尾矿库浸润线解析解及适用性分析

目前求解尾矿库浸润线大多采用数值模拟和模型试验的方法，尚没有建立起完善的尾矿库浸润线的解析解。鉴于此，建立了尾矿库浸润线的理论模型，采用能量方程和达西渗透定律推导了尾矿库浸润线的微分方程，并建立了上下游边界条件方程。在此基础上，求解了尾矿库浸润线的解析解（由于在解析解的推导过程中引入了杜比假定，该解析解更适应于库底底坡较缓的尾矿库浸润线的预测），并与数值模拟结果进行了对比分析，验证了解析解的正确性。考虑到尾矿库的复杂性，分析了尾矿砂各向异性、尾矿库地质分层和底坡地形对尾矿库浸润线分布的影响，探讨了所提出的解析解对复杂尾矿库浸润线求解的适应性，通过尾矿库实例验证了文中浸润线解析解的有效性。

Analytical solution to saturation line of tailings pond and its applicability analysis

At present, the saturation line of a tailings pond is mostly solved by the method of numerical simulation or model experiment, and there are few analytical solutions reported in the literature. In view of this, a simplified calculation model of the saturation line of a tailings pond is established in this paper. Particularly, the differential equations of the saturation line are derived by using the energy equation and Darcy's law of permeability, and the upstream and downstream boundary condition equations are established. On this basis, the analytical solution to the saturation line of tailings pond is achieved (Note: due to the Dobby's assumption in the derivation of the solution, the analytical solution is mostly suitable for the tailings pond with slight slope). By comparing with the numerical simulation results, the analytical solution is verified. Considering the complexity of a tailings pond, the influence facts on the distribution of the saturation line of a tailings pond are analyzed, such as the tailing sand anisotropy, tailing sand stratification and bottom slope topography. The applicability of the analytical solution to complex tailings pond is discussed. Finally, the validity of the analytical solution in the paper is verified by the tailings pond example.