Uncertainty analysis of correlated non-normal geotechnical parameters using Gaussian copula

Abstract

Determining the joint probability distribution of correlated non-normal geotechnical parameters based on incomplete statistical data is a challenging problem. This paper proposes a Gaussian copula-based method for modelling the joint probability distribution of bivariate uncertain data. First, the concepts of Pearson and Kendall correlation coefficients are presented, and the copula theory is briefly introduced. Thereafter, a Pearson method and a Kendall method are developed to determine the copula parameter underlying Gaussian copula. Second, these two methods are compared in computational efficiency, applicability, and capability of fitting data. Finally, four load-test datasets of load-displacement curves of piles are used to illustrate the proposed method. The results indicate that the proposed Gaussian copula-based method can not only characterize the correlation between geotechnical parameters, but also construct the joint probability distribution function of correlated non-normal geotechnical parameters in a more general way. It can serve as a general tool to construct the joint probability distribution of correlated geotechnical parameters based on incomplete data. The Gaussian copula using the Kendall method is superior to that using the Pearson method, which should be recommended for modelling and simulating the joint probability distribution of correlated geotechnical parameters. There exists a strong negative correlation between the two parameters underlying load-displacement curves. Neglecting such correlation will not capture the scatter in the measured load-displacement curves. These results substantially extend the application of the copula theory to multivariate simulation in geotechnical engineering.