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Characterization and analysis of discontinuous subsidence associated with block cave mining using advanced… Woo, Kyuseok 2011

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 CHARACTERIZATION AND ANALYSIS OF DISCONTINUOUS SUBSIDENCE ASSOCIATED WITH BLOCK CAVE MINING USING ADVANCED NUMERICAL MODELLING AND INSAR DEFORMATION MONITORING  by  Kyuseok Woo  M.S. Chung-Ang University, 2002   A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  in  The Faculty of Graduate Studies  (Geological Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)   August 2011  © Kyuseok Woo, 2011   ii Abstract  While block caving presents an economic means to develop lower grade ore deposits, it often leads to significant ground deformations threatening the safety of overlying mine infrastructure. For guidance on relationships between caving depth and surface subsidence, a comprehensive cave mining database was developed and the database clearly shows caving- induced surface deformations tend to be discontinuous and asymmetric due to large movements around the cave being controlled by geologic structures, rock mass heterogeneity and topographic effects. Also shown is that as undercut depth increases, the magnitude and extent of the caved zone on surface decreases. Numerical modelling conducted in a benchmark study testing several different numerical methods (finite-element, distinct-element, FEM-DEM with brittle fracture and 3-D finite-difference) indicates this is only the case for macro deformations and the lateral extent of smaller strain deformations increases as a function of undercut depth, which indicates caution should be taken against relying on existing empirical design charts for estimates of caving-induced subsidence where small strain subsidence is of concern, as the empirical data does not properly extrapolate beyond the macro deformations. In addition, sophisticated 3-D numerical modelling was investigated as a means of predicting the extent and magnitudes of caving-induced surface subsidence. Results from a back analysis of the cave-pit interactions at the Palabora mine were used to constrain the rock mass properties and far-field in-situ stresses derived from field characterization data. The “best fit” set of input properties obtained was then used for forward modelling. Further calibration was performed using high-resolution InSAR monitoring data. The close fit achieved between the predictive 3-D numerical model and InSAR monitoring data demonstrates the significant value of InSAR calibrated 3-D numerical models. Collectively, the results of this research help to further the characterization, assessment and understanding of block-caving subsidence, by addressing existing limitations in the use of empirical and numerical subsidence analysis methods. The limitations and uncertainty arising from mine site data are described, specifically the representation of mine geology, rock mass properties, in-situ stresses and cave propagation, together with means to constrain these   iii inputs and calibrate sophisticated 3-D numerical models through back analysis and integration with InSAR data.                 iv Preface Chapter 2 “Empirical investigation and characterization of surface subsidence related to block cave mining” was co-authored by Kyuseok Woo, Dr. Erik Eberhardt, Dr. Davide Elmo, and Dr. Doug Stead. As the lead author, Kyuseok Woo built the block caving database using materials available in the public domain, carried out the data analyses, and prepared the manuscript. Dr. Eberhardt provided guidance in the development of the database and reviewed the manuscript and provided editorial comments. Dr. Elmo provided guidance in the development of the numerical models used to support and provide insights into the trends detected. Chapter 3 “Benchmark testing of numerical capabilities for modelling the influence of undercut depth on caving-induced subsidence” was co-authored by Kyuseok Woo, Dr. Erik Eberhardt, Dr. Doug Stead, and Dr. Davide Elmo. Mr. Woo, Dr. Eberhardt, Dr. Stead, and Dr. Elmo jointly identified and designed the research program, which was developed as part of a competitive research contract with the Centre for Excellence in Mining Innovation (CEMI). CEMI specified the problem geometry and several input constraints.  Mr. Woo performed numerical modelling, completed the analytical studies, and prepared the manuscript. Dr. Eberhardt, Dr. Stead, and Dr. Elmo reviewed the manuscript and provided editorial comments. Chapter 4 “Integration of field characterization, mine production and InSAR monitoring data to constrain and calibrate 3-D numerical modelling of block caving-induced subsidence” was co-authored by Kyuseok Woo, Dr. Erik Eberhardt, Dr. Doug Stead, Dr. Bernhard Rabus, and Dr. Alex Vyazmensky. Mr. Woo, Dr. Eberhardt, and Dr. Stead identified and designed the research program. Dr. Vyazmensky provided data and input from Rio Tinto, to supplement that collected at the mine site by the research team. Dr. Rabus directed and carried out the processing of the InSAR data, Mr. Woo performed the research, data analyses and 3-D numerical modelling, and prepared the manuscript. Dr. Eberhardt, Dr. Vyazmensky, Dr. Rabus, and Dr. Stead reviewed the manuscript and provided editorial comments. Chapter 4 is currently in review. Versions of chapters 2 and 3 are to be submitted. Chapter 2: Woo, K. Eberhardt E. Elmo, D. Empirical investigation and characterization of surface subsidence related to block cave mining. (To be submitted) Chapter 3: Woo, K. Eberhardt E. Elmo, D. Stead, D. Benchmark Testing of Numerical Capabilities for Modelling the Influence of Undercut Depth on Caving-Induced Subsidence. (To be submitted) Chapter 4 Woo, KS. Eberhardt, E. Rabus, B. Stead, D. Vyazmensky, A. Integration of field characterization, mine production and InSAR monitoring data to constrain and calibrate 3- D numerical modelling of block caving-induced subsidence. (In Review)   v Table of Contents  Abstract .................................................................................................................................... ii Preface ..................................................................................................................................... iv Table of Contents .................................................................................................................... v List of Tables .......................................................................................................................... ix List of Figures .......................................................................................................................... x Acknowledgements ............................................................................................................. xvii Dedication ........................................................................................................................... xviii Chapter  1: Introduction ........................................................................................................ 1 1.1 Problem Statement ................................................................................................................. 1 1.2 Thesis Objectives ................................................................................................................... 2 1.3 Thesis Structure ...................................................................................................................... 3 1.4 Literature Review: Subsidence Induced by Block Caving ............................................... 4 1.4.1 Overview .......................................................................................................................... 4 1.4.2 Caving Subsidence Mechanism .................................................................................... 6 1.4.3 Factors Influencing Subsidence Development ............................................................ 8 1.4.4 Micro- and Macro-Subsidence .................................................................................... 10 1.5 Literature Review: Block Caving Subsidence Analysis ................................................. 11 1.5.1 Empirical Design Chart ................................................................................................ 11 1.5.2 Analytical Methods ...................................................................................................... 12 1.5.3 Numerical Modelling ................................................................................................... 13 Chapter  2: Empirical Investigation and Characterization of Surface Subsidence Related to Block Cave Mining ............................................................................................. 26 2.1 Introduction ........................................................................................................................... 26 2.2 The UBC Block Caving Subsidence Database ................................................................ 27 2.2.1 General Trends .............................................................................................................. 28 2.2.2 Caving-Induced Subsidence Data ............................................................................... 29   vi 2.3 Database Analysis: Caving and Fracture Initiation Angles ............................................ 30 2.3.1 Influence of Topography ............................................................................................. 31 2.3.2 Influence of Orebody Characteristics ......................................................................... 33 2.4 Discussion: Influence of Undercut Depth ......................................................................... 34 2.5 Conclusions ........................................................................................................................... 36 Chapter  3: Benchmark Testing of Numerical Methods for Modelling the Influence of Undercut Depth on Caving-Induced Subsidence ............................................................... 54 3.1 Introduction ........................................................................................................................... 54 3.2 Numerical Modelling Methodology .................................................................................. 55 3.2.1 Model Geometry ........................................................................................................... 55 3.2.2 Numerical Modelling Software Used ......................................................................... 56 3.2.3 Rock Mass Properties ................................................................................................... 58 3.2.4 In-Situ Stresses .............................................................................................................. 59 3.2.5 Simulation of Draw and Caving ................................................................................. 60 3.3 Numerical Analysis Results ................................................................................................ 61 3.3.1 Continuum Analysis (2-D versus 3-D) ...................................................................... 61 3.3.2 Discontinuum Analysis ................................................................................................ 62 3.3.3 Discontinuum with Brittle Fracture Results .............................................................. 63 3.4 Discussion ............................................................................................................................. 64 3.4.1 Trends with Depth ........................................................................................................ 65 3.4.2 Caving Angle ................................................................................................................. 67 3.4.3 Fracture Initiation Angle .............................................................................................. 69 3.4.4 Subsidence Angle ......................................................................................................... 70 3.5 Conclusions ........................................................................................................................... 71 Chapter  4: Integration of Field Characterization, Mine Production and InSAR Monitoring Data to Constrain and Calibrate 3-D Numerical Modelling of Block Caving-Induced Subsidence ................................................................................................. 99 4.1 Introduction ........................................................................................................................... 99 4.2 Palabora Case History ....................................................................................................... 100 4.3 Model Costraint and Calibration through Back Analysis ............................................. 101 4.3.1 Palabora 3-D Model Geometry ................................................................................. 101   vii 4.3.2 Modelling of Caving Influence ................................................................................. 102 4.3.3 Rock Mass Properties ................................................................................................. 103 4.3.4 In-Situ Stresses ............................................................................................................ 104 4.3.5 Back Analysis and Model Calibration ..................................................................... 105 4.4 InSAR Monitoring as a Means to Constrain Modelling Displacements..................... 107 4.5 Forward-Modelling of Caving-Induced Displacements (2009-2010) ......................... 108 4.5.1 Modifications to Model Geometry ........................................................................... 108 4.5.2 RADARSAT-2 Deformation Monitoring ................................................................ 109 4.5.3 FLAC3D Forward Modelling Results and Comparison with InSAR Data ......... 109 4.6 Conclusions ......................................................................................................................... 111 Chapter  5: Thesis Discussion and Conclusions ............................................................... 132 5.1 Summary ............................................................................................................................. 132 5.1.1 Empirical Investigation and Characterization of Block Caving Subsidence ...... 132 5.1.2 Benchmark Testing for Block Cave Mining Using Numerical Analysis ............ 134 5.1.3 Integration of Field Characterization, Mine Production and InSAR Monitoring Data to Constrain and Calibrate 3-D Numerical Modelling of Block Caving-Induced Subsidence ............................................................................................................................... 137 5.2 Key Conclusions and Scientific Contributions .............................................................. 138 5.3 Future Research .................................................................................................................. 140 References ............................................................................................................................ 142 Appendices ........................................................................................................................... 157 Appendix A: Derived Subsidence Data used to Develop Empirical Database ................. 157 A.1 Subsidence Data for Block Cave Operations ...................................................... 158 A.2 Subsidence Data for Panel Cave Operations ....................................................... 162 A.3 Subsidence Data for Sublevel Caving, Shringkage Stoping, and Top Slicing Operations ..................................................................................................................... 164 A.4 Subsidence Data for Sublevel Caving, Shrinkage Stoping and Top Slicing Operations ..................................................................................................................... 168 Appendix B: Detailed Background Descriptions of Subsidnece Observations Complied in the Empirical Database ..................................................................................................... 169   viii Appendix  C: Depth-Dependent Material Properties used for Benchmark Testing of Numerical Methods for Modelling the Influence of Undercut Depth on Caving-Induced Subsidence ......... 230 Appendix D: Representative Input Source Codes Used for Numerical Modelling Benchmark Study .............................................................................................................. 232 D.1 ELFEN Benchmark: 500m Deep Undercut ......................................................... 233 D.2 UDEC Benchmark: 500m Deep Undercut with Orthogonal Jointing at 0 and 90 Degrees  ........................................................................................................................ 239 D.3 UDEC Benchmark: 500m Deep Undercut with Orthogonal Jointing at 45 and 135 Degrees ......................................................................................................................... 247 D.4 FLAC3D Benchmark: 500m Deep Undercut ............................................................ 258 Appendix E: Major Lithological Units at Palabora and Summary of their Assessed Rock Mass Characteristics, Used to Develop the FLAC3D Palabora Model .............................................. 261      ix List of Tables  Table 1.1.    Summary of the evolution of subsidence models (Flores & Karzulovic, 2004) 16 Table 1.2.    Most commonly applied numerical methods for rock mechanics problems  ..... 17 Table 1.3.    Numerical studies of surface subsidence ........................................................... 17 Table 2.1.   Comparison of previous databases reporting subsidence data for mass mining operations ................................................................................................................................ 38 Table 3.1.   Rock mass properties used for conceptual benchmark model testing provided by the Centre for Excellence in Mining Innovation (CEMI) ....................................................... 73 Table 3.2.  Depth-dependent Mohr-Coulomb rock mass properties derived for the 500 to 2000m deep undercut models ................................................................................................. 73 Table 4.1.    Ranges of intack rock properties and rock mass rating values compiled from mine geotechnical reports and internal field assessments, and corresponding lower and uper bound rock mass properties derived ..................................................................................... 113 Table 4.2.    Results from Palabora in-situ stress studies and measurement campaigns ...... 113 Table 4.3.  Horizontal to vertical in-situ stress ratios (Ko) used in different numerical modelling studies for Palabora .............................................................................................. 114 Table 4.4.    Back-analyzed FLAC3D rock mass properties providing the best fit to the observed outline of the northwest wall failure. K and G denote the bulk and shear modulus, respectively, as derived from estimates of the rock mass Young’s modulus and Poisson’s ratio ....................................................................................................................................... 114      x List of Figures  Fig. 1.1. 2005 failure of the northwest wall at Palabora following break-through of the cave into the pit floor. Photograph courtesy of Rio Tinto Technical Serivces ............................... 18 Fig. 1.2. Classification of underground mining methods (from Brady & Brown, 2006) ....... 18 Fig. 1.3. Illustration of the block cave mining method (from Hamrin, 1982) ........................ 19 Fig. 1.4. Conceptual model of block caving-induced subsidence and corresponding points from associated text (from Van As et al., 2003, based on Abel & Lee, 1980) ....................... 19 Fig. 1.5. Subsidence deformation zones as defined by Van As et al. (2003) ......................... 20 Fig. 1.6. Relative importance of the main causes of subsidence in underground mines by caving methods suggested by Flores & Karzulovic (2002) .................................................... 20 Fig. 1.7. Laubscher's (2000) Mining Rock Mass Rating (MRMR) system, an empirical design chart, for assessing cave angle (angle of break) based on measurable geological parameters ............................................................................................................................... 21 Fig. 1.8. Idealized model used in limit equilibrium analysis of progressive hangingwall caving proposed by Hoek (1974). After Flores & Karzulovic (2004) .................................... 22 Fig. 1.9. (a) Finite-element modelling of cave-pit interactions (Beck & Pfitzner, 2008), and (b) 3DEC modelling of cave-pit interactions (Brummer et al., 2006) .................................... 23 Fig. 1.10. Design chart for estimating the angle of break in a transition from open pit to underground mining by block/panel caving for rock masses of different geotechnical quality and undercut level (UCL) depths in the range from 600 to 1700 metres; Poor to Fair: GSI=30-50, Fair to Good: GSI=50-70, and Good to Very Good: GSI=70-90 (GSI=Geological Strength Index) (Flores & Karzulovic, 2004) ............................................ 24 Fig. 1.11. Cave-pit interaction in the Palabor mine simulated by hybrid finite- element/discrete-element modelling technique (Vyazmensky et al. 2010b). (a) NW-SE section of the Palabora mine; (b) Pit slope deformation at cave breakthrough for model P1 (with a tensile strength increase of 100% in the foskorite and 150% in the micaceous pyroxemite); (c) Pit slope deformation at 40% ore extraction  for model P1; (d) Pit slope deformation at cave breakthrough for model P2 (with a tensile strength increase of 150% in the foskorite and 200% in the micaceous pyroxemite; and (e) Pit slope deformation at 40% ore extraction for model P2 ..................................................................................................... 25   xi Fig. 2.1. Definition of block caving deformation zones as defined by Van As et al. (2003) . 39 Fig. 2.2. General breakdown of cave mining data in database by: (a) regional distribution, (b) mining method (BC = block cave, PC = panel cave, SC = sublevel cave), and (c) resource mined. Reported are the relative percentages followed by the total number of cases in parentheses. Symbols in each legend are ordered from highest percentage to lowest ........... 40 Fig. 2.3. Breakdown of block heights being mined for the block caving cases in the database, showing a trend towards the minnig of larger blocks ............................................................. 41 Fig. 2.4. Breakdown of undercut depths associated with the block caving cases in the database showing a trend towards the development of deeper undercuts .............................. 42 Fig. 2.5. Undercut depth versus caving angle for block , panel, and sub-level caving operations. Each line segment represents the range in caving angles measured from different sides of the undercut; the greater the range the higher the degree of asymmetry ................... 43 Fig. 2.6. Undercut depth versus fracture initiation angle for block, panel, and sub-level caving operations. Each line segment represents the range in fracture initiation angles measured from different sides of the undercut; the greater the range the higher the degree of asymmetry ............................................................................................................................... 44 Fig. 2.7. Undercut depth versus caving, fracture initiation and subsidence anlges for block caving operations. Each line segment represents the range in angles measured from different sides of the undercut; the greater the range the higher the degree of asymmetry ................... 45 Fig. 2.8. Undercut depth versus caving, fracture initiation and subsidence anlges for panel caving operations. Each line segment represents the range in angles measured from different sides of the undercut; the greater the range the higher the degree of asymmetry ................... 46 Fig. 2.9. Undercut depth versus caving angle for global block and panel caving operations, colour coded according to the general characteristics of the surface topography. Each line segment represents the range in caving angles measured from different sides of the undercut; the greater the range the higher the degree of asymmetry ...................................................... 47 Fig. 2.10. Influence of topography observed visually in Google Earth satellite images: (a) flat topography (Northparkes mine, Australia), and (b) irregular topography (El Teniente mine, Chile). Surface subsidence area is marked by dashed line ..................................................... 48 Fig. 2.11. Finite-element modelling of influence of topography on caving-induced subsidence assuming typical surface profiles visually identified in the UBC database. The   xii same geological inputs used for the comparative models in Chapter 3 were applied. In order of increasing degree of assymetry (cave-surface interactions) relative to the position of the undercut below, these are: (a) flat topography, (b) mountain peak, (c) rising slope ending in a mountain peak, (d) rising slope, and (e) slope with plateau. Note that grey shaded area approximates zone of caving .................................................................................................. 49 Fig. 2.12. Undercut Depth versus caving angle for global block and panel caving operations, colour coded according to the resource being mined. Each line segment represents the range in caving angles measured from different sides of the undercut; the greater the range the higher the degree of asymmetry .............................................................................................. 50 Fig. 2.13. Influence of orebody geology on symmetry/asymmetry in surface subsidence as observed in Kimberley mine (diamond kimberlite): (a) Google Earth satellite image, and (b) geology cross section (De Beers, 2008) .................................................................................. 51 Fig. 2.14. Influence of orebody geology on symmetry/asymmetry in surface subsidence as observed in San Manuel mine (copper porphyry): (a) Google Earth satellite image, and (b) geology cross section (Sandibak, 2004).................................................................................. 52 Fig. 2.15. Caving-induced brittle fracture and subsidence for undercut depths of:  500 m (top), and  2000 m (bottom). The continuous black lines to the left and right of the undercut are bounding faults........................................................................................................................ 53 Fig. 3.1. Generalized E-W cross section through the Resolution Deposit (Rio Tinto, 2008), on which the conceptual geometry for this benchmarking study, as defined by the Centre for Excellence in Mining Innovation (CEMI), was loosely based ............................................... 74 Fig. 3.2. Conceptual panel cave mining geometry for benchmark testing specified by the Centre for Excellence in Mining Innovation (CEMI): (a) plan view, and (b) A-B section. Panel dimensions are 500 x 1000m ........................................................................................ 75 Fig. 3.3. Phase2 model geometry for the 2000m deep undercut simulation, showing the variable orientation, spacing and persistence of joint elements introduced above the undercut. For scale, the model is 10,500m in length and 4200m in depth ............................................. 76 Fig. 3.4. FLAC3D model geometry: (a) in plan view, with semi-transparency to show projection of the bounding faults through the model (dark blue), and (b) north and south section showing the fault interfaces in dark blue .................................................................... 77   xiii Fig. 3.5. (a) UDEC model geometry for the 2000m deep undercut simulation, showing (b) orthogonal joint pattern and (c) an orthogonal joint pattern superimposed with a second pattern at 45 and 135 degrees. Note that the lower close-up views are 250 by 250 m.. ......... 78 Fig. 3.6. ELFEN model geometry for the 2000m deep undercut simulation, showing the extended discrete fracture network used Note that this is the same DFN as used for the Phase2 models. (Eberahrdt et al., 2011) ................................................................................. 79 Fig. 3.7. In-situ stress information for benchmark testing as specified by CEMI, SHmax is north-south section and SHmin is east-west section (Eberhardt et al., 2011) ............................ 80 Fig. 3.8.  Method used to simulate draw for Phase2D, FLAC3D and UDEC model ............. 81 Fig. 3.9. Method used to simulate draw for ELFEN model, involving a block deletion algorithm ................................................................................................................................. 81 Fig. 3.10. Phase2 continuum subsidence results for undercut depths of 500 to 2000m. Vertical displacement contours are plotted with 1m minimum cut off .................................. 82 Fig. 3.11. Phase2 continnum subsidence results with the inclusion of joint elements, for undercut depths of 500 to 2000m. Vertical displacement contours are plotted with 1m minimum cut off ..................................................................................................................... 83 Fig. 3.12. FLAC3D subsidence results from 500 to 2000m after 200,000 (0.25m cut off): Surface section (top) and north-south section (bottom) .......................................................... 84 Fig. 3.13. UDEC subsidence results from 500 to 2000m (1m cut off) with orthogonal joint sets........................................................................................................................................... 85 Fig. 3.14. UDEC subsidence results from 500 to 2000m (1m cut off) with 45 and 135 degrees joint sets .................................................................................................................................. 86 Fig. 3.15. ELFEN subsidence results from 500 to 2000m after 200,000(1m cut off) ............ 87 Fig. 3.16. Estimated angles plotted as a function of undercut depth at north (top) and south (bottom) fault side of undercut using the 2-D continuum finite-element code Phase2.  Shown are the different trends for the caving, fracture initiation and subsidence angles with and without the inclusion of joints modelled using small-strain joint elements. ........................... 88 Fig. 3.17. Estimated angles plotted as a function of undercut depth at north and south fault side of undercut using the 3-D  continuum finite-difference code FLAC3D. Shown are the different trends for the caving, fracture initiation and subsidence angles .............................. 89   xiv Fig. 3.18. Estimated angles plotted as a function of undercut depth at north (top) and south (bottom) fault side of undercut using the 2-D discontinuum distinct-element code UDEC. Shown are the different trends for the caving, fracture initiation and subsidence angles modelled assuming two different joint patterns: orthogonal jointing at 0 and 90 degrees dip and 45 and 135 degrees dip. Joints are modelled explicitly in UDEC allowing for large strain slip, opening and closing along each joint interface ............................................................... 90 Fig. 3.19. Estimated angles plotted as a function of undercut depth at north and south fault side of undercut using the 2-D FEM/DEM brittle fracture code ELFEN. Shown are the different trends for the caving, fracture initiation and subsidence angles, modelled using the “mesh delete” and contact updating capabilities of ELFEN to more directly simulate the block cave mining process ...................................................................................................... 91 Fig. 3.20. Phase2 continuum subsidence results with the inclusion of joint elements, for undercut depths of 500 to 2000m. Vertical displacement contours are plotted with 1m minimum cut off. The inside lines define the caving angle measured based on shear point and the outside lines define the fracture angle measured based on the tension point ................... 92 Fig. 3.21. FLAC3D plasticity indicator, red line-caving angle threshold .............................. 93 Fig. 3.22. UDEC plasticity indicator: orthogonal joint pattern, red line-caving angle threshold ................................................................................................................................................. 94 Fig. 3.23. Estimated caving angle plotted as a function of undercut depth at north fault side of undercut .............................................................................................................................. 95 Fig. 3.24. Estimated caving angle plotted as a function of undercut depth at south fault side of undercut .............................................................................................................................. 95 Fig. 3.25. Open joint: (a) orthogonal joint pattern and (b) an orthogonal joint pattern superimposed with a second pattern at 45 and 135 degrees, red line-fracture initiation angle threshold .................................................................................................................................. 96 Fig. 3.26. Estimated fracture initiation angle plotted as a function of undercut depth at north fault side of undercut .............................................................................................................. 97 Fig. 3.27. Estimated fracture initiation angle plotted as a function of undercut depth at south fault side of undercut .............................................................................................................. 97 Fig. 3.28. Estimated subsidence angle plotted as a function of undercut depth at north fault side of undercut ....................................................................................................................... 98   xv Fig. 3.29. Estimated subsidence angle plotted as a function of undercut depth at south fault side of undercut ....................................................................................................................... 98 Fig. 4.1. Digital mine plans of the Palabora open pit and undercut geometries, showing their proximate location to one another. Modified after Moss et al., 2006 ................................... 115 Fig. 4.2. QuickBird image of the northwest wall failure at Palabora ................................... 116 Fig. 4.3. Geological map for Palabora showing the key lithologies. After Piteau Associates Engineering LTD., 2005 ....................................................................................................... 117 Fig. 4.4. FLAC3D model developed for back analyzing the northwest wall failure (covering the period 2002 to 2005). Shown is the detailed geology built into the model in plan and 3-D perspective views. Model dimensions are 4000 x 4000m in  plan and 2000m in depth ...... 118 Fig. 4.5. Cave geometries for different time intervals implemented within the FLAC3D models ................................................................................................................................... 119 Fig. 4.6. Back analysis comparing caving-induced displacements assuming: (a) average and (b) lower bound rock mass properties, based on the input ranges compiled in Table 4.1. Displacements are reported in metres ................................................................................... 120 Fig. 4.7. FLAC3D results for several different in-situ stress assumptions. Superimposed are the contours outlining the northwest wall failure. Displacements are reported in metres .... 121 Fig. 4.8. Best fit FLAC3D model comparing modelled vertical displacements (greater than 3 cm) to the DEM outline of the North wall failure, in plan and along a north-south section through the centre of the northwest wall failure. NS and EW horizontal stresses are assumed to be equal to the vertical stresses (Ko=1). Displacements are reported in metres. .............. 122 Fig. 4.9. RADARSAT-1 data for Palabora recorded for the two-year period following the 2005 northwest wall failure. The area highlighted by the white dashed box coincides with the extent of modelled displacements (greater than 3cm) shown in Fig. 4.8. ............................ 123 Fig. 4.10. Modified model geometry for forward modelling of caving‐induced ground deformations for the period 2009 to 2010. ............................................................................ 124 Fig. 4.11. FLAC3D forward modelling results showing the caving-induced vertical displacement for the period March 2009 to March 2010 in plan view. Displacements are reported in metres ................................................................................................................. 125   xvi Fig. 4.12. FLAC3D forward modelling results showing the caving-induced vertical displacement for the period March 2009 to March 2010: (a) N-S section, and (b) E-W section. Displacements are reported in metres  .................................................................................. 126 Fig. 4.13. RADARSAT-2 data for Palabora for the period March 2009 to March 2010, showing: (a) ascending, and (b) descending InSAR measured vertical displacements. Points colour-coded with respect to downward movements are, Red: 20-40mm, Yellow: 10-20mm, Green: 0-10mm.  ................................................................................................................... 127 Fig. 4.14. Side-by-side comparison of FLAC3D modelling results with the ascending RADARSAT-2 data for the period March 2009 to March 2010. Downward subsidence magnitudes for the zoned regions correspond to: (1) 20-40mm, (2) 10-20mm, (3) 0-10mm, and (4) shadow.  .................................................................................................................... 128 Fig. 4.15. Side-by-side comparison of FLAC3D modelling results with the descending RADARSAT-2 data for the period March 2009 to March 2010. Downward subsidence magnitudes for the zoned regions correspond to: (1) 20-40mm, (2) 10-20mm, (3) 0-10mm, and (4) shadow.  .................................................................................................................... 128 Fig. 4.16. Comparison of FLAC3D modelled and InSAR and mine geodetic measured vertical displacements between March 2009 and March 2010, for a history point/survey prism located near the main access shaft. ............................................................................. 129 Fig. 4.17. Comparison of FLAC3D modelled and InSAR and mine geodetic measured vertical displacements between March 2009 and March 2010, for a history point/survey prism located near the ventilation shaft ................................................................................ 130 Fig. 4.18. Comparison of FLAC3D modelled and InSAR and mine geodetic measured vertical displacements between March 2009 and March 2010, for a history point/survey prism located above the crest of the west wall.  ................................................................... 131          xvii  Acknowledgements  First of all, I owe special thanks to Dr. Erik Eberhardt. This dissertation would not have been possible without his sage advice, insightful criticisms, and patient encouragement. I also offer my heartfelt gratitude to the committee: Dr. Oldrich Hungr, Dr. Ken Hickey, Dr. Doug Stead, and Dr. Alex Vyazmensky. This work was funded through a Collaborative Research and Development grant from the Natural Science and Engineering Research Council of Canada (NSERC), in partnership with Rio Tinto, a grant from the Centre for Excellence in Mining Innovation (CEMI), and a grant from the Canadian Space Agency. I would like to thank these organizations for their financial supports. I would also like to thank Rio Tinto and the Palabora mine staff for providing data, and Dr. Andre van As (Rio Tinto Technical Services), and Dr. Peter Kaiser and Keith Bullock (CEMI), Guy Aube (Canadian Space Agency) and Christian Nadeau (MDA Systems) for their technical guidance. My thanks also go to Jordan Severin, Vlad Kobiljski and Dr. Tom Styles for their assistance in developing the cave geometries; Chris O'Connor and Dr. Reza Taghavi for their advice on modelling techniques; Parwant Ghuman and Jayson Eppler and Dr. Bernhard Rabus for their guidance with InSAR monitoring techniques; and Dr. Davide Elmo for the warm welcome he offered me whenever I visited his office and generosity to share his technical insights and experience with me. I cannot go without expressing my deep appreciation to Dr. Seon-Keun Hwang. Were it not for his inspiring mentoring, I would have not been able to come this far. Lastly but most importantly, I cannot thank enough my loving family for sacrifices they have made throughout my studies. Their continued love and support have kept me surviving and moving forward. I am forever indebted to: my parents, Deok-seon Woo and Bun-i Um, my four sisters, Gyeong-hi, Gyeong-suk, Gyeong-mi, and Gyeong-hwa, and my parents-in-laws, Mun-gap Jung and Geum-yeop Park.   xviii Dedication      I dedicate this dissertation to my family, especially… to Christin for her patience and understanding; to Cate for being my well of joy and energy; and to my Parents for never failing to give me moral support.  