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边坡可靠度分析的随机响应面法及程序实现

期刊名称：岩石力学与工程学报
时间：0
页码：1513-1523
分类：P642.22[天文地球—工程地质学;天文地球—地质矿产勘探;天文地球—地质学]
作者机构：[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
相关基金：国家自然科学基金重点项目（50839004）; 国家杰出青年科学基金项目（50725931）; “十一五”国家科技支撑计划重大项目（2008BAB29B01）; 教育部新世纪优秀人才计划项目（NCET-08-0415）
相关项目：暴雨诱发滑坡致灾机理、风险评估与减灾方法研究

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, slope engineering, slope reliability, stochastic response surface method, polynomial chaos, probabilistic collocation, correlated nonnormal random variables

中文摘要：

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。

英文摘要：

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 reliability computation 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 based computer 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 variables efficiently.The proposed SRSM has a higher accuracy than the conventional first-order reliability method;and its efficiency is higher than Monte Carlo simulations.Moreover,the convergence in Hilbert space of the SRSM can be ensured in any case.The mean of factor of safety for slope stability can be accurately estimated by the proposed SRSM with different orders.However,the orders of the SRSM should be selected carefully to accurately estimate the probability of rock slope failure.The calculation of factor of safety and the reliability analysis can be conducted separately within the framework of the SRSM based on reliability analysis.Slope stability analysis would be investigated systematically with the results associated with factor of safety as well as probability of failure.These results can provide a basis for extending the application of the SRSM to reliability analysis of rock slope stability.

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