顺层边坡稳定性及可靠度的随机有限元分析法

阐述了基于摄动法的随机有限元基本原理，采用以均值为中心的2阶摄动随机有限元，运用局部平均的空间离散方法，对顺层边坡的应力场进行了2阶统计均值、协方差和方差的分析，并结合顺层边坡沿软弱夹层滑动的破坏特征，推导了基于Mohr-Coulomb准则的顺层边坡整体稳定的安全系数和可靠度的计算表达式。结合典型顺层岩质路堑边坡工程实例，采用摄动随机有限元法进行了边坡稳定性和可靠度的分析计算。结果表明，文中介绍的摄动随机有限元法可以考虑多种随机变量对边坡系统的影响，可同时采用安全系数和可靠度作为边坡稳定性的评价指标，判定结果更为准确和全面。

Analysis of stability and reliability of bedding rock slope by stochastic finite element method

The basic principles of the perturbation stochastic finite element method (PSFEM) are introduced. By using the second order PSFEM where the mean value is taking as the center and the local-average space discrete method, the second order statistic mean value, covariance and deviation are analyzed. Considering the failure characteristics of the bedding rock cutting slope slipping along the soft intercalation and based on Mohr-Coulomb criterion, the formulae of the safety factor and reliability of the slope stability have been obtained. Taking a typical engineering example of the bedding rock cutting slope, the slope stability and reliability of the slope are calculated by PSFEM. The results show that PSFEM presented can be used to consider the influence of the multiple stochastic variables. The safety factor and reliability can be taken as the evaluation indexes of the slope stability at the same time. By this way, the evaluation results may be more accurate and overall.