Previous studies about probabilistic back analysis for shear strength parameters of landslides generally adopted a fixed slip surface. This setting may lead to unreliable results due to the uncertainty of slip surface location speculated by limited observations. Based on Bayes’ theorem, this paper proposes a probabilistic framework for the back analysis of landslides considering slip surface uncertainty. The posterior distributions of shear strength parameters in Bayesian inference are solved by Markov chain Monte Carlo simulation method. To improve computational efficiency, a response surface function based on extreme learning machine is constructed to approximate the relationship between shear strength parameters and the corresponding factor of safety and critical slip surface. A synthetic slope, for which the actual shear strength parameters and slip surface are known, is used to compare the proposed and traditional methods. The effects of measurement error of slip surface and prior distribution of shear strength parameters on probabilistic back analysis results are also investigated. Results show that the shear strength parameters obtained from traditional probabilistic back analyses neglecting slip surface uncertainty significantly deviate from actual values, and are greatly affected by prior mean of shear strength parameters. The proposed method performs better than traditional method and is less affected by the prior distributions of shear strength parameters, and the smaller the measurement error of slip surface, the higher the Bayesian back analysis accuracy. A practical landslide is applied to further verify the effectiveness of the proposed method.

中文翻译：

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考虑滑面不确定性的滑坡贝叶斯反分析

以往关于滑坡抗剪强度参数概率反分析的研究一般采用固定滑移面。由于有限观察推测的滑面位置的不确定性，此设置可能会导致不可靠的结果。基于贝叶斯定理，本文提出了一种考虑滑面不确定性的滑坡反分析概率框架。贝叶斯推理中剪切强度参数的后验分布通过马尔可夫链蒙特卡罗模拟方法求解。为提高计算效率，构建了基于极限学习机的响应面函数来逼近抗剪强度参数与对应的安全系数和临界滑移面之间的关系。一个合成斜坡，已知实际剪切强度参数和滑移面，用于比较所提出的方法和传统的方法。还研究了滑移面测量误差和抗剪强度参数先验分布对概率反分析结果的影响。结果表明，忽略滑面不确定性的传统概率反分析得到的剪切强度参数与实际值显着偏离，并且受剪切强度参数先验平均值的影响很大。该方法性能优于传统方法，受剪切强度参数先验分布的影响较小，滑面测量误差越小，贝叶斯反分析精度越高。