改进的Monte Carlo法应用于基坑可靠性分析

随着深基坑在城市建设中的发展,越来越多的学者关注基坑工程的可靠度问题,其中Monte Carlo法常被用于基坑可靠性分析,但传统的Monte Carlo法难以考虑各失效模式间的相关关系,且无法考虑随机变量间的互相关性。引入Sklar提出的Copula理论,其特点在于可以将任意一个联合分布函数分解为一个边缘分布函数和一个Copula函数,以此来描述变量间的相关关系。本文首先通过引入Copula理论描述各失效模式的相关关系,通过对算例的分析证明该方法比传统的Monte Carlo法更稳定高效;进一步使用Copula理论描述土的抗剪强度指标c,φ之间的相关关系,生成有相关关系的随机变量代替传统Monte Carlo法中的独立变量,使可靠性分析结果更加准确,通过工程实例证明考虑c,φ相关关系的基坑失效概率大幅降低,说明变量间的相关关系对可靠度分析的影响很大。

Application of Monte Carlo Method Improved in Reliability Analysis of Foundation Pit System

With the development of deep foundation pit in urban construction, more and more scholars are concerned about the reliability of foundation pit engineering. The Monte Carlo method is often used for the reliability analysis of the foundation pit. However, the traditional Monte Carlo method can not consider the correlation between each failure mode of the foundation pit. Meanwhile, it can not consider the intercorrelation between random variables. This paper introduces the Copula theory proposed by Sklar, which is characterized by the possibility that any joint distribution function can be decomposed into an edge distribution function and a Copula function. First, the Copula theory is introduced to describe the correlation of each failure mode, then analysis a typical example which can prove that this method is more stable and efficient than the traditional Monte Carlo method. And then use Copula theory to describe the correlation between soil shear strength index (c,φ), generate random variables with correlation, which can instead of the independent variable in the traditional Monte Carlo method. By this method, the result of reliability analysis is more accurate. Through engineering examples, it is proved that the failure probability of foundation pit is greatly reduced with the considering of c and φ, which indicate that the correlation between variables has a great influence on reliability analysis.