for 61 pit slope failure cases.  Length is through the centerline of the deformation from the toe of the rupture surface to its crest, or to the back break.  Width is the average of the maximum and minimum widths measured on the rupture surface.  Open pit operations using radar monitoring can quickly establish and measure source surface area directly (Dick et al., 2015). 125   Figure 83.  Comparison of source deformation surface area and reported volume  A validation set of twenty natural landslides match well with the proposed trend (Equation 23).    ܸ ൌ 0.238ሺ݂݁ܿܽݎݑݏ	ܽ݁ݎܽሻଵ.ସ଴଻     [23]  Practitioners should bracket site conditions with lower and upper bound volume estimates. Figure 84 is a comparison of estimated and reported source volumes.  The scatter is reasonably low and within expected precision for emergency response tools.   126   Figure 84. Comparison of reported and empirically estimated source volumes  The mean normalized index for k-fold cross-validation and the natural landslide validation set is 3.8% and 2.9%, respectively.    6.3 Selecting a runout model Three established mobility relationships calibrated for open pit slope failures are useful to estimate runout distance and create exclusion zones.  A fourth inundation area relationship can 127  be combined with runout distance to map a deposit shape from the toe. Recommended relationships are:  Fahrböschung angle vs. volume model (see Figure 40): This is an easy to implement runout solution with comparatively low model uncertainty, provided the user is cognizant of the influence of material properties and slope angle. Figure 80 is recommended to distinguish the appropriate trend.  Estimating volume remains a difficult task and users should remember pit slope failure mobility is only modestly dependent on volume.  This model is recommended as the primary runout tool and should be verified by the other relationships.   Fahrböschung angle vs. slope angle model (see Figure 54): This provides a reasonable runout estimate for slopes inclined at less than 50° (tan50° ≈ 1.2).  It has a similar model uncertainty to its volume counterpart but much lower parameter uncertainty.  This model is useful check for geometrically complex landslides where volume is difficult to estimate and pit walls are inclined less than 50°.  The user needs to decide on the relevant wall angle: the bench stack angle if the source and deposit are likely to be on the same bench stack, or the overall angle if the travel path is likely to contain ramps.  Optimized mobility index (see Figure 67): This new parameter, defined in Figure 66, unifies the effects of slope angle, fall height, volume, and pre-event deformation geometry into a single trend.  The model has similar model and parameter uncertainty to the other volume based relationships.  It requires deformation monitoring data and is 100% sensitive to fall height, therefore it is a useful check for failures where the expected fall height is easily assessed and if there is uncertainty placing the wall into the appropriate material category in Figure 80.   128   Inundation area model (see Figure 50): The inundation area of a potential pit slope failure can be reasonably approximated as A=6V2/3.  Deposit length and width can be determined using Figure 90.  This relationship is recommended to complement a runout distance model to map the deposit shape back from the estimated deposit toe.  It may also be useful to assess the degree of spreading when the landslide is obstructed by an opposing wall.  6.4 Probabilistic runout estimates: calculating P(S:L) Geological uncertainty and the holistic nature of empirical models limits the precision one can expect from these runout estimates.  Hunter and Fell (2003) noted the scatter in data around the mean, and recommended caution in using these methods without local calibration.  As such, these models are not deterministic runout calculators. Rather, data scatter is useful in statistical terms to set runout estimates in a probabilistic framework (Hungr et al., 2005; McDougall et al., 2012). The best fit shown in the preceding figures is actually a 50% exceedance limit, meaning material will runout farther than this estimate in 50% of the cases.    A probabilistic approach provides a procedure in which uncertainty and experience can be integrated into the analysis.  Figure 85 through Figure 87 are the recommended mobility relationships, incorporated into the decision work flow in Figure 82, fitted with prediction intervals analogous to the mine’s risk tolerance.  These are a probability of exceedance assuming a cumulative standard normal distribution based on error distributions.    129  Prediction intervals are a relatively easy way to model the uncertainty in runout distance for an impending landslide.  The practitioner can choose their risk tolerance and use a high and low volume estimate to bracket the expected runout.  A prediction using a 5% exceedance probability has a P(S:L) = 0.05, or 5% chance the landslide will reach the exclusion zone.     Figure 85. Prediction interval design chart for the less mobile (trend 1) Fahrböschung angle vs. volume mobility index 130   Figure 86. Prediction interval design chart for the more mobile (trend 2) Fahrböschung angle vs. volume mobility index  131   Figure 87. Prediction interval design chart for the Fahrböschung angle vs. slope angle mobility index 132   Figure 88. Prediction interval design chart for the optimized mobility index     133  6.5 Implementing the exclusion zone The exclusion zone can be as simple as a circle or cone centered at the main scarp with radius of L, the horizontal runout length assessed.  Figure 89 is an example application of the Fahrböschung angle.     Figure 89. Example application of Fahrböschung angle to defining an exclusion zone  Another implementation option is to create a hazard map based on deposit shape.  Inundation area relationships such as Figure 50 by themselves only estimate the magnitude of inundation.  To be useful we need to know the start or end of the deposit.  Working with natural landslides on volcanic slopes, Iverson et al. (1998) assumed lahar deposit began at the base of the volcano.  