Discontinuous versus continuous chemical potential across a crack in a swelling porous medium

Understanding and prediction of mechanisms of failure is needed to develop methods for prevention and treatment of failure. To increase the accuracy for the prediction of failure, advanced computational models are developed. Mesh-independent modeling of cracks in porous media is obtained by enriching the displacement field with a discontinuous shape function describing the crack. In a poroelastic finite element modeling, an enrichment of the pressure field is mandatory around the crack. Two options are available to account for the sharp pressure gradient around the crack. One is to resolve the pressure gradient using a continuous pressure enrichment, the other is not to resolve the steep gradients and use discontinuous jumps across the crack surface. In the latter case, analytical solutions of the pressure field at an interface is used to evaluate the real pressure gradient. This paper formulates criteria to decide whether to use one or the other approach. The techniques are applied to swelling media in which the pressure degree of freedom takes the form of a chemical potential