An Efficient Solution for Reliability Analysis Considering Random Fields—Application to an Earth Dam

Performing a reliability analysis using Monte Carlo Simulation (MCS) is usually time-consuming for cases with expensive-to-evaluate deterministic models or small failure probabilities. The computational burden of such analysis can be significantly alleviated by replacing the deterministic model with a meta-model. However, the meta-modeling techniques suffer from the curse of dimensionality issue. They are thus less efficient for geotechnical reliability analyses involving random fields (RF) since the considered problems are often high dimensional due to the RF discretization. This paper introduces a new procedure based on the Sparse Polynomial Chaos Expansions (SPCE) which can address the above-mentioned issues. It deals with high dimensional stochastic problems in two stages: the first stage consists in reducing the input dimension by the Sliced Inverse Regression (SIR), while the second stage constructs a SPCE with respect to the reduced dimension and then performs an MCS. Additionally, an adaptive experimental design technique is proposed for the construction of the SPCE model. The modified algorithm (termed as A-SPCE/SIR) is applied to an earth dam problem in which the cohesion and friction angle are modelled by lognormal RFs. The effects of the vertical autocorrelation distance and the input cross-correlation on the dam reliability are investigated. The efficiency and accuracy of the A-SPCE/SIR are highlighted by comparing with the direct MCS and a previous study.