Back analysis of slope failure with Markov chain Monte Carlo simulation
Back analysis of slope failure with Markov chain Monte Carlo simulation
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DOI：
10.1016/j.compgeo.2010.07.009
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发表时间：
2010-11
影响因子：
5.3
通讯作者：
Lixing Zhang;Jie Zhang;L. M. Zhang;W. Tang
中科院分区：
文献类型：
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作者：
Lixing Zhang;Jie Zhang;L. M. Zhang;W. Tang
现场观测的边坡性能可用于反算土壤特性的输入参数并评估边坡稳定性分析模型的不确定性。本文提出了一种新的概率方法用于边坡失稳反分析。所提出的反分析方法是基于贝叶斯定理制定的，并使用马尔可夫链蒙特卡罗模拟方法和 Metropolis-Hasting 算法进行求解。该方法非常灵活，因为可以使用任何类型的先验分布。当采用响应面法来近似边坡稳定性模型时，该方法的计算效率也很高。给出了假设的边坡破坏的反分析示例。研究了跳跃分布函数和样本数量对马尔可夫链效率的影响。研究发现，跳跃函数的协方差矩阵可以设置为先验分布协方差的一半，以实现合理的接受率，并且 80,000 个样本似乎足以获得该示例的稳健后验统计。研究还发现，土体黏聚力与摩擦角的相关性对边坡的后验统计和修复设计影响不显着，而先验分布的类型似乎对修复设计影响较大。
Field observed performance of slopes can be used to back calculate input parameters of soil properties and evaluate uncertainty of a slope stability analysis model. In this paper, a new probabilistic method is proposed for back analysis of slope failure. The proposed back analysis method is formulated based on Bayes’ theorem and solved using the Markov chain Monte Carlo simulation method with a Metropolis–Hasting algorithm. The method is very flexible as any type of prior distribution can be used. The method is also computationally efficient when a response surface method is employed to approximate the slope stability model. An illustrative example of back analysis of a hypothetical slope failure is presented. Effects of jumping distribution functions and number of samples on the efficiency of Markov chains are studied. It is found that the covariance matrix of the jumping function can be set to be one half of the covariance of the prior distribution to achieve a reasonable acceptance rate and that 80,000 samples seem to be sufficient to obtain robust posterior statistics for the example. It is also found that the correlation of cohesion and friction angle of soil does not affect the posterior statistics and the remediation design of the slope significantly, while the type of the prior distribution seems to have much influence on the remediation design.