Three-dimensional slope reliability and risk assessment using auxiliary random finite element method

Abstract This paper aims to propose an auxiliary random finite element method (ARFEM) for efficient three-dimensional (3-D) slope reliability analysis and risk assessment considering spatial variability of soil properties. The ARFEM mainly consists of two steps: (1) preliminary analysis using a relatively coarse finite-element model and Subset Simulation, and (2) target analysis using a detailed finite-element model and response conditioning method. The 3-D spatial variability of soil properties is explicitly modeled using the expansion optimal linear estimation approach. A 3-D soil slope example is presented to demonstrate the validity of ARFEM. Finally, a sensitivity study is carried out to explore the effect of horizontal spatial variability. The results indicate that the proposed ARFEM not only provides reasonably accurate estimates of slope failure probability and risk, but also significantly reduces the computational effort at small probability levels. 3-D slope probabilistic analysis (including both 3-D slope stability analysis and 3-D spatial variability modeling) can reflect slope failure mechanism more realistically in terms of the shape, location and length of slip surface. Horizontal spatial variability can significantly influence the failure mode, reliability and risk of 3-D slopes, especially for long slopes with relatively strong horizontal spatial variability. These effects can be properly incorporated into 3-D slope reliability analysis and risk assessment using ARFEM.

[1]  Dian-Qing Li,et al.  Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables , 2011 .

[2]  Hong-Xin Chen,et al.  A physically-based multi-hazard risk assessment platform for regional rainfall-induced slope failures and debris flows , 2016 .

[3]  Yu WangY. Wang,et al.  Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet , 2011 .

[4]  Jianye Ching,et al.  Application of the transitional Markov chain Monte Carlo algorithm to probabilistic site characterization , 2016 .

[5]  K. Phoon,et al.  Characterization of Geotechnical Variability , 1999 .

[6]  Yu Wang,et al.  Bayesian model comparison and selection of spatial correlation functions for soil parameters , 2014 .

[7]  Dian-Qing Li,et al.  Quantification of prior knowledge in geotechnical site characterization , 2016 .

[8]  Dian-Qing Li,et al.  Evaluating slope stability uncertainty using coupled Markov chain , 2016 .

[9]  Siu-Kui Au,et al.  Augmenting approximate solutions for consistent reliability analysis , 2007 .

[10]  Yu Wang,et al.  Efficient Monte Carlo Simulation of parameter sensitivity in probabilistic slope stability analysis , 2010 .

[11]  Yu Wang,et al.  Bayesian perspective on geotechnical variability and site characterization , 2016 .

[12]  A. Kiureghian,et al.  OPTIMAL DISCRETIZATION OF RANDOM FIELDS , 1993 .

[13]  Erik H. Vanmarcke,et al.  Random Fields: Analysis and Synthesis. , 1985 .

[14]  Dian-Qing Li,et al.  A multiple response-surface method for slope reliability analysis considering spatial variability of soil properties , 2015 .

[15]  Michael A. Hicks,et al.  Influence of heterogeneity on 3D slope reliability and failure consequence , 2014 .

[16]  Jian Ji,et al.  Long embankment failure accounting for longitudinal spatial variation – A probabilistic study , 2014 .

[17]  D. V. Griffiths,et al.  Three-dimensional slope stability analysis by elasto-plastic finite elements , 2007 .

[18]  P. R. Vaughan.  Discussion: Three-dimensional slope stability analysis by elasto-plastic finite elements , 2008 .

[19]  G. Schuëller,et al.  Chair of Engineering Mechanics Ifm-publication 2-374 a Critical Appraisal of Reliability Estimation Procedures for High Dimensions , 2022 .

[20]  D. V. Griffiths,et al.  Quantitative risk assessment of landslide by limit analysis and random fields , 2013 .

[21]  Jian Ji,et al.  Stratified Response Surfaces for System Probabilistic Evaluation of Slopes , 2012 .

[22]  K. Phoon,et al.  Copula-based approaches for evaluating slope reliability under incomplete probability information , 2015 .