1 Chapter 1: Introduction 1.1 Problem Statement  As a low cost underground mass mining method, block caving is increasingly being favoured by a number of mining companies targeting low-grade orebodies at depth or transitioning from open pit to underground operations due to the economic and production benefits the method provides. Mass mining through block caving, however, may lead to significant ground deformations and subsidence on surface, for which the extent and magnitudes must be accurately predicted to protect mine infrastructure and minimize environmental impacts (e.g. Moss et al., 2006). Damage, destruction and/or replacement of surface and underground infrastructure due to block caving induced subsidence are often the cause for additional capital and operation expenditures as well as for environmental degradation. To better manage this potential risk, numerous studies have been undertaken to characterize and assess caving-induced subsidence. Most of these are based on empirical procedures that relate rock mass quality to subsidence break angles (e.g. Whittaker & Reddish, 1989; Laubscher, 2000), but otherwise neglect the influence of geology in producing discontinuous and asymmetric deformations. Geologic structures, anisotropy and rock mass heterogeneity can each significantly influence the caving and subsidence process, leading to poor predictions of subsidence if not properly considered. The unexpected failure of an 800-m high pit slope above the block caving operation at Palabora in South Africa (Fig.1.1) is a key example of an unanticipated risk that as a worst case scenario threatened worker safety and could have resulted in the loss of the production and ventilation shafts for the mine, which would have led to the financial shutdown of the mine. Fortunately the shafts were not affected, but the failure has increased dilution and sterilization of ore, as well as chronic concerns as operations continue. Palabora, together with other recent ground-control failures involving mass mining operations (e.g. Northparkes, Kidd Creek, etc.), highlights the need for the use of sophisticated 3-D numerical modelling to properly account for the complex interactions between geology, surface topography, cave propagation and caving-induced subsidence. In  2 turn, this necessitates improved understanding and means to characterize the ground conditions and constrain the modelling results. With the industry now moving towards the next generation of "super" block cave mines (Resolution, Oyu Tolgoi), the long-term success of these operations will be heavily dependent on proper cave management and prediction of caving-induced ground deformations. 1.2 Thesis Objectives This study aims to further the characterization, assessment and understanding of block-caving subsidence dynamics by addressing limitations in current empirical and numerical methods used for caving-induced subsidence prediction. To do so, several thesis objectives are defined as listed below. These involve steps that link an empirical-based database developed to help define key influences and interactions that affect caving-induced subsidence with advanced numerical modelling strategies that account for these interactions, integrated with remote-sensing monitoring techniques as a means to constrain sophisticated 3-D models. The primary objectives of this thesis are: i. Develop a comprehensive database of in-situ measured subsidence information from block cave mining operations from around the world to be used to identify and investigate the key factors and ground interactions influencing subsidence behaviour; provide relationships correlating geological information to subsidence observations as a means of guiding and constraining future numerical analyses; provide a framework on which to analyze the effects of geology in promoting asymmetry and discontinuous caving-induced subsidence; and develop empirical guidelines based on the diverse information compiled in the database to aid in the initial scoping and projection of expected subsidence as a function of undercut depth, for future block caving projects. ii. Carry out benchmark testing of several different numerical techniques to investigate their abilities and limitations with respect to modelling block caving subsidence for a range of undercut depths. The comparison is being carried out for a conceptualized  3 problem involving a porphyry type deposit, incorporating faults, several different lithologies and varying rock mass properties. iii. Develop a detailed 3-D numerical model for an active operation to better understand block-caving subsidence mechanisms and to develop much-needed guidance on the use of advanced numerical modelling focusing on means to incorporate geological complexity and rock mass heterogeneity using advanced 3-D continuum modelling techniques, and investigate the use of satellite-based Interferometric Synthetic Aperture Radar (InSAR) imaging as a means to monitor block-caving subsidence and constrain complex 3-D numerical models. 1.3 Thesis Structure This thesis consists of an introduction chapter, three key research chapters, and a conclusion followed by several appendices. Chapter 1 introduces the problem and explains the thesis objectives and literature review carried out. The next three chapters elaborate on the procedures and findings of the research conducted to achieve the stated objectives. Chapter 2 describes the development of a block caving database, including descriptions of the cases examined, and the corresponding caving, fracture initiation and subsidence angles as a function of undercut depth. Empirical relationships are established and bias within the database discussed. Also included are a number of Google Earth satellite images, analyzed to characterize asymmetric subsidence patterns seen above different caving operations and correlated to basic information in the database. Detailed information on the different data sources used to develop the database is provided in Appendix B. Chapter 3 reports benchmark testing of different numerical methods based on a conceptual block caving example. These are used to test the strengths and limitations of each method in assessing the relationship between caving depth and subsidence. A comparison is drawn between numerical assumptions regarding the treatment of geology (continuum versus discontinuum), dimensionality (2-D versus 3-D), and means to simulate the mining process. The comparative analysis was carried out for assumed undercut depths of 500 to 2000 m in 500 m intervals.  4 Chapter 4 examines the problem of managing parameter uncertainty in complex 3-D numerical models, and works towards developing a constrained and calibrated 3-D subsidence model for the Palabora mine in South Africa. RADARSAT-2 InSAR monitoring data collected specifically for this study was used together with a back analysis of a 2005 caving-induced pit slope failure, to forward model the predicted subsidence arising for one year’s production (2009-2010). Finally, Chapter 5 summarizes the findings for Chapters 2 to 4 and details the key conclusions, major contributions, and topics for further research arising from this thesis. 1.4 Literature Review: Subsidence Induced by Block Caving 1.4.1 Overview Underground mining creates voids that through extraction and collapse can cause the lowering of the ground surface. Following numerous experiences in the 19th century where mining-induced subsidence resulted in damage to overlying mine infrastructure, railways, roads and homes, formal studies of subsidence were initiated (National Coal Board Subsidence Engineering Handbook, 1975; Kratzsch, 1983; and Whittaker & Reddish, 1989). These early studies laid the foundation for future subsidence research by explaining the basic mechanisms of subsidence. Today’s subsidence investigations cover structural geology, geomechanics, surveying, mining and property law, and mining methods and techniques (Singh, 1992). Underground mining methods can be classified based on their support conditions as shown in Fig.1.2 (Brady & Brown, 2006). While the principles of subsidence are similar regardless of the mining method, surface deformation shows distinctive characteristics depending on which mining method is employed. Selection of the mining method is typically based on the geometry of the orebody, its grade and the geomechanical properties of the ore and the country rock (Villegas, 2008). Mining-induced subsidence can be viewed as taking place in two phases: an active subsidence phase and a residual subsidence phase. Active subsidence follows the advance of the working face or cave back and forms 90 to 95 percent of the total subsidence in most cases. Residual subsidence takes place after mining has  5 ceased through continued collapse, loss of support and migration of old mine workings. Residual subsidence typically continues for a year but in some cases it progresses for decades; new subsidence in exhausted mining areas is mostly residual subsidence. Two types of subsidence have been observed: continuous and discontinuous (Brady & Brown, 2006). Continuous subsidence involves a smooth lowering of the ground surface. Discontinuous subsidence is characterized by abrupt changes and large vertical drops localized over smaller surface areas. Continuous subsidence is often viewed as a large trough, whereas discontinuous subsidence involves scarps, sinkholes, and tension cracks. In the past, subsidence studies were largely focused on continuous subsidence driven by investigations related to longwall coal mining where subsidence is approximately continuous. With an increasing interest in caving methods for hard rock mining, research focus is being shifted to discontinuous subsidence. The block cave mining method (Fig.1.3) was originally used to mine orebodies where rock is fractured and weak, and thus prone to caving. More recently though, it has been applied to hard rock where high induced stresses facilitate rock fracturing (Carrasco et al., 2004). Block caving requires intensive preparation and development work, but its cost is the lowest amongst the different underground mining methods. The term “block caving” is used here to include both block and panel caving; panel caving is a variant where the orebody is divided into panels which are mined sequentially. Not included in the use of this term is sublevel caving. Block caving is usually applied to large scale extraction of various metals and minerals from steep to vertical orebodies, with vertical dimensions (i.e. block heights) exceeding 100 metres. The ore block is undercut by blasting, allowing the "back" to fracture, fragment and cave. The broken ore is then extracted to create a void and initiate further caving. Whereas a sub-vertical crater eventually forms on surface through this caving process, a shallower profile may develop in weaker near-surface rocks. Factors identified by Flores & Karzulovic (2004) as influencing the steepness and geometry of the cave include rock mass quality, geological structures, and draw management.   6 1.4.2 Caving Subsidence Mechanism A conceptual model describing the caving subsidence progress has been summarized by Abel & Lee (1980) as follows (Fig.1.4): a. As ore is excavated from the drawpoints, undercutting and cave propagation upward from the extraction level and the initial collapse of the cave back begins. b. The consequence of the upward cave propagation is the thinning of the overlying cap rock. When the thinning reaches the point that the cap rock cannot transfer its load to the adjacent solid cave walls, measurable ground subsidence occurs. The cap rock begins to deflect toward the caved rock below. c. Caved ore production continues and tension cracks begin to open and subsidence increases on the surface. The result is a trough-shape subsidence profile. d. Surface deformation further progresses and a circular collapse structure called “glory hole” is formed roughly at the center over the caved area. e. If extraction continues, the rock adjacent to the caved zone slides along joints or faults, or topples into the open crater, growing the collapse structure laterally. Van As et al. (2003), examining subsidence above block caving operations, defined several distinct zones of deformation as follows (Fig.1.5): • Caved Zone: A zone of active caving typically situated above the undercut footprint and usually manifested as a collapse crater. The contents of this zone are caved ore and waste rock, ranging in size from large boulders to fines. The extent of the caved rock zone is defined by the angle of break, or caving angle, which is the inclination of the line drawn from the edge of extraction level to the in-situ/intact rock  7 boundary. The angle of break increases with depth and is sub-vertical in strong rocks (if no significant persistent dipping discontinuities are present), and less inclined where mining depths are shallow or overburden rocks are weak. • Fractured Zone: An irregular broken surface with scarps, large open tension cracks, and large blocks undergoing shear-rotation and toppling towards the caving zone. The extent of this zone is defined by the fracture initiation angle, which is the inclination of the line drawn from the edge of the undercut to the limit of surface cracking. • Continuous Subsidence Zone: An area of small-strain, continuous deformations. Lupo (1998) found that significant continuous surface subsidence can develop as far as 250 metres away from the limits of the fractured zone. The maximum extent of this zone is defined by the angle of subsidence, which is the inclination of the line drawn from the edge of the undercut to the limit of surface deformations. The boundaries between these different zones are generally obvious under normal conditions (Gilbride et al., 2005), but are less obvious when soil cover, waste dumps or erosion features cover part of the surface. Some block caving mines only show the caved rock zone. Break angles are more commonly reported with respect to the extent of surface deformation, however there are different definitions of break angle. Karzulovic et al. (1999) explained it as the angle measured from horizontal of the straight line drawn from the edge of the undercut to the edge of the crater. Brady & Brown (2006) defined the break angle as being measured as a straight line drawn from the edge of the undercut to the farthest crack on surface. The subsidence limit angle, when reported, is defined as the angle measured from horizontal of the straight line drawn from the edge of the undercut to the farthest measured deformation (Gilbride et al., 2005).     8 1.4.3 Factors Influencing Subsidence Development Mining-induced surface subsidence is the product of the complicated interactions between various factors. Crowell (2001), focussing on room and pillar coal mines, suggested the following controlling factors: • Height of mined-out area: Vertical subsidence increases proportionally to the height of the mined-out block and typically does not exceed the height of the mine void. • Width of unsupported mine roof: The area of subsidence and the width of unsupported roof has a positive relationship. Approximately, the potential area of subsidence can be estimated by adding the extraction area to the area defined by the angle of draw. • Thickness of overburden: Negative correlation exists between vertical subsidence and the depth or thickness of overburden. Since the rock bulks when it collapses, vertical surface subsidence tends to be smaller when the extraction area is deeper. • Competency (strength) of rock: Subsidence is related to the strength or competency of the overlying cap rock. • Pillar dimensions: As pillar dimensions increase, subsidence decreases. When the size of the pillars is smaller, the probability of pillar crushing or punching, and thus roof collapse is higher. • Hydrology: Fluctuating groundwater level can affect subsidence. Roof collapse becomes more likely if the roof rock is repeatedly saturated and if flowing water erodes softer rock pillars. • Fractures/joints: When discontinuities exist, the mine roof is weakened and subsidence becomes more likely to occur. The subsidence could even go beyond the limit of the mined area due to discontinuities.  9 • Time: When depth of mining and competency of the overburden rock increases, subsidence can fully develop over a longer period time. More specific to block caving, Brown (2003) identified a number of features of the orebody, local geology and surface topography that can influence subsidence development, including: • Dip and geometry of the orebody • Depth of mining and the associated in situ stress field • Strengths of the caving rock mass and of the rock and soil cover • Presence of a slope at surface (i.e. irregular surface topography) • Nature of major intersecting geological features such as faults and dikes • Previous surface mining (i.e. deep open pit) • The accumulation of caved rock or placement of fill in the formed crater • Presence of nearby underground excavations Van As et al. (2003) reported general trends regarding caving-induced subsidence as follows: • When a mining face encounters a significant discontinuity with moderate to steep dip, movement will occur on the fault regardless of the caving angle. • A stepped crack morphology will result where the fault daylights at surface. If mining is only on the hangingwall side of the fault, the limits of surface movement will coincide with the fault. • If the fault dip is steeper than the cave angle, the extent of surface subsidence will be reduced. Likewise, if the fault dip is less than the cave angle, the extent of surface subsidence will be increased.  10 Flores & Karzulovic (2002) list the relative degree of influence (high or moderate) of several factors on subsidence, as shown in Fig.1.6, based on their analysis of data from 18 block cave mining operations. 1.4.4 Mirco- and Macro-Subsidence Subsidence above block caving operations can be divided into micro- and macro deformations (Butcher, 2005). Micro deformations include those detected as tilting ground, small strains and/or vertical and horizontal displacements detectable through deformation monitoring (see subsidence zone in Fig.1.5). Although relatively small compared to macro deformations, they can still be significant in causing differential displacements of several centimetres, which in turn can affect the structural integrity of strain sensitive structures (e.g. those built with concrete). Lupo (1998) reported that micro deformations have been observed up to 250m from the perimeter of a collapse crater. Macro deformations involve those ground movements that are visually detectable such as the opening of tension cracks, development of scarps, fracturing and break back of the surface above and around the cave’s footprint, and breakthrough of the cave itself to form a large crater (see caved and fractured zones in Fig.1.5). The zone of macro deformation around or above a caving operation can have serious implications in terms of safety, damage to surface infrastructure and environmental damage. Based on experiences from caving operations in Australia and South Africa, Butcher (2006) suggested that the ground immediately above the cave footprint will subside, cave and collapse, and thus any excavations or surface infrastructure situated within the footprint will ultimately be destroyed. Predicting the zone of macro deformation with fair precision is also critical in terms of project viability as macro deformations and ground collapse into the cave can result in dilution of the ore being extracted. Dilution is one of many challenges confronting mining operations requiring extra expenditures to deal with waste material that can degrade the value of the ore below the cutoff grade.    11 1.5 Literature Review: Block Caving Subsidence Analysis There are three main approaches to caving-induced subsidence prediction: empirical, analytical, and numerical. While empirical methods are heavily relied upon in block caving geomechanics, the use of numerical modelling has opened up new opportunities to investigate the factors governing subsidence and thus develop improved prediction methodologies. 1.5.1 Empirical Design Chart Empirical methods are based on comparisons of data and experience collected from historical and existing operations, to which the new mine being designed is compared to. They represent a quick, simple to use tool, which yields fairly satisfactory results. However, as Bahuguna et al. (1993) noted, they can be limited by site-specific data bias and are not based on rock mechanic principles. Most of the published empirical methods provide guidance in the value of maximum subsidence, smax, based on a large number of measurements carried out for cases having similar geological and mining conditions. Such assessments become less reliable if there is an absence or deficiency in data of earlier observations in areas having similar conditions (Bahuguna et al., 1993). The most commonly used empirical method for estimating subsidence parameters in cave mining is Laubscher’s method (Laubscher, 2000). Laubscher proposed a design chart (Fig.1.7a) that relates the predicted cave angle to the MRMR (Mining Rock Mass Rating), density and height of the caved rock, and mine geometry (minimum and maximum span of a footprint). Fig.1.7b presents a worked example of Laubscher’s method. Laubscher’s chart does not consider the effect of geological features like faults which may cause the cave angle to steepen or flatten depending on their dip. In addition, the method only applies to the caving zone and not the full extent of subsidence, which is an important parameter in cave mine design (Flores and Karzulovic, 2004). Overall, the application of Laubscher’s method requires sound engineering judgement, geotechnical expertise and experience in similar geotechnical settings.   12 1.5.2 Analytical Methods Analytical methods generally include closed-form solutions and limit equilibrium procedures. Most of the published closed-form solutions for subsidence prediction draw upon continuum mechanics and elasticity theory, and are therefore more applicable to problems involving continuous subsidence. The force and/or moment balance techniques employed by limit equilibrium solutions on the other hand, can be applied to simplified discontinuous subsidence problems. Hoek (1974) developed a limit equilibrium model for the analysis of subsidence generated by the exploitation of an inclined orebody, using the sublevel caving method. This model aimed to predict the subsidence due to progressive hangingwall failure with increasing mining depths. The variables considered in Hoek‘s analysis are shown in Fig.1.8. The solution assumes that a planar shear failure is formed from the undercut to a surface tension crack and that the failure occurs under static conditions. The effect of the caved material is also taken into account. This model was used to analyze the subsidence at the Grängesberg iron ore mine in Sweden and showed that the break angle is highly influenced by the rock mass properties, the mining depth, and the depth of caved material (Hoek, 1974). The basic method proposed by Hoek (1974) has evolved as subsequent researchers also investigating discontinuous subsidence introduced their own modifications. The first modification was made by Brown & Ferguson (1979) in order to consider sloping ground surface and groundwater pressure in the tension crack and in the shear plane. The method was applied at the Gath’s mine, Rhodesia. In their analysis, a sloping upper surface in the hangingwall decreased the break angle and increased the tension crack depth. Although it was mentioned that during the rainy season subsidence accelerates, its effect was not evaluated. Another factor analyzed was the 3-D nature of the crater. Based on field observations, it was concluded that when the radii of curvature of the walls is small, higher break angles can be expected.  13 Kvapil et al. (1989) also extended Hoek’s analysis to define discontinuous subsidence due to block and panel caving. This model is based on the recognition that progressive failure occurs in both the hangingwall and footwall, and allows the prediction of subsidence effects from caving operations involving very steep orebodies. This model was applied to evaluate the subsidence at El Teniente mine which was using block and panel caving. Karzulovic (1990) extended Brown and Ferguson’s model to predict the evolution of the subsidence crater at the Rio Blanco mine. The theoretical break angle calculated was adjusted considering local factors such as the presence of faults and the amount of broken material in the crater. This adjustment was required to obtain improved agreement with a database of observed values for rock masses of similar quality. Lupo (1996) also extended Hoek’s model to account for the failure of the hangingwall and footwall around an inclined orebody. This model considers the failure of the hangingwall using the limit equilibrium equations derived by Hoek (1974), but also considers an active earth pressure coefficient due to the effect of the draw of broken ore. For the footwall, the limit equilibrium equations derived by Hoek (1970) for excavated slopes in open pit mines are used. This approach was used in the Kiirunavaara mine, Sweden and gave fair agreement with failure observations of the hangingwall. However, the model was not able to predict the behaviour of the footwall (Henry & Dahnér-Lindqvist, 2000); most of the mine infrastructure is located above the footwall. Flores & Karzulovic (2004) summarized the evolution of limit equilibrium to predict caving-induced discontinuous subsidence, as shown in Table 1.1. Although these provide a means to estimate the angle of break, one of the key parameters required for mine planning, the limit equilibrium techniques do not take into account complex rock structure, in-situ stresses or stress-strain relationships, thereby restricting their predictive capabilities. 1.5.3 Numerical Modelling An adequate representation of the rock mass is required for a numerical model to properly capture its physical and engineering response to mining. Hudson & Harrison (2000) describe a rock mass as being either Continuous, Homogeneous, Isotropic and Linear Elastic  14 (CHILE) or largely Discontinuous, Inhomogeneous, Anisotropic, and Non-Elastic (DIANE), with most rock masses being associated with the latter. The complex geology and its long history of formation make rock masses a difficult material for mathematical representation via numerical modelling. The most commonly applied numerical methods for rock mechanics problems are summarized in Table 1.2. Amongst these, continuum codes like the finite difference programs FLAC (Itasca, 2007) and FLAC3D (Itasca, 2009) or the finite element program ABAQUS (Dassault Systèmes, 2009; Fig.1.9a) have been the most widely used for modelling block caving subsidence (e.g., Singh et al., 1993; Van As et al. 2003; Sainsbury et al. 2008; Beck & Pfitzner, 2008). To a lesser degree, distinct element codes like UDEC and 3DEC (Fig.1.9b) or hybrid methods like that used by Vyazmensky et al. (2010b) to incorporate brittle fracture processes, have been used. The choice of method varies on a case-by-case basis, ranging from selection based on simplicity and familiarity in the modelling method to specific selection to incorporate a key process like brittle fracturing. Table 1.3 summarizes published accounts of numerical analysis of surface subsidence and block cave/open pit interactions. The modelling study by Flores & Karzulovic (2004) is arguably the first attempt after Laubscher (2000) to provide general guidance for subsidence analysis. Their study involved conceptualized FLAC/FLAC3D modelling of surface subsidence associated with block caving, including the varying of rock mass properties and consideration of the effects of an open pit with varying pit and undercut level depths. Based on their modelling results, complemented by limit equilibrium analysis, a series of design charts were developed correlating angle of break and zone of influence of caving with undercut level depth and crater depth for varying rock mass quality. Fig.1.10 shows one example of the design charts they developed. The validity of these charts though, has yet to be confirmed through mining experience. More recently, Vyazmensky (2008) applied a hybrid finite-element/discrete-element (FEM/DEM) approach to the modelling of block caving subsidence. This technique incorporates brittle fracture capabilities enabling the modelling of a continuum passing to a discontinuum in response to changes in stress and strains. Vyazmensky et al. (2010a)  15 examined preferential rock fragmentation between an ore column and surrounding host rock, together with the influence of geological structures on the development of caving-induced subsidence. In a related study, Vyazmensky et al. (2010b) investigated the interaction between a propagating block cave and overlying open pit slope, highlighting the importance of rock bridges and their incremental failure through cave-pit interactions which led to the progressive failure of the Palabora pit slope (Fig. 1.11). Overall, with the exception of Flores & Karzulovic (2004), all reviewed accounts were focused on back analysis or predictive modelling for specific mine sites. It appears that there is a need for comprehensive modelling attempts to evaluate the general principles of surface subsidence development in block caving settings. Brown (2003) recommended using a combination of empirical, analytical and numerical methods for subsidence predictions. He suggested that a preliminary estimate of the angle of break be derived using Laubscher’s chart and calibrated against observed break angles in similar mining settings (i.e. empirical). The estimated angle of break should then be checked against limit equilibrium approaches (i.e. analytical). The estimated value of the angle of break can be adjusted considering local geological features and the amount of broken material in the crater. Finally, numerical methods should be used to confirm the estimate of the angle of break and to estimate the stresses and displacements induced in the rock mass around the caved zone. As noted by Flores & Karzulovic (2004), only numerical models allow the full extent of the influence zone to be predicted (including micro-deformations). Therefore, limit equilibrium analyses must be complemented with numerical models for the prediction of the extent of the influence zone. Given the significant cost implications of locating major excavations and infrastructure beyond the influence of the underground caving operation, it is well worth the effort of using numerical modelling to ensure that the empirical and/or analytical methods are not overly conservative in their predictions (Van As et al., 2003).     16 Table 1.1. Summary of the evolution of subsidence models (Flores & Karzulovic, 2004). Author (s) Observations and Applications (Improvements) Hoek (1974) This limit equilibrium model is aimed to subsidence prediction due to progressive hangingwall failure with increasing mining depth.  It was developed to predict the surface subsidence at Grängesberg mine in Sweden.  This became the basis for subsequent limit equilibrium models. Brown & Ferguson (1979) Extended Hoek’s limit equilibrium model to account for a sloping surface and groundwater pressures in the tension crack and on the shear plane.  This model was used to evaluate the progressive failure of the hanging wall at Gath’s mine in Rhodesia. Kvapil et al. (1989) Used Hoek’s limit equilibrium model to include the progressive failure occurring in both hanging wall and foot wall in a very steeply dipping orebody.  This model was applied at El Teniente mine, in Chile, to evaluate the subsidence generated by underground block and panel caving operations. Karzulovic (1990) Used Brown and Ferguson’s limit equilibrium model to predict the discontinuous subsidence associated with block caving at Rio Blanco mine in Chile.  This model was developed to evaluate subsidence in a vertical orebody. Herdocia (1991) Proposed a simplified geometrical model for the calculation of geometrical factors affecting the stability of hanging walls in an inclined ore body using sublevel caving method.  This limit equilibrium model was used to evaluate the hanging wall stability at Grängesberg, Kiruna and Malmberget mines, in Sweden Singh et al. (1993) Carried out a study using numerical models (FLAC) to analyse the progressive development of fractures in the hanging wall and footwall with increase in mining depth in sublevel caving.  They postulated a conceptual discontinuous subsidence model for an inclined orebody using sublevel caving method.  The analysis was carried out at Rajpura Dariba mine, in India, and Kiruna mine, in Sweden, where steeply dipping ore bodies are extracted by sublevel caving. Lupo (1996) This model considers the failure of the hangingwall using the limit equilibrium equations derived by Hoek (1974) but considering an active earth pressure coefficient, and the limit equilibrium equations derived by Hoek (1970) for excavated slopes in open pit mines to analyse the footwall.  The use of an active earth pressure coefficient is intended to include the effect of the movement of broken rock during draw.  This method was applied to the conditions at the Kiruna mine, in Sweden. Karzulovic et al. (1999) Performed a study using Karzulovic’s model (1990) to predict the evolution of the horse-shoe shaped subsidence crater at El Teniente mine in Chile, and numerical models (FLAC) to assess the extent of the influence zone.  The angle of break value so calculated was adjusted to take into account of local factors such as the presence of faults and the amount of broken material in the crater. The numerical models were calibrated against field observations to define the limits of the influence zone.   17 Table 1.2. Most commonly applied numerical methods for rock mechanics problems. Continuum methods Discontinuum methods Hybrid  continuum / discontinuum models • Finite Difference Method (FDM) • Finite Element Method (FEM) • Boundary Element Method (BEM) • Discrete Element Method (DEM) • Distinct Element Method (DEM) • Particle Flow Code (PFC) • Hybrid FEM/BEM • Hybrid FEM/DEM    Table 1.3. Numerical studies of surface subsidence Author(s) Code Type of analysis Singh et al. (1993) FLAC Site specific: Rajpura Dariba and Kiruna mines Karzulovic et al.  (1999) FLAC Site specific: El Teniente mine Reported by Van As (2003) FLAC 3D Site specific: Northparkes mine Cavieres et al. (2003) 3DEC Site specific: El Teniente mine Flores & Karzulovic (2004) FLAC & FLAC 3D Conceptual Gilbride et al. (2005) PFC 3D Site specific: Questa mine Brummer et al. (2006) 3DEC Site specific: Palabora mine Elmo et al. (2007) FLAC 3D Site specific: San Manuel mine Villegas (2008) Phase2, PFC 2D Site specific: Kiruna mine Sainsbury et al. (2008) FLAC 3D Site specific: Palabora mine Beck & Pfitzner (2008) ABAQUS Site specific: Several mines Vyazmensky et al. (2010b) ELFEN Site specific: Palabora mine Elmo et al. (2010) ELFEN Site specific: Cadia East Sainsbury et al. (2010) FLAC 3D Site specific: Grace Mine   18  Fig. 1.1. 2005 failure of the northwest wall at Palabora following breakthrough of the cave into the pit floor. Photograph courtesy of Rio Tinto Technical Services.  Fig. 1.2. Classification of underground mining methods (from Brady & Brown, 2006)  19  Fig. 1.3. Illustration of the block cave mining method (from Hamrin, 1982)    (1) Initial caving            (2) Cave propagation    (3) Initial surface           (4) Cave breaches     (point a)                           toward surface             subsidence as the            surface and                                             (point b)                       crown thins                     forms a crater                                                                                  (points c-d)                     (points d-e)  Fig. 1.4. Conceptual model of block caving-induced subsidence and corresponding points from associated text above (from Van As et al., 2003, based on Abel & Lee, 1980).    Fig. 1  Fig. cavin .5. Subside 1.6. Relativ g methods s nce deforma e importanc uggested by tion zones a e of the m  Flores & K 20 s defined by ain causes o arzulovic (2  Van As et f subsidenc 002) al. (2003) e in underground mine   s by  21  Fig. 1.7. Laubscher’s (2000) Mining Rock Mass Rating (MRMR) system, an empirical design chart, for assessing cave angle (angle of break) based on measurable geological parameters. Cave Angle Factor 90° 80° 70° 60° 50° 40° 30° 20° .1             .2      .3         .5    .7     1             2       3         5     7     10           20     30       50   70   90 80 70 60 50 40 30 20 10 MRMR Factor ൌ Density of caved material 1.5 ൈ Height of caved material 100 ൈ Depth Min. span   22  Fig. 1.8. Idealized model used in limit equilibrium analysis of progressive hangingwall caving proposed by Hoek (1974). After Flores & Karzulovic (2004). H2 z2 ψp2 ψ0 ψb ψp1θ +θ −θ z1 W T φw Wc Tc φw H1 Hc Hs Working face Footwall Orebody New tension crack Tension crack from previous failure Caved material H1 H2 Hs Hc z1 z2 ψ0 ψb ψp1 ψp2 φw θ Wc W T Tc γc γ c φ Previous mining level depth Current mining level depth Depth to the caved material surface Caved material height Previous tension crack depth New tension crack depth Dip of the orebody Break angle Inclination of the previous failure plane Inclination of the new failure plane Friction angle between caved material and rock wall Inclination of the line of action of T Weight of the caved material Weight of the potentially unstable block Lateral force due to Wc on the potentially unstable block Lateral force due to Wc on the footwall Unit weight of the caved material Unit weight of the rock mass Cohesion of the rock mass Angle of friction of the rock mass  23 (a) (b) Fig. 1.9. (a) Finite-element modelling of cave-pit interactions (Beck & Pfitzner, 2008), and (b) 3DEC modelling of cave-pit interactions (Brummer et al., 2006).  24  Fig. 1.10. Design chart for estimating the angle of break in a transition from open pit to underground mining by block/panel caving for rock masses of different geotechnical quality and undercut level (UCL) depths in the range from 600 to 1700 metres; Poor to Fair: GSI=30-50, Fair to Good: GSI=50-70, and Good to Very Good: GSI=70-90 (GSI=Geological Strength Index) (Flores & Karzulovic, 2004).  25   (a)   Fig. 1.11. Cave-pit interaction in the Palabor mine simulated by hybrid finite-element/discrete-element modelling technique (Vyazmensky et al. 2010b). (a) NW-SE section of the Palabora mine; (b) Pit slope deformation at cave breakthrough for model P1 (with a tensile strength increase of 100% in the foskorite and 150% in the micaceous pyroxemite); (c) Pit slope deformation at 40% ore extraction  for model P1; (d) Pit slope deformation at cave breakthrough for model P2 (with a tensile strength increase of 150% in the foskorite and 200% in the micaceous pyroxemite; and (e) Pit slope deformation at 40% ore extraction for model P2. (d) (b) (c) (e)  26 Chapter 2: Empirical Investigation and Characterization of Surface Subsidence Related to Block Cave Mining1  2.1 Introduction Block caving is increasingly being favoured as a mining method for maximizing Net Present Value (NPV) from large, lower grade ore bodies, especially as companies target deeper resources or transition underground from open pits that have reached the end of their mine life. As a mass mining method, block caving results in significant ground collapse and extensive surface deformations. Yet despite having been in use for more than 100 years, there has been limited research conducted regarding the impact of caving on surface subsidence. Of concern is the locating of mine infrastructure on surface or the impact ground deformations may have on protected areas neighbouring the mine property. Damage of surface infrastructure, together with increased dilution due to larger than expected caving angles, are often the cause for additional capital and operation expenditures. To better understand and assess these potential geo-risks, a comprehensive database has been developed based on a thorough review of all available (i.e. public domain) sources reporting subsidence values related to both historic and present-day cave mining operations (including block, panel and sublevel caving). Empirical databases provide a means to learn from case histories, discover causal relationships between different contributing factors, establish guidelines for design, and to help provide a starting point to undertake more sophisticated analyses like numerical modelling. One of the most commonly cited is Laubscher’s method (Laubscher, 2000). Laubscher proposed a design chart (Fig.1.7) that relates the predicted cave angle to the rock mass quality (defined using the Mining Rock Mass Rating, or MRMR), density of the caved rock, height of the mined block and mine geometry (minimum and maximum span of a footprint). The resulting prediction by default assumes symmetry; i.e., the caving angle is equally projected from all points around the  1 Woo, KS. Eberhardt, E. Elmo, D. Stead, D. Empirical investigation and characterization of surface subsidence related to block cave mining. (To be submitted)   27 perimeter of the undercut. The application of Laubscher’s method requires sound engineering judgement and a full consideration of the geological and geotechnical setting in which it is being applied. The caving angle referred to by Laubscher is defined by Van As et al. (2003) as the angle of the line extending from the edge of the extraction level to the edge of the zone of active caving (Fig.2.1). The caved zone is usually located directly above the undercut footprint and thus is characterised as having the greatest surface disturbance, usually manifested as a crater filled with broken, irregular blocks. Van As et al. (2003) also defined two further subsidence zones and corresponding angles: the fracture initiation angle and subsidence angle (Fig.2.1). The fracture initiation angle is the angle measured from horizontal of the line extending from the edge of the extraction level to the edge of the zone of fracture (or zone of active movement). This zone encompasses all obvious surface deformations adjacent to the caved zone, typically characterized by large radial cracks and rotated and toppling blocks. The angle of subsidence marks the outer most zone and the limits of measurable surface deformations on surface. These are generally described as elastic or continuous non-elastic strains, with vertical displacements greater than 2 mm. The empirical database presented here was developed to more fully examine the relationships between these zones of surface subsidence and depth of undercut, together with the key factors that influence them. Data relating to geology, topography, orebody type and undercut geometry were specifically targeted to analyze their effects in promoting asymmetry and discontinuous caving-induced subsidence. Where key relationships are revealed, illustrative numerical models are used to help draw conclusions to guide preliminary assessments during the planning stages of future new mining projects. 