A non-parametric copula approach to dependence modelling of shear strength parameters and its implications for geotechnical reliability under incomplete probability information

Abstract

This paper aims to evaluate the potential of the non-parametric copula approach to dependence modelling of shear strength parameters and address the problem of copula selection for geotechnical reliability under incomplete probability information. The optimal non-parametric copula is determined by truncating the basis functions in the kernel according to the Akaike information criterion and Bayesian information criterion. The fitting of copulas to the same dataset shows that the non-parametric approach generally gives better copula models. As the non-parametric copula maximizes its relative entropy (Kullback–Leibler divergence) with respect to the independence copula subject to given constraints, the approximated copula should be the best model according to the principle of maximum entropy. The interpretation of the incomplete probability information as constraints on the expectation of a basis function is later provided, and the non-parametric copula approach is applied to solve two geotechnical reliability problems under incomplete probability information. By measuring the relative entropy of the copulas, the best reliability result and reliability-based design under incomplete probability information can be selected. The comparison between the parametric and non-parametric copula shows that the non-parametric copula almost always encodes the minimum dependence information in the context of given probability information.