Internal erosion involves the migration of fine particles through hydraulic earth structures. A thorough understanding of the fundamental mechanisms governing this process and operating at the grain scale can help to reduce the hazards that may arise therefrom. In this regard, the Discrete Element Method (DEM) has proved efficient to have a better understanding on processes at stake at pore scale. In this study, the DEM is used to prepare samples of spheres with varying gradation and density states. The void microstructure within the samples is then examined by using the weighted Delaunay tessellation associated with a recently developed merging technique. This merging criterion used to generate a poral structure eliminates some biases related to the non-robustness of the Delaunay tessellation and to the artificial partition of the space. Moreover, the filtration properties of the samples are analyzed by simulating the transport of fine particles through the filters by gravitational deposition or downward flow. The results of numerical tests show a strong correlation between the particle penetration depths and the constriction size distribution (CSD) of the material, thus supporting the relevance of the used merging criterion. Finally, dry filtration and fluid filtration showed some discrepancies that were analyzed.