Active sparse polynomial chaos expansion for reliability analysis of underground structures considering the spatial variability of soil properties

Abstract

This paper proposes a reliability analysis method based on surrogate models to estimate the failure probability of geotechnical engineering structures under spatially varying soil properties. Although Monte Carlo simulation (MCS) provides accurate results, it requires many simulations, making the computational cost often unaffordable. The proposed method utilizes efficient sparse polynomial chaos expansion (SPCE) to approximate the limit state function of the structure. Bayesian inference techniques are introduced to consider the uncertainty caused by surrogate modeling, and a cluster of SPCE models is constructed using the Laplace approximation. The reliability is estimated by combining the clusters of surrogate models via MCS. Additionally, active learning techniques reduce the cost of building surrogate models, resulting in a new reliability analysis method based on active learning Bayesian sparse polynomial chaos expansion (AL-BSPCE). The effectiveness of the proposed method is validated through numerical analysis of a foundation under elastic soil and a subway station considering soil–structure interactions using the Karhunen–Loève (K-L) expansion method for random field discretization. Furthermore, the results obtained from the proposed method are compared and discussed with those from MCS, the active learning reliability method based on Kriging (AK-MCS), and the active bPCE-based reliability analysis (A-bPCE) methods. The proposed method shows promising potential in terms of accuracy and efficiency for the given case study, indicating its application prospects in the field of structural reliability analysis and optimization design.