Exact analysis of soil slope stability by using variational limit equilibrium method

Based on the basic principles of the variational method and the limit equilibrium method, the stability analysis of soil slopes is conducted theoretically. Firstly, the basic equilibrium equation for the problem is established by using the limit equilibrium method, and the auxiliary functional for the isoperimetric problem under constraints is constructed by introducing the Lagrange multiplier. In addition, the first-order ordinary differential equations with potential sliding surface, normal stress of sliding surface, internal force of sliding body, safety factor and Lagrange multiplier as the basic unknowns are obtained by combining the Euler equation, and the slope stability analysis is transformed into a two-point boundary value problem under fixed boundary conditions by introducing the auxiliary variables. Finally, the numerical solution of the example is carried out by using the shooting method, and the accurate solutions of the position of the sliding surface, the normal stress distribution on the sliding surface and the slope stability coefficient are obtained. The results are compared with those obtained by the slice method and the finite element strength reduction method to verify the effectiveness of this method. The analysis results show that the proposed analysis method for soil slope stability can effectively avoid the search and optimization process of the sliding surface position in the traditional calculation, and can accurately obtain the shape of the slope sliding surface, the normal stress on the sliding surface and the inter-strip force distribution, which may provide a scientific and reasonable calculation method for the stability analysis of slopes.