Bivariate simulation using copula and its application to probabilistic pile settlement analysis

International Journal for Numerical and Analytical Methods in Geomechanics - Tập 37 Số 6 - Trang 597-617 - 2013
Dian‐Qing Li1, Xiao‐Song Tang1, Kok‐Kwang Phoon2, Yi‐Feng Chen1, Chuangbing Zhou1
1State Key Laboratory of Water Resources and Hydropower Engineering Science , Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering (Ministry of Education), Wuhan University , 8 Donghu South Road, Wuhan , 430072 , P.R. China
2Department of Civil and Environmental Engineering National University of Singapore Blk E1A, #07‐03, 1 Engineering Drive 2 Singapore 117576

Tóm tắt

SUMMARYThis paper aims to propose a procedure for modeling the joint probability distribution of bivariate uncertain data with a nonlinear dependence structure. First, the concept of dependence measures is briefly introduced. Then, both the Akaike Information Criterion and the Bayesian Information Criterion are adopted for identifying the best‐fit copula. Thereafter, simulation of copulas and bivariate distributions based on Monte Carlo simulation are presented. Practical application for serviceability limit state reliability analysis of piles is conducted. Finally, four load–test datasets of load–displacement curves of piles are used to illustrate the proposed procedure. The results indicate that the proposed copula‐based procedure can model and simulate the bivariate probability distribution of two curve‐fitting parameters underlying the load–displacement models of piles in a more general way. The simulated load–displacement curves using the proposed procedure are found to be in good agreement with the measured results. In most cases, the Gaussian copula, often adopted out of expedience without proper validation, is not the best‐fit copula for modeling the dependence structure underlying two curve‐fitting parameters. The conditional probability density functions obtained from the Gaussian copula differ considerably from those obtained from the best‐fit copula. The probabilities of failure associated with the Gaussian copula are significantly smaller than the reference solutions, which are very unconservative for pile safety assessment. If the strong negative correlation between the two curve‐fitting parameters is ignored, the scatter in the measured load–displacement curves cannot be simulated properly, and the probabilities of failure will be highly overestimated. Copyright © 2011 John Wiley & Sons, Ltd.

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International Journal for Numerical and Analytical Methods in Geomechanics

Tập 37 Số 6

597-617

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