2.2 The UBC Block Caving Subsidence Database A thorough search of the published literature, university theses, and government reports (e.g. U.S. Bureau of Mines) was carried out leading to a cave mine database for empirical analysis and characterization of caving-induced surface subsidence. The database is populated by more than one hundred cave mining operations throughout the world including both historic mines that have ceased to operate and those still producing. A tabular  28 format adopted for the database is designed to systematically display diverse basic information on a mine including its location, undercut depth and geology, combined with measurements related to macro- and micro-strain surface deformations. Although the study was primarily directed towards block and panel caving operations, data from sub-level caving operations were also collected. 2.2.1 General Trends Fig.2.3 shows the breakdown of cave mines by continent, mining method, and resource mined. The majority of operations reported are North American (Fig.2.2a), although these are mostly historic involving the iron mines of Michigan, where the method was first developed, the copper mines of Arizona, and asbestos mines of Quebec. Currently developing or operating cave mines are more globally distributed between South America, Asia, Australia, Africa and North America. When it comes to mining method, 62 percent of the cases involve block caving with 19 percent using sublevel caving to adapt to steeply dipping orebodies of narrower width (Fig.2.2b). Grouped with sub-level caving are mines that combined sub-level caving with similar methods like top slicing and shrinkage stoping. The reported use of two caving methods in tandem – block caving plus sublevel caving for example – were found where it was advantageous to optimize the operations relative to variations in the shape of the orebody. As for minerals produced by these mines (Fig.2.2c), copper and gold form the majority at 29 and 15 percent, respectively, followed by asbestos (9%) and diamond (9%). The large number of copper-based caving operations reflects the favorability of block and panel caving for mining low grade copper porphyry ore deposits. Based on these data, two interesting trends are evident. Fig.2.3 shows the changing trend in block height being caved. Before 1950, block caving was typically applied to block heights between 20 and 100 m at a time, employing multiple lifts of increasing depth where the height of the ore column was greater. However, this trend has transitioned to larger block heights exceeding 100 m to reduce development costs as confidence has been gained in draw sequencing practices that help minimize dilution by steering and maintaining cave propagation within the ore column. In step with increasing block heights being mined, undercut depths are likewise increasing. Fig.2.4 shows the range of undercut depths prior to  29 1950 as being 100 to 300 m, gradually increasing to depths at present of 600 m or deeper. Similarly, the size of the undercut (i.e. in plan view) has also increased as operations moves towards developing large panel caves instead of smaller blocks. 2.2.2 Caving-induced Subsidence Data The use of block caving was first reported in 1895 in the Michigan iron and copper mines where large blocks of ore were undercut, allowing the ore to mine itself under gravity and crush through comminution to a size suitable for handling (Bucky, 1945). Soon after, the economic advantages gained by the method were being tempered by reports of its impact on surface and the need to better understand the factors controlling ground movements to help safeguard against property damage and loss of life (Crane, 1929). Several detailed studies were carried out with these and other historic mines, but given the total number of mines populating the UBC database, those directly reporting subsidence measurements are actually few in number. This is reflected in earlier databases on subsidence related to mass mining (Table 2.1). Flores and Karzulovic (2002) carried out the first benchmark study as part of the International Caving Study Stage II (ICS-II), citing 242 break angles measured at various depths from 11 block, panel and sublevel caving operations. Most of these involved operations that transitioned to underground from open pit mining. For scoping and prefeasibility use, they suggest typical caving angles of >45° and >60° for MRMR values <70 and >70, respectively. Van As et al. (2003) systematically tabulated information for a number of mines including rock type, ore body dip, depth, caving angle, and angle of subsidence. Their treatment included 19 caving operations together with data from several stoping and room and pillar operations. A similar compilation was reported by Tetra Tech (2006) providing caving angle and angle of draw (defined as the greatest extent of affected ground). They note that only 20% of the mines they reviewed experienced unexpected subsidence, with most anomalies arising from geologic structure such as faults. Although these existing databases provide a starting point and means of verification, original sources were consulted for each entry to review and extract the data first hand. One of the limiting factors of the previous databases is the consideration of only those sources  30 that report subsidence data directly. This was seen to involve only 5 percent of the caving operations populating the UBC database. Closer inspection of the different published sources for each mine property revealed that in many cases, detailed cross-sections were provided that contained indirect information relating to the disturbance on surface caused by caving. In many cases, a caving angle could be measured from a scaled map or section and in some cases, a fracture initiation angle. The use of indirect data increased the number of mine properties accounted for to 44, with the number for block and panel caves (28) tripling those reported in previous databases. Furthermore, in several cases, multiple observations were provided for the same mine property, either for multiple blocks or different mine levels again almost doubling the number of data points considered (see totals in parentheses in Table 2.1). 2.3 Database Analysis: Caving and Fracture Initiation Angles  From the database, a subset of 47 direct and indirect subsidence observations were analyzed to determine the caving and fracture initiation angles for each. These are reported in Appendix A. References are provided for each data entry and a detailed background description for each is provided in Appendix B. Excluded from the analysis were those operations involving caving into a deep open pit. Where several angles are reported for different stages of cave development, only the greatest values (worst case) are reported. Emphasis was also placed on data provided in the form of cross-sections or plan view maps showing the extent of caving, surface cracks, or subsidence (see Appendix B for examples of data sources used). It was found that in many cases what was reported as a break angle or caving angle by the author(s) was actually the angle of draw (90°minus caving angle) as estimated underground, as opposed to that considering the propagation of the cave to surface and the corresponding angle of its surface expression. Based on the definitions in Fig.2.1, these were corrected where required. Figs.2.5 and 2.6 plot the caving and fracture initiation angles determined as a function of undercut depth for the entire dataset including sub-level operations. Fig.2.5 shows a rather wide range of caving angles among the sub-level caving mines as the dip of the orebody causes a large variation between the caving angle seen on the footwall side and that seen on the hangingwall. To eliminate the influence of orebody dip specific to sub-level caving  31 operations, these were excluded from subsequent analyses. Fig.2.7 and Fig.2.8 shows the relationships between caving and fracture initiation angles versus undercut depths in block and panel caving operations. Caving angles are generally seen to vary between 70 and 95°, where angles greater than 90° indicate overhanging angles (i.e. the extent of the zone in question fall within the footprint of the undercut). Angles for fracture initiation are broader and generally vary from 55 to 80°. 2.3.1 Influence of Topography Fig.2.9 shows the relationship between caving angle and surface topography. The surface topography considered is classified based on visual observation into two groups: generally flat (regular) topography and irregular topography where the mine is situated beneath a mountain peak(s) or slope/flank. Although the trend is varied, in general, the influence of a more irregular topography is seen to result in lower caving angles as well as a larger range in angles measured. A larger range in angles signifies a greater degree of asymmetry in the subsidence profile. This is reflected in Google Earth satellite images collected for the different mine sites in the database. Those for caving operations under relatively flat topography, for example Northparkes (Fig.2.10a), tend to show more symmetry in the shape of the caving zone on surface, whereas those under mountainous topography, for example Henderson (Fig.2.10b), tend to be more irregularly shaped. The influence of topography can also be clearly demonstrated using comparative numerical models. Typical surface profiles, relative to the location of the undercut beneath, were derived based on inspection of those in the caving database. These were then examined using the 2-D finite-element code Phase2 (Rocscience Software, 2009). All input parameters were kept the same, including a conceptualized geology involving a joint network of varied persistence and spacing, two bounding faults to either side of the undercut, and several geological units assigned typical rock mass properties. An orthogonal joint pattern was adopted so as to not introduce asymmetry through dipping joints. The undercut depth was kept approximately the same in each model (1500m), as was the block height caved (500m). Simulation of caving was undertaken by incrementally changing the properties of the elements above the undercut from those of rock to those of caved rock. A horizontal to  32 vertical stress ratio of 2 was assumed. Full details of the model setup are reported in Chapter 3, and are only presented here in a summarized form for illustrative purposes. The modelling results show that when assuming a flat topography (Fig.2.11a), both the caving and subsidence angles are similar on both sides of the undercut (i.e. symmetry). A similar result is obtained where the topography is irregular but approximately symmetrical relative to the position of the undercut (Fig.2.11b). This case represents a caving operation directly beneath a mountain peak with sloping flanks at different angles. The presence of the slopes above either side of the undercut results in a broader caving zone compared to the flat topography case. Fig.2.11c-e represents scenarios where the undercut is located beneath different slope configurations. The influence of a slope on the caving and subsidence angles to the left and right of the undercut is clearly visible for these different cases, with the up- slope side experiencing notably more subsidence. As the cave propagates towards surface, it undermines the slope on the uphill side promoting gravity driven down slope movements towards the cave. Thus, the empirical and numerical analyses show that symmetric surface conditions generally lead to symmetric subsidence patterns; whereas, asymmetric surface conditions in the form of a sloping surface above the undercut results in cave-surface interactions that draw cave propagation in the uphill direction resulting in asymmetric subsidence. A similar observation was made by Benko (1997) who conducted a study investigating the influence of a slope on surface subsidence above a longwall coal mine. According to Benko, surface subsidence above longwall operations where the topography is relatively flat tends to be symmetric while surface subsidence above mines where a slope is present shows a pattern of greater subsidence developing in the upper part of the slope. As for the influence of faults, in cases where the surface topography above the caving area is symmetric (Fig.2.11a, b), the area of subsidence exceeding 5 metres (see contours color coded in blue) does not extend beyond the fault interfaces. The faults effectively constrain/limit the large-strain subsidence. Where an irregular topography is present (Fig.2.11c-e), however, the area of subsidence exceeding 5 metres does extend beyond the boundary faults. This indicates a greater influence of topography on surface subsidence despite any limiting influence the faults may present. A similar observation was made by  33 Vyazmensky et al. (2010a) who conducted an extensive investigation of the influence of faults on block caving induced surface subsidence. 2.3.2 Influence of Orebody Characteristics Data on the site geology for the different cases populating the database were limited to that provided in the different sources consulted. For a number of these, there was no geology data reported and an alternative source was used instead to obtain basic geological information for the given block cave mine property. The lack of detailed data prevented any extensive analysis into the influence of geological factors on caving angle, and instead, correlations were drawn using the only information that was consistently provided – that of the ore resource being mined. Further development of the database to populate it with more detailed geological data may make it possible to better clarify and separate relationships between undercut depth, caving angles and geological influences. However, for the purpose of the analysis carried out in this study, the ore body resource was used as a simple proxy for mine geology. Fig.2.12 plots the relationship between undercut depth versus caving angle for block and panel caving operations as a function of the resource being mined. In general, diamond, iron, nickel and asbestos operations are seen to have steeper caving angles signifying a smaller impact footprint on surface. This is due in part to the typical shapes of these orebodies, which tend to be narrow and vertical, combined with strength contrasts between the weaker ore being caved and the stronger host rock. For example, diamonds are predominantly mined from vertical kimberlite pipes. These are typically intruded into a stronger host rock, meaning that caving tends to follow the boundaries of the vertical orebody resulting in steep and symmetric caving angles. Symmetry in the caving angles is signified in Fig.2.12 by a narrow range of caving angles, with those for diamond kimberlite and upturned bedded iron deposits rarely varying by more than 10°. In contrast, copper operations generally involve porphyry deposits that are more irregular in shape and have less contrast between the strength of the ore and host rock. As such, the caving angles can vary from 90° on one side of the undercut to 65° on the other side.  34 Using ore body type and mineral resource as a proxy for geology, Fig.2.12 shows that site geology has a significant influence in promoting asymmetry in caving-induced displacements. Similar to the influence of topography, the influence of geology is observable in the Google Earth satellite images in the UBC database (Fig.2.13a and Fig.2.14a). Fig.2.13a is the satellite image for the Kimberley diamond mine (kimberlite pipe). The caving zone shown in the Google Earth image is approximately symmetric in shape centered by a glory hole, which agrees with the symmetric geological distribution surrounding the kimberlite pipe illustrated in the geology cross section in Fig.2.13a. This can be compared to Fig.2.14a, which shows the outline of caving for the San Manuel copper mine. In this case the caving zone is highly irregular consistent with the asymmetric geological makeup of the mine geology presented in Fig.2.14b. These observations are consistent for like cases in the database.  2.4 Discussion: Influence of Undercut Depth A thorough examination of the block and panel caving subsidence data compiled shows that the distribution of data is heavily weighted towards caving angles and macro deformations, Very little data is reported on the extent and magnitudes of smaller strain surface deformations (also known as micro deformation). This empirical bias towards macro- deformations is largely a function of the measurement resolution available at the time of the investigation. The majority of the detailed investigations reporting on caving-induced ground deformations are more than 50 years old, and as such, rely heavily on visual mapping observations and low-resolution levelling surveys. Furthermore, the focus of the reported investigations was primarily placed on the area immediately above the undercut, thus characterizing the caving zone, and in some cases extending the survey outwards towards the edges of mine property, thus characterizing the fracture initiation zone. To examine the potential impact of this sampling bias better, specifically with respect to the influence of undercut depth on the extent of surface subsidence, a series of conceptualized numerical models were developed. To be able to fully compare both discontinuous zones of macro-deformations (caving and fracture initiation angles) and small  35 strain micro-deformations (subsidence angles) a hybrid FEM-DEM approach incorporating brittle fracture capabilities was adopted using the commercial code ELFEN (Rockfield Software, 2009). ELFEN allows for the representation of the pre-caving geological domain as a continuum populated by discrete fractures representing a brittle fracture network, that then may undergo subsequent fracturing in response to the stresses and strains induced through undercutting and cave propagation. The technique has been shown by Vyazmensky et al. (2010a) as being well-suited for capturing important block-caving mechanisms, including preferential rock fragmentation within the ore column and influence of geological structures on cave development and surface subsidence. Full details of the models shown here are provided in Chapter 3, but in summary for illustration of the effects of undercut depth, involve: a joint network of varied persistence and spacing, two bounding faults to either side of the undercut, and several geological units assigned typical rock mass properties. The assumed presence of two bounding faults was adopted as it facilitates the basic examination of how faults influence small-strain subsidence in 2-D numerical analysis. In addition, Vyazmensky et al. (2008) already analyzed the influence of shallow dipping faults on caving and fracture initiation angles, which were examined as a function of the distance between the caving area and the faults. Accordingly, this study chose steeply dipping faults and a vertical joint set to control the effect of faults and joints highlighting the role of undercut depth. As before, an orthogonal joint pattern was adopted so as to not introduce asymmetry through the presence of inclined dipping joints. A horizontal to vertical stress ratio of 2 was assumed, and caving was simulated for a block height of 200 m.  Fig.2.15 shows the results for undercut depths of 500 and 2000 m with undercutting from right to left. In both cases, the zone of caving is largely constrained by the presence of the bounding faults. For the 500 m deep undercut, where the 200 m high ore column represents a 40% extraction ratio, the impact on surface involves a caving zone extending from the edges of the undercut to the bounding faults (i.e., between 75 and 90°). For the 2000m deep undercut, the caving angles are actually overhanging (>90°). This can be explained by the lower extraction ratio (10% extraction) when assuming the same height of the ore column being caved (200 m), and therefore a less extensive cave developing and daylighting at surface. This agrees with the observations in the UBC block caving database  36 (Fig.2.12) where the caving angle is seen to increase with undercut depth and the two cases involving the deepest undercuts (> 1000 m) involve overhanging caving angles. However, when considering the extent of smaller strain deformations (<1 m), the opposite is true and the subsidence angle decreases with increasing undercut depth. For the 500 m deep undercut, the subsidence angle only partly extends beyond the bounding faults and is not significantly different from the caving and fracture initiation angles. In contrast, the zone of subsidence for the 2000 m undercut extends well beyond the bounding faults and is much farther reaching. This has important practical implications. If the location of critical infrastructure, or similarly a hazard assessment of the extent of caving-induced ground deformations, is based on empirical data then these will be biased towards observations of large-scale ground disturbance and collapse and would suggest that the impact of caving on surface is reduced for deeper undercuts. However, smaller-strain subsidence (< 1 m) may be of equal concern and its extent actually increases with undercut depth. These results therefore caution against relying on existing empirical design charts and databases for estimating the extent of caving- induced subsidence where small strain subsidence is of concern as the data being relied on does not properly extrapolate beyond the macro deformations (i.e. caving angles) that make up the majority of the observations. 2.5 Conclusions A detailed and comprehensive database of cave mining operations and caving- induced ground deformation observations has been developed to guide empirical relationships between caving depth and its impact on surface. The data shows that asymmetry in caving-induced subsidence is prevalent and largely controlled by topography and geology of the ore deposit and host rock. Where design calculations are carried out using methods that assume, directly or indirectly, symmetrical ground deformations relative to the projection of the undercut footprint at surface, caution must be taken so as to not under-predict their magnitudes and reach.  37 The availability and quality of subsidence data was also seen to be deficient as little attention has been paid to the measurement of subsidence angles compared to caving angles. The data on caving angles suggests that as undercut depth increases, the magnitude and extent of the caved zone on surface decreases. However, numerical modelling results indicate that the opposite is true with respect to smaller strain deformations (< 1 m) and that subsidence angles increase and are farther reaching with increasing undercut depths. The results therefore caution against relying on existing empirical design charts and databases for estimating the extent of caving-induced subsidence where small strain subsidence is of concern, as the data being relied upon does not properly extrapolate beyond the macro deformations (i.e. caving angles) that make up the majority of the observations. Thus, with the new generation of deep block/panel caving projects being planned, and the higher geo- risk profiles being carried due to the capital investments and development times required, the need is clear for more detailed measurements to better understand cave-surface interactions as a function of undercut depth and potential asymmetry.  38 Table 2.1. Comparison of previous databases reporting subsidence data for mass mining operations Mining Method Number of Operations (Total Observations) Flores & Karzulovic (2002) Van As et al. (2003) Tetra Tech (2006) UBC Database Block & Panel Caving 9 (229) 10 (15) 9 (9) 28 (47) Sublevel Caving/Shrinkage Stoping 1 (4) 7 (12) 10 (14) 16(49) Open Stope Caving - 1 (4) 2 (5) - Caving (Unspecified) - 1 (2) 3 (4) - Other Stoping (Sublevel, Cut & Fill) - 4 (4) 4 (4) - Room and Pillar - 4 (5) 4 (4) - Unspecified 1 (9) 9 (16) 2 (2) - Total 11 (242) 36 (58) 34 (42) 44 (96)   39  Fig. 2.1. Definition of block caving deformation zones as defined by Van As et al. (2003)   (a) (b) (c) Fig. 2 minin mine paren    .2. General g method ( d. Reported theses. Sym Aus 10% Sou 8% ( Euro 4% BC- 5% ( BC- 7% ( PC 7% Othe 5% ( Asb 9% ( Moly 5% ( Nick 3% (    breakdown BC = block  are the re bols in each tralia  (10) th America 8) pe (4) SC 5) PC 7) (7) r 5) estos 9) bdenum 5) el 3)  of cave min  cave, PC = lative perce  legend are Africa 16% (17 SC 19% (1 Iro 10% Diamon 9% (9) 40 ing data in  panel cave ntages follo ordered from Asia 19% (20) ) 9) Copper, G 14% (1 n (10) d  database by , SC = subl wed by th  highest pe Nort 4 B 62% Gold 15% (14 Copper 29% (28) old 3) : (a) regiona evel cave), e total num rcentage to h America 3% (45) C  (63) )     l distributio and (c) reso ber of cas lowest. n (b) urce es in  Fig. 2 show  .3. Breakdo ing a trend t wn of block owards the m  heights bei ining of la 41 ng mined fo rger blocks. r the block  caving cases in the data  base,  Fig. datab   2.4. Breakd ase showing own of un  a trend tow dercut dept ards the dev 42 hs associate elopment o d with the f deeper und  block cavi ercuts. ng cases in   the  43  Fig. 2.5. Undercut depth versus caving angle for block, panel, and sub-level caving operations. Each line segment represents the range in caving angles measured from different sides of the undercut; the greater the range the higher the degree of asymmetry.  44  Fig. 2.6. Undercut depth versus fracture initiation angle for block, panel, and sub-level caving operations. Each line segment represents the range in fracture initiation angles measured from different sides of the undercut; the greater the range the higher the degree of asymmetry.  45  Fig. 2.7. Undercut depth versus caving, fracture initiation and subsidence anlges for block caving operations. Each line segment represents the range in angles measured from different sides of the undercut; the greater the range the higher the degree of asymmetry.  46  Fig. 2.8. Undercut depth versus caving, fracture initiation and subsidence anlges for panel caving operations. Each line segment represents the range in angles measured from different sides of the undercut; the greater the range the higher the degree of asymmetry.  47  Fig. 2.9. Undercut depth versus caving angle for global block and panel caving operations, colour coded according to the general characteristics of the surface topography. Each line segment represents the range in caving angles measured from different sides of the undercut; the greater the range the higher the degree of asymmetry.  (a) (b) Fig. 2 topog Chile .10. Influen raphy (Nor ). Surface su ce of topog thparkes mi bsidence ar raphy observ ne, Australi ea is marked 48 ed visually a), and (b)  by dashed  in Google E irregular top line. arth satellit ography (E e images: (a l Teniente m   ) flat ine,  Fig. subsi same of inc under moun appro 2.11. Fini dence assum  geological reasing deg cut below, t tain peak, ximates zon (a) (b) (c) (d) (e) te-element ing typical inputs used ree of assy hese are: (a (d) rising s e of caving Fault Fault Fault Fault Fault modelling  surface pro for the com metry (cave ) flat topogr lope, and ( . 49 of influenc files visual parative mo -surface int aphy, (b) mo e) slope wi U e of topo ly identified dels in Chap eractions) re untain peak th plateau. Undercut Undercut Undercut ndercut Undercut graphy on  in the UB ter 3 were lative to th , (c) rising Note that g Fault Fault Fault Fault Fault  caving-ind C database. applied. In e position o slope ending rey shaded  uced  The order f the  in a area  50  Fig. 2.12. Undercut Depth versus caving angle for global block and panel caving operations, colour coded according to the resource being mined. Each line segment represents the range in caving angles measured from different sides of the undercut; the greater the range the higher the degree of asymmetry.  51 (a) (b) Fig. 2.13. Symmetric surface subsidence observed in association with a vertical kimberlite pipe - Kimberley diamond mine: (a) Google Earth satellite image, and (b) geological cross section (De Beers, 2008).   52  (a) (b) Fig. 2.14. Asymmetric surface subsidence observed in association with a copper porphyry ore deposit - San Manuel mine: (a) Google Earth satellite image, and (b) geological cross section (Sandibak, 2004). Kalamazoo Segment San Manuel Segment Gila conglomerate Rhyolite Cloudburst FM. Diabase Orezone Quartz monzonite    F b ig. 2.15. Cavin lack lines to th g-induced britt e left and right le fracture and of the undercut 53 subsidence for u are bounding fa ndercut depths ults.  of:  500 m (top), and  2000 m (bottom). The   continuous  54 Chapter 3:  Benchmark Testing of Numerical Methods for Modelling the Influence of Undercut Depth on Caving-Induced Subsidence2  3.1 Introduction Block caving represents a low cost underground mass mining method with production tonnages that are competitive with those from open pit operations. However, the method results in significant disturbance to the surface environment. Damage to and subsequent replacement of surface and underground infrastructure due to differential caving-induced ground movements are often cause for additional capital and operation expenditures as well as for environmental degradation. These include both large scale deformations, defined by the caving and fracture initiation zones (Van As et al., 2003), and small-strain deformations, defined by the continuous subsidence zone (Fig.2.1). The latter is difficult to directly measure and empirical guidelines are focused on the former. Accordingly, the analysis of subsidence is often based on numerical modelling. The complexity of geology and its brittle tectonic overprint (jointing, faulting, etc.) make rock masses a difficult material for mathematical representation via numerical modelling. Numerical techniques vary widely in their representation of geology ranging from continuum methods (e.g. finite element, finite difference), where the presence of fabric is treated implicitly through constitutive models and input properties resulting in a more computationally efficient solution especially in 3-D, to discontinuum methods (e.g. distinct element) that explicitly account for the presence of geological structures, but because of this added complexity, are more computationally demanding. A coupling of these two techniques (FEM-DEM) represents a further degree of sophistication, and computational effort, in which a continuum domain populated by discrete fractures may undergo subsequent fracturing in response to changing stresses and strains. These methods and their application are discussed in detail by Stead et al. (2006).  2  Woo, KS. Eberhardt E. Elmo, D. Stead, D. Benchmark Testing of Numerical Capabilities for Modelling the Influence of Undercut Depth on Caving-Induced Subsidence. (To be submitted)  55 Due to their faster run times, continuum codes such as the finite difference programs FLAC and FLAC3D or the finite element program ABAQUS have seen the most widespread use in the modelling of block caving subsidence (Van As et al., 2003; Singh et al., 1993; Sainsbury et al., 2008; and Beck et al., 2008). To a lesser degree, distinct element codes like UDEC and 3DEC or coupled FEM-DEM codes like ELFEN have been used (Vyazmensky et al., 2010b and Elmo et al., 2010). Yet ELFEN has been shown by Vyazmensky et al. (2010b) to be particularly well-suited for capturing important block-caving mechanisms, including preferential rock fragmentation within the ore column and influence of geological structures on cave development and surface subsidence. Ultimately, the choice of method varies on a case-by-case basis, ranging from selection based on simplicity and familiarity in the modelling method to specific requirements to incorporate a key process such as brittle fracturing. In this study, benchmark testing of several different numerical techniques was carried out to investigate their abilities and limitations with respect to modelling block caving subsidence for a range of undercut depths with added consideration of the influence of structural geology. Reviews of historic and current caving operations by Chapter 2 have shown that the average undercut depth has increased from 200 m to deeper than 600 m over the past 50 years. In effect, as near surface resources become exhausted caving operations are moving deeper and developing larger caves, raising questions as to their influence on the surface environment. The comparison carried out here focuses on a conceptual problem geometry involving a porphyry type deposit, incorporating faults, several different lithologies and varying rock mass properties. The undercut depths tested vary from 500 to 2000 m in increments of 500 m using the 2-D continuum code Phase2, 3-D continuum code FLAC3D, 2-D discontinuum code UDEC, and hybrid FEM-DEM brittle fracture code ELFEN. 3.2  Numerical Modelling Methodology 3.2.1 Model Geometry One of the larger and deepest block/panel caving projects currently in development is the Resolution Copper Mine near Phoenix, Arizona. Fig.3.1 provides a cross section of the Resolution mine (Rio Tinto, 2008), showing that the undercut and production levels will be  56 located approximately 2,000 metres beneath surface. The conceptual geometry used for this study was specified by the Centre for Excellence in Mining Innovation (CEMI), Sudbury, Ontario, as part of a sponsored benchmark study, and is illustrated in Fig.3.2. Outlined in the 3-D panel caving geometry are several faulted lithologies, with the faults located adjacent to the undercut, similar to that experienced at Resolution (Fig. 3.1). The undercut is extensive and divided into three panels (A, B and C), mined from south to north (Panel A toward Panel C). The width of each panel is 500 m. For 2-D modelling, section A-B was used. The external limits of the model were determined based on preliminary elastic modelling of the lateral extent of measureable surface subsidence for a 2500 m deep undercut. This resulted in a 2-D section 10,500 m in length and 4200 m in depth. For the 3-D geometry, the east-west width of the model is 10,000 m and the north-south width is 8000 m. The depth is 3000 m. 3.2.2 Numerical Modelling Software Used Four different numerical modelling codes were applied to the benchmark problem: Phase2, FLAC3D, UDEC and ELFEN (Rocscience Software, 2009; Itasca Consulting Group, 2010; Itasca Consulting Group, 2009; and Rockfield Software, 2009). Phase2 is a 2-D finite- element code, the governing equations for which are based on continuum solid mechanics. Although simulation of discontinuities is possible through joint elements, these are restricted to small strain movements in which the pairing between two contacting joint interfaces does not change. In finite-element treatments applying joint elements, once interconnectivity between the two sides of a joint is established upon meshing, it remains unchanged throughout the solution process, despite any displacements that occur (Riahi et al., 2010). Phase2 was used here to model the problem in Fig.3.2 with and without joint elements and the results were compared to understand the influence of small-strain joint movements on the modelling of surface subsidence. Modification of the continuum model to include a discrete fracture network (DFN) involved two joint sets of variable spacing and persistence dipping at 0 and 90 degrees (Fig.3.3). These were only applied from the undercut level up to the surface and extending outwards at an angle of 40 degrees from the edges of the undercut. The joint angles of 0 and 90 degrees were selected to minimize the degree of asymmetry that would be  57 introduced through the DFN to enable a more direct comparison to models without the DFN. Vyazmensky et al. (2010a) demonstrated the importance of inclined joints on influencing the lateral extent and asymmetry of surface subsidence. Continuum modelling was subsequently extended into 3-D using the finite-difference code FLAC3D (Fig.3.4). While 2-D codes are effective in analyzing cross-sections pertaining to an area of interest, this requires that a plane strain assumption is reasonably applicable. A typical block caving mine operation does not necessarily fit this condition. As both a 3-D and continuum analysis tool, FLAC3D does not easily allow the introduction of joints into the model. Doing so requires each discrete feature to be manually specified through matching interfaces, entailing significant pre-processing preparation time. In this case, only the large bounding faults were inserted into the FLAC3D model, with the added simplification of using vertical interfaces (Fig.3.4). Beyond the continuum treatment of the problem, all further model runs involving discontinuum techniques were modelled in 2-D given the prohibitive pre-processing and computing times required for 3-D. The influence of joint sets was further analyzed using UDEC, a 2-D discontinuum analysis tool based on the distinct-element method. UDEC models the problem domain as an assemblage of interacting deformable blocks that simulates either the quasi-static or dynamic response to loading of a rock mass containing multiple, intersecting joint structures. This approach improves on the inclusion of joint elements in a continuum treatment like Phase2 as the joints included in a UDEC model can undergo large displacement offsets in shear or through opening and block rotation. Blocks between the joints can be modelled as either elastic or elasto-plastic deformable materials, and joints can also be modelled using a number of constitutive relationships. Here a simple Coulomb slip model was applied to the joints; blocks were modelled as elasto-plastic. Fig.3.5a,b shows the model geometry used in which the joint spacing varies from 10 m in the area of interest above the undercut and simulated cave, to 50 m towards the model boundaries. Because of the versatility and ease of UDEC in representing a joint network, an alternative geometry was also modelled in which the 0 and 90 degree joint pattern is superimposed with a second coarser pattern of joints at 45 and 135 degrees (Fig.3.5c) to increase the degrees of freedom for block slip and vertical subsidence.  58 The last numerical technique employed in this benchmark study involved the hybrid FEM-DEM brittle fracture code ELFEN. Here a similar geometry was used as in the Phase2D model with respect to the DFN imported into the continuum problem domain (Fig.3.6) (Eberhardt et al., 2011). This code enables the modelling of brittle fracture initiation and propagation within a continuum finite-element domain populated by discrete fractures through adaptive remeshing of the problem during time-stepping. ELFEN was used for explicitly modelling 2-D cave propagation through brittle fracturing as ore is extracted. This allows ELFEN, unlike the other codes, to visually depict the caving and fracture initiation angles directly. Aside from their inherent differences, efforts were made to ensure these different codes were tested with identical input parameters and boundary conditions as much as possible. 3.2.3  Rock Mass Properties Depth dependent rock mass properties were derived using the UCS, mi and GSI values reported in Table 3.1. These were provided by CEMI in association with this study. Scaling was carried out using Hoek et al.’s (Hoek et al., 2002) relationships based on the Hoek-Brown failure criterion. Because not all codes have fully implemented a Hoek-Brown constitutive model, the Hoek-Brown values were converted to Mohr-Coulomb by fitting an average linear Mohr-Coulomb relationship to the non-linear Hoek-Brown envelope (Table 3.2). This was done for a range of minor principal stress values with an upper bound of σ'3max. The estimation of σ'3max for the problem geometry is complicated by differences in the stress field above the undercut, which involves extensive relaxation, and that away from the cave, which is more in line with the far-field in-situ stresses. To vary the rock mass strength properties as a function of depth, σ'3max values were estimated for each geological unit using stress values calculated by means of a Phase2 finite-element elastic stress analysis. Calculations were performed for each undercut depth assuming the presence of an undercut filled with caved material with properties that result in approximately 0.5 m of surface subsidence. This allows for a minor degree of stress relaxation above the cave back in assessing σ'3max. Because the stresses vary between the top and bottom of each geological  59 unit, the higher σ'3max values in the stress range were adopted; the justification for this is that the cave must first propagate up through the bottom of each geological unit and therefore the rock mass properties derived for the higher σ'3max values are more appropriate. Tensile strength (Trm) was estimated assuming a 25% tensile cut-off applied to the theoretical Mohr- Coulomb value and the rock mass deformation modulus, Erm, was calculated using Hoek and Diederichs’ (Hoek et al., 2006) empirical relationship. A value of fracture energy (Gf) of 43 J/m2 was applied for brittle fracturing in the ELFEN modelling. Joint strength properties for the joint elements and discrete elements were assigned assuming a linear Mohr-Coulomb slip criterion. The North and South faults, the DFN joints and, in the case of ELFEN, any new fractures generated during the simulation of caving were given the same values: a joint cohesion of zero and joint friction angle of 30°. It should be noted that specific fracture sets will generally have markedly different surface morphologies and hence different shear strengths. However, this has not been considered in the current models to maintain similarity between the comparisons of the different codes. The mechanical contact forces that govern the interactions between discrete elements in UDEC and ELFEN can be loosely defined as the forces that are required to prevent blocks from interpenetrating. Contact forces are realised at contacting nodes and are evaluated by considering the relative kinematics of surface entities. The enforcement of these constraints is established using either a prescribed joint stiffness or penalty method, based on which proportionality between the degree of constraint violation and the degree of corrective measure is assumed. A normal stiffness/penalty of 4 GPa/m and tangential stiffness/penalty of 0.4 GPa/m were assumed. While values reported in Table 3.2 were applied to all of the Phase2, UDEC and ELFEN models, an exception was made for the FLAC3D models where, to account for the larger mesh size, the rock mass properties were assumed to be lower by 75%. The full details of the material properties used in this benchmarking study are provided in Appendix C. 3.2.4 In-situ Stresses The initial stress conditions were implemented as outlined by CEMI in a background document they provided (Fig.3.7) (Eberhardt et al., 2011). The vertical stress is defined as  60 gravitational loading with a rock unit weight of 27 kN/m3. The maximum horizontal stress (σHmax) is set as 1.9 times the vertical stress and is aligned north-south. This corresponds to the in-plane direction for the 2-D model representations. The minimum horizontal stress (σHmin), aligned east-west, is set as 1.2 times the vertical stress. For the 2-D models, this was used as the out-of-plane stress condition. The external boundaries in all cases were set as zero displacement boundaries normal to the boundary, except for that representing the top surface. This was left as a free boundary. 