Complex variable analysis of soil displacement and liner deformation induced by shield excavation

The ground deformation caused by shield excavation is always a key issue. The current studies give little attention on the impacts of interaction between tunnel liner and soils. Particularly the deformation analysis of the liner is not conducted. A complex variable solution for ground displacement and liner deformation is proposed considering the interaction of liner-soil and the boundary condition for the oval deformation. In this method, the depth of tunnel affects only the thickness of ring walls after conformal mapping and the analytical region remains round. It will not affect the function analysis. Besides, after the conformal mapping this method guarantees the continuity of boundary. It can make the soil displacements zero at infinity and avoid the analytical defects. That occurs via correcting analytical solution by which the existing stress function methods keep infinity soil displacement zero. Through the case analysis, the ground settlements induced by tunnel excavation are obtained and compared with the measured data. The deformation influence law of ground and tunnel liner is acquired through parameter analyses. The results indicate that the vertical displacement curves of soils are in good agreement with the measured values. The surface maximum settlement is closer to the actual one. The depth and radius of tunnel have a great influence on the soil displacement and liner deformation. Although the influence of thickness of liner is less, it cannot be ignored. The radial displacement of liner presents a shape of supine duck egg, which is symmetrical to the axis 90^°/270^°. Its value is negative, which means that the liner shrinks as a whole. The vault and arch bottom get squashed. The shrinkage in vault is greater than that in arch bottom. The shrinkage at the left and right sides is less than that at the upper and lower sides, which shows that the liner is crushed to the left and right sides after being compressed. With the increase of the tunnel depth, the liner comes up overall. The tangential displacement of the liner presents a shape of a toppled apple which is symmetrical to the axis 0^°/180^°. The values in 90^° and 270^° are zero. The absolute values of tangential displacement increase with the increase of depth.