Geotechnical Reliability Analysis: Theories, Methods and Algorithms

✍ Scribed by Jie Zhang, Te Xiao, Jian Ji, Peng Zeng, Zijun Cao

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 323
• Category: Library

✦ Synopsis

This textbook systematically introduces the theories, methods, and algorithms for geotechnical reliability analysis. There are a lot of illustrative examples in the textbook such that readers can easily grasp the concepts and theories related to geotechnical reliability analysis. A unique feature of the textbook is that computer codes are also provided through carefully designed examples such that the methods and the algorithms described in the textbook can be easily understood. In addition, the computer codes are flexible and can be conveniently extended to analyze different types of realistic problems with little additional efforts.

✦ Table of Contents

Foreword
Preface
About This Book
Contents
About the Authors
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 Distribution
1.6.1 Covariance and Correlation Coefficient
1.6.2 Multivariate Normal Distribution
1.6.3 Multivariate Lognormal Distribution
1.7 Summary and Further Readings
References
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 AFORM 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 for System Reliability Analyses
2.4.2 Linearization Approach
2.5 Summary and Further Readings
References
3 Simulation-Based Methods
3.1 Random Sampling for 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
References
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
References
5 Spatial Variability of Soils
5.1 Modeling of Spatial Variability
5.1.1 Random Field Model
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-Loève 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
References
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 Load and Resistance Factor Design (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 Reliability Index
6.4 Full Probabilistic Design
6.4.1 General Design Framework
6.4.2 Direct MCS-Based Reliability-Based Design
6.4.3 Reliability-Based Design Using Subset Simulation
6.5 Robust Geotechnical Design
6.5.1 Concept of Robust Geotechnical Design
6.5.2 Measures of Design Robustness
6.5.3 Procedure for Implementing Robust Geotechnical Design
6.6 Method of Ratio of Safety Margin
6.7 Summary and Further Readings
References
7 Bayesian Methods
7.1 Concept of Bayesian Updating
7.1.1 Bayes’ Theorem for a Continuous Random Variable
7.1.2 Bayes’ Theorem for Multiple Random Variables
7.2 Conjugate Prior
7.2.1 Conjugate Priors for Normal Distributions
7.2.2 Misuse of Conjugate Distributions
7.3 Direct Integration Method
7.4 Maximum a Posterior Method
7.5 Markov Chain Monte Carlo Simulation
7.6 System Identification Method
7.6.1 System Identification Method for Linear Models
7.6.2 System Identification Method for Non-linear Models
7.7 Summary and Further Readings
References
Appendix MATLAB Script of AFORM Analysis of Example 2.8 Based on HLRF-x Algorithm