Application of modified EP method in steady seepage analysis

Free-surface (unconfined) seepage problems are commonly encountered in geotechnical engineering. In these problems, the determination of the free-surface usually requires sophisticated numerical techniques. Among all the proposed methods for solving free-surface seepage problems, the extended pressure (EP) method emerges as one of the easiest methods since the boundary conditions are simply imposed on the prescribed outer boundaries and those on the prior unknown free-surface are automatically satisfied. However, in the available papers on the EP method, the optimal value of ε in the ramp function Hε(p), which has significant effects on solving accuracy and computational efficiency, is rarely mentioned or simply selected as the grid spacing without a systematical analysis. In this paper, a modified EP method is proposed to improve the accuracy in simulating the free-surface and reduce the computational cost. In this modified EP method, ε is proposed as half of the under-grid spacing in y-direction through an error analysis of the finite difference equations and their iteration schemes. Compared with the original EP method, the modified EP method is more accurate and efficient due to its smooth free-surface, rational spillpoint position and low computational cost.