An exact analytical approach for determining the seepage field around underwater twin tunnels with linings

Abstract

A reasonable prediction of the seepage field around twin tunnels is important in tunnel design. In this paper, a new alternating analytical approach is proposed to obtain the exact solution of the steady-state seepage field around underwater twin tunnels in semi-infinite saturated aquifers, precisely taking into account the effect of linings or grouting regions, as well as the tunnels’ seepage flow interactions. This study is an extension of analytical research on seepage around tunnels, and rapid estimations of hydraulic heads, pore pressure and water inflows into tunnels can be gained by the proposed approach and solutions.By extending the Schwartz alternating method to problems with multi-connected domains and multiple regions, a new and relatively simple analytical approach is provided to obtain the seepage field (e.g., hydraulic head, pressure) around twin circular tunnels with linings/grouting regions. Employing conformal mapping, a single tunnel with a lining subjected to the reverse redundant hydraulic head generated in the previous step, and another lining under continuity conditions with the rock, are successively analysed in each iteration step. Only after two to three iterations can an exact solution with high precision be obtained by superposing all the solutions in the alternating steps, and good agreements are shown between the analytical solutions and the numerical results both in the surrounding rock and linings. Through a case study, the applicability of the analytical solution is validated. The functional relation between the hydraulic head and some parameters is discussed based on the proposed analytical solution, and a parametric study is conducted to investigate the influence of key parameters on the water inflow into tunnels and the water pressure outside the linings.