Analytical Solution for Seepage Fields Around Drained Diversion Tunnels Considering Arbitrary Ground Leakages

Abstract

High‐diversion tunnels are often designed as drained systems to mitigate pressure differences between the tunnel interior and surrounding soil, commonly resulting in elevated hydraulic pressure and seepage infiltration toward the ground surface, posing risks to structural integrity and surface stability. This study presents a novel analytical solution for the seepage field around drained diversion tunnels considering arbitrary ground leakages. The solution integrates conformal transformation, the method of separation of variables, and trigonometric orthogonality, and demonstrates applicability for both deep and shallow‐buried diversion tunnels. Parametric analyses reveal that both the total water outflux and the flow velocity outside the tunnel are highly sensitive to the total head difference, tunnel radius, burial depth, and spatial distribution of ground leakage regions (e.g., leakage length, interval, and proximity to the tunnel vault). Notably, hydraulic pressure between adjacent ground leakage regions and flow velocity across the leakage regions increase with a lower ratio of burial depth to tunnel radius, fewer leakage regions, shorter leakage lengths, and larger head difference. The maximum water outflux consistently localizes in the central leakage region with magnitude fluctuations governed by the parity of the total leakage regions. The proposed analytical framework is further extended to address irregular cross‐sectional tunnel shapes via a gradient descent method and can be flexibly adapted to various boundary conditions. This work provides a computationally efficient tool for optimizing drainage designs and assessing leakage‐induced risks in diversion tunnel projects.