Statistical Modeling of Joint Probability Distribution using Copula: Application to Probabilistic Pile Settlement Analysis

Abstract eng:
A procedure for modelling the joint probability distribution of bivariate uncertain data with a nonlinear dependence structure is formulated in the copula theory framework. The dependence measures and copula theory are briefly introduced first. Thereafter, the measure of dependence is represented by the Kendall rank correlation coefficient. Then, the best-fit copula is identified by the Akaike information criterion. Finally, the load-test dataset of load-displacement curve of Augered Cast-In-Place (ACIP) piles is used to illustrate the proposed procedure. The results indicate that the proposed copula-based procedure can accurately model and simulate the bivariate probability distribution of two curve-fitting parameters associated with a hyperbolic load-displacement model. The Gaussian copula, often adopted out of expedience, may result in inaccurate modeling of the two hyperbolic curve-fitting parameters. The copula should be selected carefully to obtain realistic modeling of the joint probability distribution. The simulated load-displacement curves using the proposed procedure are found to be in good agreement with the measured results. A strong negative correlation and a nonlinear dependence between the two parameters can be observed. If such correlation is ignored, the scatter in the measured load-displacement curves cannot be simulated properly.

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