(phd thesis) a model for cave propagation and subsidence assessment in jointed rock masses

8/10/2019 (Phd Thesis) a Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses

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A MODEL FOR CAVE PROPAGATION AND SUBSIDENCE

ASSESSMENT IN JOINTED ROCK MASSES

Bre-Anne Sainsbury

B.E. (Geological Engineering) Royal Melbourne Institute of Technology

M.E. (Mining) The University of New South Wales

A Thesis submitted to The University of New South Wales in fulfilment of the

requirements for the degree Doctor of Philosophy

August 2012



ORIGINALITY STATEMENT

I hereby declare that this thesis is my own work and that, to the best of my

knowledge, it contains no materials previously published or written by another

person, or substantial proportions of material which have been accepted for the

award of any other degree or diploma at UNSW or any other educational

institution, except where due acknowledgment is made within the thesis. Any

contribution made to the research by others, with whom I have worked at UNSW

or elsewhere, is explicitly acknowledged. I also declare that the intellectual content

of the thesis is the product of my own work unless otherwise acknowledged.

COPYRIGHT STATEMENT

I hereby grant The University of New South Wales or its agents the right to archive

and to make available my thesis or dissertation in whole or part in the University

libraries in all forms of media, now or here after known, subject to the provisions

of the Copyright Act 1968. I retain all proprietary rights, such as patent rights. I

also retain the right to use in future works (such as articles or books) all or part of

this thesis or dissertation. I also authorise University Microfilms to use the 350

word abstract of my thesis in Dissertation Abstract International. I have either

used no substantial portions of copyright material in my thesis or I have obtained

permission to use copyright material.

AUTHENTICITY STATEMENT

I certify that the Library deposit digital copy is a direct equivalent of the finalofficially approved version of my thesis. No emendation of content has occurred

and if there are any minor variations in formatting, they are the result of the

conversion to digital format.



ACKNOWLEDGEMENTS

The Author wishes to thank the following persons/organisations for directly and

indirectly providing assistance, support and guidance during the research.

Dr. David Sainsbury, my long suffering husband, for encouraging me to complete

this body of work and providing support along the way. In addition to being a

great husband and father you are also a remarkable engineer.

The research presented herein builds upon the initial work completed by Dr. Loren

Lorig, Dr. Mark Board, Dr. Peter Cundall and Dr. Matthew Pierce, from Itasca

Consulting Group, completed during the International Caving Study (ICS I and ICS

II) and Mass Mining Technology (MMT I) Project. My thanks for their initial work

and their ongoing support, input and interest in caving mechanics.

Thanks to the Mass Mining Technology (MMT II) Sponsors for providing financial

support to complete this body of work and for their provision of data for some of

the case-study applications. In particular, thanks to Dr. Andrew Haile and Dr.

Jonny Sjoberg who were the caving mechanics area monitors and devoted many

hours to reviewing this research.

I would also like to thank Professor Bruce Hebblewhite and Dr. Rudrajit Mitra from

the Mining Engineering Department of the University of New South Wales who

supervised the research. My thanks for your continued support and guidance.



ABSTRACT

Cave mining methods allow for the bulk extraction of large, low grade orebodies in

a cost effective manner. The fundamental mechanics of caving involves the self-

propagating yield (failure) of an in situ rock mass in response to production draw

from a mining horizon located at depth. Since the inception of large-scale

mechanised cave mining methods in the iron ore mines of northern Michigan, USA,

during the early part of the 20th century, researchers have sought to understand

and predict the nature of cave propagation through simple one-dimensional

volume based relationships and empirical methods. Although historically these

methods have successfully been applied to many cave operations, numerical

modelling is considered to be able to provide a more fundamental, rigorous and

robust assessment of cave propagation behaviour now and in the future.

A numerical model for cave propagation and subsidence assessment has been

developed based on fundamental rock mass behaviour and the development of

numerical modelling techniques. Unlike most existing techniques, the cave

volume is not introduced manually into the model; rather it is allowed to develop

based on the specified mass-based production schedule, evolving stress conditions

and the simulated constitutive behaviour of the rock mass. In doing so, hang-ups,

over-breaks and rapid advance rates can all be predicted.

The resulting numerical model is able to accurately capture rock mass strength

and deformation modulus anisotropy and scale effects as well as the effect of large-

scale discontinuities on cave propagation behaviour. In addition, the strain-

softening and bulking behaviour during the complex process of caving induced

yield and mobilisation is also considered. A production draw algorithm has been

developed that accurately reflects the mass withdrawn and drawpoint production

variability for all cave mining methods; block, panel and sub-level caving. This

algorithm is complemented by an algorithm that updates the evolving ground

surface profile to reflect the development of a crater. The methodology has been

applied to four large-scale case study back-analyses that provide validation of the

numerical techniques and assessment criteria.



iiA Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses

The Synthetic Rock Mass (SRM) Modelling Approach ....................... ..................... 662.2.3

2.2.3.1 Application of Synthetic Rock Mass Modelling for Cave Propagation

Assessment ......................................................................................................................... 71

2.2.3.2 Summary ........................ ....................... ..................... ...................... ..................... ............... 76

RESEARCH OUTLINE ............................................................................................................................... 783

3.1 Objectives ...................... ........................ ...................... ....................... .................... ........................ ..... 78

3.2 Methodology ...................... ....................... ........................ ........................ .................... ..................... 80

Simulation of Rock Mass Response to Cave Propagation ...................................... 813.2.1

3.2.1.1 Rock Mass Cohesion/Tension Softening and Post-Peak Brittleness .......... 81

3.2.1.2 Rock Mass Dilation ....................... ...................... ....................... ........................ .............. 81

3.2.1.3 Rock Mass Deformation Modulus Softening ......................... ........................ ....... 81

3.2.1.4 Simulation of Large-Scale Discontinuities ..................... ........................ ................ 82

Production Draw Simulation ...................... ........................ ....................... ........................ 823.2.2

3.2.2.1 Mass-Based Production Draw Algorithm ....................... ....................... ................. 82

3.2.2.2 Development of an Algorithm to Update Ground Surface Profile ................ 83

3.2.2.3 Sub-Level Caving Algorithm ............................ .................... ....................... ................. 83

Validation ................................................................................................................................... 833.2.3

DEVELOPMENT OF A CAVE PROPAGATION DEMONSTRATION MODEL ....................... .. 854

4.1 Geomechanical Conditions ............................ ..................... ....................... ........................ ........... 85

4.2 Production Draw Simulation .......................... ..................... ........................ ....................... ........ 86

4.3 Cave Propagation Sensitivity Studies ....................... ....................... ....................... ................. 87

Effect of Rock Mass Peak Strength on Cave Propagation ...................... ................. 874.3.1

Effect of Post-Peak Softening Rate on Cave Propagation ..................... .................. 914.3.2

Effect of Estimation of mi value on Cave Propagation ....................... ...................... 934.3.3

Effect of Stress/Depth on Cave Propagation ....................... ....................... ................. 954.3.4

4.4 Summary ....................... ...................... ....................... ........................ ...................... ...................... ..... 97

DEVELOPMENT OF THE UBIQUITOUS JOINT ROCK MASS MODEL (UJRM) .................. .. 985

5.1 Establishment of a Standard Laboratory Environment ....................... ....................... ... 101

Sample Geometry and Generation.................................................................................1015.1.1

Sample Zone Resolution ...................... ...................... ....................... ........................ .........1035.1.2

Sample Loading Conditions ....................... ....................... ....................... ....................... ..1045.1.3

Large Strain/Small-strain Calculation Mode................................... ....................... ...1065.1.4

5.2 Calibration of UJRM Response ......................... ..................... ....................... ........................ ..... 108

Summary of SRM Responses............................................................................................1085.2.1

5.2.1.1 Intact Calibration ...................... ...................... ....................... ........................ .................108



iiiA Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses

5.2.1.2 Discrete Fracture Network ......................... ...................... ........................ ..................109

5.2.1.3 Estimated Joint Strength ........................ .................... ....................... ...................... ....111

5.2.1.4 SRM Simulation Results .......................... .................... ........................ ....................... ..112

Calibration of Deformation Modulus and Poisson’s ratio ......................... ...........1125.2.2

Calibration of Matrix Friction, Cohesion and Tension ........................... ...............1125.2.3

Calibration of Ubiquitous Joint Properties ....................... ........................ .................1135.2.4

Calibration of Critical Plastic Strain ( ps

crit

ps

crit) ..............................................................1135.2.5

Calibrated Laboratory Stress-Strain Curves ........................... ....................... ...........1145.2.6

5.3 Application and Validation of the UJRM Methodology ..................... ....................... ....... 117

Calibrated SRM-UJRM in Laboratory Environment ........................ .......................1175.3.1

5.3.1.1 Calibration of Intact Response ........................ ..................... ....................... ..............117

5.3.1.2 Selection of Joint Properties .......................... ....................... ....................... ..............120

5.3.1.3 Development and Validation of a Discrete Fracture Network ....................121

5.3.1.4 Calibrated Continuum Responses ....................... ....................... ....................... ......123

UJRM Large-Scale Response.............................................................................................1265.3.2

5.4 Summary ....................... ....................... ....................... ....................... ...................... ...................... ... 128

CONSIDERATION OF THE VOLUMETRIC CHANGES THAT ACCOMPANY CAVE6

PROPAGATION ......................................................................................................................................... 130

6.1 Rock Mass Density ..................... ..................... ....................... ...................... ...................... ............ 130

6.2 Rock Mass Dilation ....................... ...................... ....................... ........................ .................... ........ 132

Implementation of Non-Constant Dilation in the Cave Demonstration6.2.1

Model .........................................................................................................................................136

6.3 Deformation Modulus .......................... ..................... ....................... ....................... ..................... 138

Implementation of Non-Linear Deformation Modulus Softening in the6.3.1

Cave Demonstration Model ..............................................................................................143

IMPACT OF LARGE-SCALE DISCONTINTIES ON CAVE PROPGATION AND7

SUBSIDENCE BEHAVIOUR .................................................................................................................. 145

7.1 Subsidence Behaviour ......................... ..................... ....................... ....................... ..................... 145

7.2 General Characteristics of Caving Induced Subsidence ....................... ........................ .. 149

7.3 Conceptual Models of Caving Induced Subsidence ........................ ........................ .......... 150

Block Caving ...........................................................................................................................1507.3.1

Chimney Caving ........................ ....................... ....................... ........................ ................... ....1517.3.2

Plug Caving ..................... ........................ ...................... ...................... ....................... ..............1527.3.3

7.4 Subsidence Features Related to Cave Mines ...................... ........................ ....................... . 154

Description of Active Subsidence Features .................................. ........................ .....1547.4.1

7.4.1.1 Caved Rock Zone............................... ........................ ........................ ........................ ......154



ivA Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses

7.4.1.2 Zone of Large-Scale Fracturing ........................ ....................... ........................ ..........155

7.4.1.3 Small-Scale Displacement Zone (Continuous Zone of Subsidence)...........156

7.4.1.4 Stable (Elastic) Zone ........................ ........................ ....................... ........................ ......157

Long-Term Time-Dependent Subsidence .......................... ..................... ...................1587.4.2

7.4.2.1 Residual Subsidence ......................... ....................... ...................... ....................... ........158

7.4.2.2 Sub-Surface Erosion ........................ ..................... ....................... ........................ ..........159

7.5 Effect of Large-Scale Discontinuities on Subsidence Limits ..................... ................... 161

Fault Impacted Caving ........................................................................................................1647.5.1

7.5.1.1 San Manuel Mine ......................... ...................... ....................... ........................ ..............164

7.5.1.2 Ridgeway Deeps Sub-Level Cave ......................... ...................... ....................... .......166

7.5.1.3 Questa Mine ....................... ....................... ........................ ....................... .................... .....167

7.5.1.4 Henderson Mine ...................... ...................... ........................ ....................... ..................168

7.5.1.5 Kimberly Mine .......................... ...................... ........................ ....................... ..................169

7.5.1.6 Summary ........................ ....................... .................... ....................... ..................... .............169

7.6 Fault Properties ....................... ........................ ...................... ....................... ..................... ............. 171

7.7 Numerical Simulation of Large-Scale Discontinuities in the Cave

Demonstration Model .......................... ..................... ....................... ...................... .................... 172

Implicit Fault Representation .........................................................................................1737.7.1

Explicit Fault Representation ........................ .................... ........................ ......................1777.7.2

7.8 Summary ...................... ....................... ....................... ....................... ....................... ..................... .... 180

DEVELOPMENT OF A PRODUCTION DRAW ALGORITHM .......................... ....................... .... 1818

8.1 Influence of Production Schedule on Cave Propagation Behaviour .................... ..... 181

Impact of Production Draw Strategy in the Demonstration Model .................1828.1.1

8.2 Influence of Rock Mass Bulking Behaviour on Cave Propagation Behaviour ....... 184

Impact of Bulking Factor in the Cave Demonstration Model .............................1848.2.1

8.3 Limitations to Height of Draw Scheduling ......................... ....................... ........................ .. 186

8.4 Development of a Mass-Based Production Schedule ....................... ....................... ........ 188

Simulation of Undercutting ..............................................................................................1888.4.1

Simulation of Production Draw ............................ .................... ....................... ...............1898.4.2

Selection of Maximum Draw Velocity (Vmax) .............................................................1908.4.3

Development of a Tonnes Based Production Cut-Off Algorithm ..................... .1928.4.4

8.5 Summary ...................... ....................... ....................... ....................... ....................... ..................... .... 192

DEVELOPMENT OF AN ALGORITHM TO CONSIDER EVOLVING GROUND SURFACE9

PROFILE ...................................................................................................................................................... 195

9.1 Impact of Topography on Subsidence Limits ....................... ........................ ...................... 195

9.2 Toppling Failure Mechanism ...................... ...................... ....................... ........................ ......... 197



vA Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses

9.3 Limitations of the Small-Strain Numerical Approach ....................... ....................... ....... 197

9.4 Development of an Algorithm to Simulate Crater Development ....................... ........ 199

DEVELOPMENT OF A SUB-LEVEL CAVING ALGORITHM ............................ ........................ ... 20510

10.1 Sub-Level Caving Mining Method ........................... ...................... ....................... ................... 205

10.2 Simulation of Blast Damage ..................... ....................... ........................ ........................ ........... 206

10.3 Mobilisation of a Previous Sub-Level ....................... ....................... ...................... ................ 208

10.4 Incremental Mass-Based Calculation ....................... ....................... ...................... ................ 209

CASE STUDY VALIDATION: CAVING INDUCED FAILURE OF THE PALABORA11

OPEN PIT .................................................................................................................................................... 210

11.1 Background ......................... ....................... ....................... ....................... ..................... ................... 210

11.2 Geomechanical Conditions ............................ ..................... ....................... ....................... .......... 211

11.3 In situ Stress ...................... ......................... ..................... ........................ ....................... ................. 213

11.4 Production History ....................... ......................... ........................ ....................... .................... ..... 214

11.5 Simulation Results ...................... ....................... ....................... ....................... ..................... ......... 215

Cave Initiation ........................................................................................................................21511.5.1

Yielding of the Crown Pillar – Q4 2002 ......................... ........................ ......................21711.5.2

Cave Break-Through – Q1 2004 ............................. ...................... ....................... ...........21811.5.3

North Wall Failure – Q4 2004 .......................... ..................... ....................... ...................22011.5.4

11.5.4.1 North Wall Failure Mechanism ......................... ...................... ........................ ...221

11.6 Summary ...................... ........................ ...................... ....................... ...................... ...................... .... 223

CASE STUDY VALIDATION : STRUCTURALLY CONTROLLED CAVING AT THE12

HENDERSON MINE ........................ ........................ ..................... ...................... ..................... ................. 225

12.1 History of the Henderson Mine ........................... ....................... ....................... ..................... .. 225

12.2 Model Geometry and Production Schedule .......................... ....................... ....................... 226

12.3 Material Properties and Pre-Mining Stresses .......................... ....................... ................... 228

12.4 Simulation Results ..................... ........................ ...................... ....................... ...................... ......... 229

12.5 Summary ....................... ........................ ..................... ........................ ..................... ...................... .... 232

CASE STUDY VALLIDATION : CAVING INDUCED SUBSIDENCE AT THE13

ABANDONED GRACE MINE PANEL CAVE................................ ...................... ........................ ....... 233

13.1 Background ........................ ....................... ....................... ........................ .................... .................... 233

13.2 Geomechanical Properties ......................... ....................... ....................... ....................... ........... 235

13.3 Local Geology.................................... ....................... ........................ ....................... .................... ..... 235

13.4 Pre-Mining Stress State ....................... ....................... ....................... ........................ .................. 237

13.5 Caving Induced Subsidence ....................... ...................... ........................ ....................... ........... 237

Evolution of Subsidence Crater and Trough ............................................. ................237 13.5.1

Visual Observation of the Limit of Large-Scale Surface Cracking ....................23913.5.2



viA Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses

Conceptual Model of Subsidence Formation at the Grace Mine ........................24013.5.3

Modelling Methodology .......................... ...................... ....................... ....................... .......24113.5.4

Predicted Evolution of Cave Mobilised and Yield Zones .......................... ............24213.5.5

Model Validation ......................... ..................... ....................... ....................... ..................... ..24413.5.6

13.6 Summary ....................... ....................... ...................... ........................ ..................... ...................... .... 245

CASE STUDY VALIDATION : CAVING INDUCED SUBSIDENCE AT THE14

KIIRUNAVAARA LAKE OREBODY SLC ............................ ....................... ....................... .................. 247

14.1 Introduction ...................... ......................... ....................... ....................... ..................... ................... 247

14.2 Historical Mining Record ................... ......................... ....................... ....................... .................. 247

14.3 Evolution of Surface Subsidence .......................... ...................... ....................... ..................... . 248

Limits of Large-Scale Fracturing / Yield Zone ........................ ....................... ...........24914.3.1

Limits of Continuous Deformation ........................ ....................... ........................ .........25014.3.2

14.4 Numerical Simulation of Caving Induced Subsidence .......................... ........................ .. 250

In situ Stress ............................................................................................................................25114.4.1

Rock Mass Properties ........................ ..................... ....................... ....................... ..............25114.4.2

Production Schedule ........................ ....................... ........................ ........................ ............25114.4.3

Simulation Results ....................... .................... ...................... ....................... ..................... ..25214.4.4

14.5 Summary ....................... ....................... ...................... ........................ ..................... ...................... .... 256

CONCLUSIONS AND RECCOMENDATIONS .......................... ....................... ........................ .......... 25715

15.1 Summary of Original Contributions .......................... ........................ ....................... .............. 258

Rock Mass Behaviour ..........................................................................................................25815.1.1

15.1.1.1 Development of the Ubiquitous Joint Rock Mass (UJRM) Model..........258

15.1.1.2 Consideration of the Volumetric Changes that Accompany Cave

Propagation ......................................................................................................................258

15.1.1.3 Impact of Large-Scale Discontinuities on Cave Propagation and

Subsidence Behaviour ..................................................................................................259

Production Simulation .......................................................................................................25915.1.2

15.1.2.1 Development of a Mass-Based Production Schedule ........................ ........259

15.1.2.2 Development of a Sub-Level Caving Algorithm ........................ ...................259

15.1.2.3 Development of an Algorithm to Consider Evolving Surface Profile ..260

15.2 Validation ..................... ......................... ..................... ....................... ..................... ....................... .... 260

15.3 Recommendations for Further Work ........................... ....................... ........................ .......... 260

Rock Mass Behaviour ..........................................................................................................260 15.3.1

15.3.1.1 Ubiquitous Joint Rock Mass ...................... ...................... ........................ .............260

15.3.1.2 Time-Dependent Processes ...................... ......................... ....................... ...........261

Numerical Techniques........................................................................................................26115.3.2



viiA Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses

15.3.2.1 Small-Strain Calculation Model ....................... ..................... ....................... .......261

15.3.2.2 Interactive Draw............................... ....................... ....................... ........................ ..261

15.3.2.3 Hardware ...................... ....................... ....................... ....................... .................... ......261

Validation .................................................................................................................................26115.3.3

REFERENCES ....................... ......................... .................... ........................ ...................... ...................... .... 26216



ixA Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses

Figure 18. Development of a discrete element model to study cave propagation

(a) particle clusters early in the caving process with superimposed

contact force chains (after Lorig et al., 1995). (b) particle clusters after

significant cave propagation showing internal fractures of blocks in the

caving zone chains (after Lorig et al., 1995). (c) forces arching around

the unstable rock mass (after Brown, 2003). .................................... ........................ . 32

Figure 19. Large-scale (mine-wide) discrete element modelling of caving and

subsidence phenomena in three-dimensions. Cross section of

subsidence mass movement from block caving and simulated synthetic

rock mass triaxial test of PFC material (after Gilbride et al., 2005). ................. 34

Figure 20. Large-scale discrete element modelling of caving and subsidence

phenomena in three-dimensions. (after Sharrock et al., 2011). ......................... 35

Figure 21. Three-dimensional strain-softening, continuum models for cave

propagation (a) logic sequence to simulate caving (b) typical

simulation results (after Pierce and Lorig, 1998). ........................... ....................... .. 37Figure 22. Simulation of production draw from large-scale, three-dimensional

strain-softening continuum models based on velocities. ........................ .............. 38

Figure 23. Large-scale back-analysis of cave propagation behaviour at the

Northparkes E26 Lift 2 Mine. (after Pierce et al., 2006). .................... .................. 39

Figure 24. Example of a mine-wide, three-dimensional, multi-scale simulation

(after Beck et al., 2011). ....................................................................................................... 40

Figure 25. Simulation of cave development using a hybrid, two-dimensional

approach (after Rogers et al., 2010). ......................... ........................ ....................... ...... 41

Figure 26. Measured rock strength-scale effect including large size specimens of

in situ test (after Pratt et al., 1972). ................................................................................ 44Figure 27. Applicability of the Hoek-Brown empirical rock mass strength

criterion at different scales (after Li et al., 2008). ...................................... .............. 45

Figure 28. Development of equivalent Mohr-Coulomb property estimates from a

fit to the Hoek-Brown curve. ............................................................................................. 47

Figure 29. Idealised stress-strain curves representing different material

behaviour used in numerical modelling. ......................... ........................ ..................... 48

Figure 30. Stages of damage within a three-dimensional, strain-softening

specimen. ................................................................................................................................... 50

Figure 31. Summary of FLAC 3D critical strain relation and data points used for

fitting. .......................................................................................................................................... 51Figure 32. Post-peak response as a function of zone resolution controlled by

sample width. ........................................................................................................................... 55

Figure 33. Schematic diagram of a tensile failure mechanism that does not affect

cohesive strength. .................................................................................................................. 59

Figure 34. Development of equivalent linear Mohr-Coulomb strength parameters

based on a fit to the Hoek-Brown strength envelope. ....................... ...................... 60

Figure 35. Schematic diagram of the mobilisation of the strength components

cohesion and friction (a) in the laboratory (b) around an underground

opening (after Hajiabdolmajid, Kaiser and Martin, 2002). ........................ ........... 61

Figure 36. Implementation of the CWFS model in a two-dimensional numericalmodel of a tunnel failure (after Barton and Pandey, 2011). ......................... ........ 62



xA Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses

Figure 37. Example of simulated bi-linear, strain-softening response (after

Sainsbury et al., 2010). ......................................................................................................... 65

Figure 38. The Smooth Joint Contact Model. (after Mas Ivars et al., 2011). ........................ 68

Figure 39. Components of a Synthetic Rock Mass sample. (after Mas Ivars et al.,

2011). .......................................................................................................................................... 69

Figure 40. Three-dimensional response of a synthetic rock mass sample tested in

three-opposing directions under unconfined compression; (after

Sainsbury et al., 2009). ......................................................................................................... 70

Figure 41. Stress-path dependent Synthetic Rock Mass approach (a) stress path,

fitted peak-strength envelope (b) estimates of brittleness obtained

from SRM testing (after Pierce et al., 2006). ......................... ....................... ............. 72

Figure 42. Validation of Synthetic Rock Mass response based on observed and

measured fracture modes and fragmentation (after Pierce et al., 2006)........ 73

Figure 43. Development of a large-scale caving model using stress-path

dependent Synthetic Rock Mass strengths (after Mas Ivars et al., 2011). ...... 75Figure 44. Research methodology plan. ........................ ....................... ...................... ...................... 84

Figure 45. Development of a numerical demonstration model: geomechanical

conditions. ................................................................................................................................. 86

Figure 46. Hoek-Brown failure envelopes and simulated rock mass stress-strain

curves for the rock mass domains in the numerical demonstration

model. .......................................................................................................................................... 87

Figure 47. Empirical estimates of rock mass caveability for four rock mass

domains simulated in the numerical demonstration model. ......................... ...... 88

Figure 48. Predicted cave propagation behaviour for variable peak strength rock

masses in the numerical demonstration model. .......................... ........................ ..... 89Figure 49. Simulated variable post-peak softening responses for the same peak

strength rock mass................................................................................................................. 91

Figure 50. Variation in cave propagation behaviour based on variable post-peak

softening rates simulated in the numerical cave propagation model. ............. 92

Figure 51. Hoek-Brown curves and equivalent bi-linear Mohr-Coulomb property

estimates for varying mi values........................................................................................ 93

Figure 52. Effect of estimates of mi on predicted cave propagation behaviour in

the numerical demonstration model. ........................... ..................... ........................ ..... 94

Figure 53. Cave propagation results for increasing stress /depth in the numerical

demonstration model. ....................... ...................... ....................... ....................... ............. 96Figure 54. Subiquitous constitutive model in FLA3D; assignment of matrix and

joint properties. ....................................................................................................................... 99

Figure 55. Stages of damage within a simulated UCS test on a subiquitous sample. ..... 100

Figure 56. Development of a UJRM sample (a) variation in sample size with equal

zone sizes; (b) joint assignment as a function of sample size. ........................... 102

Figure 57. UJRM sample testing geometry (a) sample loading conditions (b)

orientation for anisotropy tests completed for each sample loading

condition. ................................................................................................................................. 103

Figure 58. Examples of (a) poor (b) low and (c) good mesh resolution required

for large-scale analysis of cave propagation. ......................... ........................ ...........104Figure 59. Discontinuity shear strength in a triaxial cell (after Brady and Brown,

2006). ........................................................................................................................................ 105



xiA Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses

Figure 60. Simulation of different boundary loading conditions on the response of

UJRM material in the numerical UCS test environment. .......................... ............ 106

Figure 61. Investigation of UJRM response as a result of small-strain/large-strain

calculation modes. ....................... ..................... ........................ ........................ .................. .. 107

Figure 62. Joint orientations considered in the development of the DFN for (a)

carbonatite (b) micaceous pyroxenite (c) dolerite (d) foskorite (after

Sainsbury et al., 2008). ...................... ........................ ....................... ........................ .......... 110

Figure 63. Representation of DFN in a UJRM sample (a) actual DFN (b) DFN

represented in numerical model (after Sainsbury et al., 2008). ....................... 111

Figure 64. UJRM sample stress-strain responses (a) calibrated 40x80m

carbonatite UCS UJRM rock mass samples showing strength anisotropy

(b) calibrated 40x80m carbonatite triaxial UJRM rock mass samples

showing strength anisotropy. ............................... ........................ ........................ .......... 114

Figure 65. Calibrated UJRM: SRM results at 5 MPa confinement for each lithology

at Palabora in three testing directions. .......................................................................115Figure 66. UJRM UCS results for the carbonatite domain at Palabora compared to

SRM results at three different sample sizes in three loading directions. ...... 116

Figure 67. Calibrated stress-strain curves within PFC for three rock mass

domains. ................................................................................................................................... 119

Figure 68. Domain 1 fracture network views: 18m REV edge length (after

Sainsbury, Mas Ivars and Darcel, 2008)...................................................................... 121

Figure 69. Domain 2 fracture network views: 40m edge length (after Sainsbury,

Mas Ivars and Darcel, 2008). ......................................... ....................... ........................ ... 122

Figure 70. Domain 3 Fracture Network views : 18m edge length (after Sainsbury,

Mas Ivars and Darcel, 2008). ......................................... ....................... ........................ ... 122Figure 71. Quantification of GSI chart (after Cai et al., 2007). ...................... ....................... ....123

Figure 72. Domain 1 SRM test results and UJRM response represented in FLAC 3D :

1 MPa triaxial tests (after Sainsbury, Mas Ivars and Darcel, 2008). ............... 124

Figure 73. Domain 2 SRM test results and UJRM response represented in FLAC 3D :

1 MPa triaxial tests (after Sainsbury, Mas Ivars and Darcel, 2008). ............... 125

Figure 74. Domain 3 SRM test results and UJRM response represented in FLAC 3D: 1

MPa triaxial tests (after Sainsbury, Mas Ivars and Darcel, 2008). ................... 125

Figure 75. Cave propagation behaviour for varying joint orientations simulated in

the numerical demonstration model. ........................... ...................... ....................... ... 127

Figure 76. Simulated porosity profile during propagation of a block cave. ....................... 130Figure 77. Conceptual diagram of dilation associated with sliding along micro-

cracks and particles (after Zhao and Cai, 2010). ........................... ....................... ... 132

Figure 78. Typical stress-strain curve for uniaxial compression of brittle,

crystalline rock (after Rudnicki and Rice, 1975)....................... ....................... ....... 132

Figure 79. Evolution of peak dilation estimate on a rock mass during cave

propagation using the Alejano and Alonso relation. ....................... .......................136

Figure 80. Implementation of a non-constant dilation relation and its impact on

cave propagation behaviour in the numerical demonstration model

compared to the simulation of a constant dilation angle.......................... ........... 137

Figure 81. Schematic linear relationship for rock mass deformation modulusreduction based on Pierce et al. (2006) relation. ......................... ....................... ....139



xiiA Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses

Figure 82. In situ rock mass deformation modulus versus GSI for Disturbance

Factors of 0, 0.5 and 1.0 (after Hoek and Diederichs, 2006). ......................... .... 139

Figure 83. Softened deformation modulus versus porosity for particulate matter

determined by laboratory testing..................................................................................140

Figure 84. Best-fit deformation modulus softening equation to compiled

laboratory test data. ...................... ......................... ....................... ....................... ............... 141

Figure 85. Typical deformation modulus softening curves of caving rock masses

using the non-linear softening relation. ....................... ....................... ........................ 142

Figure 86. Impact on cave propagation behaviour by implementing the non-linear

modulus softening relation in the cave demonstration model.......................... 143

Figure 87. Simulated evolution of the bulk modulus in the back of demonstration

model undercut; the linear and non-linear relations compared in the

cave demonstration model. ..............................................................................................144

Figure 88. Conceptual models of subsidence a) continuous subsidence (after

Kratzsch, 1983) b) discontinuous subsidence (after Whittaker andReddish, 1989). ..................................................................................................................... 146

Figure 89. Terminology used to describe subsidence features for block- and

panel-cave mines (modified after van As et al., 2003). ......................... ................ 148

Figure 90. Conceptual model of the development of block caving subsidence

(after Sainsbury and Lorig, 2005). ........................... ...................... ....................... ........ 151

Figure 91. Conceptual model of chimney cave development (Betourney et al.,

1994), b) surface expression of a chimney pipe in a kimberlite caving

operation (after van As et al., 2003). ......................... ........................ ....................... .... 152

Figure 92. Plug subsidence mechanism at the Athens Mine in Michigan USA (after

Obert and Duvall, 1967). ...................................................................................................153Figure 93. Geometry of Lift 1 cave a) before and b) after plug caving (after Pierce,

1999). ........................................................................................................................................ 153

Figure 94. Photo showing crater and caved rock zone at Henderson Mine (after

Lupo, 1998). ....................... ......................... ...................... ....................... ..................... .......... 155

Figure 95. Photo showing large-scale surface cracking at Northparkes E26 Lift 1

Mine (after van As et al, 2003). .......................................................................................156

Figure 96. Photo showing tension crack within small-scale displacements at the

Kiirunavaara Mine (after Villegas, 2008). .............................................. .................... 157

Figure 97. Simplified subsurface erosion mechanism (after Van der Merwe 1999). .... 159

Figure 98. Photos of subsurface erosion pot holes (after Van der Merwe, 1999)........... 160Figure 99. Photo of sinkhole located outside the limit of large-scale cracking at

the abandoned Grace Mine (after Sainsbury and Lorig, 2005). ........................ 160

Figure 100. Schematic diagram of how crater shape can be modified by major

geological structure (after Stacey and Swart, 2001). ........................................ .... 162

Figure 101. Conceptual development of surface subsidence at the San Manuel Mine

(after Hatheway, 1966). ........................ ....................... ...................... ....................... ......... 164

Figure 102. Plan view, section view of subsidence crater at the San Manuel Mine

(after Hatheway 1966). ......................... ....................... ....................... ........................ ....... 165

Figure 103. Photos showing cave propagation controlled by weak vertical fault at

the Ridgeway Mine (Brunton, 2009). ......................... ....................... ........................ ... 166Figure 104. Photo of Goathill Crater at the Questa Mine (after Gilbride et al., 2005). ..... 167



xiiiA Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses

Figure 105. Irregular cave growth along a weak intrusive contact at the Henderson

Mine 7210 Level (after Sainbury et al., 2011) ....................... ........................ ...........168

Figure 106. Section through Kimberly Mine showing over-hang (after Laubscher,

2000). ........................................................................................................................................ 169

Figure 107. Simulation of subsidence crater formation for different two-

dimensional fault orientations (modified after Vyazmensky et al.,

2010). ........................................................................................................................................ 170

Figure 108. Estimated shear strength of filled discontinuities (after Wyllie and

Mah, 2007). ............................................................................................................................. 171

Figure 109. Conceptual mesh of implicit versus explicit technique for fault

representation. ....................... ........................ ...................... ....................... .................... ...... 172

Figure 110. Conceptual geological structures simulated in numerical

demonstration model. ......................... ...................... ....................... ....................... ........... 173

Figure 111. Simulated direct shear test; normal stress 10 MPa using ubiquitous

joints in FLAC 3D. ...................................................................................................................... 174Figure 112. Ubiquitous joint faults used to simulate faults within a cave-scale

model. ........................................................................................................................................ 174

Figure 113. Cross-section of mobilised zone (2m displacement) – implicit,

ubiquitous joint approach used to simulate conceptual discontinuity

surfaces. .................... ........................ .................... ........................ ....................... ..................... 176

Figure 114. Schematic diagram showing interface logic and how it can be used to

represent a discontinuity in a numerical model of caving. .................................177

Figure 115. Cross-section of mobilised zone (2m displacement) – explicit, interface

approach used to simulate conceptual discontinuity surfaces......................... . 179

Figure 116. Plan view of subsidence limits at the Grace Mine determined byobservations. .......................................................................................................................... 182

Figure 117. Effect of draw strategy on the caveability of a rock mass in the

numerical demonstration model. ..................................................................................183

Figure 118. Cave simulation results for variable maximum bulking rates in the

numerical demonstration model. ..................................................................................185

Figure 119. Schematic representation of a HOD based schedule interpreted for

numerical mesh. ...................... ........................ .................... ....................... ..................... ...... 186

Figure 120. Representation of (a) typical production schedule (b) mining

increment schedule (c) improved drawpoint scheduling method. ............ ..... 187

Figure 121. Identification of perimeter gridpoints for production draw simulationin a numerical mesh. .......................................... ........................ ....................... .................. 189

Figure 122. Simulated large-scale laboratory tests at different applied loading

velocities and the impact on the sample strength response. ............................. 190

Figure 123. Impact of selection of draw velocity on cave propagation behaviour in

the numerical demonstration model. ........................... ..................... ........................ ... 191

Figure 124. Schematic diagram of the mass-based production draw algorithm

developed. ............................................................................................................................... 193

Figure 125. Example of evolving mobilised zone based on drawpoint tonnes

algorithm.................................................................................................................................. 194

Figure 126. Photo showing the effect of topography on subsidence crate at theQuesta Mine (after Blodgett, 2002). .......................................... ....................... ............ 196



xivA Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses

Figure 127. Survey displacement map above Questa Mine D Orebody (after

Gilbride et al., 2005). ....................... ....................... ........................ ....................... .............. 196

Figure 128. Schematic diagram showing the three primary modes of toppling

(after Goodman and Bray, 1976). ............................... ..................... ....................... ....... 197

Figure 129. Schematic diagram showing the simulation of evolving surface crater

in small-strain calculation mode. ....................... ...................... ....................... ............... 198

Figure 130. Schematic diagram of subsidence algorithm logic. ..................... ........................ ...200

Figure 131. Geometry and undercut footprint of test model used to validate crater

development algorithm. ............................ ...................... ........................ ....................... ... 201

Figure 132. Subsidence limits predicted with/without surface update algorithm. ........ 202

Figure 133. Updated surface elevation in the model after the simulation of mining

with the surface update algorithm. ...............................................................................203

Figure 134. Vertical displacement simulated in the test model and the surfaces

zones that have been nulled to represent the development of the

surface crater. ........................................................................................................................ 204Figure 135. Schematic diagram of sub-level caving algorithm logic. ....................... ............... 207

Figure 136. Conceptual model of the volumetric changes in the sub-level caving

algorithm logic. ...................... ........................ ...................... ....................... .................... ....... 209

Figure 137. Photo of the failure in north wall at the Palabora open pit. ...................... .......... 210

Figure 138. The spatial location of each of the rock mass domains and faults

throughout the Palabora model mesh. ......................................... ........................ ....... 211

Figure 139. Location of large-scale structure simulated in the Palabora numerical

mesh. .......................................................................................................................................... 212

Figure 140. Estimated in situ stress orientation and magnitude at Palabora based

on back-analysis of pit slope failure and stress measurement testing. ......... 213Figure 141. Historical mining record at the Palabora block cave mine. ....................... ......... 214

Figure 142. Observed seismicity at the Palabora Mine during cave initiation and

propagation............................................................................................................................. 215

Figure 143. Numerical prediction of seismogenic zones during early production

simulation at the Palabora mine. ................................ ........................ ....................... .... 216

Figure 144. Numerical simulation - yielding of the crown pillar during Q4 2002. ............ 217

Figure 145. Numerical simulation – cave breakthrough during Q1 2004............................. 218

Figure 146. (a) Cave profiles at the Palabora Mine; April 2002 to December 2003

(after Glazer, 2006) compared to the simulated cave profile (b). .................... 219

Figure 147. Numerical simulation – north wall failure during Q4 2004. ........................ ...... 220Figure 148. North wall failure: observed versus simulated limits. ................... ...................... . 221

Figure 149. Development of the pit slope failure mechanism at the Palabora Mine

at various stages of production. .............................. ....................... ........................ ........ 222

Figure 150. Development of the Palabora block cave between 2003 and 2004 in

relation to fault structure. .................................................................................................223

Figure 151. Cross section of the Henderson Mine (after Rech, 2001). ..................... .............. 225

Figure 152. Geological domains at the Henderson Mine a) plan view of weak

contact; b) 7210 Level yield zone during December 2007. ...................... .......... 226

Figure 153. Development of the numerical model of the Henderson Mine a)

regional extents of model; b) existing cave volumes. ................... ........................ . 227Figure 154. Interface used to simulate the weak Seriate contact at the Henderson

Mine. ..........................................................................................................................................227



xviA Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses

Figure 179. Plan view of simulated subsidence limits at the end of 2010 compared

to observations at Kiirunavaara. ........................ ...................... ....................... ............... 255



xviiA Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses

TABLE OF TABLES

Table 1. Documented yield zone propagation rates from caving operations

around the world (after Sainsbury and Sainsbury, 2010). ................................... 17Table 2. Cave height as a function of brittleness (after Lorig, 2000). ......................... ....... 54

Table 3. Estimate of Hoek-Brown and equivalent Mohr-Coulomb rock mass

strength properties for four simulated domains in the numerical

demonstration model. .......................................................................................................... 87

Table 4. Mean target intact rock block properties for the lithology at Palabora. ....... 109

Table 5. Measured joint frequencies and persistence from mapping at Palabora

(after Mas Ivars et al., 2008) ....................... ....................... ........................ ...................... 109

Table 6. Estimated joint properties for the rock mass domains at Palabora

(after Mas Ivars et al., 2008). ............................ ..................... ........................ .................. 112

Table 7. SRM-derived strengths for the rock mass domains at Palabora - triaxial5-MPa confinement (after Mas Ivars et al., 2008)...................................................112

Table 8. Calibrated UJRM properties for the rock mass domains at Palabora. ............ 114

Table 9. Summary of laboratory test results for three rock mass domains. ................. 118

Table 10. Calibrated PFC micro-properties for three rock mass domains (after

Sainsbury, Mas Ivars and Darcel, 2008). ...................... ........................ .......................120

Table 11. Calibrated intact foliation strength properties in PFC 3D (after

Sainsbury, Mas Ivars and Darcel, 2008). ....................... ....................... ....................... 120

Table 12. Estimated open joint strength properties for simulation of joints in

SRM sample (after Sainsbury, Mas Ivars and Darcel, 2008). .......................... .... 121

Table 13. Calibrated continuum material properties for seven rock massdomains. ................................................................................................................................... 124

Table 14. Dilation angle in large-scale triaxial tests on rock fill material (after

Marachi et al., 1972) ......................... ....................... ....................... ........................ ............. 134

Table 15. Summary of terminology used to define discontinuous subsidence

(after Flores and Karzolovic, 2004). .......................... ..................... ....................... ....... 147

Table 16. Observed residual subsidence duration over longwall mines (after

Singh, 2003). ...................... ....................... ..................... ....................... ...................... ............ 158

Table 17. Conceptual fault shear strength and stiffness parameters represented

in numerical demonstration model. ....................... ........................ ....................... ....... 173

Table 18. Example of gridpoint velocity scaling based on variable productiondraw. ..........................................................................................................................................190

Table 19. Rock mass properties used for the representation of the granite

domain. ..................................................................................................................................... 211

Table 20. Rock mass geomechanical properties of the porphyry at the Henderson

Mine. .......................................................................................................................................... 228

Table 21. Conceptual fault shear strength and stiffness parameters estimated for

the seriate contact at the Henderson Mine. ........................ ....................... ................229

Table 22. Rock Mass Parameters used in the simulation of domains at the Grace

Mine. .......................................................................................................................................... 237

Table 23. Pre-mining stress regime at 731m below surface at the Grace Mine. ............ 237Table 24. Grace Mine production (after Eben, 2004 ). ....................... ....................... ................ 241



1 – Introduction

1A Model for Cave Propagation and Subsidence Assessment in Jointed Rock Masses

INTRODUCTION1

1.1 Cave Mining Method

Caving is a mass mining method, capable of high and sustained production rates

and is relatively low cost per tonne when compared to other mining methods. In

general, a uniform grade distribution and rock mass strength is required to assure

that the maximum potential of a deposit is achieved (Brady and Brown, 2006).

