黄土边坡可靠度的随机有限元分析

为了研究黄土边坡的可靠度，在对黄土强度参数进行变异性统计、概率分布检验及垂直向自相关距离计算的基础上，将黄土强度参数黏聚力和内摩擦角作为随机变量，将其在二维边坡剖面的空间变化作为随机场，用局部平均细分法将符合一定均值和标准差的强度参数按随机场分布在边坡剖面的有限元网格上，再采用弹-理想塑性有限元计算边坡稳定系数，用Monte-Carlo法计算其失效概率。结果表明:黄土黏聚力的变异系数多在0.30以上，内摩擦角的变异系数多在0.20以下，且黄土高原从西向东两个参数的变异性都增大；黏聚力和内摩擦角的概率分布类型对边坡失效概率计算结果影响显著，统计检验发现黏聚力采用对数正态分布、内摩擦角采用正态分布为宜；黄土地层的垂直向自相关距离多在0.7 m以内，与计算厚度的比值多小于0.2；在大部分黄土的变异系数与自相关距离水平下，采用确定场进行可靠度分析，多数情况将极大地高估了黄土边坡的失效概率，而在极端高变异系数水平下，采用确定场进行可靠度分析，又将极大地低估其失效概率。

Random Finite Element Analysis for the Reliability of Loess Slopes

In order to study the reliability of loess slopes, the variability and probability distribution characteristics of loess strength parameters were estimated with 4 018 groups of loess direct shear data, and the autocorrelation distances were analyzed with two cone penetration test(CPT) data. The cohesion and internal friction angle were taken as the random variables, which form random fields on a two-dimensional slope section. The factor of safety was calculated by the elastic-plastic finite element method based on the mean strength parameters. The probabilistic analyses used a mean and standard deviation distribution in the finite element mesh through the method of local average subdivision. The failure probability was calculated by the Monte-Carlo method. The data show that on the loess plateau of China, the coefficient of variation of the cohesion is usually more than 0.30, and that of the friction angle is less than 0.20. The cohesion and friction angle are assumed to be lognormally and normally distributed, respectively, and the autocorrelation distance is limited to 0.2 of the slope height. In a single random variable approach (autocorrelation distance is equal to infinity), the probability of failure is overestimated for low coefficients of variation, and underestimated for high coefficients of variation.