Three-dimensional analytical solutions of non-Darcy seepage in front of a grouted subsea tunnel face

In this paper, the impact of non-Darcy seepage on the steady seepage field in front of a grouted subsea tunnel face is analysed. Analytical solutions are proposed by combining the three-dimensional (3D) seepage continuity equation, which is expressed in spherical coordinates, with the Hansbo seepage model. These solutions, which are also suitable for calculating the hydraulic head distribution in front of the tunnel face without a grouted zone, are verified by a series of numerical simulations. Comparisons show that this study enabled the augmentation of the classical analytical model. Finally, the influence of relevant parameters, including the nonlinear parameters in the Hansbo seepage model, the relative permeability (i.e., kr/kg), and the grouted zone thickness, are investigated. The results show that the exponential parameter m and critical hydraulic gradient i1 in the Hansbo seepage model have a more significant impact on the water inflow than the water pressure on the grouted zone. Based on the non-Darcy seepage model, the water inflow is lower and the water pressure on the grouted zone is larger than that obtained by Darcy's model.