In the open pit data it is difficult to estimate a deposit start point because many of the deposits drape over the source or benches. Inundation area needs to be linked to runout distance.    134  The open pit data set developed in this thesis plots parallel to Iverson et al.’s (1998) inundation area regressions, which supports his assumption of self-similar deposit shape.  Figure 36 establishes that open pit failures have low width to length aspect ratios and have even more predictable spread (or lack thereof) than natural landslide events.  Using these assumptions, Figure 90 plots inundation area (equated to 6V2/3) against deposit length, with data symbolized by average deposit width.    Figure 90. Empirical deposit hazard mapping tool 135  The trend lines have the power-law form: ݀݁ݐ݅ݏ݋݌	݄ݐ݈݃݊݁ ൌ ܿሺ݁݉ݑ݈݋ݒ	݊݋݅ݐܿ݊ݑ݂ሻ଴.ଽଵ଺    [24]  where c is a width dependent constant and 0.912 is the slope of the fits.    This is not a mobility index.  Dependent variables are mixed (i.e., treated holistically), the source volume appears twice in this procedure, and the area=f(volume) and deposit length=f(volume) relationships both contain errors.  Rather, it is a tool to create a fully empirical hazard map.  Starting from the deposit toe and a broad approximation of width, projecting deposit length back towards the source and drawing a conical shape between these points produces a map of potential inundation area.      6.6 Evaluating the risk to the exclusion zone Risk estimates involve developing a landslide hazard inventory, quantifying its likelihood, and evaluating whether the consequences are acceptable.  Open pit landslide risk requires a modified procedure because mines do not have a history of creating an inventory or recording traditional F-N pairs.  The change in context requires the following clarifications:    Both individual and societal risk must be considered.  Individual risk applies to a specific person, such as a driller installing drainage at the foot of a slope.  Truck traffic is an example of societal risk where a certain number of workers travel repeatedly through a hazard path.  Society has a much higher aversion towards group accidents, whereas mine management is highly adverse to both individual and group accidents;   136   Risk equals the probability of a landslide occurring multiplied by the conditional probability that a certain location within the pit will be impacted at a time when persons are present (the consequence).  Even with a moving landslide, uncertainty remains about its timing, whether the entire volume will collapse as a single event or if acceleration will continue to increase leading to catastrophic failure;   A deforming landslide, even if not imminent, has a probability of failure close to 1.  Uncertainty comes from the magnitude (volume) and whether adequate warning is possible.  F-N pairs are required for various scenarios to characterize the hazard;   Working below a deforming landslide may be a tolerable risk subject to “as low as reasonably practicable” or ALARP, provided that the probability of a catastrophic acceleration is reasonably low.  Workers’ risk can be reduced through monitoring, TARP/evacuation plans, and through the use of exclusion zones.  Stability analyses and the observational method are minimum requirements;  Assuming risks are communicated and understood, mine workers accept voluntary risk (Terbrugge et al., 2006);   Risk levels in mines should be pre-determined;  The currency of harm for this thesis is loss of life.  All people are equally vulnerable (V=1).  Risk to damage or injury is implicit, but also beyond the scope of this thesis and can be accounted for through cost-benefit analysis;  Design event magnitude is specific for each event.  A generic magnitude probability per wall is not appropriate;  For a moving element at risk, P(T:S)  is the proportion of time that the element spends in the landslide path.  The probability of having multiple vehicles in the impact zone can be 137  simulated using a Poisson distribution of vehicle spacing.  The societal risk calculation should use a distribution of number of fatalities to account for time periods when traffic may concentrate (e.g. waiting at the shovel) or be more sparse (e.g. shift change);   Differentiating direct and indirect impacts, or hazard intensity, is beyond the capability of empirical models; and  Quantitative probabilistic hazard analysis is preferable to capture the uncertainty in the timing and volume of the event.  Qualitative ranking schemes might be applicable to contrasting movement rates and failure mechanisms that typically lead to landslides that runout versus ravel or self-stabilize.  6.6.1 F-N curves for open pit landslides If a landslide seems likely, F-N pairs in a mine are generated from the probability of occurrence without adequate warning.  This is the intersection of the uncertainty in the volume, time-of-failure, and runout estimates.  An event tree is a useful way to keep track of the possibilities and create F-N pairs.  The structure is: 1. Does an active or potential landslide exist; 2. Given a landslide exists, what are the probabilities we are over or under estimating its volume; 3. For each volume  possibility, what are the probabilities that it will occur with or without adequate warning; 4. If there is not adequate warning, what are the probabilities the landslide will reach a specific location; 5. For each location, what is the expected number of fatalities?   138   Probabilities in each branch sum to 1.  Figure 91 is an event tree framework to generate f-N pairs; a fully worked risk calculation is presented in Appendix C.  Since there is no way to know the quality of a volume prediction a priori, its uncertainty is equal to the corresponding model sensitivity.    Multiplying through each tree branch provides a frequency pairing to the number of people (fatalities) in each scenario.  Accumulating and plotting the pairs on an appropriate risk tolerance graph, like the one shown in Figure 17, gives an F-N curve for comparison with the mine’s risk tolerance.  If risk is tolerable, the exclusion zone is adequate (Figure 82).   A simplifying assumption in this thesis is the production schedules provides the number of workers at the various locations in the pit.  