Reliability analysis of cutting slopes under rainfall conditions considering copula dependence between shear strengths

Slope reliability is of great importance in geotechnical engineering, and it is susceptible to various factors, such as slope cutting and rainfall. Currently, how the copula dependence structure affects the reliability of cutting slopes under rainfall conditions is still an open question. This study investigates the influence of copula dependence structure on the reliability analysis of a real slope, considering the slope cutting and rainfall characteristics (i.e., rainfall intensity, duration, and pattern). The Gaussian, Plackett, Frank, and No.16 copulas are first employed to model the joint probability distribution of the measured soil strength parameters. The optimal copula is subsequently identified using Akaike information criterion and Bayesian information criterion. The probability of failure (Pf) and the distribution of critical slip surface (CSS) for different slope cutting and rainfall conditions are then obtained within the framework of Monte Carlo simulation. The results show that the copula dependence between shear strengths has significant influence on the Pf for the cutting slope under rainfall conditions. The commonly used Gaussian copula may underestimate the Pf, while the No.16 copula would overestimate the Pf for different slope cutting angles and rainfall intensities, durations and patterns. The differences in Pf obtained by different copula functions decrease with the increase of cutting angle, cutting distance and rainfall intensity. Furthermore, the differences in Pf obtained by different copula functions show little variations with changes in rainfall duration and pattern. Although the copula function has a significant influence on the Pf, it has negligible influence on CSS. This study provides a practical tool for the selection of copula function and valuable insights for slope design and management under slope cutting and rainfall conditions.