A Unified Analytical Solution for Seismic Response of Deep Tunnels

The cross-section shape of deep tunnels may be complex, e.g., horseshoes, semi-rectangles, rectangles, and arch-wall; and the surrounding medium of them may have complex properties. In order to obtain seismic responses of deep tunnels in these complex conditions, a unified analytical solution is proposed. The ground-liner interaction can be no-slip and full-slip, and voids behind the liner are considered. Moreover, the ground anisotropy, as well as the drained and undrained loadings are considered. The unified analytical solution can be used to obtain stresses and displacements of deep tunnels with arbitrary shapes, in various ground conditions, and with different ground-liner interactions. The complex function theory and the conformal mapping technique are employed to develop the solution. The results from the proposed analytical solution show that the cross-section shape and the incident angle have a significant impact on the seismic performance of deep tunnels.