Limit of Anisotropic Hydraulic Conductivity Ratio of Homogeneous Granular Materials

This paper presents a theoretical upper limit for the anisotropic hydraulic conductivity ratio of homogeneous granular materials with internal structure. On the basis of a volume averaging approach, a theoretical analysis is proposed to relate the permeability of granular material to the spatial distribution of pore spaces. For flow in granular materials, both the linear porosity in the flow direction and the areal porosity in the plane perpendicular to the flow direction are required to describe the directional variation of pore space. The permeability tensor is derived by considering the macroscopic momentum balance equation of the fluid in a porous medium. While the permeability is affected by the porosity and the pore space distribution, the permeability anisotropy ratio is dominated by the directional variation of the linear porosity. By accounting for the theoretical maximum and minimum porosity, it is shown that the upper limit of permeability anisotropy for homogeneous granular materials is approximately 2.5, even for very flat (or elongated) particles and pronounced preferential orientations.