Preface About the author Foreword Contents List of Tables List of Figures List of Symbols and Abbreviations Chapter 1 INTRODUCTION 1.1 Background 1.2 Objectives and scope of this book 1.3 Outline of this book Chapter 2 LITERATURE REVIEW 2.1 Introduction 2.2 Tools and design methods for underground rock caverns 2.2.1 Empirical methods 2.2.2 Observational methods 2.2.3 Physical modeling 2.2.4 Analytical solutions 2.2.5 Numerical modeling 2.2.6 A short critical review 2.3 Variability of geotechnical parameters in cavern design 2.3.1 Distribution types 2.3.2 Quantifying uncertainties in rock properties 2.4 Basic probabilistic analysis concepts 2.4.1 Factor of safety and limitations 2.4.2 Limit states 2.4.3 Probabilistic approaches 2.5 Rock failure criteria 2.6 Review of approaches to obtain limit state functions 2.6.1 Polynomial regression or logarithmic regression (LR) 2.6.2 Response surface method (RSM) 2.6.3 Artificial neural network (ANN) 2.6.4 Multivariate adaptive regression splines (MARS) 2.6.5 A short critical review 2.7 Review of probabilistic assessment methods 2.7.1 First-Order Reliability Methods (FORM) 2.7.2 Second Order Reliability Methods (SORM) 2.7.3 Monte Carlo Simulation (MCS) 2.7.4 Point Estimate Method (PEM) 2.7.5 Hybrid methods 2.7.6 System reliability 2.7.7 A short critical review 2.8 Concluding remarks Chapter 3 RELIABILITY ASSESSMENT ON ULTIMATE LIMIT STATE OF A SINGLE CAVERN 3.1 Introduction 3.2 Previous studies 3.3 Numerical modeling 3.3.1 Assumptions 3.3.2 Cross-section and boundary conditions 3.3.3 Ranges of design parameters and mechanical inputs 3.4 Modeling results and analyses of FSg_s 3.4.1 Failure mechanism 3.4.2 Modeling results of FSg_s 3.4.3 Determination of FSg_s using LR 3.4.4 Design curves of FSg_s 3.4.5 Predictions of FSg_s using BPNN 3.4.6 Predictions of FSg_s using MARS 3.4.7 Comparisons between BPNN and MARS 3.5 Probabilistic assessments on ULS 3.5.1 MCS_LR, MCS_BPNN and MCS_MARS 3.5.2 FORM_LR, FORM_BPNN and FORMMARS 3.5.3 Comparisons between probabilistic assessment methods 3.6 Concluding remarks Chapter 4 RELIABILITY ASSESSMENT ON SERVICEABILITYLIMIT STATE AND SYSTEM RELIABILITY OF A SINGLE CAVERN 4.1 Introduction 4.2 Previous studies on cavern deformations 4.3 Numerical modeling and displacement 4.4 Modeling results and analyses of Umax_s 4.4.1 Modeling results of Umax_s 4.4.2 Determination of using LR 4.4.3 Determination of Umax_s using BPNN 4.4.4 Determination of Umax_s using MARS 4.4.5 Comparisons between BPNN and MARS 4.5 Modeling results and analyses of the percent strain ��s 4.5.1 Modeling results of ��s 4.5.2 Determination of ��s using LR 4.5.3 Determination of ��s using BPNN 4.5.4 Determination of ��s using MARS 4.5.5 Comparisons between BPNN and MARS 4.6 Probabilistic assessments on SLS 4.6.1 Serviceability criterion 4.6.2 Threshold strain values 4.6.3 Comparisons between probabilistic assessment methods 4.7 System reliability 4.8 Concluding remarks Chapter 5 RELIABILITY ASSESSMENT ON ULTIMATE LIMIT STATE OF TWIN CAVERNS 5.1 Introduction 5.2 Previous studies 5.3 Numerical modeling 5.3.1 Assumptions of numerical analysis 5.3.2 Cross-section layout 5.3.3 Ranges of design parameters 5.4 Modeling results and analyses 5.4.1 Modeling results of FSg_t 5.4.2 Determination of FSg_t using LR 5.4.3 Determination of FSg_t using MARS 5.4.4 Design curves of FSg_t 5.5 Failure mechanism of twin caverns 5.5.1 Failure