Quantitative Comparison of Direct Monte Carlo Simulation to Simplified Reliability Approaches for Evaluating the Stability of Unreinforced Slopes

Abstract

Use of simplified reliability methods in geotechnical engineering has been in practice for several decades. Some of these simplified reliability methods are described in Christian et al. (1994), Tang et al. (1999) and Duncan (2000), among others. These simplified reliability methods include both first-order second moment (FOSM) and first-order reliability methods (FORM). Disadvantages to simplified reliability methods include: 1) an assumption on the distribution of the factor of safety and 2) only the standard deviation and mean of the uncertain variables are used as opposed to the entire probability density function (pdf) (Sleep and Duncan 2014, Polanco and Rice 2011). The perceived disadvantages of simplified reliability approaches and the automation of Monte Carlo simulation into many geotechnical computer programs have caused designers to shift away from simplified reliability approaches in favor of Monte Carlo simulation method. Using the context of stability calculations for unreinforced slopes, this paper compares the results of simplified reliability methods, including the Taylor Series, Point Estimate and Hasofer Lind methods, to Monte Carlo simulation methods. Reliability of modeled slope failures will be compared with Monte Carlo simulation and simplified reliability methods. Additionally, this paper explores the relationship between the uncertainty in parameter values used in stability calculations and the probability of failure.