Non-Darcy seepage analysis on subsea tunnel in fractured rock mass with grouting reinforcement

Grouting reinforcement is commonly employed in subsea tunnels. A thorough understanding of seepage behavior is vital for optimizing grouting design and evaluating its effectiveness. Previous studies employing Darcy’s law have been found inadequate for capturing the nonlinear seepage behavior under high hydraulic heads in subsea tunnels. Moreover, most analytical investigations on nonlinear seepage behavior have neglected the influence of non-circular cross-sections. Therefore, the non-Darcy seepage behavior in subsea tunnels constructed in fractured rock masses reinforced by grouting is investigated in this study. An analytical model featuring a non-circular cross-section and a grouting zone is developed based on the Izbash non-Darcy flow model using complex variable function theory and conformal mapping. Analytical solutions for water inflow and pore pressure that account for the presence of grouting zone in fractured rock masses are derived. The solutions are validated against numerical simulations results and field monitoring data from the Qingdao-Jiaozhou Bay Second Subsea Tunnel. Parametric studies are performed to quantify the influence of the Izbash empirical coefficient on the tunnel water inflow, pore pressure and hydraulic gradient. Furthermore, the effects on water-blocking performance of key grouting parameters, including the relative permeability coefficient and the thickness of grouting zone, are investigated under non-Darcy flow conditions. The results indicate that non-Darcy flow significantly affects water inflow, pore pressure and hydraulic gradient in subsea tunnels. An optimized design of the grouting zone is essential to ensure effective water-blocking performance, adequate mechanical strength, and economic feasibility. The proposed analytical model and methodology provide a theoretical foundation basis for the design of waterproofing and drainage systems in subsea tunnels in fractured rock masses.