A new and efficient theoretical model for studying the seepage field around two noncircular tunnels in sloping ground is proposed through analytical derivation. The model considers the exact interaction between two tunnels with arbitrary shapes and locations, as well as the permeability anisotropy, whose principal orientation is along any direction. By applying the Schwartz alternating method and conformal mapping, the analytical solutions of the hydraulic head and pore pressure can be obtained. These solutions strictly satisfy all governing equations and conditions. The correctness and accuracy of the analytical solutions are verified by the good agreement between the theoretical and numerical results. The proposed theoretical model can be applied to the cases with any tunnel shape, slope angle, anisotropic direction and degree. The quantitative influences of the anisotropy ratio, slope angle and tunnel shape on the seepage field are obtained, and some useful charts are provided. The proposed model can efficiently and quickly predict the seepage flow around tunnels in anisotropic sloping ground.

通过解析推导，提出了一种研究坡地两个非圆形隧道渗流场的新的、有效的理论模型。该模型考虑了任意形状和位置的两个隧道之间的精确相互作用，以及渗透率各向异性，其主要方向是沿任意方向。应用Schwartz交变法和等形映射，可以获得水头和孔隙压力的解析解。这些解严格满足所有控制方程和条件。理论结果与数值结果的良好吻合验证了解析解的正确性和准确性。所提出的理论模型可以应用于任何隧道形状、坡度、各向异性方向和程度的情况。定量分析了各向异性比、坡度和隧道形状对渗流场的影响，并提供了一些有用的图表。该模型可以有效、快速地预测各向异性坡地隧道周围的渗流。