Efficient Iterative Analytical Model for Underground Seepage around Multiple Tunnels in Semi-Infinite Saturated Media

The construction and long-term use of underwater tunnels suffer from hazards associated with the pore pressure and water inflow. Analytical approaches quickly can predict the seepage field, through which the water inflow into tunnels can be estimated. In this study, the exact analytical solution of seepage field for underwater multiple tunnel problems was addressed successfully for the first time using the Schwartz alternating method combined with conformal mapping, taking into account the arbitrary tunnel arrangement and tunnel interaction. It was validated that high-accuracy results can be obtained after only two to three iterations. Comparing the analytical results with those from numerical simulations and the mirror image superposition method, the results in this study were in good agreement with the numerical results throughout the entirety of the ground, whereas the superposition results had a large deviation from the exact values in the region close to the tunnel boundary. Through a case study, the applicability of the analytical model was verified. Finally, based on the obtained analytical solution, a parametric study was conducted to investigate the influence of the key parameters on the hydraulic head distribution and the water inflow into the tunnels. Several dimensionless charts for ease of use of practitioners are provided.