A probabilistic retention model for fine sand infiltration in granular filters based on experimental and numerical insights

Loss of fine particles in gap-graded soils under seepage forces may decrease the relative density of soil which can make it susceptible to failure by static liquefaction under unexpected loading conditions. To evaluate the potential of a remediation technique involving the replacement of eroded grains from the outside of the soil matrix, we carried out a comprehensive analysis of the elementary interplay between fine particles advected by water flow and the granular skeleton of the soil. To this end, experiments and numerical simulations have been designed for a wide range of size ratios R ( D₁₅/d₈₅ ) between the fine and the coarse grains. Both experimental and numerical results show that the capacity of the soil to retain the injected fine grains decays exponentially along the infiltration depth, allowing direct assessment of the mean infiltration distance L₀ . A micro-mechanically based probabilistic model is put forward to interpret L₀ based on the pore/constriction size distribution of the coarse sand column. The model is extended to real materials by using a modified Rayleigh distribution to represent the constriction size distribution of the coarse sample in the experiment, calibrated by two parameters directly derived from its particle size distribution. The predictive capacity of this probabilistic model is validated via the infiltration results extracted from both the experiments and numerical simulations.