An analytical model is proposed to describe the filtration process applicable to a base soil-filter system. The Navier-Stokes equations for porous media are used to capture the hydrodynamic behavior, whereas, numerically, a new algorithm is proposed to solve the Navier-Stokes equation in a nonlinear form. The various mixtures of base soil particles eroded and water flow within the system are computed using the workenergy principle incorporating the constriction size of the filter.The model can assess the filtration process through the flowrate and the accumulation and redistribution of fine particles within the filter. By discretizing the base soil and filter domains into discrete elements, the model can predict the time-dependent particle gradation of the filter for each element. Laboratory tests reported in other studies and those conducted by the authors validate the model in relation to other available models.