基于简化边界的尾矿坝浸润线解析解

Analytical solution of tailing dam seepage line on the basis of simplified boundary

浸润线的计算是尾矿坝安全状况评估的重要环节,对尾矿库安全起到至关重要的作用。为了能够用解析的方法得出浸润线,首先略掉无关紧要的部分,将尾矿坝的渗流分析区域简化为一个矩形,然后在矩形区域中选定两种符合工程实际的边界条件,最后求解渗流微分方程即求出这两种边界条件下的浸润线。求解中涉及到的偏微分方程无论是齐次还是非齐次的,都通过傅里叶级数法得到收敛的无穷级数解。该方法的突出特点就是得到的最终结果是解析解。实际应用时通过与实测浸润线数据拟合确定浸润线求解公式中的常数。通过对某尾矿坝浸润线的计算发现前面得到的公式可以用于实际浸润线的计算。

Computation of seepage line is one of the most important step of safe condition evaluation of tailings dam,so it is very important to safe of tailings dam. In order to get seepage line through analytical method,this article first ignore unimportant part and simplify the zone as an rectangle,then this article chose two kinds of boundary condition which can match practical situation of engineering in the rectangular zone,at last we can get seepage line under these two kinds of boundary condition by resolving seepage differential equation. We can get Infinite series solution which must be convergent by method of fourier series regardless of homogeneous or inhomogeneous differential equation we may meet. The main character of this method is that it ＇s final solution is analytical. In practice we can get constants of equation which can give seepage line by curve fitting of observed datum. After solving of seepage line of one tailing dam we find the equation we can be used to get seepage line of tailings dam.