Non-intrusive Reliability Analysis of Multi-layered Slopes in Spatially Variable Soils

Stochastic finite element method and random finite element method can provide rigorous tools for slope reliability analysis incorporating spatial variability of soil properties. However, both of them are difficult to be applied into practice due to the modification of finite-element codes and the low efficiency, respectively. To address these problems, this paper develops a more practical approach called non-intrusive stochastic finite element method (NISFEM) for slope reliability analysis in spatially variable soils. In the NISFEM, the random fields of spatially variable soils are generated using Karhunen-Loeve expansion, and the safety factor of slope stability is calculated using commercial finite-element package. After that, the Hermite polynomial chaos expansion is used to express the safety factor explicitly for slope reliability analysis. In addition, this paper suggests an easy dimension reduction technique to further improve the efficiency of NISFEM, namely, to adopt a relatively small truncated ratio in Karhunen-Loeve expansion. The proposed method is illustrated and verified using a multi-layered soil slope example. Through the sensitivity study, it is found that the vertical spatial variability affects the slope failure probability and the sensitivity of uncertain soil properties significantly.