and dilation angle

602 Pages·2014·25.62 MB·English

IMPROVING CONTINUUM MODELS FOR EXCAVATIONS IN
ROCKMASSES UNDER HIGH STRESS THROUGH AN
ENHANCED UNDERSTANDING OF POST-YIELD DILATANCY
by
Gabriel Walton
A thesis submitted to the Department of Geological Sciences and Geological Engineering
In conformity with the requirements for
the degree of Doctor of Philosophy (Engineering)
Queen’s University
Kingston, Ontario, Canada
(December, 2014)
Copyright © Gabriel Walton, 2014
Abstract
In recent decades, the field of rock engineering has seen an increased use of numerical
modelling tools to aid in the analysis and design of underground excavations. Although complex
numerical methods have been developed to explicitly capture the discontinuum mechanical
processes which dominate rock and rockmass deformation, continuum methods represent a viable
alternative due to their relative advantages in model runtimes and parametric simplicity. This
thesis aims to advance the state-of-art and state-practice techniques for continuum models and to
demonstrate their ability to replicate behaviours observed in-situ.
With recent advances in the understanding of rockmass strength, it is the post-yield
phenomenon of rock dilatancy which has remained the domain of greatest uncertainty in
constitutive models. Particularly in the case of brittle rockmasses, where deformation is
dominated by crack extension and dilation, the post-yield evolution of dilatancy in parallel with
strength parameters can have a very significant impact on progressive failure processes. By
improving our understanding of this evolution, continuum models for brittle rock can be
improved.
In the case of weaker rockmasses which can be adequately represented using a
conventional strain-softening approach, an existing model for dilatancy can be applied. As is
shown in this thesis, the use of a constant dilation angle to approximate the dilatant behaviour of
the rockmass in this case is appropriate; accordingly, parameter selection guidelines are
presented. In the case of brittle rockmasses, a mobilized dilation angle model which incorporates
the strain and confinement dependencies of dilatancy is required.
Through an analysis of laboratory testing data, a new model for the dilation angle is
developed. Then, using five case studies (both from the literature and novel to this thesis), the
applicability of the model to in-situ rockmass behaviour is demonstrated. Finally, the implications
of these model results for understanding support-rockmass interaction and strainbursting
phenomena are discussed.
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Co-Authorship
The thesis “Improving Continuum Models for Excavations in Rockmasses Under High Stress
Through an Enhanced Understanding of Post-Yield Dilatancy” is the product of research
conducted by the author, Gabriel Walton. Although scientific and editorial feedback were
provided by Justin Whitmore, Allan Punkkinen, Javier Arzua, Dr. Leandro Alejano, and Dr. Mark
Diederichs, the written content is solely that of the author.
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Acknowledgements
The research presented in this thesis has been made possible due to generous funding
from the Natural Sciences and Engineering Research Council of Canada (NSERC), the Nuclear
Waste Management Organization of Canada (NWMO), and the Center for Excellence in Mining
Innovation (CEMI). I would also like to thank Queen’s University and the Department of
Geological Sciences and Geological Engineering for supporting me throughout both my
undergraduate and graduate education.
I owe a great deal to those who have aided my research by providing access to data. In
particular, thanks go to Denis Labrie of the CANMET laboratory in Ottawa, and some colleagues
in the mining industry that unfortunately must go unnamed. Also, Allan Punkkinen and Justin
Whitmore of Vale’s Creighton Mine ground control team have gone above and beyond to make
sure my experiment at their mine moved successfully from concept through to execution.
There are several people within the Queen’s community without whom this work would
not be possible. The entire Geomechanics group has provided a great support network, always
there to lend a helping hand when needed. Special thanks go to some of my older (and wiser)
peers who never hesitated to help me with some of the day to day problems and questions which
arose during my research: Dr. Matthew A. Perras, Dr. J Connor Langford, Ehsan Ghazvinian,
Felipe Duran del Vale, and Jeffrey Oke. Robin Harrap has been an excellent sounding board for
everything not thesis related, and has helped keep me sane. Dr. Matt Lato has been generous in
helping me pursue my alternative research interests. Jean Hutchinson has been an outstanding
department head and supporter of my teaching activities within the department. Dr. Alan Ableson
has spent countless hours helping me troubleshoot some of the trickier aspects of my MATLAB
code. Ted – thanks for the ping-pong.
