基于响应面法的边坡稳定二阶可靠度分析

提出了基于响应面法的边坡稳定二阶可靠度分析的实用算法。选择U空间中的随机变量，通过空间变换和相关矩阵分解，计算试验点的功能函数；通过迭代算法构造响应面、以确保通过最小的计算量获得最优精度，并在此基础上进行FORM/SORM计算。以一岩石边坡的平面滑动问题为例，通过与蒙特卡洛模拟、FORM及随机响应面法的比较，证明了该方法的准确性和高效性。分析了参数的相关性及试验点取值范围对计算结果的影响，讨论了可靠度分析结果中参数敏感性和物理属性问题。该方法可为实际边坡问题的可靠度分析提供参考，并可以用来进行基于可靠度分析的加固设计。

Second order reliability analysis of slope stability using response surface method

A practical algorithm of reliability analysis for slope stability is presented based on response surface method and secondorder reliability method (SORM). Independent random variables in U-space are chosen as basic variables and transformed into correlated non-normal variables in original X-space for computing the performance functions. The response surface is constructed using an iterative algorithm to ensure its accuracy with minimum computational expense. Then, the probability of failure is evaluated using the first order reliability method (FORM) and SORM. The accuracy and efficiency of the proposed method are illustrated for a rock slope with plane failure mechanism, via comparing with Monte Carlo simulations, pure FORM and stochastic response surface method. The influence of correlation among random variables and selection of sampling range around tentative design points on the inferred reliability results are investigated. The parametric sensitivity and physical property of random variables obtained from the reliability analysis are also discussed. The proposed method can be used for reliability analysis of practical slopes and also for reliability-based design of reinforcing structures.