Upper bound solutions of supporting pressure of shallow cavities subjected to pore water pressure based on nonlinear failure criterion

Due to the effect of pore water pressure, the mechnical and deformation characteristics of underground structures located in saturated soils are different from those located in completely dry soils. According to the nonlinear failure characteristics of shallow cavities, a new curved failure mechanism is constructed. By regarding the work rate of pore water pressure as an external loading work rate, the effect of pore water pressure is introduced into the virtual work rate equation of the upper bound theorem, and the upper solution expressions of supporting pressure and detaching curve of the shallow cavities subjected to pore water pressure are derived. By using variational calculation to optimize the objective function, the optimal upper solutions of supporting pressure and collapsing block shape of shallow cavity are obtained. According to the results of parametric analysis, the pore water pressure has significant influence on the supporting pressure and collapsing surface of the shallow cavities. Furthermore, both the supporting pressure and collapsing surface increase with the increase of pore water pressure coefficient.