No data is available to create a realistic traffic distribution.  Open pit practitioners should use their GPS traffic tracking data to create a vehicle spacing Poisson distribution and extend the temporal probability in Figure 91.   139   Figure 91. Open pit landslide risk event tree analysis  6.7 Limitations Runout estimate tools presented here supplement engineering judgment.  They are holistic emergency response tools that are neither deterministic nor precise.  A short runout prediction does not provide justification to continue mining on or below the slope expected to fail.    140  Data in this study is exclusively restricted to extremely rapid slope failures with a runout component. Low energy deformation or acceleration trends that do not typically lead to catastrophic failure (regressive displacement) still require vigilance and deserve their own consequence management plan in the TARP.  Similarly, the empirical tools presented are not appropriate for bench scale failures or rock fall events.    Detailed runout assessments are outside the scope of this procedure but have their utility.  Three-dimensional runout modelling (e.g., DAN3D; McDougall and Hungr, 2004) is a useful complement to stability modeling in assessing placement of in-pit infrastructure, evacuation routes, susceptibility of ramps, or comparing failure scenarios.  Natural landslide researchers have used runout modelling to estimate the vulnerability of elements at risk and design protective measures like check dams and deflection structures (Jakob et al., 2012).  If the element at risk is infrastructure, the practitioner may re-evaluate parameter V and the cost of failure in Equation 6, as in Fell et al. (2005).  141  Chapter 7: Recommendations and conclusions 7.1 Runout observations Validating established mobility relationships in an open pit context has identified important behavior differences from natural landslides.  When applying these models, the user should be aware that:  Open pit landslide mobility is only modestly dependent on volume;  Mobility is sensitive to slope angle, fall height, and material properties;  Landslides smaller than 500,000 m3 on slopes greater than 50° appear uniformly mobile;    Open pit landslides appear to spread less than natural events and form a thicker deposit. The consequence of these observations is that natural landslide regressions generally under predict the runout distance of open pit failures but over predict the inundation area.  Mobility relationships calibrated to open pit failures provide better runout estimates.    7.2 Appropriate mobility relationships Set in a probabilistic framework, established mobility relationships calibrated for open pit slope failures are useful for creating exclusion zones.  Recommended empirical runout tools are: Fahrböschung angle vs. volume, Fahrböschung angle vs. slope angle, and a new optimized mobility index.  An inundation area vs. volume relationship can be a useful complement to simply locating the expected toe of the runout deposit.    142  7.3 Further work  7.3.1 Local calibration Like any model, empirical mobility relationships work best when the event has similar attributes to those used to develop the model.  Mines should calibrate these tools using their own internal failure databases where possible.  Complacently assigning an expected runout to an entire pit wall is problematic.    7.3.2 Societal risk to moving elements In this thesis frequency of landslide occurrence is presented as conditional probabilities and the number of fatalities is simplified to a number available from the production schedule.  In practice societal risk requires the temporal probability of multiple moving vehicles within the landslide path at the time of impact.  The velocity and quantity of moving elements at risk should be a distribution to account for periods of more concentrated (e.g. waiting at a shovel) and more sparse (e.g. shift change) traffic patterns. An interesting extension of this thesis is to use GPS tracking tools in haul trucks and shovels to develop a Poisson distribution of vehicle spacing.     7.3.3 Implementation Promising implementation strategies are: 1. Integrate with probabilistic slope design (e.g., Steffen et al., 1997) to create an operating plan sensitive to changing wall performance.  This would link the design, operation, and emergency response into a single risk-based set of procedures.   2. Automate runout into established spreadsheets and visualization tools. Several open source scripts are available to integrate empirical mobility indices into CAD or GIS 143  software.  The basic structure is: i) import a DEM, ii) define a point or line source, and iii) project a user selected Fahrböschung angle (or equivalent) to the topography below.     3. Link runout into remote sensing output to identify the main scarp and project runout predictions to the pit floor.  A radar application, for example, could be a script to project the runout estimate from the highest elevation red (i.e. critical) pixel.  7.3.4 Proactive risk planning Dynamic modelling is potentially a useful tool for running landslide scenarios for infrastructure placement, route/ramp planning, estimating ore sterilization, and designing mitigation structures.  However, there is consensus in the natural landslide research literature that resisting stress in rock avalanches are velocity dependent, not simply frictional (Hungr, 1981). No publications found in this study have velocity data, likely because there is no record.  Velocity data is required to calibrate numerical models.  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Eclogae Geologicae Helvetiae, 90(3), 415-420.    