Uncertainty in Drained Fully Softened and Residual Strength Correlations

Using previously proposed values of standard deviation ($\sigma$) for the drained fully softened and residual strength correlations, the probability of failure ($P_f$) can be calculated to supplement the drained factor of safety (FoS). Using the standard deviation ($\sigma$) of soil strength, e.g., fully softened (FS) and residual, the standard deviation of FoS (${\sigma }_{\mathrm{FoS}}$) and coefficient of variation of FoS ($V_{\mathrm{FoS}}$) can be calculated readily using slope stability software to estimate $P_f$. Being able to calculate $P_f$ allows owners, regulators, and/or engineers to select a frequency of failure for a particular slope given the consequences of failure instead of a nebulous value of FoS. For example, it is easier for owners, regulators, and/or legal representatives to understand a frequency of failure, e.g., 1 failure in 1,000 years, than a drained or effective stress FoS of greater than 1.5 with some level of uncertainty. Even more confusing to owners, regulators, and/or legal representatives is the difference between various values of drained and undrained FoS, which is simplified via the selection of a suitable value of $P_f$.