A computational procedure to assess the distribution of constriction sizes for an assembly of spheres

The effectiveness of filters to counteract internal erosion in earth structures is particularly related to their ability to capture fine particles moving under seepage flow through the porous material. More precisely, fine particles are likely to be trapped by the narrowest paths between pores: the constrictions. This paper proposes a methodology to compute the constriction size distribution of model granular filters taking into account the relative density of the material. The approach is based upon probabilistic methods which adopt stated simple geometric packing arrangements to represent the solid structure in the extreme density states. Two new models are proposed for the design of the constriction size distribution according to the type of filter grading: continuously graded or gap-graded materials. The models require the usual material characteristics: the grading curve, and the minimum and maximum void ratios for this material. Calibrated on the basis of statistical analyses over numerical assemblies of spheres generated by a discrete element method, the proposed new models constitute a promising tool to significantly improve the modeling of filtration processes in granular materials.