Analytical solutions of seepage field for underwater shallow-buried parallel twin tunnels

Most of the current analytical solutions of seepage field for twin tunnels are directly obtained by the superposition of seepage fields of two single tunnels, which does not really satisfy the conditions at the tunnel boundary and has the deviation from the actual seepage field. Based on the mass conservation law and the Darcy’s law, an analytical solution of seepage field for underwater twin parallel tunnels is derived by the Schwartz alternating method combined with the conformal mapping. After two to three iterations, an analytical solution of the problem with high accuracy is obtained. The numerical software Comsol is used to simulate the problem, and the simulated results are compared with the analytical solutions proposed in this study. It is found that they are in good agreement throughout the entirety of the ground. Compared with the direct superposition results, the two results are consistent in the region far from the tunnel, while there is a large error of the superposition results near the tunnel boundary. Finally, the influences of tunnel spacing, buried depth and relative size on the distribution of hydraulic head and the water inflow of the tunnel are discussed.