3.2.5 Simulation of Draw and Caving The simulation of cave propagation is of prime importance given its direct relationship with the caving-induced deformations being modelled. For the continuum methods, caving was implemented through an implicit approach where the geometry of the cave is built into the model, as opposed to explicitly modelling caving and cave propagation. This is a key limitation of applying continuum techniques to block caving problems. The implicit approach employed in the Phase2 and FLAC3D modelling assumes a cave geometry at several different points in its overall development over time, and incrementally changing the corresponding element properties from those of the ore to fragmented rock. A simplified cave geometry was assumed involving caving in 50 m increments up to a total block height of 200 m. Caving is initiated in Panel A and progresses through two stages (100 m cave height) before the next panel is initiated (Fig.3.8). This is continued for each panel until the cumulative height of caved rock area reaches 200 m. Table 3.2 includes the material property assumed for the caved rock. As the material responsible for the relaxation and deformation of the surrounding rock, it was found to have a significant influence on the magnitude of the modelled displacements. To avoid numerical errors related to severe mesh distortion, the caved rock material was modelled as an elastic material, using reduced elastic properties to account for the reduced deformation modulus that would be expected for caved rock, as well as allowances for the presence of a small air gap. This procedure requires redefinition of the initial stress state within the modelled cave material to coincide with the self-weight of the caved material and not the locked in tectonic stresses initially prescribed for the ore and host rocks.  61 Simulation of the propagating cave in UDEC was carried out in a similar fashion. Although the discontinuum treatment of the problem domain allows for blocks in the undercut to be deleted, thereby more directly simulating the actual mining process, the contact detection algorithm used by the code is unable to create new contacts for detached/falling blocks. The algorithm is able to create new contacts when motion occurs along a discontinuity (i.e. shear), enabling large displacements to develop in the model. However, the UDEC data structure was designed specifically to model compact rock masses (i.e., tightly packed blocks) and not multiple blocks that lose contact with neighbouring blocks. ELFEN modelling of the draw and caving process was carried out explicitly following procedures by Elmo et al. (2010). The algorithm removes all meshed elements whose centroids are located within a specified region, in this case corresponding to the undercut/production level. An iterative process is used such that the removal of elements is repeated continuously at a given numerical time step in order to return the specified draw rate (Fig.3.9). No hang ups are currently simulated at the extraction level since the simulated draw is designed to gradually fracture the rock passing through the extraction level (i.e., an ideal draw scenario is assumed in the model). 3.3 A Comparison of Numerical Analysis Results 3.3.1 Continuum Analysis (2-D versus 3-D) Fig.3.10 shows the results from a 2-D continuum elasto-plastic analysis using the Phase2 finite-element program. Results are plotted as vertical displacement contours applying a minimum threshold of one metre. These can be compared against results obtained for the models that include the small-strain joint elements (Fig.3.11). The comparison reveals that the lateral extent of subsidence is similar for the shallower undercut depths, but increases more noticeably in the jointed models as the undercut depth increase (i.e. 3% and 8% wider for the 1500 m and 2000 m deep undercuts, respectively). This tendency can be attributed to the weaker rock mass conditions associated with the inclusion of the joint sets.  62 Fig.3.12 presents the FLAC3D modelled subsidence. In general, the magnitude of subsidence seen in the 2-D continuum modelling (Phase2) is greater than that in the FLAC3D modelling. This is largely due to the 2-D plane strain condition and the added restraint provided by the third dimension in the FLAC3D model. Rocscience (2009) also cautions that the stress changes calculated based on the plane strain assumption show some exaggeration if the out-of-plane dimension of the excavation is not at least five times greater than the largest in-plane cross-sectional dimension. This is because the stress flow around the boundaries of the excavation is not taken into consideration. A final factor for the reduced subsidence magnitudes in FLAC3D is the absence of the joint sets; this is despite the reduced rock mass properties used to account for the need to use larger elements. Consequently, subsidence occurs to a lesser extent (approximately 75% less) in the FLAC3D model compared to the 2- D analyses. The larger mesh size also likely limited the extent of elasto-plastic yielding in the model. As a result, a lower bound contouring threshold of 0.25 m was used in Fig.3.12 as opposed to the 1 m cutoff used in the other plots of the benchmarking results. Comparison can be made by observing the outline of the 1 m upper bound threshold used in Fig.3.12 in blue. The FLAC3D results for the 500 m deep undercut show that the modelled extent of subsidence, when a block height of 200 m is reached in Panel A (with block heights of 150 and 100 m in panels B and C, respectively), is limited by and bound by the faults on either side of the undercut. As the undercut depth increases, the subsidence profile widens and the influence of the bounding faults diminishes. This agrees with the observations made in the 2- D Phase2 results. It is also noteworthy that the shape of the subsidence profile elongates in the north-south direction as the undercut depth increases. This coincides with the longer axis of the panels being modelled (Fig.3.2), with the effect becoming more pronounced as the undercut depth increases. In addition, the varying ratio of panel size to undercut depth with caving propagation seems to contribute to asymmetric subsidence. 3.3.2 Discontinuum Analysis The results from the UDEC discontinuum analysis are presented in Figs.3.13 and 3.14. As previously noted, two different joint geometries were considered for the UDEC  63 discontinuum analysis. Fig.3.13.presents the subsidence results for the joint configuration similar to that used for the other 2-D modelling methods (0 and 90 degrees). These can be compared to the results in Fig.3.14, which shows the results assuming the same pattern of 0 and 90 degrees superimposed with a second joint pattern dipping at 45 and 135 degrees. In Fig.3.13, the subsidence zone is about 30% narrower than that seen in the previous model results. This is due to the continuous persistence of the orthogonal joint sets used, specifically that for the vertical joint set. Given the large strain slip afforded by the distinct element formulation, most of the rock mass response is therefore concentrated on these joints directly above the growing block cave. Hence, the lateral extent of the vertical subsidence is reduced. In contrast, the extent of subsidence in Fig.3.14 is significantly increased as the 45 and 135 degree joint angles promote freer ground movement (slip) in the lateral direction. Fig.3.14 shows this response to increase with increasing undercut depth. For the 2000 m undercut, the subsidence extends so broadly that it approaches and slightly interacts with the right boundary. The asymmetry observed in these contours is related to the direction of caving (Panel A to the south being developed first before progressing towards the north and Panels B and C). The >5 m subsidence contour suggests that the other effect of the 45 and 135 degrees joint sets, relative to the 0 and 90 degree joint sets, is that although the lateral extent of subsidence increases, the magnitudes of subsidence that develop over the cave are reduced. These reduce further as a function of undercut depth, with plots for the 1500 and 2000 m deep undercuts showing that the saturated vertical displacements (> 5 m) does not extend to surface. In all cases (Fig.3.14), the results indicate that the zone of modelled caving is limited by the presence of the bounding faults despite the presence of the 45 and 135 degree joint sets; the extent of the smaller strain subsidence (1 m contour threshold) is seen to increase as a function of undercut depth despite the presence of the bounding faults. 3.3.3 Discontinuum with Brittle Fracture Results The influence of undercut depth on subsidence using the hybrid FEM-DEM code ELFEN is captured in Fig.3.15. Brittle fracturing induced by caving is mostly limited  64 between the north and south faults. In contrast, the pattern of subsidence is similar to those in the other numerical models, widening with increasing undercut depth. The key consideration in comparing the results for the different undercut depths is that the “volume” of excavated ore (or block height) in each model is the same. Since the column of rock above the undercut increases with increasing undercut depth, this means that the extraction ratio is decreasing. In the case of the 500 m deep undercut, 40% of the rock column above the undercut is caved. For the 2,000 m deep undercut, only 10% of the rock column is caved. Consequently, the modelling results for the 500 m deep undercut clearly show the importance of incorporating a "realistic" fracture network in the analysis. The natural fractures are shown to accommodate most of the caving-induced extensional strains. This, as well as the panel size to undercut depth ratio, changes as the undercut depth increases. The comparison of the subsidence profiles clearly indicates that the subsidence zone increases as a function of increasing undercut depth. The zone of caving remains within the bounding faults and its extent actually decreases with increasing undercut depth. This is due to the decreasing extraction ratio (i.e. draw height to overburden height for an equal volume of draw). In the shallow undercut, caving angle, fracture initiation angle, and subsidence angle are all similar, but in the deeper undercut, subsidence angle tends to be significantly smaller. 3.4 Discussion The caving, fracture initiation and subsidence angles, as defined by Van As et al. (2003) (Fig.2.1), are reported in Fig.3.16-19 relative to their measurement on the south and north sides of the undercut. In agreement with the definitions by Van As et al. (2003), caving angles are the largest at around 90° or over followed by fracture initiation angles and subsidence angles. The caving angles identified in the Phase2, FLAC3D, and UDEC models were measured based on the yield zone with shear indicator. In the ELFEN models, the caving angles were directly measured. Fracture initiation angles in the FLAC3D models were assumed to be the mid-values between the caving and subsidence angles, since no tension yield indicators occur in FLAC3D modelling. This is because for shallower undercut depths, the fractured zone is observable on the surface and therefore the fracture initiation angle can  65 be explicitly measured, but for deeper undercut depths, the fractured zone does not appear on the surface making the fracture initiation angle not possible to measure. One possible way to estimate the fracture initiation angle in deeper undercut depths is to interpolate the fracture initiation angle explicitly measured in shallower undercut depths based on the empirically identified trend in Chapter 2 where the influence of caving activities on the surface decreases as the undercut depth increases. But the influence of joint sets, especially their directions, on the fractured zone is uncertain as demonstrated in the UDEC modelling results. Accordingly, the mid-point value between caving and subsidence angles was determined to be an appropriate approximation of fracture initiation angle because fracture initiation angle is usually between caving and subsidence angles. The fracture initiation angles measured such in the FLAC3D models turned out to be similar to the fracture initiation angles identified in the other modelling results supporting the decision to take a value between the caving and subsidence angles. In the Fig. 3.16-19, caving angles and fracture initiation angles show similar trends. In the UDEC models, the fracture initiation angles were defined based on the point in the joints where normal stiffness (Kn) or shear stiffness (Ks) equal zero. In the ELFEN models, the fracture initiation angles were directly measured. For the subsidence angles, a 1-m cut-off was applied. 3.4.1 Trends with Depth For the Phase2 results (Fig.3.16), the general trend shows the caving, fracture initiation and subsidence angles decreasing as a function of depth (indicating a widening of each related zone with increasing undercut depth). However, the shape of these curves is convex with the rate of decrease in angle between each depth increment diminishing with depth (i.e., as the panel width-to-undercut depth ratio (P/D) decreases). In part this is due to the continuum assumption and interconnectivity of the elements across which the incremental cave growth is simulated, combined with the increasing overburden across which the caving-induced strains can be redistributed as the undercut depth increases (or the P/D ratio decreases). The higher confinement provided by the higher stresses at depth (and increase in rock mass strength accounted for in the models) would also contribute towards limiting the extent of subsidence. The results also indicate that the presence of the boundary faults have little to no significance. The differential between the caving angles and the  66 subsidence angles is 20-25 degrees for the undercut depth of 500m, and 45-50 degrees for the undercut depth of 2000m. Results from the 3-D continuum analysis carried out with FLAC3D (Fig.3.17.), show similar trends to those from the 2-D continuum analysis. The shape of the curves for the caving, fracture initiation and subsidence trends with depth are likewise convex, but not as strongly so. Here the added dimension and degrees of freedom enable caving-induced strains to be further redistributed resulting in narrower zones of influence on surface. The differential between the caving and subsidence angles is 25 degrees for the undercut depth of 500m and 37 degrees for the undercut depth of 2000m. The 3-D nature of the code, the absence of joint sets, and the larger mesh size appear to contribute to these smaller differences in angles. It should be noted again that the fracture initiation angles in the FLAC3D results were estimated based on the caving and subsidence angles. Transitioning to a discontinuum approach where a system of joints are free to open, close and slip in response to the caving-induced strains, the trends derived from UDEC (Fig.3.18) are less consistent (i.e. more irregular) but also generally show a convex shape. In the case of the 0 and 90 degree joint sets, the caving and fracture initiation angles do not vary significantly regardless of undercut depth. The presence of the meso-scale joint network together with the bounding faults appears to have some influence on the different angles, with angles at 500 and 1000 m having similar values. This influence then diminishes as the undercut depth further increases, and the curves revert to following a convex trend. It is not possible though to separate the influence of the faults from that of the joint network for the 0 and 90 degree joint set model. For the orthogonal case with added 45 and 135 degree joint sets (Fig.3.18), the trend of the subsidence curve is noticeably more convex, with the subsidence angles sharply decreasing from 500 to 1000m but then less so below this. The caving and fracture initiation angles increase before reversing, implying constraint (against widening) by the bounding faults. The differential between caving and fracture initiation angles is 10-20 degrees for the undercut depth of 500m and 35-57 degrees for the undercut depth of 2000m. This greater extent of differences appears influenced by the joint sets and discontinuum formulation, which allows large strains to develop along the fault and joint  67 contacts, whereas the continuum formulation is only limited to small strain displacements along the joint elements used. A completely different trend was observed for the ELFEN results (Fig.3.19), which showed more concave-shaped curves. In general, the caving and fracture initiation angles show an increasing trend with undercut depth, indicating that the influence of caving and its extent at surface diminishes as the undercut depth (and extraction ratio) decreases. This trend is consistent with that observed in the UBC block caving database (Chapter 2) and that reported by Van As et al. (2003). However the opposite is observed with respect to the trend of the subsidence angles. As the undercut depth increases, the subsidence angles are seen to decrease more indicating a significantly wider zone of impact on surface. This difference is likely due to the difference in how caving is simulated, as ELFEN’s unique mesh fracture, block delete (of mined caved material) and block contact update capabilities enable a more direct simulation of the block cave mining process generating more realistic results. Even so, it should be noted that the subsidence angles estimated for the undercut depth of 2000m is similar to those obtained from the other modelling results.  3.4.2 Caving Angle Caving angles approximated by the different numerical techniques applied were compared. The zone of caving is observed directly above the undercut area in each case. The saturated nature of the vertical contours when applying an upper bound plotting interval makes the estimation of the caving angle relatively easy. In Phase2, these contour plots were supplemented with plots of the plasticity indicators to help define the zone of caving, with added weighting given to the distribution of shear indicators (Fig.3.20). In the FLAC3D models too, the caving angles were measured based on the yield zone with shear indicator (Fig.3.21). A similar technique was used to define the caving zone in the UDEC models (Fig.3.22); the caving angle was estimated based on yield pattern and vertical displacement  68 contours. In the ELFEN models, the caving angles were measured directly based on the zone of completely detached blocks that develop and form the cave. Fig.3.23 and 3.24 plot the caving angles measured on the north side and the south side of undercut, respectively, for each modelling technique. The different results show similar trends with most indicating overhanging angles relative to the footprint of the undercut. The results though can be ambiguous about the influence of undercut depth on caving with the exception of the ELFEN results which show the caving angle increasing (meaning a smaller zone of disturbance on surface) with increasing undercut depth. Asymmetry is seen in the results between the north and south sides of the undercut. This is due to the initiation of caving in the simulations beginning on the south side (Panel A), meaning a more advanced state of cave development, before progressing to Panel B and then Panel C. The comparison of caving angle between the Phase2, FLAC3D results and UDEC (with vertical joint sets) reveal that the enabling of large strain slip along the joints in UDEC result in a near vertical caving angle, as would be expected given their persistence. Because the orthogonal joints somewhat restrict the lateral extent of ground movements (concentrating them in the vertical direction instead), the caving angles measured in UDEC signify a broader caving zone on surface relative to that identified in the Phase2 and FLAC3D results (which show overhanging angles for the caving zone). A further consequence of the persistent orthogonal joints is that the caving angle does not vary significantly with undercut depth. This changes when the inclined joint sets (45 and 135 degree) are added resulting in lower caving angles (broader zone on surface). This observation implies that the direction of the joint sets (i.e. rock mass fabric) is a key consideration in terms of subsidence pattern as shown by Vyazmensky et al (2010a). Through this benchmarking comparison, it is suggested that ELFEN appears to provide more realistic results, and most correct in producing caving angles that consistently increase as a function of undercut depth; i.e. the extent of the caving zone on surface decreases with decreasing extraction ratios.   69 3.4.3 Fracture Initiation Angle In Phase2, the fracture initiation angle was estimated based on the distribution of tensile yield indicators on surface observed in the plasticity plots (Fig.3.20). An exception is the 2000 m deep undercut in the Phase2 modelling where no tension yield indicators occur. This perhaps indicates that fracturing outside the caving zone does not occur due to the smaller strains resulting from the smaller extraction ratio. In UDEC (Fig.3.25), the fracture initiation angle was defined by joints on surface which show opening or slip (normal stiffness (Kn) or shear stiffness (Ks) becomes zero). In ELFEN, fracture initiation was again estimated directly based on the development of fractures at surface in the models. Comparing the different results, specifically the fracture initiation angles to the north and south of the undercut (Fig.3.26 and 3.27), some sensitivity is again seen due the interaction between the faults and panel caving sequence. Fracture initiation angles measured in the UDEC are approximately 10° lower than the caving angles from the same model (the zone of fracture is broader than the zone of caving). Again, the UDEC models with orthogonal jointing show angles that are near vertical due to the significant influence their high persistence has on slip concentrations and therefore where surface fracturing develops. In the UDEC modelling with the inclined joint sets, meanwhile, the fracture initiation angle shows a pattern of decreasing angles with undercut depth as fracturing/slip extends to the bounding faults, before reversed for the 2000 m deep undercut showing that the reduced extraction ratio results in a diminished extent of fracturing on surface. Based on the modelling results, it is observed that the fracture initiation zone does not extend beyond the bounding faults. In the ELFEN modelling, the fracture initiation angle increases with increasing undercut depth, similar to the caving angle trend. This again confirms that the influence of the bounding faults is to both promote and limit the extent of fracture initiation for the shallower undercuts (maximum cave-fault interaction). For the deeper undercuts, and smaller extraction ratios and caving-induced strains at surface, the influence of the faults significantly decreases. Interestingly, the fracture initiation angle measured in the Phase2 model decreases as undercut depth increases, which is different from the other models. This  70 suggests that the influence of the faults in Phase2 is less significant, likely due to the small- strain limitations of the joint element formulation. In the FLAC3D modelling, the fracture initiation angle was approximately 10-15° smaller than the caving angle and tends to increase as the undercut depth increases. 3.4.4 Subsidence Angle The angle of subsidence was estimated based on the vertical displacement contours defined by a 1 m lower bound cut off (Fig.3.28 and 3.29). In the UDEC model with inclined joints, the angle of subsidence although greatest sharply drops off for the deeper undercuts. The implication of this observation is that the angle of the joint sets dominates the development of the subsidence zone regardless of undercut depth, with the lowest angle attained coinciding with the dip of the joints. In the ELFEN model, the angle of subsidence decreases with increasing undercut depth indicating that unlike the caving and fracture initiation angles, the bounding faults do not significantly influence or limit the lateral extent of smaller-strain subsidence. The subsidence angles measured in the ELFEN models further imply a non-linear trend with the extent of subsidence markedly increasing as undercut depths decrease. This perhaps suggests that the bounding faults do have some influence (minor) on limiting small-strain subsidence for the shallower undercut depths, but not so for the deeper undercuts. A noteworthy observation from the comparison of subsidence patterns identified by UDEC (with inclined joint sets) and ELFEN is that the subsidence angles measured in the undercut depths of 500 and 2000 m do not differ but the difference in the subsidence angle measurements in the 1000 and 1500 m undercut depths are considerable. Movement of individual blocks on the inclined joints in response to caving appears to be more active with the shallower undercuts, having a more pronounced influence on the surface subsidence. In the case of the ELFEN results, the influence of the brittle fracture network on the lateral extent of subsidence tends to be less significant for the shallower undercuts, but that with greater undercut depths (and higher stresses), brittle fracture activity away from the immediate area above the undercut increases. The trend of subsidence angles with increasing undercut depth between ELFEN and the UDEC model with vertical joints is similar. This  71 suggests that the influence of large strain slip along joints in the UDEC models decreases with increasing confining stresses at depth, as would be expected based on a Coulomb slip law. For the FLAC3D results, where estimates of the caving and fracture initiation angles are limited by the smaller vertical displacements that develop, the subsidence angles are seen to decrease from 500 to 1000m, but then remains unchanged for the deeper undercuts. This indicates that the subsidence area increases in a consistent ratio in relation to the undercut depth increase. The subsidence angle could be consistent probably because the caving height is constant. In summary, each set of models: Phase2, UDEC, ELFEN and FLAC3D, each show a similar trend with the extent of subsidence increasing (decreasing subsidence angles) with increasing undercut depth. 3.5 Conclusions Results are presented from a benchmark study examining the relationship between the extent of caving, large-strain fracture initiation and small-strain subsidence as a function of undercut depth  using four different numerical techniques: 2-D finite-element (Phase2), 3-D finite difference (FLAC3D), 2-D distinct element (UDEC) and 2-D FEM-DEM with brittle fracture (ELFEN). All models showed a similar response with the extent of caving decreasing with increasing undercut depth (resulting in caving angles greater than 90° indicating an overhanging condition with respect to the undercut footprint). A similar decrease in the extent of macro-deformation in the form of the fracture initiation zone, was also seen to decrease with undercut depth. These responses can be explained by decreasing extraction ratios with increasing undercut depth as the simulation of caving in the models maintained the same block height of 200 m (i.e., a constant block height relative to an increasing rock column height above the undercut with increasing undercut depth corresponds to a decreasing extraction ratio). In most cases, the presence of bounding faults on either side of the undercut limited the lateral extent of caving and fracture initiation.  72 Differences in the results between the different numerical methods applied emphasize the importance of carefully defining the key objectives of the modelling together with the factors that are most important, while exercising good modelling practice when selecting a numerical modelling tool. Often the needs for fast model setup and run times are counter to those for accurate representations of the rock mass fabric (through the inclusion of DFN’s) and caving mechanics. Overall, the 2-D hybrid FEM-DEM approach allowing stress-induced brittle fracturing between joints appeared to provide the more dependable and realistic results. In addition, the contact detection algorithm used in ELFEN allows caving to be more intuitively (explicitly) simulated through a block deletion procedure which appears to work better than changing the material properties to those of caved rock as the cave advances. Ideally, using a 3-D FEM-DEM brittle fracture code would seem to incorporate all of the key requirements and needs. Computationally, though, this is prohibitively expensive with current computer and software capabilities. Where the need for a 3-D analysis is the over- riding factor, a 3-D finite-element or finite-difference code (e.g. FLAC3D) represents the most viable option at present.    73 Table 3.1. Rock mass properties used for conceptual benchmark model testing, as defined by the Centre for Excellence in Mining Innovation (CEMI) Lithology Intact rock Rock mass Block length (m) Joint conditions Jc UCS [MPa] mi E [GPa] RMR89 GSI Rhyolite 205 25 60 49 44 0.35 m 0.7 Quartz – Monzodiorite 140 20 50 43 38 0.35 m 0.5 Sandstone and Siltstone 125 18 40 52 47 0.5 m 0.7 Biotite Granodiorite 145 22 55 43 38 0.35 m 0.5 Note: UCS – Unconfined Compressive Strength, mi – the intact rock parameter, E – Young’s Modulus, RMR89 – Rock Mass Rating at 1989, and GSI - Geological Structure Index; Poisson’s ratio used is 0.25.   Table 3.2. Depth-dependent Mohr-Coulomb rock mass properties derived for the 500 to 2000 m deep undercut models. Lithology σ3max (MPa) Erm (GPa) crm (MPa) φrm (°) Trm (MPa) Rhyolite 7.5-17.5 12.6 3.3-5.9 46-52 0.6-1.2 Quartz-Monzodiorite    below the undercut    south of South fault  30 5-20  7.0 7.0  6.5 1.9-4.9  34 38-49  1.8 0.4-1.2 Sandstone and Siltstone    below the undercut    south of South fault  45-50 30-35  10.2 10.2  9.1-9.7 6.9-7.7  31-32 34-35  2.5-2.8 1.8-2.1 Biotite Granodiorite    north of North fault    south of South fault  10-40 40  7.7 7.7  3.2-8.2 8.2  33-44 33  0.7-2.3 2.3 Caved Rock  - 0.26 - - -   74  Fig. 3.1. Generalized E-W cross section through the Resolution Deposit (Rio Tinto, 2008), on which the conceptual geometry for this benchmarking study, as defined by the Centre for Excellence in Mining Innovation (CEMI), was loosely based.  75   Fig. 3.2. Conceptual panel cave mining geometry for benchmark testing specified by the Centre for Excellence in Mining Innovation (CEMI): (a) plan view, and (b) A-B section. Panel dimensions are 500 x 1000m.   (a) (b) ° ° ° ° ° ° ° ° (m)   Fig. ortho eleme m in 3.3. Phase2 gonal orien nts introduc depth.  model geo tation, and ed above th metry for th variable spa e undercut. 76 e 2000 m cing (20-50 For scale, th deep under m) and per e model is cut simulati sistence (40 10,500 m in on, showing -170m) of  length and   the joint 4200  (a) (b)  Fig. proje sectio  3.4. FLAC ction of the n showing t 3D model g  bounding he fault inte eometry: ( faults throu rfaces in da 77 a) in plan gh the mod rk blue. view, with el (dark blu semi-transp e), and (b)  arency to north and s  show outh  (a)  (b)  Fig. 3 ortho patter  .5. (a) UDE gonal joint n at 45 and C model g pattern and 135 degrees eometry for  (c) an ort . Note that t 78  (c)  the 2000 m hogonal join he lower clo  deep under t pattern s se-up views cut simulati uperimpose  are 250 by on, showing d with a se  250 m.   , (b) cond  Fig. exten Phase  3.6. ELFEN ded discrete 2 models. (  model geo  fracture n Eberhardt et metry for t etwork used  al., 2011) 79 he 2000 m . Note that deep under  this is the cut simulati same DFN on, showin  as used fo  g the r the  80  Fig. 3.7. In situ stress information for benchmark testing as specified by CEMI: SHmax is north-south  section and SHmin is east-west section (Eberhardt et al., 2011).   Fig. 3   Fig. algor .8. Method 3.9. Metho ithm. 1. In situ r 2. Undercu length o sub-und sequent  3. As the move i blocks w undercu blocks) specifie 4. Cave p creased undercu used to simu d used to s ock mass co t excavati f 1500m w ercuts with ially excava rock mass nto the un hose centro t zone ar . The dimen d regions ar ropagation: and they t zone. late draw f imulate dra nditions on: The t as divided i  a height ted. fractures, d dercut zone ids are loca e deleted sions of e e 100m (w) New distin move down 81 or Phase2D, w for ELF otal underc nto 30 of 50  of 4m a istinct bloc . All distin ted within t (light shad ach of the x 12m (h). ct blocks a wards in t  FLAC3D a EN model, ut m nd ks ct he ed 15 re he  nd UDEC m involving odel. a block del  etion    Fig. Verti  3.10. Phase cal displacem 2 continuum ent contou  subsidenc rs are plotte 82 e results fo d with a 1 m r undercut  minimum depths of cut off. 500 to 200  0 m.    Fig. under minim  3.11. Phase cut depths um cut off 2 continuum of 500 to 2 .  subsidenc 000 m. Ve 83 e results w rtical displa ith the incl cement con usion of joi tours are p nt elements lotted with   , for 1 m  Fig. 3 : Surf .12. FLAC3 ace section( D subsiden top), north- ce results fr south Sectio 84 om 500 to 2 n (bottom). 000m after 200,000m3 (   0.25m cut off)  85   Fig. 3.13. UDEC subsidence results from 500 to 2000m(1m cut off)- with orthogonal joint sets.    Depth (m)  86   Fig. 3.14. UDEC subsidence results from 500 to 2000m(1m cut off)- with 45 and 135 degrees joint sets.       Depth (m)   Fig. 3    .15. ELFEN subsidence results from 87  500 to 2000m after 200,000m3 (1m Vertical Di  cut off). spl. (m)    88    Fig. 3.16. Estimated angles plotted as a function of undercut depth at north (top) and south (bottom) fault side of undercut using the 2-D continuum finite-element code Phase2.  Shown are the different trends for the caving, fracture initiation and subsidence angles with and without the inclusion of joints modelled using small-strain joint elements.  89    Fig. 3.17. Estimated angles plotted as a function of undercut depth at north and south fault side of undercut using the 3-D  continuum finite-difference code FLAC3D. Shown are the different trends for the caving, fracture initiation and subsidence angles.   90    Fig. 3.18. Estimated angles plotted as a function of undercut depth at north (top) and south (bottom) fault side of undercut using the 2-D discontinuum distinct-element code UDEC. Shown are the different trends for the caving, fracture initiation and subsidence angles modelled assuming two different joint patterns: orthogonal jointing at 0 and 90 degrees dip and 45 and 135 degrees dip. Joints are modelled explicitly in UDEC allowing for large strain slip, opening and closing along each joint interface.   91    Fig. 3.19. Estimated angles plotted as a function of undercut depth at north and south fault side of undercut using the 2-D FEM/DEM brittle fracture code ELFEN. Shown are the different trends for the caving, fracture initiation and subsidence angles, modelled using the “mesh delete” and contact updating capabilities of ELFEN to more directly simulate the block cave mining process.   Fig. under minim the ou   3.20. Phase cut depths um cut off tside lines d 2 continuum of 500 to 2 . The inside efine the fr  subsidenc 000 m. Ve lines define acture angle 92 e results w rtical displa  the caving  measured b ith the incl cement con angle measu ased on the usion of joi tours are p red based o tension poin nt elements lotted with n shear poin t.  , for 1 m t and   Fig. 3   .21. FLAC3D plasticity indicator, r 93 ed line-caving angle threshold. Tension-p None Shear-p Shear-p, T Tension-n  ension-p , Tension-p   Fig. 3   .22. UDEC plasticity indicator: orth 94 ogonal joint pattern, re     d line-caving angle thre  shold.  95  Fig. 3.23. Estimated caving angle plotted as a function of undercut depth at north fault side of undercut.  Fig. 3.24. Estimated caving angle plotted as a function of undercut depth at south fault side of undercut.  96 (a)  (b)  Fig. 3.25. Open joint (UDEC): (a) orthogonal joint pattern and (b) an orthogonal joint pattern superimposed with a second pattern at 45 and 135 degrees, red line-fracture initiation angle threshold.  97  Fig. 3.26. Estimated fracture initiation angle plotted as a function of undercut depth at north fault side of undercut.   Fig. 3.27. Estimated fracture initiation angle plotted as a function of undercut depth at south fault side of undercut.  98  Fig. 3.28. Estimated subsidence angle plotted as a function of undercut depth at north fault side of undercut.   Fig. 3.29. Estimated subsidence angle plotted as a function of undercut depth at south fault side of undercut.  99 Chapter 4: Integration of Field Characterization, Mine Production and InSAR Monitoring Data to Constrain and Calibrate 3-D Numerical Modelling of Block Caving-Induced Subsidence3 4.1 Introduction The use of block caving to mine deep, massive, low grade orebodies is often favoured by the mining industry given its merits in terms of safety, tonnages produced and costs that can match those of open pit operations. As an underground mass mining method, however, significant ground surface deformations often develop. If these are not properly assessed and accounted for, they may threaten the integrity and safety of overlying mine infrastructure. To better manage such risks, detailed engineering studies are undertaken to characterize the ground conditions and provide input for empirical and numerical design calculations. Empirical relationships are generally used for preliminary scoping calculations, for example to estimate caving angles based on rock mass quality (Laubscher, 2000). These do not explicitly account for the influence of stress-strain interactions and geological heterogeneity that may significantly affect the ground deformation profile. Instead, investigators have increasingly turned to advanced 2-D and 3-D numerical modelling to improve the assessment and understanding of block-caving subsidence dynamics and surface-underground interactions (Karzulovic et al., 1999; Gilbride et al., 2005; Brummer et al., 2006; Beck et al., 2008; Vyazmensky, 2008; and Vyazmensky et al., 2010b). As in any modelling study, the results depend on the assumed initial conditions and material properties assumed. These can vary greatly in accordance with the geological heterogeneity and variability encountered on site, with ranges of input properties being more likely than a single value. Furthermore, the numerous surface and underground interactions  3 Woo, KS. Eberhardt, E. Rabus, B. Stead, D. Vyazmensky, A. Integration of field characterization, mine production and InSAR monitoring data to constrain and calibrate 3-D numerical modelling of block caving-induced subsidence. (In Review)   100 involved – both spatial and temporal – result in a complex 4-D problem that challenges even the most sophisticated numerical models. The resulting model and parameter uncertainty necessitates that the models be constrained and calibrated in order to gain confidence in their output. This paper examines these issues based on detailed back and forward analyses of the Palabora block caving operation in South Africa. The first part of this paper focuses on the back analysis of a large 800 m high pit slope failure that occurred in response to block caving activities below the pit. This was used to constrain a 3-D finite-difference model against the range of rock mass strength values and in-situ stress ratios derived from field investigation data. The second part of this paper reports the use of these “best fit” input properties to forward model the caving- induced subsidence at Palabora for the period 2009-2010. High resolution satellite-based Interferometric Synthetic Aperture Radar (InSAR) data was used to further calibrate the 3-D numerical model developed. Together, the results presented demonstrate the potential of InSAR as a means to calibrate sophisticated 3-D subsidence models, improving our ability to assist mining companies to execute safe, economic and sustainable mining practices. 4.2 Palabora Case History The Palabora copper mine is a large, 30,000 tonne/day block cave operation located in the eastern half of Limpopo, South Africa’s northern most province. Underground mining was commenced in April 2001 after transitioning from an earlier open pit operation with target production being achieved in May 2005. The dimensions of the pit are approximately 800 m deep and 1650 to 1900 m in diameter, with slope angles ranging from 37° in the upper half of the pit to 58° in the lower, more competent lithologies. The block cave undercut level is approximately 1200 m below surface, 400 m below the pit floor (Fig.4.1). The production level below the undercut consists of 20 cross-cuts spaced across a footprint 650 m long by approximately 250 m wide (Moss et al., 2006). Three years after the initiation of caving, cracking was observed in the northwest wall of the pit. This evolved over several months into major movements and eventually failure of the 800 m high pit wall shortly after breakthrough of the cave into the bottom of the pit (Fig.4.2). The failure extended 300 m beyond the outer perimeter of the pit, affecting access  101 and haul roads, tailings, water and power lines, water reservoirs and a railway line (Moss et al., 2006). Fortunately, other critical mine infrastructure were not affected. Moss et al. (2006) remarked that the failure at Palabora revealed deficiencies in our understanding of cave-pit interactions. Subsequently, a number of studies were carried out applying sophisticated numerical modelling to back analyze the Palabora failure (Brummer et al., 2006; Sainsbury et al., 2008; Vyazmensky, 2008; and Vyazmensky et al., 2010b). Brummer et al. (2006) first examined the failure mechanism using the 3-D distinct element code 3DEC to model the influence and kinematic control of major geological structures. Their findings show that the observed movements were potentially caused by wedges formed by pervasive joints that daylight into the cave region below the pit. Another key study was that by Vyazmensky (2008), who applied a hybrid finite- element/discrete-element modelling approach that simulates brittle fracturing within a network of non-persistent discontinuities. His work highlights the importance of joint set orientation on influencing the direction of cave propagation, as well as the importance of rock bridges and their incremental failure through cave-pit interactions leading to the progressive failure of the Palabora pit slope (Vyazmensky et al., 2010b). Although the preceding back analyses have made significant contributions to our understanding of the pit slope failure mechanism associated with block caving at Palabora, Moss et al. (2006) also stress that given the level of up-front investment in a block cave, it is extremely important to develop reliable predictive tools. This emphasizes the need for reliable, well constrained and calibrated forward analyses of block caving induced subsidence. 