Presently, there are approximately twenty operating cave mines around the world

and many more in the planning stage. Figure 1 provides the locations of the most

notable caving mines that have been, or are currently in operation.

Figure 1. Location of some historical and currently operating caving mines around theworld.

The caving process involves undercutting (blasting a horizon of in situ rock mass)

and extraction of the broken rock from drawpoints on a production horizonlocated at depth. When the plan area of the undercut footprint/active area reaches

a large enough dimension a self-sustained propagating cave will develop so long as

the ore is continued to be withdrawn. This is generally described as the critical

Hydraulic Radius (HR) which can be calculated through the ratio of the

undercut/active footprint area (m2) to the cumulative undercut/active footprint

perimeter length (m).



1 – Introduction


Cave mines require extensive infrastructure to be in place prior to any production.

Infrastructure usually includes access through a decline or shaft to an undercut

level and an extraction level that is located approximately 15-20 m below that.

Extraction level infrastructure must be designed to be stable throughout the life of

mine, often without previous experience of the large-scale rock mass response.

The three-dimensional nature of typical extraction level geometries, together with

the complex stress-redistribution around a propagating cave make completing an

accurate assessment of cave propagation and subsidence behaviour difficult. A

schematic diagram of a typical block cave mine layout is provided in Figure 2.

Figure 2. Schematic representation of a typical block cave mine (modified after AtlasCopco, 2011).

There are three variations to the cave mining method that include block, panel and

sub-level caving. In block and panel caving operations, the ore is withdrawn from a

single mining horizon (extraction level). The transition of the ore from an in situ

rock mass to a fully fragmented cave material is achieved without drilling and

blasting after the initial undercut development. The fragmentation of the rockmass is controlled by natural processes that include the in situ fracturing of the



1 – Introduction


rock mass, stress redistribution, the limiting strength of the rock mass and

progression of the material downward through the muckpile resulting in

autogenous grinding. In block caving, the orebody is fully undercut prior to

production commencing. In panel caving, production commences prior to the

orebody being fully undercut and mining progresses laterally across the orebody.

Sub-level caving typically operates on numerous mining horizons simultaneously

but progresses downwards through the orebody. Sub-level caving requires the

transition of in situ ore into a mobilised state by conventional drilling and blasting.

The material above the orebody is allowed to cave into the void created by mining.

The requirement for drilling and blasting is generally brought about by the highstrength of the rock mass, and/or the small orebody footprint.

1.2 Development of the Cave Mining Method

The cave mining method was developed in the underground coal mines of England

in the late 17th century. At this time it was referred to as the Shropshire Method,

and was developed to induce gravity caving (through undercutting) in highly

fractured, persistent and flat-lying coal seams. The area from which the coal was

extracted was generally back-filled with stone to limit surface subsidence (Energy

Information Association, 1995). As the demand for coal increased during the 18th

and 19th century, the advantages of the cave mining method were noted “… it

enabled a colliery to be opened with less capital expenditure … the yield per acres

(was) greater… (and) shot firing (could) almost be entirely dispensed with (because

the) weight on the face is, in itself, sufficient to bring down the coal… ” (Hughes,

1917).

By the late 19th century – early 20th century, coal caving had been adapted to the

metalliferous mines in Michigan, USA whereby the high in situ density of the ore

was exploited to induce a gravity caving mechanism in mining blocks

approximately 60-75 m long, 30-40 m high and 60 m wide, and, after visiting these

caving operations during the 1950s, De Beers commissioned their first diamond

caving operation (Brown, 2003) in South Africa. The ubiquitous application of

cave mining in South African diamond mines since this time has led to the

development of current day empirical cave assessment techniques (Diering and



1 – Introduction


Laubscher 1987, Laubscher 1990, 1994, 2000) that are further discussed in

Section 2.1.2. In the case of South African diamond mining, effective caving is

enabled without dilution problems by the contrast in strength between the weak

kimberlitic diamond pipe and the comparatively strong host rock mass.

As a result of the continued success of the cave mining method in coal, iron ore and

kimberlite operations and in a number of strong, (UCS, greater than 80 MPa and

GSI, greater than 50) jointed rock masses (e.g. Urad Mine, Colorado, USA; 1914-

1960; Philex Padcal Mine, Philippines, 1959-current and El Teniente, Chile,

1920’s-current), during the mid-1990’s a caving mine was planned at Rio Tinto’s

Northparkes E26 Lift 1 Orebody. Feasibility studies for the mine were carried outusing Laubscher’s empirically derived caveability chart and the orebody was

predicted to fall well within the Caving Zone (Ross and van As, 2005). Production

from the block cave commenced in 1996 and cave initiation followed. However,

once the undercut development was completed, the cave stalled at a height of 95

m. Figure 3 provides a chart showing the initial estimate of caveability at the E26

Mine (a) and the stalled geometry (b).

Figure 3. (a) Laubscher’s stability chart showing E26 predicted caveability (b) section

showing cave stall at Northparkes E26 prior to plug failure (modified afterRoss and van As, 2005).



1 – Introduction


Increased production rates failed to induce further caving of the orebody and an

air-gap developed. In order to stimulate cave growth, a hydraulic fracturing

campaign was conducted. Boundary weakening (blasting a sub-vertical slot on the

south-western boundary of the cave) methods were also employed. After a

significant amount of effort over a two year period, caving once again

recommenced. However, on Wednesday, 24th November, 1999, the cave back

advanced rapidly through to the ground surface and generated a wind-blast

through the underground workings. Four workers were killed. It is estimated that

a total amount of 13 MTonnes of material came down in this collapse - a column

height of 200 m. At the time of the accident, the air-gap was in excess of 180 m

(Ross and van As, 2005).

As a result of the unexpected stall and then rapid failure and air-blast at the

Northparkes E26 Lift 1 Mine, the International Caving Study (ICS 1997-2004) and

Mass Mining Technology (MMT I 2005-2008 and MMT II 2009-2012) projects

were initiated. These industry funded research projects have made significant

contributions to the advance of rock mechanics understanding associated with

cave mining methods in hard, jointed rock masses. The following section providesa review of the current state-of-the-art engineering for cave propagation and

subsidence assessment in hard, jointed rock masses.

1.3 Caving Mechanics

It is commonly understood that all rock masses must cave if they are undercut over

a significant enough area. Caving can occur as a result of two influences – gravity

and stress. The mechanism of caving will depend on the relationship between

induced stresses, geometry of the cave footprint, strength of the rock mass and

joint fabric (Brown, 2003).

Stress caving occurs when the induced stresses in the cave back exceed the

strength of the rock mass causing yielding and fragmentation of the rock mass into

a caved rock state. Gravity caving is characterised by low mining induced stresses

and is often analysed by knowledge of the joint fabric and simple kinematics.



1 – Introduction


Gravity induced unravelling can be expected to occur in the cave back (roof) as a

tensile failure mechanism under low stress conditions. Failure can occur through

slip along pre-existing joints as the rock is unconfined from below, or through

bending/deflection of the rock layers (voussoir beam theory). Gravity caving

usually results in coarser drawpoint fragmentation since little damage is induced

to the rock mass during its mobilisation. Primary fragmentation in this case, is

usually close to the in situ block size. Example stress-paths for both stress and

gravity caving mechanisms are presented in Figure 4. The disintegration and

mobilisation of a rock mass resulting from yield in the compressive regime is

called stress caving. In the tensile regime, it is gravity caving.

Figure 4. Typical caving stress-paths representing stress and gravity cavingmechanisms.

Self-sustained propagation of the cave stalls when a stable arch develops in the

advancing back. In this case, the induced stresses do not exceed the strength of the

intact rock bridges and/or is unable to induce failure along pre-existing joints.Time-dependent processes (i.e., stress corrosion, ground water etc.) may



1 – Introduction


eventually mobilise this material, but in most cases, artificial cave stimulation is

usually required. Cave propagation behaviour has been described by Brown

(2003) and Pierce (2010). A summary is provided in Figure 5.

Figure 5. Conceptual stress-state development around a propagating cave (modifiedafter Pierce, 2010).



1 – Introduction


As a result of the two caving processes identified in Figure 5 (stress and gravity),

Pierce, (2010) has defined seven critical factors that impact the cave propagation

behaviour of a rock mass. They are summarised below.

(a) Cohesion and Tension Weakening. During stress caving, the rock mass

undergoes a reduction in strength from its peak in situ value to a much

lower residual value (representative of a caved rock mass state). This

overall response is often termed a “strain-softening” process, and is the

result of strain-dependent material properties. Gravity caving in low

induced stress environments is driven by the ability of the in situ joint fabric

to loosen and mobilise (its tensile strength).

(b) Post Peak Brittleness. The rate at which the rock mass strength drops

from peak to residual is referred to as brittleness. Rocks that maintain their

peak strength with continued loading are referred to as perfectly plastic

(ductile) constitutive models. Rock masses that instantaneously drop to

low residual strength properties when they exceed their peak strength are

referred to as perfectly brittle. In general, brittle rock masses cave more

readily than ductile rock masses.

(c) Deformation Modulus Softening. During caving, the rock mass increases

in volume as intact rock blocks fracture, separate and rotate during the

yielding and mobilisation process. Along with this bulking, a reduction in

the deformation modulus is expected to occur. Representation of the

decrease in deformation modulus is crucial for assessing the evolving stress

state around the cave, since, as the rock mass dilates/bulks its potential to

carry stress decreases.

(d) Dilational Behaviour. Rock mass dilation is the change in volume of a rock

that occurs with shear distortion. An accurate assessment and

representation of the dilation behaviour of a jointed rock mass during cave

initiation and propagation is essential in being able to accurately predict the

correct bulking behaviour and volume increase for air gap assessment.



1 – Introduction


fundamental geomechanical principles is required to predict cave propagation

behaviour and surface subsidence prior to the investment of significant capital and

development of infrastructure.

1.4 Terminology

A conceptual model of a self-sustained propagating cave has previously been

developed by Duplancic and Brady (1999) through seismic investigations and

underground instrumentation at the Northparkes Mine, Australia. The conceptual

model includes four main behavioural regions that are shown in Figure 6.

Figure 6. Conceptual diagram of showing the main behavioural regions of a propagating cave based on underground observations and instrumentation.

The characteristics of each region are defined below:

Elastic Region - The host rock mass around the caving region behaves

mainly elastically and has properties consistent with an “undisturbed” rock

mass.



1 – Introduction


Seismogenic Zone - Microseismic (and sometimes seismic) activity is

concentrated in this region primarily due to slip along pre-existing

discontinuities and the initiation of new fractures.

The overall advance rate, thickness and spatial distribution of the

seismogenic zone has previously been determined by the criterion in

Equation [1] (after Diederichs, 1999). This criterion is based on back-

analysis of seismic response in a number of deep Canadian operations.

Where: and are the Major and Minor Principal Stress Magnitudes(MPa), is the Damage Threshold Value (%) and is the Uniaxial

Compressive Strength (MPa)

The damage threshold () has been shown to correspond to the point

at which measurable seismicity might be picked up in the mine. The simple

criterion has been successfully applied in back-analyses of the recorded

seismogenic zones at Northparkes E26 Lift 2 (Pierce et al., 2006) using a

value of 35%. Others (Beck et al., 2006) have correlated seismic

potential to Dissipated Plastic Energy (DPE - the energy in joules dissipated

as a result of yield in a mining step). The greater the DPE, the greater the

seismic potential. However, no clear guidelines have been reported to

interpret this value from a numerical model.

Yielded Zone – The rock mass in this region is fractured and has lost some

or all of its cohesive strength and provides minimal support to the overlying

rock mass. A rock mass within the yielded zone is subject to significant

damage, i.e. open holes are cut-off, Time Domain Reflectometry (TDR)

breakages are expected and cracking is observable in infrastructure. Stress

components within this region are typically low in magnitude. The

reduction in rock block size (compared to the in situ state) due to yielding in

this region can be described as primary fragmentation. Primary

fragmentation from a stress caving mechanism is generally finer than that

from gravity caving (Laubscher, 1994).



1 – Introduction


Mobilised Zone – This zone gives an estimate of portion of the orebody

that has moved in response to the production draw and may be

recoverable. Although the specific location of the cave back is difficult to

predict precisely, it is estimated to be rock that has experienced a

displacement greater than or equal to 1-2 m (after Pierce et al., 2006). The

reduction in rock block size (compared to the primary fragmentation state)

is described as secondary fragmentation. Secondary fragmentation is

affected by draw height and internal caving stresses (Laubscher, 1994).

Cave propagation behaviour and subsidence are closely linked geomechanical

processes. The surface projection of a cave after break-through can be describedby similar terminology as the underground regions. A conceptual schematic model

of the surface subsidence domains compared to the underground cave domains are

presented in Figure 7.

Figure 7. Conceptual schematic diagram showing the main behavioural regions of acave that has propagated through to the ground surface.

The characteristics of each region are described below.

A crater is a common surface feature of many caving mines; it also is

referred to as the zone of active movement (van As et al., 2003). The crater

consists of irregular blocks of rock, ranging in size from millimetres to



1 – Introduction


several metres in magnitude. It develops as the mobilised zone influence

reaches the ground surface, causing the overlying rock mass and/or side

rock to fall into the mined void. Over time, the surface of the crater may

subside as ore is withdrawn (Lupo, 1998).

Zone of Large-Scale Fracturing. The ground surface within this zone is

broken and has large open tension cracks, benches, and rotational blocks.

Usually, the primary failure mechanism of surface cracks associated with

cave mines is shear failure of the abutment rock mass, which results in the

development of stepped benches and scarps. Other types of failure

mechanisms, such as toppling and block rotation, also are present, but theyappear to be secondary mechanisms that form after the primary shear

failure develops. A total strain criterion of 0.5% has previously been used

by Sainsbury and Lorig (2005) to calibrate the limits of large-scale

fracturing at the abandoned Grace Mine in Pennsylvania, USA. This total

strain criterion has also been used to calibrate the limit of large-scale

fracturing at the El Teniente block cave mine in Chile (Cavieres et al., 2003).

Continuous Subsidence, as defined by Brauner (1973), is the response of

the rock mass to a mined void, which results in the formation of a gentle

surface depression. Generally, the continuous subsidence zone forms

between the large-scale surface cracking zone and the undisturbed surface

(elastic zone). Surface buildings, roads, underground power lines, railroads

and other structures can be impacted significantly by continuous surface

subsidence. Lupo (1998) measured continuus subsidence up to 200 mm at a

distance of 250 m from the zone of large-scale fracturing that caused heavy

damage to nearby surface structures. The strain criteria developed by

Singh (2003) has previously been used to define the extent of this region;

horizontal strain > 0.002 (0.2%) and angular distortion > 0.003 (0.3%) at

the abandoned Grace Mine (Sainsbury and Lorig, 2005).

Elastic Zone. The area beyond the continuous subsidence zone.



1 – Introduction


1.5 Thesis Outline

The research documented by this Thesis has been broken into chapters based on

unique ideas and concepts. A summary of this break-down is provided below.

Chapter 1 – summarises the problem being studied, outlines the motivations for

the research and provides some background information on the cave mining

method.

Chapter 2 – critically reviews the existing techniques being used by the mining

industry for cave propagation and subsidence analyses in hard, jointed rock

masses.

Chapter 3 – outlines the objectives and methodology for the development of a

cave propagation and subsidence assessment techniques in hard, jointed rock

masses.

Chapter 4 – outlines the development of a numerical cave propagation

demonstration model. The model has been used to investigate the effect in situ

geomechanical conditions have on cave propagation behaviour. The model has

also been used to demonstrate the implementation and impact of the research

detailed herein.

Chapter 5 – outlines the development of a new technique that allows accurate

representation of anisotropic strength and deformation modulus (as defined by

SRM testing) responses in large-scale, three-dimensional cave propagation and

subsidence numerical models.

Chapter 6 – outlines the development of new numerical algorithms that allow the

rigorous consideration of the effect of volumetric changes of a rock mass during

cave propagation that include density, deformation modulus and dilation.

Chapter 7 – examines the existing approaches for simulating large-scale

discontinuities in a numerical model and provides a detailed methodology for

incorporating large-scale structure in a cave propagation and subsidence analysis.



1 – Introduction


Chapter 8 – examines the deficiencies of the existing numerical production draw

models and develops new algorithms to simulate production draw through mass

balance calculations.

Chapter 9 – outlines the development of a new numerical algorithm to simulate

crater development in cave propagation and subsidence analyses.

Chapter 10 – outlines the development of a sub-level caving algorithm for the

simulation of production draw.

Chapter 11 – describes the implementation and validation of the numerical cave

propagation and subsidence model on a back-analysis of caving induced pit failureat the Palabora Mine in South Africa.


propagation and subsidence model on back-analysis of a structurally controlled

cave initiation and propagation at the Henderson Mine, USA.


propagation and subsidence model on a back-analysis of caving induced

subsidence at the abandoned Grace Mine in Pennsylvania, USA.


propagation and subsidence model on a back-analysis of caving induced

subsidence at the Kiirunavaara Lake Orebody sub-level cave.

Chapter 15 – provides a summary of the conclusions and recommendation for

future work arising from this research.



2 – Development of Cave Propagation and Rock Mass Modelling Techniques


Through a number of recent published case studies, these assumptions have been

shown to be incorrect. At the Ridgeway Deeps Mine in NSW, Australia, Beck et al.

(2011) documented a scenario in which cave initiation did not occur in a portion of

the undercut footprint. Carlson and Golden Jr. (2008) describe a situation at the

Henderson Mine in which migration of the propagating cave beyond the undercut

footprint was observed along a weak intrusive contact. And, at Northparkes Lift 1

Mine, Ross and van As (2005) have described in detail the highly variable caving

rate during cave initiation, propagation, stalling and rapid plug failure at this

operation.

The documentation of cave propagation rates at numerous operating minesaround the world also shows significant variability. The propagation rate has been

assessed by the ratio of the yield zone height to the average production draw

height measured in solid rock drawn. A summary is provided in Table 1.

Documented yield zone propagation rates from caving operations around theTable 1.world (after Sainsbury and Sainsbury, 2010).

Yield

PropagationOperation Method Rate Reference

El Teniente, Chile Panel 5: 1 Villegas (2008)

Henderson Mine, Colorado, USA Panel 7: 1 Board et al. (2009)

Grace Mine, Pennsylvania, USA Panel 8.2: 1 Sainsbury et al. (2005)Australian Coal Mine Longwall 8.9: 1 Hebblewhite (1995)

DOZ Mine, Indonesia Block 6-10: 1 Szwedzicki et al. (2006)

Kimberley Mines, South Africa Block 6 - 12: 1 Guest (2009)Lakeshore Mine, Arizona, USA Block 10: 1 Panek (1984)

Questa Mine, New Mexico, USA Block 10: 1 Gilbride et al. (2005)

San Manuel Mine, Arizona, USA Panel 10: 1 Gilbride et al. (2005)

Athens Mine, Michigan, USA Block 14: 1 Boyum (1961)

Palabora Mine, South Africa Block 15: 1 Sainsbury et al. (2008)

Northparkes Lift 2, Australia Block 20: 1 Pierce et al. (2006)Chinese Coal Mine Longwall 31.3: 1 Liu (1981)

Caving rates in the order of 5:1 up to 31:1 have previously been documented. This

variability can be attributed to variations in the in situ geomechanical conditions

and cave mining method. Based on the values presented in Table 1 it can be seen

that a longwall mining method provides the greatest documented propagation

rate, followed by block caving and then panel caving methods. The ability to

predict and represent this variation in propagation rates between caving methods





Figure 9. Empirical method for predicting caveability: Laubscher’s stability chart(after Laubscher, 1994).

Many mines still use Laubscher’s caving chart to estimate the undercut dimensions

required to induce self-sustained propagation, and, in most cases, good agreement

is achieved. However Lorig et al. (1995), van As and Jeffrey (2000) and De Nicola

Escobar and Fishwick Tapia (2000) have previously reported instances where

significant differences were observed between the actual and predicted cave

propagation behaviour. A detailed review of these cases by Trueman and

Mawdesley (2003) showed that the biggest variance in actual versus predicted

outcome was associated with strong (MRMR greater than 50) rock masses and

misinterpretation of the application of adjustments in the MRMR rating scheme.

As a result of this review, Trueman and Mawdesley (2003) proposed an alternate

method for the prediction of self-sustained propagation through an extension of

the Mathews stope stability chart (Mathews et al., 1981). Their extended stability

chart is provided in Figure 10.





Figure 10. Empirical method for predicting caveability: Extended Mathews StabilityChart (after Trueman and Mawdesley, 2003).

Although the development of this method extended the application of the existingempirical approach to stronger rock masses, by necessity, the method is still

limited by the dataset that it was developed from. Additional limitations of

Laubscher’s and Trueman and Mawdesley’s empirical approaches have previously

been documented by Brown (2003) and suggest that the approaches are only

satisfactory for footprint length to width ratios of three or less. Beyond this, the

technique is unable to account for variations in three-dimensional stress

redistribution around rectangular undercut footprints. In addition the influence ofonly one joint set orientation can be analysed. Experience suggests that the critical

joint set orientation may vary around the undercut footprint as the principal stress

direction changes during undercutting and cave propagation. Milne et al. (1998)

also suggest that the determination of adjustment factors can be ambiguous and

subject to personal experience. This means, for the same rock mass data set,

different caving behaviour may be interpreted.





In addition to their limited application, the use of empirical methods do not

provide any indication regarding the rate of cave propagation, nor the extent of the

cave behavioural regions. It can be assumed that the further into the caving zone

your scenario falls, the more rapid the cave propagation. However, the actual

timing or magnitude and the impact to underground and surface infrastructure

cannot be predicted without assumptions regarding the bulking behaviour of the

rock mass. In addition, limitations associated with compiling enough case study

data limit the application of empirical techniques to situations in which large-scale

discontinuities, rock mass strength anisotropy, scale effects, excavations and/or

significant topological relief and heterogeneous rock mass domains do not exist.

Numerical2.1.3

There are numerous numerical modelling methods (Boundary Element, Finite

Element, Finite Difference, Distinct Element and Hybrid) and approaches available

for performing stress and deformation analysis in geomechanics. The important

aspect of modelling is not necessarily the numerical program itself, but the

methodology for simulating the caving process, and the estimation of input

properties.

In his review of cave mining practices, Brown (2003) reasons that numerical

modelling enables a more fundamental and rigorous assessment of cave initiation

and propagation behaviour than empirical (or analytical) methods, since it may

have advantages in cases for which current experience is lacking.

The following section attempts to review the development of numerical caving

methodologies from 1970 (the time of the first known numerical caving model) to

the state-of-the-art routines that are currently being applied in geotechnical pre-

feasibility and feasibility studies today. Although other emerging numerical

techniques have been applied to the study of cave propagation such as Smooth

Particle Hydrodynamics (Karakel et al., 2011), they are not included in this

literature review since, to date, their application has not been compared to actual

case study data. For this reason, they are considered demonstration tools only.





2.1.3.1 Two-Dimensiona l Elasti c Models

Soon after the introduction of the Finite Element Method (FEM) for the numerical

analysis of stresses and displacements in continuous structures by Clough (1960),

Palma and Agarwal (1973) developed the first known two-dimensional, elastic,

finite element model to study cave propagation behaviour at the El Teniente Mine

in Chile. During this study, they identified the need to consider the nature of the in

situ rock mass fracture network and the impact of principal stress direction in

relation to the undercut dimensions on the cave propagation behaviour.

The high level of fracturing in the El Teniente rock mass was represented by

assigning zero tensile strength to all zones within the model. Although not many

details of the modelling methodology are provided, it is clear that yielding of the

rock mass immediately above the simulated undercut was assumed to propagate

when a tensile stress component was identified within a zone. Figure 11 presents

the results that clearly show the simulated impact of cave height based on in situ

stress and orientation of the undercut footprint.

Figure 11. Impact of principal stress orientation in relation to an undercut as definedby two-dimensional numerical modelling (after Palma and Agarwal 1973).





Although these simulations assumed that caving only occurred as a result of a

tensile failure mechanism, they were fundamental in understanding that strength

degradation and jointing played an important role in cave propagation behaviour.

In addition, they highlighted the importance of the orientation of a rectangular

mining block with respect to the in situ principal stress direction. It is now

understood that inducing the redistribution of the maximum principal stress over

the shorter footprint axis will promote cave propagation since the cave back

experiences greater stress concentrations when maximum principal stress hits

cave "broadside" as opposed to "end-on". In the case of “end-on”, the cave

presents a larger obstacle to stress. The concept is presented in Figure 12.

Figure 12. Conceptual diagram of effect of principal stress direction and undercut footprint dimensions on caveability.

The results of Palma and Agarwal’s work are the first known application of

computer-based numerical modelling for cave propagation analysis and

successfully provided a means for a more rigorous analysis of the tensile failure

mechanism that develops in advance of a propagating cave. In addition, they

highlighted the effect of stress field variations around the extraction level

geometry on cave propagation height. However, their consideration of a simple

elastic material model was unable to account for a stress-caving mechanism since

no failure criteria is specified. This meant that the rock mass in the cave back





could deform and become stressed infinitely without failing. This basic assumption

may be appropriate for some mining methods in very strong, massive rocks but

can lead to highly misleading results in weaker rock masses when there is the

potential for shear failure of the rock mass and redistribution of stresses.

2.1.3.2 Two-Dimensional Plasticity Models

Through the application of two-dimensional FEM simulations at the Grace Mine,

located in Pennsylvania, USA, Barla et al. (1980) introduced a softening material

model to represent the degradation of the in situ rock mass strength to a fully

weakened and bulked state during cave propagation. The use of such a material

model highlighted the limitations of elastic modelling completed by Palma and

Agarwal (1973) and the development in understanding that caving may not only

occur due to a gravity mechanism, but also a stress mechanism – as discussed in

Section 1.3.

The softening behaviour in the model was simulated through a periodic review of

the failure states in the numerical mesh. If a zone failed via a compressional or

tensile mechanism, then the strength, density and stiffness were reduced to a

residual value. Production draw was simulated through a force application in the

undercut roof. Figure 13 provides a schematic representation of their modelling

methodology.

The simulations conducted by Barla et al. (1980) do not only account for a

softening material model, but also represent the changes in deformation modulus

and density during cave propagation. In addition, they identified the importance

in being able to accurately represent the mining process within the numericalmodel in order to predict the most realistic rock mass response. However no

correlation was made regarding the amount of material withdrawn.





Figure 13. Development of two-dimensional numerical modelling approaches for cave propagation analysis. (a) Model mesh (b) section through the mining geometry (c) simulated undercutting process (d) contours of resultantmobilised strength – the shaded area represents a fully softened/caved rockmass (after Barla et al., 1980).





During the early 1990’s, Rech and Lorig (1992) conducted two-dimensional, finite

difference analyses in order to reproduce the existing cave conditions at the

Henderson Mine in Colorado, USA and predict the expected cave propagation

behaviour. These are the first simulations that attempted to correlate the

production schedule with the simulated cave propagation behaviour.

The cave zone was initialised within the model through a number of incremental

undercut expansions that corresponded to the historical and planned production

schedule. Vertical draw and a bulking factor were assumed based on the

volumetric equations outlined by Panek (1984). Stresses were reset to zero within

the cave mass and the rock mass properties were reduced to those consistent witha fully-bulked rock mass. Simulation of residual rock mass properties and reduced

vertical stress conditions within the caved mass ensured that the mining induced

stress magnitude and directions were accurately captured. However, by manually

initialising the caved rock mass within the model, a true and spontaneous cave

initiation could not be predicted. In addition, by artificially reducing stresses

within the cave, mass and energy were not conserved within the system. As a

result of this, the representation of the exact production tonnage simulated withinthe model could not be gauged and the real caving induced stress-damage may

have been under-estimated.

The algorithm used by Rech and Lorig to model the undercutting and mining

advance sequence is provided in Figure 14.





Figure 14. Methodology for the application of a continuum based numerical model forthe prediction of onset of caving (after Rech and Lorig, 1992).

During the International Caving Study (ICS 1997-2004), Karzulovic and Flores

(2003) considered the influence of depth, stress, large-scale discontinuities, rock

mass strength and groundwater on caveability through a generalised sensitivity

analysis with a two-dimensional FEM code. The caving methodology employed

assumed vertical cave propagation, similar to an analytical approach. In order to

estimate the potential for cave propagation, it was assumed that cave growth

would equal 10% of the undercut length (i.e. if the undercut length is 100 m, the

vertical propagation of the cave would be 10 m), as illustrated in Figure 15a.





Figure 15. Determination of the Cave Propagation Factor at Northparkes E26 Lift

1 (after Karzulovic and Flores 2003). Here a 480 m block height, and arock mass of fair to good geotechnical quality, (HC = 480 m, B = 180 m,K = 1.50) has been assessed. The chart indicates that the caving will not

propagate through the 480 m block.

Based upon stress redistribution around an imposed cave shape, a Cave

Propagation Factor (CPF) was used to determine if caving is ‘Problematic’,

‘Transitional’ or ‘Self-Sustained’ - much like Laubscher’s ‘Caving’, ‘Transitional’ and

‘Stable’ Zones. The CPF has been defined by Karzulovic and Flores as the ratio

between the average deviatoric stress acting on the cave back and the maximum

deviatoric stress that the rock mass can sustain. The equations used to determine

the value are presented in Figure 15.

Although simple assumptions were used in the representation of geometry, stress

redistribution (two-dimensional), rock mass plasticity and post-peak rock mass

behaviour, assessment of the CPF at the Northparkes Lift 1 Mine provided good

correlation with the actual performance of the cave that stalled in 1999 – as shown

in Figure 15b.





However, the methodology is unable to account for the time-dependent nature of

the stable arch that developed at Northparkes Lift 1 and the subsequent plug-

failure. Limitations associated with the two-dimensional nature of the modelling

and the assumptions regarding cave shape and the propagation window (defined

by W=0.1B in Figure 15a) also make it difficult for the technique to accurately

predict three-dimensional, self-sustained cave propagation, and the cave

behavioural regions presented in Figure 6. In addition, only vertical cave

propagation and homogeneous rock mass properties can be considered which

limits its applicability.

2.1.3.3

Axis-Symmetr ic Str ai n-softenin g Models

In an attempt to include a better representation of the three-dimensional shape of

the propagating cave and surrounding induced stress field, Lorig (2000) (also

reported in Brown 2003) conducted sensitivity simulations in axis-symmetric

models. A cylindrical undercut located at increasing depths was considered. The

initial state of stress within the model was assumed to be lithostatic and stress

boundaries (a support pressure) were imposed at the excavated undercut level to

ensure initial stability. To simulate production draw, the support pressure wasmonotonically reduced in the roof of the undercut (similar to the approach of Barla

and Boshcov, 1980) and the extension of the yielded rock mass (represented by a

strain-softening material model) was assessed.

A schematic representation of the modelling methodology used to simulate

production draw from these axis-symmetric models is provided in Figure 16.





Figure 16. Development of axis-symmetric numerical methods for cave propagation (a)axis-symmetric concept (b) evolution of the undercut pressure and height (c)

stepwise reduction of undercut pressure (d) details of the pressure evolutionwith a simulated reduction step (after Brown, 2003).

Through this approach, even though the true three-dimensional geometry and

stress tensor were not accurately represented, Lorig (2000) was able to predict a

hydraulic radius associated with cave initiation that compared well to Laubscher’s

empirical cave stability chart over a range of MRMR values. This technique is

considered to be an advancement on the CPF method proposed by Karzulovic and

Flores (2003) since failure was not limited to a window of rock mass in the cave





back (dictated by the undercut width), but allowed to evolve based on the rock

mass properties and stress state in the model.

Using this axis-symmetric approach, Lorig completed an analysis of theNorthparkes Lift 1 cave using the same parameters as Karzulovic and Flores

(2003). The displacement vector (a) and cohesion (b) results are illustrated in

Figure 17.

Figure 17. Development of cave geometry resulting from a two dimensional strain- softening numerical simulation, hydraulic radius 42.5m (a) displacementvectors (b) cohesion softening ; green represents no softening, red represents

fully softened rock mass(after Lorig, 2000).

For an incrementally expanding undercut size, the resulting cave yield height was

assessed in the numerical model. A hydraulic radius of 42.5 m was required to

reproduce the observed stalled yield zone height at Northparkes of 95 m. This is

consistent with the documented stalled undercut geometry by Ross and van As

(2005). However, although the cave yield height was reproduced, it is clear that the

shape of the yielded rock mass volume is not necessarily realistic when the results

are compared to the conceptual model of a cave. It is simulated with a flat back.

The modelling results of Lorig showed that a strain-softening model could be used

with confidence to predict rock mass damage and cave propagation. However, a

model that was able to simulate the failure mechanisms in the back of the cave in

more detail was required to ensure the flat back shape was addressed.





2.1.3.4 Two-Dimensional Disti nct Element Models

Two dimensional, Distinct Element Models (DEM) were developed by Lorig et al.

(1995) within the PFC 2D code (Itasca, 1995) to provide a greater understanding of

the fracturing of the in situ rock mass and an improved cave back shape based on

the models shown in Figure 17. Conceptual models of cave propagation behaviour

in a high initial stress state were developed and two fundamental failure

mechanisms associated with cave propagation were identified that included; intact

rock block failure and slip along pre-existing joints. The model results are

presented in Figure 18a and Figure 18b. Brown (2003) reports on the extension of

the two-dimensional DEM simulations to three-dimensional axis-symmetric

models which are presented in Figure 18c.

