Analytical Solution of Mechanical Response inShallow Non-circular Tunnels

The mechanical analysis of shallow noncircular tunnels is of great significance to the construction safety of urban subway tunnels. The difficulty in solving this problem originates from the influence of gravity and the determination of conformal mapping. To this end, a decoupling conformal mapping method with the framework of complex variable theory was proposed. In this method, the analytic function was decomposed into two groups of sub-functions, which were expressed in different local coordinate systems. These two sub-functions can exactly express the mechanical field of the computational domains inside the ground surface and outside the tunnel boundary. Then the ground and tunnel boundaries can be mapped independently by conformal transformation. Furthermore, the boundary condition equation used to determine the analytic function was transformed into the frequency equation using the fast Fourier transform method. Finally, the proposed method is applied to the analysis of ground settlement caused by the shallow tunnel excavation. From the results, the following conclusions can be drawn: 1) The tunnel shape has a significant effect on the ground settlement, and its main factor is the height-to-span ratio. 2) The buried depth affects both the ground settlement and the width of the settlement trough. Its sensitivity increases with the decrease of buried depth. 3) The lateral pressure coefficient has little effect on the width of the ground settlement trough. 4) Compared with the finite element method, the proposed method can obtain high-precision results at a small computational cost.