4.3 Model Constraint and Calibration through Back Analysis 4.3.1 Palabora 3-D Model Geometry A detailed 3-D geological model was constructed integrating digital mine plans (Fig.4.1) with mine geology data (Fig.4.3). The Palabora Igneous Complex (Palabora Mining Company Limited, 1976) consists of a succession of sub-vertical pipe-like bodies of alkaline and ultramafic rocks that have intruded into a host Archean granite. The copper ore body  102 occurs near the centre of the complex and is a composite vertical intrusion of micaceous pyroxenite subsequently intruded by foskorite and carbonatite. This body has then been cut by the emplacement of steeply dipping dolerite dykes. The detailed geological model was used to develop a 3-D numerical model of the pit and undercut (Fig.4.4) using the commercial finite difference code FLAC3D (Itasca Consulting Group, 2009). Implementation of the lithological units was limited in part by the resolution of the mesh; 15x15x15 m elements were used to model the primary area of interest meaning that lithological domains with widths less than 15 m were not resolved. This includes the dolerite dykes. The external boundaries of the model measure 4000 x 4000 m in plan and 2000 m in depth. A gradational mesh with larger elements extending towards the outer model boundaries was employed. The 3-D mesh was iteratively tested and modified to limit numerical errors resulting from boundary effects and element shape and size. 4.3.2 Modelling of Caving Influence The representation of the block cave and its development in the model is of prime importance given its direct relationship with the caving-induced deformations being modelled. This was implemented through an approach where the geometry of the cave is built into the model, as opposed to explicitly modelling caving and cave propagation. The latter would have required considerable effort within the continuum framework to model the caving process accurately, alternating between small strain calculations applying a seismogenic/yield zone approach to model cave propagation and large strain calculations to model the corresponding ground deformations. The former approach involves assuming the cave geometry at several different points in its development over time, and incrementally changing its properties from those of the ore body rocks to fragmented rock. This requires special consideration of the material properties of caved rock, and the redefinition of the induced stress state within the modelled cave material. Adopting the implicit cave geometry approach, a procedure was developed for determining the cave geometry at any given point in time (Fig.4.5). This involved extracting, for each time interval, the tonnages for each draw point from the mine production data, applying a 20% swell factor, and calculating the cave height above each draw point. The  103 resulting 3-D cave shape was modified according to the mine microseismic data for the same period. 4.3.3 Rock Mass Properties Rock mass properties were derived for each of the key lithologies represented in the FLAC3D models (Fig.4.3). This involved compiling data from mine geotechnical reports in which laboratory testing and rock mass characterization data were reported.  Because these reports span several different testing and field characterization campaigns (over a period of more than 25 years), all data was carefully reviewed and evaluated to establish lower and upper bound values which are the minimum and maximum values reported, respectively (Table 4.1). This work was supplemented by field-based assessments made by the UBC-SFU team during fieldwork carried out at the mine in 2008. The major lithological units represented in the model, and their rock mass characteristics, are summarized in Appendix E. The rock mass descriptions and rock strengths provided are compiled from several modelling, laboratory testing, and field measurement sources. Not included in the model are the dolerite dykes, described as being composed of very strong rock, the jointing and several large fault zones. From these, rock mass shear strength properties were estimated for use with a Mohr- Coulomb strain softening constitutive model. Most practitioners have more experience and therefore an intuitive feeling for the physical meanings of cohesion and friction on which the Mohr-Coulomb criterion is based. Accordingly Mohr-Coulomb rock mass shear strength properties for the use in the FLAC3D numerical modelling were derived through empirical procedures based on GSI, RMR and Q (e.g. Hoek et al., 2002). Several empirical procedures exist to derive Mohr-Coulomb rock mass shear strength properties, one of the more commonly used being Hoek et al.’s (2002) conversion of Hoek-Brown to Mohr-Coulomb achieved by fitting an average linear relationship to the non-linear Hoek-Brown envelope for a range of minor principal stress values with an upper bound of σ'3max. Analytical relationships are provided for estimating σ'3max, however, these do not apply to block caving. Consequently, Hoek (2007) recommends that caving analyses be carried out based either on  104 Hoek-Brown or Mohr-Coulomb parameters, assessed independently, but not on the conversion of one to the other. The applicability of these scaling relationships is noted here, but is also weighed against their required use: to simply provide an initial estimate of the rock mass shear strength properties, the values for which will then be varied and refined through the back analysis calibration exercise. Accordingly, the Hoek-Brown to Mohr-Coulomb conversion procedure was deemed adequate and a σ'3max value of 10 MPa was estimated for the conversion based on preliminary modelling of the stresses that develop between the cave and pit walls. Table 4.1 reports the corresponding ranges of equivalent rock mass cohesion and friction angle values for the lower and upper bound values established for each rock mass unit represented in the FLAC3D model. These are in general agreement with values used in previous studies by the mine’s consultants (see Table 4.3). The lower- and upper-bound values were next tested through a parametric analysis using the FLAC3D model to test the sensitivity of the modelled response to the material properties used. 4.3.4 In-situ Stresses Data for the in-situ stress boundary conditions were compiled based on regional stresses reported in the published literature and mine specific in-situ stress studies. Regional stress data reported in the World Stress Map database (Heidbach et al, 2008) and those in a study of South African mining areas (Stacey et al., 1998) suggest that stress ratios in the region fall somewhere between 0.5 and 1.5 for the major horizontal to vertical stress ratio, and 0.5 to 1.0 for the minor horizontal to vertical stress ratio. These ranges bracket values obtained from in-situ stress measurements at Palabora (SRK Consulting Group, 1992a; SRK Consulting Group, 1992b; and Gash, 1999), where investigations in 1992 and 1999 reported ratios ranging from 0.5 to 1.2 (Table 4.2). The variability seen in Table 4.2 is not uncommon for in-situ stress measurements, and may be due to local effects caused by major faults and/or geological heterogeneity. A number of reports presenting results from numerical modelling for Palabora were further reviewed to see how the in-situ stress boundary conditions were treated for different aspects of the pit and cave designs (Table 4.3). Early studies assumed an in-situ stress ratio  105 Ko of 1.0 (Martin et al., 1991), or assumed Ko to be 1.5 to 2.0 in the upper 200 m of the pit, decreasing linearly to about 1.1 at a depth of 2000 m (SRK Consulting Group, 1991). More recently, numerical analyses have used a Ko varying between 1.5 and 2.0 based on findings from the Mass Mining Technology (MMT) project of the International Caving Study. Based on this review, several different in-situ stress assumptions were tested in step with the model calibration for the best fit set of rock mass properties. 4.3.5 Back Analysis and Model Calibration FLAC3D modelling of the 2005 northwest wall failure (Fig.4.2) was carried out to back analyze and constrain the material properties and in-situ stresses to be used for subsequent forward modelling. Cave-pit interactions were modelled starting from the time of initial underground production in 2002 to the time of failure in 2005 in one year increments (Fig.4.5). Full implementation of the caving simulation involved first initializing the stresses in the ore zone (i.e. calculated according to the depth of the host rock and acting horizontal in-situ stresses), and then modelling the advancement of the cave by changing the material properties of the ore to those of the caved rock in step with the upward propagation of the cave. A key step in this process is that the initialized stresses in the elements representing the caved material must be reset with each modelled advance of the cave to correspond with the self-weight of the caved rock and not the initial tectonic stresses. Average rock mass properties and in-situ stress ratios from the ranges compiled in Tables 4.1 and 4.2, respectively, were tested and then varied depending on the closeness of the fit achieved between the modelled displacements and outline of the northwest wall failure. Several limitations in the modelling approach applied here must be noted. First, the presence of both meso-scale jointing in the northwest wall and major faults in its proximity would have played a significant role in the caving-induced slope failure process. These are not considered in the FLAC3D continuum representation of the slope. The results are also limited by the minimum element size, which influences the ability for a failure surface in the model to localize and develop. Due to these limitations, it is not possible to explicitly model the pit wall failure that occurred. Instead, the comparative analysis carried out relied on the  106 distribution of caving-induced displacements, specifically those arising from strain softening, as the measure to compare the different back analysis model runs. Results from the back analysis clearly showed a varied response for the different rock mass properties tested. Fig.4.6 compares the caving-induced displacements modelled assuming a set of average rock mass properties (Fig.4.6a) and those assuming the lower bound properties (Fig.4.6b). The latter shows increased displacements in the northwest wall of the pit that approximately coincide with the northwest wall failure. Table 4.4 reports the calibrated rock mass properties judged visually as providing the best fit for the back analyzed northwest wall failure. These include testing of different strain softening thresholds at which strength degradation through brittle fracturing would begin (correlating induced plastic strains with reduced post-peak rock mass strengths). Results using the Mohr-Coulomb strain softening constitutive model produced significantly improved results over models solved assuming a simpler Mohr-Coulomb elasto-plastic constitutive model. Model calibration suggested that the influence of strain softening was most important for the pyroxenite and glimmerite units. Also included in Table 4.4 are the material properties assumed for the caved rock. As the material responsible for the relaxation and deformation of the surrounding rock, it was found to have a significant influence on the magnitude of the modelled displacements. A detailed search of the literature proved unsuccessful in finding values for caved rock; several papers were found reporting values for broken rock as used in the construction of rockfill dams and for mine backfill and these were used as an initial starting point for the back analysis. However, these required additional calibration. To avoid numerical errors related to severe mesh distortion, the caved rock material was modelled as an elastic material, using reduced elastic properties to account for the reduced deformation modulus that would be expected for caved rock, as well as allowances for the presence of a small air gap. Model calibration of the best-fit material properties was carried out in step with calibration of the assumed far-field in-situ stress boundary condition (Fig.4.7). These showed that a uniform stress field where the NS and EW horizontal stresses equal the vertical stresses (i.e. Ko=1) provided the best fit to the outline of the northwest wall failure (Fig.4.8). This  107 stress field is in agreement with those in the World Stress Map database (Heidbach et al., 2008), those reported by Stacey and Wesseloo (1998) and values reported in Tables 4.2 and 4.3. The contours in Fig.4.8 adopt a vertical displacement cut-off of 3 cm, which is the National Coal Board’s minimum threshold (National Coal Board, 1975) for damage to surface infrastructure and an approximate indicator for the appearance of surface fractures (i.e. brittle fracturing of the rock mass). Given the continuum treatment of the problem, the closeness of the fit achieved suggests that the spatial positioning of the undercut beneath the pit was an important factor influencing the northwest wall failure. The 3-D model results clearly show that the interaction between the developing cave and open pit above was more pronounced for the northwest wall than any other area of the pit. These directed the cave towards the north where it undermined the toe of the slope eventually resulting in failure. 4.4 InSAR Monitoring as a Means to Constrain Modelling Displacements Space-borne Synthetic Aperture Radar (SAR) involves the use of satellite-based microwave radar to remotely observe characteristics of ground terrain. With repeated orbits and image capture (referred to as stacks), Interferometric SAR (InSAR) data can be processed to resolve 3-D information of surface deformations by analyzing differences in the phase between waves being transmitted and received by the satellite (Zebker et al., 1994). Ground deformations can be detected on the scale of centimetres to millimetres for a surface area resolution of several square metres using these techniques. This ability to detect shape changes in a surface area with significant resolution provides a means to monitor mining- induced differential strains, including small strain (<1 %), that develop across an irregular surface topography. Inspection of the results in Fig. 8 shows that the modelled displacement field extends to the east of the northwest wall failure. Although this at first may appear to suggest a minor mismatch between the model and observed extent of failure, subsequent integration with RADARSAT-1 data shows excellent agreement. Fig.4.9 shows the InSAR measured displacements from the analysis of RADARSAT-1 images (8-m surface area resolution) for Palabora recorded for the two-year period following the 2005 northwest wall failure. The data shows that most of the measured displacements are concentrated along the north wall,  108 especially towards the east along its crest. These would appear to be related to the instability of the pit wall in response to the cave breakthrough. Behind the pit rim and around the mine area in general, little subsidence is detected during this period. Comparing these displacements to those modelled in Fig. 8, both the areas of extent and magnitude of displacement are in close agreement. This provides an additional degree of confidence in carrying the back analyzed input values forward for subsequent analysis of the current state of caving-induced subsidence. 4.5 Forward-Modelling of Caving-Induced Displacements (2009-2010) 4.5.1 Modifications to Model Geometry The back analysis of the 2005 pit slope failure provided an important initial step in calibrating and constraining the FLAC3D subsidence model. However, the failure also represents a major change in the 3-D geometry of the mine model, including a localized deviation of the cave. These were accounted for in a modified 3-D model directed towards a forward analysis of caving-induced ground deformations for the period March 2009 to March 2010. Built into the model were the changing cave geometries for 2006 to 2010 (Fig.4.5) together with the presence of the pit wall failure debris (Fig.4.10). Thus, this modified model represents a continuation of the back analysis model incorporating the influence of the northwest wall failure. The pit wall failure debris was assigned the same properties as the caved material (i.e. broken rock). In addition, the stress conditions in the failed zone were reassigned to represent those of the collapsed ground (i.e. gravity loading instead of the Ko = 1 in-situ stress condition used throughout the rest of the model). The presence of the failure debris also required special consideration in the construction and implementation of the post-failure cave geometries. As can be seen in Fig.4.2, a significant amount of slide debris sits above and on top of the pit floor bottom where the cave has broken through. Moss et al. (2006) estimate the failure to be approximately 100 million tonnes and note that the potential exists for the slide/waste material to move at a faster rate than the ore rock within the cave as the cave is pulled due to differences in block size between the two (i.e. mechanical sieving). Thus, the production data used to project the changing volume of the cave after 2005 would likely  109 include both caved rock (associated with the changing cave geometry) and slide debris from surface entering the cave (not associated with the changing cave geometry). To correct for this, Digital Terrain Models (DTMs) and QuickBird satellite images for different periods between 2005 and 2009 were compared to approximate changes in volume of the rockslide material on surface and therefore that entering the cave. This analysis indicated that it is unlikely that debris was entering the cave prior to January 2006. Subsequent to this, however, an average volume of 2 million m3 per year was resolved as entering the cave and was corrected for in generating the cave geometries. The caving intervals analyzed include: March 2006, March 2008, March 2009, September 2009, and March 2010, where the last three intervals coincide with the beginning, mid-point and end of targeted RADARSAT-2 SAR data captures carried out as part of this study. 4.5.2 RADARSAT-2 Deformation Monitoring Through a partnership between the Canadian Space Agency, MDA Systems, the University of British Columbia and Simon Fraser University, targeted RADARSAT-2 data was collected to monitor mining-induced ground deformations at several sites, including Palabora. Launched in December 2007, RADARSAT-2 is Canada’s second-generation commercial SAR satellite, capable of providing surface area resolutions approaching 2x2 m. Together with improvements in data processing and inversion of the phase components (atmosphere, height error and displacement corrections), significant gains have been made in the robustness of the InSAR solution (Rabus et al, 2009). RADARSAT-2 data was collected for Palabora during the period March 2009 to March 2010, in 28 day intervals. The images were taken in ascending as well as descending modes. The processed InSAR deformations were then used to compare with the results from the FLAC3D forward modelling results. 4.5.3 FLAC3D Forward Modelling Results and Comparison with InSAR Data Figs.4.11 and 4.12 show the FLAC3D forward modelling results for the caving- induced displacements for Palabora between March 2009 and March 2010. These predict total displacements on the order of 5-15 mm along parts of the upper pit and crest, and 15-30  110 mm just above the bottom of the pit. Fig.4.12 shows that the cave interaction with surface will have the greatest influence on the west pit wall with minor movement of the north wall. Fig.4.13 shows the ascending and descending InSAR data for the same period. These show that most of the displacements (20-40mm) correspond to ongoing activity to the east of the 2005 northwest wall failure (primarily near the crest) and to the west extending across half of the west wall. Otherwise, displacements are less than 10mm for this time period along the east and south pit walls. Figs.4.14 and 4.15 present the side-by-side comparison of the FLAC3D results and corresponding ascending and descending InSAR images for the 2009-2010 data gathering period. Using the input properties derived from the back analysis, close agreement was achieved with respect to the spatial extent of the displacements. However, the displacement magnitudes predicted by the FLAC3D model are approximately 20% lower than those seen in the InSAR data. A better fit of the measured displacement magnitudes was subsequently achieved through minor calibration of the model in the form of decreasing the plastic strain threshold for strain softening for the pyroxenite from 0.01 to 0.005. Further comparisons of the calibrated FLAC3D subsidence model and the InSAR measured vertical displacements are shown for several targeted areas around the open pit, including the main access shaft (Fig.4.16), the ventilation shaft (Fig.4.17) and the crest above the west wall (Fig.4.18). Also included are the vertical displacements calculated from the geodetic monitoring data, which show very good agreement. The subsidence predicted by the FLAC3D model for the period of 2009-2010 closely fits the InSAR measurements during the same period time, proving the significant accuracy and reliability of the FLAC3D prediction. As for the geodetic data, the geodetic measurements show more variability in the subsidence rate than the InSAR measurements. Geodetic data are direct measurements taken on site and thus presumed to be reliable. However, there are several sources of potential measurement errors. Firstly, geodetic data are not collected on a daily basis. Secondly, measurement data are collected only in selected points. Thirdly, if multiple agents collect the geodetic data, sampling errors could occur. The variability of the geodetic data possibly resulting from measurement errors can potentially trigger false concern. In fact, the geodetic for the ventilation shaft indicates caving-induced  111 movements as shown in Fig.4.17 but much of this is scatter. In the meantime, the InSAR measurements (and the FLAC3D prediction) in the ventilation shaft do not oscillate much around the mean value. These observations vindicate the significant value of the InSAR data and thus the InSAR calibrated FLAC3D model regarding subsidence prediction. 4.6 Conclusions This study presents results from a detailed 3-D back and forward analysis of caving- induced displacements at the Palabora open pit/block cave mine in South Africa. Results from the back analysis of a 2005 pit slope failure were used to constrain uncertainty in the rock mass properties and far-field in-situ stresses, as well as to bring understanding to the problem with respect to the cave-pit interactions. The modelled outcome underscores the sensitivity and dependence of modelling results on the input required and thus the difficulty of using modelling results for predictive purposes. Agreement was found between the FLAC3D modelled zones of ground movement and the location of the 2005 northwest wall pit slope failure, as well as with RADARSAT-1 InSAR data from 2005. A “best fit” set of input properties were obtained and used for forward modelling of the caving-induced subsidence occurring at Palabora for the period 2009 to 2010. Dedicated high-resolution InSAR data from the recently launched RADARSAT-2 satellite was collected for the same period (March 2009 to March 2010). Again, close agreement was achieved with respect to the spatial extent and magnitudes of the FLAC3D predicted displacements and those measured using InSAR, allowing further calibration of the model. These were further compared with geodetic monitoring data from the mine likewise showing very good agreement. The close fit achieved between the predictive 3-D numerical model and InSAR data demonstrates the promise of InSAR as a means to calibrate and validate sophisticated numerical models, and thereby contribute to managing block caving associated subsidence hazards. The results demonstrate that satellite-based InSAR provides an effective means to identify and map spatial movements across a large open pit and beyond the pit limits. This ability is important for protecting key mine infrastructure located on surface, especially where subsidence caused by underground mass mining may be interacting with open pit  112 slopes and surrounding surface area above. Together, an advanced information product has been developed and demonstrated, integrating geology, geotechnical data sets, and 3-D numerical modelling with InSAR imagery to assist mining decision makers in their development of safe and efficient block caving and open pit mining operations.  113 Table 4.1. Ranges of intact rock properties and rock mass rating values compiled from mine geotechnical reports and internal field assessments, and corresponding lower and upper bound rock mass properties derived. Rock Type Intact Rock Properties Rock Mass Characteristics & Properties Density (kg/m3) UCS (MPa) E (GPa) mi RMR GSI crm (MPa) Φrm (°) Trm (MPa) Carbonatite 2760-4720 75-172 30-58 15-17 60-80 50-75 3-8 40-58 0.1-1.5 Foskorite 2850-4420 26-150 40 17 56-75 45-75 2-7 30-55 0.02-1.3 Pyroxenite 2800-3240 39-136 15-38 15-17 54-70 45-65 2-5 30-54 0.04-0.6 Glimmerite 3100 37 6 17 50-55 35-50 1-3 25-34 0.01-0.05 Fenite 2610-2730 133-340 10 15-17 57-75 50-75 3-10 44-58 0.2-2.9 Granite 3100 200-300 31 32-33 75 70-80 6-11 55-63 0.5-2.1 UCS = Uniaxial Compressive Strength; E = Young’s modulus; mi = Hoek-Brown intact rock parameter; RMR = Rock Mass Rating; GSI = Geological Strength Index; crm = rock mass cohesion; Φrm = rock mass friction angle; Trm = rock mass tensile strength    Table 4.2. Results from Palabora in-situ stress studies and measurement campaigns. Year (reference) Method Stresses determined 1991 (National Coal Board, 1975) Back analysis σNS = 2.0σV  σEW = 1.5σV 1992 (SRK Consulting Group, 1992a) Borehole slotter σNS = 0.65σV  σEW = 0.51σV 1992 (SRK Consulting Group, 1992b) CSIR triaxial σNS = σV  σEW = 0.97σV 1999 (Gash, 1999) CSIRO 12 σ1 = 46 MPa (16°/323°) σ2 = 38 MPa (73°/152°) σ3 = 36 MPa (4°/051°)            114 Table 4.3. Horizontal to vertical in-situ stress ratios (Ko) used in different numerical modelling studies for Palabora. Year Method Ko Notes 1991 FLAC 1.0 Assumed for model calibration. 1991 UDEC 1.5-2.0 Assumed. 1995 FLAC3D NSσ = 1 EWσ = 0.97 Based on 1992 measurements (Table 2). 1998 UDEC 1.0 Based on 1997 geotechnical review. 1999 UDEC 1.2 Based on 1999 measurements (Table 2). 2000a UDEC 1.0 Calibrated and back analyzed using monitoring data for East Wall. 2000b UDEC 0.5-1.2 Based on 1992 and 1999 measurements (Table 2). 2004 3DEC 1.0 Based on modelling report. 2005 3DEC NSσ = 1 EWσ = 1 Based on 1992 measurements ( Table 2). 2008 FLAC3D NSσ = 2.0 EWσ = 1.5 Based on MMT project results. 2009 FLAC3D NSσ = 1.5 EWσ = 2.0 Based on MMT project results.   Table 4.4. Back-analyzed FLAC3D rock mass properties providing the best fit to the observed outline of the northwest wall failure. K and G denote the Bulk and Shear modulus, respectively, as derived from estimates of the rock mass Young’s modulus and Poisson’s ratio. Rock Type Elastic Properties Rock Mass Strength Properties Density (kg/m3) K (GPa) G (GPa) crm (MPa) Φrm (°) Trm (MPa) εp (-) Carbonatite 3100 8 4 2.5 40 0.15 - Foskorite 3100 4 2 2.5 35 0.1 - Pyroxenite 3100 4 2 2 30 0.1 0.01 Glimmerite 3100 1 0.5 1.5 25 0.01 0.005 Fenite 3100 16 10 5 55 0.4 - Granite 3100 20 12 6 55 0.65 - Caved Rock 2300 0.2 0.1 - - - - K = Bulk Modulus; G = Shear Modulus; crm = rock mass cohesion; Φrm = rock mass friction angle Trm = rock mass tensile strength; εp = plastic strain threshold for material strain softening (75-90% reduction in strength)    Fig. 4 proxi .1. Digital mate locatio  mine plans o n to one ano f the Palab ther. Modif 115 ora open pit ied after Mo  and underc ss et al.,200 ut geometri 6. es, showing   their  Fig. 4.2. QuickBird image of the northwe 116 st wall failure at Palabora.   Fig. Engin 4.3. Geolog eering LTD ical map fo ., 2005. r Palabora s 117 howing the key lithologies. After Piteau Asso  ciate  Fig. 4 the p persp .4. FLAC3 eriod 2002 t ective view D model de o 2005). Sh s. Model dim veloped for own is the d ensions are 118 back analyz etailed geol  4000 x 400 ing the nort ogy built in 0 m in plan hwest wall to the mode and 2000 m  failure (cov l in plan and  in depth. . ering  3-D  119  Fig. 4.5. Cave geometries for different time intervals implemented into the FLAC3D models     (  F b a) ig. 4.6. Back a ased on the inp nalysis compar ut ranges comp ing caving-ind iled in Table 4. 120 uced displacem 1. Displacemen  (b) ents assuming: ts are reported i  (a) average, an n metres. d (b) lower bound rock mass  properties,  Fig. 4 the co .7. FLAC3 ntours outli D results fo ning the nor r several di thwest wall 121    fferent in-sit  failure. Dis u stress ass placements umptions. S are reported uperimpose  in metres.    d are  Fig. 4 cm) t throu to be .8. Best fit o the DEM gh the centr equal to the N FLAC3D m  outline of e of the nor  vertical stre odel compa the North w thwest wall sses (Ko=1) 122  ring modell all failure, failure. NS . Displacem ed vertical d in plan and and EW hor ents are repo isplacemen  along a no izontal stre rted in met   ts (greater th rth-south se sses are assu res. S an 3 ction med  Fig. 2005 exten 4.9. RADA northwest w t of modelle RSAT-1 dat all failure. d displacem a for Palab The area hig ents (greate 123 ora recorded hlighted by r than 3cm)  for the tw  the white d shown in Fi o-year peri ashed box c g. 4.8. od followin oincides wit  g the h the  Fig. defor 4.10. Modi mations (wi fied model th respect to  geometry  the slope fa 124 for forward ilure) for th  modelling e period 200  of caving 9 to 2010.  ‐induced gr  ound  Fig. displa repor   4.11. FLA cements fo ted in metre C3D forwa r the period s. rd modelli  March 200 125  ng results 9 to March showing t  2010 in pl he caving- an view. D induced ve isplacement  rtical s are  (a)   (b)  Fig. displa sectio     4.12. FLA cements fo n. Displace C3D forwa r the period ments are re rd modelli  March 20 ported in m 126 ng results 09 to Marc etres. showing t h 2010: (a) he caving-  N-S sectio induced ve n, and (b)   rtical E-W  127 (a) (b)  Fig. 4.13. RADARSAT-2 data for Palabora for the period March 2009 to March 2010, showing: (a) ascending, and (b) descending InSAR measured vertical displacements. Points colour-coded with respect to downward movements are, Red: 20-40mm, Yellow: 10-20mm, Green: 0-10mm.  Fig. RAD magn and (     Fig. RAD magn and (    4.14. Side- ARSAT-2 d itudes for th 4) shadow. 4.15. Side- ARSAT-2 d itudes for th 4) shadow. by-side com ata for the e zoned re by-side com ata for the e zoned re parison of  period Ma gions corres parison of  period Ma gions corres 128  FLAC3D rch 2009 t pond to: (1  FLAC3D rch 2009 t pond to: (1 modelling o March 2 ) 20-40mm, modelling r o March 2 ) 20-40mm, results with 010. Downw  (2) 10-20m esults with 010. Downw  (2) 10-20m  the ascen ard subsid m, (3) 0-10  the descen ard subsid m, (3) 0-10  ding ence mm,  ding ence mm,  129    Fig. 4.16. Comparison of FLAC3D modelled and InSAR and mine geodetic measured vertical displacements between March 2009 and March 2010, for a history point/survey prism located near the main access shaft.  130    Fig. 4.17. Comparison of FLAC3D modelled and InSAR and mine geodetic measured vertical displacements between March 2009 and March 2010, for a history point/survey prism located near the ventilation shaft.  131    Fig. 4.18. Comparison of FLAC3D modelled and InSAR and mine geodetic measured vertical displacements between March 2009 and March 2010, for a history point/survey prism located above the crest of the west wall.  132 Chapter 5: Thesis Discussion and Conclusions This thesis presents the results from a detailed investigation examining the characterization and assessment of block caving-induced subsidence using empirical and numerical techniques. First, findings from an extensive block caving database were reported identifying and defining key influences and interactions that affect the symmetry and extent of large-strain discontinuous and small-strain continuous subsidence. Results were then presented from a benchmarking study employing several different numerical techniques in which different modelling assumptions were compared (continuum, discontinuum, 2-D, 3-D, etc.). Specific focus was placed on the influence of undercut depth on the extent of different classes of subsidence: caving zone, fracture initiation zone and continuous subsidence zone. Lastly, a detailed case study of the Palabora block cave mine in South Africa was presented in which field characterization and remote-sensing data were used to constrain an advanced 3-D numerical model that simulates the ground response and interactions with an overlying deep open pit over several years of cave development. Together, the results from this research help to further: 1) the characterization, assessment and understanding of block-caving subsidence, and its evolution, by addressing existing limitations in the use of empirical and numerical subsidence analysis methods;2) the understanding of the fundamental processes involved in the progressive caving and its expression at surface as small-strain subsidence or larger strain fracturing; and 3) the application of sophisticated 3-D numerical modelling techniques by detailing the limitations and uncertainty arising from mine site data, specifically the representation of mine geology, rock mass properties, in-situ stresses and cave propagation, and means to constrain these input and calibrate the models through back analysis and integration with high resolution monitoring data. 5.1 Summary 5.1.1 Empirical Investigation and Characterization of Block Caving Subsidence A detailed and comprehensive database of cave mining operations and caving- induced ground deformation observations has been developed from an exhaustive search of  133 published literature, university theses, and government reports for guidance on relationships between caving depth and surface subsidence. Emphasis was placed on the examination of the relationships between the caved, fractured, and subsidence zones of surface subsidence and depth of undercut as well as the effects of geology, topography, orebody type and undercut geometry in promoting asymmetry and discontinuous caving-induced subsidence. From the database, a trend emerged showing the transition by mining companies to larger and deeper caving operations indicating the need to understand the effect of undercut depth on surface subsidence more fully. Direct and indirect subsidence observations in the database were analyzed to determine the caving and fracture initiation angles as a function of undercut depth. The range of caving and fracture initiation angles for individual sites, derived from differences relative to which side of the undercut the measurement is made (north, south, etc.), were rather large signifying a significant degree of asymmetry in the subsidence profile. This was seen to be strongly influenced by topography, the mechanism for which was demonstrated by comparative numerical modelling using the 2-D finite-element code Phase2. The numerical results showed that generally symmetric surface conditions, whether it be a flat surface or a cave centered under the peak of a mountain, generally lead to symmetric subsidence patterns; whereas asymmetric topographic conditions, primarily in the form of a sloping surface, results in asymmetric subsidence. A secondary factor influencing asymmetry involved the ore body geology as observed in variations in caving angles as a function of the resource being mined. Diamond, iron, nickel and asbestos operations were seen to have steeper caving angles and more symmetry. In the case of diamond kimberlites and asbestos deposits, the high strength contrasts between the weaker ore being caved and the stronger host rock also work to promote symmetry. In contrast, copper and molybdenum operations involving porphyry-type deposits were seen to have a significant degree of asymmetry in their caving profiles due to the more irregular shape of these types of deposits. Furthermore, a smaller strength contrast generally exists between the ore and host rock for these types of deposits. Using ore body type and mineral resource as a proxy for geology, these results show that site geology in addition to topography has a significant influence in promoting asymmetry in caving-induced displacements. This was also evident where large faults and/or rock mass fabric also influenced the directionality of caving.  134 These influencing factors become an important point of consideration when undertaking any subsidence analysis, as many commonly used design tools (e.g. the use of empirical design charts), do not account for the influence of topography or geological variations. The result is that symmetrical predictions of the extent of caving are produced, leading to the possibility that these may under-or over-predict the extent and magnitudes of caving-induced subsidence. Where these are under-predicted, the risk to surface infrastructure and safety may be heightened, and dilution may be more problematic than expected affecting the economics of the operations. Another important finding from the examination of the empirical database was that the data revealed a distribution heavily weighted towards the reporting of caving angles and macro-scale deformations (large open tension cracks and offset scarps). Very little data is reported on the extent and magnitudes of smaller strain surface deformations. To examine the potential impact of this sampling bias, specifically with respect to the influence of undercut depth on the extent of surface subsidence, a series of conceptualized numerical models were developed using the commercial FEM-DEM brittle fracture code ELFEN. The modelling results, based on undercut depths between 500 and 2000 m, show a decreasing footprint on surface with increasing undercut depth with respect to the caving and macro-scale fracturing zones. This agrees with trends observed in the empirical database. When considering the extent of micro deformations (<1m), however, the opposite is true and the subsidence zone increases with increasing undercut depth. Again, these results caution against relying on existing empirical design charts and databases which do not properly extrapolate beyond the macro deformations for estimating the extent of caving-induced subsidence where small strain subsidence is of concern. 