Flow-induced compaction of soft porous media and the interaction with gravitational and mechanical loading

Flow-induced compaction of deformable porous media is characteristically non-uniform due to gradients in the fluid pressure. The constitutive laws for effective pressure and permeability encode the rheology of the solid matrix; these laws separate porous media into two 'types' based on the limit of large applied pressure difference. This classification of types is found to be intrinsically linked to the well-known poroelastic diffusivity. Industrial and geographical applications motivate the consideration of porous media that naturally slump due to gravitational stresses, the significance of which is characterised by a non-dimensional gravity term that captures the relative importance of gravitational stress and elastic stresses. Further, if a medium is mechanically compressed between two plates, as is the case in various industrial processes, then it takes up an external load which must be relieved before any bulk flow-induced compaction can occur. In particular, in this 'pre-strained' state, the flow can compact some regions and decompress others, such that it is possible for the overall depth to remain fixed which is not possible in the non-pre-strained regime. The interplay between these distinct types of compaction is explored, and consideration is given to how understanding of behaviour can inform industrial choices.