160  Appendices    161       Appendix A  Empirical database 162   Label Mine Pit Wall ID Country Date1 Afsin-Elbistan Kislakoy Northwest Turkey July 1, 19842 Afsin-Elbistan Çöllolar Southwest Landslide B Turkey February 6, 20113 Afsin-Elbistan Çöllolar Northeast Landslide A Turkey February 10, 20114 Afton Southeast Canada 19865 Aguas Claras Northwest Brazil April 29, 19926 Angooran Northwest Iran 20087 Baguanhe West China Not reported8 Batu Hijau Southwest SS_P4_028 Indonesia October 12, 20079 Batu Hijau West WS_P5_064 Indonesia August 24, 201010 Berkeley Berkeley Southeast USA March 17, 197811 Bingham Canyon Northeast 1st event USA April 10, 201312 Bingham Canyon Northeast 2nd event USA April 10, 201313 Boron North E-17 USA 197014 Boron North 22250 USA 197915 Boron North 23250 USA 198216 Boron North 20900 USA 198417 Boron North 19500 USA 198418 Boron North 20500 USA 198619 Boron North USA 199220 Boron North 19500 USA 199521 Boron North USA 199622 Boron Northwest USA 199723 Boron Northwest USA 199724 Boron Northeast USA 199825 Brenda West Canada April 14, 200126 Chuquicamata Southeast Chile February 18, 196927 Cowal West Australia July 200728 Cowal Southwest Australia December 20, 200729 Cuajone East D15 Peru February 199930 Daye Iron Mine East Pit North A2 China July 13, 199631 Geita Nyankanga Southwest Tanzania February 3, 200732 Gold Quarry East Phase 2 USA December 1, 200433 Gold Quarry East Phase 2 USA December 27, 200434 Gold Quarry East Phase 2 USA October 12, 200535 Gold Quarry East USA July 19, 200736 Gold Quarry East Nine Points USA April 26, 200937 Gold Quarry East South Ramp Slide USA October 14, 200938 Gold Quarry East Nine Points USA December 24, 200939 Goldstrike Betze-Post Southeast SE-96-A USA March 199740 Goldstrike Betze-Post Southeast S-97-B USA March 199741 Goldstrike Betze-Post Southeast S-01-A USA August 29, 200142 Goldstrike Betze-Post Southwest S-05-B USA May 22, 200543 Goldstrike Betze-Post South S-07-B USA September 10, 200744 Goldstrike Betze-Post South USA October 9, 200845 Goldstrike Betze-Post South S-09-B USA 200946 Grande Cache No. 12S B2 North Canada July 7, 200647 Grasberg South Indonesia October 9, 200348 Hindustan Lalpeth India August 11, 199549 Hogarth Hogarth Northwest Canada June 23, 197550 Homestake Pitch North East USA March 198351 Homestake Pitch North East USA October 198352 Huckleberry East Zone North Canada June 22, 200753 Junad South India August 13, 2006163   Label Mine Pit Wall ID Country Date54 Kagemori South Japan September 20, 197355 Kawadi India June 24, 200056 KBI Morgul Cakmakkaya East Turkey 198957 Kemess Northwest Canada May 200458 Kirka Borax Northwest Turkey 197459 Kumtor Northeast Kyrgyzstan July 13, 200660 Leigh Creek Upper Series Northeast U24 Australia June 6, 200161 Letlhakane DK1 West Botswana July 14, 200562 Liberty USA May 196663 Luscar 51-B-2 North Canada November 197964 Monroe County North USA April 26, 200065 Mt Keith Southeast Australia December 7, 200166 Navachab East Namibia December 199767 Navachab East Namibia March 200168 Navin Kundata India August 23, 200169 Nchanga South Zambia April 198070 Nchanga Pit 20 North 21E Zambia July 16, 200471 New Majri West India June 30, 200572 Niljai India August 12, 200273 Permanente North Pit Northwest Main Slide USA 198774 Steep Rock Roberts West No. 2 Canada October 196875 Steep Rock Roberts West No.4 Canada September 197276 Rotowaro Waipuna Northeast New Zealand Not reported77 Santa Barbara North Italy 198378 Sanu Tinti Stage 1 Footwall Guinea 199879 Savage River North East Australia June 17, 201080 Savage River North East Australia August 20, 201081 Savage River North East Australia July 201282 ShengLi East D1 Mongolia May 200583 Shirley Basin Southeast USA April 197184 Shirna India October 15, 200085 Sunrise Dam Cleo Southwest Australia December 200086 Telfer Pit 1A Highwall Australia October 31, 199287 Tom Price South East Prongs South Australia January 8, 200788 Tom Price NTD East Australia September 28, 200989 Twin Buttes South USA 1970-197190 Wallaby West Scallop Australia 200691 Wallaby Southwest Alpha Australia January 1, 200592 West Angelas Centre Pit North North Australia Febuary 3, 201093 "Mine X" Not reported94 Anonymous East Not reported95 Anonymous Northeast USA January 4, 201196 Anonymous Southwest Canada 200497 Anonymous East Canada March 1, 198498 Anonymous Southwest Canada July 25, 201499 Anonymous East Canada April 24, 2001100 Anonymous South USA May 17, 2014101 Anonymous North USA December 9, 2008102 Anonymous South USA 1992103 "Case 2" Not reported104 "Case 2" Not reported105 Anonymous North Canada October 14, 2003164   Label Material Group Lithology Fabric OrientationStrength GradeRMR(1976)Unit Weight(KN/m3)1 Sedimentary Lignite Horizontal R0 Poor 172 Sedimentary - Out of slope R1 Poor 173 Sedimentary - Parallel to slope R1 Poor 174 Igneous Diorite No fabric R4 Poor 295 Metamorphic Hematite and Itabirite Out of slope R0 Very poor 226 Sedimentary Limestone In to slope R5 Fair 257 Sedimentary Limestone Out of slope R0 - 248 Igneous Tonalite No fabric R3 - -9 Igneous Volcanic No fabric R3 - -10 Altered Igneous Oxidized quartz monzonite No fabric R0 Fair 2811 Igneous Quartz monzonite Out of slope R5 Good 2312 Igneous Quartz monzonite Out of slope R1 Good 2313 Sedimentary Weakly cemented arkose Out of slope R1 Poor 2114 Sedimentary Weakly cemented arkose Out of slope R1 Poor 2115 Sedimentary Weakly cemented arkose Out of slope R1 Poor 2116 Sedimentary Weakly cemented arkose Out of slope R1 Poor 2117 Sedimentary Weakly cemented arkose Out of slope R1 Poor 2118 Sedimentary Weakly cemented arkose Out of slope R1 Poor 2119 Sedimentary Weakly cemented arkose Out of slope R1 Poor 2120 Sedimentary Weakly cemented arkose Out of slope R1 Poor 2121 Sedimentary Weakly cemented arkose Out of slope R1 Poor 2122 Sedimentary Weakly cemented arkose Out of slope R1 Poor 2123 Sedimentary Weakly cemented arkose Out of slope R1 Poor 2124 Sedimentary Weakly cemented arkose Out of slope R1 Poor 2125 Igneous Quartz diorite Out of slope R5 Fair 3026 Igneous Granodiorite No fabric R5 Fair 2627 Saprolite Saprolite No fabric R0 Very poor -28 Saprolite Saprolite No fabric R0 Very poor -29 Igneous Basaltic andesite No fabric R1 Poor 2630 Igneous Diorite No fabric R3 Fair -31 Igneous - No fabric R2 Fair 2732 Altered Igneous Carlin formation No fabric R0 Very poor 1633 Altered Igneous Carlin formation No fabric R0 Very poor 1634 Altered Igneous Carlin formation (laminated tuff) No fabric R0 Very poor 1635 Metamorphic Carlin formation No fabric R1 Fair -36 Altered Igneous Carlin formation No fabric R0 Very poor 1637 Altered Igneous Carlin formation No fabric R0 Very poor 1638 Altered Igneous Carlin formation No fabric R0 Very poor 1639 Altered Igneous Altered granodiorite (SAG) No fabric R3 Poor 2340 