Reliability analysis of slopes with incomplete probability information

Reliability analysis of slopes with incomplete probability information is a challenging problem. This paper aims to propose Copula-based methods for the reliability analysis of slopes with incomplete probability information. First, the method for constructing the joint probability distribution of shear strength parameters using Copulas is briefly introduced. Thereafter, the concept of nominal factor of safety for slope stability analysis is defined. The dispersion of probability of slope failure is derived. Finally, an example of reliability analysis for an infinite slope is presented to demonstrate the capability and validity of the proposed methods. The results indicate that the probability of slope failure can not be determined uniquely based on the incomplete probability information of shear strength parameters. The probabilities of slope failure produced by different Copulas can differ considerably. Such differences directly lead to large dispersion of probability of slope failure. The dispersion of probability of slope failure increases with increasing nominal factor of slope safety, and it increases with decreasing probability of slope failure. The proposed three Copula-based methods can narrow the dispersion of probability of slope failure effectively, which can improve the reliability estimation of slopes efficiently. These methods provide an effective tool for the reliability analysis of slope failure with incomplete probability information.