The Complex Variable Solution for the Displacement and Stress Caused by Shallow Rectangular Tunnel Grouting Pressure Considering the Gravity Effect

This study presents an analytical elastic solution using the complex variable approach to determine the soil disturbance surrounding a shallow rectangular tunnel, taking into account the effect of gravity and considering the influence of grouting pressure applied at the tunnel boundary. A theoretical calculation model is first established by applying stress boundary conditions along the tunnel boundary. To handle the geometric complexity of the rectangular cavity, a conformal mapping function suitable for non-circular opening is adopted. This function maps the original half-infinite region with a rectangular cavity onto an annulus in the transformed plane, thereby converting the irregular cavity problem into a more tractable configuration. The boundary conditions at the ground surface and the tunnel interface are then addressed using Fourier series expansion. By solving these series-expanded equations, all unknown coefficients of the analytical functions are determined, leading to an analytical elastic solution for soil disturbance. Numerical verification validates the accuracy of the proposed approach. Moreover, parametric studies are conducted to evaluate the effects of soil mechanical properties and tunnel geometry on the soil disturbance. The findings offer a valuable reference for future investigations into construction-related issues associated with rectangular tunnels.