Analytical solutions on non-Darcy seepage of grouted and lined subsea tunnels under dynamic water levels

For the grouted and lined subsea tunnels, the fluid in the low permeability media follows non-Darcy's law rather than Darcy's law. To address this, we provide analytical solutions for the grouted and lined subsea tunnel with dynamic water levels. Our method uses complex variable functions and Hansbo non-Darcy seepage model. The analytical solutions divide into three cases according to the critical water inflow and can degenerate into the traditional method following Darcy's law. The numerical simulation, experimental data, in-situ data, and other analytical solutions are adopted to verify our proposed method. The calculated results subjected to non-Darcy seepage are close to the in-situ data compared with other analytical solutions. When degenerating into the traditional method, the results agree well with those of previous methods following Darcy's law. It reveals that our method is suitable and universal. The parametric analyses of the non-linear flow index m, the critical hydraulic gradient il, the dynamic water level xi ci, the thickness of lining zone tl, and the relative permeability coefficient ratio of the grouting zone and lining zone kg/kl are carried out. The results show that non-linear seepage parameters and dynamic water levels significantly affect the water inflow and water head. The denser grouting material can apportion more water heads and make the lining apportion fewer water heads to protect the lining from fluctuation influencing of dynamic water levels.

Automated summary

For grouted and lined subsea tunnels, fluid flow follows non-Darcy's law and analytical solutions are provided for the dynamic water levels using complex variable functions and the Hansbo non-Darcy seepage model. The solutions can be degenerated into traditional methods following Darcy's law and are validated using numerical simulation, experimental and in-situ data. The results show that the method is suitable and universal, with parametric analyses demonstrating the significant impact of non-linear seepage parameters and dynamic water levels on water inflow and water head.