5.1.2 Benchmark Testing for Block Cave Mining Using Numerical Analysis A benchmarking study was performed comparing a 2-D finite-element continuum code (Phase2), a 3-D finite-difference continuum code (FLAC3D), a 2-D distinct-element discontinuum code (UDEC), and a 2-D hybrid FEM-DEM brittle fracture code (ELFEN). Tested was the ability of these numerical techniques in assessing large-strain macro- deformations (caving and fracture initiation zones) and small-strain micro-deformations  135 (continuous subsidence), and the trends of these measures as a function of undercut depth. A conceptual geometry and set of site conditions were used as defined by the sponsoring partner for the study, the Centre for Excellence in Mining Innovation (CEMI). These were based on the panel caving of a large porphyry type deposit, incorporating faults, several different lithologies and varying rock mass properties. The first comparison involved the results from a 2-D elasto-plastic finite-element analysis in which a network of non-persistent small-strain joint elements were either included or not. The results show that the lateral extent of subsidence is similar for the shallower undercut depths, but increases more noticeably in the jointed models as the undercut depth increases. This trend can be attributed to the weaker rock mass conditions associated with the inclusion of the rock mass fabric (i.e. joint sets). These results were then compared to those derived in 3-D using FLAC3D. Here the magnitude of subsidence was seen to be considerably less than that in 2-D, pointing to the influence of the 2-D plane strain condition in concentrating more of the strain distribution (and therefore subsidence) in the plane of analysis. The FLAC3D results for the 500 m deep undercut show that the modelled extent of subsidence is limited by the bounding faults on either side of the undercut. The subsidence profile then widens and the influence of the bounding faults diminishes as the undercut depth increases. This agrees with the 2-D observations made in Phase2. It is also noteworthy that the 3-D shape of the subsidence profile elongates in the north-south direction more so than the east-west direction as the undercut depth increases. This coincides with the north-south cross section analyzed in the 2-D modelling. Results from the 2-D distinct-element discontinuum analysis (UDEC) showed that although being able to explicitly represent the dip and dip direction of discontinuities is important, so is the accurate representation of joint persistence. The extent of the subsidence zone modelled in UDEC was directly related to the dip direction with a significantly narrower zone being modelled when the joint sets were oriented at 0 and 90 degrees compared to the 2-D continuum analyses where the same joint orientations were used. This was due in part to the large strain slip along discontinuities allowed in UDEC, relative to the small strain capabilities in the finite element analysis, and the fully persistent nature of the orthogonal joint sets used. Where jointing in UDEC was set to orientations of 45 and 135  136 degrees, the fully persistent nature of the discontinuities used results in a wider zone of subsidence matching the 45 and 135 degree dip angles. Results from the hybrid FEM-DEM brittle fracture code ELFEN showed a pattern of subsidence similar to those in the other numerical models, but produced results that were interpreted as being more reliable than the others. As with the other methods, the caving angles were constrained by the bounding faults to the north and south of the undercut. While the different model results show similar trends with most indicating overhanging angles relative to the footprint of the undercut, the results are ambiguous with respect to the influence of undercut depth on caving with the exception of the ELFEN results which show the extent of caving at surface decreases with increasing undercut depth. This is due to the decreasing extraction ratio as the height of caving for each undercut depth was kept constant while the column of rock above the undercut across which the caving-induced strains are redistributing increases with increasing undercut depth. A similar result was seen for the zone of fracture initiation with the UDEC and ELFEN results showing that the fracture initiation zone does not extend beyond the bounding faults. In the ELFEN modelling, the fracture initiation zone at surface is again seen to decrease with increasing undercut depth. Thus, the ELFEN results confirm the influence of the bounding faults in limiting the extent of large- strain macro-scale deformations. As the depth of the undercut increases, the influence of the faults is less significant as the smaller extraction ratios limit the extent of surface disturbance. The opposite was seen to be true for the small-strain continuous subsidence, even when applying large cut off threshold of > 1 m. Each set of models: Phase2, FLAC3D, UDEC and ELFEN, showed a similar trend with the extent of small strain subsidence increasing with increasing undercut increased. The bounding faults showed little influence in limiting the extent of subsidence. Thus the results of the benchmark study confirm earlier results cautioning against relying on or scaling subsidence assessments based on macro deformations where small strain subsidence is of concern. Different characteristics of the different numerical methods applied, and resulting differences in results, emphasize the importance of carefully defining the key objectives of the modelling and factors that are most important. The selection of a modelling method often  137 involves the trade-off between fast model setup and run times, and accurate representations of the rock mass fabric and caving mechanics. Overall, the 2-D hybrid FEM-DEM approach allowing stress-induced brittle fracturing between joints appeared to provide the more dependable and realistic results. However, although a 3-D FEM-DEM brittle fracture analysis would seem to incorporate all of the required key elements for a block caving subsidence hazard assessment, the required computing times are still prohibitive. This will likely change, as computer hardware and software capabilities evolve. Today, where a 3-D analysis is required, continuum-based finite-element or finite-difference codes like FLAC3D seem to be most suitable. 5.1.3 Integration of Field Characterization, Mine Production and InSAR Monitoring Data to Constrain and Calibrate 3-D Numerical Modelling of Block Caving-Induced Subsidence Results were reported from an advanced 3-D back and forward analysis of caving- induced displacements at the Palabora open pit/block cave mine in South Africa using the commercial finite difference code FLAC3D. The representation of the block cave and its development in the model was implemented through an approach where the geometry of the cave is built into the model. Rock mass properties were derived for each of the key lithologies. From these, rock mass shear strength properties were estimated for use with a Mohr-Coulomb strain softening constitutive model. Data for the in-situ stress boundary conditions were compiled based on regional stresses reported in the published literature and mine specific in-situ stress studies. A number of reports presenting results from numerical modelling for Palabora were further reviewed and several different in-situ stress assumptions were tested based on this review for the best fit set of rock mass properties. First, FLAC3D modelling of the 2005 northwest wall failure at Palabora was carried out to back analyze and constrain the material properties and in-situ stresses to be used for subsequent forward modelling. Results from the back analysis clearly showed a varied response for the different rock mass properties tested and the “best fit” rock mass properties were obtained. Historic InSAR data from RADARSAT-1 was examined and used to further calibrate the model. The close agreement achieved on the spatial extent and magnitudes of  138 the FLAC3D predicted displacements and those measured using InSAR increased the degree of confidence in the validity of the input values used in the back analysis. These were then applied to a forward analysis (with respect to the pit slope failure date) of subsidence over the block caving operation at Palabora for the period 2009 to 2010. Whereas the back analysis of the 2005 pit slope failure represents a substantial initial step in calibrating and constraining the FLAC3D model, the failure caused a major change in the 3- D geometry of the model and this was accounted for in a modified 3-D model for the forward analysis. The results from the FLAC3D forward modelling were then compared with InSAR deformation data from the recently launched RADARSAT-2 satellite collected for the same period (2009 to 2010), in 28 day intervals. A close fit was observed between the subsidence predicted by the FLAC3D model and the InSAR measurements using the back analysis properties and the assumptions of cave growth for the same time period. The close agreement achieved on the spatial extent and magnitudes of the FLAC3D predicted displacements and those measured using InSAR (and geodetic monitoring data from the mine) allowed a greater degree of confidence in the 3-D model as a hazard assessment tool. The value of the high resolution InSAR data was shown to be significant as a means to calibrate and constrain sophisticated numerical analyses and subsidence predictions. 5.2 Key Conclusions and Scientific Contributions The following are the key contributions of this study: 1. The block caving database developed as part of this study serves as the most thorough developed to date and a substantial source of preliminary information that can be utilized by mines in assessing the feasibility of selecting block caving as the mining method. The results highlight a bias in published experiences towards trends that are only applicable for large strain macro deformations. For these, the correlation between the extent of the caving and fracture initiation zones on surface with undercut depth (seen as decreasing with undercut depth) provide a useful guidance in assessing the “fit” of a site as a block caving candidate. Caution must be exercised though where small strain micro deformations may have adverse effects.  139 2. The application of advanced numerical modelling in this study demonstrated the value of such tools in helping to fill data and knowledge gaps where empirical data may be limited or biased. Results examining the influence of undercut depth on small strain continuous subsidence, where little experience exists in its direct measurement, show that its extent increases with increasing undercut depth. Because this is the opposite of what is shown for macro-scale deformations, caution is highlighted for block caving operations involving deep undercuts where the impact of subsidence is assessed based on conventional assessments. Furthermore, whereas bounding faults may serve to limit the zones of caving and fracture initiation, this is not the case for the smaller strain subsidence zone. In deeper undercuts, the extent of the subsidence zone increases despite the presence of faults. 3. This study helps lay the groundwork on which to develop, calibrate and constrain 3-D numerical models directed towards assessing caving-induced subsidence patterns. The back analysis of subsidence and pit slope deformations at the Palabora mine in South Africa served to identify factors that contributed to the unexpected slope failure and helped constrain input parameters for an advanced 3-D forward model. The 3-D forward model was compared to and further calibrated using high resolution satellite InSAR monitoring data, demonstrating the value of this new data source. Together, the potential of a fully calibrated 3-D subsidence model as a predictive tool was tested and verified for its ability to assess the extent of caving-induced subsidence for time intervals as small as 6 months. In summary, this study completed a comprehensive block caving investigation linking empirical and numerical assessments of caving, fracture initiation and subsidence zones, from feasibility studies for a new block caving project, to mine design and production planning (e.g. draw sequencing) to mitigate potential subsidence hazards. The value of advanced numerical modelling was demonstrated as a means to address data gaps in direct measurement of subsidence across areas farther reaching than the mine footprint or property. Advanced numerical modelling was able to define and explain the relationship between  140 undercut depth and subsidence angle, and the capabilities of 3-D numerical modelling as a subsidence prediction tool where care is taken to fully integrate and implement all available relevant data and to constrain and calibrate the model using high resolution, wide spatial coverage data such as that offered by satellite InSAR. Doing so enabled an advanced information product to be developed and demonstrated, integrating geology, geotechnical data sets, and 3-D numerical modelling with InSAR imagery to assist mining decision makers in their development of safe and efficient block caving and open pit mining operations. 5.3 Future Research 1. The UBC block caving database developed should be updated as new data sources become available. One such data set briefly analyzed is satellite imagery like QuickBird and Google Earth. These show the full surface pattern of macro-scale caving, which through the use of pattern recognition software, may lead to further means to quantify and classify macro-scale caving-induced surface deformations. 2. This study highlighted the practical value of 3-D continuum analyses using codes like (FLAC3D). This was able to produce relatively fast results, enabling multiple model runs to test parameter sensitivity, calibration tests, etc. However, this required numerous simplifications of the mine site geology specifically in the form of the explicit representation of geological structures. These have been shown through 2-D analyses as having an important effect in properly accounting for asymmetry that may arise. However, with continuous advances in computation speed and software pre- and post-processing capabilities, further research should explore the application of 3- D discontinuum codes like 3DEC or 3-D hybrid FEM-DEM brittle fracture analyses using EFLEN. Although these demand significantly more data processing and computing capacity, they allow an improved treatment of the rock mass fabric, heterogeneity and simulation of caving mechanics. 3. The modelling performed in this study demonstrated the value of considering post- peak behaviour through the application of a strain softening model. However, this could benefit from a more thorough examination of the sensitivity of the results to  141 different critical strain thresholds and application of more complex constitutive models that better account for the influence of depth and confinement on both the peak and post-peak behaviour (e.g. Hoek-Brown with strain softening). 4. As shown in the benchmarking study, the 3-D modelling results showed sensitivity to the full 3-D stress field initialized, especially for deeper undercut depths. Under high stress conditions, preliminary results suggest that subsidence tends to be more sensitive to the stress condition than to the rock mass fabric. Given the industry trend towards deeper undercuts, it is recommended that further numerical analysis be carried out on the importance and influence of the intermediate principal stress. 5. While the benchmarking study suggests the importance of considering small-strain subsidence in mine design, limitations and errors inherent in numerical modelling (e.g. related to mesh size effects) could be more significant for small-strain subsidence. Rigorous examination of such errors especially in relation to the mesh size needs to be performed to further validate the argument of the importance of small-strain subsidence. 6. 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Proceedings of the 1st International FLAC/DEM Symposium on Numerical Modelling, Minneapolis. Minneapolis: Itasca Consulting Group; 2008. Paper 06-02, pp. 241–50. Sainsbury, D., Sainsbury, B. & Lorig, L. Investigation of caving induced subsidence at the abandoned Grace Mine. In Potvin(ed), Caving2010: Proceedings of the Second International Symposium on Block and Sublevel Caving, Perth, 20-22 April 2010. Perth: Australian Centre for Geomechanics, pp. 189-204. Sandibak, L. Caving and subsidence at San Manuel mine, Arizona. The 5th Biennial Workshop was offered by the Interstate Technical Group on Abandoned Underground Mines (ITGAUM). Tucson, 2004 Singh, M. M. Mine Subsidence. SME Mining Engineering Handbook, 2nd edition, (Ed: H L Hartman).1992; 10: 938-971.  Society for Mining, Metallurgy and exploration: Littleton, Colourado.  153 Singh, U. K., Stephansson, O. J. & Herdocia, A. Simulation of progressive failure in hanging-wall and footwall for mining with sub-level caving. 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Version 7.0; 2009: Rocscience Inc, Toronto, Canada Thomas, L. A. Subsidence and Related Caving Phenomena at the San Manuel Mine. Magma Copper Company, San Manuel Division, San Manuel, Arizona. 1971;  87 pp. Torres, R., Encina, V. & Segura, C. Damp mineral and its effect on block caving with gravity transfer. In Design and Operation of Caving and Sublevel Stoping Mines, D.R. Stewart, Editor. Society of Mining Engineers: New York. 1981; pp. 251-282. Trischka, C. Subsidence following extraction of ore from limestone replacement deposits, Warren Mining District, Bisbee, Arizona. Transactions of the American Institute of Mining and Metallurgical Engineers. 1934;  109: 173-180. Tyler, D., Campbell, A. & Haywood, S. Development and measurement of the subsidence zone associated with SLC mining operations at Perseverance – WMC, Leinster Nickel Operations. In MassMin 2004, Proceedings, Santiago. A. Karzulovic and M.A. Alfaro, Editors. Mineria Chilena: Santiago.2004;  pp. 519-525. 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Sci (to be Submitted) Woo, K., Eberhardt, E. & Van As, A. Characterization and Empirical Analysis of Mining- Induced Subsidence over Block Caving Operations, Symposium and Workshops on Rock Engineering in Difficult Conditions, 3rd Canada-US Rock Mechanics Symposium , Toronto, Canada; 2009  156 Woo, K., Eberhardt, E. & Elmo, D. Empirical investigation and characterization of surface subsidence related to block cave mining. International Journal of Rock Mechanics and Mining Sciences (To be submitted) Zebker,  H. A. & Rosen,  P. A. On the derivation of coseismic displacement fields using differential radar interferometry: The Landers earthquake. Journal of Geophysical Research 1994; 99(B10): 19,617–19.      157 Appendix A: Derived Subsidence Data used to Develop Empirical Database  158 A.1 Subsidence data for block cave operations caving to surface exclusive of those caving into an open pit. Angles are reported as ranges where asymmetry occurs between the hangingwall and footwall sides of the ore body. Angles greater than 90° refer to overhanging angles. Mine (location) Orebody/Lift Mining Period Reported Undercut Depth (m) Caving Angle Fracture Initiation Angle Angle of Subsidence Data Confidence/Comments  Source Alaska-Juneau (Alaska, USA) South 1923-1929 200 67-80 60-67 - Good (cross-section with scale bar). Lower fracture initiation angle in range corresponds with dip of large fault. Bradley, 1929 Alaska-Juneau (Alaska, USA) North 1923-1944 450 88-93 - - Marginal (cross-section with scale bar). No information is given on mining operations. Petrilloand Hilbelink, 1999 South 1923-1944 255 52-82 52-62 - Perseverance 1886-1921 440 77-88 - - Andina Rio Blanco (Chile) Panel I (Block 1) 1970-1980 135 85-89 - - Marginal (cross-section without scale bar but with mine levels and depths; assumed to be drawn to scale). Early stage of cave development and production depicted. Torres et al , 1981 Andina Rio Blanco (Chile) Panels I & II 1978-1995 390 61-76 - - Poor (cross-section without scale bar but with mine levels; depths determined from other sources; assumed to be drawn to scale). Lower angle in range corresponds with uphill side of sloping surface.  Flores and Karzulovic , 2002 Athens (Michigan, USA) Blocks 1-4 and 1 & 2, Lift 2 1919-1951 670 84-94 80-90 - Good (cross-section with scale bar). Caving and subsidence on surface partly concealed by thick blanket of glacial till. Cave propagation and boundaries partly controlled by vertical dykes. Boyum, 1961 Bagdad (Arizona, USA) West 1937-1947 265 84-90 72-86 Marginal (subsidence map with scale bar; depths determined from secondary information and used to calculate angles). Boundary level drifts used to control the lateral extent of caving. Hardwick, 1959 Catavi (Bolivia) Block 2 1948-1957 115 60-90 - Marginal (cross-section with scale bar; full limits of caving zone not shown but reported in text). Undercut is located under steep topography. Weisz, 1958  159 Mine (location) Orebody/Lift Mining Period Reported Undercut Depth (m) Caving Angle Fracture Initiation Angle Angle of Subsidence Data Confidence/Comments  Source Climax (Colorado, USA) Phillipson Level 1940-1945 145 86-95 61-95 - Good (cross-section with scale bar). Lower angles in ranges correspond with uphill side of sloping surface and retrogressive slumping towards cave. Vanderwilt , 1949 Corbin (B.C, Canada) No. 6 Mine – West 1917-1934 80 60-83 - - Poor (cross-section without scale bar but with mine levels; depths determined from other sources; assumed to be drawn to scale). Mining of thick interval of coal using multiple lifts. Neighbouring section mined by top slice method. Warburton, 1936 Crestmore (California, USA) Stanley Bed – Block 1A 1930-1954 60 70-90 55-88 - Good (cross-section with scale bar). Vertical cutoff stopes excavated on all four sides of block to control caving angles. Caving on footwall side of block extended beyond this to align with a dipping fault (lower angle in fracture initiation range). Long and Obert, 1958 Grasberg (Indonesia) IOZ 1994-2000 650 68-73 63-68 Good (cross-section with scale bar). Undercut is located under a steep slope; lower caving angle in range corresponds to the uphill side. Barber et al, 2001, Hubert et al, 2000  Inspiration (Arizona, USA) Transfer Block 1947-1963 70 85-105 - - Good (cross-section with scale bar). Caving of small transfer block following transition from block caving to open pit mining. Hardwick, 1963 Jenifer (California, USA) Jenifer 1952-1957 160 81-95 81-95 81-95 Good (subsidence map and cross-section with scale bars). Periphery of caving zone marked by single, continuous, steep-wall face with little to no change in subsidence outside this area. Obert and Long, 1962 King (Zimbabwe) West Flank;  W11-14 Blocks ? – 1988 275 80-84 72-78 - Marginal (cross-section without scale bar but with mine levels and depths; assumed to be drawn to scale). Steeper angle in ranges coincides with caving parallel to footwall of dipping orebody; lower angles occur on uphill side of caving zone. Brumleve, 1988, Duffield, 2000  160 Mine (location) Orebody/Lift Mining Period Reported Undercut Depth (m) Caving Angle Fracture Initiation Angle Angle of Subsidence Data Confidence/Comments  Source Lake Superior (Michigan, USA) Marquette range (Case C; Types D-F) ? 450 80 70 - Poor (schematic cross-section without scale bar; assumed to be roughly drawn to scale). No direct indication given of mining depth. Bedrock is covered by a thick blanket of glacial till that partly obscures the caving and subsidence zones at surface. Crane, 1929 Miami (Arizona ,USA) Low Grade Orebody 1926-1929 195 71-84 50-73 - Good (cross-section with scale bar). Caving limits controlled by vertical boundary drifts. Caving on one side extends into the “Main Orebody” previously mined by sublevel caving. Lower angles are sub-parallel to foliation of schist. MacLenn- an, 1929 Stope 11 1928-1929 195 83-92 76-87 - Good (cross-section with scale bar). Caving limits controlled by vertical boundary drifts.   Miami (Arizona ,USA) Main/Low Grade Orebodies 1910-1939 195 62-84 40-70 - Marginal (subsidence map with scale; depths determined from secondary information and used to calculate angles). Caving limits controlled by vertical boundary drifts. Angles reported to have flattened considerably since 1929 measurements. Fletcher, 1960 720 -1000 Levels 1910-1958 300 60-69 47-56 - Good (cross-section with scale bar). 1000 Level mined without vertical boundary cut-off drifts. Northparkes (Australia) E26 Lift 1 1993-2000 450 84-88 - - Marginal (cross-section without scale bar but with mining level; scale estimated from other source; assumed to be roughly drawn to scale). Collapse of crown pillar related to change in geology resulted in near-vertical cave angles. Lift also caved into the bottom Duffield, 2000  161 of small open pit. Mine (location) Orebody/Lift Mining Period Reported Undercut Depth (m) Caving Angle Fracture Initiation Angle Angle of Subsidence Data Confidence/Comments  Source Questa (New Mexico, USA) Goathhill 1983-2000 300 70-85 51-84 32-81 Good (subsidence map with scale bar; depths determined from secondary information and used to calculate angles). Lower angle in ranges coincide with deformations related to shallow rockslide movements undercut by cave.  Gilbride et al, 2005 D – Block 1 2000-2005 550 - - 55-85 Marginal (subsidence map with scale bar; depths determined from secondary information and used to calculate angles). Subsidence not developed enough to allow measurement of caving or fracture initiation angles. San Manuel (Arizona, USA) South Orebody, Lift 1 1956-1960 420 64-95 53-95 - Good (cross-sections and subsidence map with scale bars). Gilbride et al, 2005, Buchanan and Buchella, 1960  San Manuel (Arizona, USA) South Orebody, Lift 1 1956-1962 420 56-90 56-66 - Good (subsidence map with scale bar). Final reporting of subsidence for mining of South orebody, Lift 1. Thomas, 1971 South Orebody, Lift 2 1962-1970 605 63-80 63-80 - Good (cross-sections and subsidence map with scale bars). Active subsidence contained within established boundaries for Lift 1, with only minor activity outside this periphery. North Orebody, West 1959-1970 390 78-86 66-74 - Good (subsidence map with scale bar). West and East blocks separated from one another by a 200 m pillar. North Orebody, East 1962-1970 390 75-87 66-72 - Good (subsidence map with scale bar). West and East blocks separated from one another by a 200 m pillar. Shabani (Zimbabwe) 52 & 58 1987-1999 630 75-83 - - Good (cross-section with scale bar). Inclined undercut dipping at Wilson, 2000  162 approximately 30° from horizontal. A.2   Subsidence data for panel cave operations caving to surface exclusive of those caving into an open pit. Angles are reported as ranges where asymmetry occurs between the hangingwall and footwall sides of the ore body. Angles greater than 90° refer to overhanging angles. Mine (location) Orebody/Lift Mining Period Reported Undercut Depth (m) Caving Angle Fracture Initiation Angle Angle of Subsidence Data Confidence/Comments  Source Climax (Colorado, USA) 600 Level 1945-1980 325 72-74 - - Marginal (cross-section without scale bar but with mine levels and depths; assumed to be drawn to scale). Continuation following transition from block to panel caving. Vera, 1981 Creighton (Ontario, Canada) 23 Level 1951-1955 420 90 - - Poor (cross-section without scale bar but with mine levels; depths determined from other sources; assumed to be drawn to scale). Blasting used to induce caving beyond limits of previously mined stopes. Brock et al , 1956 Creighton (Ontario, Canada) 1900 Level 1951-1963 420 74-88 62-79 55 Good (subsidence map with measured angles together with cross-section without scale bar but with mine levels; depths determined from other sources; assumed to be drawn to scale). Dickhout, 1963 El Teniente (Chile) South 1 (Ten 1 Sur) 1940-1980 510 60-88 - - Marginal (cross-section without scale bar but with mine levels; depths determined from other sources; assumed to be drawn to scale). Undercut is positioned under a steep slope; lower caving angles occur on the uphill side. Ovalle, 1981, North 4 (Ten 4 Norte) 1960-1980 540 70-80 - - Ovalle, 1981, Kvapil et al , 1989 El Teniente (Chile) Regimiento 4 1982-1998 250 82-87 - - Poor (empirical chart of caving angle versus depth based on numerical modelling and field observations; no depth is reported for the undercut but can be estimated from other sources). Brown, 2003 El Teniente (Chile) Esmeralda 1997-2001 800 65-77 58-67 - Marginal (cross-section without scale bar but with mine levels and depths, together with empirical chart of caving angle versus depth). Undercut is positioned under a steep Rojas et al 2003  163 slope; lower angles in range correspond to the uphill side of cave. Mine (location) Orebody/Lift Mining Period Reported Undercut Depth (m) Caving Angle Fracture Initiation Angle Angle of Subsidence Data Confidence/Comments  Source  Grace (Pennsylvania, USA)  1958-2004 750 80-110 70-86 - Marginal (subsidence map showing limits of surface cracking; angles estimated based on average depth of undercut). Inclined panel cave (20-30°). Cave breakthrough only occurred above half of the undercut, facilitated by a steeply dipping fault. Sainsbury et al, 2010 Henderson (Colorado, USA) 8100 Level Panel 1 1976-1983 1050 90-98 86-92 - Good (cross-section with scale bar together with subsidence map). Vertically spaced boundary cutoff drifts together with steeply dipping faults contribute to vertical nature of cave. Brumleve and Maier, 1981, Stewart et al, 1984 Henderson (Colorado, USA) 7700 level 1976-2000 1150 90-100 - - Poor (cross-section without scale bar but with mine levels; depths determined from other sources; assumed to be drawn to scale) Rech et al, 2000 Salvador (Chile) Inca West 1994-2000 700 70-76 - - Marginal (cross-section without scale bar but with mine levels and depths; assumed to be drawn to scale). Caving zone depicted prior to and after air blast collapse of cave back. Escobar, 2000 Urad (Colorado, USA) 1100 Level 1967-1969 150 90 82 - Poor (cross-section without scale bar but with mine levels; depths determined from other sources; assumed to be drawn to scale). Undercut beneath steep hill. Caving limits controlled by vertical boundary cut- off stopes (shrinkage stopes). Considerable blasting required to aid caving. Kendrick, 1970      164  A.3  Subsidence data for sublevel caving/shrinkage stoping/top slicing operations caving to surface exclusive of those caving into an open pit. Angles are reported as ranges where asymmetry occurs between the hangingwall and footwall sides of the ore body. Angles greater than 90° refer to overhanging angles. Mine (location) Orebody/Lift Period Reported Undercut Depth (m) Caving Angle Fracture Initiation Angle Angle of Subsidence Data Confidence/Comments  Source Cambria Jackson (Michigan, USA) 260 Sublevel 1942-1945 350 86-94 71-72 - Good (cross-section with scale bar). Cave propagation through competent diorite sill capping weak hematite iron formation. Boyum, 1961 Copper Mountain (B.C., Canada) Contact Block 1937-1949 350 79-90 69-74 65 Good (cross-section with scale bar). Nelson and Fahrni, 1950 122-East Block 1941-1949 210 82-90 67-74 - Good (cross-section with scale bar). Lower angle in range aligns with dipping fault. Copper Queen – East Orebody (Arizona, USA) 600 & 650 Lift 1925-1927 155 68-98 58-95 - Good (multiple cross-sections without scale bars but with mine levels and depths; assumed to be drawn to scale). Lower angles correspond with weak hangingwall rock, relative to higher angles in stronger footwall rock. Kantner, 1934 725 Lift 1927-1928 180 64-88 56-72 - 850 Lift 1928-1930 215 57-75 54-72 - 950 Lift 1930-1931 240 56-75 52-72 - 1100 Lift 1931-1933 290 54-70 45-67 - Copper Queen – Queen Hill (Arizona, USA Queen Hill Block 1913-1933 100 78 78 78 Marginal (cross-section without scale bar but with mine levels and depths; assumed to be drawn to scale). Caved block is bound on all sides by faults, along which the block drops and across which subsidence is limited. Flores and Kazulovic, 2002 Corbin (B.C, Canada) No. 6 Mine - East 1917-1934 80 40-52 - - Marginal (cross-section without scale bar; scale estimated from other data provided; assumed to be roughly drawn to scale). Undercut inclined at 38°, extending from surface to same level at depth of neighbouring section mined by block caving. Warburton, 1936  165    Mine (location) Orebody/Lift Mining Period Reported Undercut Depth (m) Caving Angle Fracture Initiation Angle Angle of Subsidence Data Confidence/Comments  Source  Gath’s (Rhodesia/ Zimbabwe) 99 Level 1971-1976 60 50-75 50-75 - Good (cross-section with caving angles reported). Lower angles correspond with dip of orebody; steeper angles correspond to caving in dipping hangingwall. Brown and Ferguson, 1979 158 Level 120 50-65 50-65 - 183 Level 145 50-56 50-56 - Grangesberg (Sweden) 140 Level ?-1921 140 62-80 - - Marginal (cross-section without scale bar but with caving angles and sublevel depths). Caving angle on footwall side coincides with dip of inclined orebody at 62°. Hoek, 1974 180 Level 1921-1933 180 62-88 - - 190 Level 1933-1936 190 62-80 - - 210 Level 1936-1939 210 62-80 - - 240 Level 1939-1943 240 62-64 - - 300 Level 1943-1961 300 60-62 - - Grangesberg (Sweden) 410 Level 1960-1974 410 64-83 - - Marginal (cross-section without scale bar but with sublevel depths; assumed to be roughly drawn to scale). Caving angle on footwall side coincides with dip of inclined orebody at 64°. Sisselman, 1974 Havelock (Swaziland) Level 1 1952-1972 135 52-82 52-78 - Good (cross-section with scale bar). Lower angles in range controlled by dip of bedding in footwall. Deformation in hangingwall develops through flexural toppling and shearing along bedding. Heslop, 1974 Level 2 1963-1972 180 52-90 52-64 - Level 3 1966-1972 225 52-90 52-60 - Kiirunavaara/ Kiruna (Sweden) 700 Level 1965-1995 465 60-94 53-74 40-60 Marginal (subsidence map but without indication of the sublevel depth; sublevel depth estimated from other sources). Caving angle on footwall side coincides with dip of orebody. Higher caving angle points to overhanging nature of dipping hangingwall. Henry and Dahnér- Lindqvist, 2000 Henry et al, 2004 Kiirunavaara/ Kiruna (Sweden) 785 Level 1965-2000 500 50-82 50-60 40-50 Marginal (subsidence map; angles calculated based on projection of lowest sublevel undercut and depth at time of Henry et al, 2004  166 data reporting). Angles on the footwall side are shown to coincide with one another at 50°. Mine (location) Orebody/Lift Mining Period Reported Undercut Depth (m) Caving Angle Fracture Initiation Angle Angle of Subsidence Data Confidence/Comments  Source  Kiirunavaara/ Kiruna (Sweden) 400 Level 1965-1971 165 - 60-74 - Good (cross-section without scale bar but with sublevel depths; assumed to be drawn to scale). Only fracture initiation angle on hangingwall side provided; no indication of caving angles for the same periods. Fracture initiation angle on footwall side reported as coinciding with dip of orebody (60°). Villegas, 2008 415 Level 1971-1974 180 - 60-66 - 425 Level 1974-1977 190 - 60-61 - 465 Level 1977-1981 230 - 60-63 - 530 Level 1981-1985 285 - 60-63 - 570 Level 1985-1989 325 - 60-61 - 750 Level 1989-1995 505 - 60-66 - 865 Level 1995-2005 615 - 60-73 - Lake Superior (Michigan, USA) Gogebic range (Case B; Type C) ? 300 86-105 - - Poor (cross-section without scale bar or mining depth, but with caving angles; assumed to be drawn to scale). Caving occurs primarily along steeply dipping footwall slates. Crane, 1929 Malmberget (Sweden) Pillar Recovery 300 Level 1970-1974 300 78-92 - - Good (cross-section with scale bar). Lower angle coincides with footwall, whereas higher angle points to overhanging hangingwall. Hannweg and Van Hout, 2001 Miami (Arizona ,USA) Main Orebody 1910-1925 180 60-84 60-68 - Good (cross-section with scale bar). Mostly mined by top slicing and sublevel caving. Caving limits controlled by vertical boundary drifts. Lower angles are sub-parallel to foliation of schist. MacLennan, 1929 Mt. Lyell (Tasmania) Cape Horn (#5 Stope) 1972-1980 160 70-86 70-72 - Marginal (cross-section without scale bar but with sublevel depths; assumed to be drawn to scale). Lower angles coincide with dip of footwall (70°). North and Callaghan, 1980 Perseverance (Australia) 9920 Level 1989-1997 640 66-79 - - Good (cross-section with scale bar). Sublevel caving beneath large open pit. Lower caving angle extends beyond pit limits on hangingwall side of orebody.  Jarosz et al, 2007  167    Mine (location) Orebody/Lift Mining Period Reported Undercut Depth (m) Caving Angle Fracture Initiation Angle Angle of Subsidence Data Confidence/Comments  Source  Perseverance (Australia) 10130 Level 1989-1995 390 84-90 - - Marginal (subsidence map without scale bar; depths determined from secondary information and used to calculate angles; assumed to be drawn to scale). Sublevel caving beneath large open pit. Lower caving and fracture initiation angles extend beyond pit limits on hangingwall side of orebody. Tyler et al , 2004 10100 Level 1995-1996 420 66-90 - - 10030 Level 1996-1997 490 66-87 63-90 - 9920 Level 1997-1998 600 73-81 63-81 - 9870 Level 1998-1999 650 74-80 63-80 - 9860 Level 1999-2000 660 70-80 62-80 - 9850 Level 2000-2001 670 70-83 62-83 - 9815 Level 2001-2002 705 73-85 65-85 - 9760 Level 2002-2003 760 72-84 66-83 - Rajpura Dariba (India) South 465 Level ? 185 70-90 55-70 - Poor (no data provided; angles cited in text). 70° angle coincides with dip of footwall. Singh, 1993 San Giovanni (Italy) Contatto Ovest 1985-1990 100 75-92 - - Marginal (subsidence map and cross- section without scale bar but with mining levels and depths; assumed to be drawn to scale). Balia et al, 1990           168  A.4   Subsidence data for block cave operations caving to surface into an open pit. Mine (location) Orebody/Lift Mining Period Reported Undercut Depth (m) Caving Angle Fracture Initiation Angle Angle of Subsidence Data Confidence/Comments  Source Finsch (South Africa) Block 4 2004-2006 700 74-82 - - Good (cross-section with scale bar). Block caving into existing workings mined by open stoping, and earlier by large open pit. Caving angles coincide with walls of already existing crater. Preece and Liebenberg, 2007 Jagersfontein (South Africa) 1870 level 1947-1962 550 75-82 - - Good (cross-section with scale bar). Block caving into existing underground workings and open pit. Caving angles incorporate open pit and sloughing of wall rock. Stucke, 1965 Koffiefontein (South Africa) 49 Level 1987-2001 480 90 - - Poor (cross-section without scale bar but with mine levels; depths determined from other sources; assumed to be drawn to scale). Hannweg and Van Hout, 2001 Palabora (South Africa) Lift 1 2001-2007 1200 84-86 60-84 - Poor (cross-section without scale bar but with mining level; depths determined from other sources). Lower fracture initiation angle coincides with back scarp of large rockslide that developed in deep open pit. Pretorius,2007  169 Appendix B : Detailed Background Descriptions of Subsidence Observations Compiled in the Empirical Database   170 Alaska-Juneau (Alaska, USA) – 1929 Source: Bradley (1929) Caving Period Reported: 1916-1929 Summary: Block cave mining methods applied to the Alaska-Juneau gold mine are reported. In describing the system of caving, a schematic cross-section is included that depicts the caving zone and surface fractures that develop over a single block undercut from the 4 Level at 200 m depth. It is assumed that the section is based on visual indicators; no indication is given that subsidence measurements were made. The sections are to scale and show the depth of the undercut workings and original surface. Blasting was used to aid the caving process, and the presence of a dipping fault plays a controlling role in the extent of caving and subsidence on the footwall side of the orebody.       171 Alaska-Juneau (Alaska, USA) – 1944 Source: Petrillo & Hilbelink (1999) Caving Period Reported: 1923-1944 Summary: The history of the Alaska-Juneau gold mine is reported, encompassing the North, South and Perseverance orebodies, which were mined using a combination of block caving and shrinkage stoping. Minimal data is provided regarding the mining operations and no specific data regarding subsidence measurements are reported. However, a scaled cross- section is provided, which shows the caving zone and undercuts from which the caving angles can be estimated.     Andi Sourc Cavin Summ descr of the form based provi the d moun show  na-Rio Blan e: Torres et g Period Re ary: The b ibed. This i  first block of subsiden  on visual o ded, but the epth of mini tain. Howev n to be influ co (Chile)  al. (1981) ported: 197 lock cavin ncludes a cr in Panel I, a ce measurem bservations  different m ng can be a er, the earl enced by to – Panel I 0-1980 g operation oss-section nd the corre ents is give . It is also a ine levels ar pproximated y stage of c pography. 172 s for Pane showing the sponding ca n, but it is a ssumed the e shown wit . The under ave develop l I at And  surface pr ved area at ssumed that cross-sectio h their resp cut is locat ment and pr  ina’s Rio B ofile, underc surface. No  the altered n is to scale ective eleva ed under the oduction de lanco mine ut level, m direct data i surface prof ; no scale b tions from w  steep slope picted is no  are ining n the ile is ar is hich  of a t yet  Andi Sourc Cavin Summ (form will b state is to depth The c cavin of bre for d meas range MRM   na-Rio Blan e: Flores & g Period Re ary: Data erly the Rio e mined by of caving ab scale; no sc  can be app aving zone g correspon ak angles, ifferent rang ured with re s cited are R 61 to 70. co (Chile)  Karzulovic ported: is reported  Blanco mi  panel cavin ove Panels ale bar is p roximated b is located u ds with the defined as t es of MRM spect to the 52-90° for M  – Panel I & (2002) from the ne). Focus i g. However I and II, mi rovided, bu ased on the nder the stee uphill side he mean inc R values.  undercut le RMR 41 173  II ICS II benc s placed on , a schemat ned by bloc t the under reported ele p slope of a of sloping s lination of t However, b vel, they ar to 50, 58-90  hmarking  the planned ic cross-sec k caving. It cut levels a vations of th  mountain, urface. The he caving c ecause the e not report ° for MRM study for th  third lift (P tion is provi is assumed re indicated e Panel II a for which th report also rater walls angles do n ed in the ab R 51 to 60 e Andina anel III), w ded showin the cross-se  from whic nd III under e lower ang provides a r at various d ot appear t ove Tables , and 70-90 mine hich g the ction h the cuts. le of ange epths o be . The ° for   174 Athens (Michigan, USA) – 1932 Source: Allen (1934) Caving Period Reported: 1918-1932 Summary: Data is reported for the Athens mine in the Marquette iron range. This is one of the unnamed regions reported by Crane (1929); see Lake Superior District below. The caving period reported is from the start of mining to the completion of Blocks 1 and 2 at 630 m depth. Mining was carried out using a combined block caving and top slicing approach progressing upward in successive blocks to the east. A scaled cross-section is provided based on surface observations of caving features, which shows the extent of caving on surface, depth of mining and caving angles. The cross-section also shows that a thick blanket of glacial till covers the bedrock, partly obscuring the subsidence zones at surface. Upward propagation of the cave is shown to be bounded and controlled in part by two vertical diorite dykes.      Athe Sourc Cavin Summ the ex opera with 2 to 6 cavin cavin obser on su dykes    ns (Michiga e: Boyum ( g Period Re ary: This re tension of tions in 195 data for the 70 m depth g and top s g at surface ved despite rveys of su  that partly n, USA) – 1 1961) ported: 191 port update the subsiden 1. Repeated mining of th  (from 630 licing appro  relative to the thick bl bsidence pi bound and c 950 8-1950 s the subsid ce zone for  are the da e neighbou m). As befo ach. A scal the undergr anket of gla ns laid out ontrol the u 175 ence observ  the mining ta for the m ring blocks re, mining ed cross-se ound worki cial till that on a grid ov pward propa ations of All  carried out ining of Bl (3 and 4) an was carried ction is pro ngs. Also in covers the b er the area gation of th en (1934), p  up to the s ocks 1 and d extension out using a vided showi cluded are edrock. The . Present ar e cave. roviding da uspension o 2, suppleme  of Blocks  combined b ng the exte surface frac  section is b e vertical d ta on f the nted 1 and lock nt of tures ased iorite   Bagd Sourc Cavin Summ cavin boun (note the u fractu althou subsi coinc block drifts ad (Arizon e: Hardwick g Period Re ary: Minin g of the W dary of the  that only th ndercut (29 re initiation gh it is as dence but m ides with an  caving for  were used t a, USA) (1959) ported: 193 g methods est orebody subsidence e northwest 90 Level, 2  angles. No sumed that ore likely  area where  the remain o control th 7-1944 applied at t . A scaled area, severa  half of the u 65 m below indication i it is not at fracture ini  the top of ing West o e lateral exte 176 he Bagdad  surface sub l collapse f ndercut wa  surface), i s given as to  a resolutio tiation. The the ore bloc rebody was nt of caving mine are re sidence m eatures, and s caved). Ba t is possible  how the su n that depi  source not k is close to  gradually .  