A model for strain-induced permeability anisotropy in deformable granular media

In a deformable granular medium, shear deformation results in a change in pore volume, thereby causing a change in permeability. In previous studies, it is assumed that the change in absolute permeability is a function of porosity or volumetric strain, which in turn is a function of the mean or minimum effective stress. In such semi-empirical correlations, the changes in permeability are equal in all directions, even though the changes in strains are different in each direction. This paper proposes a new model accounting for permeability anisotropy induced by strains in deformable porous media. This model is derived from the well-known phenomenological Kozeny-Carman equation with some modifications. It was proven that tensor parameters embedded in the Kozeny-Carman equation (hydraulic radius and tortuosity of flow channels) can be expressed in terms of principal strains for granular assemblies of idealized packings. This approach allows one to formulate the evolution of changes in permeability in three directions under continuous shearing. The model explicitly states that the permeability changes are anisotropic, dependent on the induced strains. A comparison between experimental data and predicted results is presented to show the validity of the proposed model.