Upper bound limit analysis for 3D slope stability analysis based on rigid block structure

In this paper, an upper bound limit analysis for 3D slope stability analysis based on rigid block structure (SLU-3D) is proposed. Specifically, a slope is discretized into a range of rigid blocks in the proposed method, with the block velocity as the main variable and the solution to the minimum safety factor as the objective function. The velocity compatibility, associated flow rule and functional equilibrium that satisfy the requirements of the upper bound theorem are used as constraint conditions. On the premise of not introducing other assumptions, an optimization mathematical model is proposed for 3D slope stability analysis. Considering the difficulty of solving the highly nonlinear optimization model with a large number of degrees of freedom, an effective method suitable for the 3D slope stability analysis optimization model is also constructed using the iterative algorithm of logical judgement based on the introduction of virtual work into the functional equilibrium equation. The rationality and reliability of the proposed method are validated using four typical numerical examples.