Rapid Calculation Method for the Factor of Safety of a Uniform Slope

The limit equilibrium method (LEM) and the strength reduction method (SRM) are popular tools used for assessing the stability of slopes. However, they require complex numerical geomechanical models to be constructed and iterative computations to be performed. This study presents a rapid calculation method for the factor of safety of homogeneous and uniform slopes. First, the critical failure state curve is established to represent the relationship among all the parameters associated with slope stability, including the slope angle, slope height, unit weight, cohesion, and friction angle, when the slope is at the critical failure state. Second, based on the proposed critical failure state curve, an explicit expression is derived to directly provide the factor of safety for any homogeneous and uniform slope taking the soil Mohr-Coulomb parameters (i.e., cohesion and friction angle), unit weight, slope height, and slope angle as inputs. In contrast, once the soil's mechanical parameters are determined, for a given factor of safety, the slope height and angle may be calculated. Finally, the proposed method is applied to three cases to illustrate its applicability and validity. The results for all three cases show good agreement with those from the LEM software Slide 6.0.