Abstract: This study investigates the distribution characteristics and influencing factors of water pressure outside tunnel with external drainage. The semi-infinite seepage region is transformed into a rectangular area using conformal transformation and is divided into four sub-regions based on the boundary conditions. The analytical solution for the seepage field of the external drainage tunnel, accounting for the effect of the grouted circle at any burial depth, is derived using the method of separation of variables. The water pressure outside the lining and the drainage volume calculated from the analytical solution are compared with those obtained from the ABAQUS numerical solution and the existing mirror image method to validate the accuracy of the analytical solution. The influence of parameters, such as the permeability coefficient of the grouted circle, on the effectiveness of water pressure reduction using the extracorporeal drainage method is analyzed and discussed. The results indicate that the external drainage method significantly reduces water pressure at the tunnel invert; however, the pressure reduction effect on the arch and side wall areas is minimal. Increasing the permeability coefficient of the grouted circle and the radius of the drainage hole enhances the pressure reduction effect but also increases drainage volume. This drainage method reliably and effectively reduces water pressure at the tunnel crown across various burial depths. The findings of this study provide theoretical support for the design of drainage systems and the assessment of water pressure reduction effectiveness.

Key words: external drainage method, arbitrary burial depth, seepage field, analytical solution, water pressure, grouted circle, tunnel