Analytical solutions for seepage fields of underwater tunnels with arbitrary burial depth

A summary about the analytical solutions in the literatures for the seepage fields of underwater tunnels is given, whose advantages and disadvantages are pointed out. Based on the governing equation for the steady-state seepage, the analytical solutions for the seepage fields of underwater tunnels are derived rigorously using the conformal mapping method. The water inflow and water pressure distribution for the grouted lined underwater tunnel with arbitrary burial depth can be obtained according to the new solutions. The analytical solutions can be degenerated to two limit cases including the unlined underwater tunnel and the underwater pipeline. A numerical model is established using the software Comsol to validate the newly derived solutions. The effects of the burial depth of tunnel, the permeability of lining and the thickness of lining on the water inflow, the pore water pressure around the lining and the distribution of the total water head are investigated. It is found that the maximum water pressure appears at the top of the lining when the tunnel is buried shallowly, which is opposite for the case with a large burial depth. The average pore pressure and the non-uniform degree of distribution of the pore water pressure around the lining decrease first then increase as the burial depth increases gradually. And for a given working condition, there is a burial depth or thickness of lining, which can make the pore water pressure around the lining distributed uniformly.