Altered Igneous Altered granodiorite (SAG) No fabric R3 Poor 2341 Altered Igneous Altered granodiorite (SAG) No fabric R2 Poor 2342 Metamorphic Metasediments Out of slope R3 Fair 2543 Metamorphic Metasediments Out of slope R3 Fair 2544 Metamorphic Metasediments Out of slope R3 Fair 2545 Metamorphic Metasediments Out of slope R3 Fair 2546 Sedimentary Shale and coal In to slope R1 - 2547 Igneous Intrusives complex No fabric - Poor -48 Sedimentary Overburden+sandstone No fabric R2 Very poor 1749 Igneous Diorite No fabric R5 - -50 Igneous Sericite clay and weathered pegmatite No fabric R1 Poor 2051 Igneous Sericite clay and weathered pegmatite No fabric R1 Poor 2052 Igneous Andesite No fabric R3 Fair 2753 Sedimentary Overburden and sandstone No fabric R2 Very poor 17165   Label Material Group Lithology Fabric OrientationStrength GradeRMR(1976)Unit Weight(KN/m3)54 Sedimentary Limestone No fabric R5 Fair -55 Sedimentary Overburden and sandstone No fabric R2 Very poor 1756 Altered Igneous Weathered dacite and tuffite No fabric R1 Very poor 2657 Altered Igneous Clay altered lapilli tuff No fabric R3 Poor -58 Landslide debris - In to slope R0 Very poor 2359 Igneous - Out of slope R4 Fair 2860 Sedimentary Mudstone Parallel to slope R1 Poor 1861 Sedimentary Sandstone In to slope R3 Good 2262 Fault material - No fabric R2 Fair 2963 Sedimentary Interbedded sandstone and siltstone Out of slope R2 Fair 2564 Metamorphic Gneiss In to slope R0 Fair -65 Saprolite Saprolite Out of slope R0 Very poor -66 Metamorphic Schist Out of slope R5 Fair 2767 Metamorphic Schist Out of slope R5 Fair 2768 Soil Overburden No fabric R1 Very poor 1769 Sedimentary Interbedded sandstone and quartzite Out of slope R1 Poor 2570 Sedimentary Shale In to slope R2 Poor 2571 Soil Overburden and waste rock No fabric R0 Very poor 1772 Soil Overburden No fabric R0 Very poor 1773 Metamorphic Greenstone No fabric R1 Poor 2574 Igneous Faulted ashrock No fabric R0 - -75 Igneous Ashrock No fabric R2 - -76 Sedimentary Claystone Out of slope R2 - -77 Soil Lacustrine overburden No fabric R0 Very poor 1778 Saprolite Saprolite No fabric R0 Very poor 2779 Metamorphic Amphibolite In to slope R4 Fair 3580 Metamorphic Amphibolite In to slope R4 Fair 3581 Metamorphic Amphibolite In to slope R4 Fair 3582 Sedimentary Mudstone No fabric R1 - 2083 Sedimentary Shale In to slope R1 - 1784 Sedimentary Sandstone Out of slope R2 Very poor 1785 Soil Transported lake clay No fabric R0 Very poor -86 Sedimentary Interbedded sandstone and siltstone In to slope R2 Fair -87 Sedimentary Dale Gorge formation Out of slope R1 Poor -88 Sedimentary Shale Out of slope R1 Poor -89 Sedimentary Quartzite, conglomerate, tuff, andesite, and dacite No fabric R5 Fair -90 Sedimentary Sandy claystone No fabric R0 Poor -91 Sedimentary Sandy claystone No fabric R0 Poor -92 Sedimentary Shale Out of slope R1 Fair 3093 Igneous Diorite No fabric R4 Fair 2594 Igneous Rhyolite tuff No fabric R5 Good 2295 Sedimentary Oxidized rock In to slope R1 Poor 2596 Igneous Tonalite No fabric R3 Fair 2797 Igneous Weathered tonalite No fabric R4 Fair 2798 Igneous Tonalite No fabric R4 Fair 2799 Sedimentary Sandstone No fabric R1 Poor -100 Sedimentary Conglomerate and waste rock No fabric R1 Poor 22101 Igneous Quartz monzonite porphyry No fabric R4 Fair 25102 Metamorphic Schist Out of slope R3 Poor 24103 Igneous Intrusives No fabric - - -104 Sedimentary Sandstone In to slope R3 Fair -105 Igneous Granodiorite No fabric R3 Fair 26166   Label Failure Mechanism Trigger Volume(Mm3)Mass(tonnes)Number of events1 Rock planar slide Daylighted structure 1.60 - 12 Rock planar slide Daylighted structure 7.90 - 13 Rock compound slide Not reported 42.00 - 14 Rock block topple Mined too steep 0.10 3.0E+05 Retrogressive5 Soil planar slide Mined too steep 0.70 2.0E+06 16 Rock planar slide Freeze thaw cycle 12.00 2.5E+07 17 Rock planar slide Daylighted structure 4.50 1.1E+07 18 Rock irregular slide Not reported 0.48 - 19 Rock irregular slide Daylighted structure 0.25 - 210 Rock rotational slide Precipitation event 0.30 8.0E+05 Not reported11 Rock planar slide Not reported 27.50 - 112 Rock planar slide Not reported 27.50 - 113 Rock planar slide Daylighted structure 2.50 5.3E+06 114 Rock planar slide Daylighted structure 0.07 1.5E+05 115 Rock planar slide Daylighted structure 2.46 5.2E+06 116 Rock planar slide Daylighted structure 0.18 3.7E+05 117 Rock planar slide Daylighted structure 0.09 1.9E+05 118 Rock planar slide Daylighted structure 1.07 2.2E+06 119 Rock planar slide Daylighted structure 1.08 2.3E+06 120 Rock planar slide Daylighted structure 0.16 3.3E+05 121 Rock planar slide Daylighted structure 2.11 4.4E+06 122 Rock planar slide Daylighted structure 9.00 1.9E+07 123 Rock planar slide Daylighted structure 5.30 1.1E+07 124 Rock planar slide Daylighted structure 6.35 1.3E+07 125 Rock planar slide Blasting 2.00 1.5E+07 226 Rock irregular slide Earthquake 1.50 4.1E+06 127 Debris slide Precipitation event 0.75 - 128 Debris slide Precipitation event 0.20 - 129 Rock rotational slide Precipitation event 4.60 1.2E+07 130 Rock wedge slide Mined too steep 0.09 - Retrogressive31 Rock wedge slide Precipitation event 2.70 7.3E+06 Not reported32 Debris slide Precipitation event 0.19 3.0E+05 133 Debris slide Precipitation event 0.25 4.0E+05 134 Debris slide Precipitation event 0.79 1.3E+06 335 Rock wedge slide Precipitation event 0.40 6.4E+05 Not reported36 Debris slide Precipitation event 4.00 8.0E+06 137 Debris slide Precipitation event 1.13 1.8E+06 138 Debris slide Precipitation event 6.50 1.2E+07 239 Rock wedge slide Precipitation event 7.30 1.8E+07 Retrogressive40 Rock wedge slide Precipitation event 2.02 5.0E+06 141 Rock wedge slide Mined too steep 19.00 4.7E+07 142 Rock wedge slide Daylighted structure 2.00 5.0E+06 143 Rock irregular slide Daylighted structure 0.20 5.0E+05 144 Rock irregular slide Daylighted structure 0.25 - 145 Rock irregular slide Long-term weakening 1.10 2.7E+06 146 Rock rotational slide Precipitation event 0.06 1.5E+05 247 Rock irregular slide Precipitation event 1.10 2.5E+06 148 Debris slide Precipitation event 0.11 - 149 Rock block topple Precipitation event 0.20 - Retrogressive50 Rock compound slide Precipitation event 0.86 - 151 Rock compound slide Precipitation