边坡可靠度分析的非侵入式随机有限元法

Reliability analysis of slope using non-intrusive stochastic finite element method

提出基于非侵入式随机有限元法的边坡可靠度分析方法,并编写计算程序NISFEM。采用有限元滑面应力法计算边坡安全系数,将Hermite随机多项式展开与SIGMA/W和SLOPE/W模块有机结合实现边坡可靠度非侵入式随机分析。根据随机多项式展开系数,给出边坡安全系数前4阶统计矩(均值、标准差、偏度和峰度)和Sobol指标解析表达式,并采用Sobol指标进行边坡可靠度参数敏感性分析。最后,以均质土坡可靠度问题为例,证明该方法在边坡可靠度分析中的有效性。结果表明,边坡可靠度分析的非侵入式随机有限元法能够有效地考虑边坡变形对边坡可靠度的影响,计算效率远远高于蒙特卡罗模拟方法(MCS),是解决复杂边坡可靠度问题一种有效地分析手段;黏聚力和内摩擦角变异性对边坡安全系数前四阶统计矩具有明显的影响,重度变异性对安全系数前4阶统计矩几乎没有影响;抗剪强度参数间负相关性对边坡安全系数均值几乎没有影响,但对安全系数标准差、偏度和峰度均有明显的影响。此外,随着抗剪强度参数间负相关性的增加,边坡安全系数由近似正态分布逐渐变为明显的非正态分布。

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.