Abstract:Tunnels with non-circular cross-sections such as rectangles, straight walls, and arches are becoming more and more common in engineering construction. It is also a basic fact that natural soils are mostly permeable anisotropic media due to geological movement and their own gravity. The existing analytical research theories on the seepage field of underwater tunnels often assume that the shape of the tunnel cross-section is circular, to simplify the calculation of the seepage field of underwater tunnels. Few analytical studies on tunnels with non-circular cross-sections also fail to consider the effect of anisotropy of permeation of the surrounding medium on the seepage field. Based on this, two mutually perpendicular permeability coefficients are used to represent the permeability anisotropy of the surrounding soil of the tunnel. Based on groundwater seepage theory, coordinate transformation, conformal mapping, and optimization techniques, the sub-regions of the seepage area of underwater non-circular tunnels are mapped into concentric rings. On this basis, the steady seepage continuity equations are solved separately, and then simultaneously solved according to the seepage continuity principle, and the analytical formulas of seepage flow and water head in underwater non-circular tunnels in semi-infinite porous media with the permeation anisotropy are derived. Based on an elliptical underwater tunnel, the correctness of the analytical solution is verified by numerical simulation, and compared with the equivalent perimeter method and the equivalent area method, it is found that this method is more consistent with the numerical simulation results. The study also finds that if the seepage anisotropy of the surrounding soil is not considered, the seepage flow of the tunnel and the water head outside the lining will be underestimated, which will bring safety hazards to the design of the tunnel support structure. The method is suitable for the analytical study of the seepage field of any shape underwater tunnel considering the seepage anisotropy and provides support for the rapid and accurate prediction of the seepage flow of the non-circular section tunnel and the external water pressure of the support structure.