event 1.70 - 152 Rock compound slide Daylighted structure 2.00 5.4E+06 153 Rock planar slide Precipitation event 0.20 - 1167   Label Failure Mechanism Trigger Volume(Mm3)Mass(tonnes)Number of events54 Rock irregular slide Long-term weakening 0.35 - 155 Debris slide Precipitation event 0.25 - 156 Rock rotational slide Precipitation event 0.85 - 157 Rock planar slide Precipitation event 0.56 1.5E+06 Retrogressive58 Rock irregular slide Precipitation event 52.00 1.2E+08 159 Rock irregular slide Precipitation event 1.00 - 160 Rock planar slide Daylighted structure 1.10 - 161 Rock block topple Not reported 0.23 5.2E+05 Not reported62 Rock wedge slide Precipitation event 6.00 7.0E+06 163 Rock planar slide Precipitation event 1.07 - Not reported64 Rock irregular slide Blasting 0.64 2.0E+06 Not reported65 Debris slide Precipitation event 0.37 1.0E+06 Retrogressive66 Rock wedge slide Blasting 0.04 1.2E+05 167 Rock planar slide Precipitation event 0.00 1.1E+05 268 Soil rotational slide Precipitation event 0.10 - 169 Rock planar slide Precipitation event 10.00 - 170 Rock block topple Daylighted structure 1.80 4.5E+06 271 Soil rotational slide Precipitation event 0.20 - 172 Soil rotational slide Precipitation event 0.30 - 173 Rock irregular slide Not reported 2.70 - 274 Rock irregular slide Precipitation event 0.50 - 175 Rock compound slide Precipitation event 0.77 - 176 Rock rotational slide Not reported 0.46 - 177 Soil rotational slide Precipitation event 12.00 - 178 Debris slide Precipitation event 0.30 - 179 Rock wedge slide Long-term weakening 0.14 4.0E+05 180 Rock wedge slide Not reported 0.07 2.0E+05 181 Rock wedge slide Not reported 0.67 1.9E+06 182 Rock wedge slide Precipitation event 0.35 - Retrogressive83 Rock rotational slide Mined too steep 1.07 - 184 Rock planar slide Precipitation event 0.14 - 185 Debris slide Precipitation event 0.17 - 286 Rock planar slide Underground subsidence 0.16 - Retrogressive87 Rock rotational slide Precipitation event 0.35 1.0E+06 Retrogressive88 Rock planar slide Precipitation event 0.40 1.0E+06 189 Rock wedge slide Precipitation event 1.13 3.0E+06 Retrogressive90 Debris slide Precipitation event 0.18 - 191 Debris slide Precipitation event 0.12 - 192 Rock planar slide Daylighted structure 0.20 6.0E+05 193 Rock irregular slide Mined too steep 0.10 - 194 Rock compound slide Not reported 6.00 - 195 Rock block topple Not reported 0.08 - 196 Rock block topple Not reported 0.14 4.0E+05 197 Rock wedge slide Not reported 0.10 2.7E+05 198 Rock planar slide Precipitation event 0.25 - 199 Rock rotational slide Blasting 0.05 - 1100 Rock irregular slide Long-term weakening 0.70 - 1101 Rock wedge slide Blasting 0.04 1.1E+05 1102 Rock wedge slide Mined too steep 1.80 - Retrogressive103 rock flexural topple Not reported 1.00 - 1104 rock flexural topple Not reported 0.60 - 2105 Rock irregular slide Daylighted structure 0.27 6.0E+05 1168   LabelSlope Angle(°)Fall Height(m)Runout Length(m)Average Width(m)Inundation Area(m2)Path Obstruction1 20 50 175 250 - Unobstructed2 40 250 685 - 3.6E+05 Unobstructed3 21 250 1300 800 6.2E+05 Obstructed4 45 198 275 80 1.3E+04 Unobstructed5 44 325 778 200 7.4E+04 Obstructed6 45 185 410 430 2.2E+05 Unobstructed7 40 275 720 200 - Unobstructed8 55 90 165 200 - Unobstructed9 55 105 140 100 - Unobstructed10 43 120 190 240 - Unobstructed11 29 640 2330 550 8.7E+05 Channelled12 29 850 2930 550 5.9E+05 Channelled13 25 112.776 399.288 - - Unobstructed14 19 36.576 115.824 - - Unobstructed15 25 103.632 350.52 - - Unobstructed16 25 45.72 97.536 - - Unobstructed17 25 38.1 82.296 - - Unobstructed18 25 79.248 213.36 - - Unobstructed19 25 109.728 292.608 - - Unobstructed20 25 42.672 97.536 - - Unobstructed21 19 128.016 411.48 - - Unobstructed22 19 179.832 853.44 - - Unobstructed23 19 115.824 381 - - Unobstructed24 19 190.5 762 - - Unobstructed25 45 335 500 150 6.0E+04 Unobstructed26 46 209 333 225 4.7E+04 Unobstructed27 29 120 325 150 - Obstructed28 29 90 206 100 - Deflected29 36 300 640 430 1.6E+05 Unobstructed30 45 240 330 80 5.6E+03 Obstructed31 48 200 380 355 6.7E+04 Unobstructed32 46 60 98 90 - Unobstructed33 46 60 98 90 - Unobstructed34 46 156 310 225 5.4E+04 Unobstructed35 35 76 138 180 - Unobstructed36 30 250 745 400 - Deflected37 30 110 280 230 - Unobstructed38 24 220 700 400 3.5E+05 Unobstructed39 38 280 775 400 - Unobstructed40 38 170 350 300 - Unobstructed41 27 550 1341 450 3.7E+05 Obstructed42 38 195 382 250 5.1E+04 Unobstructed43 44 146 187 155 1.4E+04 Lies on wall44 44 110 160 73 1.0E+04 Lies on wall45 44 210 382 135 4.1E+04 Lies on wall46 44 40 64 100 - Unobstructed47 40 294 686 190 7.0E+04 Obstructed48 37 41 65 - - Not reported49 52 185 249 - - Unobstructed50 42 190 370 125 - Channelled51 42 230 495 125 7.6E+04 Channelled52 36 315 570 500 1.1E+05 Obstructed53 25 77 170 125 1.3E+04 Not reported169   LabelSlope Angle(°)Fall Height(m)Runout Length(m)Average Width(m)Inundation Area(m2)Path Obstruction54 50 150 210 100 - Unobstructed55 48 75 135 - - Not reported56 35 240 580 220 9.5E+04 Unobstructed57 47 160 280 130 - Lies on wall58 33 170 700 480 - Obstructed59 36 237 460 190 5.8E+04 Lies on wall60 32 100 240 650 - Unobstructed61 52 112 150 138 2.7E+04 Unobstructed62 33 175 440 350 - Unobstructed63 36 105 195 245 - Unobstructed64 60 67 91 100 3.0E+04 Obstructed65 31 95 230 100 3.7E+04 Unobstructed66 63 40 45 - - Unobstructed67 63 80 65 107 - Unobstructed68 26 42 95 - - Not reported69 30 184 680 850 - Obstructed70 35 180 360 200 5.4E+04 Unobstructed71 41 110 225 85 - Obstructed72 21 147 325 95 2.1E+04 Obstructed73 47 300 675 265 5.3E+04 Unobstructed74 42 130 245 240 3.0E+04 Unobstructed75 42 230 360 204 3.6E+04 Obstructed76 44 120 220 170 3.0E+04 Unobstructed77 30 150 600 580 - Unobstructed78 32 50 125 250 - Unobstructed79 61 135 185 80 - Unobstructed80 61 80 90 90 - Unobstructed81 61 165 240 210 4.2E+04 Unobstructed82 26 90 155 - - Unobstructed83 38 87 172 250 - Unobstructed84 32 60 65 - - Obstructed85 38 85 189 90 - Unobstructed86 60 80 91 200 - Unobstructed87 40 135 280 265 - Unobstructed88 26 45 192 180 3.1E+04 Unobstructed89 45 138 250 300 4.9E+04 Unobstructed90 43 136 250 90 2.1E+04 Unobstructed91 42 135 178 140 - Obstructed92 40 140 250 220 2.6E+04 Unobstructed93 40 195 290 80 - Unobstructed94 30 300 720 300 