Graph theory for stability analysis of rock/soil slopes based on numerical manifold method

The widely-used analysis methods for slope stability based on the limit equilibrium conditions have limitations. In the limit equilibrium method, the constitutive model for soils or rocks cannot be considered, and assumptions are needed between slices of soils/rocks. The strength reduction method, another dominant method for slope stability analysis, requires iterative calculations and cannot represent the effect of stress paths. Besides, it does not give the slip surface directly. Based on the current stress state of slopes, the numerical manifold method, which can unify the continuum analysis and discontinuum analysis with its dual covers, is adopted to calculate the stress distributions of soil slopes or rock slopes with joints. Then the slope stability analysis is converted to a graph problem, and the Bellman-Ford algorithm is used to obtain the slip surface and the safety factor which is defined as the ratio of the resistant force and the slip force along the slip surface. The proposed method removes the difficulties in iterative calculations and unifies the stability analysis of rock/soil slopes, and is capable of including the effects of stress paths.