Semi-analytical solution of external water pressure of water rich tunnel considering waterproof and drainage system

Water rich tunnels are often subject to lining seepage and water leakage. The water pressure behind lining is the main factor that causes the tunnel diseases. To calculate the water pressure of tunnel lining, axisymmetric analysis, mirror image method, and conformal transformation method are commonly used. However, axisymmetric analysis and mirror image method are only applicable to the tunnels in high water level. The conformal transformation method can be applied to both high and low water level tunnels, but cannot consider the effects of grouting rings and lining. This paper simplified the seepage of groundwater into a fan-shaped vertical shaft seepage problem, and derived the analytical formula of lining water pressure considering the shape of tunnel. A semi-analytical method of lining water pressure considering the influence of waterproof and drainage systems was proposed. The results show that the water pressure is related to the height of the initial water head, permeability coefficient of materials and geometric sizes of lining. According to the reduction degree of water pressure, it can be divided into three areas, namely, uniform reduction area of arch, discharge area of longitudinal drainage pipe and uniform reduction area of invert. With the increase of water head of the tunnel vault, the water pressure difference between vault and invert increases gradually, and the invert is easy to be damaged. The research results can provide guidance for the structural design and optimization of water rich tunnel.