A large reason for the success of my research was the willingness of Dr. Leandro Alejano
to host me at the Universidad de Vigo for a month in 2013. His kindness, hospitality, and
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scientific insight have been invaluable. He has been like a second supervisor to me, and for that I
am eternally grateful. Thanks also to Javier Arzua and the rest of the student team at Universidad
de Vigo for their friendship and scientific support.
Without question, Mark Diederichs has surpassed my expectations of what a supervisor
could be. Mark has been a true mentor to me, and has provided me with countless opportunities
that otherwise would not have been available. Despite his hectic schedule and frequent
international trips, he has always been there when it counted. I cannot overstate the impact that
his insight, generosity, and belief in me have had on my professional development.
Finally, I want to thank Anna for continuing to be my biggest supporter, my proofreader,
my technical advisor, and most importantly, a caring and loving partner.
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Table of Contents
Abstract ............................................................................................................................................ ii
Co-Authorship ................................................................................................................................ iii
Acknowledgements ......................................................................................................................... iv
List of Figures ............................................................................................................................... xiii
List of Tables ............................................................................................................................. xxvii
List of Abbreviations & Symbols ............................................................................................... xxix
Chapter 1 .......................................................................................................................................... 1
1.1 Purpose of Study .................................................................................................................... 1
1.2 Significance of Failure Mode ................................................................................................. 2
1.3 Thesis Objectives ................................................................................................................... 6
1.4 Thesis Scope .......................................................................................................................... 7
1.5 Thesis Outline ........................................................................................................................ 7
Chapter 2 ........................................................................................................................................ 10
2.1 Fundamentals of Plasticity Theory ...................................................................................... 10
2.1.1 Elastic Behaviour .......................................................................................................... 12
2.1.2 Yield Criteria ................................................................................................................ 15
2.1.2.1 Commonly Used Yield Criteria ............................................................................. 16
2.1.3 Plastic Strains and Dilation ........................................................................................... 24
2.1.3.1 Dilation in Classical Plasticity Theory ................................................................... 29
2.1.3.2 Mobilized Dilation ................................................................................................. 38
2.2 Numerical Methods .............................................................................................................. 45
2.2.1 Continuum Methods ...................................................................................................... 46
2.2.1.1 The Finite Element Method (FEM) ....................................................................... 49
2.2.1.2 The Finite Difference Method (FDM) ................................................................... 58
2.2.2 Discontinuum Methods ................................................................................................. 64
2.2.2.1 The Distinct Element Method ................................................................................ 66
2.2.2.2 Discontinuous Deformation Analysis (DDA) ........................................................ 70
2.2.3 Hybrid Modelling Approaches...................................................................................... 72
2.2.3.1 FEM/DEM Hybrid Codes ...................................................................................... 72
2.3 Preliminary Investigation of Post-Yield Response in Continuum Models .......................... 77
2.3.1 Instability and Localization in Continuum Models ....................................................... 77
2.3.2 Post-Yield Behaviour in Phase2 (2D Implicit Solution FEM) ...................................... 79
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2.3.3 Post-Yield Behaviour in FLAC3D (Explicit Solution FDM) ......................................... 87
2.3.4 Implications of Strain Localization on Modelling Excavation Behaviour .................... 90
Chapter 3 Brittle Rock Failure and its Implications for Modelling Dilatancy ............................... 92
3.1 Damage in Intact Rock ......................................................................................................... 93
3.1.1 Determination of Damage Parameters from Laboratory Testing Data ....................... 100
3.2 Damage, Spalling and Dilatancy in Excavations ............................................................... 101
3.2.1 Lessons Learned from the AECL Mine-By Experiment ............................................. 102
3.2.2 Further Conceptual Advances in Understanding Brittle Failure ................................. 109
3.3 Modelling Brittle Failure in Continuum Models ............................................................... 111
3.3.1 Issues with Classical Strength Models ........................................................................ 111
3.3.2 The Cohesion-Weakening-Friction-Strengthening Model .......................................... 112
3.3.3 Dilatancy and the CWFS Model ................................................................................. 117
3.4 Brittle Dilatancy – Theoretical Considerations .................................................................. 118
3.5 A Closer Look at Pre-Peak Dilatancy and the Determination of “Plastic” Strains from
Laboratory Test Data ............................................................................................................... 121
3.5.1 Determining Irrecoverable Strains from Loading-Unloading Cycles ......................... 123
3.5.1.1 Accounting for Non-Zero Stresses in the “Unloaded” State ................................ 125
3.5.1.2 Mechanistic Considerations ................................................................................. 126
