An Analytical Solution for Groundwater Flow Induced by Localized Leakage in a Tunnel

ABSTRACT Tunnel engineering often faces water leakage challenges. However, theoretical studies examining the effect of a localized leakage defect on tunnel structures remain scarce. This study systematically investigates the groundwater flow field in deeply buried tunnels, with a focus on a localized leakage defect, and develops corresponding analytical solutions. By employing the image method and seepage mechanics, the semi‐infinite seepage field is transformed into an infinite field containing the actual tunnel and its virtual image. For unlined tunnels, the solution reduces to the classical forms proposed by Goodman and Harr, confirming its theoretical soundness. Furthermore, the proposed solutions are rigorously verified against both 2D and 3D numerical simulations, demonstrating the accuracy of the analytical derivation and the applicability of the equivalent diameter method for spatial leakage analysis. In addition, a comprehensive parameter analysis is conducted to explore the influence of the permeability coefficient, crack width, burial depth, tunnel radius, lining thickness, and grouting ring thickness on the groundwater flow field. Finally, design recommendations for the grouting ring are provided, considering the combined effects of leakage inflow and water pressure on tunnel structures.