Simplified analytical solution for circular tunnel under obliquely incident SV wave

Abstract

A simplified analytical solution is developed for estimating the thrusts and bending moments of the circular tunnel in half space under the obliquely incident SV wave. The seismic waves impinging on the tunnel is obtained according to the elastic wave motion theory in half space firstly, which is the superposition of the incident and reflected SV waves and reflected P wave. Then, by considering the tunnel lining as a thick-wall cylinder, analytical solutions for internal forces of circular tunnel due to the incident and reflected SV waves and the reflected P wave are deduced, which enables more precise forecasts than previous analytical solutions by the thin shell model. The total tunnel internal forces are obtained finally through the superposition of the above solutions under three kinds of waves. The accuracy of the proposed analytical solution is verified by comparing with the dynamic numerical results. Moreover, the discussion about the effect of critical factors on the accuracy of the proposed analytical solutions is conducted, including the tunnel structure inertia, the seismic wavelength, the lining thickness and the tunnel depth. These results demonstrate that the proposed analytical solution performs well and can be adopted to predict the internal forces of circular tunnel under obliquely incident SV wave in seismic design.