Analytical Model for Particle Migration within Base Soil-Filter System

Abstract

This study highlights a mathematical (analytical) model simulating the filtration phenomenon applicable to a base soil-filter system, incorporating the hydraulic conditions and the relevant material properties such as porosity, density, friction angle, and the shape and distribution of particles. The model is founded on the concept of critical hydraulic gradient derived from limit equilibrium considerations, where the migration of particles is assumed to occur under applied hydraulic gradients exceeding this critical value. The rate of particle erosion, and hence, the filter effectiveness is quantified on the basis of mass and momentum conservation theories. By dividing the base soil and filter domains into discrete elements, the model is capable of predicting the time-dependent particle gradation and permeability of each element, thereby the amount of material eroded from or retained within the system. Laboratory tests conducted on a fine base material verify the validity of the model. The model predictions are also compared with the available empirical recommendations, including the conventional grading ratios.