Simplified analytical solutions for seismic response on cross section of circular tunnel with composite linings

Abstract

Simplified analytical solutions are very useful tools for the seismic preliminary design of tunnels and can quickly and easily give seismic responses to structures. This study presents simplified analytical solutions for the stress and deformation of circular composite-lined tunnels subjected to in-plane S-waves. Unlike previous solutions for single-lined tunnels, the proposed analytical solutions are suitable for tunnels with arbitrary numbers of linings. Moreover, tunnel linings are treated as multilayer thick-walled cylinders in the new solutions. Compared with thin shell or beam models used in previous analytical solutions, thick-walled cylinders provide more precise forecasts. In addition, the slippage effect at the lining-lining and ground-lining interface is considered by introducing a spring-type flexibility coefficient into the interaction force–displacement relationship. To verify the proposed analytical solutions, dynamic numerical examples are studied. The proposed solutions have good agreement with the dynamic numerical results and outperform previous analytical solutions. Finally, parameter studies are conducted to investigate the effect of the flexibility coefficient, degraded zone around the outermost lining and steel plate supporting the innermost lining on the seismically induced stresses and deformations. The proposed analytical solutions are applicable for approximately evaluating the seismic responses of circular tunnels with composite linings.