8.4E+04 Unobstructed95 43 90 115 60 - Unobstructed96 45 107 132 125 - Unobstructed97 38 294 486 - - Unobstructed98 40 76 128 99 - Unobstructed99 35 57 103 65 - Unobstructed100 34 200 475 360 8.0E+04 Unobstructed101 44 212 270 105 2.0E+04 Unobstructed102 43 206 535 150 4.9E+04 Unobstructed103 44 365 521 - - Unobstructed104 50 300 450 - - Obstructed105 41 344 538 300 - Obstructed170   Label Sources1 Aydan et al. (1996)2 Farina et al. (2013); UNOSAT (2011); Tutuoglu et al. (2010)3 Farina et al. (2013); UNOSAT (2011); Tutuoglu et al. (2010)4 Reid and Stewart (1986); Martin (1990)5 Martin and Stacey (2013); da Franca (1997); Fisher (2009)6 Behbahani et al. (2013); Moarefvand et al. (2012); Darbor et al. (2010)7 Sheng and Lui (1995)8 Asof et al. (2010)9 Almenara et al. (2011)10 Goldberg and Frizzell (1989)11 Pankow et al. (2014); Moharana and Lonergan (2014); Hibert et al. (2014); Ross and Sutherlin (2015)12 Pankow et al. (2014); Moharana and Lonergan (2014); Hibert et al. (2014); Ross and Sutherlin (2015)13 Yost (2009)14 Yost (2009)15 Yost (2009)16 Yost (2009)17 Yost (2009)18 Yost (2009)19 Yost (2009)20 Yost (2009)21 Yost (2009)22 Yost (2009)23 Yost (2009)24 Yost (2009)25 Weichert (1994); Sjöberg (1996)26 Voight and Kennedy (1979)27 Sharon (2011); Sharon et al. (2013)28 Sharon (2011); Sharon et al. (2013)29 Hormazabal et al. (2013); Rippere et al. (1999)30 Zhou et al. (2008)31 Dyke (2009)32 Sheets (2011)33 Sheets (2011)34 Bates et al. (2005); Sheets (2011)35 Sheets (2011)36 Sheets et al. (2014); Yang et al. (2011a)37 Sheets (2011)38 Sheets et al. (2014); Yang et al. (2011a)39 Rose and Sharon (2000)40 Rose and Sharon (2000)41 Rose (2011)42 Rose (2011); Armstrong and Rose (2009)43 Rose (2011); Armstrong and Rose (2009)44 Armstrong (2011)45 Rose (2011); Armstrong and Rose (2009)46 Tannant and LeBreton (2006)47 Moffett and Adkerson (2003); Srikant et al. (2007); Ginting et al. (2011)48 Jhanwar and Thote (2011)49 Brawner et al. (1975); Brawner and Stacey (1979)50 Cremeens (2003); Cremeens et al. (2000)51 Cremeens (2003); Cremeens et al. (2000)52 EMPR (2007)53 Jhanwar and Thote (2011)171   Note: Case history citations are included in the reference list. Label Sources54 Yamaguchi and Shimotani (1986)55 Jhanwar and Thote (2011)56 Nasuf et al. (1993)57 Yang et al. (2011b)58 Tűrk and Koca (1993)59 Oldcorn and Seago (2007)60 Coulthard et al. (2004)61 Kayesa (2006); Mercer (2006)62 Broadbent and Zavodni (1981); Brawner (1986); Rose and Hungr (2007)63 Cruden and Masoumzadeh (1987); MacRae (1985)64 Kelly et al. (2002)65 Mercer (2006)66 Roux et al. (2006); Mercer (2006); de Jager and Ludik (2007); Lynch and Malovichko (2006)67 Roux et al. (2006); Mercer (2006); de Jager and Ludik (2007); Lynch and Malovichko (2006)68 Jhanwar and Thote (2011)69 Terbrugge and Hanif (1981)70 Naismith and Wessels (2005); Wessels (2009)71 Jhanwar and Thote (2011)72 Jhanwar and Thote (2011)73 Golder Associates (2011)74 Coates et al. (1979)75 Coates et al. (1979)76 Johnson et al. (2007)77 D'Elia et al. (1996)78 Fourie and Haines (2007)79 Hutchinson et al. (2013); MacQueen et al. (2013)80 Hutchinson et al. (2013); MacQueen et al. (2013)81 Hutchinson et al. (2013); MacQueen et al. (2013)82 Yanbo et al. (2010); Jiang et al. (2012)83 Atkins and Pasha (1973); Clough et al. (1979)84 Jhanwar and Thote (2011)85 Speight (2002)86 Dight (2006); Szwedzicki (2001)87 Day and Seery (2007)88 Venter et al. (2013)89 Seegmiller (1972)90 Jones et al. (2011)91 Jones (2011)92 Joass et al. (2013)93 Kramadibrata et al. (2012)94 Anonymous95 Anonymous96 Anonymous97 Anonymous98 Anonymous99 Anonymous100 Anonymous101 Anonymous102 Anonymous103 Rose and Hungr (2007)104 Wyllie (1980)105 Anonymous172       Appendix B  Remote sensing observations used to develop empirical database   173  Case Number: 2 and 3 Mine:  Afsin-Elbistan  Image source: UNOSAT, public domain Image date: 2011 Contribution to data point: Runout length, surface area, back break    174  Case Number: 4 Mine:  Afton  Image source: Author’s personal photo Image date: 2006 Contribution to data point: Context       175   Case Number: 5 Mine:  Aguas Claras Image source: Google Earth Pro, reproduced with permission. Image date: 2002 Contribution to data point: Context, width    176  Case Number: 11 and 12 Mine: Bingham Canyon Image source: Google Earth Pro, reproduced with permission. Image date: 2013 Contribution to data point: Surface area, width, locating main scarp of first event    177  Case Number: 25 Mine: Brenda Image source: Google Earth Pro, reproduced with permission. Image date: 2004 Contribution to data point: Back break, rupture surface width    178  Case Number: 27 and 28 Mine: Cowal Image source: www.savelakecowal.org, public domain. Image date: 2008 Contribution to data point: Context, obstruction   179  Case Number: 30 Mine: Daye iron mine Image source: Google Earth Pro, reproduced with permission. Image date: 2012 Contribution to data point: Context    180  Case Number: 34 Mine: Gold Quarry Image source: Google Earth Pro, reproduced with permission. Image date: 2006 Contribution to data point: Context, back break    181  Case Number: 38 Mine: Gold Quarry Image source: Google Earth Pro, reproduced with permission. Image date: 2010 Contribution to data point: Runout length, surface area, deposit width    182  Case Number: 43, 44, 45 Mine: Goldstrike Image source: Google Earth Pro, reproduced with permission. Image date: 2010 Contribution to data point: Width, back break, context    case 45 case 43 case 44 183  Case Number: 52 Mine: Huckleberry Image source: Aerial photograph, reproduced with permission of UBC air photo library. Image date: 2007 Contribution to data point: Width, back break, context    184  Case Number: 53 Mine: Junad Image source: Google Earth Pro, reproduced with permission. Image date: 2007 Contribution to data point: Context, rupture surface width    185  Case Number: 53 Mine: Kumtor Image source: Google Earth Pro, reproduced with permission. Image date: 2007 Contribution to data point: Runout length, surface area, width    186  Case Number: 65 Mine: Mount Keith Image source: Google Earth Pro, reproduced with permission. Image date: 2005 Contribution to data point: Context, back break     187  Case Number: 70 Mine: Nchanga Image