Analytical study of steady state seepage field in tunnels with localized water leakage under the effect of grouting circle

When water leakage occurs in tunnels with grouting circle, the grouting circle can well prevent the inflow of groundwater and maintain the pore pressure around the tunnel, and its seepage field is quite different from that of tunnels without considering the grouting circle, therefore, it is necessary to study the seepage field of the tunnels with localized leakage under consideration of the grouting circle. Since there is no analytical study that can accurately consider both localized water leakage in tunnels and the effect of the grouting circle, this study proposes an analytical solution for the steady-state seepage field in tunnels with localized line leakage under the effect of the grouting circle. In the solution process, the seepage field in the non-grouted soil region as well as in the grouting circle are solved separately by combining the conformal transformation and the separation of variables method, and the principle of orthogonality of trigonometric functions and equality of seepage volume are utilized to construct a system of non-homogeneous equations to solve all the unknowns in the analytical solution. The correctness of the analytical solution is verified by comparison with the numerical simulation results. The influencing factors of the accuracy of the analytical solution are also analyzed, and it is found that the permeability of the grouting circle has a certain influence on the accuracy of the pore pressure calculation results. However, when kr/kg = 10, the absolute value of the relative error between the solution and the numerical simulation results is reduced to within 4 %, which is a completely acceptable accuracy. Finally, by analyzing the role of the grouting circle when water leakage occurs, it can be seen that a suitable permeability coefficient of the grouting circle can simultaneously achieve the purpose of maintaining the pore pressure around the tunnel and preventing the inflow of groundwater when water leakage occurs in the tunnel. This study not only proposes an analytical solution for calculating the distribution characteristics of the seepage field when water leakage occurs in tunnels with grouting circle, but also provides a certain reference for the design of tunnels and the prevention and control of water leakage.