Seismic response of a cylindrical tunnel with construction joints subjected to longitudinal ground displacement

A seismic response analysis for a mountain tunnel is often two-dimensional, using the tunnel cross-section. However, responses in the longitudinal direction should not be neglected, especially when considering the tunnel lining damage that has been caused by recent earthquakes. A critical factor in the evaluation of the longitudinal seismic response of mountain tunnels is the construction joints, which exist at intervals of approximately 10 m along the lining. In this study, elastic solutions for a cylindrical tunnel with construction joints subjected to longitudinal ground displacement are presented. The surrounding ground is considered to be an infinite elastic, homogeneous, isotropic medium. The lining is treated as an elastic, homogeneous, isotropic medium. The zeroth mode component of an obliquely incident plane harmonic shear wave, which contributes to compression-extension deformation, is used as the longitudinal ground displacement. A no-slip boundary condition is applied at the ground-lining interface, and a traction-free boundary condition is imposed between the interface of the lining blocks. The point-matching method is used to satisfy the boundary conditions at the ground-lining interface approximately. The numerical results show that there is no difference in the seismic response between the case with and the case without the inclusion of construction joints except for the large surface loading in the area neighboring the joints. However, in actuality, the slippage between the ground and the lining can occur and cannot be neglected. Therefore, seismic resistance can be improved by construction joints. When considering slippage, unusually large normal surface loading is required to cause longitudinal seismic damage. Smoothing of the interface between the sheet membrane and the lining, which can also prevent the destruction of the waterproofing membrane and the production and growth of cracks due to drying shrinkage, is an effective countermeasure to prevent the longitudinal seismic damage of mountain tunnels.