Analytical Slope Stability Analysis Based on Statistical Characterization of Soil Primary Properties

The role of statistical tools in the modeling of slope stability has been increasingly studied in the last decades. Mainly, this growth can be related to the availability of fast computational routines which enable massive-repetition numerical algorithms such as Monte Carlo simulations. On the other hand, analytical approaches to this problem, in the majority of cases, rely on considering the random variables of interest being normally distributed. This latter assumption tends to provide incorrect results while dealing with skewed data since normal distribution is symmetric about its mean value. In order to address this issue, a complete statistical study of a set of porosities data is undertaken. A total of seven well-known statistical distributions are adjusted to such data, showing that normal distribution is the worst possible fit for the considered data set. By means of an empirical correlation between strength properties and porosity, the probability density function of the factor of safety of a hypothetical slope is analytically derived based on a Mohr-Coulomb failure criterion. This way, it is shown that the probability of failure can be explicitly obtained by means of solely the distribution of a primary property of the material in study, namely, its porosity. Also, the results obtained by considering the porosity data normally distributed are compared to the ones hereby developed showing considerable differences.