Kriging in Slope Reliability Analysis

Cover
Half Title
Title
Copyright
Contents
1 Introduction
	1.1 Background
		1.1.1 Uncertainties in slope engineering
		1.1.2 Reliability analysis of slopes
		1.1.3 Reliability-based design of slopes
		1.1.4 Kriging in slope reliability analysis
	1.2 Layout of the book
	References
2 Overview of geostatistics and spatial sampling
	2.1 Background of geostatistics
	2.2 Review of geostatistics
	2.3 Variogram and variogram modeling
		2.3.1 Introduction of variogram
		2.3.2 Modeling of variogram
	2.4 Applications of geostatistics
	2.5 Spatial sampling
	References
3 Basic theory of Kriging
	3.1 Introduction
	3.2 Ordinary Kriging theory
	3.3 Other types of Kriging
		3.3.1 Simple Kriging
		3.3.2 Universal Kriging
		3.3.3 Co-Kriging
		3.3.4 Disjunctive Kriging
		3.3.5 Bayesian Kriging
	3.4 Determination of model parameter
	References
4 Application of Kriging in slope reliability analysis
	4.1 Introduction
	4.2 Reliability analysis of slopes
		4.2.1 Slope stability analysis
		4.2.2 Slope reliability analysis
		4.2.3 Slope reliability considering parameter uncertainty
	4.3 Kriging-based surrogate model
	4.4 Kriging-based conditional random field modeling
	References
5 Genetic algorithm-optimized Taylor Kriging surrogate model for system reliability analysis of soil slopes
	5.1 Introduction
	5.2 Kriging methodology
		5.2.1 Classical Kriging theory
		5.2.2 Theory of TK
	5.3 GATK surrogate model
		5.3.1 Genetic algorithm
		5.3.2 GATK model
		5.3.3 Analytical validation of GATK – example #1
		5.3.4 Analytical validation of GATK – example #2
	5.4 System reliability analysis using the GATK surrogate model
	5.5 Illustrative examples
		5.5.1 A homogeneous c–φ slope
		5.5.2 A heterogeneous two-layered soil slope
	5.6 Discussions
	5.7 Conclusions
	References
6 Adaptively selected-autocorrelation structure-based Kriging metamodel for slope reliability analysis
	6.1 Introduction
	6.2 The proposed GAWMK method
	6.3 Implementation procedure of the proposed method for slope reliability analysis
	6.4 Validation of the proposed method and the modified DACE toolbox
		6.4.1 A one-dimensional cubic function
		6.4.2 A three-dimensional data fitting problem
	6.5 Applications to slope reliability analysis
		6.5.1 Example 1: a homogeneous c–φ slope
		6.5.2 Example 2: a two-layered cohesive soil slope
		6.5.3 Example 3: a three-layered cohesive soil slope
		6.5.4 Example 4: a three-layered c–φ slope
	6.6 Summary and conclusions
	References
7 System reliability analysis of soil slopes using an advanced Kriging metamodel and quasi Monte Carlo simulation
	7.1 Introduction
	7.2 Probabilistic analysis of soil slope stability using QMCS
	7.3 Advanced Kriging metamodel
		7.3.1 Genetic algorithm optimized Kriging
		7.3.2 Construction of the advanced Kriging method
	7.4 AKQMCS for system reliability analysis of soil slopes
	7.5 Illustrative examples
		7.5.1 Example #1: a two-layered cohesive slope
		7.5.2 Example #2: a three-layered c–φ slope
		7.5.3 Example #3: a single-layered sand slope
	7.6 Summary and conclusions
	References
8 Efficient slope reliability analysis and risk assessment based on multiple Kriging surrogate models
	8.1 Introduction
	8.2 The proposed MK method for slope reliability analysis and risk assessment
		8.2.1 General idea of MK method
		8.2.2 Slope reliability analysis based on the proposed MK method
		8.2.3 Slope risk assessment based on the proposed MK method
	8.3 Implementation procedure of the proposed MK method
	8.4 Illustrative examples
		8.4.1 Example 1: a two-layered cohesive soil slope
		8.4.2 Example 2: Congress Street cut slope
	8.5 Discussions
	8.6 Conclusions
	References
9 A new active learning Kriging surrogate model for structural system reliability analysis with multiple failure modes
	9.1 Introduction
	9.2 The proposed ALK-SD method for system reliability analysis
		9.2.1 Basic idea of ALK-SD
		9.2.2 Identification of significant domain
		9.2.3 Determination of ATSs
		9.2.4 System reliability analysis based on ALK-SD
		9.2.5 Implementation procedure
	9.3 Numerical examples
		9.3.1 Example 1: a series system with four branches
		9.3.2 Example 2: a parallel system with three failure modes
		9.3.3 Example 3: a series system with three failure modes
		9.3.4 Example 4: a parallel system with disconnected failure regions
		9.3.5 Example 5: a mass gravity retaining wall with five random variables
	9.4 Discussion
		9.4.1 The determination of Φ (δ)
		9.4.2 Comparison with other U-function series methods
		9.4.3 Comparison of computational efficiency and robustness
		9.4.4 The locations of the ATSs
	9.5 Conclusion
	References
10 New Kriging methods for efficient system slope reliability analysis considering soil spatial variability
	10.1 Introduction
	10.2 Review of MK-based slope reliability analyses
	10.3 The proposed new Kriging methods
		10.3.1 Basic idea
		10.3.2 RALK method
		10.3.3 MK-RSS-SIR method
		10.3.4 MK-RSS method
	10.4 Example 1: a three-layered cohesive slope
		10.4.1 Results of RALK method
		10.4.2 Results of MK-RSS-SIR method
		10.4.3 Results of MK-RSS method
	10.5 Example 2: a four-layered slope with a soft band
		10.5.1 Results of RALK method
		10.5.2 Results of MK-RSS-SIR method
		10.5.3 Results of MK-RSS method
	10.6 Discussion
		10.6.1 Comparison of the computational accuracy
		10.6.2 Comparison of the computational efficiency
		10.6.3 Slope types applicable to three methods
	10.7 Summary and conclusions
	References
11 Conditional random field reliability analysis of a cohesion-frictional slope
	11.1 Introduction
	11.2 Simulation of unconditional random field
	11.3 Simulation of conditional random field
	11.4 Probabilistic analysis of a slope based on SS
	11.5 Implementation procedure of conditional probabilistic analysis
	11.6 Illustrative example
		11.6.1 Basic model
		11.6.2 Reliability results based on unconditional random fields
		11.6.3 Reliability results based on conditional random fields
	11.7 Summary and conclusions
	References
12 Reliability analysis and risk assessment of pile-reinforced slopes considering spatial soil variability and site investigation
	12.1 Introduction
	12.2 Simulation of soil spatial variability based on random field theory
		12.2.1 Conditional random field
		12.2.2 Conditional stationary random field based on investigation boreholes
	12.3 Probabilistic analysis of pile-reinforced slope
		12.3.1 Stability analysis of pile-reinforced slopes
		12.3.2 RFDM for slope reliability analysis and risk assessment
	12.4 Implementation procedure for the proposed framework
	12.5 Illustrative example
		12.5.1 Influence of investigation scheme on soil uncertainty
		12.5.2 Influence of investigation scheme on probabilistic characteristics of slope safety
		12.5.3 Influence of investigation scheme on slope failure probability and quantitative risk
		12.5.4 Influence of investigation scheme on pile structural responses
	12.6 Summary and conclusions
	References
13 Summary and concluding remarks
Index