基于随机响应面法和Sarma法的边坡可靠度分析

Analysis of Reliability of Slope Stability with Stochastic Response Surface Method and Sarma Method

研究目的:提出基于线性无关原则概率配点法的随机响应面法,并采用于C#语言的计算程序WHUSRSM。将随机响应面法和边坡稳定分析的Sarma法相结合,能够有效地分析极限状态方程为隐式的边坡稳定可靠度问题。研究结论:本文采用公路边坡工程算例证明了随机响应面法的有效性,并与传统响应面法及蒙特卡罗模拟方法的计算结果进行了比较。结果表明,随机响应面法的计算精度和计算效率均优于传统响应面法,且计算效率远远高于蒙特卡罗模拟方法。基于线性无关原则的概率配点法求解Hermite多项式展开的待定系数时,不仅可以消除系数矩阵的奇异性问题,而且大大地提高了计算效率;潜在滑体的可靠指标随着黏聚力和内摩擦角间负相关性增加而增大,不考虑这种负相关性得出的结果偏于保守。

Research purposes： This paper aims to propose a stochastic response surface method based on the principle of linearly independent collocation and compile a C #- language based on computer program WHUSRSM （Wuhan University Stochastic Response Surface Method）. Using the proposed stochastic response surface method along with the Sarma can effectively evaluate the reliability of slope stability in the implicit limit state. Research conclusions： In this paper, the analysis of the stability of highway slope is presented to demonstrate the validity of the proposed stochastic response surface method. The results indicate that stochastic response surface method is better than the conventional response surface method in the accuracy and efficiency , and better than Monte Carlo simulation method in the calculation efficiency . The stochastic response surface method based on the principle of linearly independent collocation can not only remove the singularity of coefficient matrix associated with the estimation of coefficients in the Hermite polynomial chaos expansion, but also greatly improve the computational efficiency. The Reliability index of the potential landslide increases with the increases of the negative correlation coefficient between cohesion and friction angle, so the results are somewhat conservative if the negative correlation is not considered.