Limit equilibrium variational method for stability analysis of fractured rock slopes under generalized H-B strength criterion

Due to the complex nonlinear characteristics often exhibited in the shear failure behavior of rock mass， existing theoretical methods face challenges in analyzing the stability of fractured rock slopes. In this study，a limit equilibrium(LE) variational method for assessing the stability of rock slopes is proposed. This method utilizes the variational method to derive the differential control functions for the slip surface and its associated stress. Additionally, the LE principle is employed to establish the calculation formulas for the factor of safety (FOS) of the slope and the unknown variable related to the slip surface stress. Furthermore，to address the interdependent relationship among the shape of the slip surface，the normal stress on the slip surface，and the instantaneous shear strength parameters under the generalized Hoek-Brown(H-B) strength criterion，a discrete calculation approach coupled with a correlational solving strategy is applied to overcome the challenges posed by the direct incorporation of the nonlinear strength criterion. Building on this foundation，the global vraiational extremum problems of the slope are considered as multiple deterministic boundary variational extremum problems. Subsequently，the slip surface parameters are treated as optimization variables, with the objective of minimizing the slope FOS while satisfying the variational extreme conditions. A multi-objective optimization genetic algorithm is introduced to achieve a precise and rapid search for the critical slip surface of the slope，ensuring the removal of movable boundary cross-sectional conditions and strict adherence to the variational control conditions. The feasibility and practicability of the proposed method are verified through comparisons with several examples. This research contributes to the advancement and refinement of the LE theory for slope stability and provides an effective computational framework for the stability analysis of fractured rock slopes under complex conditions.