A semi-analytical solution to steady-state groundwater inflow into a circular tunnel considering anisotropic permeability

Abstract The groundwater inflow into the tunnel will cause various adverse effects on the tunnel and a proper estimation of the groundwater inflow is of great significance for tunnel drainage system design. In this paper, a semi-analytical solution, which considers the anisotropic permeability of the soil mass, is developed to assess the steady-state groundwater inflow into the tunnel. The solution is developed based on the coordinate transformation and conformal mapping technique. The present solution only requires once conformal mapping and has the advantage of effectively avoiding the distortion of the ground surface during conformal mapping. Two typical boundary conditions on the tunnel surface, the zero water pressure and the constant total water head, both of which are commonly encountered in tunneling engineering, are considered in the present solution. The proposed solution is validated by comparing with the results extracted from a finite element model, which shows that the present solution is capable of predicting the total water head and the pressure head around the tunnel, and the inflow rate along the tunnel surface with sufficient accuracy. Extensive parametric studies are conducted to investigate the effects of permeability ratio, depth of the tunnel centre from the ground surface, and water depths above the ground on the groundwater inflow. The results show that the anisotropy of the permeability has a significant effect on the inflow rate along the tunnel surface under the two boundary conditions. The proposed solution not only provides an efficient approach for assessing the groundwater into the tunnel, but also can serve as a benchmark for calibration of numerical simulations.