Figure 18. Development of a discrete element model to study cave propagation (a) particle clusters early in the caving process with superimposed contact forcechains (after Lorig et al., 1995). (b) particle clusters after significant cave

propagation showing internal fractures of blocks in the caving zone chains(after Lorig et al., 1995). (c) forces arching around the unstable rock mass(after Brown, 2003).

Within these models, each intact rock block is represented by particles that are

glued together. Upon initiation of the undercut, the bonds between the particles

are broken if the induced force is greater than the bond strength (stress caving).





Unstable particles that have broken their bonds or are unconfined, are free to

dislocate and fall moving into the space created by the undercut. Figure 18C

shows the force distribution in the particles around the cave periphery. The

increased caving induced stresses are seen as arching of these forces around the

cave limits.

These models illustrate the capacity of DEM codes to simulate the two primary

caving mechanisms in a jointed rock mass (stress and gravity). However, at the

present time, the size of these models is limited due to the computational intensity

of the modelling technique.

2.1.3.5

Thr ee-Dim ensional Disti nct Element Models

In spite of the computational intensity of the modelling technique, Gilbride et al.

(2005) and Sharrock et al. (2011) have most recently used a three-dimensional

DEM approach to model the mechanisms of caving for large-scale subsidence

analyses. Gilbride has calibrated a large-scale rock mass response through rock

mass simulations in a laboratory environment and used the results in a large-scale

model. His results are presented in Figure 19.





Figure 19. Large-scale (mine-wide) discrete element modelling of caving and subsidence phenomena in three-dimensions. Cross section of subsidence mass movement from block caving and simulated synthetic rock mass triaxial test of PFC

material (after Gilbride et al., 2005).

Since there is no comparison between actual field data, or presentation of the data

used for the calibration, it is difficult to determine the accuracy of the model

results.

Sharrock et al. (2011) calibrated a response through large-scale observations of

surface subsidence, as presented in Figure 20.





Figure 20. Large-scale (mine-wide) discrete element modelling of caving and subsidence phenomena in three-dimensions. Plan view cave zones: measured (blue) andsimulated (red) (after Sharrock et al., 2011).

In this case, there is significant difference between the model result and the

subsidence observations on the eastern limits of the crater.

It seems in each case, computational inefficiency of the DEM technique, has limited

the particle size within the models to 13-24 m, and thus restricted the size of the

physical phenomena that can be resolved. As a result of this, the small-scale

cracking / dislocation of the rock mass achieved by Lorig et al. (1995) was unableto be reproduced with such a large-scale model due to the minimum particle size

required to achieve this scale of model.

As shown by Gilbride et al. (2005) and Sharrock et al. (2011), at present, it is not

practical to simulate the complex large-scale mining/geological processes in DEM

codes due to the computational intensity of the numerical technique. It seems at

the current time, computational constraints continue to limit application of DEM

simulations to small-scale (e.g. <100 m) boundary value problems in densely





jointed rock. As a result of this, continuum methods continue to be used to ensure

that the regional mine scale changes can be captured in the one model.

2.1.3.6

Thr ee-Dim ensional Conti nuum Methods

Based on computational limitations of simulating the large-scale caving process in

DEM codes, Pierce & Lorig (1998) describe an improved methodology developed

in a three-dimensional continuum code compared to the axis-symmetric approach

reported by Brown (2003). In this model, sequential undercuts of constant width

were simulated to reproduce the increasing undercut hydraulic radius during cave

initiation. Production draw was simulated by monotonically reducing stresses at

the undercut level using the same methodology presented in Figure 16. For each

undercut increment, the model was stepped to equilibrium before subsequent

undercut expansions were simulated. In addition to the dynamic nature of the

undercut expansion, Pierce & Lorig implemented a user-defined function that

modified material properties and stresses based on plasticity state and strain

within the numerical model. Through this approach, the point at which self-

sustained propagation (the critical HR) could be determined based on the actual

three-dimensional stresses distributing around the undercut. A diagram thatrepresents the modelling methodology is provided in Figure 21a along with typical

model results (Figure 21b). It can be seen that the modelling methodology

generally still results in a flat cave back - Figure 21B-7.





Figure 21. Three-dimensional strain-softening, continuum models for cave propagation(a) logic sequence to simulate caving (b) typical simulation results (afterPierce and Lorig, 1998).

By reducing the stresses uniformly across the undercut, material was withdrawn

preferentially from the higher stress areas in the undercut. This methodology

highlighted the need for better control on production draw simulation.

As an advancement on this technique, Pierce et al. (2006) simulated production

draw based on the pseudo-static application of small downward-oriented

velocities in the back of the undercut. By doing so, the amount of material being

removed from an area could be controlled. Details of this methodology are

summarised in Figure 22.





Figure 22. Simulation of production draw from large-scale, three-dimensional strain- softening continuum models based on velocities.

Through this velocity controlled production draw, Pierce et al., (2006) were able to

simulate the evolving cave behaviour at Northparkes Lift 2 cave that was

consistent with the conditions observed in situ. The numerical results presented in

Figure 23 have been validated against measurements of openhole blockages, TDR

breakages and the progression of the seismogenic zone. Material properties

within the model were generated using the Synthetic Rock Mass (SRM) modelling

technique, which is discussed in Section 2.2.3.





Figure 23. Large-scale back-analysis of cave propagation behaviour at the Northparkes E26 Lift 2 Mine. Progression of predicted mobilised zone

limit (white iso-surface) and overlying yield zone limit (blue iso-surface)versus TDR breakage locations (blue spheres) and open hole blockagelocations (red squares) (after Pierce et al., 2006).





The numerical model was able to accurately predict the rate and shape of the

mobilised and yielded rock mass zones through a large-scale application.

Similar to this approach, Beck et al. (2007) developed a methodology for theassessment of cave propagation behaviour using the numerical modelling package

ABAQUS (Simulia, 2011). An example of some of the results from one of these

models is provided in Figure 24.

Figure 24. Example of a mine-wide, three-dimensional, multi-scale simulation (afterBeck et al., 2011).

An attempt was made to review the caving approach that has been developed in

Abaqus based on a number of publications (Beck et al., 2006; Beck et al., 2011).

However, at the present time there are insufficient details provided in these (and

associated) publications to allow for a detailed critical review. As a result of this, it

was not possible to comment on the appropriateness of the underlying

methodology, constitutive behaviours and associated assumptions for simulating

caving using Abaqus.





2.1.3.7 Hybr id Techni ques

Cave propagation behaviour of a jointed rock mass is strongly governed by the

unique nature of joints fabric together with the intact strength of rock-bridges that

make up a rock mass (Lorig et al., 1995). Apart from the DEM’s, most of the

current methodologies discussed to date represent the rock mass as an isotropic

material.

Pine et al. (2007) and Vyazmensky et al. (2007) used the combined finite element-

discrete element ELFEN code (Rockfield, 2007) to insert physical fractures into a

continuum finite element mesh that is gradually degraded into discrete blocks

through systemic sampling of the tensile strength and principal stress tensors.

The approach includes an adapted Mohr-Coulomb failure criterion that has been

coupled with a smeared crack model to trace the crack propagation process and

crack interaction. Initially, material is embedded with an initial fragmentation

profile based on a site specific fracture network. Results of recent simulations

conducted with this approach are presented in Figure 25.

Figure 25. Simulation of cave development using a hybrid, two-dimensional approach(after Rogers et al., 2010).

The modelling of a jointed rock mass using such an explicit technique requires the

precise specification of the joint locations and mechanical properties. It is

considered impractical to suggest that every joint can be defined and modelled in a

deterministic way for a large scale problem such as a caving. In addition, this

approach, although well able to represent brittle failure, still relies on a macro





failure criterion to determine the initiation of new cracks within the continuum

mesh.

In addition, the hybrid finite element / distinct element modelling methodology iscurrently limited to two-dimensions. Numerical modelling conducted by Palma

and Argawal (1973) have already shown that cave propagation is a three-

dimensional problem. The two-dimensional plane strain nature of the ELFEN

model, and the over simplified production draw simulation routine (i.e., uniform

draw over the entire footprint) can over-estimate the influence of major structures

and is not well suited to studying the potential for cave propagation to stall, as it

does not allow for the three-dimensional concentration of stresses in the caveback. Significant research has been conducted that demonstrates that a three-

dimensional analysis is required to accurately account for the influence of the

major principal stress orientation, undercut advance orientation, (Palma an

Agarwal, 1973) and three-dimensional structure (faults and joints) orientation and

persistence during cave propagation (Phillips and Hellewell, 1994).

Although many conceptual block cave models have been documented (Rogers et

al., 2010; Pine et al., 2007 and Vyazmensky et al., 2007) this approach has not

been validated against observed behaviour at an existing mine.

Summary2.1.4

The understanding of failure and deformation of jointed rock masses surrounding

underground and surface excavations has been a problem for centuries. However,

it was only during the 1970’s and 80’s and the rapid development of computer

technology that enabled numerical methods in rock mechanics to explore these

issues.

As a result of the low cost nature of the cave mining method, very large caving

operations are currently being planned around the world and the empirical caving

design methods which have long served the industry are no longer adequate for

the assessment of complex rock failure and deformation processes expected at

these locations. In addition, these empirical techniques do not satisfy the

increasingly stringent risk-based criteria for approving the large capital

expenditure in caving mines prior to production.





It is clear that the last ten years have seen significant developments in numerical

modelling methodologies that facilitate the ability to simulate the rock mass

behaviour and failure mechanisms associated with large, cave-scale problems.

Through its consideration of fundamental rock mass behaviour and evolving

production draw schedule, the caving algorithm described by Pierce et al., (2006)

is considered to be the current “state-of-the-art in block and panel caving from a

geomechanics perspective (Brown, 2003)” and should be used as the basis for an

expanded numerical model moving forward.





2.2 Rock Mass Modelling Techniques

Introduction2.2.1

The strength and deformation behaviour of a jointed rock mass is governed

strongly by (a) the intact strength of the rock and (b) the presence of

joints/discontinuities (Brown, 2003).

The strength of the intact rock bridges is generally assumed to be the same as the

intact strength of the rock determined by laboratory testing. However, it is well

established that uniaxial compressive strength of intact rock decreases as

specimen size increases. This kind of change in the mechanical properties of rock

with size is referred to as scale effects. Previous investigations (Hoek and Brown,

1980; Pratt et al., 1972) have shown that this scale-dependent decrease may vary

between 20-80% of the measured intact value in the laboratory. The large-scale in

situ and laboratory scale tests of Pratt et al. (1972) are provided in Figure 26.

Figure 26. Measured rock strength-scale effect including large size specimens of in situtest (after Pratt et al., 1972).





The strength of rock joints is dependent on their properties, level of interaction

and loading conditions. Bandis et al. (1983) showed through laboratory

investigation of the deformation characteristics of rock joints under normal and

shear loading that, at both low and high stress levels, the deformation of pre-

existing joints dominates the behaviour of a rock mass. It has previously been

shown by Mas Ivars et al. (2011) that preferred joint orientations can induce a

marked anisotropy in deformation modulus, strength and brittleness of the rock

mass. In addition, joint density and persistence must be considered relative to

problem size – as shown in Figure 27.

Figure 27. Applicability of the Hoek-Brown empirical rock mass strength criterion atdifferent scales (after Li et al., 2008).

It is not possible to derive material properties of a rock mass based on laboratory

tests due to the size requirements of a sample scale large enough to achieve

repeatable strength results (i.e. Representative Elemental Volume, REV). In

addition, the field testing programs of a sufficient magnitude and nature are

expensive and relatively crude. Therefore, the current practice for the

characterisation of jointed rock masses is based on either empirical or numerical

methods.





The following section reviews the current techniques used to represent the

strength response of jointed rock masses that can be used for an assessment of

cave propagation and subsidence behaviour.

Hoek-Brown Strength Criterion2.2.2

The Hoek-Brown failure criterion is widely accepted as the standard for rock mass

strength estimation and is routinely applied to rock mechanics problems. The

criterion was developed during the 1980’s (Hoek and Brown, 1980) based on the

results of research into the brittle failure of intact rock and simulations of jointed

rock mass behaviour. The criterion uses the properties of intact rock and applies

some reduction factors based on the characteristics of jointing to represent a large-

scale peak strength response.

During 1983, most numerical modelling codes were written in terms of the Mohr-

Coulomb criterion and Bray (1983) developed a solution to relate the non-linear m

and s parameters of the Hoek-Brown strength envelope to the Mohr-Coulomb

strength criterion. This allowed Hoek-Brown strength to be expressed in terms of

cohesion and friction and therefore be easily used in numerical modelling

simulations of rock mass strength.

Using the method developed by Bray, values for cohesion and friction can be

obtained by a least-square fit to the Hoek-Brown failure envelope. A bi-linear,

Mohr-Coulomb fit to the Hoek-Brown curve can be used to more accurately

represent the actual non-linearity of the failure envelope. The range of stress over

which the Mohr-Coulomb properties are fit can be limited to ensure a better match

over the range of expected induced stresses. The impact of applying a bi-linear

versus linear fit can be seen in Figure 28a along with the requirement of estimating

the range of 3 expected (Figure 28b).





Figure 29. Idealised stress-strain curves representing different material behaviour usedin numerical modelling.

Linear Elastic - An isotropic elastic model provides the simplest representation of

material behaviour. This model is valid for homogeneous, isotropic, continuous

materials that exhibit linear stress-strain behaviour with no hysteresis on

unloading. There is no representation of the post-peak response. In reality, rock

only exhibits elastic behaviour until a certain yield stress is reached, beyond which

it ceases to behave elastically.

Perfectly Plastic - During perfectly plastic straining, plastic strains continue

indefinitely at constant stress. The ratio of plastic strain is related to the yield

stress, which also represents the failure stress. A perfectly plastic rock is

characterised by the assumption that the stress causing the permanent non-

recoverable strain must reach a certain value before any extension or contraction

can take place. When the yield stress is reached, the rock deforms permanently

and continues to yield at this stress.





Linear Elastic-Perfectly Plastic - An assumption is made by an elastic-perfectly

plastic relationship that the stress - strain response can be represented by two

straight lines that describe an initial linear elastic stiffness and the yield stress or

strength at failure during plastic straining. Rock behaves elastically for stresses

less than the yield stress, then deforms without limit at the yield stress. A rock that

exhibits such a response can be considered perfectly ductile.

Perfectly Brittle - Rock that exhibit a stress-strain response similar to Figure 29E

are called perfectly brittle materials. For a brittle rock, the stress strain curve is

nearly linear at all stress levels, up to and including the final fracture stress. Brittle

failure is the process by which sudden loss in strength occurs. During brittlefailure the strength of the rock mass reduces to a residual value instantaneously.

Strain-softening - When stress has exceeded the elastic limit, the rock mass

begins to yield. It continues to yield until the peak strength is reached before

reducing to a residual value.

Strain-softening behaviour best describes a rock mass response during caving

since it is able to represent the progressive nature of the strength reduction. A

strain-softening model has previously been used by Pierce et al. (2006) to simulate

the complex process of the progressive failure and disintegration of a rock mass

from an intact, jointed material to a bulked rock mass during the caving process.

An example of simulated strain-softening behaviour in is provided in Figure 30. In

this instance, both the intact and joint response is considered during simulated

sample straining.





The study of the post-peak behaviour of rock is limited (Hoek and Karzulovic,

2000; Russo et al., 1998; Cai et al., 2007) since few apparatus exist that have the

capacity to test large-scale samples. In addition, it is known that the post-peak

behaviour of rocks tested in the laboratory is dependent on specimen geometry

(height: diameter ratio) (Hudson et al., 1971). As a result of this, the current

understanding of the strain-softening behaviour of jointed rock masses is based

largely upon large-scale numerical back-analyses and physical observations.

2.2.2.2 Estimat ion of Cr it ical Plasti c Str ain ,

Cundall et al. (2005) have previously estimated the FLAC 3D (Itasca, 2009), post-

peak softening rate ( ) of a rock mass based on the numerical back-analyses of a

number of large-scale case studies. The data is presented as the blue data points in

Figure 31.

Figure 31. Summary of FLAC 3D critical strain relation and data points used for fitting.

The results indicated a dependence of on the Geological Strength Index (GSI)

and, by linear regression:

[2]

Where GSI is the Geological Strength Index and is the critical plastic strain of a

10m zone in FLAC 3D. It is important to note that this equation is only valid for GSI





values ranging from 0 to 98. The value may be scaled with respect to edge length

by Equation [3].

[3]

Where z is the element width or edge length of zone in model.

The values derived from this relation are consistent with the typical stress-

strain relations provided by Hoek and Brown (1997) for strain-softening rock

masses which show that rock masses with higher GSI values are more brittle than

rock masses with a lower GSI.

Since the development of the relation by Cundall et al. (2005), additional case

studies have been completed as part of this research (presented in Sections 11, 12,

13 and 14) and are provided as the red data points in Figure 31. A new linear

relation [4] is proposed to determine a value that fits the combined datasets

and is valid for all GSI values from 0 to 100.

[4]

In the case of caving, softening of the tension and cohesion at this rate should be

applied to ensure the rock mass in its post-peak state is represented with the

greatest accuracy.

2.2.2.3 Mesh Dependency

Trueman and Mawdesley (2003) suggest that numerical methods that use a strain-

softening approach are not robust since the post-peak response is highly sensitiveto mesh size. This is true, if mesh dependency is not accounted for in the

development of material property responses.

There are at least two methods that can be used to alleviate the problem of mesh

dependency as outlined by Dawson and Cundall (1995). They include Cosserat

Theory and the Standard Regularisation Method.





Where s is the softening slope, is the change in material property value and

is the change in displacement.

In order to obtain mesh-independent results, a scaled softening slope can be inputsuch that the slope is dependent on the element width as shown in Equation [7].

[7]

Where is constant and relates to Equation [4] and, in the case is

independent of and can be re-written as Equation [8].

[8]

Using this relationship, for example, if the zone size is doubled, then the critical

strain must be halved for comparable results.

Through this approach Lorig (2000) showed that cave simulation results are

repeatable with different sized meshes. His results are provided in Table 2.

Cave height as a function of brittleness (after Lorig, 2000).Table 2.

Critical Plastic Strain Cave Height

Grid ( ps

crit

ps

crit) (m)

Coarse 0.1 160

Fine 0.02 150Coarse 0.005 200

Fine 0.01 205

Coarse 0.0025 225

Fine 0.005 250

This scaling approach has also been used by other researchers to account for mesh

dependency in the numerical simulation of other geomechanical processes (Crook

et al., 2003).

Scale-Dependent Brittleness2.2.2.3.3

It can be shown that for the same numerical zone size, increasing the size of a test

sample will result in a more brittle post-peak response. This is shown in Figure 32

where Unconfined Compressive Strength (UCS) testing has been conducted on a

strain-softening material. The zone size and critical strain have remained





consistent between all simulations, along with the applied loading rate at the

specimen ends.

Figure 32. Post-peak response as a function of zone resolution controlled by samplewidth.

It can be seen that, as the sample increases in size, the peak-strength remains the

same, but the post-peak response becomes more brittle. This phenomenon has

been considered by Hajiabdolmajid and Kaiser (2003) and is believed to be the

result of differences in failure mechanisms leading to different material brittleness

– or “scale-dependent brittleness”.

This phenomenon has been described by Detournay (2009) by considering a

triaxial test on a sample of height L. For simplicity Detournay considered that all

the deformation is concentrated along a band, and that the band is at an angle

with the direction of the axial load. The slope of the axial stress-strain behaviour

at the platen can be then given by Equation [9].





[9]

Where

is the axial reaction pressure,

is the global axial displacement (both

measured at the platen), L is the sample height and is the axial strain.

With all the deformation being associated with the band, the quantity u can be

considered as a material band property. This may be achieved since softening

behaviour may be understood by considering that, viewed from the outside, the

band behaviour is characterised by a stress-displacement law with the slope (S )

characterised by Equation [10].

[10]

Where α is the band angle in reference to the direction of the axial load.

Thus, the overall stress-strain law is dependent on sample size, and the larger the

size, more brittle the global behaviour. So, in performing simulated laboratory

tests for calibration of material responses, the observed softening rate will be

proportional to sample size and the observed mode of localisation.

Similar modelling results can be achieved in each of the test samples by:

Increasing the zone resolution on the smallest sample size to be consistent

with that of the largest samples size. This will yield the same brittle post-

peak response as the largest sample ; or

Decreasing the zone resolution on the largest sample size to be consistent

with that of the smallest sample size. This will yield the same post-peakresponse as the smallest sample.

The post-peak brittleness of the numerical constitutive model must be an

emergent behaviour since, small and large-scale failure mechanisms must be able

to develop naturally to allow the natural cave propagation behaviour. Calibration

of material responses must be undertaken at a scale consistent with the detail of

failure that is required to be resolved within the simulation. The selection of zone

and sample size is further discussed in Section 2.2.2.3.4.





Localisation and Bifurcation2.2.2.3.4

Zones of localised deformation (shear bands) are a common feature of brittle

jointed rock masses that have failed in compression, both in the laboratory and

naturally as earth faults (Rudnicki and Rice, 1975).

Localisation refers to the “occurrence of strong strain gradients in specific areas of a

material that finally become discontinuities” (Varas et al., 2005). The possibility of

localisation occurs when one or more stress components in an element are able to

decrease with increasing strain. Cundall (1991) suggests that there are three

possible ways that stress in an element can decrease with increasing strain:

large geometrical distortions (i.e., buckling of a thin beam)

material softening in which the intrinsic material becomes weaker (i.e.,

dilatant material becomes looser and hence weaker), or a

change in stress state such that at least one stress component decreases.

It is the latter two of these possibilities that are expected to occur during caving.

Localisation has been shown to occur by Santarelli (1989) and Besuelle (2001) at

stresses levels of between 60% and 90% the peak strength. However, shear bands

are already in place by the time that the material softening commences. The

development of shear bands is triggered by very small local variations in the initial

conditions of the problem – known as bifurcation. Bifurcation is well known in

laboratory settings, where, for example, in a simple shear test, a sample may either

deform uniformly or develop shear bands. Within numerical modelling codes,

bifurcation entails the occurrence of multiple solutions compatible with

equilibrium equations and boundary conditions.

In a previous study, Cundall (1991) shows that the process of shear band

formation is one of crack coalescence rather than propagation. When the

numerical simulation is run for a long time, bands are seen to coalesce, grow both

in length and intensity and finally become dormant. Furthermore, Cundall (1991)

also shows that the formation of one band will inhibit the formation of anotherlaterally nearby, i.e., two bands cannot form close together. The inhibiting effect





Figure 33. Schematic diagram of a tensile failure mechanism that does not affectcohesive strength.

This phenomenon has previously been described by Pine et al. (2007). “Crack

growth orthogonal to the direction of dilation in a compressive stress field does not

immediately produce a mechanical instability, as observed in tensile fields…It is thisstable fracture process in compression that results in large differences between

tensile and compressive strengths.”

Palma and Agarwal (1973) have previously considered this mechanism of

independent tensile softening in an analysis of caving at the El Teniente Mine

through a continuous sampling of stresses within a numerical model. The same

approach is proposed for the numerical model of cave propagation. In addition to

softening tension and cohesion at the same rate based on plastic strain (discussed

in Section 2.2.2.2), tension should be allowed to soften independent of cohesion in

the instance of a tensile yield state within the model. This will ensure that a

gravitational mode of caving can accurately be represented within the model and

develop independently of a stress caving mechanism.

The implementation of such a relation suggests that a rock mass is perfectly brittle

in tension. Previous investigations by Cai (2010) suggest that this is a reasonable

assumption.





2.2.2.5 Fr ict ion Hardening

If linear Mohr-Coulomb fits are derived for a Hoek-Brown strength envelope at

varying 3 values (see Figure 34), it is clear that; as confinement decreases,

friction increases and cohesion decreases. This suggests some dependency of

cohesion and friction on confinement levels.

Figure 34. Development of equivalent linear Mohr-Coulomb strength parameters basedon a fit to the Hoek-Brown strength envelope.

Through laboratory testing, Schmertmann and Osterberg (1960) showed that the

two strength components, cohesion and friction are not necessarily mobilised

simultaneously during straining and that the cohesive component of strength is

mobilised early in compression tests, while friction (and dilation) requires

additional straining to reach full capacity.

Previous research conducted by Diederichs (2007) has shown that the response of

a rock mass during stress-yielding is predominantly a result of a tensile failure

mechanism, as pre-existing joints propagate. As a result of this, the impact of

friction (and dilation) is limited until a failure plane localises.





Hajiabdolmajid, Kaiser and Martin (2002) have explored this concept in relation to

failure in laboratory specimens and around underground openings. They relate

the mobilisation of the cohesion and frictional strength components to

accumulated plastic strain. A sketch showing their conceptual model is presented

in Figure 35.

Figure 35. Schematic diagram of the mobilisation of the strength components cohesionand friction (a) in the laboratory (b) around an underground opening; c i andc r and ε c

p and ε f p represent the plastic strain components when the friction

and cohesion strength components have reached ultimate values (afterHajiabdolmajid, Kaiser and Martin, 2002).

The simplest Cohesion Weakening Friction Strengthening (CWFS) model has

previously been described by Ettema et al. (1989) as a bi-linear function. “One

(friction) value is taken at the peak of the stress-strain curve … Its value is affected by

initial porosity and confining pressure prior to shearing. The other value is taken

after considerable straining … when further straining occurs without significant

change in either porosity or confining pressure.” This is known as the constant or

residual friction angle. Pierce et al. (2006) have previously reported residual

values of 43-45 degrees for jointed rock masses.





In order to account for the generalisation of frictional strength by Ettema et al.

(1989), a dynamic cohesion and friction model was proposed by Hoek, Kaiser and

Bawden (1995) whereby instantaneous friction and cohesion values were

calculated based on the relationships between normal and shear stress, joint

condition (JRC and JCS) and an initial estimate of a Basic Friction Angle ().

Although good modelling results were achieved, limitations associated with the

scale of the problem arise when implementing such an equation when joint

condition and orientation with respect to normal and shear stress is not constant.

Hajiabdolmajid and Kaiser (2002), Diederichs (2002) and Zhao and Cai (2010)

propose a plastic-strain dependent CWFS model whereby the softeningcharacteristics are related to site-specific case study applications. Within this

constitutive relation, after mobilisation to a peak value, friction is gradually

reduced to a residual value. An example of such an implementation is provided in

Figure 36.

Figure 36. Implementation of the CWFS model in a two-dimensional numerical model

of a tunnel failure (after Barton and Pandey, 2011).





A CWFS model has successfully been used in the back-analysis of two breakouts in

different rock types at the Underground Research Laboratory (Hajiabdolmajiod et

al., 2002) as well as in two slope failures in jointed rock (Hajiabdolmajiod and

Kaiser, 2003; Eberhardt et al., 2002). However, it is noted that in a numerical

back-analysis of one of the tunnel break-outs presented in Hajiabdolmajiod and

Kaiser (2002), the non-uniformity of the mesh (i.e., not aspect ratio zones) and no

discussion of critical strain scaling may be affecting the simulation results.

Pierce et al. (2006) have modelled friction as a strain-softening value whereby the

peak value has been estimated by a linear Mohr-Coulomb fit to the Hoek-Brown

curve. Friction is modified to a residual value in response to plastic shear strain (atthe same rate as cohesion) and volumetric strain. Barton and Pandey (2011)

developed a similar approach; however, their friction value is dynamic and has

been calibrated based on the application at two case study locations.

In order to account for the CWFS behaviour of a rock mass, it is proposed that the

peak friction angle/s be estimated by the bi-linear technique described in Section

2.2.2. The values should be modified to a residual value of 43-45 degrees after a

fully bulked rock mass state is achieved and/or at the same softening rate as

cohesion.

A fully bulked rock mass state (or maximum volumetric strain achievable) can be

estimated based on the maximum porosity (η) of a rock mass previously

determined by Pierce et al. (2006) to be approximately 0.4. Based on this, a

volumetric strain cut-off, , of approximately 66% can be determined by

Equation [11].

[11]

Where η is the rock mass porosity. In this instance, the fully bulked rock mass will

have properties consistent with gravel e.g., frictional strength only.

2.2.2.6 Summary

It is generally accepted by the geotechnical engineering community that the Hoek-

Brown Failure Criterion, is the most widely adopted standard for expressing the

strength of a jointed rock mass. It is therefore considered the starting point for the





representation of rock mass strength for a cave propagation and subsidence

assessment.

As a result of this, a bi-linear CWFS constitutive relation is proposed for thenumerical model of cave propagation. Initial cohesion and friction values are

determined from a bi-liner Mohr-Coulomb fit to the Hoek-Brown curve.

Cohesion and tension should be softened to a residual strength of zero in relation

to which can be determined from Equation [4]. In addition, tension softening

must be allowed to occur independently of cohesion softening through the

constant querying of plasticity states. A residual friction angle of 43-45 degrees is

simulated once a maximum volumetric strain is exceeded and/or at the same rate

as cohesion. This maximum value can be determined by Equation [11].

Provided mesh dependency is accounted for within the calibrated rock mass

response, the simulated laboratory response of a bi-linear, strain-softening rock

mass under uniaxial compression and triaxial compression loading conditions

(illustrated in Figure 37) provides the general elastic, peak strength, post-peak

softening and dilatancy mechanisms expected in an isotropic rock mass asconfinement is increased.





Figure 37. Example of simulated bi-linear, strain-softening response (after Sainsburyet al., 2010).

However, limitations associated with the application of this failure criterion

include:

Assumes an isotropic rock mass, i.e. same strength in all directions.

Previous studies by Mas Ivars et al. (2008) shows that most jointed rock

masses display some anisotropic strength characteristics.





No consideration of the post-peak response. This is required to be

estimated based on an empirical relation developed by Cundall et al. (2005)

and modified herein (Equation [4]).

Developed by extensive curve fitting. Its extrapolation beyond the data

limits (i.e., in rock masses that exhibit very low or very high GSI values), and

rock-type for which the curve was developed has not been validated.

Requires the selection of a confining stress for equivalent Mohr-Coulomb

strength parameters. The selection of the stress range poses problems

when conducting large-scale analyses under a number of different

confinement conditions (depths) or stress paths.

The strength is derived for a specific sample size – in relation to the

problem description. There is no way to simulate the scale-dependent rock

mass strength response within the one analysis.

The Synthetic Rock Mass (SRM) Modelling Approach2.2.3

Due to the inherent difficulty of testing large-scale rock mass samples in the

laboratory or field, reliance has been placed on empirical classification rules and

systems derived from practical observations (i.e., GSI, MRMR, etc.). Despite the fact

that these systems and relations are in widespread use in engineering design, their

ability to consider strength anisotropy (resulting from a preferred joint fabric

orientation), scale effect (resulting mainly from the combined effect of joint density

and joint persistence), and post-peak strength response remains limited.

Previous investigations (Hoek and Brown, 1980) have shown that the strength and

deformation behaviour of a jointed rock mass is governed strongly by (a) the intact

strength of the rock and (b) the presence of joints/discontinuities. The Hoek-

Brown strength criterion accounts for each of these components implicitly by

using a global strength value and smearing the effect of joints through an isotropic

rock mass response. A technique is required that allows for the independent

failure and degradation of each of these components (joints and intact blocks).

Based on the small-scale failure mechanisms that are required to be resolved in

order to simulate a propagating cave, Synthetic Rock Mass (SRM) modelling was





developed (Pierce et al., 2006) to allow for the detailed consideration of the rock

mass joint fabric in the determination of rock mass response at large scales – i.e. 10

to 100 m. The SRM methodology uses PFC 3D (Itasca, 2007) to explicitly represent a

Discrete Fracture Network (DFN) embedded within an intact rock matrix.

The intact rock matrix is simulated using the Bonded Particle Model (BPM). The

BPM represents the rock as rigid particles (grains) glued together at their contacts

by parallel bonds that represent a normal and shear stiffness. As a result of these

bonds, the BPM does not impose theoretical assumptions and limitations on

macroscopic material behaviour, as continuum models do. Micro-cracks are able

to form, interact, and coalesce into macroscopic fractures according to localconditions. In this manner, macroscopic material behaviours not encompassed by

current continuum theories can be investigated. The BPM has a demonstrated

ability to reproduce many features of rock behaviour, including elasticity,

fracturing, acoustic emission, and damage accumulation producing material

anisotropy, hysteresis, dilation, post-peak softening, and strength increase with

confinement (Mas Ivars et al., 2011); all of which have been validated based on

instrumented laboratory tests. The micro-properties of the intact rock in SRMsamples are chosen via a calibration process based on matching laboratory test

results (intact rock UCS, Young’s modulus, and Poisson’s ratio).

Discontinuities within the rock mass samples are represented via the Smooth Joint

contact Model (SJM) which allows the simulation of a smooth interface between

particles regardless of the local particle contact orientations along the alignment as

shown in Figure 38.





Figure 38. The Smooth Joint Contact Model. (a) Graphical representation of how thesmooth joint contact model can be used to realign the default contactorientation to one that honours a macroscopic joint orientation. (b) Byusing the smooth joint contact model to reorient all contacts lying along themacroscopic joint plane, sliding along a smooth planar feature can be moreaccurately simulated (after Mas Ivars et al., 2011).

With the SJM, macroscopic joints with a given dimension and orientation can be

embedded within the assembly and can experience shearing in the manner of a

smooth, frictional surface without resorting to particle size refinement or particle

relocation along the joint surface (Mas Ivars et al., 2011). It has been demonstrated

that the model can be used to reproduce the extension and coalescence of multiple,

isolated, embedded flaws observed in laboratory experiments (Deisman et al.,

2008).

A SRM sample can explicitly account for the presence of intact rock bridges

between terminating fractures – similar to in situ rock mass conditions. Through

simulated testing of the synthetic samples, it is possible to derive large-scale rock

mass failure mechanisms and properties such as deformation modulus, strength

and brittleness. An example SRM composite sample is presented in Figure 39.





Figure 39. Components of a Synthetic Rock Mass sample. (a) Three-dimensionalDFN, (b) the corresponding three-dimensional synthetic rock mass sample,and (c) synthetic rock mass basic components. The colours in (b) and (c)denote intact rock blocks bounded by joints. Notice the internal non- through-going jointing in the ‘‘intact’’ rock blocks (after Mas Ivars et al.,2011).

Simulations of uniaxial compression testing on a SRM sample are presented in

Figure 40. For each of the tests, the full stress-strain curve and the percentage of

bond breakages versus total initial bonds have been recorded (percent damage).

These parameters provide an estimate of the pre-peak and post-peak behaviour of

the rock mass along with an estimate of the amount of intact damage occurring

within the sample during loading.





Figure 40. Three-dimensional response of a synthetic rock mass sample tested in three- opposing directions under unconfined compression; testing directions east- west, north-south and vertical (after Sainsbury et al., 2009).

The potential power of SRM is that it allows for site-specific consideration of joint

fabric, loading conditions and material property variations. This may be

particularly useful in cases where the joint fabric is highly anisotropic (as shown in

Figure 40) or where the problem is sensitive to post-peak strength. In addition,

large-scale samples can be tested in significant detail – ensuring an accurate failure

mechanism is represented.

Based on a review of the SRM technology, Hoek and Martin (2010) believe that

“there is no doubt that the tools assembled in the SRM approach are the most

advanced available to us today ” and that they “believe the physics in the SRM

approach is sound ”. In addition they go on to say that “we believe very strongly that

the Bonded Particle Model (BPM), the modelling foundation for the SRM, is the only

commercially available code that can be used to properly capture the behaviour of

intact rock. Sufficient published and independent research using the BPM has been





carried out over the past 10 years to show that the BPM logic can be used to match

the laboratory behaviour of intact rock… We are optimistic that the SRM

methodology should be suitable for studying the behaviour of discontinuous rock

masses; because we believe it has the best representation of the processes that are

active in a yielding discontinuous rock mass… Claims have been made by users of …

ELFEN … that many of the SRM features can be reproduced by these codes. However,

it is difficult to verify some of these claims as critical comparisons are seldom carried

out ”. It can be said that this statement rings true for just about all of the existing

numerical techniques for cave propagation assessment (reviewed in Section 2.1),

apart from the technique outlined by Pierce et al. (2006) since, little validation

against real-life case studies has been completed and documented in detail for

verification purposes.

The review by Hoek and Martin endorses the SRM approach developed in PFC 3D for

rock mass characterisation above all other SRM approaches that have been

proposed (e.g. Vyazmensky et al., 2007; Beck et al., 2007) and therefore forms the

basis for the characterisation of rock mass strength in the numerical model of cave

propagation behaviour and subsidence assessment detailed herein.

2.2.3.1 Appli cati on of Synt heti c Rock Mass Modell in g for Cave Pr opagat ion

Assessment

Previous caving investigations have been conducted using the SRM approach at the

Northparkes Mine (Pierce et al., 2007). Through simulated testing of synthetic

samples and carrying tests through to complete disintegration (residual strength),

both pre-peak properties (modulus, damage threshold and peak strength) and

post-peak properties (brittleness, dilation angle, residual strength and

fragmentation) were developed as shown in Figure 41.

The material response of SRM samples has been validated through a comparison of

fracture orientations produced when a SRM sample is subjected to the same

mining induced stress path and that has seismic monitoring data available (Figure

42a); and a comparison of SRM fragmentation predictions with drawpoint

observations (Figure 42b).





Figure 42. Validation of Synthetic Rock Mass response based on observed andmeasured fracture modes and fragmentation (after Pierce et al., 2006).





In the case study of Northparkes (above) it can be seen that the microseismic

response generated in SRM samples matches with seismic observations

underground. In addition the predicted SRM fragmentation, after stress-path

dependent testing, closely matches with fragmentation measured at production

drawpoints.

In order to use SRM strengths in a large-scale analysis, Pierce et al. (2006)

calibrated continuum constitutive model responses. Although good results were

achieved when cave propagation behaviour was simulated for a specific instance

as shown in Figure 43, the SRM simulations were only applicable to those domains

and stress paths immediately surrounding the Northparkes Lift 2 cave.





As a result of this, the more generalised SRM testing methodology (described by

Mas Ivars et al. 2008) is considered more universally appropriate for

implementation in caving models. Mas Ivars et al. (2008) describe how the SRM

methodology has been developed to allow testing of a rock mass in all three

opposing loading directions and at a number of different scales. Three industry-

standard tests, (direct tensile test, uniaxial compressive-strength test and triaxial

test) were selected to provide measures of rock-mass tensile strength (),

unconfined compressive strength () and compressive strength at several

confinement levels (σ3i , σ3ii , etc). This ensures that the material constitutive

properties derived from this technique are not specific to one particular stress

path, and they may be applied to a number of different large-scale

mining/geological processes.

