基于实域总势能计算渗流溢出点位置

Calculation of seepage spill point position based on total potential energy in real domain

渗流对坝体稳定有重要影响,溢出点位置的确定是求解渗流场的关键问题之一。目前求解渗流溢出点的方法以有限元数值计算为主,通过比较假定溢出点水头值与位置高程的大小确定溢出点位置,这类方法具有迭代次数多,不易收敛的缺点。为此提出了一种基于全域总势能计算渗流溢出点位置的新方法：计算出每个可能溢出点对应的全域总势能,其最小值所对应的位置即为溢出点位置。但是全域总势能包含了自由面以上区域（虚域）的势能,给计算结果带来了误差。在全域总势能的基础上,提出了实域总势能的概念,将自由面通过的单元分为干区和湿区两部分,并将干区及其以上单元中的虚域势能从全域总势能中扣除,以消除因计入虚域势能而产生的误差,进一步提高了计算精度。

Seepage plays an important role in dam stability, and the determination of spill point position（SPP） is one of the key problems when solving the seepage field question. The current methods for solving SPP are mainly the finite element ones by comparing the hydraulic head of a possible given spill point and its elevation value. This kind of method has disadvantages such as large iteration times and difficult convergence. Therefore, a new method based on the global total potential energy to calculate SPP is proposed： the global total potential energy corresponding to each possible point is calculated, and the position corresponding to the minimum value is just the SPP. However, the total potential energy of the global domain contains the energy of the region above the free surface（virtual domain） and inevitably introduces errors. On the basis of the global total potential energy, the concept of the total potential energy in the real domain is proposed. The whole domain is divided into the dry region and the wet region by the free surface, and the virtual potential energy in the dry region is deducted from the global total potential energy to eliminate the error caused by including the virtual domain so as to improve the calculation accuracy.