Effect of copula dependence structure on the failure modes of slopes in spatially variable soils

Abstract

The copula dependence structure underlying the correlated shear strength parameters of soils can significantly affect the results of slope reliability analysis and risk assessment of slope failure. Currently, how do copula dependence structures affect the failure modes of slopes in spatially variable soils still remains an open question. This study systematically investigates the effect of copula dependence structures on the failure modes of a cohesive-frictional slope in spatially variable soils via an adapted random finite difference method (RFDM) that incorporates the copula-based random fields. The proposed RFDM proceeds with the simulation of cross-correlated random fields considering the copula dependence between the shear strength parameters of the slope. The strength reduction analyses are then performed within the framework of Monte Carlo simulation to obtain the stability analysis results, including the critical slip surface (CSS) and associated factor of safety (FS) and sliding volume. Finally, various statistical analyses on the number and distribution of CSS, FS and sliding volume as well as the failure modes versus different statistics of soil properties are analyzed considering different dependence structures. The results show that the overall distribution range of CSS obtained by the commonly used Gaussian copula is more concentrated, whereas the result by the No. 16 copula is the widest. The differences in the overall distribution range of CSS among different copulas decrease with the increase of the scale of fluctuation, coefficient of variation, and cross-correlation coefficient of the strength parameters. The proportions of different failure modes are comparable for the Gaussian, Plackett and Fran copulas, whereas the No.16 copula has the smallest proportion for the shallow failure and largest proportions for the deep and multi-slip failures. The influence of copula dependence structure on the slope failure mode is more significant than the statistical parameters of soil properties. The results provide useful references for copula selection when the underlying dependence structure is difficult to be determined.