2.2.3.2 Summary

Based upon the limitations of empirical techniques to consider, strength

anisotropy and scale effects, the SRM technique is considered an advancement in

the determination of rock mass behaviour when compared to the Hoek-Brown

approach. A review of SRM technology (Hoek and Martin, 2010) has provided apositive response and their assessment concludes the SRM provides “(the best)

representation of the processes that are active in a yielding discontinuous rock mass”.

However, the application of three-dimensional SRMs to large-scale (e.g. >100 m)

boundary value problems in densely jointed rock has been relatively limited to

date. Current limitations of the technique include computational constraints that

continue to restrict application of the technique to smaller-scale boundary value

problems. Pierce et al. (2006) have previously shown how a continuum

constitutive model can be calibrated to SRM strength responses. Cave propagation

analyses conducted using this technique provided numerical results that match

well with the observed conditions during cave propagation at the Northparkes E26

Lift 2 Mine. However their responses were limited to a specific application and a

more generalised calibrated continuum response is required.





In lieu of SRM strength responses, the Hoek-Brown strength criterion can be

considered in instances when strength anisotropy or scale effects are expected to

be minimal.



3 – Research Outline


RESEARCH OUTLINE3

3.1 Objectives

The ability to assess the advance rate and shape of a propagating cave in response

to a production draw schedule is critical in being able to plan mining infrastructure

since, once production commences, the ability to modify the mine design is limited.

The requirement to make predictions with confidence, from drill-core data, prior

to the rock mass being exposed on a large-scale (i.e., scanline mapping of a drift) is

of paramount importance.

Based on a review of the current literature, it is clear that numerous approaches to

assess cave propagation and subsidence behaviour exist. The objective of this

research is to develop a state-of-the-art numerical model of cave propagation and

subsidence assessment that is rigorous and robust and that can be used to focus

geotechnical studies and provide a greater understanding of cave propagation and

subsidence behaviour.

The numerical model will extend the existing numerical techniques reviewed in

Section 2 through the improvement of:

the existing height of draw production scheduling technique described by

Pierce et al. (2006) and implementation of a mass based production

schedule as a direct input to the numerical modelling algorithm.

the simulated rock mass constitutive behaviour that governs the volumetric

response of a material due to caving. This includes the development andimplementation of relationships between volumetric strain and density,

dilation and deformation modulus.

simulation of rock mass response around a propagating cave due to the

presence of large-scale persistent structures.





And the development of:

a validated constitutive model that is able to account for rock mass strength

and deformation anisotropy as described by Synthetic Rock Mass testingoutlined by Mas Ivars et al. (2008).

a generalised production algorithm that is able to simulate all three, block,

panel and sub-level caving scenarios.

an algorithm that is able to update the ground surface profile as a result of

the development of a subsidence crater. This will ensure that the

subsidence limits predicted by the numerical model will be rigorous.

In addition, the development of the numerical model must:

ensure that the requirement for geotechnical information is limited to that

which is already contained within a typical geotechnical database.

not rely on assumptions having to be made regarding initiation, cave shape

and the rock mass dilation (bulking) response to ensure that cave stalls can

be predicted.

be based on a clear and unambiguous methodology which is thorough,

robust and transparent and that provides results that are clear, easy to

interpret and meaningful. The results should be presented in terms of

evolving cave shape, interaction with other mining areas, location/extent

of cave behavioral domains, bulking factors, propagation rates, expected

magnitude and extent of damage (surface and underground) and potentialfor cave stalling.

consist of well documented and transparent algorithms that can easily be

implemented within any commercially available numerical modelling

package.

be validated against a number of case study back-analyses.





3.2 Methodology

Based on a review of the current cave assessment techniques, outlined in Section 2,

it is clear that the caving algorithm described by Pierce et al. (2006) represents the

current state-of-the-art in rock mechanics for cave propagation analyses. In

addition to addressing five of the six key rock mass behaviours that affect caving

(defined by Pierce, 2009 and Brown, 2003 – outlined in Section 1.3) the Pierce et

al. (2006) caving model has been extensively documented and can be implemented

in any commercially available modelling code that can support a strain-softening

constitutive model.

The current research aims to further develop the caving model described by Pierce

et al. (2006) – herein described as the 2006 model - through the consideration of

each of the key rock mass behaviours that affect caving – as outlined in Section 1.3.

At the current time the 2006 caving model is limited by:

Stress-Path dependent calibrated SRM-continuum material inputs,

Linear modulus reduction relation,

Constant rock mass dilation relation,

Consideration of large-scale discontinuities based on an implicit

methodology

Height of Draw (HOD) based production scheduling technique; and

Application to block and panel caving methods only. Sub-Level caving is not

considered.

Based on these limitations, the development of a numerical model for cave

propagation can be addressed in two separate streams that include; rock mass

behaviour and production scheduling techniques.





Simulation of Rock Mass Response to Cave Propagation3.2.1

3.2.1.1 Rock Mass Cohesion / Tension Softeni ng and Post-Peak Br it tl eness

The SRM methodology uses the Particle Flow Code PFC 3D to explicitly represent a

DFN embedded within an intact rock matrix. SRM samples can explicitly account

for the joint fabric and its impact on rock mass strength anisotropy and scale

effects.

Previous investigations (Mas Ivars et al., 2011) have shown that it is possible to

determine generalised cohesion/tension weakening and post-peak brittleness

from the testing of SRM samples through a standard suite of laboratory tests. A

procedure is required to allow for the accurate representation of the standard

suite of SRM responses in cave propagation models.

3.2.1.2 Rock Mass Dilat ion

An accurate assessment of the peak rock mass dilatancy within and around an

evolving cave is crucial to ensure that the bulking behaviour of the caved mass is

accurate. Few of the documented cave propagation assessment models discuss the

consideration of this parameter. A critical review of the current understanding of

rock mass dilational behaviour and existing relations is required. This review will

form the basis of the formulation of a rock mass dilational response for cave

propagation and subsidence assessment.

3.2.1.3 Rock Mass Deformat ion Modul us Softeni ng

During cave propagation, the rock mass increases in volume as intact rock blocks

fracture, separate and rotate during the yielding and mobilisation process. Along

with this bulking, a reduction in the deformation modulus is expected to occur.

Representation of the decrease in deformation modulus is crucial for assessing the

evolving stress state around the cave, since, as rock mass softens its potential to

carry stress decreases.

The rate at which the deformation modulus decreases from an in situ state to a

fully bulked state in response to production draw has previously been simulated as

a linear decrease based on volumetric strain in the 2006 cave propagation model.

However, Hoek and Diederichs (2006) report that deformation modulus softening





is non-linear in nature. A thorough review of published laboratory test data

associated with granular material is required to develop a relationship between

volumetric strain and deformation modulus for use in the numerical model of cave

and subsidence assessment.

3.2.1.4 Simulat ion of Large-Scale Discont in ui ti es

The influence of large-scale discontinuities on subsidence and cave propagation is

recognised to be important by many researchers. In situ observations have shown

that the impact of structure can be varied based on persistence, strength and

orientation relative to the undercut footprint and major principal stress direction.

There are various numerical techniques available to simulate large-scale

discontinuities within a three-dimensional numerical model. A thorough

investigation of all approaches is required to ensure the most accurate method is

implemented within the numerical model of cave propagation and subsidence

assessment.

Production Draw Simulation3.2.2

The development and implementation of state-of-the-art numerical techniques for

a more accurate and adaptable production draw simulation is implemented within

the numerical model of cave propagation and subsidence assessment.

3.2.2.1 Mass-Based Pr oducti on Draw Algor it hm

The rate of production draw and shape of the undercut footprint has previously

been identified by Laubscher (1990, 1994) to impact the caveability of a rock mass.

Evolution of the footprint shape and evolving hydraulic radius can be simulatedthrough the constant updating of the active production area in the model. At the

current time, most of the methodologies control production draw by a Height of

Draw (HOD) schedule that is estimated based on a pre-determined bulking factor

for the in situ rock mass.

A mass-based production draw algorithm is required to ensure the production

schedule is accurately represented in the numerical model of cave propagation.

This is most important during cave initiation when the production tonnes are low

and caving rates will be at their maximum. By allowing a cave to develop as a





result of minor variations in the production schedule, cave initiation and stalling

can be predicted with rigour.

3.2.2.2

Development of an Algor it hm to Update Gr ound Sur face Pr ofile

When a cave breaches the ground surface a crater is formed. The development of

the crater in the numerical model of cave propagation needs to be simulated to

ensure that the subsidence limits are assessed correctly and that toppling

instability around the crater slope may be predicted and incorporated into

mobilised zone for infrastructure planning purposes.

3.2.2.3 Sub-Level Cavin g Algor it hm

In block and panel caving, mobilisation of the ore is achieved without drilling and

blasting. Sub-level caving requires the transformation of in situ ore into a mobile

state by drilling and blasting. There is currently no documented methodology that

considers a sub-level caving production draw schedule. An algorithm is required

to be developed in the numerical model of cave propagation that considers this

cave mining method.

Validation3.2.3

An outline for the development and validation of each of the caving algorithm

components (rock mass constitutive behaviour and production scheduling) is

provided in Figure 44. In addition, a number of case study applications are

required to be completed to validate the model response and ensure that the

methodology described herein can be applied with some confidence.





Figure 44. Research methodology plan. Red tasks indicate developments that considerrock mass behaviour and its impact on caving. Green tasks indicatedevelopments that are associated with numerical modelling techniquesrequired to simulate caving.



4 – Development of a Cave Propagation Demonstration Model


Figure 45. Development of a numerical demonstration model: geomechanical conditions.

4.2 Production Draw Simulation

To simulate the undercutting and production process at the start of each mining

advance increment, undercut zones are deleted and the support it provided to the

surrounding rock mass is replaced with reaction forces. Draw is simulated by

applying a small downward-oriented velocity to all gridpoints in the back of the

undercut. This velocity is set low enough to ensure pseudo-static equilibrium

throughout the model. Displacements that match the production height of draw in

the back of the undercut are induced in the back of the undercut zones.





4.3 Cave Propagation Sensitivity Studies

Effect of Rock Mass Peak Strength on Cave Propagation4.3.1

The effect that rock mass strength has on propagation behaviour has been

explored in the Cave Demonstration Model. Four different strength rock masses

have been defined (RM1, RM2, RM3 and RM4) and bi-linear, strain-softening

material responses have been developed for each property set based on the

methodology described in Section 2.2.2. A summary of the measurable material

properties and Mohr-Coulomb strength estimates for each of the rock masses are

provided in Table 3 based on a minor principal stress fit of 15 MPa.

Estimate of Hoek-Brown and equivalent Mohr-Coulomb rock mass strengthTable 3. properties for four simulated domains in the numerical demonstration model.

Seg. 1 Seg. 2

UCS Erm Tens. Coh. Coh.

(MPa) GSI MRMR mi (GPa) (MPa) (MPa) (Deg.) (MPa) (Deg.)

RM1 120 48 52 12 8.9 0.25 0.2 1.7 50 5.8 35

RM2 120 55 58 14 13.3 0.25 0.3 2.2 52 6.8 38

RM3 145 59 65 16 16.7 0.25 0.4 3.0 54 8.1 42

RM4 170 70 75 20 31.6 0.25 0.9 5.2 57 11.4 47

The Hoek-Brown failure envelopes for each of the rock masses and stress-strain

material responses at different confinement levels are provided in Figure 46.

Figure 46. Hoek-Brown failure envelopes and simulated rock mass stress-strain curves for the rock mass domains in the numerical demonstration model.





The empirical estimates of caveability (after Laubscher, 2000) for each of the rock

masses are provided in Figure 47 for a HR of 30. Each of the rock masses are

classified as having a different caveability potential based on their MRMR values

ranging from ‘caving’ to ‘stable’.

Figure 47. Empirical estimates of rock mass caveability for four rock mass domainssimulated in the numerical demonstration model.

The RM4 rock mass falls within the ‘Stable’ region which suggests that cave

initiation and propagation may be problematic. Caving in the RM1 and RM2 rock

masses is not expected to be problematic. The caveability of RM3 is unable to be

determined since it falls within the ‘Transitional Zone’. The numerical simulationresults are provided in Figure 48. Propagation rates for both the mobilised and

yield zones have been calculated based on their simulated height above the

undercut level and the simulated HOD.





Figure 48. Predicted cave propagation behaviour for variable peak strength rock masses

in the numerical demonstration model.





It can be seen that as the rock mass strength increases, the propagation rate

decreases (from 18:1 in the case of RM1 to 1:1 in the case of RM4). Self-sustained

cave propagation in the lower strength RM1 and RM2 rock masses is predicted.

Stalling is seen in the simulation of caving in RM3 (depicted by the co-incident cave

and yield zones in Figure 48A) at a height of approximately 25 m above the

undercut. The cave fails to initiate in the strong rock mass RM4.

The evolution of the bulked caved mass for each rock mass is also presented for

each of the rock mass strengths through a review of the evolving rock mass

density. It can be seen that bulking is not uniform within the caved mass. Higher

bulking (lower densities) can be seen at the edges of the cave. Results of the RM4model provide a full-bulked caved rock across the entire undercut footprint, while

the RM1 and RM2 rock masses only reach a maximum bulked rock mass density

around the cave periphery - where the shearing stress is at a maximum. These

numerical results are considered to represent more closely the actual response of a

rock mass during caving than assuming a constant reduced density for production

calculations (such as Beck et al., 2011)

Maximum principal stress magnitudes in the mining abutments of the lower

strength RM1 and RM2 rock masses reach larger values than the higher strength

RM3 and RM4. This shows that minimal stress redistribution has occurred in the

high strength cases. It is expected with the additional simulation of production

draw, abutments stresses will continue to increase in the RM1 and RM2 models

until the cave intersects the ground surface.

The Damage Threshold (

) values plotted for each of the rock masses provide

two important pieces of information that include if damage is occurring in the rock

mass; and where this damage is occurring. This is important in understanding the

ongoing caveability of the rock mass and where the cave is likely to evolve.

The simulation of caving in each of the rock mass types agrees with the initial

estimates of caveability based on the Laubscher (2000) caveability chart. In

addition, in the case of RM4 the inability of the cave to initiate and problematic

caving was predicted in the case of RM4 and RM3 respectively are a significant

result.





The prediction of the critical hydraulic radius and the potential for cave stalling is

imperative, and, at the current time there are no other documented numerical

methodologies that are able to do this.

Effect of Post-Peak Softening Rate on Cave Propagation4.3.2

The rate at which the degradation from the in situ to caved state occurs within a

rock mass is referred to as the post peak brittleness. Lorig (2000) has shown,

through numerical simulations of caving in two-dimensions, that cave height is

strongly dependent on the brittleness of the rock mass. In lieu of SRM testing

results to provide an estimate of post-peak brittleness, the response can be

estimated based on a relationship with GSI and zone size within the numerical

model presented in Equation [4].

The effect of variable post-peak brittleness on cave performance has been studied

in the Cave Demonstration Model by modifying the post-peak response of the RM1

rock mass. The stress-strain results of computer simulated, large-scale, laboratory

tests that represent a ductile, average, and brittle post-peak response for RM1 are

provided in Figure 49A. The actual

values used are documented in Figure 49B.

Figure 49. Simulated variable post-peak softening responses for the same peak strengthrock mass.

In each case, the rock mass responses have been developed based on the same

peak strength properties. The only difference is the value required to reduce

the strength of the rock mass from a peak to residual value. The effect of each of

the post-peak responses after 10 m draw have on cave propagation behaviour in





the demonstration model have been simulated. The results are provided in Figure

50.

Figure 50. Variation in cave propagation behaviour based on variable post-peaksoftening rates simulated in the numerical cave propagation model.

It can be seen that the cave propagation rate is strongly influenced by the post-

peak response of the rock mass. Problematic cave initiation and propagation is

simulated with a ductile post-peak response. Similar propagation rates aresimulated for the Average and Brittle post-peak responses, however, it can been





Figure 52. Effect of estimates of m i on predicted cave propagation behaviour in the

numerical demonstration model.

It can be seen that an increase in the estimated mi reduces (marginally) the

propagation rate of a cave. This decrease can be attributed to the increased stress

at which failure must occur with increasing mi values. In each case, the bulked

cave mass profiles (Figure 52B) are similar. Increased seismic potential – based on

the empirically derived equation developed by Diederichs (2000) within the cave

back is predicted with an increased mi value (Figure 52D). This reflects the stress





caving mechanism required to be associated with the propagation of strong rock

masses.

Effect of Stress/Depth on Cave Propagation4.3.4

During cave propagation , in situ stresses are redistributed around the evolving

cave mass as it propagates. The effect that the in situ stress magnitude has on the

evolving cave has been investigated by simulating mining at different depths. The

RM1 rock mass properties have been simulated. It can be seen from Figure 53A

and Figure 53D that, the cave propagation rate, and seismic potential increases

with increased stress/depth. In addition, as the stress magnitude increases, the

rate of the advance of the yield zone in front of the mobilised zone also increases

(Figure 53A). It can be seen that stresses increase at the extraction level, the cave

propagation rate increases. Significant increases are seen between the 600m –

650m simulations as the in situ stress at the extraction level approaches the rock

mass peak strength.





Figure 53. Cave propagation results for increasing stress /depth in the numericaldemonstration model. Significant increases are seen between the 600m –650m simulations as the in situ stress at the extraction level approaches therock mass peak strength.





4.4 Summary

Through the development and application of the demonstration model, it can be

seen that the numerical approach developed by Pierce et al. (2006) allows cave

propagation to evolve as a function of the constitutive behaviour of the rock mass

and, induced stress conditions.

Based on these results of the numerical demonstration model it is clear that the

rate and shape of cave propagation through the in situ rock mass will be affected

by the geomechanical conditions at the site (rock mass behaviour and in situ

stress). However, as discussed previously (Section 3) limitations to this model

exist. These will be explored in the following chapters and developments to the

existing model will be implemented to address these limitations. The

demonstration model will be used to exhibit and validate responses for the

extended numerical model of cave propagation and subsidence assessment.



5 – Development of the Ubiquitous Joint Rock Mass Model (UJRM)


DEVELOPMENT OF THE UBIQUITOUS JOINT ROCK5

MASS MODEL (UJRM)

At present, it is not practical to simulate large-scale mining/geological processes

using the SRM methodology due to the computational intensity of the numerical

technique. For this reason, continuum codes are required.

Continuum models of jointed rock masses are routinely used in rock mechanics;

Salamon (1968), Singh (1973), Chappell (1975), Gerrard (1982), Fossum (1985),

Cai and Hori (1993), Sitharam and Latha (2002), Zhu and Tang (2003), Yoshida

and Hori (2004), Samadhiya et al. (2004), Liang et al. (2004) and Nicieza et al.

(2006). Within these models the rock mass is considered as an isotopic continuum

with equivalent material properties, with the effect of joints accounted for

implicitly. Although the impact of joint frequency and persistence on strength is

considered by this approach, the joint orientation and its impact on strength

anisotropy is not.

The Subiquitous constitutive model in FLAC 3D (Itasca, 2009) is routinely used to

represent laminated materials that exhibit non-linear material hardening or

softening. Clark (2006) used FLAC (Itasca, 2005) to demonstrate that the

assignment of ubiquitous joint orientations at the zone level (from a known joint-

orientation distribution) results in realistic rock mass behaviour and can yield

properties that are consistent with empirical techniques. Pierce et al. (2006)

calibrated stress-path dependent SRM results to a continuum constitutive

response and used the results in a successful analysis of cave behaviour at

Northparkes E26 Lift 2. Details regarding the continuum calibration are not

known.

Within the Subiquitous constitutive model, both matrix and joint properties are

specified, as illustrated in Figure 54. For each of the Mohr-Coulomb strength

properties, softening tables are defined. The softening tables provide the peak and

residual strength values along with the rate at which softening from the peak to

the residual value will occur. A full description and validation of the Subiquitousconstitutive model can be found in Itasca (2009).





Figure 54. Subiquitous constitutive model in FLAC 3D ; assignment of matrix and joint properties.

An example of the damage evolution within a subiquitous sample can be seen

through the progressive degradation of matrix cohesion and ubiquitous joint-

failure plots at various stages of sample loading – illustrated in Figure 55.





Figure 55. Stages of damage within a simulated UCS test on a subiquitous sample.

Since both the rock block and joint conditions can be modelled with this

constitutive model, the calibration of anisotropic SRM sample responses can be

achieved. The development of a calibrated SRM rock mass response within FLAC 3D

using the subiquitous constitutive model has been termed a Ubiquitous Joint Rock

Mass (UJRM) model. The SRM standard laboratory testing environment described

by Mas Ivars et al. (2008) has been used as the basis for the development of this

methodology.





5.1 Establishment of a Standard Laboratory

Environment

Sample Geometry and Generation5.1.1

To match the SRM testing environment developed by Mas Ivars et al., (2011) a

rectangular shape has been used for the generation of each test sample.

This shape:

matches the shape and volume of the SRM samples that have been tested;

ensures ease associated with the scaling of critical strain values during the

subsequent modelling process;

ensures ease associated with applying stresses in all three axial directions

(σxx:E-W, σyy:N-S, σzz:vertical) during the laboratory testing process; and

minimises end effects.

Examples of sample geometry are provided in Figure 56.





Figure 56. Development of a UJRM sample (a) variation in sample size with equalzone sizes; (b) joint assignment as a function of sample size.

Note that in Figure 56, the zone size in each sample remains constant. However,

the resolution decreases in the small scale samples - increasing the impact of the

joint assignment and ensuring sample scale bias is honoured. Figure 57 illustrates

the simulated axial loading conditions for each of the UCS, triaxial and direct

tension tests, and the three sample loading orientations that are completed for

each of the simulated loading conditions (UCS, triaxial and direct tension).





Figure 57. UJRM sample testing geometry (a) sample loading conditions (b)orientation for anisotropy tests completed for each sample loading condition.

Sample Zone Resolution5.1.2

A standard zone size is selected for the generation of each sample geometry. To

minimise the zone resolution dependency, described in detail in Section 2.2.2.3, the

UJRM material should be calibrated with the same zone size and shape to be used

in the large-scale model. This size will be dictated by the dimensions of the

undercut footprint to be modelled to ensure a reasonable zone resolution. In

practical terms, at least 8-10 zones are required across the shortest footprint





dimension (or undercut increment) to achieve the most accurate results.

Examples of poor and good mesh resolutions are provided in Figure 58.

Figure 58. Examples of (a) poor (b) low and (c) good mesh resolution required forlarge-scale analysis of cave propagation.

Sample Loading Conditions5.1.3

The loading and end conditions in analytical solutions, physical laboratory tests

and simulated numerical loading experiments can have a significant effect on the

test result. The problem is discussed by Brady and Brown (2006) and illustrated in

Figure 59.





Figure 59. Discontinuity shear strength in a triaxial cell (after Brady and Brown,2006).

It is clear from Figure 59a, that if relative shear displacement of the two parts of

the sample is to occur, there must be lateral as well as axial relative translation.

Laboratory testing is often conducted with spherical seats (Figure 59b and Figure

59c) which can cause rotation of the sample during loading. An alternative end-

condition involves the use of lubricated discs, as illustrated in Figure 20d. This

laboratory technique allows the lateral component of translation to freely occur,

however, this unrestrained end-condition is not encountered in situ.

In reality, laboratory UCS tests conducted on intact samples are performed by

loading the sample between two steel platens. These platens provide a small

amount of confinement to the test specimen due to frictional resistance. In anumerical sample loading conditions may be modelled by (a) allowing the sample

ends to move in all directions perpendicular to the loading direction, (b) fixing the

sample ends in all directions, or (c) modelling the steel platens above and below

the sample, and installing an interface between the two materials that is assigned a

stiffness and frictional resistance. The effect of each of these loading conditions on

the sample response is shown in Figure 60.





Figure 60. Simulation of different boundary loading conditions on the response ofUJRM material in the numerical UCS test environment.

To be consistent with the end conditions used throughout the SRM testing

conducted by Mas Ivars et al. (2008), fixed end conditions have been applied in the

UJRM testing environment on samples with a length: diameter ratio of 2:1.

However, it is important to note here, the varied strength response that is

generated based on the simulated end-conditions in the tests. By fixing the end

conditions in the model, artificial confinement conditions are simulated, resulting

in higher rock mass strength estimates that what is achieved in situ.

Large Strain/Small-Strain Calculation Mode5.1.4

Some numerical modelling packages are able to calculate numerical solutions in

both a large-strain and small-strain mode. In small-strain mode, gridpoint

coordinates are not updated during mechanical calculations; in large-strain mode,

gridpoint coordinates are updated at each time step. The application of small-

strain mode is most useful when controlling boundary and applied conditions

when large displacements are expected in relation to the grid size. For large-scale





cave analyses, the small-strain calculation mode is required due to the large

displacements (>100 m) induced in the model. The effect of each of these

calculation modes on the behaviour of a UJRM sample has been investigated by

conducting a series of UCS tests on a material that has varying joint orientations.

The results are summarized in Figure 61.

Figure 61. Investigation of UJRM response as a result of small-strain/large-strain

calculation modes.

It can be seen that small-strain and large-strain calculation modes yield the same

results for those samples that have horizontal and random joints sets. However,

significant differences in the peak and residual strengths are apparent in the

sample that has a vertical joint set. The small-strain sample yields much higher

peak strength. The large-strain sample yields in tension along the joint surfaces

and, as expected, progresses to a fully degraded state with the continued

application of load. In order to allow for very large displacements, the UJRM rock

mass is calibrated using the small-strain calculation mode. Provided the same

calculation mode is used for the SRM calibration and the large-scale cave

propagation analysis, this should not cause any issues.





5.2 Calibration of UJRM Response

The following section outlines the methodology for the selection of the input

parameters for calibration of a UJRM to SRM responses. The methodology has

been based on four rock mass units detailed in Mas Ivars et al. (2008).

For the calibration of UJRM samples, it is assumed that all input properties can be

estimated based on measurable rock mass parameters. By modifying the input

strength parameters (defined in Figure 54), the calibration of deformation

modulus, unconfined compressive strength (UCS), tensile strength and the

softening behaviour of different sample sizes and in different loading directions

can be completed. In addition, SRM failure mechanisms are also honoured through

the monitoring of progressive matrix degradation, joint slip and joint dislocation

within the sample during failure.

Summary of SRM Responses5.2.1

As discussed in Section 2.2.3, the SRM methodology has been developed to define

generalised stress-strain curves of a large-scale sample of a rock mass in three

opposing loading directions, and at a number of different scales. This ensures that

the material properties derived from the technique are not specific to one

particular stress path (as in the case of Pierce et al., 2006) and may be applied to a

number of different numerical modelling applications (i.e. cave analysis, slope

stability).

Commensurate with the development of the SRM standard suite of laboratory

tests, a testing environment used to calibrate the response of a subiquitous sample(direct tensile test, uniaxial compressive strength test and triaxial test) has also

been developed.

5.2.1.1 Int act Calibr ation

The standard suite of laboratory tests, as discussed in Section 2.2.3 have been

carried out on four rock mass domains at the Palabora Mine in South Africa. A

detailed description on the testing program and results can be found in Mas Ivars

et al. (2008). The measured rock mass UCS strength used for the intact calibration

is provided in Table 4.





Mean target intact rock block properties for the lithology at Palabora.Table 4.

Foskorite Carbonatite Dolerite Pyroxenite

Mean measured UCS (MPa) 139 320 90 63

Estimated rock-block strength (MPa) 111 256 72 50

Mean modulus of Deformation (GPa) 58 90 72 78

Mean Poisson’s ratio, v 0.33 0.30 0.35 0.27

5.2.1.2 Discr ete Fr actur e Netw or k

A Discrete Fracture Network (DFN) for each of the rock mass domains was

developed by Mas Ivars et al. (2008) based on borehole and scanline data (from

both underground and open pit exposures). The DFN models encompassed

statistical distributions for the fracture persistence and orientation, coupled to a

density parameter. The DFN realisation is calibrated both to fracture frequencies

and orientation distributions observed. A summary of the mapping data is

compiled in Table 5.

Measured joint frequencies and persistence from mapping at Palabora (afterTable 5. Mas Ivars et al., 2008)

Lithology Mean joint frequency (min.–max.) Mean joint dia. (min.–max.)

Open PitCarbonatite 0.77m-1 (0.21–3.33) 15m (10–354.7)

Dolerite 2.26m-1 (0.35–16.00) 7.5m (5–658)

Pyroxenite 0.37m-1 (0.12–0.73) 15m (10–246)

Underground

Carbonatite West 0.83m-1 (0.16–3.33)

Carbonatite South 0.53m-1 (0.04–3.64)Dolerite West 1.88m-1 (0.02–4.80)

Dolerite South 2.54m-1 (0.16–10.00)

Pyroxenite West 0.39m-1 (0.04–0.94)

Joint orientation data for each of the domains is provided in Figure 62.





Figure 62. Joint orientations considered in the development of the DFN for (a)carbonatite (b) micaceous pyroxenite (c) dolerite (d) foskorite (afterSainsbury et al., 2008).

Fractures are represented within the sample as ubiquitous joints. The assignment

of the joint dip, dip direction and radius is achieved via a random sampling

procedure from the DFN developed for the rock. The persistence of joints can be

honoured throughout the grid via extrapolating the joint dip and dip direction to

adjoining zones, which honours the fracture radius. To ensure complete

randomness in the model, a random list of all the zones is generated for the

importation of the fracture network and the presence of existing joints is honoured

(i.e., not overwritten) when importing the DFN.

An example of the ubiquitous joint orientations represented by this sampling

procedure is provided in Figure 63b. The actual joint orientation data is provided

in Figure 63a.





Figure 63. Representation of DFN in a UJRM sample (a) actual DFN (b) DFNrepresented in numerical model (after Sainsbury et al., 2008).

5.2.1.3

Estim at ed Join t Str ength

The joint properties were estimated from the roughness and hardness of joints

measured in the open pit at Palabora. The joint properties are listed in Table 6.

The friction and cohesion values were considered as direct inputs for the

ubiquitous joint strength.





the matrix material based on plasticity state has also been assumed for the

calibration as discussed in Section 2.2.2.4.

Calibration of Ubiquitous Joint Properties5.2.4

Joint cohesion was varied to achieve a match in peak strength between the SRM

and UJRM materials. Joint cohesions between 0.1% and 1% of the matrix cohesion

were required to calibrate the UJRM response. A summary of the calibrated joint

cohesion values for each lithology is provided in Table 8.

Joint friction angles were set for each lithology based on estimates determined for

SRM testing. For simplicity, it was assumed that joint friction did not soften. A

summary of the friction values used in each UJRM calibration is provided in Table

8. Joint tension was assumed to be zero. This is consistent with the description of

an open fracture.

Calibration of Critical Plastic Strain, 5.2.5

Both matrix and joint critical strain values were varied to achieve calibration of the

UJRM sample. Matrix critical strains, (

) between 0.01 and 0.15 were required

and joint critical strains ( ) less than 1% of the matrix values were required to

achieve calibration with SRM results. A summary of the calibrated critical strain

values is provided in Table 8.





Calibrated UJRM properties for the rock mass domains at Palabora.Table 8.

Carbonatite Foskorite Pyroxenite Dolerite

MatrixDeformation Modulus (% Intact value) 50% 50% 30% 30%

Cohesion (MPa) 15 7 10 37Tension (% of Cohesion) 40% 40% 36% 56%

Friction (Degrees) 40 35 49 47 0.15 0.1 0.015 0.025

JointCohesion (% of Matrix Cohesion) 1% 0.1% 0.2% 0.1%

Friction (Degrees) 30 30 34 26

(% of ) <1% <1% <1% <1%

Calibrated Laboratory Stress-Strain Curves5.2.6

Calibration of a UJRM for each of the four lithologies has been completed in three

different testing environments, in three loading directions, and at three different

scales. Results of simulated UCS and triaxial tests at 5 MPa confinement for the

Carbonatite domain are provided in Figure 64.

Figure 64. UJRM sample stress-strain responses (a) calibrated 40x80m carbonatiteUCS UJRM rock mass samples showing strength anisotropy (b) calibrated40x80m carbonatite triaxial UJRM rock mass samples showing strengthanisotropy.

Calibrated UCS results from all the domains are provided in Figure 65.





Figure 66. UJRM UCS results for the carbonatite domain at Palabora compared toSRM results at three different sample sizes in three loading directions.

Result of the testing show that, as sample size increases the rock mass strength

decreases and becomes less variable and that, in this case the calibrated numerical

UJRM/SRM responses are only valid for resolving failure mechanisms that have a

volume greater than 64,000m3 (40m x 40m x 40m).

It is interesting to note the UJRM sample responses in comparison to the

traditional isotropic Hoek-Brown strength estimates in Figure 66. In this case,

only two co-incident comparable values are obtained between the UJRM and

equivalent estimated Hoek-Brown strengths.





5.3 Application and Validation of the UJRM

Methodology

Calibrated SRM-UJRM in Laboratory Environment5.3.1

In order to test and validate the methodology developed for the calibration of

UJRM-SRM samples, three additional UJRM materials have been calibrated using

the same procedure developed for the lithology at Palabora discussed in Section

5.2. Two of the units exhibit distinct foliation as a result of metamorphism. A

summary of the rock mass characteristics and SRM testing results are provided

below. Details of the SRM testing can be found in Sainsbury, Mas Ivars and Darcel(2008).

5.3.1.1 Cali br at ion of Int act Response

The values that have been used for the intact calibration have been determined

from laboratory testing. The presence of foliation in two units (Domain 1 and 3)

was considered to be an intact property since the spacing between foliation planes

is in the order of millimetres. This is due to the fact that in order to adequately

define a rock block within PFC , at least 5 particle diameters are required and thus,

representing the foliation in a real-life scale would produce a SRM sample that

would be impossible to test with our current computer efficiency.

As a result of this intact strength anisotropy, the intact strength calibration has

been completed in four directions (parallel, perpendicular and at angles of 30

degrees and 60 degrees to the foliation). Values for the intact and foliation failure

have been defined by the description of the failure mechanism in the laboratorytesting database. A summary is provided in Table 9.





Summary of laboratory test results for three rock mass domains.Table 9.

The intact rock calibrations have been completed on samples sizes of 2 m, 5.2 m

and 2 m height (2:1 height: width ratio) for the Domain 1, 2 and 3 rock massesrespectively. Figure 67 illustrates the calibrated UCS response for each of the rock

mass domains.





Figure 67. Calibrated stress-strain curves within PFC for three rock mass domains.





The calibrated PFC 3D micro-properties required to simulate the strength and

deformation behavior of the intact rock for each of the domains are provided in

Table 10.

Calibrated PFC micro-properties for three rock mass domains (after Sainsbury,Table 10. Mas Ivars and Darcel, 2008).

Domain 1 Domain 2 Domain 3

Minimum particle radius (m) 6.18e-2 1.37e-1 6.18e-2Particle radius ratio* 1.66 1.66 1.66

Particle density (kg/m3) 4109 4109 4109

Particle E (Pa) 154e9 105e9 78e9

Particle friction 2.5 2.5 2.5

Particle k ratio 4.6 4.5 4.6Parallel bond E (Pa) 154e9 105e9 78e9Parallel bond k ratio 4.6 4.5 4.6

Parallel bond mean normal strength (Pa) 94e6 84e6 204e6

Parallel bond normal strength St. Dev. (Pa) 18.8e6 16.8e6 40.8e6

Parallel bond shear normal strength (Pa) 94e6 85e6 204e6

Parallel bond shear strength St. Dev. (Pa) 18.8e6 16.8e6 40.8e6

The properties of the foliation planes that have been used in the calibration of the

intact responses for the domains are summarised in Table 11.

Calibrated intact foliation strength properties in PFC 3D (after Sainsbury, MasTable 11.Ivars and Darcel, 2008).


Kn (GPa/m) 10 n/a 10Ks (GPa/m) 1 n/a 1

Friction (Deg.) 15 n/a 15

Cohesion (MPa) 0 n/a 0

Tension (MPa) 0.2 n/a 0.2

5.3.1.2 Selecti on of Join t Pr oper ti es

The joint properties for each of the domains have been completed based on an

assessment of the roughness and planarity of the joints (roughness, waviness,

planarity, JRC, JCS, Js, Jw, Ja, aperture, infilling, weathering etc). A summary of the

estimated joint strength properties for each of the domains is provided in Table 12.





Estimated open joint strength properties for simulation of joints in SRMTable 12.sample (after Sainsbury, Mas Ivars and Darcel, 2008).


Joint Kn (GPa/m) 150 150 150Ks (GPa/m) 15 15 15

Friction (Deg.) 30 30 27

Cohesion (MPa) 0 0 0

Tension (MPa) 0 0 0

5.3.1.3 Development and Valida ti on of a Discr ete Fr actur e Netw or k

For each of the rock mass domains, a DFN has been developed based on borehole

and scanline data. A complete description can be found in Sainsbury, Mas Ivars

and Darcel (2008). A summary is provided below.

A REV for Domain 1 has been estimated to be a cubic volume with a side length of

18 m. Scanline traces along theoretical boreholes in the SRM rock mass yield P10

values of 0.55 - 0.59. This relates to an average fracture spacing of 1.7 - 1.8 m or

block volume of approximately 6 m3. A graphical representation of the Domain 1

DFN is provided in Figure 68.

Figure 68. Domain 1 fracture network views: 18m REV edge length (afterSainsbury, Mas Ivars and Darcel, 2008).

A REV for Domain 2 has been calculated as a cubic volume with a size length of 40

m based on a review of the fracture spacing and persistence. Scanline traces along

theoretical boreholes in the SRM rock mass yield P10 values of 0.94. This relates to

an average fracture spacing of approximately 1 m – 1.42 m or block volume of





approximately 3 m3. A graphical representation of the Domain 2 DFN is provided

in Figure 69.

Figure 69. Domain 2 fracture network views: 40m edge length (after Sainsbury, MasIvars and Darcel, 2008).

