Analytical method for predicting the soil disturbance induced by shallow rectangular tunnel grouting pressure under slope condition

This study derives an analytical solution for soil disturbance induced by grouting pressure of shallow rectangular tunnel on sloping terrain, taking into account the soil gravity effect. First, using asymmetric arbitrary cavity conformal mapping method and complex variable theory, the basic equations for soil displacement and stress and the governing equations for the stress boundary conditions in the image plane are obtained. Then, the Fourier transform approach is employed to expand the complex terms in the stress boundary condition equations into Fourier series, and an equation set for solving the potential functions is established. Subsequently, series method is adopted to determine the potential functions, ultimately yielding the surrounding soil disturbance. Finally, by comparing with the finite element numerical results, the correctness of the analytical solution is verified, and the effect of soil and tunnel parameters on the soil disturbance is investigated. The method presented in this article can be used as a tool for evaluating the soil disturbance caused by tunnel grouting in the preliminary design stage.