Bayesian back analysis of landslides considering slip surface uncertainty

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.