Simplified Analytical Solutions for Deep Tunnels Subjected to vertically incident shear wave with arbitrary vibration direction

Abstract

A circular tunnel in a homogeneous infinite ground subjected to a vertically incident shear wave with an arbitrary vibration direction in the horizontal plane is considered in this study. A simplified analytical solution with explicit formulations for the deformation and stress of the tunnel lining is presented here. The superposition of two solutions under SH and SV waves are derived first. In the analytical solutions, the tunnel lining is taken as a thick-walled cylinder, which enables more precise forecasts and is much closer to practical engineering than the thin shell model adopted in other previous solutions. Moreover, the analytical solutions consider the slippage effect at the ground-lining interface by introducing a spring-type flexibility coefficient into the interaction force-displacement relationship. The results of the analytical solutions are verified by a comparison with the results of the dynamic numerical solutions via a 3-D ground-lining interaction model under earthquakes; the results show good agreement. By using the analytical solutions, the effects of the vibration direction, ground condition, lining thickness and flexibility coefficient on the seismic response of the tunnel are investigated. Additionally, the appropriate range of seismic wavelengths for the analytical solutions is discussed. The proposed solutions can be applied to the seismic analysis and design of tunnel structures.