Method for analyzing waterproof tunnels considering the effect of a thin water layer behind the lining

Waterproof tunnels are designed by assuming that water pressure acts on the lining uniformly. This assumption is made because the waterproof membrane and geotextile ensure that a thin water layer forms behind the lining. In designing waterproof tunnels with the conventionally used beam–spring model, the effect of the thin layer is considered by applying depth-dependent water pressure to the outer surface of the lining and using no-tension springs. When designing tunnels by adopting numerical analyses such as finite element analysis, the thin water layer is often ignored. Even considering the thin water layer, it is difficult to model it directly. Hence, a simplified method considering the effect indirectly is needed to estimate the stresses in the lining. This paper presents a method for analyzing waterproof tunnels. A thin water layer with zero thickness was assumed to exist at the boundary between the ground and waterproof lining. The effect of the thin layer was modeled by considering the contact–separation conditions at the ground and lining boundaries using contact elements and applying a pressure loading equivalent to the pore pressure at the interface to both boundaries. In addition, an analytical solution for a circular tunnel lining subjected to depth-dependent water pressure was derived assuming that the contact between the ground and lining was only at the crown, to clarify the basic response of the waterproof lining and to validate the numerical results. The results show that the magnitude of the bending stress varied greatly depending on the contact area of the ground and lining, and the bending stress in the lining was non-negligible relative to the axial stress. Therefore, estimating the bending stress is important in the design of waterproof tunnels. The main cause of the bending stress was the difference in buoyancy due to the depth-dependent water pressure and the total weight inside the tunnel structure. Minimizing this difference contributes to the rational design of waterproof tunnels.