Geotechnical Reliability Analysis:Theories,Methods,and Algorithms（岩土工程可靠

如何考虑岩土工程的设计、施工和运营中存在大量的不确定性因素是岩土工程的关键难点之一，也是国内外岩土工程领域的研究热点。本教材系统讲述了岩土工程可靠度原理、方法和算法，包括概率基础、一阶可靠度算法、抽样方法、响应面方法、土体空间变异性、基于可靠度设计理论、贝叶斯方法等七章内容。教材包含大量的实例、算法和实现代码，可作为高年级本科生和研究生的教材，也可做为岩土工程和地质工程等相关从业人员的参考书。教材包含了岩土工程可靠度领域诸多学者（包括编者）的重要研究成果。

张洁，男，41岁，岩土工程专业，博士，同济大学教授、博士生导师，教育部长江学者青年学者，研究方向为岩土可靠度理论。本教材是作者多年教学及科研成果的总结。

Preface Chapter 1 Basics of Probability Theory 1.1 Set Theory 1.1.1 Elements of Set Theory 1.1.2 De Morgan's Rule 1.2 Conditional Probability 1.2.1 Axioms of Probability 1.2.2 Conditional Probability and Multiplication Rule 1.3 Total Probability Theorem 1.4 Discrete Random Variables 1.4.1 Bernoulli Sequence and Binomial Distribution 1.4.2 The Poisson Process and Poisson Distribution 1.5 Continuous Random Variables 1.5.1 Normal Distribution 1.5.2 Lognormal Distribution 1.6 Multivariate Distributions 1.6.1 Covariance and Correlation of Coefficient 1.6.2 Multivariate Normal Distribution 1.6.3 Multivariate Lognormal Distribution 1.7 Summary and Further Readings Chapter 2 First Order Reliability Methods 2.1 Concept of Geotechnical Reliability 2.2 Mean Value First Order Second Moment Method (MVFOSM) 2.3 Advanced First Order Reliability Method (AFORM) 2.3.1 Hasofer-Lind Reliability Index for Uncorrelated Normal Variables 2.3.2 AFORM for Uncorrelated Non-normal Variables 2.3.3 AFORM for Correlated Normal Variables 2.3.4 A.FORM for Correlated Non-normal Variables 2.3.5 EXCEL-Based AFORM 2.3.6 AFORM for Implicit Performance Function 2.4 System Reliability Analysis 2.4.1 Ditlevsen's Bounds 2.4.2 Linearization Approach 2.5 Summary and Further Readings Chapter 3 Simulation-based Methods 3.1 Random Sampling for an Univariate Variable 3.1.1 Inverse Transformation Method 3.1.2 Acceptance-rejection Method 3.1.3 Markov Chain Monte Carlo Simulation 3.2 Random Sampling for Multivariate Variables 3.2.1 Independent Variables 3.2.2 Correlated Normal Variables 3.2.3 Correlated Non-normal Variables 3.3 Monte Carlo Simulation 3.4 Latin Hypercube Sampling 3.5 Importance Sampling 3.6 Subset Simulation 3.7 Summary and Further Readings Chapter 4 Response Surface Methods 4.1 Classical Response Surface Method (RSM) 4.1.1 Calibration of a Second Order Polynomial Function 4.1.2 Reliability Analysis 4.1.3 Iterative RSM 4.2 Kriging-based RSM 4.2.1 Kriging Model 4.2.2 Determination of Experimental Points 4.2.3 Reliability Analysis 4.2.4 Active-learning Kriging Model 4.3 Support Vector Machine (SVM)-based RSM 4.3.1 SVM Model 4.3.2 Calibration of SVM and Reliability Analysis 4.3.3 Active-learning SVM 4.3.4 Application in Slope Reliability Analysis 4.4 Summary and Further Readings Chapter 5 Spatial Variability of Soils 5.1 Modeling of Spatial Variability 5.1.1 Random Field Modal 5.1.2 Spatial Averaging 5.2 Characterization of Spatial Variability 5.2.1 Mean-crossings Method 5.2.2 Method of Moments 5.2.3 Maximum Likelihood Estimation 5.3 Simulation of Random Fields 5.3.1 Covariance Matrix Decomposition 5.3.2 Karhunen-Love Expansion 5.3.3 Expansion Optimal Linear Estimation 5.3.4 Sequential Gaussian Simulation 5.4 Multidimensional and Multivariate Random Field 5.4.1 Spatial Correlation Modeling with Separable Correlation Functions 5.4.2 Simulation of Multidimensional Random Field 5.4.3 Simulation of Multivariate Random Field 5.5 Effects of Spatial Variability on Geotechnical Reliability 5.6 Summary and Further Readings Chapter 6 Reliability-based Design 6.1 Calibration of a Single Resistance Factor 6.1.1 Assessment of Reliability Level of an Existing Design 6.1.2 Calibration of Resistance Factor 6.2 Calibration of Multiple Resistance Factors 6.2.1 Design Point Method 6.3 Challenges in Implementation of LRFD in Geotechnical Engineering 6.3.1 Methods for Applying Partial Factors 6.3.2 Robustness of the Resistance Factors 6.3.3 Difficulties in Specifying the Characteristic Values 6.3.4 Selection of Target Relia