On two definitions of the factor of safety commonly used in the finite element slope stability analysis

In the 2D finite element slope stability analysis, there are two commonly used definitions on the factor of safety. The first is the strength reserving definition, which defines the factor of safety as the factor by which the shear strength of the soil would have to be divided to bring the slope into the state of critical equilibrium. The second is the overloading definition, which defines the factor of safety as the ratio of total resisting forces to total driving forces along a certain slip line. This study formulates a uniform initial value problem of ordinary differential equations for locating the critical slip lines corresponding to the two definitions and proposes a prediction–correction procedure for the initial value problem. Through solving the relevant initial value problem, the critical slip line can be located without specifying its shape and location. It is also demonstrated that while the finite element method is utilized for analyzing slope stability, the critical slip lines based on the overloading definition might be for the most part shallower than those by the strength reserving definition and the conventional limit equilibrium methods, and hence the design based on the overloading definition might be precarious.