Generation Of Multivariate Cross-correlated Geotechnical Random Fields

Abstract A geotechnical problem that involves several spatially correlated parameters can be best described using multivariate cross-correlated random fields. The joint distribution of these random variables cannot be uniquely defined using their marginal distributions and correlation coefficients alone. This paper presents a generic methodology for generating multivariate cross-correlated random fields. The joint distribution is rigorously established using a copula function that describes the dependence structure among the individual variables. The cross-correlated random fields are generated through Cholesky decomposition and conditional sampling based on the joint distribution. The random fields are verified regarding the anisotropic scales of fluctuation and copula parameters.

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

[2]  Jie Zhang,et al.  Optimization of site exploration program for improved prediction of tunneling-induced ground settlement in clays , 2014 .

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

[4]  George Deodatis,et al.  Effects of random heterogeneity of soil properties on bearing capacity , 2005 .

[5]  Dian-Qing Li,et al.  Bivariate distribution models using copulas for reliability analysis , 2013 .

[6]  Zhe Luo,et al.  Optimization of site investigation program for improved statistical characterization of geotechnical property based on random field theory , 2017, Bulletin of Engineering Geology and the Environment.

[7]  Abdul-Hamid Soubra,et al.  Probabilistic analysis and design at the ultimate limit state of obliquely loaded strip footings , 2010 .

[8]  D. McLaughlin,et al.  An efficient multivariate random field generator using the fast Fourier transform , 1998 .

[9]  William H. Press,et al.  Numerical Recipes 3rd Edition: The Art of Scientific Computing , 2007 .

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

[11]  Li Min Zhang,et al.  Characterizing geotechnical anisotropic spatial variations using random field theory , 2013 .

[12]  Dian-Qing Li,et al.  Performance of translation approach for modeling correlated non-normal variables , 2012 .

[13]  Abe Sklar,et al.  Random variables, joint distribution functions, and copulas , 1973, Kybernetika.

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

[15]  Tamara Al-Bittar,et al.  Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion , 2011 .

[16]  Li Min Zhang,et al.  Evaluating suction profile in a vegetated slope considering uncertainty in transpiration , 2015 .

[17]  Y. Xu,et al.  Field testing of erodibility of two landslide dams triggered by the 12 May Wenchuan earthquake , 2011 .

[18]  E. Vanmarcke.  Probabilistic Modeling of Soil Profiles , 1977 .

[19]  G. Fenton,et al.  Simulation of random fields via local average subdivision , 1990 .

[20]  Kok-Kwang Phoon,et al.  Random field characterisation of stress-normalised cone penetration testing parameters , 2005 .

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

[22]  C. Letchford,et al.  Simulation of Multivariate Stationary Gaussian Stochastic Processes: Hybrid Spectral Representation and Proper Orthogonal Decomposition Approach , 2005 .

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

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

[25]  Robert L. Mokwa,et al.  Investigation of the Resistance of Pile Caps to Lateral Loading , 1999 .

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

[27]  Li Min Zhang,et al.  Uncertainties in Geologic Profiles versus Variability in Pile Founding Depth , 2010 .

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

[29]  Gordon A. Fenton,et al.  Probabilistic Analysis of Coupled Soil Consolidation , 2010 .

[30]  Andrew Simon,et al.  Stream Bank Stability in Eastern Nebraska , 2003 .

[31]  D. V. Griffiths,et al.  Reliability analysis of beams on random elastic foundations , 2013 .

[32]  Alexander J. McNeil,et al.  Likelihood inference for Archimedean copulas in high dimensions under known margins , 2012, J. Multivar. Anal..

[33]  J. Ching,et al.  Simulating Spatial Averages of Stationary Random Field Using the Fourier Series Method , 2013 .

[34]  ChingJianye,et al.  Multivariate distribution for undrained shear strengths under various test procedures , 2013 .

[35]  S. Rice.  Mathematical analysis of random noise , 1944 .

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

[37]  Mark Cassidy,et al.  Probabilistic identification of soil stratification , 2016 .

[38]  H. Akaike.  A new look at the statistical model identification , 1974 .

[39]  M. E. Johnson,et al.  A Family of Distributions for Modelling Non‐Elliptically Symmetric Multivariate Data , 1981 .

[40]  Siu-Kui Au,et al.  Three-dimensional slope reliability and risk assessment using auxiliary random finite element method , 2016 .

[41]  T. Gneiting,et al.  Matérn Cross-Covariance Functions for Multivariate Random Fields , 2010 .

[42]  Dian-Qing Li,et al.  Bivariate simulation using copula and its application to probabilistic pile settlement analysis , 2013 .

[43]  Gordon A. Fenton,et al.  Estimation for Stochastic Soil Models , 1999 .

[44]  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.

[45]  M. Jaksa.  Discussion of Random Field Modeling of CPT Data by Gordon A. Fenton , 2000 .

[46]  S. M. Dasaka,et al.  Spatial variability of in situ weathered soil , 2012 .

[47]  Han-long Liu,et al.  Error Assessment for Spectral Representation Method in Random Field Simulation , 2012 .

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

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

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

[51]  G. Deodatis.  Simulation of Ergodic Multivariate Stochastic Processes , 1996 .

[52]  R. Nelsen.  An Introduction to Copulas , 1998 .

[53]  M. Shinozuka,et al.  Simulation of Stochastic Processes by Spectral Representation , 1991 .

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

[55]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .