Fracturing dry and saturated porous media, Peridynamics and dispersion

Peridynamics is currently widely used because of its superior ability to model dynamic crack propagation and branching. This is particularly important in geophysics problems involving seismicity, in steering of hydraulic fracture operations and in fracturing saturated/partially saturated geomaterials. Unfortunately, Peridynamics may exhibit an undesirable dispersion behavior. It is shown that in coupled peridynamics/finite element models for multiphase porous media the dispersion behavior is substantially improved because of the presence of a Laplacian in the mass balance equation of the fluid linked to Darcy flow. The ensuing rate dependence and connected length scales in 1D and 2D/3D situations are recalled. Numerical experiments show that the resulting behavior due to these length scales is generally acceptable.