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

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.