ported, inc ap is provid  the outline sed on the r  to estimate bsidence are cts the limi es that the  surface. Su phased out. luding the b ed showing  of the und eported dep  the caving a was meas ts of contin subsidence bsequent to  Boundary lock  the ercut th of  and ured, uous area  this, level  Cam Sourc Cavin Summ Marq by C repor was provi direct surfa hema bria Jackso e: Boyum ( g Period Re ary: Data uette Iron R rane (1929) ting was at 3 initially top ded showing  indication ce surveys w tite iron form n (Michiga 1961), Cran ported: 194 is reported ange of the ; see Lake 50 m depth  slicing and  the origina is given as ere carried ation but a n, USA) e (1929) 1-1945 for a suble  Negaunee d Superior D  (260 level)  then chan l topograph to how the  out. Cave lso through 177 vel caving istrict. This istrict below , with 50 m ced to sub y and the zo  subsidence propagation a competen operation  is one of th . The low of mined or level caving nes of cavin was measu  occurs prim t diorite sill  in hematite e unnamed ermost leve e above. Th . A scaled g and fractu red, but it c arily throu near surface iron ore in regions rep l at the tim e mining me  cross-secti re initiation an assumed gh a thick, .  the orted e of thod on is . No  that weak  Cata Sourc Cavin Summ cross with meas exten are n occur  vi (Bolivia) e: Weisz (1 g Period Re ary: The bl -section sho the corresp urements is ding from th ot included, red above th 958) ported: 194 ock caving wing the or onding cave  given, but e 160 level  but the so e undercut 8-1957 operations f iginal surfa d area at s  the cross  (115 m dep urce text re level in the 178 or the Catav ce profile, u urface. No section is th). The ext ports that su first year of i tin mine a ndercut lev  direct data drawn to sc ended limits rface subsi block cavin  re described els, and mi  in the form ale. Caving  of the subs dence of ap g. . This inclu ning of Blo  of subsid  is depicte idence boun proximately des a ck 2 ence d as dary  60°  Clim Sourc Cavin Summ cavin cavin (1943 and m from initia up slo    ax – 1945 (C e: Vanderw g Period Re ary: Groun g above the g extending ) and updat apping and which an a tion appears pe through olorado, U ilt (1949) ported: 194 d movemen  Phillipson  to surface ed caving an  shows the o ngle of fra  to be affect retrogressiv SA) 0-1945 ts are repo Level. The . A represen gles (1945) riginal topo cture initiat ed by the sl e slumping 179 rted for th average und tative cross . The cross- graphy toge ion can be oping surfac of the upper e Climax m ercut depth -section is section is b ther with a inferred. No e topograph  rock scarp. olybdenum for this leve provided th ased on surf clear zone o tably, the a y with subs   mine for b l is 145 m, at reports i ace observa f caving/col ngle of fra idence exten lock  with nitial tions lapse cture ding   Clim Sourc Cavin Summ retrea levels cross minin provi surfa spaci depth less d on th    ax – 1980 (C e: Vera (19 g Period Re ary: Caving t panel cav . No direct -section is in g across th ded from w ce resulting ngs between  of 325 m. etailed than e general op olorado, U 81) ported: 194  operations ing from blo data is prov cluded whi ree levels. hich the sca  in variable  levels, the The caving  the earlier erations. SA) 5-1980  at Climax a ck caving o ided in the ch shows th No scale ba le can be in  depths to  600 Level angle inform data provid 180 re described f the Philli form of sub e increase in r is provid ferred. The the lowerm is 180 m b ation prov ed by the V , reporting t pson level a sidence me  the caving ed, but the panel caves ost undercu elow the Ph ided in the anderwilt, a he changeov s the mine asurements, zone with th elevations  are located t (600 Lev illipson and cross sectio s the paper er to contin moves to de  but a schem e progressi of the level  under a slo el). With 9  has an ave n is signific is more focu  uous eper atic on of s are ping 0 m rage antly ssed  Copp Sourc Cavin Summ cavin cases (Cont provi scarp angle subsi paral based calcu    er Mounta e: Nelson & g Period Re ary: Subsid g of two cop , the caved act Block) a ded for bot s and zone s of fracture dence meas lel to a dip  on surface late ratios o in (B.C., Ca  Fahrni (19 ported: 193 ence data i per porphy  ground ex nd 210 m ( h blocks sh of caving/c  initiation a ured from ping fault. surveys, ma f total subsid nada) 50) 7-1949 s reported f ry ore bodie tends to su 122-East Blo owing the ollapse. Fro nd caving c the cross-se The subside pping and a ence to ore  181 or a combin s, named Co rface. The ck) with su original top m these, th an be inferr ction varie nce feature erial photog  extraction f ation of shr ntact Block maximum b-levels abo ography, ex e angle of ed. For the s with the s reported i raphs. Thes or the two b inkage stop  and 122-Ea undercut de ve. Scaled c tent of sub  subsidence 122-East Bl lower angle n these cro e were subs locks. ing and sub st Block. In pths are 35 ross-section sidence, su  is reported ock, the ang  reported b ss-sections equently us level  both 0 m s are rface  and le of eing were ed to   Copp Sourc Cavin Summ (East repre The i respe surve natur angle termi refere break as ref influe relati north obser    er Queen B e: Kantner g Period Re ary: Data  Orebody), sentative of nitial and fin ctively. Cav ys), tension e of the cav  of subside nology used nce is mad  angle being erring to th nce the res ve to those  and northw ved for a pe ranch – Ea (1934) ported: 192 is reported which due a sublevel c al undercut ing at surf  cracks and ing. A sca nce for eac  here by V e to subside  the limit o e caving an ulting angl that develop est may als riod of time st Orebody 5-1933 for block ca to their sh aving opera  levels in th ace appear several sma led cross-se h lift. Howe an As et al nce being t f visible cra d fracture in es, with low  in the stro o play a co .  182  (Arizona, ving of sev ort heights tion (and is e source pap s in the fo ll glory hole ction is pro ver, the ter . (2003). In he steeper cking in the itiation ang er angles nger footwa ntrolling ro USA) eral lifts of (9-36 m) a  classified a er are 140 a rm of mea s, the latter vided repor ms used by  the Discus angle of “m  same sectio les, respect developing ll. The pres le as no cra  a copper p nd inclined s such in th nd 285 m b sured subsi likely reflec ting the ang  the author sion that fo arked” subs n. These are ively. Rock in the wea ence of a m cking beyon orphyry de nature, is e above Tab elow the sur dence (elev ting the sub le of break  differ from llows the p idence, wit  interpreted  mass condi ker hanging ajor fault t d this fault posit more les). face, ation level  and  the aper, h the  here tions wall o the  was   Copp Sourc Cavin Summ but s was u tabul 210 m that n 1913 also c being subsi   er Queen B e: Trischka g Period Re ary: Data i eparate from tilized with ar orebody. . A cross-s o indicatio replacing a orresponds  bounded on dence distur ranch – Qu  (1934) ported: 191 s provided f  the East O  two main l The mining ection is pr n is given a  square set to the cavin  all four sid bance is lim een Hill Bl 3-1933 or the Quee rebody blo evels being  levels cros ovided show s to when method). Re g angle and es by faults ited. 183 ock (Arizon n Hill Block ck described caved (200 s under a st ing the pre mining was ported is th  subsidence , along whi a, USA)  of the Cop  above. Th and 300 Le eep hill wit -mining and  completed; e fracture in  angle as the ch the block per Queen m e top slicing vels) along h depths ran  “present” t  top slicing itiation ang  caved bloc  drops and ining area,  mining me a sub-horizo ging from opography  was initiat le, although k is describ across whic   near thod ntal, 30 to (note ed in  this ed as h the  Corb Sourc Cavin Summ sectio block which slicin Leve under provi align     in e: Warburto g Period Re ary: Data i ns, West an  was mined  being at 80 g, the unde l at 95 m dep cut depths ded that allo s with the di n (1936) ported: 191 s provided f d East, sepa  by block c  m at the ti rcut for whi th. A schem can be est ws the scal p of the und 7-1934 or the mini rated by a r aving using me of report ch is inclin atic cross-s imated. No e to be appr ercut. 184 ng of a thic ock instruct  a number ing. The ne ed, dipping ection is pro  scale is p oximated. T k coal seam ion (i.e. wed of lifts at 2 ighbouring at 38° and vided from rovided, bu he lower cav  (No. 6 min ge of waste 0 m interva East block w extending f  which the c t associated ing angle f e) split into  rock). The ls, the lowe as mined b rom surface aving angle  informatio or the East b  two West st of y top  to 2 s and n is lock   Creig Sourc Cavin Summ minin mine shrink cavin estim Draw rock    hton (Onta e: Brock et g Period Re ary: Data g by shrink d stopes. A age stoping g along the ated at the t  in the pane above hangi rio, Canad al. (1956) ported: 195 is reported age stoping. schematic c  beneath a  strike of ime of break l cave is lim ngwall. a) – 1955 1-1955 for panel c  Blasting w ross-section 60 m deep o the orebody  through at ited by a c 185 aving at the as used to in  is provided pen pit, an . From thi surface, but ut-off grade  Creighton duce caving  that show d the neighb s cross-sect  little additio  given the d  mine, subs  beyond lim s the caved ouring cave ion, a cavin nal informa ilution aris equent to e its of previo stopes mine  mined by p g angle ca tion is prov ing from the arlier usly d by anel n be ided.  cap  186 Creighton (Ontario, Canada) – 1963 Source: Dickhout (1963) Caving Period Reported: 1951-1963 Summary: Mining operations and ground control issues for the Creighton mine are reported. The increased time interval from that reported by Brock et al. represents a more fully developed cave, which although not specified, appears to include the pillar between the earlier shrinkage stoping operation and subsequent panel caving. No direct subsidence measurements are reported, however a general cross-section is provided that shows the development of caving relative to the different levels, from which the depth of mining can be estimated (420 m). Furthermore, in the Discussion that follows the paper, it is explained that the outline of the surface cave closely follows the outline of the completed undercut, with the exception of the hangingwall where the cave extends beyond the footprint of the undercut. A plan view map showing the outline of the limit of fracturing is provided and the angles of caving and fracture initiation relative to the undercut are specified. Strain gauge measurements are also reported with respect to specifying the angle of subsidence.        Crest Sourc Cavin Summ No d sectio surfa possi four s footw fault.     more (Cali e: Long and g Period Re ary: Minin irect data is n is includ ce and a rou ble. The dep ides of the all side of  fornia, USA  Obert (195 ported: 193 g operations  provided in ed illustratin gh outline th of the un block to lim block exten ) 8) 0-1954  are reporte  the form o g the mini of the fractu dercut is 60 it the caving ded beyond  187 d for the b f subsidenc ng of Block re initiation  meters. Ver  angle. How  the cutoff lock caving e measurem  1A. Includ  from whic tical cutoff ever, the fr stope to alig of a dippin ents, but a ed are the h an estima stopes were acture initia n with a sh g limestone schematic c caved grou te of its ang  excavated o tion angle o allower dip  bed. ross- nd at le is n all n the ping   188 El Teniente (Chile) – South 1 & North 4 Source: Ovalle (1981), Kvapil et al. (1989) Caving Period Reported: 1940-1980 Summary: Mining operations at the El Teniente mine are reported for the panel caving of the South and North blocks from the Teniente 1 and 4 levels, respectively. No direct data is provided with respect to subsidence measurements, however two schematic cross-sections are included illustrating the mining of the North and South blocks. Shown are those caves already exhausted and those currently in production, together with the original and caved surface profiles. A similar cross-section for the North block is produced by Kvapil et al. but is less detailed. No scale bar is provided, but the different mine levels are shown from which the undercut depths can be estimated. Because the mine is positioned below a steep slope, with the South block being downslope of the North block, the depths to the respective undercut levels, Teniente 1 and 4, are approximately the same (510 and 540 m, respectively). The lower caving angles occur on the uphill side.    El Te Sourc Cavin Summ Leve funct vertic data t based made based topog curve niente (Ch e: Brown (2 g Period Re ary: A rev l, Regimien ion of depth al, graduall he curves ar  on observa  to the use o  on other so raphy). Fro s. ile) – Regim 003) ported: 198 iew of brea to Sector. C  along the y flattening e based on. tions of fra f numerica urces can be m this, the iento 4 2-1998 k angles is urves are p crater walls  towards su Similar curv cturing in g l models cal  estimated t caving ang 189 reported for rovided for . These show rface. Minim es for other alleries at d ibrated agai o be approx le at surfac  the caved  estimating  that angle al details a  sectors at E ifferent leve nst observa imately 250 e can be es zone above break angle s near the u re given wi l Teniente a ls. In this c tions. No de  m deep (av timated from  El Tenient s measured ndercut are th respect t re reported ase, referen pth is given eraging for  the respe e’s 4  as a  sub- o the to be ce is , but steep ctive  190 El Teniente (Chile) – Esmeralda Source: Rojas et al. (2001) Caving Period Reported: 1997-2001 Summary: Panel caving operations for the Esmeralda sector are reviewed. Included is a design chart of break angles as a function of height above the undercut, based on numerical models calibrated against crater geometry data and observations of fracturing in galleries at different elevations. Separate curves are provided for the uphill and downhill sides of the cave. A cross-section is also provided that depicts the caving angle and angle of fracture initiation referred to as the “influence level”. The undercut is located under steep slope at an average depth of approximately 800 m.        Finsc Sourc Cavin Summ Finsc occur pit th techn coinc h (South A e: Preece & g Period Re ary: Cave m h diamond s over a blo at had been iques. A cr ides with th frica)  Liebenberg ported: 200 anagemen mine. Cavi ck height of subsequentl oss-section e angles of t  (2007) 4-2006 t operations ng of the k  150 m that y deepened is provided, he already e 191  are reporte imberlite pi then opens by the minin  which show xisting crate d for the blo pe above th up into the b g of previo s the limit r. ck caving o e undercut ottom of a us blocks us s of the cav  f Block 4 a at 700 m d 550 m deep ing open sto ing zone, w t the epth open ping hich  Gath Sourc Cavin Summ suble Cavin The d a 100 break orebo    ’s (Zimbab e: Brown an g Period Re ary: Data i vels (99, 15 g occurs in epth of each  m deep ope  and surface dy coincide we) d Ferguson ported: 197 s provided 8 and 183  the hanging  level is var n pit slope.  tension cra  with the dip  (1979) 1-1976 for a sub-le Levels; bloc wall and ex iable as the A cross-sec cks for each  of the oreb 192 vel shrinka k caving is tends to sur  topography tion is provi  sub-level. C ody and foo ge stoping  planned fo face above  above is ste ded, which aving angl twall parall operation fo r subsequen the 40-50° ep across w shows the d es on the foo el jointing.  r three diff t deeper lev dipping oreb hat appears ifferent angl twall side o erent els). ody. to be es of f the  193 Grace (Pennsylvania, USA) Source: Sainsbury (2010) Caving Period Reported: 1958-1977 Summary: Subsidence observed after the closure of the Grace iron mine is reported following panel caving of the deposit from 1958 to 1977. Reported are surface observations together with survey data based on levelling measurements of subsidence pins. A subsidence map is provided showing the limits of surface cracking and the outlines of a lake that formed in the caving zone and the relative position of the undercut. Based on the approximate depth of the undercut, caving and fracture initiation angles can be estimated. It should be noted that cave breakthrough only occurred above one half of the undercut, facilitated by a steeply dipping fault.    Gran Sourc Cavin Summ suble appro sectio refere the c footw orebo    gesberg (Sw e: Hoek (19 g Period Re ary: Hangi vels (from 1 ximately 54 n showing t nces pointin aving, the lo all side is s dy and host eden) - 19 74) ported: 192 ngwall failu 40 to 300 m  m thick dip he caving a g to a Swed wer the cav hown to be  rock. 61 1-1961 res induced  depth) duri ping at 64° ngle for eac ish report a ing angle o  constant (w 194  by sub-lev ng the mini . Data is pro h sublevel. F s the origina n the hangi ith depth), el caving a ng of an iron vided in th ew addition l source. It ngwall side coincident w re reported  ore deposi e form of a al details ar was observe . The angle ith the con for six diff t. The orebo simplified c e provided, d that the de of caving o tact betwee erent dy is ross-  with eper n the n the   Gran Sourc Cavin Summ use Appr the ex appro meas coinc gesberg (Sw e: Sisselma g Period Re ary: Minin of both su oximately 7 tent of the ximately 5 urement of ident with th eden) - 19 n (1974) ported: 196 g operations blevel and 0% of the m caving zon 4 m thick surface subs e contact b 74 0-1975  at the Gra  block cav ining is by e relative to dipping at idence. The etween the o 195 ngesberg iro ing metho  block cavin  the undercu 64°. No de  angle of ca rebody and n ore mine ds dependi g. A cross- t level at 4 tails are pr ving on the host rock.   are describ ng on the section is p 10 m depth ovided with footwall sid ed, reportin  ore thick rovided sho . The orebo  respect to e is shown g the ness. wing dy is  the to be  196 Grasberg (Indonesia) – IOZ Source: Hubert et al. (2000), Barber et al. (2001) Caving Period Reported: 1980-2000 Summary: Block caving of P.T. Freeport’s Ertsberg East Skarn System is reported, including the operations for the Gunung Bijih Timur (GBT), Intermediate Ore Zone (IOZ) and Deep Ore Zone (DOZ) caving sectors. Focus is given to the IOZ. No direct data is provided in the form of subsidence measurements in either source, but scaled cross-sections are included showing the development of caving above the IOZ. Included are the boundaries of the caving zone relative to the undercut level at 650 m depth. The cross-section in Hubert et al. also includes the limits of fracture initiation referred to as the “subsidence zone”. The IOZ undercut is located under a steep slope, for which the lower caving angle corresponds with the uphill side.       Have Sourc Cavin Summ asbes inform cross toppl corre side a on th dip o   lock (Swaz e: Heslop ( g Period Re ary: Data tos operatio ation for d -section is p ing and su sponding to re seen to re e footwall fo f the foliatio iland) 1974) ported: 195 is reported n. The low epth is giv rovided, wh rface fractu  the develop main const otwall side n and beddi 2-1966 for three l ermost und en; estimate ich shows t ring above ment of the ant, while th  are likewise ng. 197 evels of a ercut is at s can be m he different  the hang  different le e zone of fr  shown as b shrinkage s approximat ade based o  angles of c ingwall for vels. Cavin acture initiat eing consta toping and ely 225 m n a scaled aving and e  different g angles on ion increase nt and align sublevel ca depth (no d cross-section xtent of fle periods of  the hanging s. Caving a ed parallel t  ving irect ). A xural time wall ngles o the  198 Henderson (Colorado, USA) – 8100 Source: Brumleve & Maier (1981), Stewart (1984) Caving Period Reported: 1976-1983 Summary: Subsidence at Henderson is reported by Stewart for panel caving of the 8100 Level along Panel 1. The cave zone is reported to have appeared on surface four years after caving was initiated, with cave growth and subsidence being measured using aerial photography, surface surveys and TDR. Data is provided in the form of a block diagram and subsidence maps showing the outline of the caving zone on surface relative to the undercut at 1050 m depth. A cross-section showing the caving angles extended from the undercut is provided by Brumleve & Maier in their description of the rock mass response to panel caving. These were used to estimate the angles of caving. Vertically spaced boundary cutoff drifts together with steeply dipping faults contributed to the vertical nature of the cave that developed. The caving zone was observed to not change in its direction despite the advance of the caveline, likely due to the controlling influence of topography and faulting.   Hend Sourc Cavin Summ minin m be form boun the d sectio steep    erson (Colo e: Rech et a g Period Re ary: An up g of the 77 low the 810 of subsiden daries of the ifferent leve n is roughl ly dipping fa rado, USA l. (2000) ported: 197 date on the 00 Level fo 0 Level at ce measure  caving zon ls are show y drawn to ults contrib ) – 7700 Le 6-2000 panel cavin llowing the approximate ments, but e above the n from wh  scale. Vert ute to the ve 199 vel g operations depletion of ly 1150 m a schematic  7700 Leve ich the sca ically space rtical nature  at Henerso  the 8100 L depth. No d  cross-secti l undercut. N le can be c d boundary  of the cave n is reporte evel. The 7 irect data is on is includ o scale bar alculated. It  cutoff drif  that develo d, describin 700 Level is  provided i ed showing  is provided  is assumed ts together ped. g the  100 n the  the , but  the with   Inspi Sourc Cavin Summ adjac block repor scale cavin  ration (Ari e: Hardwick g Period Re ary: The hi ent to the M  caving to o ted from an d cross-sect g angles can zona, USA) (1963) ported: 195 story of min iami block pen pit min  undercut 7 ion showing  be calculat  4 ing operatio  cave mine ing in 1954 0 m below  the outlin ed. 200 ns at Inspir . The report . Specificall  the pit bot es of the c ation is revi  includes d y, the block tom. Data i aving zone ewed; the In etails on the  caving of a s provided over time,  spiration mi  transition  transfer blo in the form from which ne is from ck is  of a  the  201 Jagersfontein (South Africa) Source: Stucke (1965) Caving Period Reported: 1947-1962 Summary: Plans to block cave a new lift at the Jagersfontein diamond mine are reported. The description includes a schematic cross-section showing the current block caving undercut level at 550 m depth and earlier workings, including an older open pit operation. The cross section shows that the limits of the caving zone roughly coincide with the boundaries of the kimberlite pipe and already existing crater. It is reported that approximately one million tonnes of waste rock from the crater walls slough into the crater each year.     Jenif Sourc Cavin Summ borat depth exten cavin and a Both One o contin occur   er (Californ e: Obert & g Period Re ary: Data e deposit, w  of 160 m w ded to surfa g of the ore  plan view show that t f the uniqu uous, steep red over the ia, USA) Long (1962 ported: 195 is reported here previo ith a block ce, althoug . A scaled cr map is prov he caved gr e features o -wall face. L  4.5 year pe ) 2-1957 for a single us mining w height of 70 h longhole oss-section ided showin ound propa f the caving ittle to no riod followi 202  block cav as by room  m. Caving blasting at is provided g subsidenc gated slight zone was th change in th ng the initia e experimen  and pillar  of the oreb intermediate showing a c e contours ly to the sou at its periph e peripheral l subsidence t in a thick . The under ody and ove  depths wa lear zone of (with 10’ co theast of th ery was ma  outline of t . , sub-horiz cut level is rlying cap r s required t  caving/coll ntour interv e undercut rked by a si he subsided ontal  at a ocks o aid apse, als). area. ngle,  area   King Sourc Cavin Summ descr and e is 275 on su inclu an ea angle    (Zimbabw e: Brumlev g Period Re ary: Block ibed. Cavin xtended tow  m. Schema rface relativ ding lines co rlier stage s on the foo e) e (1988), W ported: Non  caving of t g of the stee ards its 250 tic cross-se e to the un nnecting th of cave dev twall side of ilson 2000 e given (<1 he West Fl ply dipping  m high pe ctions are pr dercut on t e undercut t elopment.  the orebody 203 983 – 1988 ank (W11-1  orebody wa ak; the corre ovided in b he 276 Lev o surface fr Neither cro  are shown  ) 4 blocks) o s initiated b sponding av oth sources el. Wilson’s actures (frac ss-section in  to coincide f the King elow the fo erage depth showing the  section sh ture initiati cludes a sc with the dip asbestos mi ot of a steep  of the und  extent of ca ows more d on angle) bu ale bar. Ca  of the oreb ne is  hill ercut ving etail, t for ving ody.   204 Kiirunavaara/Kiruna (Sweden) - 1995 Source: Lupo (1997), Henry & Dahnér-Lindqvist (2000) Caving Period Reported: 1965-1995 Summary: Analysis of the progressive failure of the hangingwall and footwall at the Kiirunavaara iron ore sublevel cave mine is reported. The source papers briefly describe the history of hangingwall failures above the sublevel caving, and the more recent failure of the footwall (previous caving angles had coincided with the footwall contact of the orebody dipping at 60°). Lupo provides an air photo outlining the zones of caving, surface cracking and subsidence. The exact depth of the sublevel undercut for these zones is not reported but can be estimated as approximately 560 m depth. Henry & Dahnér-Lindqvist provide a scaled cross section for the same footwall failure event from which the undercut level and caving angle can be estimated. The caving angle on the footwall side coincides with the dip of the orebody, whereas the higher caving angle results from the overhanging nature of the dipping hangingwall. Values for the caving, fracture initiation and subsidence angles from these sources is also reviewed. .     205 Kiirunavaara/Kiruna (Sweden) - 2000 Source: Henry et al. (2004) Caving Period Reported: 1965-2000 Summary: The application of InSAR monitoring of mining-induced deformations is reported for the Kiirunavaara iron ore sublevel cave mine. The source largely focuses on InSAR principles, but includes a subsidence map of the caving, fracture initiation and subsidence zones. These are based on surface geodetic and benchmark surveys. The outline of the lowermost sublevel undercut for the measurement period (500 m depth) is not provided on the map, but can be approximated, from which the respective angles can be calculated. Caving, fracture initiation and subsidence angles on the footwall side are shown to coincide with one another at approximately 50°.        Kiiru Sourc Cavin Summ the K provi mode show orebo the f provi cavin side.  navaara/K e: Villegas g Period Re ary: A thes iirunavaara ded (rock lling results ing the exte dy for seve racture init ded, they ca g angles for iruna (Swe (2008) ported: 196 is study is r iron ore sub mass chara . A simplifi nt of the f ral different iation zone. n be approx  the same pe den) - 2005 5-2005 eported inv level cave m cteristics, p ed cross-sec arthest surfa  time period  Although imated from riod, or the 206  olving the n ine. A deta roperties an tion is also ce crack ob s. These are exact unde  the cross-  caving and umerical an iled descript d in situ  provided as served on  interpreted rcut depths section. No fracture init alysis of th ion of the m stresses), to  a form of the hanging  as represen  for each s indication i iation angle e hangingw odelling inp gether with model cons wall side o ting the lim ublevel are s given as t s on the foo  all at ut is  the traint f the its of  not o the twall  207 Koffiefontein (South Africa) Source: Hannweg (2001) Caving Period Reported: 1987-2001 Summary: Caving operations at the Koffiefontein diamond mine are reported, describing the use of a front caving method that combines aspects of block and sub-level caving. The undercut occurs at 480 m depth and caves into previous underground workings and the bottom of a deep open pit. This is shown in a schematic cross-section, from which the caving angles can be estimated. These are shown as being sub-vertical and confined within the limits of the pit bottom.       Lake Sourc Cavin Summ speci cases hangi cavin angle neces provi to be Case angle minin made refer the c inform partly   Superior D e: Crane (1 g Period Re ary: Data i fic reference ” reported, ngwall has g cases are s observed sarily the a ded for two  sublevel or B (also Typ  of caving o g depth. Re  to multiple to the block aving angle ation prov  obscures th istrict (Mic 929) ported: non s presented  to the min most appe occurred, a also includ undergroun ngles repre cases, show  block cavin e C), involv n the footwa ference is m  depths and  caving of l  extending ided sugges e caving an higan, USA e for several e location, m ar to invo lthough ind ed. Angles d with refer senting the ing example g mines. B ing an iron- ll side align ade to 300  sub-levels. enticular iro  from the ts a depth o d subsidenc 208 ) cases involv ining perio lve open s ication is of break ar ence to the extension o s of caving oth are with bearing form s with the d -400 m as a The second n ore depos undercut, b f 450 m, inc e zones at su  ing copper d or mining toping whe given that a e reported,  backs of h f caving to  and subside out scale b ation lying ip of the sla  minimum,  case (Case its. A cross ut again, n luding a thi rface. and iron m  method. Ba re failure  small num but these ar angingwall  surface. C nce at surfa ars. The firs on highly in tes. No dept although re C, Types D  section is p o scale is ck blanket o ines, but wi sed on the “ (caving) of ber of sub e defined a failures and ross-section ce, which ap t is describ clined slate h is given fo ferences are ,E,F), appea rovided sho provided. O f glacial til thout type  the level s the  not s are pear ed as . The r the  also rs to wing ther l that   Malm Sourc Cavin Summ meth multi as su invol direct inclu levels lower cavin hangi  berget (Sw e: Haglund g Period Re ary: Recov od referred ple use of su ch in the T ved a combi  data is pro ded showing  below. Th  levels actin g zone on t ngwall colla eden) & Heberg ( ported: 197 ery of a 1 to as ‘slot blevels, mo ables abov nation of sh vided in the  the bound e most relev g more lik he footwall pses into th 1975) 0-1974 60 m high blocking’. H re closely re e. Previous rinkage and  form of sub aries of the ant is the b e a sublevel side aligns e cave. 209 pillar is de owever, th sembles a s  and subse  sublevel sto sidence me caving zone lock caving  caving ope with the ore scribed usin e dipping ublevel cavi quent minin ping and su asurements,  on surface  of the 300 ration. The body conta g a modifi nature of t ng approach g of the ir blevel and b  but a scaled  relative to  Level (300 cross-sectio ct, whereas ed block ca he orebody  and is clas on ore dep lock caving  cross-secti several und  m depth), n shows tha the overhan ving  and sifies osits . No on is ercut with t the ging   210 Miami – 1928 (Arizona, USA) Source: Maclennan (1929) Caving Period Reported: 1926-1928 Summary: The source reports data from the block caving of two ore bodies, referred to as Main and Low Grade, together with a smaller block named Stope 11. Earlier mining was by shrinkage stoping and top slicing. At the time of reporting, mining of the Low Grade orebody was still in progress. The depths of the three undercuts vary from 180-195 m for ore blocks 65 to 120 m high. Boundary caving drifts were driven at suitable vertical intervals to limit the amount of caving beyond them. The south boundary of the Low Grade block caves into the already caved Main block. A plan view subsidence map and several cross-sections are provided showing the extent of measured subsidence on surface relative to the undercut level, including limiting scarps from which the angle of fracture initiation can be estimated. Caving angles and angles for fracture initiation are reported in the paper, but are measured from the top of the mined block (i.e. ore column); angles reported here, in the Tables above, have been corrected to be measured from the extraction level. Lower caving/fracture initiation angles for the Main and Low Grade blocks were observed to be sub-parallel to foliation of schist.   211        212 Miami – 1958 (Arizona, USA) Source: Fletcher (1960) Caving Period Reported: 1910-1958 Summary: This report updates the subsidence observations of MacLennan (1929) with an intermediate set of observations from 1939 and current measurements as of 1958. The data for 1939 involves a plan view map showing the limits of caving and fracture initiation relative to the caved ore bodies. This period continues the mining of the low grade orebody, as reported in 1929, from the same mining depth (approximately 195 m). As before, boundary caving drifts were driven at different vertical intervals to limit the amount of caving beyond them. Fletcher (1960) reports that the caving angles have flattened considerably since the 1929 set of measurements. The data reported for the mining period up to 1959 incorporates an extension of the High Grade orebody to greater depths through lifts at the 700 and 1000 (foot) Levels, with a bottom undercut at 300 m depth. Unlike previous blocks, those undercut at the 1000 Level were done so without the vertical boundary cutoff drifts. Scaled cross-sections are provided for the deeper lifts, showing the original topography, extent of subsidence, and surface scarps. It should be noted that although a large fault (the Miami fault) cuts across the deposit, separating the schist-hosted orebody from the conglomerate cap, it is not seen to have any influence on the caving or fracture initiation limits.     213   Mt. L Sourc Cavin Summ Lyell stopin under The l side i yell – Cave e: North & g Period Re ary: Subsid , including g. A schem cut at 160 m atter is desc s shown to c  Horn (Tas Callaghan ( ported: 197 ence related the Cape H atic cross-s  depth, tog ribed as a oincide wit mania, Aus 1980) 2-1980  to the min orn orebod ection is pro ether with th concentric p h the dip of 214 tralia) ing of sever y mined by vided that e angle of f attern of su the orebody al different  a combina shows the ex racture initi rface crack  (70°).  orebodies i tion of sub tent of cav ation above ing. Caving  s reported a level caving ing above th the hanging  on the foo t Mt.  and e #5 wall. twall  215 Northparkes (Australia) – E26 Lift 1 Source: Duffield (2000) Caving Period Reported: 1993-2000 Summary: The design of the second lift for the Northparkes’ E26 mine is reported. Included in this description is a geological cross-section showing the outline of the mined out Lift 1 block cave. No direct data is provided in the form of subsidence measurements, but caving angles for Lift 1 can be approximated from the cross-section supplemented by subsidence- related information in the source paper. Caving of Lift 1 involved the collapse of the crown pillar into an air gap beneath the cave back, owing in part to a change in the geology related to a gypsum leached zone. As a result, the cave angles are near vertical. The lift also caved into the bottom of a small open pit; the caving zone measured does not include ground disturbed due solely to open pit mining.   216 Palabora (South Africa) Source: Pretorius (2007) Caving Period Reported: 2001-2007 Summary: The effects of dilution resulting from a 130 million ton pit wall failure above an active block cave are reported. The block cave undercut is approximately 400 m below the bottom of the 800 m deep pit at a depth of 1200 m. The source reports the caving angles originally projected to open up into the floor of the pit, and the unexpected caving-induced triggering of a large pit wall failure. Physical and numerical modeling predicted a loss of around 30% of the original ore reserve. The source paper reports the caving angle at 86-88 degrees. The fracture initiation angle is projected with respect to the location of the back scarp of the rockslide behind the crest on the north wall of the pit.      217 Perseverance (WA, Australia) - 2000 Source: Jarosz et al. (2007) Caving Period Reported: 1994-2000 Summary: A report is provided on the use of InSAR to measure mining-induced deformations above a sublevel caving operation. Included is a cross-section that shows the caving profile above the sublevel undercut at 640 m depth (9920 Level). These underground operations are located below a large open pit with caving on the hangingwall side extending beyond the pit. InSAR data is also presented, however, no indication is given as to how the monitored displacements relate spatially to the undercut sublevels.     218 Perseverance (Australia) - 2004 Source: Tyler et al. (2004) Caving Period Reported: 1994-2004 Summary: Subsidence above the Perseverance sub-level caving nickel mine is reported. Subsidence maps are provided for several different years and mining levels, showing the limits of caving and fracture initiation based on the interpretation of air photographs, walk- over surveys and GPS/prism data. Caving and fracture initiation angles calculated based on stated mining depths and outlines of the caving levels relative to the outlines of caving on surface. Caving occurs beneath a large open pit with caving on the hangingwall side extending beyond the pit limits.     219 Questa (New Maxico,USA) Source: Gilbride (2005) Caving Period Reported: 1979-2005 Summary: Subsidence at the Questa mine related to historic block caving (Goathill orebody) and block caving of a new orebody (“D”) is reported. Data is provided for the measured historic subsidence over the Goathill orebody in the form of an air photo outlining the caving and fracture initiation zones, and limits of ground deformation (i.e. continuous subsidence zone). The respective angles are reported with reference to the undercut level at 300 m depth. The limits depicted are based on field measurements and air photo analysis. Incorporated in the subsidence zone is a shallow-seated slide undercut at its toe by the caving zone. A subsidence contour map is provided for the ground deformations over the D orebody, Panel 1 undercut (600 m depth). Deformations were measured by surface surveys across a grid. At the time of reporting, subsidence over Panel 1 was not developed enough to allow the measurement of the caving or fracture initiation angles. The subsidence magnitudes, however, were large enough to initiate large-scale sliding of the hillside above. Subsidence above the D Orebody was first detected in April 2003, 30 months after caving was initiated. Caving propagated to surface through 550 m of overburden at an average rate of 0.21 m per day.   220    221 Rajpura Dariba (India) Source: Singh (1993) Caving Period Reported: ? Summary: Numerical modelling of progressive hangingwall failure is reported, including a brief description of a case history of the Rajpura Dariba sublevel caving mine. No direct data is reported but the caving and fracture initiation angles on the hangingwall side of the orebody are reported together with the mining depth. The respective angles on the footwall side are assumed to be aligned with the 70° dip of the footwall.    Salva Sourc Cavin Summ is rep stable prese devel origin     dor (Chile) e: Escobar g Period Re ary: The in orted. This  arch had nted in the opment of t al topograp  & Tapia (20 ported: 199 vestigation involved the formed resu form of sub he collapse hy relative t 00) 5-1999 into the 199  sudden co lting in th sidence me  is provided o the underc 222 9 air blast ev llapse of the e developm asurements,  which incl ut level (at ent at the S  cave back ent of a la  but a scale udes the ou 700 m depth alvador pan in the Inca W rge void. N d cross-sect tline of the ). el cave oper est area a o direct da ion showin caving zone ation fter a ta is g the  and   223 San Giovanni (Italy) Source: Balia et al. (1990) Caving Period Reported: 1985-1990 Summary: Analysis of progressive hangingwall failure is reported for the San Giovanni lead- zinc mine. The mining methods employed include cut and fill stoping in the lower levels, and sub-level caving and shrinkage stoping in the upper levels. The undercut depth for the lowermost sublevel caving level is at 100 m depth. Data is provided in the form of a longitudinal cross-section and subsidence map outlining the caving zone. The caving angle calculated for the footwall side of the orebody approximately coincides with the dip of the footwall at 75-80°.    224  San Manuel (Arizona, USA) Source: Buchanan & Buchella (1960); Johnson & Soulé (1963) Caving Period Reported: 1956-1960 Summary: Data is reported for the block caving of the South orebody, Lift 1 (1450 Level undercut) from two different sources. The South ore body is the largest of the three ore bodies at San Manuel. The data from Johnson & Soulé (1963) provides more detail at a higher resolution and is the primary source used here. The undercut for Lift 1 is at a depth of 420 m with a block height of 180 m. At the time of reporting, only the central third of the ore zone has been caved. Surface subsidence data is provided in the form of a cross-section showing the subsidence profile for different intermediate stages of caving, several cross- sections showing the caving angle and angle of subsidence for different profiles above the undercut, and a subsidence contour map (with 25’ contour intervals) showing the limits of scarp development and surface cracking. Note that the definitions from Kantner (1934) are used with angle of subsidence referring to the limits of caving on surface and break angle being applied to the limit of visible cracking in the same section. These are interpreted here as referring to the caving and fracture initiation angles, respectively. A general recommendation was provided to assume a setback distance of 230 m of lateral distance on surface for each 300 m of depth mined in order to protect structures and ensure safety.   San M Sourc Cavin Summ 1 (Jo minin comp (1450 depth gradu appro under the f exten subsi withi The i cavin anuel (Ar e: Thomas g Period Re ary: Data i hnson & So g of Lift 2 rised of two  Level) was . Lift 2 for ally modifi ach was ap cuts effecti orm of sev sion of the dence profil n well estab ncreased de g zones for izona, USA (1971) ported: 195 s provided s ulé 1963), (2015 Level  blocks, We  at 420 m d the South o ed to follo plied to the vely resulte eral subside  caving zon es. Active s lished boun pth of Lift the North or ) 6-1970 ummarizing subsequent ), and data f st and East, epth, where rebody was w a panel  North oreb d in block b nce contou e with tim ubsidence f daries for Li  2 therefore ebody, Wes 225  that previo  data for it or the minin  separated b as the under  mined by caving typ ody, althou eing caved. r maps (w e, together or the South ft 2, with on  results in t and East, r usly reporte s completio g of the No y a 200 m p cut for Lift block cavin e sequencin gh the smal  Surface su ith 50’ con with scaled  orebody, L ly minor ac a steepening emained sep d for the So n in mid-19 rth orebody illar. The un 2 (2015 Lev g, although g. A simil l size of th bsidence da tour interva  cross-secti ift 2, is pri tivity outsid  of the cav arate.  