Reliability Analysis of Seismic Slope Stability with Uncertain Probability Distributions

The probability density function or cumulative distribution function of shear strength parameters is commonly unknown, and the first-order reliability method, second-order reliability method, and Monte Carlo simulation cannot be applied. Considering this challenge, a method to calculate the failure probabilities of two- and three-dimensional seismic slopes based on the fourth-moment normal transformation (FMNT) is proposed in this study. Moreover, there is a well-known negative correlation among shear strength parameters, which is commonly neglected in reliability analyses. Generally, only the marginal distributions and correlation coefficients of variables are known. In this case, the FMNT is no longer applicable. Therefore, a copula-based sampling method (CBSM) was proposed to construct the negative correlation among the shear strength parameters in this study. The effects of different probability distributions of shear strength parameters on the failure probabilities were investigated by CBSM and FMNT for seismic slope stability in this study. Two study cases were addressed to investigate the difference in reliability analysis of seismic slopes between CBSM and FMNT.