Analytical Solution for Circular Tunnel under Obliquely Incident P Waves considering Different Contact Conditions

An analytical solution for the seismic-induced thrust and moment of the circular tunnel in half-space under obliquely incident P waves is developed in this study, which is the superposition of the solution for deep tunnels under incident and reflected P waves and the reflected SV waves. To consider tangential contact stiffness at the ground-tunnel interface, a spring-type stiffness coefficient is introduced into the force-displacement relationship. Moreover, the tunnel lining is treated as the thick-wall cylinder, providing more precise forecasts than beam or shell models used in previous analytical solution, especially for tunnels with thick lining. The reliability of the proposed analytical solution is assessed by comparing with the dynamic numerical results. Based on the proposed analytical solution, parametrical studies are conducted to investigate the effect of some critical factors on the tunnel’s seismic response, including the incident angles, the tangential contact stiffness at the ground-tunnel interface, and the relative stiffness between the ground and the tunnel. The results demonstrate that the proposed analytical solution performs well and can be adopted to predict the internal forces of circular tunnels under obliquely incident P waves in seismic design.