A REV for Domain 3 has been calculated as a cubic volume with a side length of 18

m. Scanline traces along theoretical boreholes in the SRM rock mass yield P10

values of 0.77 - 0.6. This relates to an average fracture spacing of 1.7 - 1.3 m or

block volume of approximately 3 m3- 6 m3. A graphical representation of the DFN

is provided in Figure 70.

Figure 70. Domain 3 Fracture Network views : 18m edge length (after Sainsbury, Mas Ivars and Darcel, 2008).

Cai et al. (2007) has previously developed a GSI chart that is based on quantitative

properties of the rock mass jointing. It is provided in Figure 71. When the field

estimates of joint strength properties and block sizes of Domain 1, 2 and 3 are used

to estimate GSI based on this chart, the results are consistent with the GSI values





developed from synthetic scanline mapping for each of the domains (Sainsbury,

Mas Ivars and Darcel, 2008).

Figure 71. Quantification of GSI chart (after Cai et al., 2007).

5.3.1.4 Cali br ated Cont in uum Responses

The calibrated material input properties used for the UJRM sample are provided in

Table 13 along with the original dataset used to develop the technique for

comparison to provide validation of the developed methodology.





Calibrated continuum material properties for seven rock mass domains.Table 13.

1 2 3 Carbonatite Foskorite Pyroxenite Dolerite

Zone size Calibrated (m3) 1 8 1 1000 1000 1000 100

Matrix

Deformation Modulus (% Intact) 70% 70% 70% 50% 50% 30% 30%

Poisson Ratio 0.29 0.33 0.29 0.33 0.35 0.27 0.3Cohesion (MPa) 19 12 48 15 7 10 37

Tension (% Cohesion) 48% 50% 50% 40% 40% 36% 56%

Friction (Degrees) 36 39 33 40 35 49 47

Dilation (Degrees) 6 6 6 10 10 10 10 0.4 0.01 0.4 0.15 0.1 0.015 0.025

Joint

Cohesion (% of Matrix) 5% 30% 5% 1% 0.1% 0.2% 0.1%Friction (Degrees) 30 30 27 30 30 34 26 1.0e-06 1.0e-01 1.0e-02 1.5e-03 1.0e-03 1.5e-04 2.5e-04

The stress-strain results of the calibration for Domains 1, 2, 3 are provided in

Figure 72, Figure 73 and Figure 74.

Figure 72. Domain 1 SRM test results and UJRM response represented in FLAC 3D : 1 MPa triaxial tests (after Sainsbury, Mas Ivars and Darcel, 2008).





Figure 73. Domain 2 SRM test results and UJRM response represented in FLAC 3D : 1 MPa triaxial tests (after Sainsbury, Mas Ivars and Darcel, 2008).

Figure 74. Domain 3 SRM test results and UJRM response represented in

FLAC 3D : 1 MPa triaxial tests (after Sainsbury, Mas Ivars and Darcel,2008).





The peak strength and post-peak behaviour of the UJRM samples provide good

correlations with the SRM test results. In addition, it can be seen from Table 13

that the material input parameters are consistent across the entire suite of seven

calibrated SRM-UJRM samples – the four from Palabora developed in Section 5.2

and the three Domains (1,2 and 3) described here. As a result of this it can be said

that the methodology developed for deriving calibrating UJRM samples to SRM

responses has been validated for peak strength and post peak responses. The

simulation of more realistic deformation modulus values is described in Section

6.3.

UJRM Large-Scale Response5.3.2

In order to demonstrate the importance of detailed consideration of the in situ

joint fabric in a cave propagation analyses and how a UJRM can capture a varied

response, four jointed rock masses have been simulated using the Subiquitous

constitutive model in FLAC 3D. Each of the rock masses has the same commonly

defined rock mass properties (UCS, mi, GSI). However, in each of the rock masses,

the persistence and orientation of the joint fabric have been modified.

The jointed rock mass scenarios include:

Random joints; i.e. isotropic rock mass.

Horizontal joints.

Vertical joints.

Joints orientated at 45°.

Using the rock masses described above, production draw has been simulated in the

demonstration model (as described in Section 4). The cave propagation results are






Figure 75. Cave propagation behaviour for varying joint orientations simulated in thenumerical demonstration model.

Compared to the empirical approach for cave analysis, where the rock mass is

considered to be an isotropic material (Figure 75(a)), the consideration of jointing

(albeit extreme) allows significant variation (Figure 75(b)–(d)) in the cave shape

and rate of propagation to emerge as a result of production draw.

Based on the simplistic Cave Demonstration Models presented, the following

conclusions can be made:

Joints that are orientated perpendicular to the direction of draw (i.e. in

most cases horizontal joints) are most favourable for cave propagation. The

mobilised zone advances vertically at the most rapid rate. In this case, the

rate at which the mobilised zone progresses far exceeds the production

draw rate.

Joints that are orientated parallel to the direction of draw (i.e. in most cases

vertical joints) are not favourable for cave propagation. Minimal

displacement of the rock mass is achieved above the mining footprint. In





this scenario, shear failure of the rock bridges must occur to enable this

rock mass to yield and the cave to propagate.

Joints that are orientated at an angle to the direction of draw result in apreferred cave propagation direction. The principle stress direction can

either promote shear and tensile failure along the existing joints, causing

displacement of the rock mass beyond the lateral extents of the mining

footprint, or, cause clamping of the joints and result in hang-ups in the cave

back.

In this respect the consideration of joint orientations and rock mass fabric is

essential in determining cave propagation behaviour and the UJRM approach is

able to capture this variability.

5.4 Summary

Calibration of a UJRM assumes that the SRM testing is an accurate representation

of the rock mass strength and deformation behaviour in the simulated tested

loading directions and sample scales. Based on the calibration of SRM test results

of seven different rock mass domains, it has been shown that the UJRM method can

reproduce accurate failure mechanisms and strength anisotropy as well as the

expected scale effects shown by SRM testing. In addition, the implementation of a

UJRM approach in the Cave Demonstration Model highlights the potential impact

that a rock mass which exhibits significant strength anisotropy can have on cave

propagation behaviour.

By nature, the development of SRM responses is limited by the complex nature of

inputs required that include; a more thorough laboratory (intact) testing program

that is required to characterise variability in intact strength as a result of micro-

defects and or/veining as described by Pierce et al. (2009).

In addition, the development and validation of a characteristic DFN is difficult

since a more detailed level of fracture characterisation is required to develop a

robust model. The development of DFN’s are also limited to a few specialist

scientists in this area at the current time.





The time required to develop and implement SRM technology is generally greater

than the current time constraints put on geotechnical feasibility studies. However,

it is considered state-of-the-art and should be applied in instances where

significant strength anisotropy and/or scale effects are expected. In lieu of SRM

testing, the Hoek-Brown approach for strength estimation is considered a

reasonable starting point for cave propagation and subsidence assessment.



6 – Consideration of the Volumetric Changes the Accompany Cave Propagation


Within the caving model described by Lorig (2000), density of the rock mass

varied in proportion to plastic strain accumulation. This process is not physically

correct since mass is lost due to volumetric expansion (and mobilisation) and not

strength reduction. For example, a rock mass may have yielded due to an increase

in major principal stress but still be confined, and thus, no density changes should

have occurred.

In the Pierce et al. (2006) caving algorithm, the evolving rock mass bulked density

was related to increases in porosity through Equation [12].

[12]

Where is the rock mass bulked density (kg/m3), is the rock mass

undisturbed in situ density (kg/m3) and is porosity. To prevent bulking of the rock mass to unrealistic levels within the model, a

maximum volumetric strain was set within the model that could not be exceeded

as discussed in Section 2.2.2.5. To implement this density reduction relation in the

numerical model of cave propagation, Equation [13] can used.

[13]

Where is the volumetric strain increment as defined in FLAC 3D.





6.2 Rock Mass Dilation

Based on research conducted by Hill (1950), it is known that plastic deformation of

a rock mass must be accompanied by an increase in volume. This phenomenon is

known as dilation and can be described by the sliding of micro-cracks (joints) or

particles (intact rock blocks) when subjected to shear strain. This mechanism is

represented in Figure 77. It is most commonly described by an angle, .

Figure 77. Conceptual diagram of dilation associated with sliding along micro-cracksand particles (after Zhao and Cai, 2010).

Dilation is generally considered with an associated flow rule ( ) or a non-

associated flow rule ( ).

A typical stress-strain curve displaying the essential features of brittle rock

behaviour under triaxial compression is presented in Figure 78A based on

Rudnicki and Rice (1975).

Figure 78. Typical stress-strain curve for uniaxial compression of brittle, crystallinerock (after Rudnicki and Rice, 1975).





The curve can be divided into four regions:

A. Slightly convex up portion that is characterised by the initial mobilisation

of rock mass strength through clamping of joints.

B. A nearly linear portion that is characterised by random joint shear failure

C. A non-linear region of decreasing slope characterised by minor intact

yielding and uniform joint shear failure; and

D. A maximum is reached the curve decreases representing intact yield

localisation and contiguous joint shear failure.

The corresponding stress/volumetric strain curve is presented in Figure 78B. The

stress – volumetric strain curve can also be divided into the four regions displayed

on the stress-axial strain curve in Figure 78A.

A. Non-linearity is due to the elastic closing of cracks,

B. Unloading of this region causes little hysteresis,

C. Initiation of dilatant volume increase and non-linearity due to micro-crack

growth and frictional sliding on micro-crack surfaces, and

D. The initiation of this region is less clearly defined, but is characterised by

accelerated micro-crack growth and rapid increase of dilatant volume

change leading to failure.

It is clear, based on these curves that dilation is not constant and it must be varied

as the rock mass yields and mobilises during cave propagation.

According to Detournay (1986), dilatancy depends on the porosity of a rock mass,

plastic strain (yielding) and the confining stress – all of which vary during cave

propagation. Relations with scale dependency are also expected (Sterpi, 1999).

Within the Lorig et al. (1995) caving algorithm, the dilation angle of the rock mass

was increased above the friction angle to induce fracturing parallel to the cave

back (i.e., perpendicular to 3) as the primary mode of failure. In this model, active





yielding was confined to the surface of the material since dilation causes build-up

of isotropic stress in the interior elements, thus causing failure.

Results of SRM testing conducted by Pierce et al. (2006) indicate that alternativeand/or additional fracture modes are likely within the cave back. As a result,

Pierce et al. (2006), simulated dilation as a constant value that was reduced to zero

when the maximum bulking potential was reached.

Based on the published information it appears that the constant dilation angle

assumed by most models is not realistic but should vary with rock mass damage

(decreasing GSI values) and confinement. This is confirmed by triaxial testing of

intact samples undertaken by Medhurst (1996) and Ribacchi (2000) and Zhao and

Cai (2010).

Table 14 presents a summary of the dilation angles calculated from large-scale

triaxial tests conducted on granular material by Marachi et al. (1972).

Dilation angle in large-scale triaxial tests on rock fill material (after MarachiTable 14.et al., 1972)

Vermeer and de Borst (1984) conclude that the dilation angle is at least 20o less

than the friction angle.

Other researchers have provided guidelines for the selection of a dilation angle.

Hoek and Brown (1997) suggest that dilation is greatest in competent rock masses,

and tends to zero as damage accumulated:

Maximum

Particle

Size

Confining

Stress

Dilation

Angle

Source [mm] [MPa] [Degrees]

Oroville Dam 50 1 6.5

Oroville Dam 150 1 4

Oroville Dam 50 0.2 13

Oroville Dam 150 0.2 11

Crushed basalt 50 0.2 7.5

Crushed basalt 150 0.2 9

Pyramid Dam 50 0.2 7.5Pyramid Dam 150 0.2 6.5





GSI = 75 dilation angle is 25% of the friction angle of the rock mass ; 11o –

16o

GSI = 50 dilation angle is 12.5% of friction angle of the rock mass; 6o – 8o

GSI ≤ 30 dilation angle is zero.

Based on laboratory test results of Duncan-Farmer, (1993) Medhurst (1996) and

Ribacchi (2000); Alejano and Alonso (2005) developed a relationship for the

estimation of peak dilation angle based on confinement, friction angle and UCS. It

is presented in Equation [14].

[14]

Where is the peak dilation angle (o), ø is the angle of friction (degrees), isthe Intact Unconfined Compressive Strength (MPa) and is the inor Principal

Stress magnitude (MPa).

It is also assumed, that dilation must tend to zero at zero confinement (after

Barton and Bandis, 1982) and once the maximum volumetric strain has been

reached (estimated by Equation [11]).

The implementation of the Alejano and Alonso (2005) relation is considered the

most appropriate for cave propagation and subsidence analysis since it is based on

the reinterpretation of previously published compressive test results for a range of

rocks. The relationship reflects dependencies on confining stress, plasticity and

indirectly on scale through UCS estimates.

The relation does not increase the number of parameters needed to model the

strain-softening rock mass and can be easily implemented with the existing

information in the subiquitous constitutive model.

The implementation of this equation on a conceptual rock mass with a UCS of 100

MPa and friction angle of 45 degrees is provided in Figure 79.





Figure 79. Evolution of peak dilation estimate on a rock mass during cave propagationusing the Alejano and Alonso relation.

Based on Figure 79, it is clear that in this relationship dilation decreases with

increasing confinement and peak dilation occurs at low confinement levels when

rock blocks are free to bulk and rotate. Dilation does not exceed friction angles at

its maximum and is close to the Hoek-Brown estimate of dilation at increased

confinement levels.

Implementation of Non-Constant Dilation in the Cave6.2.1

Demonstration Model

The result of implementing the Alejano and Alonso (2005) dilation relation within

the Cave Demonstration Model – compared to a constant dilation angle of 20o is

presented in Figure 82. The impact on the evolving dilation, deformation modulus

and propagation rate is noted.





Figure 80. Implementation of a non-constant dilation relation and its impact on cave

propagation behaviour in the numerical demonstration model compared tothe simulation of a constant dilation angle.

Increased bulking (lower densities) immediately above the extraction level in the

demonstration model is seen with the implementation of the Alejano and Alonso

dilation relation. The height of the cave back will be controlled by the confinement

exerted by the bulked rock at the cave periphery.





6.3 Deformation Modulus

It is generally assumed that the modulus of deformation is equal in all directions

regardless of confinement and/or failure mode. This assumption has previously

been questioned by Fairhurst (1961), Adler (1970), Haimson and Tharp (1974),

Passaris (1977), Sundaram and Corrales (1980), Khan and Yuan (1988) and Chen

and Stimpson (1993).

A depth (confinement) dependent deformation modulus has previously been

described by Barton and Pandy (2011) in the context of open stope performance

and Hutchinson and Diederichs (1996) via observations of tunnel failure. In both

these cases, the greater the distance from an excavation face (or the greater the

confinement) the greater the estimated rock mass deformation modulus.

In the case of cave mining, the reverse can be considered. As the rock mass bulks

during the caving process, the point-to-point contacts that are created are

inherently softer than the face-to-face contacts when the rock mass is sitting in

situ.

The rate at which the deformation modulus decreases from an in situ state to a

fully bulked state in response to production draw has previously been simulated as

a linear decrease based on volumetric strain in the 2006 cave propagation model.

The methodology is based on the implementation of Equation [15].

[15]

Where

is the Bulked Deformation Modulus (GPa),

is the in situ rock

mass deformation modulus (MPa), is the fully bulked rock mass

deformation modulus (GPa) and is an Expansion Factor, determined by

Equation [16].

[16]

Where is the volumetric strain increment and is rock mass porosity.





A value of 250 MPa has previously been determined for a fully bulked deformation

modulus (Pierce et al., 2006). A schematic representation of the linear softening

relation (defined in Equation [15]) is provided in Figure 81.

Figure 81. Schematic linear relationship for rock mass deformation modulus reductionbased on Pierce et al. (2006) relation.

However, Hoek and Diederichs (2006) report that the deformation modulus isnon-linear in nature and can be related to GSI of the rock mass as shown in Figure

82.

Figure 82. In situ rock mass deformation modulus versus GSI for Disturbance Factorsof 0, 0.5 and 1.0 (after Hoek and Diederichs, 2006).





A compilation of laboratory test data completed on particulate matter is presented

in Figure 83. Here, the softened modulus (Ecave) has been presented as a fraction of

its initial value (Ein situ) and related to porosity. Porosity is considered in this case

since in situ density and deformation modulus will vary between rock mass

domains. It is assumed, for computational ease, that the in situ pre-mining state of

the rock mass represents a porosity of zero.

Figure 83. Softened deformation modulus versus porosity for particulate matterdetermined by laboratory testing.

A second degree polynomial with a maximum porosity of 0.4 (as previously

determined by Pierce et al., 2006) is considered as the best-fit for this data and is






Figure 84. Best-fit deformation modulus softening equation to compiled laboratory testdata.

An equation to describe the non-linear modulus softening relation is presented in

Equation [17].

[17]

Where is the Bulked Deformation Modulus (GPa), is the in situ rock

mass deformation modulus (MPa) and η is the rock mass porosity (%).

To implement this in the numerical model of caving porosity can be related tovolumetric strain through Equations [18] and [19].

Where initial pre-softened modulus and is the equivalent porosity

computed by Equation [19].





Where is the volumetric strain increment, is the maximum volumetric

strain achievable (%) defined by Equation [11] and

Default values of 0.4 and 0.66 are recommended

for and respectively.

Using the equations of Hoek and Diederichs (2006) to estimate the initial in situ

deformation modulus, the non-linear softening curves (based on the non-linear

relation) of four different rock mass domains at increasing levels of porosity are


Figure 85. Typical deformation modulus softening curves of caving rock masses using

the non-linear softening relation.

Fully softened deformation modulus values are predicted that range between 200

MPa and 500 MPa which is consistent with those values previously reported by

Pierce et al. (2006) for a fully bulked rock mass.





Implementation of Non-Linear Deformation Modulus Softening6.3.1

in the Cave Demonstration Model

The results of implementing the non-linear deformation modulus relation in theCave Demonstration Model are presented in Figure 86. Cave propagation

behavior is compared to the linear relation developed by Pierce et al. (2006). The

impact on the density, modulus and propagation rate has been presented.

Figure 86. Impact on cave propagation behaviour by implementing the non-linearmodulus softening relation in the cave demonstration model.

A greater reduction in the deformation modulus is seen with the implementation

of the non-linear relation. To further compare the modeling results, the evolving

bulk modulus has been tracked immediately in the cave back and at heights of 10

m and 20 m above the undercut. The results are presented in Figure 87.





Figure 87. Simulated evolution of the bulk modulus in the back of demonstrationmodel undercut; the linear and non-linear relations compared in the cave

demonstration model.

Significant variations in the simulated modulus values within each of the linear and

non-linear model relations are presented. The non-linear relation provides results

that soften the rock mass at a greater rate than the linear model. These simulated

differences between the two relations will affect the capacity of the caved rock

mass to carry stress/load and impact propagation rates.

This relation will provide a more rigorous estimate of the cave propagation rates

and allow more realistic bulking factors to develop within the cave.



7 – Impact of Large-Scale Discontinuities on Cave Propagation Behavioiur


IMPACT OF LARGE-SCALE DISCONTINTIES ON CAVE7

PROPGATION AND SUBSIDENCE BEHAVIOUR

7.1 Subsidence Behaviour

Cave propagation behaviour and subsidence are closely linked geomechanical

processes. Mining-induced subsidence is the lowering of the ground surface

following the underground extraction of ore. To a greater or lesser extent, it results

from all forms of underground mining, but it is particularly pronounced in caving.

As the orebody caves and is extracted progressively, the overlying cap rock also

caves and moves downward, with the remaining ore producing a characteristic

surface depression (Brown, 2003).

Brady and Brown (1993) classify subsidence into two types, continuous and

discontinuous. Continuous (or trough) subsidence refers to the formation of a

smooth surface subsidence profile that does not have step changes as illustrated in

Figure 88a. This type of subsidence is the result of the extraction of a thin orebody

such as coal when a longwall mining method is used (Brady and Brown, 1993;National Coal Board, 1975 and Peng, 1992). Discontinuous subsidence involves

large surface displacements and the formation of steps (or discontinuities) of the

surface as illustrated in Figure 88b. This type of subsidence may be associated

with several mining methods including sub-level, block and panel caving. In these

cases, the subsidence crater can be very large.





Figure 88. Conceptual models of subsidence a) continuous subsidence (after Kratzsch,1983) b) discontinuous subsidence (after Whittaker and Reddish, 1989).

Subsidence associated with the extraction of coal seams has been studied in detailsince the late 19th Century. The mechanisms and associated terminologies used in

the analyses are now well understood and largely standardised. However, in

metalliferous mining and especially in massive orebodies, the mechanisms are not

as well established and the terminology used is not standardised. Consequently

there is still some debate over the terminology used and the key parameters used

to analyse or predict discontinuous subsidence. Numerous researchers have

proposed conceptual models of subsidence which have used diverse terminologyas presented in Table 15.





Summary of terminology used to define discontinuous subsidence (after FloresTable 15.and Karzolovic, 2004).

Author (s) Key terminology

Hoek (1974)

This model defined four zones and two angles:

Zones: Angles:

- a crater area - an angle of break

- an unstable area - the dip of a subsequent failure plane

- a partially stable area

- a stable area

Brown andFerguson

(1979)

This model used the terminology defined by Hoek (1974).

Kvapil et al. (1989)

This model established three zones and two angles:

Zones: Angles:

- devastation area (crater) - an angle of break

- transition area - an angle of sliding- stable area

Karzulovic(1990)

This model used the same terminology defined by Brown and Ferguson’s model.

Herdocia(1991)

This model defined three zones and two angles:

Zones: Angles:

- a crater area - an angle of caving

- an unstable area - an angle of fracturing

- a stable area

Singh et al.

(1993)

This model defined four zones and four angles:

Zones: Angles:

- a crater area - an angle of caving

- an unstable area - an angle of unstable fracture

- a stable fractured area - an angle of fracture initiation

- a deformed area - an angle of deformation

Lupo (1996)


Zones: Angles:- a caved rock area - an angle of cracking

- a cracking area - an angle of deformation

- a deformation area

Karzulovic et al.

(1999)


Zones: Angles:


- a cracked zoned - an angle of influence

- a stable area

van As et al. (2003)

This model defined four zones and three angles:

Zones: Angles:


- an fractured zone - a fracture initiation angle

- continuous subs. zone - an angle of subsidence- a stable area

Flores andKarzulovic

(2004b)

This model defined three zones and one angle:

Zones: Angles:


- an influence zone

- a stable area





There is particular confusion regarding the “Angle of Break” term. Kvapil et al.

(1989), Karzulovic et al et al. (1999) and van As et al. (2003) define the Angle of

Break as the angle between the edge of the undercut and the limit of the crater

wall. However, Flores and Karzulovic (2004) propose the angle of break to be the

angle between the edge of the undercut and the limit of the discontinuous

deformation, or fractured zone.

van As et al. (2003) proposed the terminology presented in Figure 89 to

standardise the description of subsidence features related to block and panel

caving. This terminology has been adopted for the discussion of results in the cave

propagation and subsidence model developed herein.

Figure 89. Terminology used to describe subsidence features for block- and panel-cavemines (modified after van As et al., 2003).

Historically, mining engineers have defined the extent of subsidence features using

angles measured from the base of the undercut. However, extreme caution should

be used when using such quoted angles to predict subsidence, because factors such

as the mining depth and rock mass properties can have a significant impact on the

angles of break. The use of angles measured from the base of the undercut implies

Caved (Broken) Material

Angle of Break / Cave Angle(Angle of Draw = 90-C)

C

Tension Cracks

Local Geology AffectsZone of Influence

Crater

AB

Fracture Initiation Angle

Angle of Subsidence

StableZone

Subsidence Zone of Influence

StableZone

Small-ScaleDisplacement Zone

(Continous Subsidence)

Small-ScaleDisplacement

Zone(Continous

Subsidence)

Large-ScaleSurfaceCracking

(FracturedZone)





that the failure mechanism develops along a plane, although the actual failure

surface may take any shape in situ.

7.2 General Characteristics of Caving Induced

Subsidence

A number of orebody, local geologic and topographic features can influence the

nature and extent of subsidence. Some of these factors include:

the dip of the orebody

the shape of the orebody in plan

the depth of mining and the associated in-situ stress field

the strengths of both the orebody and host rock mass

the slope of the ground surface

major geological features such as faults and dykes intersecting the orebody

and host rock

prior surface mining

the placement of fill in a pre-existing or newly produced crater, and

nearby underground excavations.

In order to accurately predict subsidence behaviour, the numerical model of cave

propagation and subsidence assessment must include all of these factors.





Figure 90. Conceptual model of the development of block caving subsidence (afterSainsbury and Lorig, 2005).

If ore extraction continues, the surface breach will grow laterally near the surface.

The rock adjacent to the subsided crater either slides along geologic weaknesses,

such as joints or faults, or topples into the open crater.

Chimney Caving7.3.2

Chimney caves are secondary draw-collapse structures that may develop over the

mined area. Chimney caves form when the flow channel of the drawpoint(s)

reaches the surface. At this point, the caved ore-flow ellipse changes into

cylindrical flow (Kvapil, 1982), as illustrated in Figure 91.





Figure 91. Conceptual model of chimney cave development (Betourney et al., 1994), b)surface expression of a chimney pipe in a kimberlite caving operation (aftervan As et al., 2003).

van As et al. (2003) suggest that chimney caves are usually the result of poor cave

management, in that, excessive draw from an isolated drawpoint is allowed to

occur that causes these features.

Plug Caving7.3.3

Plug caving (or plug subsidence) is a form of chimney caving that occurs suddenly

rather than progressively and is controlled by one or more major structural

features which provide low strength surfaces on which the plug of undercut rock

may slide under the influence of gravity. In this case, the rock will undergoessentially rigid body displacement without breaking up or dilating if the vertical

distance through which it falls is restricted (Brown, 2003). Figure 92 illustrates the

observed plug subsidence controlled by intrusive dykes at the Athens Mine, in

Michigan, USA.





Figure 92. Plug subsidence mechanism at the Athens Mine in Michigan USA (afterObert and Duvall, 1967).

Plug caving resulted in a fatal air-blast at the Northparkes E26 Lift 1 Mine in 1999

as discussed in Section 1.2. The plug cave resulted in the formation of a circular

subsidence crater at the ground surface as illustrated in Figure 93.

Figure 93. Geometry of Lift 1 cave a) before and b) after plug caving (after Pierce,1999).





7.4 Subsidence Features Related to Cave Mines

The time associated with subsidence resulting from mining is composed of two

distinct phases: (1) active and (2) residual. Active subsidence refers to all

movements occurring simultaneously with the mining operations, while residual

subsidence is that part of the surface deformation that occurs after the cessation of

mining. The duration of residual subsidence is of particular importance from the

standpoint of evaluating the extent of liability of underground mine operators and

developers for post-mining subsidence and land use.

Description of Active Subsidence Features7.4.1

A review of large-scale surface disturbances from block and panel caving mines

was conducted by Lupo (1998), who found that the primary surface features that

develop as a result of block and panel caving include the following zones:

• a caved rock zone

zone of large-scale fracturing;

a small-scale surface displacement (continuous surface subsidence) zone,

and

a stable (elastic) zone.

The following section provides a discussion on their distinct features.

7.4.1.1 Caved Rock Zone

The caved rock zone is a common surface feature of many caving mines; it also is

referred to as the zone of active cave movement (van As et al., 2003) or the crater.

Caved material consists of irregular blocks of mobilised rock, ranging in size from

millimetres to several metres. The caved rock zone develops as the underground

caving influence reaches the ground surface, causing the overlying rock mass

and/or side rock to fall into the mined void. Over time, the surface of the caved-

rock zone may subside as ore is continued to be withdrawn (Lupo, 1998). Figure

94 illustrates the formation of a crater in steep terrain at the Henderson Mine inColorado.





Figure 94. Photo showing crater and caved rock zone at Henderson Mine (after Lupo,1998).

7.4.1.2 Zone of Large-Scale Fr actur in g

The zone of large-scale fracturing consists of an area in which the ground surface is

broken and has large open tension cracks, benches, and rotational blocks. The

primary failure mechanism of surface cracks associated with cave mines is shear

and tensile failure of the side rock, which results in stepped benches and scarps.

Other types of failure mechanisms, such as toppling and block rotation, are also

present, but they appear to be secondary mechanisms that form after the primaryshear failure develops. Figure 95 illustrates the typical scarp and cracking features

observed at Northparkes E26 Lift 1 Mine, in NSW, Australia.





Figure 95. Photo showing large-scale surface cracking at Northparkes E26 Lift 1 Mine (after van As et al, 2003).

Sainsbury et al. (2010) report that a total strain criterion of 0.005 (0.5%) can be

used to assess the limits of the large-scale fracturing at the Grace Mine. This totalstrain criterion has also been used to calibrate the limit of large-scale fracturing at

the El Teniente block cave mine in Chile (Cavieres et al., 2003).

7.4.1.3 Smal l-Scale Displacement Zone (Cont inuous Zone of Subsidence)

Continuous surface subsidence, as defined by Brauner (1973), is the response of

the rock mass to a mined void, which results in the formation of a gentle surface

depression. Generally, the continuous subsidence zone forms between the large-

scale fractured zone and the undisturbed surface.

Surface buildings, roads, underground power lines, railroads and other structures

can be impacted by continuous surface subsidence. Lupo (1998) reports measured

subsidence up to 200 mm in a continuous subsidence zone at a distance of 250 m

from a large-scale fractured zone that caused heavy damage to nearby surface

structures.





Sainsbury et al. (2010) report that the limit of measured small displacements at

the abandoned Grace Mine can be derived by generating a contour line that

encompasses all areas of horizontal strain > 0.002 (0.2%) and angular distortion >

0.003 (0.3%). These strain criteria are based on the surface subsidence required to

cause damage to a masonry structure during active subsidence (Singh, 2003).

Figure 96 illustrates a small tension crack within the small-scale displacements

zone at the Kiirunavaara Mine.

Figure 96. Photo showing tension crack within small-scale displacements at theKiirunavaara Mine (after Villegas, 2008).

7.4.1.4

Stabl e (Elast ic) Zone

The area outside the small-scale displacement zone is termed the stable zone; it

usually is defined as the area in which mining-induced surface displacements are

insufficient to cause any architectural damage.





Long-Term Time-Dependent Subsidence7.4.2

7.4.2.1 Residual Subsidence

Almost all of the limited research conducted on residual mining-induced

subsidence is associated with underground coal-mining methods. The time span

during which surface subsidence occurs varies considerably with the mining

method used. Longwall coal mines generally induce subsidence beginning almost

immediately after the commencement of mining. With room and pillar systems,

major occurrences of surface subsidence may be delayed for decades until the

support pillars deteriorate and collapse.

The duration of reported residual subsidence movements above longwall coal

mines is relatively short, typically varying between a few weeks and about 5 years.

Singh (2003) reports that the magnitude of these movements rarely exceeds about

10% of the total subsidence. The time spans reported in the literature are

summarised in Table 16.

Observed residual subsidence duration over longwall mines (after Singh, 2003).Table 16.

Reference Country Residual Subsidence Duration

Institution of Municipal Engineers UK 2 - 10 years(Anon., 1947)Orchard and Allen (1974) UK 3 - 6 years (strong overburden)

Collins (1977) UK 2 - 4.5 years

Grard (1969) France 6 - 12 monthsBrauner (1973) Germany 1 - 2 years

Brauner (1973) USSR 2 years (shallow mines)

4 - 5 years (deep mines)

Shadrin and Zomotin (1977) USSR 0.2 - 2 yearsGray et al. (1977) US 0.3 - 3 years

Hood et al. (1981) US 1 year

Luo and Peng (2000) suggest that the main cause of residual subsidence for

longwall coal-mining operations is the compaction in the overburden strata that

was disturbed during the active subsidence process. This mechanism is captured

in the cave propagation model via the non-linear deformation modulus function

that is related to volumetric strain.





The only observation of residual subsidence at a panel-caving mine noted in the

literature is continued crater expansion at Henderson Mine between 1982 and

1983. Stewart et al. (1984) postulate that the continued crater expansion was

caused by compaction of the caved material.

7.4.2.2 Sub-Sur face Er osion

Several years, or even decades, after mining-induced subsidence has stabilised, pot

holes have been observed on the surface, mainly around the perimeter of the

subsided area where tension cracks existed at the time of subsidence at the

abandoned Grace Mine (Sainsbury and Lorig, 2005).

Coincident with subsidence, deep-seated tension cracks develop in the rock and

the overlying soils on the surface. van der Merwe (1999) suggests that, due to

surface erosion, the cracks within the soil are filled with loose soil and become

healed, but the deep-seated cracks within the bedrock remain open and become

natural conduits for percolating surface water. As water percolates through the

soil into the cracks, the surface soils are eroded and form a cavity that eventually

breaks through to the surface. A conceptual model of a sub-surface erosion

mechanism is presented in Figure 97.

Figure 97. Simplified subsurface erosion mechanism (after Van der Merwe 1999).





In reality the surface expression of these mechanisms look like pot holes as shown

in Figure 98.

Figure 98. Photos of subsurface erosion pot holes (after Van der Merwe, 1999).

A similar mechanism has been observed at the abandoned Grace Mine panel cave,

whereby a sinkhole was observed outside the limit of large-scale surface many

years after the cessation of mining, as illustrated in Figure 99.

Figure 99. Photo of sinkhole located outside the limit of large-scale cracking at theabandoned Grace Mine (after Sainsbury and Lorig, 2005).





The time of development of sub-surface erosion cannot be predicted reliably.

However, van der Merwe (1999) reports that it is conceivable that the mechanism

may take decades to centuries to fully develop. As a result of this time dependency,

the ability to capture such a process in a numerical model is difficult at the current

time. As a result of this, the numerical model of cave propagation and subsidence

assessment with focus on predicting the active subsidence limits only.

7.5 Effect of Large-Scale Discontinuities on Subsidence

Limits

The influence of large-scale discontinuities on cave propagation and subsidence is

recognised to be important by many researchers (Crane 1929, Heslop 1974,

Boyum 1961, Fletcher 1960, Parker 1978, Laubscher 1990, Mahtab 1976, Hoek

1974, Holla and Buizen 1990, Shadbolt 1978, Shadbolt 1987 and Hellewell 1988).

In situ observations by Crane (1929), Parker (1978), van As et al. (2003), Blodgett

(2002) and Hatheway (1968) have shown that the impact of discontinuities can be

varied based on persistence, strength and orientation relative to the undercut

footprint and principal stress direction. Quantifying the effects of large-scale

discontinuities on cave propagation is complicated by the fact that many features

have not reacted adversely when subjected to subsidence and the results of

scientific investigations are in some instances, contradictory.

Laubscher (2000) suggests that major discontinuities must have sufficient

continuity to influence the caveability of the rock mass. Butcher (2005), after

Stacey and Swart (2001) reports that major discontinuities can modify or enlarge acrater perimeter by further break back as illustrated in Figure 100.





Figure 100. Schematic diagram of how crater shape can be modified by major geologicalstructure (after Stacey and Swart, 2001).

Based on Figure 100, the presence of a steeply dipping fault can terminate the

angle of draw short of its normal value. Whereas, if a gently dipping fault intersects

the collapsing rock column the lateral extent of surface subsidence can increase

outward to the place where the fault intersects the ground surface. Abel and Lee

(1980) report that whether or not this takes place depends primarily on the shear

strength of the fault zone.





Many observations of the influence of discontinuities have been made; however,

only a modest amount of research work has been carried out to qualify and

quantify their influence.

Crane (1929) carried out extensive measurements of caving at iron ore mines in

Michigan, USA and developed a system for predicting angle of draw based on joint

measurements. Crane’s observations led him to conclude that rock breaks

according to a systematic arrangement of planes of weakness (joints) with slight

irregularities due to breaking between joints, and, in the absence of faults and

dykes, joint dip determines the angle of break. This is consistent with the results

of the Cave Demonstration Models presented in Figure 75.

Parker (1978) also notes that geological structure is a major controlling factor in

subsidence. In weak rocks there may be no significant geologic structure, hence the

reported cave angles are usually consistent and can be predicted with reasonable

confidence. In stronger rocks however, the cave angle is usually controlled by

geological structures. A well-defined fault plane, which is parallel to a mining face

and steep to moderately inclined, will result in a cave which propagates to surface

fairly rapidly and is defined on the surface by the trace of the fault plane. If the

predominant joints and faults are roughly perpendicular to the mining front,

caving may be inhibited and negative cave angles (overhangs) may occur.

van As et al. (2003) report that in most cases when a mining face encounters a

significant discontinuity with a moderate to steep dip, movement will occur on the

fault regardless of the cave angle. A stepped crack will result where the fault

daylights at the surface. If mining is only on the hangingwall side of the fault there

will only be surface movements on the one side. If the fault dip is steeper than the

cave angle, the extent of surface subsidence will be reduced, conversely, if the fault

dip is less than the cave angle the extent of surface subsidence will be increased.





Fault Impacted Caving7.5.1

The following section provides documented case histories of when large-scale

discontinuities have impacted cave growth. These documented case studiesprovide the basis for validating an appropriate numerical modelling technique for

representing cave propagation behaviour in the numerical model of cave

propagation and subsidence assessment.

7.5.1.1 San Manuel Mine

Faults at the San Manuel Mine are important factors in causing and forming

boundaries to surface subsidence (Blodgett, 2002). Hatheway (1966) reported that

vertical cave propagation was halted and then deflected by the shallow dipping San

Manuel fault, as illustrated in Figure 101.

Figure 101. Conceptual development of surface subsidence at the San Manuel Mine(after Hatheway, 1966).





In addition, steeply dipping north-west trending faults at the San Manuel Mine

were observed to exert a major influence on the orientation of tension cracks and

development of the subsidence crater. The Cholla fault arrested the development

of the subsidence crater in a north-easterly direction for several years as

illustrated in Figure 102.

Figure 102. Plan view, section view of subsidence crater at the San Manuel Mine (afterHatheway 1966).

Based on this case study, it can be seen that sub-vertical faults limit the subsidence

crater beyond their extent and faster propagation rates can be expected as the

mobilised rock mass propagates unravelling along them.





