Analysis of ultimate bearing capacity of foundation based on variational limit equilibrium method

Based on the basic principles of the variational method and the limit equilibrium method, the ultimate bearing capacity of foundation for strip foundations is analyzed. Based on the static equilibrium equation of sliding soil in the foundation, an isoperimetric model for the functional extremum of the ultimate bearing capacity of foundation is established. On this basis, the auxiliary functional under constraint conditions is constructed by introducing Lagrange multiplier. The Euler equation is used to obtain the first-order ordinary differential equations with potential sliding surface, normal stress on sliding surface, and Lagrange multiplier as basic unknowns, and the analysis of the ultimate bearing capacity of foundation with movable boundaries is transformed into a two-point boundary value problem under fixed boundary conditions by introducing auxiliary variables. Finally, the numerical solution of the coupled nonlinear differential equation system is carried out by using the shooting method, and the exact solution of the problem is obtained. Meanwhile, the effectiveness of the model and method is verified through numerical examples.