Advanced Slope Reliability Analysis

Uncertainty is patent in a variety of topics in engineering. Slope stability analysis is not an exception. Traditional approaches for slope stability analysis focused on defining the critical failure sliding slip surface. Their efforts for defining soil parameters as random quantities were almost negligible. Currently, literature has seen efforts for incorporating uncertainty in slope stability. However, the uncertainty is used to solely being propagated into the Factor of Safety (FoS.) Thus, commercial software applications and some practitioners erroneously assess the probability of failure (p_f) using Monte Carlo simulation on the FoS. The FoS concept is observed closely and reviewed in the current document in light of the structural reliability analysis. This fact leads us to verify FoS lack of invariance, yet more importantly to propose an improved approach to really assess risk failure associated with a p_f robust quantification. The document introduces to the geotechnical practitioners the foundations of the mainstream reliability analysis by presenting the reliability index, β, and the probability of failure, p _f computation when the statistical information of the uncertainty sources is as complete as possible in the geomechanical properties. As a result, with this novel approach, the widely known Limiting Equilibrium Method applied to slope stability analysis shows certain drawbacks and allows us to use a limit state function other than the FoS as it has been usually formulated: quotient between the Resistance, R and the Solicitation, S. Finally, it is also numerically demonstrated that pf has nothing to do with the overlap of the R and S probability density distribution functions as it is normally thought in practice.