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.