基于广义子集模拟样本加权法的边坡多失效模式可靠度分析

doi:10.13722/j.cnki.jrme.2017.0643

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摘要边坡通常包含多个潜在的破坏模式，边坡多失效模式系统可靠度计算的蒙特卡洛模拟方法在求解小失效概率问题时计算效率较低。为此，提出基于广义子集模拟样本加权法的边坡多失效模式可靠度分析方法，推导了多失效模式对应于不同失效阈值时的失效概率计算公式。采用概率故障树模型构建边坡多失效模式系统可靠度分析模型，通过耦合系统模式的广义子集模拟驱动变量划分整体样本空间，基于广义子集模拟执行过程中的样本子空间概率权来估计相应空间中样本权系数，通过样本权系数计算失效模式在不同失效阈值下的失效概率。以岩质边坡楔形体稳定问题为例阐明所提方法的有效性。结果表明：提出的广义子集模拟样本加权方法极大地提高了边坡系统可靠度及其分量失效模式可靠度的计算效率。该方法不仅能够通过一次模拟实现多模式可靠度的求解，避免针对不同失效模式进行重复模拟的问题，而且能够显著地提高估计低概率水平失效模式可靠度的计算效率。此外，提出的广义子集模拟样本加权方法不仅能够高效地估计临界失效阈值对应的失效概率，也能够同时计算多模式在任一失效阈值时的失效概率。

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	杨智勇1
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	李典庆1
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	曹子君1
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	唐小松1
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关键词 ：边坡工程, 多失效模式, 失效阈值, 系统可靠度, 广义子集模拟, 样本权

Abstract：It is not uncommon that a slope involves multiple possible failure modes. Monte Carlo simulation provides a way to estimate the failure probabilities of these multiple modes. However，it incurs frequent criticisms because of its low efficiency at small failure probability levels. To address this problem，a sample weighting method combined with the generalized Subset Simulation(GSS) is proposed in this paper to estimate efficiently the reliabilities of geotechnical structure system and the multiple failure modes involved in this system. The equations for calculating the failure probability at various failure threshold values of each mode are derived. The probabilistic fault tree model is employed to establish the limit state function of sophisticated system response. This limit state function of system is then incorporated into the driving variable of GSS to divide the whole random sample space into several mutually independent and collectively exhaustive sub-spaces. In the implementation of GSS，the probability weighting coefficients of different sub spaces are determined adaptively. With the probability weighting coefficients，the weighting coefficients of samples in each sub space are estimated properly，which can be further used to compute the failure probability of each failure mode in the system with different failure threshold values. A rock wedge slope is employed to demonstrate the performance of the proposed method. It was found that the proposed method improved significantly the computational efficiency in estimating the reliabilities of the multiple failure modes in the geotechnical structure system. The proposed method not only estimate the reliabilities of multiple failure modes through a single simulation and avoid the repeated simulation for different failure modes，but also enhance the efficiency of computing the failure probability of failure modes at low failure probability level. Moreover，it provides the failure probability values corresponding to various failure threshold values for all the modes concerned.

Key words： slope engineering multiple failure modes failure threshold value system reliability generalized subset simulation sample weighting

引用本文:

杨智勇1，2，李典庆1，2，曹子君1，2，唐小松1，2. 基于广义子集模拟样本加权法的边坡多失效模式可靠度分析[J]. 岩石力学与工程学报, 2018, 37(3): 630-641.
YANG Zhiyong1，2，LI Dianqing1，2，CAO Zijun1，2，TANG Xiaosong1，2. Efficient analysis of slope reliability with multiple failure modes using sample weighting method in generalized subset simulation. , 2018, 37(3): 630-641.

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http://www.rockmech.org/CN/10.13722/j.cnki.jrme.2017.0643 或 http://www.rockmech.org/CN/Y2018/V37/I3/630

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