边坡可靠度分析的随机响应面法及程序实现-中国科学技术协会.docVIP

边坡可靠度分析的随机响应面法及程序实现 李典庆1，21，21，21，21，21. 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。收敛性在数学意义上是有保证的RELIABILITY ANALYSIS OF SLOPE USING STOCHASTIC RESPONSE SURFACE METHOD AND CODE IMPLEMENTATION LI Dianqing1，2，1，2，1，2，1，2，1，2(1. State Key Laboratory of Water Resources and Hydropower Engineering Science，uhan University，Wuhan，Hubei 430072，China；2. Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering，Ministry of Education，uhan University，Wuhan，430072，China) Abstract：his 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