Analytical study on the seepage field of different drainage and pressure relief options for tunnels in high water-rich areas

•Proposed analytical solution for tunnel seepage field with any number of drain holes.•The analytical solution can be calculated very quickly, in about 1 s.•Drain holes evenly distributed over tunnels is the best plan to reduce water pressure.•In evenly distribution case, the number of drain holes beyond 5 is little significant.•Drain holes of more than 0.1 m diameter are of little significance. The arrangement of tunnel drainage measures is closely related to the tunnel seepage field and water pressure outside the lining, especially for tunnels in water-rich areas with high water tables. A reasonable drainage hole that actively controls drainage pressure relief is an important measure that ensures the safety of the surrounding rock and lining structure. Since no analytical studies of the seepage field of a tunnel with an arbitrary number of drainage holes have been conducted, this paper derives an explicit analytical solution for the two-dimensional steady-state seepage field of a tunnel with an arbitrary number of drainage holes by means of conformal mapping and the separation of variables method and solves for the unknowns in the analytical solution using orthogonality. The correctness and superiority of the analytical solution proposed in this paper are verified by comparing it with numerical software and existing pipe leakage solutions from various aspects. The influence of the drainage hole arrangement scheme, the number of drainage holes and the diameter of the drainage holes on the seepage field was explored through extensive parametric analysis, and the results show that a uniform arrangement of drainage holes in the tunnel lining centred on the bottom of the arch is the best solution for reducing the water pressure in the lining. The number of drainage holes and the diameter of the holes have a significant effect on the water pressure and seepage volume of the tunnel lining, and based on the results of the analysis, design recommendations for the drainage hole arrangement are provided.