含相关非正态变量边坡可靠度分析的子集模拟方法

Reliability analysis of slope stability involving correlated non-normal variables using subset simulation method

提出了分析含相关非正态变量高维小失效概率可靠度问题的子集模拟方法,采用Nataf变换方法成功地解决了输入变量相关时子集模拟方法样本点的模拟问题.编写了基于MATLAB语言的计算程序SUBSETREL,并以岩质边坡稳定可靠度问题为例证明了所提方法的有效性.结果表明:该子集模拟方法能够有效地分析含相关非正态变量高维小失效概率的边坡可靠度问题.子集模拟方法的计算精度和蒙特卡洛模拟方法相当,计算效率远远高于传统的蒙特卡洛模拟方法.此外,该方法在分析含有复杂的隐式及非线性功能函数的边坡可靠度问题方面体现出明显的优越性.研究成果极大地拓展了子集模拟方法在边坡可靠度分析中的应用.

This paper aims to propose a reliability method named subset simulation（SS） method for estimation of small failure probability in high dimensions of slope stability problems involving correlated non-normal random variables.The Nataf transformation is used to transform the correlated non-normal random variables into the independent standard normal variables,which facilitates the simulation of correlated non-normal samples in failure domain and reliability computation using the SS method.A MATLAB-language based computer program called SUBSETREL is developed to carry out the reliability computations.Two examples of reliability analysis for rock slope stability with plane failure are presented to demonstrate the validity and capability of the proposed method.The results indicate that the proposed SS method can compute small failure probability in high dimensions of rock slope stability involving correlated non-normal random variables accurately and efficiently.Furthermore,the proposed SS method can result in the same accuracy as the traditional Monte Carlo simulations;and its efficiency is significantly higher than the traditional Monte Carlo simulations,which can be considered as a potential method for reliability analysis of slope stability,especially for slope stability involving implicit and nonlinear performance function.These results highly extend the application of the SS method to reliability analysis of slope stability.