Practical copula-based FORM for efficient slope reliability analysis involving correlated non-normal variables

This study develops a practical copula-based FORM in an original physical space for an efficient slope reliability analysis involving correlated non-normal variables. First, the copula theory for modeling the joint probability distribution of cohesion and friction angle of soils is briefly introduced. Second, the traditional expanding dispersion ellipse perspective of the FORM is reviewed. Then, a new expanding dispersion contour perspective of the copula-based FORM is formulated in detail. Finally, two illustrative slope examples are presented to illustrate and demonstrate the developed copula-based FORM and its expanding dispersion contour perspective. The results indicate that the developed copula-based FORM has good accuracy and efficiency in deriving the reliability index and design point for a typical slope reliability problem. It operates in an original physical space and thus is suitable for a complex slope reliability problem with an implicit performance function. The copulas for characterizing various dependence structures between the cohesion and friction angle of soils have a significant impact on slope reliability index, especially under a high reliability level and a strong degree of negative correlation. The proposed expanding dispersion contour perspective facilitates the understanding of the copulabased FORM, which can readily explain the slope reliability results produced by various copulas. The derived design points are obtained by simultaneously considering the marginal distributions, correlation as well as various non-Gaussian dependence structures of soil parameters.