Analytical solutions of non-Darcy seepage of grouted subsea tunnels

Abstract Fluid flow in porous media is very important in a wide range of hydraulic and geotechnical engineering fields. The theoretical basis of fluid flow in porous media is based on the Darcy’s law. There are evidences that the fluid flow in porous media does not follow the Darcy’s law at very low velocity. The Darcy’s law is inappropriate for the low-permeability grouting zone of a subsea tunnel. Therefore, in this paper, we propose the impact of nonlinearity of low velocity flows on the drainage design of grouted subsea tunnels. The analytical solutions are derived by complex variable functions based on Hansbo's non-Darcy seepage model. The advantages of considering non-Darcy effects in the design of tunnel drainage system have been proved by both field monitoring and experimental data. The applicable conditions of our analytical solutions in subsea tunnel design and constructions are given. The analytical solutions are verified by numerical simulations and analytical analyses. The influences of non-Darcy parameters on the total hydraulic head and water inflow of grouted subsea tunnels are discussed. The design parameters of the grouted subsea tunnels, such as the ratio of permeability coefficients kr/kg and the grouted zone thickness hc, are investigated considering non-Darcy seepage. The results show that the non-linear seepage parameters have great influences on water inflow and water pressure of subsea tunnels. Our proposed methods can provide references for the drainage design in subsea tunnel projects.