Abstract: Based on the variational limit equilibrium method, the ultimate bearing capacity of composite foundation with vertical reinforcement is studied. Firstly, based on the static equilibrium equation of sliding soil in composite foundation with vertical reinforcement and combined with the variational principle, an isoperimetric constraint model for the functional extremum of the ultimate bearing capacity of foundation is established. On this basis, the control equations with potential sliding surface, normal stress on sliding surface, and Lagrange multiplier as basic unknowns are obtained using the Euler equation, and the movable boundary is transformed into a fixed boundary by introducing auxiliary variables. Finally, the shooting method is used to numerically solve the coupled two-point boundary value problem, obtaining an accurate solution and comparing it with the simplified equivalent strength index method in composite foundation design. Simultaneously, the numerical examples are used to analyze the effects of displacement rations, reinforcement cohesion, and internal friction angle on the ultimate bearing capacity of the foundation. The numerical results show that the simplified equivalent strength index method can effectively analyze the ultimate bearing capacity of composite foundation with vertical reinforcement.

Key words: composite foundation, vertical reinforcement, ultimate bearing capacity, variational limit equilibrium method, shooting method