Analytical solution for seismic response of tunnels with composite linings in elastic ground subjected to Rayleigh waves

In this study, a simple method was proposed to calculate the equivalent loadings in ground induced by Rayleigh waves at the critical second. Subsequently, a closed-form solution was established for the seismic response of tunnels with composite linings subjected to Rayleigh waves. The composite linings were modelled as thick-walled cylinders, and the displacements across interfaces were assumed to be discontinuous to consider the ground (lining)-lining interactions. Lastly, parametric studies were conducted to evaluate the effects of Rayleigh waves, the interface stiffness, and the isolation layer on the seismic performance of tunnels. The results show that decreasing the interface stiffness or installing a soft layer could effectively decrease the internal forces in the inner lining but increase the internal forces in the outer lining. This study can be used to verify relevant numerical solutions and to facilitate the seismic design of tunnels with composite linings subjected to Rayleigh waves.