Kriging in Slope Reliability Analysis - Liu, Lei-Lei

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Résumé :

1 Introduction 1

1.1 Background 1

1.1.1 Uncertainties in slope engineering 1

1.1.2 Reliability analysis of slopes 3

1.1.3 Reliability-based design of slopes 4

1.1.4 Kriging in slope reliability analysis 5

1.2 Layout of the book 6

References 8

2 Overview of geostatistics and spatial sampling 11

2.1 Background of geostatistics 11

2.2 Review of geostatistics 11

2.3 Variogram and variogram modeling 13

2.3.1 Introduction of variogram 13

2.3.2 Modeling of variogram 14

2.4 Applications of geostatistics 17

2.5 Spatial sampling 19

References 21

3 Basic theory of Kriging 23

3.1 Introduction 23

3.2 Ordinary Kriging theory 24

3.3 Other types of Kriging 26

3.3.1 Simple Kriging 26

3.3.2 Universal Kriging 27

3.3.3 Co-Kriging 27

3.3.4 Disjunctive Kriging 28

3.3.5 Bayesian Kriging 29

3.4 Determination of model parameter 29

References 31

4 Application of Kriging in slope reliability analysis 33

4.1 Introduction 33

4.2 Reliability analysis of slopes 33

4.2.1 Slope stability analysis 33

4.2.2 Slope reliability analysis 35

4.2.3 Slope reliability considering parameter uncertainty 39

4.3 Kriging-based surrogate model 40

4.4 Kriging-based conditional random field modeling 41

References 43

5 Genetic algorithm-optimized Taylor Kriging surrogate model for system reliability analysis of soil slopes 47

5.1 Introduction 47

5.2 Kriging methodology 49

5.2.1 Classical Kriging theory 49

5.2.2 Theory of TK 50

5.3 GATK surrogate model 51

5.3.1 Genetic algorithm 51

5.3.2 GATK model 52

5.3.3 Analytical validation of GATK?example #1 53

5.3.4 Analytical validation of GATK?example #2 57

5.4 System reliability analysis using GATK surrogate model 59

5.5 Illustrative examples 59

5.5.1 A homogeneous c-? slope 60

5.5.2 A heterogeneous two-layered soil slope 64

5.6 Discussions 70

5.7 Conclusions 73

References 73

6 Adaptively selected-autocorrelation structure-based Kriging metamodel for slope reliability analysis 76

6.1 Introduction 76

6.2 The proposed GAWMK method 78

6.3 Implementation procedure of the proposed method for slope reliability analysis 80

6.4 Validation of the proposed method and the modified DACE toolbox 83

6.4.1 A one-dimensional cubic function 83

6.4.2 A three-dimensional data fitting problem 88

6.5 Applications to slope reliability analysis 90

6.5.1 Example 1: a homogeneous c-? slope 90

6.5.2 Example 2: a two-layered cohesive soil slope 96

6.5.3 Example 3: a three-layered cohesive soil slope 98

6.5.4 Example 4: a three-layered c-? slope 101

6.6 Summary and conclusions 102

References 104

7 System reliability analysis of soil slopes using an advanced Kriging metamodel and quasi Monte Carlo simulation 108

7.1 Introduction 108

7.2 Probabilistic analysis of soil slope stability using QMCS 111

7.3 Advanced Kriging metamodel 112

7.3.1 Genetic algorithm optimized Kriging 112

7.3.2 Construction of the advanced Kriging method 113

7.4 AKQMCS for system reliability analysis of soil slopes 116

7.5 Illustrative examples 119

7.5.1 Example #1: a two-layered cohesive slope 119

7.5.2 Example #2: a three-layered c-? slope 124

7.5.3 Example #3: a single-layered sand slope 129

7.6 Summary and conclusions 132

References 134