Analytical solution for seismic response of deep tunnels with arbitrary cross-section shapes

The pseudo-static method considering ground-structure interaction is widely used in seismic design and analysis of tunnels, and especially, the analytical solution based on this method can serve as an effective tool for practitioners. However, the existing methods in literatures are only applicable for circular or rectangular tunnels. An analytical solution for seismic response of deep tunnels with arbitrary cross-section shapes in homogeneous ground is presented. The lining is assumed as a shell, and the effects of the middle wall as well as two typical soil-structure contact conditions (i.e., no-slip and full-slip) are also considered. First, the governing equations for the tunnel structure and the ground are introduced. Then, the complex variable function and the conformal mapping method are employed to obtain the analytical solution. The validation of the proposed solution is verified by comparison with the results from FEM. Finally, parametric analyses are carried out using the solution, and the influences of the relative stiffness ratio of the ground to the structure as well as the thickness of middle wall are analyzed. The results show that the internal force of the tunnel increases with the increase of the ground-structure relative stiffness ratio, while the deformation of the tunnel decreases. The internal force of the tunnel under no-slip condition is larger than that under full-slip condition, while, oppositely, the structural deformation under no-slip condition is less than that under full-slip condition. Compared to that of the case neglecting the middle wall in the tunnel, the maximum internal force of the tunnel significantly increases when the thickness of the middle wall is 1.5 times larger than the thickness of the tunnel lining.