文档介绍：边坡可靠度分析的随机响应面法及程序实现
李典庆1,2,周创兵1,2,陈益峰1,2,姜清辉1,2,荣冠1,2
(1. 武汉大学水资源与水电工程科学国家重点实验室,湖北武汉 430072;2. 武汉大学水工岩石力学教育部重点实验室,湖北武汉 430072)
摘要:提出分析相关非正态变量可靠度计算问题的随机响应面法,采用Nataf变换成功地解决输入变量相关时随机响应面法的配点问题及可靠度计算问题。推导4~6阶Hermite随机多项式展开的解析表达式,并编写基于C#语言的随机响应面法计算程序。以岩质边坡平面滑动破坏模式为例证明随机响应面法在边坡可靠度分析中的有效性。研究结果表明,基于Nataf变换的随机响应面法能够有效分析含有相关非正态变量的边坡可靠度问题。随机响应面法的计算精度优于传统的FORM方法,其计算效率高于传统的蒙特卡罗模拟方法,其收敛性在数学意义上是有保证的。随机多项式展开的阶数几乎对边坡安全系数均值的估计没有影响,但是在边坡失效概率的计算中要选择适当的随机多项式展开的阶数。在基于随机响应面法的可靠度分析框架内,边坡安全系数计算和可靠度分析2个过程分开独立进行,同时计算安全系数和失效概率能够更加系统地进行边坡稳定性分析。研究成果为拓展随机响应面法在边坡可靠度分析中的应用奠定了一定的基础。
关键词:边坡工程;边坡可靠度;随机响应面法;随机多项式;概率配点;相关非正态变量
中图分类号:P 文献标识码:A 文章编号:1000–6915(2010)08–1513–11
RELIABILITY ANALYSIS OF SLOPE USING STOCHASTIC
RESPONSE SURFACE METHOD AND CODE IMPLEMENTATION
LI Dianqing1,2,ZHOU Chuangbing1,2,CHEN Yifeng1,2,JIANG Qinghui1,2,RONG Guan1,2
(1. State Key Laboratory of Water Resources and Hydropower Engineering Science,Wuhan University,Wuhan,Hubei 430072,China;2. Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering,Ministry of Education,Wuhan University,
Wuhan,Hubei 430072,China)
Abstract:This paper aims at proposing a stochastic response surface method(SRSM) for reliability analysis involving correlated random variables. The Nataf transformation is adopted to effectively transform the correlated nonnormal random variables into the independent standard normal variables,which facilitates the collocation points associated with the correlated random variables and putation using the SRSM. Explicit polynomials are derived for fourth-order to sixth-order Hermite polynomial chaos expansions of any number of random variables. A C#-language puter program WHUSRSM (Wuhan University SRSM) is developed. An example of reliability analysis of rock slope stability with plane failure is presented to demonstrate the validity and capability of the proposed SRSM. The results indicate that the proposed SRSM can evaluate the reliability of rock slope stability involving correlated random va