[23]  Miroslav Vořechovský,et al.  Simulation of simply cross correlated random fields by series expansion methods , 2008 .

[24]  A. Burls.  Critical appraisal , 2016, Australasian psychiatry : bulletin of Royal Australian and New Zealand College of Psychiatrists.

[25]  Michael A. Hicks,et al.  On the estimation of scale of fluctuation in geostatistics , 2014 .

[26]  Reza Jamshidi Chenari,et al.  Effects of anisotropy in correlation structure on the stability of an undrained clay slope , 2015 .

[27]  Dian-Qing Li,et al.  Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method , 2014 .

[28]  E. Vanmarcke.  Reliability of Earth Slopes , 1977 .

[29]  Wilson H. Tang,et al.  Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering , 2006 .

[30]  Dian-Qing Li,et al.  Response surface methods for slope reliability analysis: Review and comparison , 2016 .

[31]  D. V. Griffiths,et al.  SLOPE STABILITY ANALYSIS BY FINITE ELEMENTS , 1999 .

[32]  Chuangbing Zhou,et al.  Two-dimensional probabilistic infiltration analysis with a spatially varying permeability function , 2013 .

[33]  Michael A. Hicks,et al.  Influence of heterogeneity on the reliability and failure of a long 3D slope , 2010 .

[34]  Jian Ji.  A simplified approach for modeling spatial variability of undrained shear strength in out-plane failure mode of earth embankment , 2014 .

[35]  Wei Zhou,et al.  Bivariate distribution of shear strength parameters using copulas and its impact on geotechnical system reliability , 2015 .

[36]  E. Vanmarcke,et al.  Random Fields: Analysis and Synthesis (Revised and Expanded New Edition) , 2010 .

[37]  Andrew J. Whittle,et al.  Effect of spatial variability on the slope stability using Random Field Numerical Limit Analyses , 2016 .

[38]  Dian-Qing Li,et al.  Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using Subset Simulation , 2016, Landslides.

[39]  Dian-Qing Li,et al.  Efficient System Reliability Analysis of Slope Stability in Spatially Variable Soils Using Monte Carlo Simulation , 2015 .

[40]  Rong-Her Jimmy Chen,et al.  Three-Dimensional Slope Stability Analysis , 1981 .

[41]  Kok-Kwang Phoon,et al.  Effects of soil spatial variability on rainfall-induced landslides , 2011 .

[42]  Dian-Qing Li,et al.  Effect of spatially variable shear strength parameters with linearly increasing mean trend on reliability of infinite slopes , 2014 .

[43]  Gordon A. Fenton,et al.  On the reliability of earth slopes in three dimensions , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[44]  Guan Rong,et al.  Impact of copula selection on geotechnical reliability under incomplete probability information , 2013 .

[45]  Kok-Kwang Phoon,et al.  Risk and Reliability in Geotechnical Engineering , 2018 .

[46]  Fan Wang,et al.  Stochastic response surface method for reliability problems involving correlated multivariates with non-Gaussian dependence structure: Analysis under incomplete probability information , 2017 .

[47]  E. Vanmarcke,et al.  Risk of Limit-Equilibrium Failure of Long Earth Slopes: How It Depends on Length , 2011 .

[48]  J. Beck,et al.  Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation , 2001 .

[49]  Michael A. Hicks,et al.  Comparative analyses of slope reliability in 3D , 2015 .

[50]  Helmut J. Pradlwarter,et al.  Local Domain Monte Carlo Simulation , 2010 .

[51]  Gordon A. Fenton,et al.  Probabilistic slope stability analysis by finite elements , 2004 .

[52]  Siu-Kui Au,et al.  Engineering Risk Assessment with Subset Simulation , 2014 .

[53]  Yu Wang,et al.  Probabilistic slope stability analysis by risk aggregation , 2014 .

[54]  Dian-Qing Li,et al.  Efficient and consistent reliability analysis of soil slope stability using both limit equilibrium analysis and finite element analysis , 2016 .

[55]  Thi Minh Hue Le,et al.  Reliability of heterogeneous slopes with cross-correlated shear strength parameters , 2014 .