Risk estimation of soil slope stability problems

For successful design of any real-life engineering structures, it is important to quantify the risk of failure. Most of the geotechnical engineers find it suitable to define risk mathematically in terms of well-known metric called probability of failure. The inherent spatial variability of the soil strength parameters also makes the design of soil slopes suitable for stochastic interpretations. In the present study, probabilistic slope stability analysis has been performed for both, cohesive soil as well as cohesive frictional, i.e., c-ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c-\phi$$\end{document} soil. The estimation of the factor of safety of the soil slope has been carried out using ordinary method of slices. Probabilistic analysis has been carried out using the single random variable approach with the assumption that the cohesion and angle of internal friction of soils follow lognormal distribution. The variation in soil shear strength is taken into account with the help of statistical parameter known as coefficient of variation. The effect of the coefficient of variation, the spatial correlation length, and local averaging on the probability of failure and the factor of safety has been investigated. This phenomenon indicates a gradual variation of probability of failure with respect to the factor of safety at higher coefficient of variation values. The presented analyses can be used to determine the factor of safety of a soil slope for which the slope should be designed with a predefined probability of failure.