7.5.1.2 Ridgeway Deeps Sub -Level Cave

At the Ridgeway Mine located in NSW, Australia, the vertically orientated North

Fault significantly altered the propagation rate of the sub-level cave and rapid cave

propagation rate was caused by the weak fault strength, as illustrated in Figure

103.

Figure 103. Photos showing cave propagation controlled by weak vertical fault at theRidgeway Mine (Brunton, 2009).

Rapid cave propagation occurred along this fault and surface break-through

occurred much sooner than was anticipated. The cave back advanced at three-

times its previous rate, unravelling along this structure (Brunton, 2009).





7.5.1.3 Questa Mine

The crater at the Questa Mine in New Mexico, USA, has been affected by sliding

along large scale structures (Gilbride et al., 2005). Slide features include

escarpments, fresh cracks, block toppling, surface rubblisation, tree tilting, and

disturbance to hillside vegetation. While no sub-surface measurements of

movement exist, the gross surface expression of the east wall slide suggests that

the slide is relatively shallow-seated (<60 m deep) and is occurring along a planar

or near-planar surface. Sliding originally occurred along a high-angle, southeast-

dipping fault in mid-1997, forming a large head scarp. The head scarp currently

measures more than 60 m in height. The slide and head scarp are shown in Figure

104.

Figure 104. Photo of Goathill Crater at the Questa Mine (after Gilbride et al., 2005).





7.5.1.4 Henderson Mine

Geological contacts have also been reported throughout the literature to effect the

formation of surface subsidence features. Crane (1929) reports that igneous

intrusions such as dykes and sills within the iron ore deposits of the Michigan

Upper Peninsula have a significant effect on cave propagation.

Carlson and Golden Jr. (2008) report that a weak intrusive contact at the edge of

the 7210 Production Level at the Henderson Mine was observed to cause a low

angle of break during initiation of the 7210 cave as illustrated Figure 105.

Figure 105. Irregular cave growth along a weak intrusive contact at the Henderson Mine 7210 Level (after Sainbury et al., 2011)

Further investigation of this phenomena is considered in Section 12.





7.5.1.5 Kimberl y Mine

Laubscher (2000) has previously reported on structurally controlled cave shapes

at the De Beers Kimberly Mine. In this case, the structure has impacted the cave

shape at depth, and overhangs that result in negative break angles can form in

structurally unfavourable areas or along geological contacts. Figure 106 shows a

section through the De Beers Kimberley Mine that shows an overhang against the

contact between the host rock and kimberlite pipe.

Figure 106. Section through Kimberly Mine showing over-hang (after Laubscher,2000).

7.5.1.6

Summary

Based on these case studies, it is clear that in order for a geologic feature to be

considered significant (i.e. to influence the cave angle) two conditions must be met:

movement on the feature must be kinematically feasible; and

the forces driving movement must be greater than the forces resisting

movement. These forces are dependent upon many factors including: dip of

the feature, cohesive strength of infilling material, roughness and planarity

of feature, water pressure in feature and stress.





Parametric studies have previously been conducted by Vyazmensky et al. (2010) to

study the effect of joint fabric and large-scale discontinuities on block caving

induced surface subsidence. Figure 107 illustrates the predicted crater formation

for a single fault that intersect the base of a 200 m deep conceptual block cave at a

number of different locations.

Figure 107. Simulation of subsidence crater formation for different two-dimensional faultorientations (modified after Vyazmensky et al., 2010).

It is clear from these simulations that the greatest impact on caving is seen when a

sub-vertical fault forms the boundary of mining limits. In this case rapid cave

growth can be expected along its extent. However, this study does not discuss the

strength of the discontinuities used in the simulation which are known to affect

caving behaviour.





7.6 Fault Properties

One of the first problems associated with analysing the effects of geologic structure

on ground movements is characterising the properties of the discontinuities. These

properties are highly variable and include: orientation, infill, previous

displacement, planarity and shear strength.

There is limited information available regarding the large-scale shear strength of

fault structures. Figure 108 illustrates the results of direct shear tests carried out

to determine the peak friction angle and cohesion of filled discontinuities as

reported by Wyllie and Mah (2007).

Figure 108. Estimated shear strength of filled discontinuities (after Wyllie and Mah,2007).

It can be seen that the range of fault properties derived from numerical backanalyses is highly variable, and, at the current time, there is no real way to

determine these properties from large-scale in situ testing. As a result of this,

sensitivity studies are required to determine the range of caving and subsidence

behaviour expected when large-scale discontinuities are present within and

around a propagating cave.





Figure 110. Conceptual geological structures simulated in numerical demonstrationmodel.

As discussed, whether or not a discontinuity affects cave propagation andsubsidence depends primarily on its shear strength. Based upon the range of shear

strength parameters, provided in Figure 108, three property sets have been

defined for analysis as presented in Table 17.

Conceptual fault shear strength and stiffness parameters represented inTable 17.numerical demonstration model.

Coh. Tens. Kn Ks

(kPa) (Deg.) (kPa) (GPa) (GPa)Strength 1 0 20 0 1 0.1

Strength 2 75 30 0 10 1

Strength 3 200 40 0 50 5

Implicit Fault Representation7.7.1

Implementation of an implicit scheme for fault representation can be considered

by the same methodology as joints within a UJRM sample (discussed in Section 5).

Figure 111 illustrates the results of a simulated direct shear test conducted on a

rock mass with a horizontal discontinuity embedded along a group of zones

(coloured red) at the block contacts. The fault has been simulated with a

ubiquitous joint cohesion of zero and friction angle of 30 degrees. Matrix

properties are consistent with a rock mass of UCS 100, GSI 60 and mi of 25. A

normal stress of 30 MPa has been applied to the sample during test simulation.





Figure 111. Simulated direct shear test; normal stress 10 MPa using ubiquitous jointsin FLAC 3D .

The same ubiquitous joint technique has been used to simulate the presence of

fault structures within a large-scale cave model, as illustrated in Figure 112.

Figure 112. Ubiquitous joint faults used to simulate faults within a cave-scale model.





Figure 113. Cross-section of mobilised zone (2m displacement) – implicit, ubiquitous joint approach used to simulate conceptual discontinuity surfaces.





A minor increase in vertical cave propagation is associated with Fault A and the

weakest fault property set. However, all of the other fault orientations and fault

properties show only a very minor effect on the predicted mobilised zone. Little

impact on the cave growth rate and shape is noted with this approach, unless a low

strength fault is orientated sub-vertically at the cave periphery. These results are

not consistent with the observations from previous documented case studies

presented in Section 0 and therefore the implicit approach is not considered

adequate for the representation of faults in the numerical model of cave

propagation and subsidence assessment .

Explicit Fault Representation7.7.2

Most modelling codes have the capability to simulate interfaces that are

characterised by Coulomb sliding and/or tensile separation. Interfaces have the

properties of friction, cohesion, and dilation, normal and shear stiffness, as


Figure 114. Schematic diagram showing interface logic and how it can be used torepresent a discontinuity in a numerical model of caving.





Although there is no restriction on the number of interfaces or the complexity of

their intersections, historically, interfaces have not been used to simulate

geological structures due to difficulties in creating complicated geometries.

Advances in mesh generation through the programs such as Kubrix (Simulation

Works, 2012) and more specifically the tetra-split meshing option have made it

possible to create models with many irregular and intersecting interfaces, as

illustrated in Figure 114b. In addition, a new methodology developed within

FLAC 3D allows the specification of peak and residual strength properties along the

interface.

Figure 115 illustrates the predicted mobilised zone when interfaces are used to

simulate faults within the Cave Demonstration Model. The model results display

much greater influence of the fault structures than what was predicted with the

implicit (ubiquitous joint) approach. Significant over break is predicted with Fault

B and the weakest fault properties, whilst the effect of increasing fault strength

and stiffness is clearly observed.





Figure 115. Cross-section of mobilised zone (2m displacement) – explicit, interfaceapproach used to simulate conceptual discontinuity surfaces.





The simulation of explicit faults in a numerical model of caving provides results

that indicate faulting has a significant impact on cave shape growth. The numerical

simulation results provide cave shapes that are intuitive and match with those

observations made at various mine sites around the world documented in Section

7.5.1.

7.8 Summary

Based on the simulation results provided for both an implicit and explicit

numerical modelling technique, it is recommended that the explicit fault approach

be adopted within the numerical model of cave propagation and subsidence

assessment to ensure the most rigorous assessment of fault behaviour is achieved.

Most of the available information on the effect of geological structures on cave

propagation behaviour throughout the literature is qualitative in nature. In order

to validate the modelling methodology with the use of interface elements to

simulate large-scale geological structures, the observed and monitored structurally

controlled cave propagation behaviour at the 7210 Level of the Henderson Mine

has been studied. A summary of the modelling results are provided in Section 12.



8 – Development of a Production Draw Algorithm


DEVELOPMENT OF A PRODUCTION DRAW8

ALGORITHM

8.1 Influence of Production Schedule on Cave

Propagation Behaviour

The impact of the production draw schedule on cave propagation behaviour has

previously been documented by Laubscher (1994). Previous experience at the

Northparkes Mines suggests that the success of a mine plan in hard, jointed rock

masses will rely on the ability of the rock mass to cave at a rate greater than the

production draw rate to ensure continuous cave propagation without creation of

an air-gap. The rate of caving can be slowed by controlling the draw as the cave

can only propagate if there is space into which the rock can move. The rate of

caving can be increased by advancing the undercut more rapidly but problems can

arise if this allows an air gap to form over a large area (Laubscher, 2000).

From simulations conducted in the Cave Demonstration Model thus far, it is clear

that the cave propagation rate can vary significantly between orebodies, working

panels and adjacent drawpoints. As a result of this, the realistic and accurate

representation of a mining schedule is essential in being able to accurately assess

the bulking/dilation behaviour and cave propagation rate. As seen previously in

Table 1, the production methodology can have a significant effect on the cave

propagation behaviour as a result of the induced bulking behaviour internal to the

cave mass.

The magnitude and orientation of the regional stress on and around the mining

footprint also plays a significant role in caving (Laubscher, 2000). Caveability is

promoted when the major principal stress direction is perpendicular to the short-

axis of a cave footprint as discussed in Section 1.3.

The redistribution of stresses around a propagating cave causes the cave volume to

evolve into the most stable shape. In most cases this is circular or elliptical. This

phenomenon was observed at the abandoned Grace Mine as illustrated in Figure

116.





Figure 116. Plan view of subsidence limits at the Grace Mine determined byobservations.

As a result of this, an accurate representation of the evolving cave shape and draw

rate is required to ensure that stress redistribution around, above and below the

yielded rock mass is an accurate representation of the evolving in situ conditions.

Impact of Production Draw Strategy in the Demonstration8.1.1

Model

When planning a cave mine, there are a number of production controls that can be

implemented to ensure optimum cave performance. The effect that a production

schedule has on cave performance has been considered within the Cave

Demonstration Model by simulating a) uniform draw block caving, b) variable

draw block caving and c) incremental draw (panel caving). For each of these

scenarios an average height of draw of 10 m has been simulated across the entire

undercut footprint. The simulation results are provided in Figure 117.





Figure 117. Effect of draw strategy on the caveability of a rock mass in the numericaldemonstration model.

By simulating perfectly uniform draw (zero variability in drawbell production), an

increase in the propagation rate is seen in Figure 117A since; shear stresses within

the caved mass will be decreased, resulting in a reduction of the bulking behaviour

of the rock mass. The effect that a uniform draw strategy has on a cave

propagation rate has been documented by Pierce et al. (2006) during a numerical

back analysis of the Northparkes E26 Lift 2 caving behaviour. In addition, by

staggering production and simulating an incremental draw strategy (where mining





Figure 118. Cave simulation results for variable maximum bulking rates in thenumerical demonstration model.

It can be seen from Figure 118A that as the maximum BF of a rock mass decreases,

the cave propagation rate increases. The results of these simulations identify the

problematic nature of assuming bulking rates with analytical cave propagation

assessment techniques.





8.3 Limitations to Height of Draw Scheduling

Within the Pierce et al. (2006) cave model, production is simulated by inducing a

small downwards velocity on gridpoints that are located in the undercut. The

induced gridpoint displacement corresponds to the scheduled Height Of Draw

(HOD). Although the 2006 cave model is able to control the production draw in the

model, the HOD production schedule is not ideal.

At the present time most cave mines use the commercially available block cave

production scheduler PCBC (GEMCOM, 2012) for production planning and

operations control. In instances when PCBC HOD’s are used for scheduling

purposes for geomechanical caving simulations, such as Pierce et al. (2006), this

may lead to over-draw during the early stages of the model simulation. However,

during the later stages of draw, production may be underestimated as a result of

the uniform bulking factors applied to estimate the tonnes withdrawn in the PCBC

schedule. A schematic example of the PCBC-HOD approach is provided in Figure

119.

Figure 119. Schematic representation of a HOD based schedule interpreted fornumerical mesh.

In addition, using this technique, production draw is simulated based on

production increment (groups) that are defined by generalised areas of draw for

any given time period. Prior to production simulation, the extent of the mining

footprint must be defined. The mining footprint is divided into groups that

represent the progressive nature of the expanding hydraulic radius, or different





draw rates during cave initiation. These groups are difficult to change during the

production simulation, and future mining is controlled by average heights of draw

in these initial groupings of model zones. For each production increment, an

average draw rate is assigned based on production tonnes. In general, mining

increments are fixed for the life of mine and defined by the initial undercut

strategy. An example of a mining increment schedule is presented in Figure 120b.

The actual production schedule it may represent is provided in Figure 120a.

Figure 120. Representation of (a) typical production schedule (b) mining incrementschedule (c) improved drawpoint scheduling method.

Using this technique it is known, based on the simulations presented in Figure 117,

that cave propagation rates may be over predicted due to the lack of bulking /

shear induced within the cave mass. The majority of the shear strain will

accumulate at the cave periphery and the internal caved massed will be withdrawn

uniformly as an ‘intact plug’.





Simulation of Production Draw8.4.2

The perimeter of the undercut footprint is identified through a function that

determines internal (good) and perimeter (bad) gridpoints as shown in Figure121.

Figure 121. Identification of perimeter gridpoints for production draw simulation in anumerical mesh.

The identification of perimeter zones is important in distinguishing production

areas from “static” areas in the numerical model, since gridpoints/nodes above a

boundary pillar should not be disturbed.

Production draw continues to be simulated the same way as the Pierce et al.

(2006) model by applying a small downward-oriented velocity to gridpoints in the

model that correspond to drawpoint locations. However, rather than being

generalised over the entire footprint, the velocity of draw (Vdraw) is scaled at the

individual drawpoint level – based on the planned production schedule tonnes.

For example, if the maximum tonnes extracted from a drawpoint over a production

period is 100, and another drawpoints has 50 tonnes scheduled to be withdrawn

from it, then it would be assigned a Vdraw of 50%.





To determine the actual draw velocity within the model, the Vdraw is multiplied by a

maximum draw velocity (Vmax). The maximum velocity should be set low enough to

ensure pseudo-static equilibrium throughout the model.

Representation of the variable draw assigned to production gridpoints is provided

in Table 18.

Example of gridpoint velocity scaling based on variable production draw.Table 18.

# Easting Northing Elevation Tonnes DrawVelocity

1 1 1 0 1 1/3 Vmax

2 1 2 0 2 2/3 Vmax

3 1 3 0 3 3/3 Vmax

Selection of Maximum Draw Velocity (Vmax)8.4.3

The selection of the Vmax within the model to simulate mining production should be

based on the deformation modulus of the rock mass and the zone size within the

model. Simulated laboratory tests (UCS and direct tension) with varying applied

loading velocities are shown in Figure 122.

Figure 122. Simulated large-scale laboratory tests at different applied loading velocitiesand the impact on the sample strength response.





It can be seen from these simulations that as the loading rate (draw velocity)

increases, the simulated compressive strength of the rock mass increases and the

tensile strength decreases.

Implementation of a Vmax that is too high results in a tensile failure mechanism in

the undercut roof that prohibits cave initiation. This has been shown through

production draw simulation in the Cave Demonstration Model where the velocity

of draw applied to a rock mass has been varied. The results are presented in

Figure 123.

Figure 123. Impact of selection of draw velocity on cave propagation behaviour in thenumerical demonstration model.





It can be seen that when the applied Vmax is greater than the maximum draw

velocity to maintain pseudo static equilibrium, then a tensile failure develops

immediately above the undercut and the cave stalls as a result of numerical

conditions and not the rock mass strength.

Development of a Tonnes Based Production Cut-Off Algorithm8.4.4

Production in the numerical model of cave and subsidence assessment is

controlled by mass balance calculations that are performed regularly during model

stepping after an initial pre-mining value is established. As mass is removed from

the system (as result of mesh deformation and the resulting density changes

according to the description in Section 6.1), the mining tonnes can be calculated by

the difference in the pre-mining and current mass states. It is important to note

that production draw should only be calculated based on the mass removed from

the system above the extraction level elevation in the model. This ensures that

material that is removed from the system to facilitate the numerical draw

algorithm is not included in the cumulative production tonnes.

8.5 Summary

A schematic diagram that outlines the implementation of the mass-balance

production draw algorithm as described in this section is presented in Figure 124.





Figure 124. Schematic diagram of the mass-based production draw algorithm developed.

An example of an evolving cave shape based on the mass-balance production

algorithm is provided in Figure 125.





Figure 125. Example of evolving mobilised zone based on drawpoint tonnes algorithm.

It can be seen that the evolution of the mobilised zone is strongly affected by small

variations in production draw from adjacent draw points. The implementation of

the drawpoint tonnes scheme will allow the bulking behaviour associated with

differential draw over the undercut footprint (and between drawpoints) to evolve.

By drawing all drawpoints by the same velocity over the mining increment,

minimal bulking behaviour is simulated and higher propagation rates may be

predicted. The algorithm assumes that the isolated movement zones from

drawpoints overlap at a height just above the drawpoint. This assumes a low

height of interaction and makes it difficult to represent isolated draw conditions

within the model. The coupling of results with a flow program such as REBOP

(Itasca, 2012) is recommended to predict these conditions.



9 – Development of an Algorithm to Consider Evolving Ground Surface Profile


DEVELOPMENT OF AN ALGORITHM TO CONSIDER9

EVOLVING GROUND SURFACE PROFILE

9.1 Impact of Topography on Subsidence Limits

A crater is a common surface feature of many caving mines; it is also referred to as

the zone of active cave movement (van As et al., 2003). Caved material consists of

irregular blocks of rock, ranging in size from millimetres to several metres in

magnitude. The crater develops as the mobilised zone influence reaches the

ground surface, causing the overlying rock mass and/or side rock to fall into the

mined void. Over time, the surface of the crater may subside as ore is withdrawn

(Lupo, 1998).

Toppling of the crater slopes often occurs (Laubscher, 2000) and this is generally

more pronounced when the crater intersects the side of a slope. At the Questa

Mine, Gilbride et al. (2005) report that large-scale sliding/toppling of the west-

facing hillside above the D Orebody occurred during cave breakthrough as

illustrated in Figure 126. Figure 127 illustrates the surveyed displacementssurrounding the crater.





Figure 126. Photo showing the effect of topography on subsidence crate at the Questa Mine (after Blodgett, 2002).

Figure 127. Survey displacement map above Questa Mine D Orebody (after Gilbride etal., 2005).





9.2 Toppling Failure Mechanism

Toppling failure has been defined by Hoek and Bray (1981) as the ‘rotation of

columns or blocks of rock about some fixed base’. Three types of primary toppling

modes have previously been defined by Goodman and Bray (1976) that include;

block, flexural and block-flexure. A schematic diagram of their modes is presented

in Figure 128.

Figure 128. Schematic diagram showing the three primary modes of toppling (afterGoodman and Bray, 1976).

In each of the toppling cases, it is clear that an unconfined face is required to allow

the failure mechanism to develop through the rotation of the blocks.

9.3 Limitations of the Small-Strain Numerical Approach

As discussed previously, due to the large displacements associated with cave

mining; numerical simulations are run in small-strain calculation mode. I.e.,

displacements are accumulated but the mesh is not updated. As a result of this

small-strain calculation mode, the maximum extent of the cave crater and zone of

large-scale fracturing may be under-estimated, since there is limited ability for a

toppling failure mechanism at the crater edge to develop - since the ground surface

profile is not updated, and, a bulked/yielded rock mass is simulated in the crater

which provides support to the fractured rock mass walls – as shown in Figure 129.





Figure 129. Schematic diagram showing the simulation of evolving surface crater insmall-strain calculation mode.

As a result of this small-strain calculation mode, an algorithm is required that

updates the ground surface profile to reflect the evolving crater and allow toppling

failures to develop at the crater limits.





9.4 Development of an Algorithm to Simulate Crater

Development

The development of the subsidence algorithm can be defined by a series of queries

that are performed periodically during model stepping. They are defined below.

1. Identify surface zones

2. Calculate average displacement of gridpoints associated with surface zones

3. If average displacement is greater than the surface zone edge length then

the zone is deleted to form a free face.

The algorithm is presented as a schematic in Figure 130.





The implementation of the subsidence algorithm has been completed through a

function that is called periodically during production simulation. Its

implementation has been assessed through a subsidence assessment of a block

caving scenario. The validation model geometry is provided in Figure 131.

Figure 131. Geometry and undercut footprint of test model used to validate craterdevelopment algorithm.

Results with and without the algorithm are provided in Figure 132 below.





Figure 132. Subsidence limits predicted with/without surface update algorithm. The

darker (more bold) lines represent the subsidence limits predicted with thesurface update algorithm switched on, and the lighter (fainter) lines representthe predicted subsidence without using the surface update algorithm.

The implementation of the algorithm shows that the subsidence limits are

increased when a toppling failure mechanism is allowed to develop at the crater

edges. Additional model results are provided in Figure 133 that shows the

updated surface elevation within the model as a result of the algorithm. Any

changes to the topography shown in the figure are due to the implementation of

the algorithm since the small-strain calculation mode has been used. The

development of a crater (depicted by the blue coloured zones) is clearly seen after

the simulation of mining.





Figure 133. Updated surface elevation in the model after the simulation of mining withthe surface update algorithm.

The removal of this material from the model is accounted for in the production

tonnes calculation. The ‘nulled’ zones are depicted by the grey zones in Figure 134.





Figure 134. Vertical displacement simulated in the test model and the surfaces zones

that have been nulled to represent the development of the surface crater.



10 – Development of a Sub-Level Caving Algorithm


DEVELOPMENT OF A SUB-LEVEL CAVING10

ALGORITHM

10.1 Sub-Level Caving Mining Method


blasting. The disintegration is brought about by natural processes that include the

in situ fracturing of the rock mass, stress redistribution, the limited strength of the

rock mass and gravitational forces. Sub-level Caving (SLC) requires the

transformation of in situ ore into a mobile state by conventional drilling and

blasting. This may be a result of a high rock mass strength or strategy to reduce

dilution.

The sub-level caving method is thought to have evolved as an up-scaling technique

to the top slicing mining method (Peele, 1918). Block caving, in turn, was the

logical scale-up from sub-level caving. In the first application of sub-level caving,

the ore was not drilled and blasted completely between two sub-levels, but only

parts were broken by induced caving; hence the name sub-level caving (Janelid,1972). At current day SLC operations, the ore mass between the sub-levels is

blasted. As a result of this, the primary concern with SLC mining methods is not

the strength of the orebody itself but the competency of the hangingwall material

(for subsidence and dilution predictions) and prediction of fragmentation and

gravity flow of the blasted ore material through the SLC rings.

Existing caving algorithms described by Pierce et al. (2006) have been developed

based on a block and panel caving scenarios only. In order to simulate sub-level

caving, some modifications are required.





10.2 Simulation of Blast Damage

It is very difficult to estimate the effects of blasting of an in situ rock mass without

site specific trial and/or calibration of numerical results. Empirical evidence from

traditional de-stress blasting in highly stressed mine pillars indicates that blast

patterns with high energy explosives and closely spaced drill holes have been

shown to reduce the strength and deformation modulus of the pillar to some

degree (Andrieux and Hadjigeorgiou, 2008).

The simulation of blasting and damage to the rock mass within the orebody for the

SLC algorithm has been achieved through the modification of joint orientations

within the limits of the blasted sub-level ring. Previous numerical modelling

(Figure 75) has shown that the re-orientation of joints perpendicular to the

direction of draw (in most cases horizontally) will reduce the tensile strength of

the rock mass and promote cave propagation. In order to do this a constitutive

model that allows the specification of joints within the matrix has been used (i.e.,

Subiquitous model in FLAC 3D). To ensure an accurate representation of the rock

mass strength, properties were estimated based on the approach discussed in

Section 2.2.2 with the ubiquitous joints glued up and orientated vertically. To

simulate blast damage within the SLC, the joint properties within active sub-level

limits were reduced to zero cohesion and zero tension and the joint orientations

redefined as horizontal. In doing this the rock mass strength was reduced in situ

without causing any damage to the surrounding rock mass material. A schematic

representation of this implementation is presented in Figure 135.





Figure 135. Schematic diagram of sub-level caving algorithm logic.





10.3 Mobilisation of a Previous Sub-Level

The sub-level caving technique requires the development of draw points within

the ore zone and the subsequent mobilisation of this infrastructure into the caved

mass as production continues on progressively lower levels.

The numerical model of cave propagation, as described in Section 8, requires the

deletion of zones immediately below the mining horizon in order to induce

displacement in the material above (see Figure 135). As a result of the production

on the active sub-level that has been completed, these “nulled” zones are required

to be mined as the active sub-levels get progressively deeper. This requires their

re-instatement into the mesh with properties consistent with the in situ rock mass.

However, since they were previously used to induce displacement in the sub-level

above, a significant amount of compaction of their volume has occurred. As a result

of this, when this material is reinstated it has a negative volumetric strain (due to

its compression) as shown in Figure 136.

Since production in the numerical model is tied to density decreases in a zone, and

this is dependent on increasing volumetric strain (expansion), production from

this re-instated material is impossible unless the displacements are reset to zero.

Doing so transfers the negative volumetric strain to the overlying sub-level

allowing the easy volumetric expansion of material from the currently active sub-

level. A schematic implementation of this algorithm is provided in Figure 136.

As a result of these modifications to the displacements within historical sub-levels,

simulated production tonnes are mainly withdrawn from the active sub-level. This

may impact the effect of being able to simulate secondary/tertiary draw since it is

assumed that all tonnes are produced during primary draw. This will impact the

timing of subsidence in the model and, in reality the subsidence may be delayed.





Figure 136. Conceptual model of the volumetric changes in the sub-level caving algorithmlogic.

10.4 Incremental Mass-Based Calculation

Since production in the numerical model of caving is controlled by the gradual

reduction of densities within the model, the spontaneous deletion of mass and re-

introduction of mass within the SLC system must be accounted for. As a result of

this, the mass-balance within the numerical model should be completed on a

mining-increment basis rather than from the initial pre-mining state and mass

density calculations are completed based on the state immediately prior to mining

on the sub-level.



11 – Palabora Mine Case Study


CASE STUDY VALIDATION: CAVING INDUCED11

FAILURE OF THE PALABORA OPEN PIT

11.1 Background

The Palabora mine began operations as an open cut copper mine in 1964. Today

the pit is approximately 450 m deep and measures nearly 2 km in diameter. A

change in mining method to caving was implemented in the year 2000. Soon after

the breakthrough of the cave to the base of the open pit, a significant pit slope

failure occurred on the north wall, as illustrated in Figure 137.

Figure 137. Photo of the failure in north wall at the Palabora open pit.

Based upon initial numerical back-analyses, the failure mechanism has been

attributed to a persistent joint set that intersects the cave volume at depth

(Brummer et al., 2006).





11.2 Geomechanical Conditions

For each of the caving rock mass domains at Palabora, calibrated continuum

responses have been developed based on the SRM results of Mas Ivars et al.

(2008). The development and calibration of the UJRM’s is discussed in Section 5.

The spatial distribution of each of these domains is provided in Figure 138.

Figure 138. The spatial location of each of the rock mass domains and faults throughoutthe Palabora model mesh.

A Hoek-Brown strength estimate has been developed for the granite rock mass

domain that is outside the caving column. The strength properties used to

represent this domain are provided in Table 19.

Rock mass properties used for the representation of the granite domain.Table 19.





Four faults have been represented in the numerical model as presented in Figure

139. Each of the faults has been represented in the model via interfaces as

described in Section 7.7.2. They have been assigned the properties; cohesion = 1.5

MPa, tension = 0.0 MPa and friction = 34 Degrees. These values are consistent with

the joint properties derived for the rock mass and have been developed based on a

sensitivity analysis and calibration to the existing conditions. The joint normal and

shear stiffness’s have been estimated at 1.5 GPa and 0.15 GPa respectively based

on the stiffness of the rock mass and are zone size dependent.

Figure 139. Location of large-scale structure simulated in the Palabora numerical mesh.





11.3 In sit u Stress

There is high uncertainty associated with the magnitude and orientation of the in

situ stress regime at the Palabora Mine. Previous stress testing studies have

resulted in significant variation in the principal stress magnitudes and the

orientation of the principal stress direction has previously been measured at

orientations varying between 0o and 340o. A schematic diagram representing the

variance in magnitude and orientation in the principal stress directions are


Figure 140. Estimated in situ stress orientation and magnitude at Palabora based onback-analysis of pit slope failure and stress measurement testing.





The horizontal stress magnitudes and and orientation =340o have been simulated for the numerical analysis. This in situ stress condition

was selected based on a sensitivity analysis of the existing north wall slope failure.

This principal stress orientation is consistent with:

(a) The orientation of the large-scale faults mapped at Palabora that strike

north-south and east-west.

(b) The orientation of the major joint sets that strike WNW and NNE.

(c) It is also consistent with the magnitudes derived from a calibration the

existing conditions conducted during 1991 – although the orientation for

this calibration is unknown.

11.4 Production History

Production draw within the model has been simulated based on the methodology

outlined in Section 8. The historical production schedule simulated in the

numerical is provided in Figure 141. The historical heights of draw are provided.

Figure 141. Historical mining record at the Palabora block cave mine.





During the simulated production draw, each of the cave behavioural regions were

tracked and compared to physical observations made at the Palabora mine during

that time period.

11.5 Simulation Results

Cave Initiation11.5.1

The location and magnitude of seismic events recorded during the early stages of

production at the Palabora mine are illustrated in Figure 142(a). Based on this

data, the location of the yield zone (or aseismic zone) has been inferred to extend

approximately 55–83 m beyond the mobilised zone. As illustrated in Figure

139(b), the predicted yield zone within the numerical model extends

approximately 50–80 m above the cave zone, providing a good correlation with the

monitoring data.

Figure 142. Observed seismicity at the Palabora Mine during cave initiation and propagation (a) observed mobilised, yield and seismogenic zones during production (after Glazer and Hepworth, 2004); (b) numerical prediction ofmobilised and yield zones during production simulation at the Palaboramine.





The seismogenic zone has been predicted at various stages of production in the

numerical model using the methodology described by Diederichs (1999). A

value of 0.42 has been used based on a calibration to SRM test results (Mas Ivars et

al., 2006). As illustrated in Figure 143, the seismogenic zone is seen to manifest

immediately beneath the floor of the open pit in the early stages of mining. As

mining progresses and the crown pillar fails, seismicity migrates to the lateral

extents of the undercut footprint, prior to progressing beneath the extraction level

as production continues. This sequence is consistent with the seismic record

collected on site and discussed by Glazer and Hepworth (2004).

Figure 143. Numerical prediction of seismogenic zones during early productionsimulation at the Palabora mine.





Yielding of the Crown Pillar – Q4 200211.5.2

During the fourth quarter of 2002, the yielded rock mass (aseismic) zone connects

through to the open pit. Prior to this time, an un-yielded crown pillar remains.The yielding of the crown pillar drives seismicity (high induced stresses) beneath

the extraction level. The results of the numerical simulation for this period in time

are provided in Figure 144.

Figure 144. Numerical simulation - yielding of the crown pillar during Q4 2002.

The simulated yielded rock mass zone within the numerical model breaks through

to the open pit at the same time as the aseismic zone on site that was interpreted

by Glazer (2006).





Cave Break-Through – Q1 200411.5.3

During the first quarter of 2004, the mobilised zone connects through to the pit

floor. Immediately after this first instance of mobilisation, a crater emerges.Mobilisation within the numerical model occurs initially along pre-existing fault

traces in the base of the open pit as presented in Figure 145.

Figure 145. Numerical simulation – cave breakthrough during Q1 2004.

The simulation results show that the mobilised zone intersects the pit floor during

Q1 -2004. This is consistent with the interpretations made by Glazer (2006). In

addition, immediately prior to the development of the crater within the pit, the

shape of the cave back in the numerical model (Figure 146b) is consistent with the

shape of the cave back interpreted by Glazer (2006) that is provided in Figure

146a.





Figure 146. (a) Cave profiles at the Palabora Mine; April 2002 to December 2003(after Glazer, 2006) compared to the simulated cave profile (b).





North Wall Failure – Q4 200411.5.4

During the fourth quarter of 2004, mining on the extraction level extends further

west. As material is withdrawn from these drawbells the mobilised zone intersectsa number of faults that act, along with localised jointing, as a failure surface.

During this increment, the mobilisation and fracturing of the ground surface up to

the top of the pit in the area of the north wall failure occurs in the model. The

simulated model state at the end of 2004 is provided in Figure 147.

Figure 147. Numerical simulation – north wall failure during Q4 2004.

The timing of this event in the numerical model is consistent with the observations

made on site.





11.5.4.1 Nor th Wall Failu r e Mechanism

An analysis of the location of the north wall failure within the numerical model in

relation to the observed location of the large-scale failure on site is presented in

Figure 148. A good match is observed between the numerical model and the

observed limits of the north wall failure at the ground surface.

Figure 148. North wall failure: observed versus simulated limits.

Evolution of the pit slope failure mechanism is illustrated in Figure 149. An

increase in production draw from the western portion of the undercut footprint is

observed to cause a rapid vertical advance of the yield zone which intersects the

base of the pit. Breakthrough of the cave volume is observed to mobilise the sub-

vertical joints in the pit slope immediately above the yielded zone.





Figure 149. Development of the pit slope failure mechanism at the Palabora Mine atvarious stages of production.

Based on the current model results, the north wall failure manifests as a result of

mining on the extraction level that progresses west and undermines the slope. The

presence of intersecting faults and an unfavourable joint orientation provides

release surfaces for the slope to unravel along. A view of the model results in

relation to the simulated faults is provided in Figure 150.





Figure 150. Development of the Palabora block cave between 2003 and 2004 inrelation to fault structure.

11.6 Summary

The numerical model used for the simulation of historical conditions at Palabora

are able to provide a propagation rate and cave shape that fits with the interpreted

cave behaviour during 2002-2004.

This suggests that:

(a) The geomechanical property estimates are reasonable assessments ofthe rock mass strength at Palabora. This verifies the SRM testing

behaviour, and the implementation of the calibrated continuum

responses in the model.

(b) The production schedule simulated provides an accurate assessment of

the bulking/dilation of the caved rock mass. This verifies the

implementation of the new production scheduling techniques as well as

the rock mass dilatational and softening constitutive behaviour.





(c) The effect of structure on the evolution of the cave has been accurately

accounted for within the numerical model through the implementation

of the explicit fault technique.

(d) The criteria for assessing the cave behavioural regions based on the

caving and subsidence criteria outlined in Section 1.4 are valid at the

Palabora Mine site.



12 – Henderson Mine Case Study


CASE STUDY VALIDATION : STRUCTURALLY12

CONTROLLED CAVING AT THE HENDERSON MINE

12.1 History of the Henderson Mine

A weak geological contact has been observed to effect cave propagation and cave

shape on the 7210 Level of the Henderson Mine (Carlson and Golden Jr., 2008).

Climax Molybdenum Company’s Henderson Mine is an underground panel-caving

mine located in Clear Creek County Colorado and is 14 km west of Empire,

Colorado, USA. Figure 151 provides a general cross-section of the mining

geometry.

Figure 151. Cross section of the Henderson Mine (after Rech, 2001).

During undercutting of the 7210 Level in 2005, cave initiation was observed with a

relatively small undercut hydraulic radius (22 m) compared to what has been

observed during other cave initiations at the Mine (HR 35 m). Carlson and Golden

Jr. (2008) report that the presence of intrusive contacts along the northern

boundary of the 7210 Level undercut are responsible for the premature cave





initiation (Figure 152a). Past experience at the Henderson Mine has shown that

intrusive contacts are weak zones that fail quickly.

During early August 2006, migration of the propagating cave beyond the undercutfootprint on the north and west sides was observed along the weak intrusive

contact. Figure 152b illustrates the shape of the 7210 Level yield zone during

December 2007.

Figure 152. Geological domains at the Henderson Mine a) plan view of weak contact;b) 7210 Level yield zone during December 2007.

12.2 Model Geometry and Production Schedule

A large-scale FLAC 3D model was constructed to simulate the regional extents of the

Henderson Mine, as illustrated in Figure 153a. The existing cave volumes (8100

and 7700), developed prior to the 7210 Level were initialised within the model

based upon historical mining records, as illustrated in Figure 153b.





Figure 153. Development of the numerical model of the Henderson Mine a) regionalextents of model; b) existing cave volumes.

The weak contact between the Seriate and Urad Porphyry was simulated with an

interface element as illustrated in Figure 154.

Figure 154. Interface used to simulate the weak Seriate contact at the Henderson Mine.

The evolution of production draw height simulated within the model (based upon

the actual production records) is illustrated in Figure 155. It is represented as

solid rock HOD bars.





Figure 155. Simulated production schedule (cumulative solid rock height of draw) basedon actual draw heights.

12.3 Material Properties and Pre-Mining Stresses

Multiple geotechnical domains have been mapped throughout the 7210 Level. Thegeomechanical properties used to simulate the main caving domain, the Urad

Porphyry, are presented in Table 20.

Rock mass geomechanical properties of the porphyry at the Henderson Mine.Table 20.

Seg.1 Seg.2

ci Erm Tens. Coh Coh.

(MPa) GSI mi (GPa) v (MPa) (MPa) (Deg.) (MPa)

(Deg.)

