Analytical solutions for steady seepage into an underwater circular tunnel

Based on the conformal mapping of the complex variable methods, analytical solutions are derived for two-dimensional, steady ground water flow into a horizontal tunnel in a fully saturated, homogeneous, isotropic, and semi-infinite aquifer. Main application of the equations is to calculate the distribution of the hydraulic head and the pore pressure in the rock mass surrounding the tunnel, and it takes constant hydraulic head and constant water pressure boundary conditions at the tunnel perimeter into consideration. Moreover, a comparison of the analytical solution and FLAC3d shows that the solutions match well for points around the tunnel. When Harr’s solution is compared to the solution presented here, it appears that the surface has a large effect on the water pressure around the tunnel, even for relatively deep tunnels.