Simplified analytical solution for nonlinear longitudinal deformation of shield tunnels under surface surcharge

Surface surcharge will induced longitudinal deformation of shield tunnels, which threats the safety of running trains. The current prediction methods for the settlement of shield tunnels are not taken the nonlinear deformation of soils into consideration. Based on the proposed nonlinear foundation model, the simplified analytical solution for nonlinear longitudinal deformation of a shield tunnel under surface surcharge is derived. The additional load on the shield tunnel due to surface surcharge is estimated by the Boussinesq solution, and the deformation of the shield tunnel is modeled using continuous long beam. The differential function for the settlement of the shield tunnel is then obtained. The numerical solution of tunnel settlement is solved using the combined method of the finite difference and Newton’s iteration method. The effectiveness of the proposed method is verified using 3D FEM model. The proposed method may provide a theoretical support for evaluating the deformation of shield tunnels under surface surcharge.