3.5.2 Calculating Plastic Strains Using Elastic Moduli ....................................................... 129
3.5.3 Results ......................................................................................................................... 131
3.5.4 Model Sensitivity to Pre-Peak Dilatancy .................................................................... 135
3.5.5 Conclusions ................................................................................................................. 139
Chapter 4 Dilation and Post-peak Behaviour Inputs for Practical Engineering Analysis ............ 141
4.1 Introduction ........................................................................................................................ 141
4.1.1 Material Models in Rock Engineering ........................................................................ 141
4.1.2 Dilation in Plasticity Theory ....................................................................................... 142
4.1.3 Mobilized Dilation Angle Models .............................................................................. 143
4.1.4 Dilatancy in Continuum Models ................................................................................. 149
4.2 Methodology ...................................................................................................................... 150
4.2.1 Connecting Numerical Models to Reality ................................................................... 150
4.2.2 Displacements Around Excavations (Considering Mobilized Dilation) ..................... 152
4.2.3 Comparing Mobilized Dilation to Constant Dilation .................................................. 154
4.3 Model Results .................................................................................................................... 157
4.3.1 Parameters Tested ....................................................................................................... 158
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4.3.2 Quality of the Constant Dilation Angle Approximation ............................................. 159
4.3.3 Best Fit Dilation Angle Parameter Sensitivities.......................................................... 161
4.4 Selection of Dilation Angle for Numerical Models ........................................................... 163
4.5 The Constant Dilation Angle Approximation for Near-Hydrostatic Stresses and Near-
Circular Excavations ................................................................................................................ 169
4.5.1 Determining Best Fit Constant Dilation Angle Using Finite-Difference Models ....... 169
4.5.2 Best Fit Dilation Angle Sensitivity to Stress Conditions ............................................ 170
4.5.3 Best Fit Dilation Angle Sensitivity to Rate of Strength Loss ..................................... 174
4.5.4 Best Fit Dilation Angle Sensitivity to Excavation Geometry ..................................... 177
4.6 Example of the Methodology as Applied to Real Data ..................................................... 179
4.7 Conclusions ........................................................................................................................ 183
4.8 Appendix to Chapter 4 – Calculation of Plastic Zone Displacements ............................... 184
Chapter 5 A laboratory-testing based study on the strength, deformability, and dilatancy of
carbonate rocks at low confinement ............................................................................................ 187
5.1 Introduction ........................................................................................................................ 187
5.2 Rocks Investigated ............................................................................................................. 189
5.2.1 Indiana Limestone ....................................................................................................... 191
5.2.2 Carrara Marble ............................................................................................................ 191
5.2.3 Toral de Los Vados Limestone ................................................................................... 192
5.3 Test Methods ...................................................................................................................... 193
5.3.1 Test Setup.................................................................................................................... 193
5.3.2 Data Analysis .............................................................................................................. 195
5.4 Interpretation of Results ..................................................................................................... 202
5.4.1 Strength ....................................................................................................................... 209
5.4.2 Deformability .............................................................................................................. 215
5.4.3 Dilatancy ..................................................................................................................... 224
5.4.3.1 Model of Zhao and Cai (2010a) ........................................................................... 224
5.4.3.2 Simplified Model for Peak Dilation and Dilation Decay ..................................... 229
5.5 Summary and Conclusions ................................................................................................ 232
Chapter 6 A New Model for the Dilation of Brittle Rocks Based on Laboratory Compression Test
Data with Separate Treatment of Dilatancy Mobilization and Decay ......................................... 234
6.1 Introduction ........................................................................................................................ 234
6.1.1 Laboratory-Based Plasticity Models for Brittle Rock Behaviour ............................... 234
6.1.2 Rock Dilatancy ............................................................................................................ 236
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6.1.3 Existing Yield and Dilatancy Models ......................................................................... 237
6.1.4 Rock Types Studied .................................................................................................... 241
6.2 Analysis of Laboratory Data to Obtain Dilation Angle Estimates ..................................... 242
6.2.1 Methodology ............................................................................................................... 242
6.2.2 Considerations on Data Reliability ............................................................................. 243
6.3 A New Model for Rock Dilation........................................................................................ 245
6.4 Mechanistic Interpretation ................................................................................................. 248
6.5 Proposed Model Sensitivity to Confinement ..................................................................... 251
6.5.1 Pre-Mobilization Dilation ........................................................................................... 251
