Energy Dissipation During Mode I Fracture Propagation in Shale: Comparison between a Continuum Damage Model, a Cohesive Zone Model and the Extended Finite Element Method
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We modeled mode I fracture in shale with an equivalent damage zone (CDM), a cohesive zone (CZM) and discontinuous enrichment functions (XFEM). In the Differential Stress Induced Damage model (DSID model) used in the continuum approach the total work input is equal to the sum of the energy released by crack debonding, the energy dissipated by crack opening, and the elastic strain energy stored in the bulk outside of the damage zone. In CZM and XFEM, the overall stiffness of the rock mass in the process zone drops as soon as the fracture starts propagating (unstable fracture propagation), whereas rock elastic properties in the CDM equivalent damage zone evolve smoothly with the displacement imposed at the boundary of the domain. In the CZM and XFEM, fracture propagation stabilizes after a turning point : this point coincides with damage initiation in the DSID model. As a result, the total energy of the rock mass calculated with CDM is about twice as large as in CZM and XFEM. The relative energy components of the rock mass are in the same order of magnitude and follow the same trends in the three models. This numerical study compares the evolution of dissipated energy potentials during mode I fracture propagation, and is expected to provide a basis to predict the amount of energy released by discrete fracture growth vs. damage propagation in the fracture process zone.