关键词: 边坡稳定性, 有限元, 可靠度, 非侵入式随机有限元法, 随机多项式展开

Abstract: This paper aims at proposing a non-intrusive stochastic finite element method for reliability analysis of slope stability. A computer program for non-intrusive stochastic finite element method is developed. The non-intrusive stochastic analysis is achieved using the polynomial chaos expansion combined with SIGMA/W and SLOPE/W modules. The finite element method of sliding surface stress analysis is used to calculate the factor of safety of slope. The closed-form expressions of the first four statistical moments of factor of safety (mean, standard deviation, skewness, and kurtosis) and Sobol indices are provided using the coefficients of polynomial chaos expansion. A global parametric sensitivity analysis based on Sobol indices is carried out to identify input uncertain parameters that have the most contribution in the variability of factor of safety. An example of reliability analysis of homogeneous soil slope is presented to demonstrate the validity and capability of the proposed method. Also, a parametric study is performed to investigate the effect of variability and correlation of input parameters on the statistical moments of factor of safety and sensitivities of input random variables. The results indicate that the proposed non-intrusive stochastic finite element method can effectively evaluate slope reliability with a consideration of slope deformation. It is more efficient than the traditional Monte Carlo simulation method(MCS), which provides an effective way for reliability problem of complex slopes. The variability in shear strength parameters has a significant influence on the first four statistical moments, whereas the variability in unit weight almost has no influence on them. The mean value of factor of safety is slightly influenced by the negative correlation between shear strength parameters, whereas such negative correlation greatly influences the standard deviation, skewness, and kurtosis of factor of safety. The distribution of factor of safety is changed from approximate normal distribution to strong non-normal distribution as the negative correlation becomes stronger.

Key words: slope stability, finite elements, reliability, non-intrusive stochastic finite element method, polynomial chaos expansion