A new method for defining the local factor of safety based on displacement isosurfaces to assess slope stability

Slope stability is mainly assessed by the factor of safety (FS) parameter. As an improvement to the integral FS derived from the conventional limit equilibrium method (LEM), the local factor of safety (local FS) is used to describe the FS of each material element. However, although current slope stability algorithms with LEM rely on only strength criteria, some areas of a slope show almost no displacement, even though plastic yielding is occurring within the slope. For these reasons, we developed a new approach for defining the local FS based on the displacement isosurface. Adopting the Mohr–Coulomb (M–C) strength criterion, this new algorithm calculates the local FS in the potential sliding zone with a change in the apparent displacement. Based on the shear strength reduction technique, the distributions of the local FS within 2D homogeneous slopes with different shear strengths and within a real 3D slope with a complex topography are analyzed. Firstly, the applicability of the new approach was examined and we found that the local FS decreases significantly only when the direction of the yielding surface approaches the displacement direction, which also reveals that the LEM may underestimate the FS. In addition, the areas of a slope where the local FS strongly changes depend on the slope geometry and also control the instability patterns. Further, the results of a local FS in a 3D slope analysis show that complex topography and internal structure can cause the alternation of stable and unstable blocks in the slope and that the mobilities of the blocks induced by the instability differ in different areas. Finally, some local optimized retaining countermeasures were successfully implemented for supporting a real engineering slope guided by the local FS. Our results indicate that this improved algorithm can provide a more suitable and accurate local FS with which to assess slope stability and reveal more realistic instability patterns than approaches using the integral FS.