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This paper describes an analytical model of filtration for granular media, based on the mechanics of particle migration under hydraulic loads. A new equation to predict the probability of particle movement through a 3D network model of the filter voids has been developed. Void constriction sizes are determined based on the particle-size distribution and relative density of the filter. An important new development is the differentiation between particles that form part of the filter structure and fine particles that are loose within the filter voids, or coarse particles that are enmeshed in a matrix of fines. The rate of particle erosion and transport is governed by the consideration of mass and momentum conservation. The model describes the time-dependent change of flow rate and base and filter particle-size distribution, porosity, and permeability. The model has application in the design of granular filters for noncohesive uniform, well-, and broadly graded base and filter materials.
Locke et al. (Fri,) studied this question.