过去三、四十年间，地下洞室的设计计算方法取得长足进步。传统的确定性设计方法的一个不足是不能明确考虑岩体性质的随机性、原位应力场不确定性及工程的几何复杂性等。相比而言，不确定性的概率分析方法可弥补此缺陷。ZHANG Wengang著的《地下洞室群的概率风险评价（英文版）（精）》建立了单、双地下洞室的承载能力极限状态和正常使用极限状态预测模型，据此提出了一些简单实用的设计图表以供初步设计或安全评估。

ZHANG Wengang is Full Professor in School of Civil Engineering, ChongqingUniversity, China. He obtained his BSc and MSc degrees in Hohai University,China, as well as PhD degree in Nanyang Technological University, Singapore.He worked with Prof. Anthony Goh in NTU continuously as Project Officers,Research Student, Research Associate, and Research Fellow from 2009 to early2016. He joined Chongqing University as "Hundred Young Talent Researcher" inMay 2016 and later in 2017 he was awarded the "1000 Plan Professorship forYoung Talents". His research interests include probabilistic assessment of under-ground caverns, numerical modeling of deep braced excavation and reliability a-nalysis, big data and machine learning methods in geotechnical engineering. He isnow the members of International Society for Soil Mechanics and GeotechnicalEngineering (ISSMGE) Technical Committee TC304 Reliability and Tca09 Ma-chine Learning. Dr. Zhang acts as the Lead Guest Editor of Geoscience Frontierfor special issue of Reliability of Geotechnical Infrastructures.

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 εs
4.5.1 Modeling results of εs
4.5.2 Determination of εs using LR
4.5.3 Determination of εs using BPNN
4.5.4 Determination of εs 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 c