Modellization of hydraulic fracturing of porous materials

We review microstructural fracture growth models suitable for the study of hydraulic fracture processes in disordered porous materials and present some basic results. It is shown that microstructural models exhibit certain similarities to corresponding theories of continua. These similarities are most easily demonstrated for simple crack geometries, i.e., straight cracks (finite size scalings). However, there exist even scaling relations which are completely independent of the particular employed crack structure. Furthermore it is demonstrated that disorder in cohesional/flow properties can influence the crack growth and the resulting fracture geometry in an essential way.