Porphyry 118 55 10 11 0.2 0.4 2.3 48 6.3 35

Table 21 presents the interface material properties used to simulate the weak

geological contact.





Conceptual fault shear strength and stiffness parameters estimated for the seriateTable 21.contact at the Henderson Mine.

Coh. Tens. Kn Ks

(kPa) (Deg.) (kPa) (GPa) (GPa)Strength 1 0 20 0 1 0.1

Due to the significant topographic relief and complex previous mining history at

Henderson, it is difficult to estimate the pre-mining stress regime. A stress

calibration exercise has previously been conducted at Henderson whereby nine

stress measurements taken from 1970 to 1989 were calibrated determining the in

situ tectonic stresses that result in a best-fit of model predicted stress to thosemeasured by over coring. The results of the stress calibration exercise, which

indicated a major principal stress oriented at 155 degrees, were directly applied to

the back-analysis model.

12.4 Simulation Results

The evolution of the model-predicted yield zone is illustrated in Figure 156. The

modelled yield zone is observed to provide a close match to the TDR breakages

(blue spheres) monitored during cave propagation. Shear failure along the weak

contact can be observed to develop along the interface - coincident with vertical

propagation of the yield zone. After initial breakthrough of the yield zone to the

overlying 7700 Level in January 2006, the yield zone is observed to follow the

weak contact outside the northern and western limits of the undercut footprint.

The modelled cave breakthrough timing and dimensions match closely the

observed 7700 level breakthroughs as shown Figure 156.





Figure 156. Simulated evolution of the cave yield zone at Henderson compared tounderground instrument observations.





Figure 157 illustrates a comparison between the shape modelled and actual yield

zones after September 2006. The model provides a close match to the actual

observed conditions.

Figure 157. Comparison of modelled verses actual cave shape at break-through to theoverlying lift at the Henderson Mine.

In order to demonstrate the effect of the weak contact on cave initiation, an

analysis was conducted without the structure. As illustrated in Figure 158, the

yield zone height is significantly impacted by the weak interface with height

reduced by approximately 30 m at the June 2005 state. Clearly, the cave shape and

growth and the ability to predict this behaviour depends on the presence of the

weak interface.

Figure 158. Comparison of cave initiation at the Henderson Mine simulated with andwithout a weak structure.





12.5 Summary

The numerical model used for the simulation of historical conditions at the

Henderson Mine are able to provide a propagation rate and cave shape that fits

with the interpreted cave behaviour for the 7210 Level.

This suggests that:

(e) The use of a bi-linear Mohr-Coulomb fit to the Hoek-Brown Curve

provides geomechanical property estimates that are reasonable

assessments of the rock mass strength and softening responses.

(f) The production schedule simulated provides an accurate assessment of



the rock mass dilational and softening constitutive behaviour.

(g) The effect of structure on the evolution of the cave has been accurately

accounted for within the numerical model through the implementation

of the explicit fault technique.

(h) The criteria for assessing the cave behavioural regions based on the

caving criteria outlined in Section 1.4 are valid at the Henderson Mine

site.



13 – Grace Mine Case Study


CASE STUDY VALLIDATION : CAVING INDUCED13

SUBSIDENCE AT THE ABANDONED GRACE MINE

PANEL CAVE

13.1 Background

Iron ore mining began in south-eastern Pennsylvania before the American

Revolutionary War (1775–1783) and reached the peak of activity during the

1880s. In 1948, airborne magnetometer surveying conducted by the Bethlehem

Steel Corporation led to the discovery of a large, deep magnetite deposit located

approximately 3.2 km north of Morgantown, in Berks County, south-eastern

Pennsylvania. Diamond drilling from 1949 to 1951 delineated the orebody, which

was named the Grace Mine.

Development of the Grace Mine commenced in 1951 with construction of two

vertical shafts to gain access to the orebody. Shaft A was developed to a depth of

784 m, and shaft B was developed to a depth of 938 m with a diameter of 5.3 m.

The two shafts and all surface infrastructures were constructed outside an area

formed by a conservative 45o subsidence angle (measured from the base of the

underground workings). None of the existing Grace Mine buildings have shown

signs of subsidence induced damage to date. The Grace Mine orebody contained an

estimated 107 million tonnes of magnetite averaging 40% iron ore. During the

active mining period 1958–1977, approximately 33 million tonnes of ore were

mined primarily with the inclined panel caving method.

Figure 159a illustrates the extent of the underground development at Grace Mine

together with the approximate undercut outline. Figure 159b illustrates a

schematic of the inclined panel caving method employed at the Grace Mine. Mining

operations ceased in 1977 due to an influx in foreign steel imports, increased costs

of environmental regulation and increased costs of underground mining.





Figure 159. Geometry of the Grace Mine a) extent of underground production drives(plan view) b) two-dimensional schematic of panel caving at Grace Mine(after Stafford, 2002).

At the completion of mining, mining induced subsidence had significantly altered

the topography above the mine workings. Mine dewatering continued until 1981-

2. Upon recovery of the water table, a lake formed over the subsided area, as


Figure 160. Photo showing present day subsidence lake at the Grace Mine.





13.2 Geomechanical Properties

Currently, the only core information available from the Grace Mine site is drilling

logs from a diamond drilling programme conducted in 1998 to investigate the near

surface conditions for construction of a large scale industrial facility near the

western edge of the subsidence lake. Owing to the location of the drill holes above

the mining horizon, the intersected rock mass has been disturbed by the caving

process and does not represent the in situ (pre-mining) rock mass condition.

The following descriptions of the rock units at the Grace Mine have been compiled

from the aforementioned drilling logs, mapping of surface outcrops and other

available literature.

13.3 Local Geology

Three rock types are associated with the Grace Mine: diabase footwall, replaced

limestone and Triassic sediments. Sims (1968) suggested that the magnetite

deposit occurs in a lens of Cambrian limestone that is overlain unconformably by

Triassic sedimentary rocks. The magnetite deposit was formed by replacement ofcontact metamorphic minerals in the limestone lens, caused by the intrusion of an

underlying diabase sheet. The orebody is roughly tabular in shape, strikes

approximately 60o and dips 20–30o to the northeast. It is approximately 1067 m

long and 213–457 m wide, and ranges from less than 15 m to more than 121 m in

thickness. Figure 161a illustrates an isometric view of the original ground surface

and orebody shape. The surfaces were reconstructed from the original mine

geological cross-sections.





Figure 161. Isometric view of orebody and surface topography at the Grace Mine.

Of interest to the investigation of mining induced subsidence is the nature of the

sedimentary rocks that overlie the orebody. Sims (1968) and Basu (1974) identified

the Triassic sedimentary rocks that formed the hangingwall of the ore deposit as

the Stockton Formation. The formation consists of inter-bedded sandstone, shale

and conglomerate. The Stockton Formation is overlain by the Brunswick

Formation, which also consists of poorly sorted inter-fingered sandstone, shale

and conglomerate layers. The top of the Brunswick Formation has been eroded to

form the ground surface directly above the orebody. Surface outcrops of the

Stockton Formation near the Grace Mine are thinly bedded and highly fractured,

with very closely spaced (<100 mm) vertical and open joints. The conglomerate

layers of the Stockton Formation are thickly bedded (0.5–1.5 m) and moderately

fractured (0.5–2 m), with vertical and open joints.





Rock Mass Parameters used in the simulation of domains at the Grace Mine.Table 22.

UCS

Material (MPa) GSI mi

Sediments 60 45 12

Limestone 90 55 12Magnetite 40 45 9

Diabase 200 60 25

13.4 Pre-Mining Stress State

The pre-mining stress was measured directly at Grace Mine using the United States

Bureau of Mines (USBM) Deformation Gage Technique. Agarwal et al. (1973)

detailed the measurement procedure for 36 deformation measurements from

three separate boreholes. The boreholes were located to ensure that the measured

stress regime was representative of the pre-mining stress regime (unaffected by

nearby excavations). The stress regime presented in Table 23 is an average of

measurements made at a depth of 731m below the ground surface.

Pre-mining stress regime at 731m below surface at the Grace Mine.Table 23.

Stress Magnitude (MPa) Dip (Deg.) Azimuth (Deg.)

1 51.5 16 027

2 29.0 22 103

3 26.2 85 181

13.5 Caving Induced Subsidence

Evolution of Subsidence Crater and Trough13.5.1

From 1959 to 1969, engineers from the USBM monitored the evolution of surface

subsidence at the Grace Mine. No USBM report of investigation was published on

the extensive subsidence monitoring programme. However, during the course of

this investigation, several hand written memorandums from USBM Engineers to

management of the Grace Mine were recovered from former Grace Mine

superintendent, Mr Charles Taylor’s private collection. Goodman (1970) reported

the evolution of the subsidence trough as follows:

10 December 1962: first indication that subsidence was beginning





18 February 1963: cracks on the surface were noted, and a slumped zone

widened and steadily descended

16 December 1963: the underground caved to the surface

17 April 1964: cracks extended to circle the crater and extended in a

concentric pattern

8 June 1965: the subsidence trough was observed to progress to the

northeast

3 June 1969: the subsidence trough moves to the northeast following the

development and extraction pattern.

Figure 162 illustrates different aerial views of the subsidence trough. The initial

cave breakthrough appears to have been facilitated by the presence of a steeply

dipping joint/fault structure oriented at approximately 60o. As the subsidence

trough progressed to the northeast, the actual cave did not break through to the

surface. In the south-western section of the subsidence trough, large concentric

surface cracks can be observed, while two sets of cracks oriented at approximately60o and 110o are observed in the north-eastern section. The ground within the

approximate extent of surface cracking can be clearly observed to be highly

fractured and disturbed.

Approximately 30 monuments were installed on the surface above the mining

horizon and monitored by the USBM between 1962 and 1969. Surveying

techniques used over the monitoring period included chaining, levelling and

triangulation. The maximum elevation change as of 1969 was reported to be 35 m.

Goodman (1970) noted that uplift generally occurred in pins around the periphery

of the orebody outline, while acceleration of subsidence was greatest directly over

recently developed panels. Surface uplift outside the undercut footprint was also

monitored at the Lakeshore Mine, in Arizona (Panek, 1984).





Figure 162. Photos showing the evolution of subsidence from 1963 to 1978 at theGrace Mine.

Visual Observation of the Limit of Large-Scale Surface Cracking13.5.2

Figure 163 illustrates the results of a field survey conducted during June 2004 to

identify the extent of large-scale surface cracking surrounding the subsidence

trough. The furthest observable surface cracks from the orebody outline have been

mapped and used to generate a contour line that represents the limit of the large-

scale surface-cracking zone (fractured zone).

In the southwest section of the subsidence trough, a shear-failure mechanism

appears to be predominant. Large scarps with offsets of approximately 3 m can be

observed. In the northeast section of the subsidence trough, both large tension

cracks and shear failure scarps can be observed. In the western section of the

subsidence trough, a continuous trough-like basin has formed over the shallower,

thinner section of the orebody. A sinkhole that developed after reclamation of the

waste dumps can be observed within the limits of the mine workings.





Figure 163. Limit of large-scale surface cracking observed at the Grace Mine during2005 (after Sainsbury and Lorig, 2005).

Conceptual Model of Subsidence Formation at the Grace Mine13.5.3

Figure 164 illustrates a conceptual model of the caving and subsidence formation

at the Grace Mine. In the years after initial breakthrough, the size of the actual

crater did not increase significantly, indicating that bulking-controlled caving had

prevented the progression of the caved zone to the ground surface. The

subsequent subsidence was observed to manifest as a subsidence trough following

the direction of mining.





Figure 164. Conceptual model of subsidence formation at the abandoned Grace Mine(after Sainsbury and Lorig, 2005).

Modelling Methodology13.5.4

In order to simulate the mass based production schedule at the Grace Mine,

recovered from actual hoist records (Table 24), production simulation within the

numerical caving model has completed based on the methods described in Section

8.

Bi-linear Mohr-Coulomb material properties were derived from a least-squares fit

to the Hoek-Brown failure envelope for each rock type using the GSI, UCS and mi

values presented in Table 22.

Grace Mine production (after Eben, 2004 ).Table 24.

1958 1961 1962 1965 1967 1969 1972 1975- - - - - - - -

1960 1962 1963 1964 1966 1968 1971 1974 1977

MTonnes 1.18 2.89 2.35 2.23 4.04 3.65 5.74 5.74 4.82

Figure 165(a) illustrates the regional model geometry, while Figure 165(b)

illustrates the reconstructed undercut geometry used to represent the historical

production schedule.





Figure 165. Development of a numerical model of the Grace Mine a) regional extents ofmodel b) simulated undercut footprint.

Predicted Evolution of Cave Mobilised and Yield Zones13.5.5

The evolution of the cave mobilised and yield zones above the undercut footprint

is illustrated in Figure 166. The predicted cave behaviour provides a close match

with the reported evolution of cave breakthrough and subsidence trough

formation. The yield zone is predicted to intersect the ground surface during 1962

(Figure 166b); while the mobilised zone is predicted to intersect the ground

surface towards the end of 1963 (Figure 166c). This coincides with the first

indication of subsidence reported on Dec. 10, 1962 and the breakthrough of the

caved (mobilised zone) on Dec. 16, 1963.

As production progresses to the thinner and deeper extents of the orebody (to the

east), the predicted mobilised zone does not reach the ground surface (Figure

166f). This coincides with the formation of a subsidence trough, rather than an

extension of the subsidence crater over the northeast region of the orebody.





Figure 166. Predicted evolution of cave mobilised and yield zones (looking south) duringsimulation of production from the Grace Mine.





Model Validation13.5.6

The predicted vertical displacement was monitored within the model at the same

locations as the USBM subsidence monitoring monuments that were documentedby Goodman (1970). The measured versus predicted vertical displacement at three

survey monuments surrounding the subsidence trough are illustrated in Figure

167. The predicted surface displacements provide a close match to the monitoring

results and provide good confidence in the predicted surface displacements

beyond 1969.

Figure 167. Measured verses predicted vertical displacements from numerical model ofGrace Mine.

The introduction of the tonnes-based production schedule (rather than traditional

height of draw) has highlighted the mechanism for the glory hole at the surface

that was created during 1963. A typical PCBC HOD schedule usually under-

estimates the tonnes withdrawn as a result of the uniform bulking factor applied.

The result of assuming a HOD production schedule with a typical Bulking Factor of

0.2 is provided in Figure 168.





Figure 168. Comparison of cave propagation results (a) HOD schedule - uniformbulking factor of 0.2 (b) mass balance (tonnes-based) schedule.

13.6 Summary

The numerical model used for the simulation of historical conditions at the

abandoned Grace Mine are able to provide a propagation rate and cave shape that

fits with the interpreted cave behaviour.

This suggests that:

(a) The use of a bi-linear Mohr-Coulomb fit to the Hoek-Brown Curve


assessments of the rock mass strength and softening behaviour at the

abandoned Grace Mine.




the rock mass dilational and softening constitutive behaviour.





(c) The criteria for assessing the cave behavioural regions based on the

caving criteria outlined in Section 1.4 are valid at the abandoned Grace

Mine site.



14 – Kiirunavaara Lake Orebody Case Study


CASE STUDY VALIDATION : CAVING INDUCED14

SUBSIDENCE AT THE KIIRUNAVAARA LAKE

OREBODY SLC

14.1 Introduction

The Kiirunavaara mine, owned and operated by LKAB, is located in northern

Sweden near the township of Kiruna, approximately 180 km north of the Arctic

Circle. The orebody is 4 km long, 80-160 m thick and the mineralisation reaches a

depth of at least 2 km. It dips 50° to 60° to the east and plunges to the north-

northeast as the orebody lens tapers out. The orebody has been divided into two

main regions of mining; the Main Orebody and the Lake Orebody. The Lake

Orebody defines the northern extent of the mine and is located immediately west

of the township of Kiirunavaara (Figure 169).

Figure 169. Location and extent of the Lake and Main Orebody at the Kiirunavaara

Mine.

14.2 Historical Mining Record

Kiirunavaara is a transverse, sub-level caving mine that commenced underground

operation during the early 1960s after initially being mined as an open pit since

the start of the 20th century. Production from the non-daylighting Lake Orebody

commenced in 2003 when workings in the Main Orebody were on the 792 Level

(550 m below ground surface). During the years 2003-2010, the lowest level of





production from the Lake Orebody was the 792 Level, and the 935 m Level (693 m

below ground surface) in the Main Orebody (Figure 169).

14.3 Evolution of Surface Subsidence

Since sub-level caving commenced at the Kiirunavaara Mine, the hangingwall has

experienced surface displacements ranging from millimetres up to several metres

in magnitude. The development of caving induced subsidence around the Lake

Orebody has been monitored through routine ground surveys since production

commenced in 2003. The following section provides a summary of the

observations and measurements. The observations are made in reference to cave

subsidence zones that are described in Section 1.4. A view of the existing surface

conditions are presented in Figure 170.

Figure 170. Subsidence regions at Kiirunavaara.

Approximately three years after mining commenced in the Lake Orebody, a crater

developed on the northern extents of the existing open pit - as illustrated in Figure

171. Initially developed as an isolated subsidence feature during 2006, additionalproduction during 2007 and 2008 caused the enlargement of the crater towards





the south. The development of this isolated crater can best be described as a

chimney or plug cave. Lupo (1997) completed a detailed review of the chimney

subsidence features that occur east of the Main Orebody, and suggested that they

are formed when the flow channel of a sub-level ring reaches the ground surface.

Figure 171. Photos showing the development of a crater at northern extent of LakeOrebody during 2006 and its subsequent enlargement.

Limits of Large-Scale Fracturing / Yield Zone14.3.1

The progression of the large-scale fracture limits at the ground surface between1997 and 2006 is presented in Figure 172. An angle of break for the fractured

zone of approximately 60o has been reported by Villegas et al. (2011), Lupo (1996)

and Stephansson et al. (1978). Surface disturbances in this zone have previously

been documented by Lupo (1997) and consist largely of surface cracks, and shear

displacements.

Figure 172. Fracture mapping at Kiirunavaara (a) plan above Lake Orebody (b)section through Main Orebody (modified after Villegas et al., 2011).





Limits of Continuous Deformation14.3.2

GPS data shows that an area of continuous deformation extends approximately

150-200 m beyond the limits of large-scale fracturing (Villegas et al., 2011). Themeasured surface displacements from 2002 – 2010 above the Lake Orebody are

provided in Figure 173. Surface displacements in the order of 0-250 mm were

measured prior to the commencement of mining of the Lake Orebody in 2003.

Figure 173. Evolution of measured surface total displacement profile around the LakeOrebody.

14.4 Numerical Simulation of Caving Induced Subsidence

A three-dimensional model of the Kiirunavaara Mine and its surroundings has

been developed to assess the impact of the production schedule on the

development of the surface displacement profile that is evident today. The model

extents are provided in Figure 174.

Figure 174. Regional extents of Kiirunavaara numerical mesh.





In situ Stress14.4.1

The pre-mining in situ stresses at the Kiirunavaara Mine have previously

documented by Sandström (2003). The major principal stress is estimated to bealigned perpendicular to the orebody and is approximately 1.28 times the vertical

stress. Equations for deriving the principal stress components in MPa are

provided below.

0.37 3.7 ymW

0.28 2.8 ym NS h 0.029 2.9v ym Where y m represents the depth below -100m RL and the stresses are expressed in

terms of MPa.

Rock Mass Properties14.4.2

Historically, material properties for the Lake Orebody have been developed based

on a calibrated response of drive scale displacements and failure mechanisms in

the Main Orebody. Previous analyses conducted by Perman et al., (2011) have

derived a lower bound property set for the hangingwall domain in the Main

Orebody that is defined by a UCS 130 MPa, GSI 58, mi 16 and Erm 15.8 GPa. This

GSI value has been confirmed for the Lake Orebody by scanline mapping

conducted during 2010.

A bi-linear, Mohr-Coulomb, strain-softening constitutive model has been used to

simulate the complex process of the progressive failure and disintegration of the

rock mass from an intact, jointed material to a bulked state during the caving

process in the numerical model. The low magnitude in situ stresses in relation to

the strength estimates suggest a gravity driven caving mechanism is dominant at

Kiirunavaara.

Production Schedule14.4.3

In order to ensure an accurate induced stress state in the model prior to the

simulation of mining from the Lake Orebody, simulation of the extents of open-cut

mining was conducted during the development of the initial model state.

Production from the Main Orebody has been simulated based on an elevation and





tonnes basis. Production from the Lake Orebody has been scheduled on a

drawpoint and tonnes basis consistent with the technique described in Section 8.

Simulation Results14.4.4

Based on the displacement and strain criteria outlined in Section 3, the

development of historical caving induced subsidence from the Lake Orebody has

been assessed. The simulated crater and limit of large-scale fracturing is


Figure 175. Simulated evolution of crater and limits of large-scale fracturing within thenumerical model of Kiirunavaara.

Mobilisation of the ground surface above the Lake Orebody during 2006 is

observed in the numerical model. The location of this initial break-through is on

the northern extents of the existing open pit and is consistent with the in situ

observations. As the mining simulation continues beyond 2006, the crater is

observed to advance towards the south and joins with the main orebody crater

during the production years 2007 – 2008.

The development and enlargement of this crater can be attributed to the draw

schedule at the mine, since it occurred immediately above an area where draw was

occurring on multiple sub-levels that overlapped each other (vertically) at the

same time (Figure 176). The crater has formed when the flow channels of the sub-





level rings have combined. The rapid propagation to the surface suggests that the

secondary and tertiary flow channels have also contributed to the formation of the

isolated crater.

Figure 176. Production rate versus simulated mobilised zone within the numerical modelof Kiirunavaara.

Simulated displacements on the ground surface immediately above the Lake

Orebody from 2002 – 2010 are presented in Figure 177. The initial pre-mining

displacements along with the development of the crater location and shape are

consistent with the measured displacements. Since the monitoring points used in

each of the contour plots (as shown in Figure 177) are not consistent between the

observation years, significant interpretation between them has been completed. In

addition, the methodology used to complete the observation measurements does

not provide a great level of accuracy (+/- 0.3 m) and only general trends can be

interpreted.





Figure 177. Simulated evolution of total surface displacements within the numericalmodel of Kiirunavaara compared to observations onsite.

The 1 m displacement contour has been used to define the crater limits within the

numerical model at the end of 2010 (Figure 178). The simulated limits compare

well with the in situ observations based on their comparison to the visual

observations presented in Figure 171.

Figure 178. Plan view of simulated displacement and strain-based subsidence criteriaand subsidence zone of influence at the end of 2010 as simulated in thenumerical model of Kiirunavaara.





A total strain criterion of 0.5% was used to confirm the limits of large-scale

fracturing that have an angle of draw consistent with approximately 60o. The

simulated extent and shape also compares well to the fracture limits defined by

Stöckel et al. (2012) presented in Figure 179.

The limits of continuous subsidence at the end of 2010 have been derived by

generating a contour line that encompasses all the areas of horizontal strain >0.2%

and angular distortion >0.3%. It extends approximately 200 m beyond the limits

of large-scale fracturing which is consistent with previous observations

documented by Villegas et al. (2011).

Figure 179. Plan view of simulated subsidence limits at the end of 2010 compared toobservations at Kiirunavaara.





14.5 Summary

The observed limits of caving induced subsidence at the Kiirunavaara Lake

Orebody have been accurately assessed by a numerical simulation of sub-level

caving from 2003-2010. Established displacement and strain-based criteria have

been used to successfully back-analyse the evolution of caving induced subsidence.

This suggests that:

(a) The use of a bi-linear Mohr-Coulomb fit to the Hoek-Brown Curve


assessments of the hangingwall rock mass response at the Lake

Orebody.



implementation of the new SLC production scheduling techniques as

well as the rock mass dilational and softening constitutive behaviour.

(c) The criteria for assessing the cave behavioural regions based on the

caving and subsidence criteria outlined in Section 1.4 are valid at the

Kiirunavaara Mine site.



15 - Recommendations


CONCLUSIONS AND RECOMENDATIONS15

Since the development of numerical methods in the 1970’s, the numerical

assessment of cave propagation has been continuously researched and improved

to help minimise the geotechnical risks associated with cave mining methods.

Since this time, numerical methodologies have evolved from being able to

accurately assess the primary risk of whether a cave will stall and develop an air-

gap, to now being able to assess detailed cave behaviour. Contrary to the opinion

of Laubscher (2000) who believes that “…modelling is not capable of coping with …

four dimensions”. Today, cave modelling methodologies are limited only by the

quality of data that can be collected in situ.

The numerical model of cave propagation and subsidence assessment that has

been developed provides an assessment of the evolving cave propagation

behaviour and subsidence zones of influence in response to the actual production

draw at the undercut/extraction level. The evolving cave shapes, propagation

rates, abutment stresses and subsidence limits can be readily assessed within the

one numerical model.

Comparison of the model predictions with the results of the four large-scale back-

analyses demonstrates that the model and cave and subsidence assessment

criteria are robust.





15.1 Summary of Original Contributions

A model for cave propagation and subsidence assessment in jointed rock masses

has been developed that relies on the fundamental behaviour of rock masses for

caving analyses. In the process, original contributions were made to the numerical

simulation of rock mass behaviour and numerical methods for cave propagation

and subsidence assessment. A summary of the contributions are provided below.

Rock Mass Behaviour15.1.1

15.1.1.1 Development of t he Ubiqu it ous Join t Rock Mass (UJRM) Model

Synthetic Rock Mass Modelling (SRM) is generally accepted as the existing state-of-

the-art in anisotropic rock mass behaviour analysis. A methodology has been

developed that can be used to derive material input properties for the FLAC 3D

Subiquitous (Strain-Softening Ubiquitous Joint) constitutive model so that it

exhibits strength and deformation behaviours similar to what may be derived from

SRM testing. The successful implementation of these strengths in a large-scale

caving back-analysis at the Palabora Mine provides validation for the technique.

15.1.1.2 Considerat ion of the Volumetr ic Changes th at Accompany Cave

Propagation

Due to computational constraints at the present time, the numerical model of cave

propagation must be implemented using a small-strain calculation mode. As a

result of this, the manual modification of the density and bulking/dilational

behaviour of the rock mass during volumetric expansion is required. A non-linear

deformation modulus softening and dilation relation has been implemented withinthe numerical model of cave propagation to provide a more rigorous assessment of

rock mass bulking. The methodology has been validated based on four large-scale

back-analyses of cave propagation behaviour detailed herein.





15.1.1.3 Impact of Lar ge-Scale Discont in ui ti es on Cave Pr opaga ti on and

Subsidence Behavi our

The impact of large-scale structures on cave propagation and subsidence

behaviour is well known. Two methodologies used to simulate large-scale fault

structures in numerical meshes have been investigated. Based on the numerical

results and their comparison to case study observations, an explicit approach to

fault simulation has been validated and is recommended for the simulation of

large-scale discontinuities in caving analyses. The approach has been validated

through a large-scale back-analysis of caving behaviour at the Henderson Mine.

Production Simulation15.1.2

15.1.2.1 Development of a Mass-Based Pr oducti on Schedul e

The existing methods for the simulation of production draw in a numerical model

have been expanded to include the simulation of production draw through mass-

balance calculations - rather than HOD estimates. In addition, a methodology has

been outlined that provides a production scheduling technique based on

drawpoint tonnes to allow for the accurate consideration of the bulking/dilational

behaviour evolving within the cave. The methodology has been validated based on

four large-scale back-analysis of cave propagation behaviour detailed herein.

15.1.2.2 Development of a Sub-Level Caving Algor it hm


blasting. The disintegration is brought about by natural processes that include the

in situ fracturing of the rock mass, stress redistribution, the limited strength of the

rock mass and gravitational forces. Sub-level caving requires the transformation of

in situ ore into a mobile state by conventional drilling and blasting. The existing

numerical techniques for cave behaviour analysis were unable to represent a SLC

mining method. A technique has been developed that allows a sub-level caving

scheduled to be accurately reflected in the numerical model of cave propagation. It

has been validated through a large-scale back-analysis of caving behaviour at the

Kiirunavaara Lake Orebody.





15.1.2.3 Development of an Algori thm to Consider Evolving Sur face Pr ofile

Since the numerical simulations are conducted in small-strain (i.e., the mesh

gridpoint locations are not updated as a result of displacement) toppling failure

cannot be simulated around the evolving crater trough. An algorithm has been

developed that updates the ground surface profile as ore is withdrawn. This

allows additional instability around the crater trough to be predicted and a better

assessment of large-scale fracturing to be predicted for infrastructure stability

assessment.

15.2 Validation

Validation of the numerical model for cave propagation and subsidence

assessment has been completed at four large-scale case study applications that

include the Palabora Mine, the Abandoned Grace Mine, Henderson Mine and

Kiirunavaara Mine.

15.3 Recommendations for Further Work

The following research is recommended to assist in the further development of the

model presented in this thesis.

Rock Mass Behaviour15.3.1

15.3.1.1 Ubiqu it ous Join t Rock Mass

Calibration of the UJRM assumes that the SRM testing is an accurate representation

of the rock mass strength and deformation behaviour in the tested loading

directions and sample scales. As changes are made to the SRM technique, a review

of the UJRM methodology is required to ensure that it still provides calibrated

results.

Although the existing UJRM technique has provided good calibrated results for the

case studies undertaken the methodology could be further validated through

additional application.

The tensile strength of the rock mass may currently being over predicted since

only one ubiquitous joint orientation can be specified for each zone. The ability to





define up to three joint orientations for each zone would reduce this mesh

dependency on the tensile strength results.

15.3.1.2

Time-Dependent Processes

Successful cave mining greatly depends on knowledge and understanding of rock

mass behaviour in different stress environments. Time-dependence is one of the

aspects of rock mass behaviour which is not understood completely, but plays an

important role in rock performance. The most important time-dependent

processes that may impact caving behaviour include; ground water and stress-

corrosion. At the present time, these time-dependent processes are not included in

the numerical model of cave propagation and subsidence.

Numerical Techniques15.3.2

15.3.2.1 Smal l-Str ain Calculat ion Model

The small-strain calculation mode does not allow the simulation of movement of

material through the cave or along slopes in a state of collapse. The

implementation of some large-strain marker logic would assist in interpreting

these conditions within the model.

15.3.2.2 Int er active Draw

The current algorithm assumes overlapping interactive draw at a minimal height

above the drawpoint. As a result of this, the impacts of isolated draw are not well-

handled. Coupling the large-scale modelling result with a flow program such as

REBOP is recommended to be able to simulate the response of isolated draw.

15.3.2.3

Hardware

Simulation run times are still prohibitive. The development of technology to enable

the model to run on high performance clusters or supercomputers would be

beneficial.

Validation15.3.3

The application of this numerical technique to additional back-analyses is critical

in establishing confidence in the model predictions and further limitations that

need to be addressed.



References


REFERENCES16

Abel, J.F. and Lee, F.T. (1980) Subsidence Potential in Shale and Crystalline Rocks, USGS,

OFR 80-1072.

Adler, L. (1970) Double elasticity in drill cores under flexure. Int. J. Rock Mech. Min. Sci.Geomech. Abstr. 7, 357-370.

Agarwal, R., Eben, C. and Taylor, C. (1973) Rock mechanics program at Grace Mine,Technical report No. 3, Henry Krumb School of Mines, Columbia University, NewYork, USA, 1973.

Alejano, L. and Alonso, E. (2005) Considerations of the dilatancy angle in rocks and rock

masses. International Journal of Rock Mechanics and Mining Sciences, Vol. 42, pp.481-507.

Andrieux P. & Hadjigeorgiou, J. (2008). The Destressability Index Methodology for theAssessment of the Probability of Success of a Large-Scale Confined Destress Blast inan underground Mine Pillar. International Journal of Rock Mechanics & MiningSciences 45 (2008) 407–421.

Anon (1947) Report of the Special Committee on Mining Subsidence, Institution ofMunicipal Engineers, London.

Atlas Copco (2011). www.atlascopco.com.au. Accessed 22 November 2011.

Balia, R., Manca P.P. and Massacci G., (1990) Progressive Hangingwall Caving andSubsidence Prediction at the San Giovanni Mine, Italy, Proc. 9th Int. Conf. On Ground

Control in Mining, ed. S. Peng., pp 303-311.

Bandis, S., Lumsden, A. and Barton, N. (1983) Fundamentals of rock joint deformation.International Journal of Rock Mechanics and Mining Sciences . 1983, Vol. 20, 6.

Barla, G., Boshkov, S. and Pariseau, W. (1980) Numerical modeling of block caving at theGrace Mine. Geomechanics applications in underground hardrock mining, Turin,Italy. pp. 241-256.

Barton, N. and Bandis, S. (1982) Effects of block size on the shear behaviour of jointedrocks. 23rd US Symposium on Rock Mechanics, Vol. 10, Rotterdam: Balkema,pp.739-760.

Barton, N. and Pandey, S.K. (2011). Numerical modelling of two stoping methods in twoIndian mines using degradation of c and mobilisation of friction based on Q-parameters. International Journal of Rock Mechanics and Mining Sciences, 48, pp.1095-1112.

Basu, D. (1974) Genesis of the Grace Mine magnetite deposit, Morgantown, Berks County,Southeastern Pennsylvania, PhD thesis, Lehigh University, Bethlehem, PA, USA,1974.

Beck, D. and Pfitzner, M. (2012) Interaction between deep block caves and existing,overlying caves or large open pits. Beck Engineering Pty Ltd, accessed 19th March,

212, < http://www.beckengineering.com.au/web/be_downloads.html>.

http://www.atlascopco.com.au/

http://www.beckengineering.com.au/web/be_downloads.html

http://www.beckengineering.com.au/web/be_downloads.html

http://www.atlascopco.com.au/



References


Beck, D., Reusch, F. and Arndt, S. (2007) Estimating the probability of mining-inducedseismic events using mine-scale, inelastic numerical models. Int. Symposium Deepand High Stress Mining, 2007. The Australian Centre for Geomechanics, Perth,Australia.

Beck, D., Reusch, F., Arndt, S., Thin, I., Stone, C., Heap, M. and Tyler, D. (2006) NumericalModelling of Seismogenic Development during Cave Initiation, Propagation andBreakthrough. Deep and High Stress Mining 2006.

Beck, D., Sharrock, G. and Capes, G. (2011) A coupled DFE-Newtonian Cellular Automata

scheme for simulation of cave initiation, propagation and induced seismicity. 45thUS Rock Mechanics/Geomechanics Symposium held in San Francisco, CA, June 26-29.

Besuelle, P. (2001) Evolution of strain localisation with stress in a sandstone : brittle andsemi-brittle regimes. Phys. Chem. Earth (A) Vol 26, No 1-2, pp. 101-106.

Bétournay, M. C., Mitri, H. S. and Hassani, F., (1994) Chimneying disintegration failure

mechanisms of hard rock mines. Rock Mechanics Models and Measurements -Challenges from Industry, Proceedings 1st North American Rock MechanicsSymposium, Austin, (Eds: P Nelson and S Laubach), 987-996. Balkema: Rotterdam.

Blodgett, S. (2002) Subsidence Impacts at the Molycorp Molybdenum Mine Questa, NewMexico, Centre for Science in Public Participation.

Blodgett, S. and Kuipers, J. (2002) Underground Hard-Rock Mining: Subsidence andHydrologic Environmental Impacts, Centre for Science in Public Participation.

Board, M. and Pierce, M. (2009). A review of recent experience in modelling of caving.International Workshop on Numerical Modelling for Underground Mine Excavation

Design, June 28, 2009. Asheville, North Carolina in conjunction with the 43rd USRock Mechanics Symposium.

Boyum, B. H. (1961) Subsidence case histories in Michigan mines. Proceedings 4thSymposium on Rock Mechanics, Bulletin, Mineral Industries Experiment Station,Pennsylvania State University, No 76: 19-57.

Brady, B. H. G. and Brown, E. T., (1993) Rock Mechanics for Underground Mining, 2ndedition, 571 p. Chapman and Hall: London.

Brady, B.H.G. and Brown, E.T. (2006) Rock Mechanics For underground mining. Springer;4th edition. Dordrecht; London: Kluwer Academic Publishers 2004, xviii, 626 p.

Brauner, G. (1973) Subsidence Due to Underground Mining, U.S. Bureau of Mines, IC 8571.

Bray, J. W. (1983) Rankine Lecture.

Brown, E. T. and Ferguson, G. A., (1979) Progressive hangingwall caving at Gath’s mine,

Rhodesia. Trans Instn Min Metall, Sect A: Min Industry, 88: A92-105.

Brown, E.T. (2003) Block Caving Geomechanics, JKMRC Monograph Series in Mining andMineral Processing 3. Julius Kruttschnitt Mineral Research Centre, the University ofQueensland: Brisbane. ISBN 1-74112-000-4.

Brown, E.T. and Trollope, D.H. (1970) Strength of a model of jointed rock. Journal of SoilMechanics; Foundations Division ASCE. 1970, 96.



References


Brumleve C.B. (1987) Rock Reinforcement of a Caving Block in Variable GroundConditions, King Mine, Zimbabwe, Trans. Instn Min. Metall., sect A, April.

Brumleve C.B. and Maier M.M., (1981) Applied Investigations of Rock Mass Response toPanel Caving, Henderson Mine, Colorado, in Design and Operation of Caving andSub-level Stoping Mines, ed R.D. Stewart, AIME, New York, 843 p.

Brummer, R., Li, H. and Moss, A. (2006) The transition from open pit to undergroundmining : an unusual slope failure mechanism at Palabora. Proceedings InternationalSympoisum on Stability of Rock Slope in Open Pit Mining and Civil Engieering. TheSouth African Institute of Mining and Metallurgy. pp. 411-420.

Brunton, I. (2009). Personal Communication.

Butcher, R. (2005) Subsidence effects associated with block and sub-level caving ofmassive orebodies, Australian Centre for Geomechanics Newsletter, Volume No. 25

Butcher, R.J. (2005) Subsidence effects associated with block and sub-level caving ofmassive orebodies, Australian Centre for Geomechanics Newsletter, Volume No. 25.

Cai, M. and Horii, H. (1993) A constitutive model and FEM analysis of jointed rock masses.International Journal of Rock Mechanics and Mining Sciences. 1993, Vol. 30.

