Efficient estimation of cumulative distribution functions of multiple failure modes using advanced generalized subset simulation

It is important to estimate the cumulative distribution function (CDF) of a failure mode in a geotechnical system, because failure of the mode is often characterized by some empirical and/or semi-empirical thresholds and geotechnical engineers sometimes might be interested in the probability of failure associated with various thresholds. The geotechnical systems also generally contain multiple failure modes. This requires an efficient estimation of cumulative distribution functions (CDFs) of multiple failure modes, which poses a significant challenge in application of conventional geotechnical reliability analysis methods. To address this challenge, this study proposes an advanced generalized subset simulation-based method (AGSS) to efficiently estimate the CDFs of multiple failure modes of the geotechnical system. The proposed method utilizes the probability weights of samples generated in each sample sub-space to efficiently estimate the CDFs, instead of using the conditional probability formula that may yield incorrect CDFs due to the sample "jumping" properties existing in generalized subset simulation (GSS). A cantilever retaining wall example and a parallel system example are employed to demonstrate the proposed method. It is found that the proposed method can effectively estimate the CDFs of multiple failure modes with high computational efficiency.