On the onset of flow instabilities in granular media due to porosity inhomogeneities

The paper concerns a theoretical description able to capture the onset of instabilities in saturated sands at high filtration velocities (e.g. the onset of piping phenomena). Motivated by own experiments we propose a thermodynamical two component model which accounts for a threshold effect at a critical value of the relative velocity of components. This property is incorporated in the source term of momentum balance equations by means of a nonlinear contribution accounting for spatial variations of the porosity. We prove the thermodynamical admissibility of such a model. By means of a linear stability analysis we show the existence of the onset of instability for realistic values of material parameters gained from experiments.