Abstract: The problem of unsteady seepage with a free surface is widely recognized in hydraulic engineering and geotechnical engineering. The free surface, usually changing dynamically with time, poses a dynamic boundary problem, and is a key and difficult issue in unsteady seepage research. A free surface numerical simulation method of unsteady seepage based on the finite element method and the improved conservation Level Set method is presented in this paper. We use the Level Set method to capture unsteady seepage free surfaces implicitly on a fixed grid, subtly avoiding the difficulty of other fixed grid methods in handling free surfaces, and have achieved convenient calculations with a good conservation of mass and good accuracy. This paper first discusses the governing equations and numerical discretization of unsteady seepage in porous media, then describes a method for free surface tracking and an algorithm for interpolating physical characteristic parameters. Finally, the accuracy and effectiveness of this new method are verified via several classical examples, such as homogeneous earth dams, heterogeneous rectangular dams, and riverbed seepage problems.

Key words: seepage calculation, unsteady seepage flow, seepage free surface, physical parameter interpolation, ICLS