In embankments and earth dams, the granular filter used to protect the base soil from being eroded by the fluid flow is a major safety device. In this paper, the migration mechanism of the base soil through this type of filters with a fluid flow in the base soil-filter system is studied by using the coupled distinct element method and computational fluid dynamics (DEM-CFD) model. The time-dependent variations of the system parameters such as the total eroded base soil mass, the distribution of the eroded particles within the filter, the porosity, the pore water pressure, and the flow discharge are obtained and analyzed. The conceptions of the trapped particle and the trapped ratio are proposed in order to evaluate the trapped condition of the base soil particles in the filter. The variation of the trapped ratio with time is also analyzed. The results show that the time evolutions of the parameters mentioned above are directly related to the gradation of the filter, which is defined as the representative particle size ratio of the base soil to the filter using an empirical filter design criterion. The feasibility of the model is validated by comparing the numerical results with some experimental and numerical results.