Cai, M. Kaiser, P.K., Tasaka, Y. and Minami, M. (2007) Determination of residual strengthparameters of jointed rock masses using the GSI system. International Journal ofRock Mechanics and Mining Sciences 44 (2007) 247–265.

Cai. M. (2010) Practical estimates of tensile strength and Hoek-Brown strength parametermi of brittle rocks. Rock Mechanics and Rock Engineering, 2010, Vol. 43 pp.167-184.

Carlson, G. and Golden Jr. R. (2008). Initiation, growth, monitoring and management of the7210 cave at Henderson Mine – A Case Study in Proceedings of the 5th InternationalConference and Exhibition on Mass Mining, Lulea Sweden 9-11 June, 2008. LuleaUniversity of Technology Press, Lulea, Sweden.

Cavieres, P., S. Gaete, L. Lorig and P. Gómez. (2003) Three-Dimensional Analysis ofFracturing Limits Induced by Large Scale Underground Mining at El Teniente Mine,in Soil and Rock America 2003 (Proceedings of the 39th U.S. Rock Mechanics

Symposium, Cambridge, Massachusetts, June 2003), pp. 893-900. P. J. Culligan, H. H.Einstein and A. J. Whittle, Eds. Essen: Verlag Glückauf.

Chappell, B. (1975) Component characteristics of jointed rock masses. International

Journal of Rock Mechanics, Mining Sciences and Geomechanics. 1975, Vol. 12.

Chen, R. and Stimpson, B. (1993) Interpretation of indirect tensile strength tests whenmoduli of deformation in compression and in tension are different. Rock Mechanicsand Rock Engineering. Volume 26, Number 2, 183-189, DOI: 10.1007/BF01023622.

Clark, I.H. (2006) Simulation of Rock mass Strength Using Ubiquitous Joints. In: R. Hart andP. Varona (eds), Numerical Modeling in Geomechanics — 2006; Proc. 4thInternational FLAC Symposium, Madrid, May 2006. Paper No. 08-07, Minneapolis:Itasca.

Clough, R.W. (1960) The finite element method in plane stress analysis. Proceedings of the

Second ASCE Conference on Electronic Computation, Pittsburgh, PA.

Collins, P.J. (1977) Measurement and Analysis of Residual Mining Subsidence Movements,Large Ground Movements and Structures, in Proceedings of the Conference at



References


Diering, J.A.C. and Laubscher, D.H. (1987) Practical approach to the numerical stressanalysis of mass mining. Transactions of the Institution of Mining and Metallurgy,Section A: Minerals Industry, 96: A179-A188.

Duncan-Fama M.E. (2003) Numerical modelling of yield zones in weak rock. In: Hudson J,editor. Comprehensive rock engineering, vol. 2. Oxford: Pergamon Press; 1993. p.49–75.

Duplancic, P. and Brady, B.H. (1999) Characterization of caving mechanisms by analysis ofseismicity and rock stress, Proceedings 9th International Congress on RockMechanics (Paris) Vol. 2, pp. 1049–1053. Balkema, Rotterdam.

Eberhardt, E., Kaiser, P.K., Stead, D, (2002) Numerical analysis of progressive failure innatural rock slopes. In: da Gama, Dinis, eSousa, Ribeiro (Eds.), EUROCK 2002 —Proc. ISRM Int. Symp.on Rock Eng. for Mountainous Regions, Funchal, Madeira.Sociedade Portuguesa de Geotecnia, Lisboa, pp. 145–153.

Eberthard, E. (2011) Impacts of Underground Mass Mining on Surface: Lessons Learnedfrom the Palabora Cave-Pit Interaction Study. CEMI Lecture Series, March 31, 2011.

Energy Information Administration (1995) Longwall Mining. DOE/EIA-TR-0688Distribution Category UC-950. Office of Coal, Nuclear, Electric and Alternate Fuels,U.S. Department of Energy, March 1995.

Ettema, R. and Urroz, G. E. (1989). On internal friction and cohesion in unconsolidated ice

rubble. Cold Regions Science and Technology, 16, pp. 237-247. Elsevier SciencePublishers B.V., Amsterdam.

Fairhurst, C. (1961) Laboratory measurement of some physical properties of rock.

Proceedings 4th Symposium of Rock Mechanics, 105-118.

Fletcher J.B. (1960) Ground Movement and Subsidence from Block Caving at Miami Mine,AIME Transactions, v. 217, pp 413-421.

Flores, G and Karzulovic, A, (2004a) Surface Crown Pillar Guidelines. Prepared forInternational Caving Study, Stage II, JKMRC: Brisbane.

Flores, G and Karzulovic, A, (2004b) Geotechnical Guidelines Subsidence. Prepared forInternational Caving Study, Stage II, JKMRC: Brisbane.

Fossum, A. (1985) Effective elastic properties for a randomly jointed rock mass.

International Journal of Rock Mechanics and Mining Sciences. 1985, Vol. 22, 6.

GEMCOM (2012) PCBC Software. Gemcom Software International Inc. Vancouver, B.C.Canada .

Gerrard, C.M. (1982) Elastic models of rock mass having one, two and three sets of joints.International Journal of Rock Mechanics and Mineral Sciences. 1982, Vol. 19.

Gilbride, J. Free, K. S. and Kehrman, R (2005) Modeling Block Cave Subsidence at theMolycorp, Inc., Questa Mine, Alaska Rocks 2005, The 40th U.S. Symposium on RockMechanics (USRMS), June 25 - 29, 2005 , Anchorage, AK

Glazer, S. and Hepworth, N. (2004) Seismic Monitoring of Block Cave Crown Pillar.

Proceedings MassMin 2004. Santiago.



References


Glazer, S. (2006). Applications of Mines Seismology Methods in Block Cave Mining.Proceedings 1st International Symposium on Block and Sub-Level Caving. TheSouth African Institute of Mining and Metallurgy. pp.281-302.

Goodman, R.E. & Bray, J.W. 1976, Toppling of rock slopes. Rock engineering forfoundations and slopes; proceedings of a specialty conference, Vol. 2 p201-233, Am.Soc. Civ. Eng.. New York.

Goodman, T. (1970) Internal USBM monthly subsidence monitoring report.

Grard, C. (1969) Mining Subsidence and the Means Permitting the Limiting of their Effectson the Surface (in French), Revue de l’Industrie Mineral, 51, (January).

Gray, R.E., Bruhn, R.W. and Turka, R.J. (1977) Study and Analysis of Surface SubsidenceOver Mined Pittsburgh Coalbed, U.S. Bureau of Mines, J0366047.

Guest, A. (2009) Personal Communication.

Haimson, B. C. and Tharp, T., Real stresses around boreholes, Soc. Petrol. Engr. J., 14, 145–151, 1974.

Hajiabdolmajid, V. and Kaiser, P. K. (2003) Brittleness of rock and stability assessment inhard rock tunnelling. Tunnelling and Underground Space Technology, 18 (1): 35-48.

Hajiabdolmajid, V., Kaiser, P. K., and Martin, C. D. (2002) Modelling brittle failure of rock.

International Journal of Rock Mechanics and Mining Sciences, 39 (6): 731-741

Hatheway, A.W., (1966) Engineering geology of subsidence at San Manuel mine, PinalCounty, Arizona: M.S. thesis, University of Arizona, Tucson, 110 pp.

Hebblewhite, B. (1995) Ground Control Newsletter. The Department of MiningEngineering, The University of New South Wales, Sydney, Australia.

Hellewell, F.G. (1988) The Influence of Faulting on Ground Movement due to Coal Mining:The U.K. and European Experience. Mining Engineer, 147, pp 334-337.

Herdocia, A, (1991) Hanging wall stability of sub-level caving mines in Sweden. PhDthesis (unpublished), Luleå University of Technology, Luleå, Sweden.

Heslop T.G. (1974) Failure by Overturning in Ground Adjacent to Cave Mining at HavelockMine, 3rd. ISRM Congress, Denver.

Heslop T.G. (1984) The Application of Interactive Draw Theory to Draw Control Practice inLarge Chrysotile Asbestos Mines, Chamber of Mines Journal (S.A.) June 1984, pp 23-41.

Hill, R. (1950) The mathematical theory of plasticity. Oxford:ClarendonPress;1950.

Hoek E. and Martin, D. (2010) Synthetic Rock Mass Review. Confidential ReportSubmitted to Dr Gideon Chitombo, MMT2 Technical Director, The SustainableMinerals Institute. The University of Queensland, Brisbane, Australia.

Hoek E., Kaiser P.K. and Bawden W.F. (1995) Support of underground excavations in hardrock. p. 215. Rotterdam, Balkema.

Hoek, E. (1974) Progressive caving induced by mining an inclined orebody. Trans Inst.Min Metall., Sect A: Min Industry, 83: A133-139.



References


Hoek, E. and Bray, J.W. (1981) Rock Slope Engineering. 2nd Edition. Institute of Miningand Metallurgy, London, 358 pp.

Hoek, E. and Brown, E T. (1997) Practical estimates of rock mass strength. InternationalJournal of Rock Mechanics and Mineral Sciences. 1997, Vol. 34, 8.

Hoek, E. and Brown, E.T. (1980) Underground excavations in rock. London : Institution ofMining and Metallurgy, 1980.

Hoek, E. and Diederichs, M.S. (2006) Empirical estimation of rock mass modulus,International Journal of Rock Mechanics and Mining Sciences, Vol 43, pp. 203-215.

Hoek, E. and Karzulovic, A. (2000) Rock-Mass properties for surface mines. In SlopeStability in Surface Mining (Edited by W. A. Hustralid, M.K. McCarter and D.J.A. vanZyl), Littleton, CO: Society for Mining, Metallurgical and Exploration (SME), pages59-70.

Holla, L. and Buizen, M., (1990) Strata Movement Due to Shallow Longwall Mining and theEffect on Ground Permeability. Proc. Aus. IMM, No. 1, pp 11-18.

Hood, M., Ewy, R.T. and Riddle, L.R. (1981) Empirical Methods of Subsidence Prediction —A Case Study, Workshop on Surface Subsidence Due to Underground Mining, WestVirginia University, Morgantown.

Hudson, J.A., Crouch, S.L and Fairhurst, C. (1971) Soft, stiff and servo-controlled testingmachines: a review with reference to rock failure. Engineering Geology Vol 6, Issue3, October 1972, pp. 155-189.

Hughes, H.W. (1917) A text-Book of Coal Mining. 6th Edition. London: Charles Griffen &Co, Ltd. P. 200.

Hutchinson, D.J. and Diederichs, M.S. (1996) Cablebolting in Underground Mines. BitechPublishers Ltd., Vancouver. 416p.

Itasca Consulting Group, Inc. (1995) PFC – Particle Flow Code in 2 Dimensions, Ver. 1.1,User’s Manual. Minneapolis: Itasca.

Itasca Consulting Group, Inc. (2000) FLAC – Fast Lagrangian Analysis of Continua, Ver. 4.0,User’s Manual. Minneapolis: Itasca.

Itasca Consulting Group, Inc. (2005) FLAC – Fast Lagrangian Analysis of Continua, Ver. 5.0,User’s Manual. Minneapolis: Itasca.

Itasca Consulting Group, Inc. (2007) PFC 3D – Particle Flow Code in 3 Dimensions, Ver. 4.0.User's Manual. Minneapolis: Itasca.

Itasca Consulting Group, Inc. (2009) FLAC 3D – Fast Lagrangian Analysis of Continua in 3Dimensions, Ver. 4.0. User's Manual. Minneapolis: Itasca.

Itasca Consulting Group, Inc. (2012) REBOP – Rapid Emulator Based on the Particle FlowCode. User's Manual. Minneapolis: Itasca.

Janelid, I. (1972), Study of the gravity flow process in sub-level caving. International Sub-level Caving Symposium, Stockholm, September.

Johnsone G.H. and Soule J.H., (1963) Measurements of Surface Subsidence . San ManuelMine, Pinal County, Arizona, USBM R.I. 6204.



References


Ju, J.W. and Chen, T.M. (1994) Micromechanics and effective moduli of elastic compositescontaining randomly dispersed ellipsoidal inhomogeneities. Acta Mechanica, 103,103-144.

Kakavas, P.A. and Anifantis, N.K. (2003) Effective moduli of hyperelastic porous media atlarge deformation. Acta Mechanica 160, 127–147 (2003) DOI 10.1007/s00707-002-0982-1

Kantner, W.H., (1934) Surface Subsidence Over Porphyry Caving Blocks, Phelps DodgeCorporation, Copper Queen Branch, AIME Transactions V. 109, pp 181-194.

Karekal, S., Das, R., Losse, L. and Cleary, P.W (2011). Application of a mesh-free continuummethod for simulation of rock caving processes. International Journal of RockMechanics and Mining Sciences, 48(5): 703-711.

Karzulovic, A., (1990) Evaluation of angle of break to define the subsidence crater of RioBlanco Mine’s Panel III (in Spanish). Technical Report, Andina Division, CODELCO-

Chile.

Karzulovic, A., Cavieres, P. and Pardo, C., (1999) Caving subsidence at El Teniente Mine (inSpanish). Pro-ceedings Symposium on Mining Engineering, SIMIN 99, Santiago.Department of Mining Engineering, University of Santiago: Santiago.

Karzulovic, A. and Flores, H. (2003) Geotechnical guidelines for a transition from open pitto under-ground mining. Report to International Caving Study, July, 2003.

Khan, A.S. and Yuan, S. (1988) A three-dimensional finite element program for brittlebimodular rock-like material. Int. J. Numer. Anal. Methods Geomech. 12, 599-609.

Kratzsch, H., (1983) Mining Subsidence Engineering, 543 p. Springer-Verlag: Berlin.

Kubrix (Simulation Works, 2012)

Kvapil R., (1982) The Mechanics and Design of Sub Level Caving Systems, UndergroundMining Methods Handbook, Am. Inst. of Min, Metall. and Pet. Eng.,pp 880-897.

Kvapil, R., Ceccarelli, B. and Lonergan, J., (1989) Quantitative Analysis of Subsidence at ElTeniente Mine. Technical Report, El Teniente Division, CODELCO-Chile.

Laubscher, D. (1990) A geomechanical classification system for the rating of rock mass inmine de-sign. Journal of the South African Institute of Mining and Metallurgy. Vol.90, No. 10, pp. 257-273.

Laubscher, D.H. (1975). Class distinction in rock masses. Coal, Gold, Base Metals, SouthAfrica. Vol. 23, August.

Laubscher, D.H. (1994) Cave mining – the state of the art. Journal of the South AfricanInstitute of Mining and Metallurgy, October 1994, pp. 279-293.

Laubscher, D.H. (2000) Block Caving Manual. Prepared for International Caving Study.JKMRC and Itasca Consulting Group, Brisbane.

Laubscher, D.H., (1990) A geomechanics classification system for the rating of rock mass inmine design. South African Institute for Mining and Metallurgy 90 (10), 257–273.

Li, A.J., Merifield, R.S. and Lyamin, A.V. (2008) Stability charts for rock slopes base don theHoek-Brown failure criterion. International Journal of Rock Mechanics & MiningSciences 45 (2008) 689-700.



References


Liang, Z.Z., Tang, C.A., Li, H.X., Xu, T. and Zhang, Y.B. (2004) Numerical simulation of 3-dfailure process in hetrogeneous rocks. International Journal of Rock Mechanics andMining Sciences. SINOROCK2004, 2004, Vol. 41, 3.

Liu, Y.A. (1981) Novel High Gradient Magnetic Separation (HGMS) Processes forDesulfurization of Dry Pulverized Coal, Chapter 9, in Recent Developments inSeparation Science, Volume VI, pp. 149-171, Normal N. Li, editor, CRC Press, BocaRatan, FL.

Lorig, L., Board, M., Potyondy, D. and Coetzee, M. (1995) Numerical modelling of cavingusing continuum and micro-mechanical models. CAMI'95:3rd Canadian Conference

on Computer Applications in the Mineral Industry. Montreal, Quebec, Canada,October 22-25, 1995, pp. 416-425.

Lorig, L. (2000) The Roel of Numerical Modelling in Assessing Caveabilty, ItascaConsulting Group Inc., Report to the International Caving Study, ICG00-099-3-16,October 2000.

Luo, Y. and Peng, S.S. (2000) Long-Term Subsidence Associated with Longwall Mining —

Its Causes, Development and Magnitude, Mining Engineering, 52(10), (October).

Lupo, J.F. (1996) Evaluation of Deformations Resulting from Mass Mining of an Inclined

Orebody. Ph.D. thesis (unpublished), Colorado School of Mines, Golden, Colorado.

Lupo, J.F. (1997). Progressive Failure of Hangingwall and Footwall at the KiirunavaaraMine, Sweden. Int. J. Rock Mech. and Min. Sci. 34:3-4, paper No. 184.

Lupo, J.F. (1998) Large-scale surface disturbances resulting from underground massmining, Int. J. Rock Mech. Min. Sci., 35(4-5), Paper No. 25.

Mahtab M., (1976) Influence of Rock Fractures on Caving, Trans. AIME, Vol 260.

Marachi, N., Chan, C. and Seed, H. (1972) Evaluation of properties of rockfill materials.Journal Soil Mechanics, Div ASCE. 1972, 98.

Mas Ivars, D., Deisman, N., Pierce, M. and Fairhurst, C. (2007) The Synthetic Rock Massapproach - A step forward in the characterization of jointed rock masses. 11thCongress of the International Society for Rock Mechanics. 2007, 485-490.

Mas Ivars, D., Pierce, M., Darcel, C., Reyes-Montes, J., Potyondy, D., Young, P. and Cundall, P.(2011) The synthetic rock mass approach for jointed rock mass modelling.International Journal of Rock Mechanics & Mining Sciences 48 (2011) 219–244.

Mas Ivars, D., Pierce, M., DeGagné, D. and Darcel, C. (2008) Anisotropy and scaledependency in jointed rock mass strength – A synthetic rock mass study. In R. Hart,C. Detournay and P. Cundall (eds), Proceedings of the First International FLAC/DEMSymposium on Numerical Modeling, August 25-27, 2008, Minneapolis, MN USA.Minneapolis: Itasca.

Mathews, K.E, Hoek, E., Wyllie, D.C and Stewart, S. (1981) Prediction of stable excavationspans for mining at depths below 1000m in hard rock. Report No. DSS SerialNo.OSQ80-00081, DSS File No. 17SQ.233440-0-9020, 43 p.

Medhurst, T.P. (1996) Estimation of the in situ strength and deformation of coal for

engineering design. PhD Thesis. University of Queensland.



References


Milne, D., Hadjigeorgiou, J. and Pakalnis, R. (1998) Rock mass characterization forunderground hard rock mines. Tunnelling and Underground Space Technology13(4):383-391.

National Coal Board, (1975) Subsidence Engineers Handbook, 2nd edition. National CoalBoard Mining Dept, London.

Nelson W.I. and Fahrni K.C., (1950) Caving and Subsidence at the Copper Mountain Mine,CIM Transactions Bulletin, v. 43, pp 2-10.

Nicieza, C.G., A´lvarez Ferna´ndez, M.I., Menendez Dı´az, A., A´lvarez Vigil, A.E. (2006)Modification of rock failure criteria considering the RMR caused by joints.Computers and Geotechnics 33 (2006) 419–431.

Nielsen, L. (1990) Strength and stiffness of porous materials. Journal American CeramicsSociety. Vol 73, No. 9, pp. 2684-2689.

Obert L. and Long A.E., (1962) Underground Borate Mining, Kern Country, California,USBM R.I.

Obert, L. and Duvall, W. I., (1967) Rock Mechanics and the Design of Structures in Rock,650 p. J Wiley & Sons: New York.

Orchard, R.J. and Allen, W.S. (1974) Time-dependence in Mining Subsidence, ProceedingsInternational Symposium on Minerals and the Environment, Institution of Miningand Metallurgy, London, pp. 643-659.

Palma, R. and Agarwal, R. (1973) A Study of the Caveability of Primary Ore at the ElTeniente Mine, Technical Report from Colombia University, NY.

Panek, L.A. (1984) Subsidence in Undercut-Cave Operations, Subsidence Resulting fromLimited Ex-traction of Two Neighboring-Cave Operations, Department of MiningEngineering, Michigan Technological University, Houghton, Michigan.

Pappas, D. and Mark, C. (1993) Behaviour of Simulated Longwall Gob Material. Report ofInvestigations 9458. United States Department of the Interior, Bureau of Mines.

Parker J., (1978) What Can Be Learned From Surface Subsidence, E&MJ, July 1978.

Passaris, E.K.S. (1977) The effect of directional anisotropy on the mechanical behaviour ofrocksalt. Proceedings, Conference Rock Engineering, British Geotechnical Society,Department of Mining Engineering. Newcastle upon Tyne, U.K., 11-31.

Peele, R. (1918), Mining Engineers’ Handbook. John Wiley & Sons, New York.

Peng, S.S. (1992) Surface Subsidence Engineering, Society For Mining, Metallurgy andExploration Inc. , Littleton, Colorado. 161 pp.

Perman, F. and Sjoberg, J. (2011) Numerisk analys av brytningssekvenser i block 19.LKAB Utredning 11-776, 2011-05-20 (in Swedish).

Phillips, K.A.S. and Hellewell, F.G. (1994) Three-dimensional ground movements in thevicinity of a mining activated geological fault. Quarterly Journal EngineeringGeology, 27, 7-14.

Pierce, M., Cundall, P., Potyondy, D. and Mas Ivars, D. (2007) A synthetic rock mass modelfor jointed rock. Rock Mechanics: Meeting Society's Challenges and Demands –



References


Eberhart, Stead and Morrison (eds) 2007 Taylor and Francis Group, London, ISBN978-0-415-44401-9, 341-349.

Pierce, M. (1999) Stress Changes resulting From Plug Caving of Lift 1 at Northparkes Mine.Itasca report to Northparkes Mine, ICG99-1043-14F (Confidential)

Pierce, M. (2010) Personal Communication.

Pierce, M. and Lorig, L. (1998) FLAC 3D Analysis of Caveability of the Northparkes E26 Lift 2

Orebody, Itasca Consulting Group, Inc. Report to Northparkes Mines, Parkes, NSW,Australia # 1017, November, 1998.

Pierce, M., Cundall, P. Mas Ivars, D., Darcel, C., Young, R.P., Reyes-Montes, J. and Pettitt, W.(2006) Six Monthly Technical Report, Caving Mechanics, Sub-Project No. 4.2:Research and Methodology Improvement, and Sub-Project 4.3, Case StudyApplication, Itasca Consulting Group Inc, Report to Mass Mining Technology Project,2004-2007, ICG06-2292-1-Tasks 2-3-14, March.

Pierce, M., Cundall, P., Potyondy, D. and Mas Ivars, D. (2007) A synthetic rock mass modelfor jointed rock, In Rock Mechanics: Meeting Society's Challenges and Demands,Proc. 1st Canada-U.S. Rock Mechanics Symposium Vol. 1, pp. 341-349

Pierce, M., Gaida, M. and Degagne, D. (2009) Estimation of rock block strength.ROCKENG09. Proceedings 3rd CANUS Rock Mechanics Symposium, Toronto, May,2009. Paper No. 4360. M. Diederichs and G. Grasselli, eds.

Pierce, M., Mas Ivars, D. and Sainsbury, B. (2009). Use of Synthetic Rock Masses (SRM) toinvestigate jointed rock mass strength and deformation behaviour in Proceedings ofthe International Conference on Rock Joints and Jointed Rock Masses in Tucson,

Arizona. May 14 and 15, 2009.

Pine, R.J. Owen, D.R.J., Coggan, J.S. and Rance, J.M. (2007) A new discrete fracturemodelling approach for rock masses. Ge´otechnique 57, No. 9, 757–766 [doi:10.1680/geot.2007.57.9.757]

Portu, G.D. and Vincenzini, P. (1981) XIII Siliconf. Vol. 1 (1981) Budapest, Hungary, p. 265.

Pratt, H.R., Black, A.D., Brown, W.S., Brace, W.F. (1972) The effect of specimen size on themechanical properties of unjointed diorite. Int. J. Rock Mech. Min. Sci. 9, 513–529.

Rech, W.D, 2001. Underground Mining Methods. Engineering Fundamentals and

International Case Studies, Chapter 48 - Henderson Mine. Hustrulid, W. and R.

Bullock (eds). Society for Mining and Exploration.Rech, W. and Lorig, L. (1992)Predictive numerical stress analysis of panel caving at the Henderson Mine.MASSMIN’92, Johannesburg, SAIMM, 1992, pp 55-62.

Rech, W.D. and Lorig, L. (1992) Predictive numerical stress analysis of panel caving at theHenderson Mine. MASSMIN ’92. Pp 55-62, Johannesburg, SAIMM, 1992.

Ribacchi, R. (2000) Mechanical Tests on Pervasively Jointed Rock Material: Insight intoRock Mass Behaviour. Rock Mech. Rock Engng. (2000) 33 (4), 243-266.

Rice, G. (1934) Ground movement from mining in Brier Hill mine, Norway, Michigan.Mining and Metallurgy, v 15, n 325, p.12-14.

Rice, R. (1976) Extension of the Exponential Porosity Dependence of Strength and ElasticModuli. Journal of The American Ceramic Society-Discussions and Notes Vol. 59, No.11- 1, pp 536-537.



References


Rockfield (2007) ELFEN. User Guide. Technium, Kings Road, Prince of Wales Dock,Swansea, SA1 8PH, West Glamorgan, U.K.

Rocscience (2002) PHASE2. Finite element analysis and support design for excavations.Toronto: Rocscience, Inc.

Rocscience (2012). RocLab Users Guide,http://www.rocscience.com/products/14/RocLab. Accessed January 30, 2012.

Rogers, S., Elmo, D., Webb, G. and Catalan, A. (2010) Simulating the impacts of hydraulicfracture preconditioning on cavability and fragmentation at the planned Cadia Eastpanel cave in Proceedings of the Second International Symposium on Block and Sub-level Caving (Perth, April 2010). Y. Potvin, Ed. Australian Centre for Geomechanics,pp. 663-676.

Rojas, E., Molina, R and Cavieres, P. (2001) Preundercut caving in El Teniente, Chile.Underground Mining Methods: Engineering Fundamentals and International Case

Studies, SME, Colorado.

Ross, I. and van As, A. (2005) Northparkes Mines – Design, Sudden Failure, Air-Blast andHazard Management at the E26 Block Cave. Ninth Underground OperatorsConference, Perth, WA, 7-9 March, 2005.

Rudnicki, J.W. and Rice, J.R. (1975) Conditiosn for the locatlization of deformation inpressure-senstivie dilatant materials. J. Mech. Phys. Solids, 1975, Vol 23, pp 371-394.

Russo, G., Kalamaras, G.S. and Grasso, P.A. (1998) Discussion on the concepts of

geomechnical classes behaviour categoris and technical classes for an underground

project. Gallerie e Grandi Opere Sotterranee 1998; 54.

Sainsbury B., Mas Ivars, D. and Darcel C. (2009). Synthetic Rock Mass Simulations of the1200, 1700 and 1800 Domains at the Mt Keith Open Pit. Itasca Consulting Group.Technical report number 08025.

Sainsbury, B. (2010) Sensitivities in the numerical assessment of cave propagation inCaving 2010: Second International Symposium on Block and Sub-level Caving. 20–

22 April 2010, Australian Centre for Geomechanics.

Sainsbury, B., Mas Ivars, D. and Darcel, C. (2008) Synthetic Rock Mass Simulations of the1200, 1700 and 1800 Domains at the Mt Keith Open Pit. Itasca Australia Report08025 to BHP Billiton Nickel West.

Sainsbury, B., Pierce, M. and Mas Ivars, D. (2008) Analysis of Caving Behaviour Using aSynthetic Rock Mass —Ubiquitous Joint Rock Mass Modelling Technique, InProceedings of the 1st Southern Hemisphere International Rock MechanicsSymposium (SHIRMS), Y. Potvin, J. Carter, A. Dyskin and R. Jeffrey (eds), 16–19

September 2009, Perth, Australia, Australian Centre for Geomechanics, Perth, Vol. 1– Mining and Civil, pp. 243–254.

Sainsbury, D. and Lorig, L. (2005) Caving Induced Subsidence at the Abandoned GraceMine. ICG Report to Arcadia Land Company.

Sainsbury, D., Board, M. and Sainsbury, B. (2010) Analysis of Caving Behaviour and

Extraction Level Performance at the Cadia East Underground Project – 2010Feasibility Study. Itasca Australia Pty Ltd Report No. 10001D to Newcrest MiningLimited.

http://www.rocscience.com/products/14/RocLab

http://www.rocscience.com/products/14/RocLab



References


Sainsbury, D., Lorig, L. and Sainsbury, B. (2010) Investigation of caving induced subsidenceat the abandoned Grace Mine, in Caving 2010: Second International Symposium onBlock and Sub-level Caving. 20–22 April 2010, Australian Centre for Geomechanics.

Sainsbury, D. and Sainsbury, B. (2010) A Review of Caving Induced Surface Subsidence.Itasca Australia Report # 10007 to CEMI.

Salamon, M. (1968) Elastic moduli of a stratified rock mass. International Journal of RockMechanics and Mining Sciences. 1968, Vol. 5.

Samadhiya, N, Viladkar,m and Singh, B. (2004) Three-dimensional analysis of apowerhouse cavern in an anisotropic rock mass. International Journal of RockMechanics and Mining Sciences. SINOROCK2004, 2004, Vol. 41, 3.

Sandström, D. (2003) Analysis of the Virgin State of Stress at the Kiirunavaara Mine.Licentiate thesis 2003:02, Luleå University of Technology, Luleå, Sweden.

Santarelli, F.J. (1989) Theoretical and experimental investigation of the stability of theaxisymmetric wellbore. PhD thesis, Imperial College, London.

Schmertmann, J.H. and Osterberg, J.O. (1960) An experimental study of the developmentof cohesion and friction with axial strain in saturated cohesive soils. Proc. ASCEResearch Conference on the Shear Strength of Cohesive Soils, Boulder, Colorado,19060, pp 643-694.

Serafirm, J.L. and Pereira, J.P. (1983) Considerations of the geomechanical classification ofBieniawski. Proceedings, International Symposium on Engineering Geology andUnderground Construction, Lisbon, Vol 2, pp II-33 to II-42, LNEC, Lisbon.

Shadbolt C.H. (1978) Mining Subsidence - Historical Review and State of the Art, Conf. onLarge Ground Movements and Structures, Cardiff. Pantech Press, London, ed. J.D.Geddes. pp 705-748.

Shadbolt C.H., (1987) A Study of The Effects of Geology On Mining Subsidence in the EastPennine Coalfield. Ph.D. Theses, University of Nottingham.

Shadrin, A.G. and Zomotin, V.B. (1977) Calculating the Durations of Surface Movements (inRussian), Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Isopaemykh, No. 6.

Sharrock, G. (2010). Personal communication.

Sharrock, G., Vakili, A., Duplancic, P. and Hastings, N. (2011) Numerical analysis of

subsidence for Perserverence Deeps Block Cave in Continuum and Distinct ElementNumerical Modelling in Geomechanics, 2011. Sainsbury, Hart, Detournay andNelson (eds.), Paper 06-03, Itasca International Inc, Minneapolis, ISBN 978-0-9767577-2-6.

Sims, S.J. (1968) The Grace Mine magnetite deposit, Berks County, Pennsylvania, in Oredeposits of the United States, 1933–1967: the Graton-Sales volume (ed. J. D. Ridge),

Vol. 1, 108–124; 1968, New York, AIME.

Simulation Works (2012). Kubrix. Minneapolis, MN, USA.

Simulia (2011) ABAQUS, Dassault Systèmes, 2004, 2012 - All Rights Reserved.

Singh, B. (1973) Continuum characterization of jointed rock masses Part I - Theconstitutive equations. International Journal of Rock Mechanics and MineralSciences. 1973, Vol. 10.



References


Singh, M.M., (2003) Mine Subsidence. SME Mining Engineering Handbook (3rd ed.).Littleton,CO: Society for Mining Metallurgy and Exploration, Inc.

Singh, U K, Stephansson, O J and Herdocia, A, (1993) Simulation of progressive failure inhanging-wall and footwall for mining with sub-level caving. Trans Instn Min Metall,Sect A: Min Industry, 102: A188-194.

Sitharam, T.G. and Latha, G.M. (2002) Simulation of excavations in jointed rock massesusing a practical equivalent continuum approach. International Journal of RockMechanics and Mining Sciences, Vol. 39, No. 4, pp. 517-525.

Sluys, L.J. (1992) Wave Propagation, Localization and Dispersion in Softening Solids. Ph.DThesis, Delft University Technology, Netherlands.

Spinner, S., Knudsen, F.P. and Stone, L. (1963) J. Res. Natl. Bur. Stand. 67C, 39.

Stacey, T.R. and Swart, A.H. (2001) Practical rock engineering practice for practice for

shallow and opencast mines. SIMRAC The safety of mines research advisorycommittee, 66pp.

Stafford, B. (2002) The Grace Mine story. Bee Line, 2002, 24, (3–4), 55.

Stephansson, O., Borg, T. and Bäckblom, G. (1978) Sprickbildning i norra Kiirunavaarashängvägg. Teknisk rapport 1978:51T, Avdelningen för Bergmekanik, Högskolan iLuleå.

Sterpi, D. (1999) An analysis of geotechnical problems involving strain-softening effects.Int. J. Numer. Anal. Meth. Geomech. 1999;23:1427–54.

Stewart, D., Rein, R. and Firewick, D. (1984) Surface Subsidence at the Henderson Mine, in

Geomechanics Applications in Underground Hardrock Mining, SME/AIME, NewYork.

Stöckel, B-M., Sjoberg, J., Makitaavola, K. and Savilahti, T. (2012) Mining-induced groundeformations in Kiirunavaaraand Malmberget, EUROCK 2012, 28-30 May, Stockholm,Sweden. (in press).

Sundaram, R.N. and Corrales, J.M. (1980) Brazilian tensile strength of rocks with differentelastic properties in tension and compression. International Journal Rock MechanicsMining Geomechanics Abstracts, 17, 131-133.

Szwedzicki, T., Widijanto, E. and Sinaga, F. (2006) "Propagation of a Caving Zone, A Case

Study from PT Freeport, Indonesia." in Proud to Be Miners (MassMin 2004, Santiago,August 2004), Santiago: Mineria Chilena.

Taylor, C. (1993) Personal communication

Thomas, L.A., (1971) Subsidence and related caving phenomena at the San Manuel mine,San Manuel, Arizona: Magma Copper Company, San Manuel Division, unpublishedreport.

Tiwari, R. and Rao, S. (2006). Post failure behaviour of a rock mass under the influence oftriaxial and true triaxial confinement. Engineering Geology 84 (2006) 112–129.

Trueman, R. and Mawdesley, C. (2003) Predicting cave initiation and propagation, CIMBulletin; May 2003; 96, 1071; ProQuest Science Journals, p. 54.



References


van As, A, Davison, J. and Moss, I. (2003) Subsidence Definitions for Block Caving Mines.Rio Tinto Technical report. 59pp

van As, A. and Jeffrey, R. (2000) Hydraulic fracturing as a cave inducement technique atNorthparkes Mines. Proceedings, MassMin 2000. The Australian Institute of Miningand Metallurgy. Publica-tions Series No. 7/2000, p. 165-172.

van As, A., Davison, J. and Moss, A. (2003) Subsidence Definitions for Block Caving Mines.Rio Tinto Technical report. 59pp.

van der Merwe, N.J. (1999) Sub-surface Erosion — A Post Subsidence Phenomenon, inProceedings of the 9th ISRM Congress on Rock Mechanics, Paris, Balkema,Rotterdam, Vol. 1.

Vanderwilt J.W. (1946) Ground Movement Adjacent to a Caving Block in the ClimaxMolybdenum Mine, Technical Paper #200, Mining Technology.

Varas, F., Alonso, E., Alejano, L.R., Fdez-Manin G. (2005) Study of bifurcation in theproblem of unloading a circular excavation in a strain-softening material. Tunnel.Undergr. Space Technol., 20 (2005), pp. 311–322

Vermeer, P.A. and de Borst. R. (1984) Non-associated plasticity for soils, concrte and rock.Heron, Vol 29, 1984, no. 3.

Villegas, T. (2008) Numerical Analyses of the Hangingwall the the Kiirunavaara Mine.Licentiate Thesis 2008:11. Division of Mining and Geotechnical Engineering,. LuleaUniversity of Technology, Sweden.

Villegas, T., Nordlund, E. and Dahner-Lindqvist, C. (2011) Hangingwall surface subsidenceat the Kiirunavaara Mine, Sweden. Eng. Geol., doi:10.1016/j.enggeo.2011.04.010

Vongpaisal S. (1974) Prediction of Subsidence Resulting From Mining Operations, PhD.Thesis, McGill University, Montreal.

Vyazmensky, A., Elmo, D. and Stead, D. (2010) Role of Rock Mass Fabric and Faulting in theDevelopment of Block Caving Induced Surface Subsidence, Rock Mech. Rock Eng43:533–556

Vyazmensky, A., Elmo, D., Stead, D. and Rance, J. (2007) Combined finite-discrete elementmodeling of surface subsidence associated with block caving mining. Proceedings of1st Canada-U.S. Rock Mechanics Symposium. Vancouver, Canada. 467-475.

White, D. (1984) Premining stress and its impact on block caving. AIME. GeomechanicsApplications in Underground Hardrock Mining . s.l. : AIME , 1984.

Whittaker, B N and Reddish, D J, (1989) Subsidence, Occurrence, Prediction and Control,528 p. Elsevier: Oxford.

Wyllie, D. and Mah, C. (2007) Rock Slope Engineering, 4th Edition. Taylor and Francis,Hampshire, United Kingdom. ISBN 041528001X

Yoshida, H and Horii, H. (2004) Micromechanics-based continuum model for a jointed rockmass and excavation analyses of a large-scale cavern. International Journal of RockMechanics and Mining Sciences. 2004, 41.

Zhang, Z. (2005) Finite Element Analysis of Ductile Fracture Behaviour of Pipe Sectionswith SurfaceD Crack. PhD Thesis. Norwegian University of Science andTechnology.

(phd thesis) a model for cave propagation and subsidence assessment in jointed rock masses

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