mechanisms of pillars 5.5.2 Maximum principal stress in pillar 5.5.3 Vertical stress in pillar core 5.5.4 Principal stress difference in pillar core 5.5.5 ANN Model for determining overlap of the plastic zones 5.5.6 Ratio of shear strength to shear stress ��f/�� 5.5.7 Average pillar strength and pillar stress calculation 5.6 Probabilistic assessments on ULS 5.7 Concluding remarks Chapter 6 RELIABILITY ASSESSMENT ON SERVICEABILITY LIMIT STATE AND SYSTEM RELIABILITY OF TWIN CAVERNS 6.1 Introduction 6.2 Numerical modeling and the dependent responses 6.3 Modeling results and analyses of Umax_t 6.3.1 Modeling results of Umax_t 6.3.2 Influences of overlap of the plastic zones on cavern displacements 6.3.3 Determination of Umax_t using MARS 6.4 Modeling results and analyses of ��t 6.4.1 Modeling results of ��t 6.4.2 Influences of overlap of the plastic zones on the percent strains 6.4.3 Determination of st using MARS 6.5 Probabilistic assessments on SLS 6.5.1 Serviceability criterion 6.5.2 Threshold strain values 6.5.3 Comparisons between probabilistic assessment methods 6.6 System reliability 6.7 Concluding remarks Chapter 7 A CASE STUDY:EVALUATING STABILITY OF UNDERGROUND ENTRY-TYPE EXCAVATIONS USING MULTIVARIATE ADAPTIVE REGRESSION SPLINES AND LOGISTIC REGRESSION 7.1 Overview of this chapter 7.2 Background 7.3 Critical span graph 7.4 MARS_LR approach 7.4.1 LR method 7.4.2 Modeling accuracy 7.5 The database and MARS_LR modeling results 7.5.1 The database 7.5.2 MARS_LR model and modeling results 7.6 Summary Chapter 8 CONCLUSIONS AND RECOMMENDATIONS 8.1 Summary and conclusions 8.1.1 Estimation of Mohr-Coulomb parameters from empirical equations 8.1.2 Prediction of cavern(s) performances in terms of design limit states 8.1.3 Surrogate models and design charts for performance predictions of cavern(s) 8.1.4 Approaches of developing surrogate models 8.1.5 Failure mechanism interpreted in terms of pillar performance 8.1.6 Framework incorporating limit state functions into reliability assessment methods to perform reliability analysis 8.1.7 A rational and practical approach to ensure the system reliability 8.1.8 A case study illustrating the MARS_LR use in evaluating stability of underground entry-type excavations 8.2 Recommendations for future work References Table of Contents for the Appendices Appendix A MATLAB BP algorithm adopted for the BPNN models Appendix B MARS algorithms adopted for the built models using MATLAB Appendix C Training data results of FSg_s for BPNN and MARS Appendix D Procedures for partitioning of BPNN weights for FSg_s of single cavern Appendix E Calculation of BPNN output FSg_s Appendix F Training data results of Umax_s for BPNN Appendix G Training data results of Umax_s for MARS and relative error Appendix H Procedures for partitioning of BPNN weights for Umax_s Appendix I Calculation of BPNN output Umax_s Appendix J Training data results of ��s for BPNN Appendix K Training data results of ��s for MARS and relative error Appendix L Procedures for partitioning of BPNN weights for ��s Appendix M Calculation of BPNN output ��s Appendix N Training data results of FSg_t for MARS and relative error Appendix O Training data results of H(X) for BPNN Appendix P Procedures for partitioning of BPNN weights for H(X) Appendix Q Calculation of BPNN output H(X) Appendix R Training data results of Umax_t for MARS Appendix S Training data results of et for MARS