Analytical Solution for Fine Particle Accumulation in Soil Filters

Abstract

This paper presents a mathematical solution for fine particle accumulation in soil filters. The solution accounts for particle transport in the base soil and uses a lumped parameter to account for the effects of physicochemical forces influencing particle deposition. It considers particle release without subsequent entrapment in the base soil and particle deposition without subsequent release in the filter, and thus represents an upper-bound solution. The particle capture probability approach is adopted to determine the deposition in the filter. The model is demonstrated using a soil filter typically used in practice to protect fine-grained soils, and the potential for fine particle accumulation in the filter is assessed. The results show that fine particle accumulation in the filter material is significantly influenced by a deposition coefficient which is a function not only of the physical characteristics of the material, such as its particle size and pore size distributions, but also of the pore fluid composition and the size of the migrating particles in the pore stream. Because of its closed-form nature, the solution can be easily adopted in practice to assess the potential of fine particle accumulation in soil filters. A stepwise procedure is suggested to use the solution.