Markov Chain Monte Carlo-Based Stability Analysis For Pingzi Shan Landslide

China is a country with a vast territory, and the topographic features are rather complicated, therefore, there are many types of natural geological disasters herein. Among those geological disasters, the instability of landslides is generally common, throwing a great threat to the engineering construction, especially the security of people in the mountainous area in the northwest and southwest China. Because of this, the stability analysis of landslide has attracted more and more attention in recent years. But due to the inherent variability of soil/rock sourced from its formation, the traditional method and analysis for the stability analysis of landslide, using only one set of parameters (e.g., one value of effective friction angle, cohesion and unit weight) cannot meet the requirements of engineers and practitioners. Engineers have realized the importance of the inherent of soil/rock properties, and then tried to probabilistically characterize and determine the stability of landslides. This needs extensive experiments in situ or in laboratory. However, for medium or small projects, only limited data are available in general because of the limitation of costs. This makes it a challenging problem to implement the probabilistic characterization of soil/rock properties in practice and to calculate the stability of landslides considering the inherent variability of soil/rock. If the stability of landslides is analyzed based on the probabilistic characterization of soil/rock properties using limited data, computational error/mistakes might, or probably occurs.This paper aims to solve this problem by proposing a method. The method rationally and systematically integrates the knowledge from limited data from in situ and prior knowledge (e.g., engineering experience and engineering judgment etc.) using the Bayesian framework and the Theorem of Total Probability. Based on the integrated knowledge, the posterior probability distributions of soil/rock properties are obtained. As these posterior probability distributions of soil/rock properties are too complicated to express explicitly and analytically, Markov Chain Monte Carlo is adopted in this paper to deal with this problem. It is a numerical process that simulates a great amount of equivalent samples as a Markov Chain with the posterior probability distributions of soil/rock properties as its limiting stationary distribution. The characteristics of these equivalent samples effectively portray these probability distributions. The soil properties of Pingzi Shan landslide are probabilistically characterized using the above method. Then, the stability of Pingzi Shan landslide is analyzed and the failure probabilities for different profiles are obtained. In addition, further analysis is implemented using Bayesian theory to determine the main influence factors, providing theoretical evidence for its protection and mitigation.