It is widely recognized that the uncertainties involved in geotechnical engineering are muchlarger than those in other disciplines such as structural engineering. The reliability theory isone of the most effective ways for modeling and assessing the effect of uncertainties in ageotechnical design, which has been the basis for the ongoing revision of many currentgeotechnical codes in Japan, Europe, Canada, and USA. There are two types of uncertaintiesin the geotechnical engineering, i.e., the uncertainties associated with input parameters,and the uncertainties associated with calculation models. Fundamental to geotechnicalreliability analysis is the knowledge about both parameter and model uncertainties. While thevariability of model input parameters have been studied extensively, how to determine themodel uncertainty has been considered as difficult for a long time.

As any model is only an abstraction of the real world, model uncertainty always exists. Ingeotechnical engineering, the model uncertainty could be large. Lack of knowledge about modeluncertainty may lead to unrealistic predictions. When back analysis from observed performances,model uncertainty is often mixed with parameter uncertainty and observational uncertainty. Hence itis generally difficult to isolate and characterize model uncertainty. This book introduces the state-of-the-art theories and methodologies for geotechnical model uncertainty characterization based on theBayesian theory, including both rigorous solution and approximate but practical solutions, where theeffects of parameter uncertainty and observational uncertainty on model uncertainty characterizationare appropriately addressed. The theories and methodologies are illustrated in detail with variousgeotechnical problems. The book will be of general interest to readers in the profession andparticularly useful for those specializing in geotechnical inverse analysis and geotechnical reliability.

Preface

Chapter 1 Introduction

 1.1 Background

 1.2 Objective and Scope

 1.3 Organization of the Book

Chapter 2 Literature Review

 2.1 Within-System Characterization

2.1.1 Least Square Method

2.1.2 Maximum Likelihood Method

2.1.3 Bayesian Method

2.1.4 Extended Bayesian Method

2.1.5 Model Comparison and Multi-model Inference

 2.2 Cross System Characterization

 2.3 Bayesian Method and Computational Techniques

2.3.1 Maximum Posterior Density Method

2.3.2 First order Second moment Bayesian Method (FSBM)

2.3.3 Laplace Method

2.3.4 System Identification Method

2.3.5 Sampling Based Methods

 2.4 Summary

Chapter 3 Bayesian Framework for Characterizing Model Uncertainty

 3.1 Parameter, Model, and Observation Uncertainties

 3.2 Bayesian Estimation of Model Uncertainty

3.2.1 Extension to Multiplicative Model Correction Factor

3.2.2 Extension to Censored Observed Data

3.2.3 Extension to Model Correction Functions

 3.3 Characteristics of Cross System Model Uncertainty Characterization

3.3.1 Role of Prior Information

3.3.2 Interpretation of Determined Model Uncertainty

 3.4 Assignment of Prior Uncertainties

3.4.1 General Guidelines for Determining f(xi)

3.4.2 Prior Distribution for Model Uncertainty Parameters

 3.5 Decision Involved in Model Uncertainty Characterization

3.5.1 Selection of Model Correction Factors

3.5.2 Use of Model Correction Function

 3.6 Prediction of System Responses

 3.7 Possible Solutions to the Bayesian Framework

 3.8 Summary

Chapter 4 Simplified Bayesian Framework for Characterizing Model Uncertainty

 4.1 Introduction

 4.2 Approximate Formulation for Characterizing Model Uncertainty

 4.3 Discussion of Prior Distributions on Model Uncertainty Parameters

 4.4 Characterizing Model Uncertainty based on the Approximate Formulation

4.4.1 Maximum Posterior Density Method

4.4.2 Grid Calculation Method

4.4.3 MCMC Simulation

 4.5 Comparison of Model Uncertainty Factors

4.5.1 Spreadsheet Method

4.5.2 Grid Calculation Method

 4.6 Approximate Prediction of System Response

 4.7 Extension to Model Correction Functions

 4.8 An Illustration Example

4.8.1 Background

4.8.2 Prior Knowledge in Model Uncertainty Parameters

4.8.3 Test Uncertainty

4.8.4 Calculation of μG(x) and σG(x)

4.8.5 Spreadsheet Implementation of the Maximum Posterior Method

4.8.6 Comparison of Methods for Model Uncertainty Characterization

 4.9 Summary

Chapter 5 Efficient Markov Chain for Identifying Geoteehnieal Model Uncertainty

 5.1 Introduction

 5.2 Study of Efficient Markov Chain for Characterizing Model Uncertainty

5.2.1 Markov Chains under Investigation

5.2.2 Comparison of Markov Chains

 5.3 Hybrid Markov Chain for Model Uncertainty Characterization in the Original Bayesian Framework

5.3.1 Structure of the Hybrid Markov Chain

5.3.2 Determination of the Jumping Functions

5.3.3 Check of Convergence

 5.4 Application to the Slope Stability Model Example

5.4.1 Performance of the Markov Chain

5.4.2 Check of Convergence

5.4.3 Posterior Distributions

5.4.4 Accuracy of Approximate Methods

 5.5 Extension to Model Correction Function Calibration

 5.6 Summary

Chapter 6 Probabilistic Back-Analysis of Slope Failure

 6.1 Introduction

 6.2 Further Study on Model Uncertainty of Limit Equilibrium Methods

6.2.1 Effect of Test Uncertainty

6.2.2 Effect of Quality of Test Data

6.2.3 Effect of Amount of Test Data

 6.3 Back Analysis of Slope Failure with Unknown Model Uncertainty

6.3.1 Bayesian Formulation

6.3.2 MCMC Simulation

6.3.3 Response Surface Approximation

6.3.4 Illustrative Example

 6.4 Back Analysis of Slope Failure with Known Model Uncertainty

6.4.1 Theory of Back Analysis with Known Model Uncertainty

6.4.2 Step-by-step Implementation

6.4.3 Reanalysis of Shek Kip Mei Landslide

 6.5 Summary

Chapter 7 Reliability Based Design of Pile Foundation

 7.1 Introduction

 7.2 Problem Description

 7.3 Model Uncertainty Characterization

7.3.1 Model Uncertainty Characterization Using Approximate Methods

7.3.2 Model Uncertainty Characterization in the Original Bayesian Framework

7.3.3 Comparison of Results

7.3.4 Effect of Data Censoring on Model Uncertainty Characterization

7.3.5 Role of Model Uncertainty in Pile Capacity Prediction

 7.4 Comparison of Probabilistic Models for Model Uncertainty

Characterization

7.4.1 Use of Additive Model Correction Factor

7.4.2 Use of Model Correction Functions

 7.5 Reliability Based Design of Pile Foundations

7.5.1 Design Point Method

7.5.2 Application to Pile Capacity Model

7.5.3 Adjustment in Consideration of Structural Codes

7.5.4 Regression Analyses of Partial Factors

 7.6 Reliability Based Design with Effective Stress Approach

 7.7 Comparison of the SPT Method and Effective Stress Method

 7.8 Summary

Chapter 8 Characterizing the Model Uncertainty of a Liquefaction Model

 8.1 Introduction

 8.2 Problem Description

8.2.1 Liquefaction Model under Investigation

8.2.2 Calibration Database

8.2.3 Parameter Uncertainty

 8.3 Determination of Model Uncertainty

8.3.1 Bayesian Formulation

8.3.2 Choice-based Sampling Bias

8.3.3 Prior Probabilistic Analysis of Liquefaction Data

8.3.4 Calibration Results

8.3.5 Role of Model Uncertainty in Liquefaction Potential Evaluation

8.3.6 Determination of Target Factor of Safety

 8.4 Summary

Appendix A

Appendix B

References