Study on calculation method of bending moment and deflection of underlying layer under soil pressure

Surface layer is an important part of foundation pit supporting system. For the purpose of designing the surface layer reasonably, this paper established a forced model of the surface layer by using the small deflection bending theory of thin plate, and the forced analysis was carried out on the surface layer of shotcrete foundation pit support type. In order to simplify the calculation, the concrete surface layer is assumed to be an elastic body, and the surface layer is simplified as a rectangular thin plate with four sides simply supported on the foundation pit slope, which derives in the general expressions of the deflection and bending moment of the bottom layer under active earth pressure. And the bending moment and deflection of the bottom layer after the foundation pit excavation are simulated by the finite difference software FLAC^3D. The results show that the theoretical values of the deflection and bending moment are in agreement with those of numerical simulation, the margin of error between the calculation value and the simulation value of the maximum deflection and maximum bending moment are 6 % and 13 % respectively, the distribution laws which simulation cloud pictures of the deflection and bending moment show are consistent with those calculated by the formulas. The deflection and bending moment both reduce gradually from the surface center to boundary, which verifies the effectiveness of the proposed method. The formulas can provide reference for the design of surface layer.