Implications of single or multiple pressure degrees of freedom at fractures in fluid-saturated porous media

The physical consequences of modelling the fluid pressure across a fracture using one, two or three degrees of freedom are elucidated. The implications are demonstrated for each model through numerical examples for different boundary value problems. When fracture propagation is mainly driven by mechanical loads a single pressure degree of freedom is normally sufficient. Modelling of the pressure as a discontinuous quantity can be done using a double degree of freedom, similar to the modelling of displacements. Historically, this has been proposed first, but it appears to be less well applicable, except for cases where there is no significant fluid transport along the fracture, as in shear failures. Modelling the pressure with a triple degree of freedom for the pressure at the fracture is the most versatile approach, and is physically the most reasonable and efficient approach to model the propagation of internally pressurised cracks (hydraulic fracturing).