Propagating discontinuities in ionized porous media

Ionized porous media swell or shrink under changing osmotic conditions. Examples of such materials are shales, clays, hydrogels and tissues. The materials are represented as a multi-phase material consisting of a solid part and a fluid part with fixed charges embedded in the solid matrix and counter charges in the fluid. The presence of the so-called fixed charges causes an osmotic pressure difference between the material and surrounding fluid and with that prestressing of the material. The response of the material to load is dependent on the presence of the fluid, charges and cracks. Understanding the mechanisms for fracture and failure of these materials are important for the oil industry (such as hydraulic fracturing and borehole instability), material development (diapers, orthopaedic prosthesis and seals) and in medicine (intervertebral disc herniation and tissue engineering). The relation between presence of cracks and fluid flow has had little attention, but the relation between failure and osmotic conditions has had even less attention. The aim has therefore been to study with the Finite Element Method the effect of osmotic conditions on propagating discontinuities under different types of loads for osmoelastic saturated porous media. The work covers three parts. The first part is an analytical solution of a dislocation in a swelling medium, the second is the partition of unity modeling of a mode-II crack in a swelling medium and the third is the partition of unity modeling of a mode-I crack in a swelling medium. The analytical solution for a dislocation is used as a benchmark to verify the partition of unity modeling in the simplified situation of a non-propagating dislocation. The method through which fluid flow around the crack is modeled is essentially different for mode-I compared to mode-II. In mode-I, the pressure is assumed continuous in the crack area, while in mode-II the pressure is assumed discontinuous across the crack. The numerical results show that in mode-II, the crack propagation is reasonably mesh-independent. In mode-I the crack path is mesh independent, but the induced fluid flow and speed of propagation is not mesh-independent for low stiffness, low permeability cases. The reason for the mesh dependence is probably the insufficient capture of high gradients in the crack area, which require a very fine mesh around the crack. Step-wise crack propagation through the medium is seen. This is because the propagation of the crack alternates with pauses in which the crack-tip area consolidates. The consolidation results in a progressive transfer of the load from the fluid to the solid. As the load on the solid increases, the failure load is reached and the crack propagates again. This step-wise propagation is observed both for mode-II as for mode-I. Furthermore, propagation is shown to depend on the osmotic prestressing of the medium. The dependence is present for mode-II and mode-I. In mode-II the prestressing has an influence on the angle of growth. In mode-I, the prestressing is found to enhance crack propagation or protect against failure depending on the load and material properties. It is also found that osmotic prestressing in itself can propagate fractures without external mechanical load. This mechanism may be an explanation for the tears observed in intervertebral discs as degeneration progresses.