Kriging in Slope Reliability Analysis

Lei-Lei Liu is an associate professor in the Department of Geological Engineering at Central South University, China. He is the co-author of Analysis, Design, and Construction of Foundations, also published by CRC Press.Jing-Ze Li is a research associate at Central South University, China. His PhD research was undertaken jointly with Central South University, China and Université Grenoble Alpes, France.Lei Huang is an associate professor at Sanming University, China. He received his PhD in The Hong Kong Polytechnic University.

• 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 334.1 Introduction 334.2 Reliability analysis of slopes 334.2.1 Slope stability analysis 334.2.2 Slope reliability analysis 354.2.3 Slope reliability considering parameter uncertainty 394.3 Kriging-based surrogate model 404.4 Kriging-based conditional random field modeling 41References 435 Genetic algorithm-optimized Taylor Kriging surrogate model for system reliability analysis of soil slopes 475.1 Introduction 475.2 Kriging methodology 495.2.1 Classical Kriging theory 495.2.2 Theory of TK 505.3 GATK surrogate model 515.3.1 Genetic algorithm 515.3.2 GATK model 525.3.3 Analytical validation of GATK−example #1 535.3.4 Analytical validation of GATK−example #2 575.4 System reliability analysis using GATK surrogate model 595.5 Illustrative examples 595.5.1 A homogeneous c–ϕ slope 605.5.2 A heterogeneous two-layered soil slope 645.6 Discussions 705.7 Conclusions 73References 736 Adaptively selected-autocorrelation structure-based Kriging metamodel for slope reliability analysis 766.1 Introduction 766.2 The proposed GAWMK method 786.3 Implementation procedure of the proposed method for slope reliability analysis 806.4 Validation of the proposed method and the modified DACE toolbox 836.4.1 A one-dimensional cubic function 836.4.2 A three-dimensional data fitting problem 886.5 Applications to slope reliability analysis 906.5.1 Example 1: a homogeneous c–ϕ slope 906.5.2 Example 2: a two-layered cohesive soil slope 966.5.3 Example 3: a three-layered cohesive soil slope 986.5.4 Example 4: a three-layered c–ϕ slope 1016.6 Summary and conclusions 102References 1047 System reliability analysis of soil slopes using an advanced Kriging metamodel and quasi Monte Carlo simulation 1087.1 Introduction 1087.2 Probabilistic analysis of soil slope stability using QMCS 1117.3 Advanced Kriging metamodel 1127.3.1 Genetic algorithm optimized Kriging 1127.3.2 Construction of the advanced Kriging method 1137.4 AKQMCS for system reliability analysis of soil slopes 1167.5 Illustrative examples 1197.5.1 Example #1: a two-layered cohesive slope 1197.5.2 Example #2: a three-layered c–ϕ slope 1247.5.3 Example #3: a single-layered sand slope 1297.6 Summary and conclusions 132References 1348 Efficient slope reliability analysis and risk assessment based on multiple Kriging surrogate models 1388.1 Introduction 1388.2 The proposed MK method for slope reliability analysis and risk assessment 1408.2.1 General idea of MK method 1408.2.2 Slope reliability analysis based on the proposed MK method 1428.2.3 Slope risk assessment based on the proposed MK method 1448.3 Implementation procedure of the proposed MK method 1458.4 Illustrative examples 1478.4.1 Example 1: a two-layered cohesive soil slope 1488.4.2 Example 2: Congress Street cut slope 1538.5 Discussions 1588.6 Conclusions 160References 1619 A new active learning Kriging surrogate model for structural system reliability analysis with multiple failure modes 1659.1 Introduction 1659.2 The proposed ALK-SD method for system reliability analysis 1679.2.1 Basic idea of ALK-SD 1679.2.2 Identification of significant domain 1699.2.3 Determination of ATSs 1739.2.4 System reliability analysis based on ALK-SD 1749.2.5 Implementation procedure 1759.3 Numerical examples 1779.3.1 Example 1: a series system with four branches 1779.3.2 Example 2: a parallel system with three failure modes 1819.3.3 Example 3: a series system with three failure modes 1829.3.4 Example 4: a parallel system with disconnected failure regions 1869.3.5 Example 5: a mass gravity retaining wall with five random variables 1879.4 Discussion 1929.4.1 The determination of Φ(δ) 1929.4.2 Comparison with other U-function series methods 1949.4.3 Comparison of the computational efficiency and robustness 1959.4.4 The locations of the ATSs 1979.5 Conclusion 199References 20210 New Kriging methods for efficient system slope reliability analysis considering soil spatial variability 20510.1 Introduction 20510.2 Review of MK-based slope reliability analyses 20810.3 The proposed new Kriging methods 20810.3.1 Basic idea 20810.3.2 RALK method 20910.3.3 MK-RSS-SIR method 21810.3.4 MK-RSS method 21810.4 Example 1: a three-layered cohesive slope 21810.4.1 Results of RALK method 22010.4.2 Results of MK-RSS-SIR method 23110.4.3 Results of MK-RSS method 23410.5 Example 2: a four-layered slope with a soft band 23610.5.1 Results of RALK method 23910.5.2 Results of MK-RSS-SIR method 24110.5.3 Results of MK-RSS method 24310.6 Discussion 24410.6.1 Comparison of the computational accuracy 24410.6.2 Comparison of the computational efficiency 24510.6.3 Slope types applicable to three methods 24610.7 Summary and conclusions 247References 24911 Conditional random field reliability analysis of a cohesion-frictional slope 25511.1 Introduction 25511.2 Simulation of unconditional random field 25711.3 Simulation of conditional random field 26011.4 Probabilistic analysis of a slope based on SS 26211.5 Implementation procedure of conditional probabilistic analysis 26411.6 Illustrative example 26711.6.1 Basic model 26711.6.2 Reliability results based on unconditional random fields 26811.6.3 Reliability results based on conditional random fields 27011.7 Summary and conclusions 280References 28312 Reliability analysis and risk assessment of pile-reinforced slopes considering spatial soil variability and site investigation 28612.1 Introduction 28612.2 Simulation of soil spatial variability based on random field theory 28812.2.1 Conditional random field 28812.2.2 Conditional stationary random field based on investigation boreholes 28912.3 Probabilistic analysis of pile-reinforced slope 29112.3.1 Stability analysis of pile-reinforced slopes 29112.3.2 RFDM for slope reliability analysis and risk assessment 29412.4 Implementation procedure for the proposed framework 29512.5 Illustrative example 29712.5.1 Influence of investigation scheme on soil uncertainty 30112.5.2 Influence of investigation scheme on probabilistic characteristics of slope safety 30512.5.3 Influence of investigation scheme on slope failure probability and quantitative risk 31112.5.4 Influence of investigation scheme on pile structural responses 31312.6 Summary and conclusions 316References 31713 Summary and concluding remarks 321Index 323