uth orebody 62, data fo , Lift 1, whi dercut for L el) was at 6 the method ar panel ca e West and ta is provid ls) showing ons showing marily conta e this perip ing angles. , Lift r the ch is ift 1 05 m  was ving  East ed in  the  the ined hery.  The  226     227    Shab Sourc Cavin Summ repor from direct inclu under  ani (Zimba e: Wilson ( g Period Re ary: Block ted. Caving horizontal,  data is pro ded that out cut level. A bwe) 2000) ported: - 19  caving and  involves a with blocks vided in the lines the ca n average d 99  ground su n inclined u  being deve  form of sub ving zone a epth of 630 228 pport pract ndercut dip loped to tar sidence me bove two m m is shown ices at the ping at an get discrete asurements, ined blocks for the dippi Shabani as angle of ap , elongated  but a scaled  (52 and 5 ng undercut  bestos mine proximately pods of ore  cross-secti 8) relative t .  are  30° . No on is o the  Urad Sourc Cavin Summ heigh to its requi angle mine      (Colorado e: Kendrik g Period Re ary: Data i t of the ore  position un red to aid th  can be estim d (shrinkage , USA) (1970) ported: 196 s reported f varies from der a steep e caving pr ated assum  stoping) to 7-1969 or panel cav 60 to 210 m  slope. Co ocess. A sch ing the sket limit the ex  229 ing from th  and the ov nsiderable p ematic draw ch is to scal tent of the c e 1100 Lev erall depth v re-splitting ing is prov e. Vertical b aving zone. el of the U aries from 1 and induct ided from w oundary cu  rad deposit 20 to 300 m ion blasting hich the ca t-off stopes . The  due  was ving were   230 Appendix C: Depth-Dependent Material Properties used for Benchmark Testing of Numerical Methods for Modelling the Influence of Undercut Depth on Caving-Induced Subsidence The following tables provide in detail the input properties used in the benchmark study, varied as a function of depth. Values used for the FLAC3D modelling were similar except for the cohesion, friction and tension values which were scaled to 75% of those used in the 2-D modelling.  Table 1. Mohr-Coulomb rock mass properties derived for the 500 m deep undercut. Lithology σ3max (MPa) Erm (GPa) crm (MPa) φrm (°) Trm (MPa) Rhyolite 7.5 12.6 3.3 52 0.6 Quartz-Monzodiorite    below the undercut    south of South fault  30 5  7.0 7.0  6.5 1.9  34 49  1.8 0.4 Sandstone and Siltstone    below the undercut    south of South fault  45 30  10.2 10.2  9.1 6.9  32 35  2.5 1.8 Biotite Granodiorite    north of North fault    south of South fault  10 40  7.7 7.7  3.2 8.2  44 33  0.7 2.3  Table 2. Mohr-Coulomb rock mass properties derived for the 1000 m deep undercut. Lithology σ3max (MPa) Erm (GPa) crm (MPa) φrm (°) Trm (MPa) Rhyolite 15 12.6 5.3 47 1.1 Quartz-Monzodiorite    below the undercut    south of South fault  30 17.5  7.0 7.0  6.5 4.5  34 39  1.8 1.1 Sandstone and Siltstone    below the undercut    south of South fault  50 30  10.2 10.2  9.7 6.9  31 35  2.8 1.8 Biotite Granodiorite    north of North fault    south of South fault  17.5 45  7.7 7.7  4.7 8.9  40 32  1.1 2.5   231 Table 3. Mohr-Coulomb rock mass properties derived for the 1500 m deep undercut. Lithology σ3max (MPa) Erm (GPa) crm (MPa) φrm (°) Trm (MPa) Rhyolite 17.5 12.6 5.9 46 1.2 Quartz-Monzodiorite    below the undercut    south of South fault  30 20  7.0 7.0  6.5 4.9  34 38  1.8 1.2 Sandstone and Siltstone    below the undercut    south of South fault  50 25  10.2 10.2  9.7 6.1  31 37  2.8 1.5 Biotite Granodiorite    north of North fault    south of South fault  25 45  7.7 7.7  6.0 8.9  37 32  1.5 2.5  Table 4. Mohr-Coulomb rock mass properties derived for the 2000 m deep undercut. Lithology σ3max (MPa) Erm (GPa) crm (MPa) φrm (°) Trm (MPa) Rhyolite 17.5 12.6 5.9 46 1.2 Quartz-Monzodiorite    below the undercut    south of South fault  30 20  7.0 7.0  6.5 4.9  34 38  1.8 1.2 Sandstone and Siltstone    below the undercut    south of South fault 50 35  10.2 10.2  9.7 7.7  31 34  2.8 2.1 Biotite Granodiorite    north of North fault    south of South fault  40 40  7.7 7.7  8.2 8.2  33 33  2.3 2.3  The following tables provide in detail the input properties used in the benchmark study, including their variation with depth to account for increased strength with increasing confinement.    232 Appendix D: Representative Input Source Codes Used for Numerical Modelling Benchmark Study   233 D.1 ELFEN  Benchmark: 500m Deep Undercut  #  Material database    = cemi #  Material selected    = Sandstone and Siltstone-south Material_data { 4   Material_name {    "Sandstone and Siltstone-south"   }   Elastic_material_flags { NFGELA { 4 }   0 1 0 0   }   Elastic_properties { NMPRP { 15 }   1.02e+010 0 0 0.25    0 0 0 0 0 0 0 0 2700    0 0   }   Number_state_variables {    12   } } #  Material database    = cemi #  Material selected    = Quartz-Monsodiorite-Undercut Material_data { 5   Material_name {    "Quartz-Monsodiorite-Undercut"   }   Elastic_material_flags { NFGELA { 4 }   0 1 0 0   }   Elastic_properties { NMPRP { 15 }   7e+009  0 0 0.25    0 0 0 0 0 0 0 0 2700    0 0   }   Number_state_variables {    12   } } #  Material database    = cemi #  Material selected    = Biotite Granodiorite-north Material_data { 6   Material_name {    "Biotite Granodiorite-north"   }   Elastic_material_flags { NFGELA { 4 }  234   0 1 0 0   }   Elastic_properties { NMPRP { 15 }   7.7e+009 0 0 0.25    0 0 0 0 0 0 0 0 2700    0 0   }   Number_state_variables {    12   } } #  Material database    = cemi #  Material selected    = Rhyolite Material_data { 7   Material_name {    "Rhyolite"   }   Elastic_material_flags { NFGELA { 4 }   0 1 0 0   }   Elastic_properties { NMPRP { 15 }   1.26e+010 0 0 0.25    0 0 0 0 0 0 0 0 2700    0 0   }   Number_state_variables {    12   } } #  Material database    = cemi #  Material selected    = Quartz-Monsodiorite-south #  Non linear Criterion = mc_rc #     Non linear prop 1=cohesion #     Non linear prop 2=friction_angle #     Non linear prop 3=dilation #     Non linear prop 4=tensile #     Non linear prop 5=gf Material_data { 8   Material_name {    "Quartz-Monsodiorite-south"   }   Elastic_material_flags { NFGELA { 4 }   0 1 0 0   }   Elastic_properties { NMPRP { 15 }   7.0e+009 0 0 0.25    0 0 0 0 0 0 0 0 2700    0 0  235   }   Plastic_material_flags { NMFPLS { 2 }   0 19   }   Plastic_properties { NPRPLS { 5 }   1.9e6 49 5 0.35e6 63   }   Failure_material_flags { 3     0  2  1   }   Failure_properties { 1   0.002   }   Fracturing_material_flags { 2     0  1   }   Fracturing_properties { 1     0   }   Number_state_variables {    12   } } #  Material database    = cemi #  Material selected    = Biotite Granodiorite-north #  Non linear Criterion = mc_rc #     Non linear prop 1=cohesion #     Non linear prop 2=friction_angle #     Non linear prop 3=dilation #     Non linear prop 4=tensile #     Non linear prop 5=gf Material_data { 9   Material_name {    "Biotite Granodiorite-north"   }   Elastic_material_flags { NFGELA { 4 }   0 1 0 0   }   Elastic_properties { NMPRP { 15 }   7.7e+009 0 0 0.25    0 0 0 0 0 0 0 0 2700    0 0   }   Plastic_material_flags { NMFPLS { 2 }  236   0 19   }   Plastic_properties { NPRPLS { 5 }   3.2e6 44 5 0.7e6 63   }   Failure_material_flags { 3     0  2  1   }   Failure_properties { 1   0.002   }   Fracturing_material_flags { 2     0  1   }   Fracturing_properties { 1     0   }   Number_state_variables {    12   } } #  Material database    = cemi #  Material selected    = Rhyolite #  Non linear Criterion = mc_rc #     Non linear prop 1=cohesion #     Non linear prop 2=friction_angle #     Non linear prop 3=dilation #     Non linear prop 4=tensile #     Non linear prop 5=gf Material_data { 10   Material_name {    "Rhyolite"   }   Elastic_material_flags { NFGELA { 4 }   0 1 0 0   }   Elastic_properties { NMPRP { 15 }   12.6e+009 0 0 0.25    0 0 0 0 0 0 0 0 2700    0 0   }   Plastic_material_flags { NMFPLS { 2 }   0 19   }  237   Plastic_properties { NPRPLS { 5 }   3.3e6 52 5 0.55e6 63   }   Failure_material_flags { 3     0  2  1   }   Failure_properties { 1   0.002   }   Fracturing_material_flags { 2     0  1   }   Fracturing_properties { 1     0   }   Number_state_variables {    12   } } #  Material database    = cemi #  Material selected    = Sandstone and Siltstone-undercut #  Non linear Criterion = mc_rc #     Non linear prop 1=cohesion #     Non linear prop 2=friction_angle #     Non linear prop 3=dilation #     Non linear prop 4=tensile #     Non linear prop 5=gf Material_data { 2   Material_name {    "Sandstone and Siltstone-undercut"    }   Elastic_material_flags { NFGELA { 4 }   0 1 0 0   }   Elastic_properties { NMPRP { 15 }   10.2e+009 0 0 0.25    0 0 0 0 0 0 0 0 2700    0 0   }   Plastic_material_flags { NMFPLS { 2 }   0 19   }   Plastic_properties { NPRPLS { 5 }   9.1e6 32 5 2.5e6 63  238   }   Failure_material_flags { 3     0  2  1   }   Failure_properties { 1   0.002   }   Fracturing_material_flags { 2     0  1   }   Fracturing_properties { 1     0   }   Number_state_variables {    12   } } #  Material database    = cemi #  Material selected    = Quartz-Monsodiorite-south Material_data { 3   Material_name {    "Quartz-Monsodiorite-south"   }   Elastic_material_flags { NFGELA { 4 }   0 1 0 0   }   Elastic_properties { NMPRP { 15 }   7e+009  0 0 0.25    0 0 0 0 0 0 0 0 2700    0 0   }   Number_state_variables {    12   } }   239 D.2   UDEC  Benchmark: 500m Deep Undercut with Orthogonal Jointing at 0 and 90 Degrees  new  ro 0.5 set edge 5  ;config cell 2100 840  ;; commands for build model geometry ;------------------------------------------------------------- block 0 -700  0 3500  10500 3500  10500 -700  ;cal readprop.fis  ;--------------------------------------------------- ;; define regions for generate joints, generate density and assign properties,  jreg id 1 0,3500  4485,3500  4338.386,2750.876  0,2750.876  ;granodiorite jreg id 11 0,2750.876  4338.386,2750.876  4172.096,1901.222  0,1901.222 jreg id 12 0,1901.222  4172.096,1901.222  3800,-700  0,-700  jreg id 2 4485,3500  6180,3500  6180,2345  4338.386,2750.876  ;rhyolite between faults jreg id 3 4338.386,2750.876  6180,2345  6180,1500   4172.096,1901.222 ; qtz monzodiorite jreg id 4  4172.096,1901.222  6180,1500  6180,-700  3800,-700  ; sanstone/siltstone  jreg id 5 6180,3500  10500,3500  10500,2635  6180,2635  ;qtz monzodiorite right of fault jreg id 6 6180,2635  10500,2635  10500,2030  6180,2030  ; sandstone/siltstone jreg id 7 6180,2030  10500,2030  10500,-700  6180,-700  ; granodiorite ;------------------------------------------------------  ; faults crack 4485 3500 3800 -700 crack 6180 3500 6180 -700  ; jointing  jset 0,0  5000,0 0,0 100,0 range jreg 12 jset 90,0 5000,0 0,0 100,0 range jreg 12  jset 0,0  5000,0 0,0 100,0 range jreg 4 jset 90,0 5000,0 0,0 100,0 range jreg 4  jset 0,0  5000,0 0,0 100,0 range jreg 7 jset 90,0 5000,0 0,0 100,0 range jreg 7  jset 0,0  2000,0 0,0 50,0 range jreg 11 jset 90,0 2000,0 0,0 50,0 range jreg 11  jset 0,0  2000,0 0,0 50,0 range jreg 3 jset 90,0 2000,0 0,0 50,0 range jreg 3  jset 0,0  2000,0 0,0 50,0 range jreg 6 jset 90,0 2000,0 0,0 50,0 range jreg 6  jset 0,0  2000,0 0,0 50,0 range jreg 1  240 jset 90,0 2000,0 0,0 50,0 range jreg 1  jset 0,0  2000,0 0,0 50,0 range jreg 2 jset 90,0 2000,0 0,0 50,0 range jreg 2  jset 0,0  2000,0 0,0 50,0 range jreg 5 jset 90,0 2000,0 0,0 50,0 range jreg 5  ;elastic subsidence zone jreg id 17 2500,3300 4450,3300  4450,3000  2500,3000 jset 0,0  5000,0 0,0 25,0 range jreg 17 jset 90,0 1000,0 0,0 25,0 range jreg 17  jreg id 18 6050,3300 6180,3300  6180,3000  6050,3000 jset 0,0  5000,0 0,0 25,0 range jreg 18 jset 90,0 1000,0 0,0 25,0 range jreg 18  jreg id 19 6180,3300 8000,3300  8000,3000  6180,3000 jset 0,0  5000,0 0,0 25,0 range jreg 19 jset 90,0 1000,0 0,0 25,0 range jreg 19  jreg id 20 0,3300 2500,3300 2500,3500 0,3500 jset 0,0  5000,0 0,0 25,0 range jreg 20 jset 90,0 1000,0 0,0 25,0 range jreg 20  jreg id 21 8000,3300 10500,3300 10500,3500 8000,3500 jset 0,0  5000,0 0,0 25,0 range jreg 21 jset 90,0 1000,0 0,0 25,0 range jreg 21  ; plastic subsidence zone jreg id 14 2500,3300 4435,3300  4485,3500  2500,3500 jset 0,0  5000,0 0,0 12.5,0 range jreg 14 jset 90,0 1000,0 0,0 12.5,0 range jreg 14  jreg id 15 4435,3300 6180,3300  6180,3500  4485,3500 jset 0,0  5000,0 0,0 12.5,0 range jreg 15 jset 90,0 1000,0 0,0 12.5,0 range jreg 15  jreg id 16 6180,3300 8000,3300  8000,3500  6180,3500 jset 0,0  5000,0 0,0 12.5,0 range jreg 16 jset 90,0 1000,0 0,0 12.5,0 range jreg 16  ; ore column jreg id 13 4450,2900  6050,2900  6050,3300  4450,3300 jset 0,0  2000,0 0,0 12.5,0 range jreg 13 jset 90,0 500,0 0,0 12.5,0 range jreg 13  del area 2 jdelete  save orth-500-geom.sav  rest orth-500-geom.sav   ;--------------------------------- ; change rigid block into deformable gen edge 50 range jreg 17 gen edge 50 range jreg 18 gen edge 50 range jreg 19 gen edge 50 range jreg 20 gen edge 50 range jreg 21   241 gen edge 50 range jreg 13 gen edge 50 range jreg 14 gen edge 50 range jreg 15 gen edge 50 range jreg 16  gen edge 100  save orth-500-mesh.sav  rest orth-500-mesh.sav  ;-----------------------------  ;assign properties  ; define different properties of rocks prop mat 1 dens=2700 bulk=8.4e9 shear=5.1e9 coh 3.3e6  & fric 52  ten 0.6e6  dil 5 ;Rhyolite  prop mat 2 dens=2700 bulk=4.7e9 shear=2.8e9 coh 6.5e6  & fric 34  ten 1.8e6  dil 5 ;Quartz-Monzonite(Undercut)  prop mat 3 dens=2700 bulk=6.8e9 shear=4.1e9 coh 9.1e6  & fric 32  ten 2.5e6  dil 5 ;Sand & Silt(Undercut)  prop mat 4 dens=2700 bulk=5.1e9 shear=3.1e9 coh 3.2e6  & fric 44  ten 0.7e6  dil 5 ;Biotite(N of Fault)  prop mat 5 dens=2700 bulk=4.7e9 shear=2.8e9 coh 1.9e6  & fric 49  ten 0.4e6  dil 5 ;Quartz-Monzonite(S of Fault)  prop mat 6 dens=2700 bulk=6.8e9 shear=4.1e9 coh 6.9e6  & fric 35  ten 1.8e6  dil 5 ;Sand & Silt(S of Fault)  prop mat 7 dens=2700 bulk=5.1e9 shear=3.1e9 coh 8.2e6  & fric 33  ten 2.3e6  dil 5 ;Biotite(S of Fault)  prop mat 8 dens=2700 bulk=8.4e9 shear=5.1e9 coh 3.3e6  & fric 52  ten 0.6e6  dil 5 ;Panel A ore column Rhyolite  prop mat 9 dens=2700 bulk=8.4e9 shear=5.1e9 coh 3.3e6  & fric 52  ten 0.6e6  dil 5 ;Panel B ore column Rhyolite  prop mat 10 dens=2700 bulk=8.4e9 shear=5.1e9 coh 3.3e6  & fric 52  ten 0.6e6  dil 5 ;Panel C ore column Rhyolite  ; assign rock properties to different regions  change mat 4 cons 1 range jreg 1 change mat 4 cons 1 range jreg 11 change mat 4 cons 1 range jreg 12 change mat 4 cons 1 range reg 2500,3300 4435,3300 4485,3500 2500,3500 ; plastic change mat 4 cons 1 range reg 2500,3300 4450,3300 4450,3000 2500,3000  change mat 1 cons 1 range jreg 2 change mat 1 cons 3 range reg 4435,3300 6180,3300 6180,3500 4485,3500 ;plastic change mat 1 cons 3 range reg 6050,3300 6180,3300 6180,3000 6050,3000  change mat 2 cons 1 range jreg 3 change mat 3 cons 1 range jreg 4  change mat 5 cons 1 range jreg 5 change mat 5 cons 1 range reg 6180,3300 8500,3300 8500,3500 6180,3500 ;plastic  242 change mat 6 cons 1 range jreg 6 change mat 7 cons 1 range jreg 7  change mat 8 cons 1 range xr 5500 6000 yr 3000 3200 ;ore column - Panel A change mat 9 cons 1 range xr 5000 5500 yr 3000 3200 ;ore column - Panel B change mat 10 cons 1 range xr 4500 5000 yr 3000 3200 ;ore column - Panel C   ; assign properties for horizontal and vertical joint sets prop jmat 1 jkn=1e10 jks=1e9 jfric=30.0 jcoh=0.1 ;fault, joints change jmat 1 jcons 2  ;--------------boundary condition boun yvel=0 range 0 10500  -701 -699  ;bottom boun xvel=0 range -1 1 -700 3500      ; left boun xvel=0 range 10499 10501 -700 3500   ;right  ;---------------------------------------------- ;in situ stress ;(k=1.925 for y , k=1.222 for z)  insitu stress -181.9e6 0 -94.5e6 szz -115.4e6 &        ygrad 5.2e4, 0, 2.7e4 zgrad 0,3.3e4  set grav 0 -10  step 5000  sav ini-500-orth.sav  rest ini-500-orth.sav  reset displ jdispl vel rot hist  set ovtol 1  hist unbal   ; hist 1 hist ydis  500,3500 ;hist 2 hist ydis  10000,3500 ;hist 3  hist ydis  1000,3500 ;hist 4 hist ydis  9500,3500 ;hist 5  hist ydis  1500,3500 ;hist 6 hist ydis  9000,3500 ;hist 7  hist ydis  2000,3500 ;hist 8 hist ydis  8500,3500 ;hist 9  hist ydis  2500,3500 ;hist 10 hist ydis  8000,3500 ;hist 11  hist ydis  3000,3500 ;hist 12 hist ydis  7500,3500 ;hist 13  hist ydis  3500,3500 ;hist 14 hist ydis  7000,3500 ;hist 15  hist ydis  3750,3500 ;hist 16 hist ydis  7250,3500 ;hist 17  hist ydis  4000,3500 ;hist 18 hist ydis  6500,3500 ;hist 19  243  hist ydis  4250,3500 ;hist 20 hist ydis  6250,3500 ;hist 21  hist ydis  4500,3500 ;hist 22 hist ydis  6000,3500 ;hist 23  ; change to plastic  change mat 4 cons 3 range jreg 1 change mat 4 cons 1 range jreg 11 change mat 4 cons 1 range jreg 12  change mat 1 cons 3 range jreg 2 change mat 1 cons 3 range jreg 15;plastic  change mat 2 cons 1 range jreg 3 change mat 3 cons 1 range jreg 4  change mat 5 cons 3 range jreg 5 change mat 6 cons 1 range jreg 6 change mat 7 cons 1 range jreg 7  ;caved rock prop mat 20 dens=2300 bulk=0.1e9 shear=0.05e9  change mat 20 cons 1 range  5500 6000  3000 3020  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3020  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-A-20-orth.sav  change mat 20  cons 1 range  5500 6000  3000 3040  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3040  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-A-40-orth.sav  change mat 20  cons 1 range  5500 6000  3000 3060  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &  244         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3060  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-A-60-orth.sav  change mat 20  cons 1 range  5500 6000  3000 3080 change mat 20  cons 1 range  5000 5500  3000 3020  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3080 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3020  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-B-20-orth.sav  change mat 20  cons 1 range  5500 6000  3000 3100 change mat 20  cons 1 range  5000 5500  3000 3040  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3100 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3040  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-B-40-orth.sav  change mat 20  cons 1 range  5500 6000  3000 3100 change mat 20  cons 1 range  5000 5500  3000 3040  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3100 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3040  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone  245 change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-B-40-orth.sav  change mat 20  cons 1 range  5500 6000  3000 3120 change mat 20  cons 1 range  5000 5500  3000 3060  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3120 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3060  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-B-60-orth.sav  change mat 20  cons 1 range  5500 6000  3000 3140 change mat 20  cons 1 range  5000 5500  3000 3080 change mat 20  cons 1 range  4500 5000  3000 3020  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3140 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3080 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 4500,5000  3000,3020  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-C-20-orth.sav  change mat 20  cons 1 range  5500 6000  3000 3160 change mat 20  cons 1 range  5000 5500  3000 3100 change mat 20  cons 1 range  4500 5000  3000 3040  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3160 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3100 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &  246         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 4500,5000  3000,3040  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-C-40-orth.sav  change mat 20  cons 1 range  5500 6000  3000 3180 change mat 20  cons 1 range  5000 5500  3000 3120 change mat 20  cons 1 range  4500 5000  3000 3060  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3180 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3120 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 4500,5000  3000,3060  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-C-60-orth.sav  change mat 20  cons 1 range  5500 6000  3000 3200 change mat 20  cons 1 range  5000 5500  3000 3140 change mat 20  cons 1 range  4500 5000  3000 3080  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3200 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3140 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 4500,5000  3000,3080  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-C-80-orth.sav  return    247 D.3 UDEC  Benchmark: 500m Deep Undercut with Orthogonal Jointing at 45 and 135 Degrees  new  ro 0.1 ;config cell 2100 840  ;; commands for build model geometry ;------------------------------------------------------------- block 0 -700  0 3500  10500 3500  10500 -700  ;cal readprop.fis  ;--------------------------------------------------- ;; define regions for generate joints, generate density and assign properties,  jreg id 1 0,3500  4485,3500  4338.386,2750.876  0,2750.876  ;granodiorite jreg id 11 0,2750.876  4338.386,2750.876  4172.096,1901.222  0,1901.222 jreg id 12 0,1901.222  4172.096,1901.222  3800,-700  0,-700  jreg id 2 4485,3500  6180,3500  6180,2345  4338.386,2750.876  ;rhyolite between faults jreg id 3 4338.386,2750.876  6180,2345  6180,1500   4172.096,1901.222 ; qtz monzodiorite jreg id 4  4172.096,1901.222  6180,1500  6180,-700  3800,-700  ; sanstone/siltstone  jreg id 5 6180,3500  10500,3500  10500,2635  6180,2635  ;qtz monzodiorite right of fault jreg id 6 6180,2635  10500,2635  10500,2030  6180,2030  ; sandstone/siltstone jreg id 7 6180,2030  10500,2030  10500,-700  6180,-700  ; granodiorite ;------------------------------------------------------  ; faults crack 4485 3500 3800 -700 crack 6180 3500 6180 -700  ; jointing  jset 45,0  5000,0 0,0 200,0 range jreg 12 jset 135,0 5000,0 0,0 200,0 range jreg 12  jset 45,0  5000,0 0,0 200,0 range jreg 4 jset 135,0 5000,0 0,0 200,0 range jreg 4  jset 45,0  5000,0 0,0 200,0 range jreg 7 jset 135,0 5000,0 0,0 200,0 range jreg 7  jset 45,0  2000,0 0,0 50,0 range jreg 11 jset 135,0 2000,0 0,0 50,0 range jreg 11  jset 45,0  2000,0 0,0 50,0 range jreg 3 jset 135,0 2000,0 0,0 50,0 range jreg 3  jset 45,0  2000,0 0,0 50,0 range jreg 6 jset 135,0 2000,0 0,0 50,0 range jreg 6  jset 45,0  2000,0 0,0 50,0 range jreg 1 jset 135,0 2000,0 0,0 50,0 range jreg 1  jset 45,0  2000,0 0,0 50,0 range jreg 2 jset 135,0 2000,0 0,0 50,0 range jreg 2  248  jset 45,0  2000,0 0,0 50,0 range jreg 5 jset 135,0 2000,0 0,0 50,0 range jreg 5  ;elastic subsidence zone jreg id 17 2500,3300 4450,3300  4450,3000  2500,3000 jset 0,0  5000,0 0,0 20,0 range jreg 17 jset 90,0 1000,0 0,0 20,0 range jreg 17  jreg id 18 6050,3300 6180,3300  6180,3000  6050,3000 jset 0,0  5000,0 0,0 20,0 range jreg 18 jset 90,0 1000,0 0,0 20,0 range jreg 18  jreg id 19 6180,3300 8000,3300  8000,3000  6180,3000 jset 0,0  5000,0 0,0 20,0 range jreg 19 jset 90,0 1000,0 0,0 20,0 range jreg 19  jreg id 20 0,3300 2500,3300 2500,3500 0,3500 jset 0,0  5000,0 0,0 20,0 range jreg 20 jset 90,0 1000,0 0,0 20,0 range jreg 20  jreg id 21 8000,3300 10500,3300 10500,3500 8000,3500 jset 0,0  5000,0 0,0 20,0 range jreg 21 jset 90,0 1000,0 0,0 20,0 range jreg 21  ; plastic subsidence zone jreg id 14 2500,3300 4435,3300  4485,3500  2500,3500 jset 0,0  5000,0 0,0 10,0 range jreg 14 jset 90,0 1000,0 0,0 10,0 range jreg 14  jreg id 15 4435,3300 6180,3300  6180,3500  4485,3500 jset 0,0  5000,0 0,0 10,0 range jreg 15 jset 90,0 1000,0 0,0 10,0 range jreg 15  jreg id 16 6180,3300 8000,3300  8000,3500  6180,3500 jset 0,0  5000,0 0,0 10,0 range jreg 16 jset 90,0 1000,0 0,0 10,0 range jreg 16  ; ore column jreg id 13 4450,2900  6050,2900  6050,3300  4450,3300 jset 0,0  2000,0 0,0 10,0 range jreg 13 jset 90,0 500,0 0,0 10,0 range jreg 13  del area 5 jdelete  save ini-500-geom.sav  rest ini-500-geom.sav  ;--------------------------------- ; change rigid block into deformable gen edge 50 range jreg 17 gen edge 50 range jreg 18 gen edge 50 range jreg 19 gen edge 50 range jreg 20 gen edge 50 range jreg 21  gen edge 20 range jreg 13 gen edge 20 range jreg 14 gen edge 20 range jreg 15 gen edge 20 range jreg 16   249 gen edge 100  save ini-500-mesh.sav  rest ini-500-mesh.sav  ;-----------------------------  ;assign properties  ; define different properties of rocks prop mat 1 dens=2700 bulk=8.4e9 shear=5.1e9 coh 3.3e6  & fric 52  ten 0.6e6  dil 5 ;Rhyolite  prop mat 2 dens=2700 bulk=4.7e9 shear=2.8e9 coh 6.5e6  & fric 34  ten 1.8e6  dil 5 ;Quartz-Monzonite(Undercut)  prop mat 3 dens=2700 bulk=6.8e9 shear=4.1e9 coh 9.1e6  & fric 32  ten 2.5e6  dil 5 ;Sand & Silt(Undercut)  prop mat 4 dens=2700 bulk=5.1e9 shear=3.1e9 coh 3.2e6  & fric 44  ten 0.7e6  dil 5 ;Biotite(N of Fault)  prop mat 5 dens=2700 bulk=4.7e9 shear=2.8e9 coh 1.9e6  & fric 49  ten 0.4e6  dil 5 ;Quartz-Monzonite(S of Fault)  prop mat 6 dens=2700 bulk=6.8e9 shear=4.1e9 coh 6.9e6  & fric 35  ten 1.8e6  dil 5 ;Sand & Silt(S of Fault)  prop mat 7 dens=2700 bulk=5.1e9 shear=3.1e9 coh 8.2e6  & fric 33  ten 2.3e6  dil 5 ;Biotite(S of Fault)  prop mat 8 dens=2700 bulk=8.4e9 shear=5.1e9 coh 3.3e6  & fric 52  ten 0.6e6  dil 5 ;Panel A ore column Rhyolite  prop mat 9 dens=2700 bulk=8.4e9 shear=5.1e9 coh 3.3e6  & fric 52  ten 0.6e6  dil 5 ;Panel B ore column Rhyolite  prop mat 10 dens=2700 bulk=8.4e9 shear=5.1e9 coh 3.3e6  & fric 52  ten 0.6e6  dil 5 ;Panel C ore column Rhyolite  ; assign rock properties to different regions  change mat 4 cons 1 range jreg 1 change mat 4 cons 1 range jreg 11 change mat 4 cons 1 range jreg 12 change mat 4 cons 1 range reg 2500,3300 4435,3300 4485,3500 2500,3500 ; plastic change mat 4 cons 1 range reg 2500,3300 4450,3300 4450,3000 2500,3000  change mat 1 cons 1 range jreg 2 change mat 1 cons 3 range reg 4435,3300 6180,3300 6180,3500 4485,3500 ;plastic change mat 1 cons 3 range reg 6050,3300 6180,3300 6180,3000 6050,3000  change mat 2 cons 1 range jreg 3 change mat 3 cons 1 range jreg 4  change mat 5 cons 1 range jreg 5 change mat 5 cons 1 range reg 6180,3300 8500,3300 8500,3500 6180,3500 ;plastic change mat 6 cons 1 range jreg 6 change mat 7 cons 1 range jreg 7  change mat 8 cons 1 range xr 5500 6000 yr 3000 3200 ;ore column - Panel A change mat 9 cons 1 range xr 5000 5500 yr 3000 3200 ;ore column - Panel B  250 change mat 10 cons 1 range xr 4500 5000 yr 3000 3200 ;ore column - Panel C  ; assign properties for horizontal and vertical joint sets prop jmat 1 jkn=1e10 jks=1e9 jfric=30.0 jcoh=0.1 ;fault, joints change jmat 1 jcons 2  ;--------------boundary condition boun yvel=0 range 0 10500  -701 -699  ;bottom boun xvel=0 range -1 1 -700 3500      ; left boun xvel=0 range 10499 10501 -700 3500   ;right ;---------------------------------------------- ;in situ stress ;(k=1.925 for y , k=1.222 for z)  insitu stress -181.9e6 0 -94.5e6 szz -115.4e6 &        ygrad 5.2e4, 0, 2.7e4 zgrad 0,3.3e4  set grav 0 -10  step 5000  sav ini-500.sav  rest ini-500.sav  reset displ jdispl vel rot hist  set ovtol 1  hist unbal   ; hist 1 hist ydis  500,3500 ;hist 2 hist ydis  10000,3500 ;hist 3  hist ydis  1000,3500 ;hist 4 hist ydis  9500,3500 ;hist 5  hist ydis  1500,3500 ;hist 6 hist ydis  9000,3500 ;hist 7  hist ydis  2000,3500 ;hist 8 hist ydis  8500,3500 ;hist 9  hist ydis  2500,3500 ;hist 10 hist ydis  8000,3500 ;hist 11  hist ydis  3000,3500 ;hist 12 hist ydis  7500,3500 ;hist 13  hist ydis  3500,3500 ;hist 14 hist ydis  7000,3500 ;hist 15  hist ydis  3750,3500 ;hist 16 hist ydis  7250,3500 ;hist 17  hist ydis  4000,3500 ;hist 18 hist ydis  6500,3500 ;hist 19  hist ydis  4250,3500 ;hist 20 hist ydis  6250,3500 ;hist 21  hist ydis  4500,3500 ;hist 22 hist ydis  6000,3500 ;hist 23   251 ; change to plastic  change mat 4 cons 3 range jreg 1 change mat 4 cons 1 range jreg 11 change mat 4 cons 1 range jreg 12  change mat 1 cons 3 range jreg 2 change mat 1 cons 3 range jreg 15;plastic  change mat 2 cons 1 range jreg 3 change mat 3 cons 1 range jreg 4  change mat 5 cons 3 range jreg 5 change mat 6 cons 1 range jreg 6 change mat 7 cons 1 range jreg 7  ;caved rock prop mat 20 dens=2300 bulk=0.1e9 shear=0.05e9  change mat 20 cons 1 range  5500 6000  3000 3020  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3020  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-A-20.sav  change mat 20  cons 1 range  5500 6000  3000 3040  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3040  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-A-40.sav  change mat 20  cons 1 range  5500 6000  3000 3060  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3060  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  252  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-A-60.sav  change mat 20  cons 1 range  5500 6000  3000 3080 change mat 20  cons 1 range  5000 5500  3000 3020  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3080 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3020  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-B-20.sav  change mat 20  cons 1 range  5500 6000  3000 3100 change mat 20  cons 1 range  5000 5500  3000 3040  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3100 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3040  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-B-40.sav  change mat 20  cons 1 range  5500 6000  3000 3100 change mat 20  cons 1 range  5000 5500  3000 3040  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3100 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3040  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  253  step 5000 save 500-B-40.sav  change mat 20  cons 1 range  5500 6000  3000 3120 change mat 20  cons 1 range  5000 5500  3000 3060  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3120 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3060  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-B-60.sav  change mat 20  cons 1 range  5500 6000  3000 3140 change mat 20  cons 1 range  5000 5500  3000 3080 change mat 20  cons 1 range  4500 5000  3000 3020  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3140 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3080 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 4500,5000  3000,3020  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-C-20.sav  change mat 20  cons 1 range  5500 6000  3000 3160 change mat 20  cons 1 range  5000 5500  3000 3100 change mat 20  cons 1 range  4500 5000  3000 3040  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3160 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3100 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 4500,5000  3000,3040  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  254  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-C-40.sav  change mat 20  cons 1 range  5500 6000  3000 3180 change mat 20  cons 1 range  5000 5500  3000 3120 change mat 20  cons 1 range  4500 5000  3000 3060  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3180 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3120 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 4500,5000  3000,3060  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-C-60.sav  change mat 20  cons 1 range  5500 6000  3000 3200 change mat 20  cons 1 range  5000 5500  3000 3140 change mat 20  cons 1 range  4500 5000  3000 3080  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3200 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3140 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 4500,5000  3000,3080  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-C-80.sav  change mat 20  cons 1 range  5500 6000  3000 3200 change mat 20  cons 1 range  5000 5500  3000 3160 change mat 20  cons 1 range  4500 5000  3000 3100  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3200 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3160 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 4500,5000  3000,3100  255  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-C-100.sav  change mat 20  cons 1 range  5500 6000  3000 3200 change mat 20  cons 1 range  5000 5500  3000 3180 change mat 20  cons 1 range  4500 5000  3000 3120  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3200 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3180 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 4500,5000  3000,3120  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-C-120.sav  change mat 20  cons 1 range  5500 6000  3000 3200 change mat 20  cons 1 range  5000 5500  3000 3200 change mat 20  cons 1 range  4500 5000  3000 3140  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3200 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3200 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 4500,5000  3000,3140  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-C-140.sav  change mat 20  cons 1 range  5500 6000  3000 3200 change mat 20  cons 1 range  5000 5500  3000 3200 change mat 20  cons 1 range  4500 5000  3000 3160   256 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3200 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3200 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 4500,5000  3000,3160  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-C-160.sav  change mat 20  cons 1 range  5500 6000  3000 3200 change mat 20  cons 1 range  5000 5500  3000 3200 change mat 20  cons 1 range  4500 5000  3000 3180  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3200 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3200 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 4500,5000  3000,3180  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000 save 500-C-180.sav  change mat 20  cons 1 range  5500 6000  3000 3200 change mat 20  cons 1 range  5000 5500  3000 3200 change mat 20  cons 1 range  4500 5000  3000 3200  insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5500,6000  3000,3200 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 5000,5500  3000,3200 insitu stress  -23.7e6,0, -71.3e6 szz -23.7e6 &         ygrad 7.67e3, 0, 2.3e4 zgrad 0,7.67e3 range 4500,5000  3000,3200  prop jmat 1 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0; subsidence zone change jmat 1 jcons 2  prop jmat 2 jkn=1e9 jks=1e8 jfric=30.0 jcoh=0;block height change jmat 2 jcons 2 range xr 4500 6000 yr 3010 3300  prop jmat 3 jkn=1e9 jks=1e8 jfric=40.0 jcoh=0 change jmat 3 jcons 2 range xr 0 10000 yr -700 3010  step 5000  257 save 500-C-200.sav return   258 D.4 FLAC3D Benchmark: 500m Deep Undercut  new rest mesh.sav  model mohr prop density 2700 bulk 5.1e9 shear 3.1e9    coh 2.4e6  fric 33  ten 0.5e6 dil 5 range group Biotite-granodiorite-NofF prop density 2700 bulk 5.1e9 shear 3.1e9    coh 6.2e6  fric 25  ten 1.7e6 dil 5 range group Biotite-granodiorite-SofF prop density 2700 bulk 8.4e9 shear 5.1e9    coh 2.5e6  fric 39  ten 0.5e6 dil 5 range group Rhyolite prop density 2700 bulk 4.7e9 shear 2.8e9    coh 1.4e6  fric 37  ten 0.3e6 dil 5 range group Quartz-Montonite-SofF prop density 2700 bulk 4.7e9 shear 2.8e9    coh 4.9e6  fric 26  ten 1.4e6 dil 5 range group Quartz-Montonite-undercut prop density 2700 bulk 4.7e9 shear 2.8e9    coh 4.9e6  fric 26  ten 1.4e6 dil 5 range group Quartz-Montonite-WofF prop density 2700 bulk 6.8e9 shear 4.1e9    coh 5.2e6  fric 26  ten 1.4e6 dil 5 range group Sandstone-Siltstone-SofF prop density 2700 bulk 6.8e9 shear 4.1e9    coh 6.8e6  fric 24  ten 2e6 dil 5 range group Sandstone-Siltstone-undercut  inter 1 prop kn 1e9 ks 1e8 fric 30 coh 0.1 inter 2 prop kn 1e9 ks 1e8 fric 30 coh 0.1 inter 3 prop kn 1e9 ks 1e8 fric 30 coh 0.1      ini szz  -81e6 grad 0 0 2.7e4     ini syy  -155.92e6 grad 0 0 5.2e4 ;1.925     ini sxx  -98.98e6 grad 0 0 3.3e4  ;1.222      fix x range x -2010.1 -1900.1     fix x range x 7899.9 8100.1     fix y range y -10.1 100.1     fix y range y 7999.9 8000.1     fix z range z -10.1 100.1      set gravity 0 0 -10  hist unbal solve  save mesh-ini.sav  cal cave.dat  new rest mesh-ini.sav set large ini xdis=0 ydis=0 zdis=0  model elas range x 3500 4500 y 3250 3750 z 2500 2550 prop  density 2300 bulk 2e8 shear 1e8 range x 3500 4500 y 3250 3750 z 2500 2550     ini szz  -58.65e6 grad 0 0 2.3e4 range  x 3500 4500 y 3250 3750 z 2500 2550     ini syy  -19.55e6 grad 0 0 7.67e3 range  x 3500 4500 y 3250 3750 z 2500 2550     ini sxx  -19.55e6 grad 0 0 7.67e3 range  x 3500 4500 y 3250 3750 z 2500 2550  solve  save 500-step1.sav  ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;   259 model elas range x 3500 4500 y 3250 3750 z 2500 2600 prop  density 2300 bulk 2e8 shear 1e8 range x 3500 4500 y 3250 3750 z 2500 2600      ini szz  -59.8e6 grad 0 0 2.3e4 range  x 3500 4500 y 3250 3750 z 2500 2600     ini syy  -19.9e6 grad 0 0 7.67e3 range x 3500 4500 y 3250 3750 z 2500 2600     ini sxx  -19.9e6 grad 0 0 7.67e3 range x 3500 4500 y 3250 3750 z 2500 2600  model elas range x 3500 4500 y 3750 4250 z 2500 2550 prop  density 2300 bulk 2e8 shear 1e8 range x 3500 4500 y 3750 4250 z 2500 2550      ini szz  -58.65e6 grad 0 0 2.3e4 range  x 3500 4500 y 3750 4250 z 2500 2550     ini syy  -19.55e6 grad 0 0 7.67e3 range  x 3500 4500 y 3750 4250 z 2500 2550     ini sxx  -19.55e6 grad 0 0 7.67e3 range  x 3500 4500 y 3750 4250 z 2500 2550  solve save 500-step2.sav  ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; model elas range x 3500 4500 y 3250 3750 z 2500 2650 prop  density 2300 bulk 2e8 shear 1e8 range x 3500 4500 y 3250 3750 z 2500 2650      ini szz  -60.95e6 grad 0 0 2.3e4 range  x 3500 4500 y 3250 3750 z 2500 2650     ini syy  -20.32e6 grad 0 0 7.67e3 range  x 3500 4500 y 3250 3750 z 2500 2650     ini sxx  -29.32e6 grad 0 0 7.67e3 range  x 3500 4500 y 3250 3750 z 2500 2650  model elas range x 3500 4500 y 3750 4250 z 2500 2600 prop  density 2300 bulk 2e8 shear 1e8 range x 3500 4500 y 3750 4250 z 2500 2600      ini szz  -59.8e6 grad 0 0 2.3e4 range  x 3500 4500 y 3750 4250 z 2500 2600     ini syy  -19.9e6 grad 0 0 7.67e3 range x 3500 4500 y 3750 4250 z 2500 2600     ini sxx  -19.9e6 grad 0 0 7.67e3 range x 3500 4500 y 3750 4250 z 2500 2600  model elas range x 3500 4500 y 4250 4750 z 2500 2550 prop  density 2300 bulk 2e8 shear 1e8 range x 3500 4500 y 4250 4750 z 2500 2550      ini szz  -58.65e6 grad 0 0 2.3e4 range  x 3500 4500 y 4250 4750 z 2500 2550     ini syy  -19.55e6 grad 0 0 7.67e3 range  x 3500 4500 y 4250 4750 z 2500 2550     ini sxx  -19.55e6 grad 0 0 7.67e3 range  x 3500 4500 y 4250 4750 z 2500 2550  solve save 500-step3.sav ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;  model elas range x 3500 4500 y 3250 3750 z 2500 2700 prop  density 2300 bulk 2e8 shear 1e8 range x 3500 4500 y 3250 3750 z 2500 2700      ini szz  -62.1e6 grad 0 0 2.3e4 range x 3500 4500 y 3250 3750 z 2500 2700     ini syy  -20.7e6 grad 0 0 7.67e3 range x 3500 4500 y 3250 3750 z 2500 2700     ini sxx  -20.7e6 grad 0 0 7.67e3 range x 3500 4500 y 3250 3750 z 2500 2700  model elas range x 3500 4500 y 3750 4250 z 2500 2650 prop  density 2300 bulk 2e8 shear 1e8 range x 3500 4500 y 3750 4250 z 2500 2650      ini szz  -60.95e6 grad 0 0 2.3e4 range  x 3500 4500 y 3750 4250 z 2500 2650     ini syy  -20.32e6 grad 0 0 7.67e3 range  x 3500 4500 y 3750 4250 z 2500 2650     ini sxx  -29.32e6 grad 0 0 7.67e3 range  x 3500 4500 y 3750 4250 z 2500 2650  model elas range x 3500 4500 y 4250 4750 z 2500 2600 prop  density 2300 bulk 2e8 shear 1e8 range x 3500 4500 y 4250 4750 z 2500 2600      ini szz  -59.8e6 grad 0 0 2.3e4 range  x 3500 4500 y 4250 4750 z 2500 2600     ini syy  -19.9e6 grad 0 0 7.67e3 range x 3500 4500 y 4250 4750 z 2500 2600     ini sxx  -19.9e6 grad 0 0 7.67e3 range x 3500 4500 y 4250 4750 z 2500 2600  260  solve save 500-step4.sav  261 Appendix E: Major Lithological Units at Palabora and Summary of their Assessed Rock Mass Characteristics, Used to Develop the FLAC3D Palabora Model Unit Geological Description Rock Mass Characteristics Carbonatite Igneous rock composed predominantly of carbonate minerals. Represented by two mineralogically similar units: a fine-grained Transgressive Carbonatite, which lacks significant foliation, and a medium- to coarse- grained Banded Carbonatite with vertical to steeply dipping foliation. Both units are relatively strong, with average UCS values of 120 MPa. They are described as being moderately fractured to massive (GSI 50 to 75) with mostly vertical jointing. Both are treated as one unit within the numerical model given their complex boundary contact and similar rock mass properties. Foskorite Coarse-grained ultra-basic igneous rock composed of olivine, magnetite, apatite and phlogopite. It occurs on all walls as a broad zone between the Pyroxenite and the Carbonatite. Typically strong and competent with an average UCS of 90 MPa. This unit is described as being moderately to highly fractured (GSI 45 to 75) with mostly vertical jointing. Pyroxenite Ultramafic igneous rock consisting essentially of minerals of the pyroxene group. Represented by two units: Feldspathic and Micaeous Pyroxenite. Feldspathic Pyroxenite occurs in limited quantities, primarily on the north and west sides of the pit. Micaceous Pyroxenite occupies a large portion of the north, west and east walls as well as a narrow band within the south wall. The UCS of Feldspathic pyroxenite is typically higher than the Micaceous, with average values of 100 and 85 MPa, respectively. These units are described as being highly fractured to massive (GSI 45 to 65) with mostly vertical jointing. Both are treated within the numerical model as one geomechanical unit. Glimmerite An ultrabasic igneous rock, consisting almost wholly of essential dark mica, either phlogopite or biotite. Occurs in limited quantities on the western side and southwest corner of the pit. Highly variable strength, with an average UCS of 40 MPa. This unit is described as being highly fractured and sheared (GSI 35 to 50) with mostly vertical jointing. Glimmerite represents the weakest rockmass material present. Fenite Na- and K-rich silicate rock developed through alteration of the Archean granite contact. Fenite occupies a large portion of the South Wall and a narrow band behind the western and north- western pit crest. A hard, strong rock with an average UCS of 200 MPa. This unit is described as being moderately fractured (GSI 50 to 75) with mostly both vertical and horizontal jointing. Granite Medium to coarse grained intrusive, felsic, igneous rock. The Archean granite surrounds the complex and occupies a small section of the upper southwest pit wall. A hard, strong rock with an average UCS of 200 MPa. This unit was described as being relatively massive (GSI 70 to 80).    

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