A theoretical study on the hydraulic conductivity of anisotropic granular materials by implementing the microstructure tensor

A theoretical study on the hydraulic conductivity of fully saturated anisotropic granular materials for a 2D fluid flow has been made by making use of the microstructure tensor as the anisotropy descriptor. The assemblage of particles was assumed to be the representative elementary volume of materials with void spaces as a multiply-connected continuum through which a Stokesian flow can pass. The Navier–Stokes equations have been then solved to find the mean velocity vector under different pressure boundary conditions. A tensorial form of the hydraulic conductivity with constants being functions of the invariants of the microstructure tensor, as the geometric measure of the anisotropy, has been presented based on a number of realizations for different GSD curves. Verifications with available experimental data exhibit a reasonable accuracy of the suggested equation. Graphical abstract