Modelling of spatial variability of soil undrained shear strength by conditional random fields for slope reliability analysis

Abstract Conditional random field model can make best use of limited site investigation data to properly characterize the spatial variation of soil properties. This paper aims to propose a simplified approach for generating conditional random fields of soil undrained shear strength. A numerical method is adopted to validate the effectiveness of the proposed approach. With the proposed approach, the analytical posterior statistics of spatially varying undrained shear strength conditioned on the known values at measurement locations can be obtained. The conditional random field model of undrained shear strength is constructed using the field vane shear test data at a site of the west side highway in New York and the probability of slope failure is estimated by subset simulation. A clay slope under undrained conditions is investigated as an example to illustrate the proposed approach. The effects of borehole location and borehole layout scheme on the slope reliability are addressed. The results indicate that the proposed approach not only can well incorporate the limited site investigation data into modelling of the actual spatial variation of soil parameters by conditional random fields, but also can capture the depth-dependent nature of soil properties. The realizations of conditional random fields generated by the proposed approach can be well constrained to the site investigation data.

[1]  Xueyou Li,et al.  Using Conditioned Random Field to Characterize the Variability of Geologic Profiles , 2016 .

[2]  G. Fenton.  Random Field Modeling of CPT Data , 2000 .

[3]  Iason Papaioannou,et al.  Bayesian analysis of rare events , 2016, J. Comput. Phys..

[4]  Iason Papaioannou,et al.  Learning soil parameters and updating geotechnical reliability estimates under spatial variability – theory and application to shallow foundations , 2017 .

[5]  Scott W. Sloan,et al.  Updating reliability of single piles and pile groups by load tests , 2016 .

[6]  Sung-Eun Cho,et al.  Effect of spatial variability of cross‐correlated soil properties on bearing capacity of strip footing , 2010 .

[7]  Iason Papaioannou,et al.  Bayesian Updating with Structural Reliability Methods , 2015 .

[8]  Dong Zheng,et al.  Embankment prediction using testing data and monitored behaviour: A Bayesian updating approach , 2018 .

[9]  G. Baecher.  Reliability and Statistics in Geotechnical Engineering , 2003 .

[10]  Hicks,et al.  Investigation of the reduction in uncertainty due to soil variability when conditioning a random field using Kriging , 2012 .

[11]  Lei-Lei Liu,et al.  Conditional random field reliability analysis of a cohesion-frictional slope , 2017 .

[12]  Iason Papaioannou,et al.  Bayesian inference with Subset Simulation: Strategies and improvements , 2018 .

[13]  Iason Papaioannou,et al.  Bayesian updating of slope reliability in spatially variable soils with in-situ measurements , 2018 .

[14]  D. V. Griffiths,et al.  Another look at the stability of slopes with linearly increasing undrained strength , 2015 .

[15]  A. Asaoka,et al.  Spatial variability of the undrained strength of clays : J Geotech Engng Div ASCE, V108, NGT5, May 1982, P743–756 , 1982 .

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

[17]  Y. Hoffman,et al.  Gaussian Fields and Constrained Simulations of the Large-Scale Structure , 2008 .

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

[19]  D. Cruden,et al.  Probabilistic slope stability analysis for practice , 2002 .

[20]  Iason Papaioannou,et al.  MCMC algorithms for Subset Simulation , 2015 .

[21]  Shui-Hua Jiang,et al.  Bayesian Updating of Slope Reliability in Undrained Clay with Vane Shear Test Data , 2017 .

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

[23]  Michael A. Hicks,et al.  Uncertainty reduction and sampling efficiency in slope designs using 3D conditional random fields , 2016 .

[24]  D. V. Griffiths,et al.  Determining an appropriate finite element size for modelling the strength of undrained random soils , 2015 .

[25]  Shui-Hua Jiang,et al.  Quantitative risk assessment of slope failure in 2-D spatially variable soils by limit equilibrium method , 2017 .

[26]  Shui-Hua Jiang,et al.  Efficient slope reliability analysis at low-probability levels in spatially variable soils , 2016 .

[27]  Michael L. Stein,et al.  Interpolation of spatial data , 1999 .

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

[29]  D. V. Griffiths,et al.  Probabilistic Stability Analysis of Slopes by Conditional Random Fields , 2017 .

[30]  Markus König,et al.  A probabilistic analysis of subsoil parameters uncertainty impacts on tunnel-induced ground movements with a back-analysis study , 2015 .

[31]  C. Juang,et al.  Probabilistic analysis of tunnel longitudinal performance based upon conditional random field simulation of soil properties , 2018 .

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

[33]  P. Lumb,et al.  Probabilistic design of slopes , 1987 .

[34]  Kok-Kwang Phoon,et al.  Evaluation of Geotechnical Property Variability , 1999 .

[35]  M. Lo,et al.  Probabilistic Analyses of Slopes and Footings with Spatially Variable Soils Considering Cross-Correlation and Conditioned Random Field , 2017 .

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

[37]  Mircea Grigoriu,et al.  Bayesian methods for characterizing unknown parameters of material models , 2016 .

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

[39]  Gordon A. Fenton,et al.  Influence of spatial variability on slope reliability using 2-D random fields. , 2009 .

[40]  Gregory B. Baecher,et al.  Estimating Autocovariance of In‐Situ Soil Properties , 1993 .

[41]  R. Rackwitz,et al.  Reviewing probabilistic soils modelling , 2000 .