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.

Introduction

It is well known that tunnels experience lower rates of damage than surface structures during earthquake events. Nevertheless, some mountain tunnels have experienced significant damage in recent earthquakes, including the 1995 Kobe (Asakura and Sato, 1996), the 1999 Chi-Chi (Wang et al., 2001; Chen et al., 2002), the 2004 Niigata (Yashiro et al., 2007), the 2008 Wenchuan (Tianbin, 2008; Li, 2012), and the 2016 Kumamoto (Zhang et al., 2018) events. Seismic response analyses performed on mountain tunnels are often two-dimensional to evaluate ovaling deformation (Hashash et al., 2005; Kontoe et al., 2008; Amorosi and Boldini, 2009), using only the tunnel cross-section and neglecting the longitudinal direction. However, considering tunnel lining damage caused by recent earthquakes (Wang et al., 2001; Yashiro et al., 2007; Li, 2012; Zhang et al., 2018), responses in the longitudinal direction are also significant. For example, many cracks in the transverse direction of the lining of Tawarayama tunnel were observed to the result from the 2016 Kumamoto earthquake. The most significant deformation mode for the longitudinal seismic response of mountain tunnels is the compression-extension deformation mode, which causes a large longitudinal thrust loading to be applied to the lining (Yasuda et al., 2019). This deformation mode can cause more severe damage to the lining than ovaling deformation mode, which mainly causes bending deformation, because large thrust can cause sudden compression failure.