Pseudo-static analytical solution for seismic response of deep tunnels with arbitrary cross-sections considering interface slippage effects under vertically incident SV waves

Abstract

To evaluate the seismic response of deep tunnels, this study proposes an analytical solution for the seismic response of deep tunnels with arbitrary cross-sections based on the extended complex function method and the boundary collocation approach, which realistically accounts for the interface properties between the lining and the surrounding rock and the lining thickness. The accuracy of the computational results of the analytical solution is validated through numerical simulations based on three tunnels with typical cross-sections. Moreover, this study compares the advantages, disadvantages, and applicability of analytical solutions based on the conventional and extended complex function methods for seismic analysis of tunnels. Finally, the considerable influence of the stiffness ratio between the lining and the surrounding rock, the interface properties, and the cross-section geometry on the seismic response of the tunnel is evaluated. The results demonstrate that for horseshoe, rectangular and straight-wall-top-arch tunnels, the discrepancies between the analytical and dynamic numerical results are less than 2.20 %, 4.48 %, and 6.65 %, respectively. In comparison to the conventional complex function method, the extended complex function method has enhanced computational accuracy, however, it demands greater computational resources and is more intricate to operate. A positive correlation exists between the stiffness ratio between the lining and the surrounding rock and both lining thrust and moment, while a negative correlation is observed between the stiffness ratio and displacement. The thrust of the tunnel lining all decreases rapidly as the interfacial flexibility coefficient increases, but the effect of the flexibility coefficient on the moments and displacements of the tunnel lining varies for different cross-sections and is related to the ground conditions. The seismic response strength of tunnels with varying cross-sections is as follows: rectangular tunnel > straight-wall-top-arch tunnel > horseshoe tunnel > circular tunnel. This solution can be readily implemented in preliminary analyses and predictions of seismic responses for deep tunnels with arbitrary cross-sections, thereby offering a theoretical foundation and a valuable tool for seismic design and safety assessment.