Progressive Failure of Slopes: Stochastic Simulation Based on Transition Probabilities and Markov Chains

A reliability analysis framework for the stochastic simulation of slope progressive failure is proposed in the current work. Progressive failure is addressed as a local failure propagation process that takes place along individual segments upon a critical slip surface. The probabilities of progressive failure are evaluated by transition probabilities and Markov chains theory. Slope stability computations are performed by elastoplastic finite element models. The point estimate method is used for the direct integration of geotechnical uncertainty within stability computations. For the various safety states during local failure advancement, progressive failure probabilities are expressed through a transition probability matrix. The effect of certain factors, such as the cross-correlation between shear strength components, the performance function’s probability distribution, and the initial stress ratio at rest, are also investigated and discussed.