Suffusion is a phenomenon commonly observed in gap-graded soils that involve the detachment and transport of the finest grains under the action of an internal fluid flow. This can have detrimental effects, as the significant loss of fines may trigger mechanical instabilities in the material, posing a potential risk of catastrophic failure for hydraulic structures, possibly in the form of static liquefaction. To address this risk, an innovative approach is being considered – the injection of fines back into the remaining granular skeleton, primarily comprised of coarse sand grains. This remediation technique draws inspiration from recent numerical findings, which indicate that the inclusion of weakly loaded grains can substantially enhance the mechanical stability of granular materials.

In this work, we propose to use the discrete element method (DEM) to analyze the fine infiltration process into the suffused coarse material. Both dry and flow-driven infiltration are considered with the simultaneous release of a small number of fine grains above a gravity-deposited coarse sand column following the grading of the Hostun sand used in the laboratory. For the flow case, we use the Pore scale Finite Volume (PFV) scheme introduced by Chareyre et al. (\cite{article3}). Besides, different fine/coarse size ratios ($D_{50}/d$ from 3.4 to 11.3) and different void ratios (from loose to dense) of sand column are considered. Both the lateral and vertical displacements of fine grains are analyzed to understand the infiltration behaviors of injected fines in terms of infiltration depth and lateral diffusion. Similarly to previous experiments, the distribution of fine grains penetration depth in both dry and immersed cases are fitted by exponential decay curves to determine the characteristic length of infiltration.

To further analyse the numerical results, an analytical pore-constriction-based network model is use to predict the infiltration depths without running DEM simulations with both coarse and fine grains(\cite{article4,article5}). By utilizing the Delaunay tessellation method, we describe a coarse assembly of grains as a network of interconnected pores, which allows us to precisely identify and study pore constrictions, crucial points where fine particles may get clogged during infiltration. The analytical nature of the model enables us to simulate various infiltration scenarios, examining the influences of different parameters, such as grain size distribution, pore connectivity, and hydraulic gradients. Consequently, we gain valuable insights into the intricate mechanisms governing fine infiltration processes within the sand column.