Probabilistic Assessment for Slope Using the Generalized Chebyshev Inequalities

Abstract

This paper aims to estimate the probability of failure (Pf) of slope based on Chebyshev inequalities. Traditionally, for a slope reliability analysis, the supposed distribution types of shear strength parameters are employed; this is not accurate because the distribution types of parameters are uncertain. Chebyshev inequalities can estimate the probability even when the distribution types of variables are unknown. The upper bound value of the probability of failure (Pf) of a step-shaped slope is derived based on the Chebyshev inequalities. Additionally, the bootstrap method combined with the Akaike information criterion (AIC) are adopted to validate the accuracy and efficiency of the proposed method. It can be concluded from the illustrative example that the Pf of a slope can be estimated by the Chebyshev inequalities. Compared with traditional probabilistic methods, Chebyshev inequalities are a quick and easy way to assess the upper bound value of Pf.