source: Google Earth Pro, reproduced with permission. Image date: 2004 Contribution to data point: Runout length, surface area, width    188  Case Number: 71 Mine: Niljai Image source: Google Earth Pro, reproduced with permission. Image date: 2004 Contribution to data point: Runout length, surface area, width, back break, obstruction    189  Case Number: 73 Mine: Permanente Image source: http://www.lahopenspace.com/Permanente/CurrentSituation.htm, public domain. Image date: 2005 Contribution to data point: Context     190  Case Number: 76 Mine: Rotowaro Image source: Google Earth Pro, reproduced with permission. Image date: 2002 Contribution to data point: Context, back break    191  Case Number: 81 Mine: Savage River Image source: Google Earth Pro, reproduced with permission. Image date: 2013 Contribution to data point: Runout length, surface area, width    192  Case Number: 88 Mine: Tom Price Image source: Google Earth Pro, reproduced with permission. Image date: 2010 Contribution to data point: Runout length, surface area, width, back break    193  Case Number: 90 and 91 Mine: Wallaby Image source: Google Earth Pro, reproduced with permission. Image date: 2013 Contribution to data point: Context, width, back break    Case 90Case 91194  Case Number: 92 Mine: West Angelas Image source: Google Earth Pro, reproduced with permission. Image date: 2010 Contribution to data point: Runout length, surface area, width, back break         195      Appendix C  Example risk calculation   196  C.1 Scenario A landslide is developing at the crest of a 300 m high wall at overall angle=40°. The pit floor is 250 m across to the opposing wall.  You create an exclusion zone 150 m from the slope toe.  A dozer is building a berm at the edge of the exclusion zone and trucks make 1 minute deliveries every 10 minutes.  Using a coarse prism network the time-of-failure analysis estimates the wall will likely collapse in 30 days and you estimate a 95% probability of failure this year.  Your volume estimate is 100,000 m3.  Calculate the risk to a) the most exposed individual and b) the group working at the edge of the exclusion zone.  Note: This example evaluates risk to a single location in the pit.  A more robust evaluation should include all locations, including traffic on ramps and people concentrating around shovels.    C.2 Assumptions  The rock is fresh, massive, granite;  You are confident in your volume estimate, so you choose to use the H/L vs. V mobility index.  Model sensitivity to volume is 6% symmetrically distributed about the mean (Section 4.7);  You are 90% confident in your monitoring system.  There remains a possibility part of the wall may collapse between prisms;  No crest back break.  197  C.3 Estimating P(S:L) Length from the failure scarp to the edge of the exclusion zone is 508 m.  For a 300 m fall height, the tangent of the Fahrböschung angle is 0.59.  Figure C1 shows the probability of exceedance of this runout estimates for the base case volume and +/- 100% contingency estimates.   Figure C1. Probabilistic runout estimates for risk calculation example 198  C.4 Estimating P(T:S) Truck traffic at the edge of the exclusion zone varies from none (lunch break) to several trucks backed up waiting to dump.  This problem assumes there could be up to three trucks at the edge of the exclusion zone at one time.  An operating mine should use their traffic data to create a Poisson distribution.  Traffic is distributed as: Probability no one is present: 10% Probability of the dozer and no trucks: 76% Probability of the dozer and one truck: 10% Probability of the dozer and two trucks: 3% Probability of the dozer and three trucks: 1%  Since the truck is stationary when it is dumping and one truck per ten minutes, there are 144 1-minute long occurrences a truck will be present in the exclusion zone per day.  The time spent in the exclusion zone is 0.1 for the truck drivers: ሺ்ܲ:ௌሻ ൌ ൬144	݉݅݊݁ݐݑ	݃݊݋݈	1,440ݏ݁ܿ݊݁ݎݑܿܿ݋	ݏ݁ݐݑ݊݅݉	ݎ݁݌	ݕܽ݀ 	൰ ൌ 0.1   Figure C2 is an accounting of the scenario probabilities. 199   Figure C2. Event tree calculation for example risk calculation  C.5 Individual risk The dozer operator is the most exposed individual.  Individual risk to loss of life is: ܴ݅݇ݏ ൌ෍ ሺܲ௅ሻ ൈ ሺܲௌ:௅ሻ ൈ ሺ்ܲ:ௌሻ ൈ ܸ	 ൈ ܧ௡௜ୀଵ 200  ܴ݅݇ݏ ൌ ሾ0.95	 ൈ 0.88	 ൈ 0.1 ൈ 0.04 ൈ 0.76	 ൈ 1 ൈ 1ሿ൅ ሾ0.95	 ൈ 0.06	 ൈ 0.1 ൈ 0.03 ൈ 0.76	 ൈ 1 ൈ 1ሿ൅ ሾ0.95	 ൈ 0.06	 ൈ 0.1 ൈ 0.06 ൈ 0.76	 ൈ 1 ൈ 1ሿ ܴ݅݇ݏ ൌ 0.0029 Therefore the dozer operator is exposed to individual risk of 1:1,000.  C.6 Societal risk Each scenario in Figure C2 generates an f-N pair and accumulate to generate F-N pairs.  Plotting them into an F-N curve such as Figure C3 gives a comparison of the scenario to risk criteria.  The mine should develop their own version of Figure C3 by discussing acceptable risk criteria with the stakeholders.   Dozer + 0 trucks: ܴ݅݇ݏ ൌ ܴ݅݇ݏ௩௢௟௨௠௘	௔௦	௘௦௧௜௠௔௧௘ௗ ൅ ܴ݅݇ݏ଴.ହ௩௢௟௨௠௘ ൅ ܴ݅݇ݏଶ௩௢௟௨௠௘ ܴ݅݇ݏଵ ൌ ሾ0.95	 ൈ 0.88	 ൈ 0.1 ൈ 0.04 ൈ 0.76	ሿ ൅ ሾ0.95	 ൈ 0.06	 ൈ 0.1 ൈ 0.03 ൈ 0.76ሿ൅ ሾ0.95	 ൈ 0.06	 ൈ 0.1 ൈ 0.06 ൈ 0.76ሿ ܴ݅݇ݏଵ ൌ 0.0075  Dozer + 1 truck: ܴ݅݇ݏ ൌ ܴ݅݇ݏ௩௢௟௨௠௘	௔௦	௘௦௧௜௠௔௧௘ௗ ൅ ܴ݅݇ݏ଴.ହ௩௢௟௨௠௘ ൅ ܴ݅݇ݏଶ௩௢௟௨௠௘ ܴ݅݇ݏଶ ൌ ሾ0.95	 ൈ 0.88	 ൈ 0.1 ൈ 0.04 ൈ 0.1	ሿ ൅ ሾ0.95	 ൈ 0.06	 ൈ 0.1 ൈ 0.03 ൈ 0.1ሿ൅ ሾ0.95	 ൈ 0.06	 ൈ 0.1 ൈ 0.06 ൈ 0.1ሿ ܴ݅݇ݏଶ ൌ 0.0046 201   Dozer + 2 trucks: ܴ݅݇ݏ ൌ ܴ݅݇ݏ௩௢௟௨௠௘	௔௦	௘௦௧௜௠௔௧௘ௗ ൅ ܴ݅݇ݏ଴.ହ௩௢௟௨௠௘ ൅ ܴ݅݇ݏଶ௩௢௟௨௠௘ ܴ݅݇ݏଷ ൌ ሾ0.95	 ൈ 0.88	 ൈ 0.1 ൈ 0.04 ൈ 0.03	ሿ ൅ ሾ0.95	 ൈ 0.06	 ൈ 0.1 ൈ 0.03 ൈ 0.03ሿ൅ ሾ0.95	 ൈ 0.06	 ൈ 0.1 ൈ 0.06 ൈ 0.03ሿ ܴ݅݇ݏଷ ൌ 0.00012  Dozer + 3 trucks: ܴ݅݇ݏ ൌ ܴ݅݇ݏ௩௢௟௨௠௘	௔௦	௘௦௧௜௠௔௧௘ௗ ൅ ܴ݅݇ݏ଴.ହ௩௢௟௨௠௘ ൅ ܴ݅݇ݏଶ௩௢௟௨௠௘ ܴ݅݇ݏସ ൌ ሾ0.95	 ൈ 0.88	 ൈ 0.1 ൈ 0.04 ൈ 0.01	ሿ ൅ ሾ0.95	 ൈ 0.06	 ൈ 0.1 ൈ 0.03 ൈ 0.01ሿ൅ ሾ0.95	 ൈ 0.06	 ൈ 0.1 ൈ 0.06 ൈ 0.01ሿ ܴ݅݇ݏସ ൌ 0.000039  Cumulative frequency of N or more fatalities per year: Scenario f N Dozer + 0 trucks Risk1 + Risk2 + Risk3 + Risk4 = 0.012 1 Dozer + 1 truck Risk2 + Risk3 + Risk4 = 0.0047 2 Dozer + 2 trucks Risk3 + Risk4 = 0.00015 3 Dozer + 3 trucks Risk4 = 0.000039 4  202   Figure C3. F-N plot for example risk calculation   The exclusion zone is inadequate and workers are exposed to an unacceptably high risk to loss of life.  The exclusion zone should be extended until the risk is in the tolerable or acceptable ranges.   

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