6.5.2 Peak Dilation ............................................................................................................... 254
6.5.3 Post-Mobilization Dilation .......................................................................................... 263
6.5.4 Mechanistic Changes with Increasing Confinement ................................................... 266
6.6 Summary and Conclusions ................................................................................................ 267
Chapter 7 Verification of a laboratory-based dilation model for in-situ conditions using
continuum models ........................................................................................................................ 269
7.1 Introduction ........................................................................................................................ 269
7.2 Models for Rock Dilation .................................................................................................. 270
7.2.1 Mobilized Dilation Models ......................................................................................... 271
7.2.1.1 The Walton-Diederichs (2014b) Dilation Model ................................................. 274
7.3 Comparison of Modelling Approaches .............................................................................. 280
7.3.1 Strain Weakening ........................................................................................................ 283
7.3.2 Cohesion-Weakening-Friction-Strengthening (CWFS) .............................................. 286
7.3.2.1 Sensitivity Analysis for Dilation Model Parameters ............................................ 289
7.4 Case Studies from the Couer D’Alene Mining District ..................................................... 292
7.4.1 Lucky Friday Mine – Silver Shaft ............................................................................... 292
7.4.2 Caladay Shaft .............................................................................................................. 297
7.5 Strain Localization In-Situ ................................................................................................. 300
7.5.1 Evidence of Irregular Strain Localization In-Situ ....................................................... 301
7.5.2 Modelling Brittle Strain Localization ......................................................................... 303
7.6 Conclusions ........................................................................................................................ 305
Chapter 8 A mine shaft case study on the accurate prediction of yield and displacements in
stressed ground using laboratory-derived material properties ..................................................... 307
8.1 Introduction ........................................................................................................................ 307
8.2 Rock and Rockmass Data .................................................................................................. 310
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8.2.1 Geotechnical Properties .............................................................................................. 311
8.2.2 Post-Yield Dilatancy ................................................................................................... 323
8.2.3 Extensometer Data ...................................................................................................... 330
8.3 Finite Difference Modelling .............................................................................................. 333
8.3.1 Analysis Using Laboratory Properties ........................................................................ 333
8.3.2 Sensitivity of Results to Finite Difference Grid Used ................................................ 341
8.3.3 Back Analysis to Optimize Rockmass Parameters ..................................................... 343
8.4 Non-uniqueness in Plasticity Models ................................................................................. 347
8.5 Summary and Conclusions ................................................................................................ 352
8.6 Appendix to Chapter 8 – Equations of the W-D Dilation Model ...................................... 353
Chapter 9 A Pillar Monitoring and Back Analysis Experiment at 2.4 km Depth in the Creighton
Mine, Sudbury, Canada................................................................................................................ 355
9.1 Introduction ........................................................................................................................ 355
9.2 Creighton Mine .................................................................................................................. 356
9.2.1 Study Area .................................................................................................................. 359
9.2.1.1 Mining Sequence ................................................................................................. 362
9.2.1.2 Mining Method .................................................................................................... 362
9.3 Monitoring Program........................................................................................................... 363
9.3.1 Results and Interpretation ........................................................................................... 364
9.4 Geomechanical Characterization ....................................................................................... 368
9.4.1 Post-Yield Dilatancy ................................................................................................... 372
9.5 Finite Difference Modelling .............................................................................................. 376
9.5.1 Modelling Philosophy ................................................................................................. 376
9.5.2 Mesh and Boundary Conditions .................................................................................. 380
9.5.3 Sequencing .................................................................................................................. 382
9.5.4 Elastic Calibration ....................................................................................................... 384
9.5.5 Modelling Brittle Pillar Behaviour ............................................................................. 388
9.5.5.1 Model Calibration ................................................................................................ 389
9.5.5.2 The Influence of Dilatancy on Pillar Yield .......................................................... 396
9.5.5.3 Linking Continuum Models to Progressive Pillar Yield Mechanisms ................. 398
9.5.5.4 Discussion ............................................................................................................ 407
9.6 Conclusions ........................................................................................................................ 408
9.7 Appendix to Chapter 9 – Equations of the W-D Dilation Model ...................................... 408
Chapter 10 Discussion and Conclusions ...................................................................................... 410
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