Phase-Field Modeling of Fracture Under Compression and Confinement in Anisotropic Geomaterials

Strongly anisotropic geomaterials, such as layered shales, have been observed to undergo fracture under compressive loading. This paper applies a phase-field fracture model to study this fracture process. While phase-field fracture models have several advantages—primarily that the fracture path is not predetermined but arises naturally from the evolution of a smooth non-singular damage field—they provide unphysical predictions when the stress state is complex and includes compression that can cause crack faces to contact.

Building on a recently developed phase-field model that accounts for compressive traction across the crack face, this paper extends the model to the setting of anisotropic fracture. The key features of the model include the following: (1) a homogenized anisotropic elastic response and strongly anisotropic model for the work to fracture; (2) an effective damage response that accounts consistently for compressive traction across the crack face, that is derived from the anisotropic elastic response; (3) a regularized crack normal field that overcomes the shortcomings of the isotropic setting, and enables the correct crack response, both across and transverse to the crack face.

To test the model, we first compare the predictions to phase-field fracture evolution calculations in a fully resolved layered specimen with spatial inhomogeneity, and show that it captures the overall patterns of crack growth. We then apply the model to previously reported experimental observations of fracture evolution in laboratory specimens of shales under compression with confinement, and find that it predicts well the observed crack patterns in a broad range of loading conditions. We further apply the model to predict the growth of wing cracks under compression and confinement. Prior approaches to simulate wing cracks have treated the initial cracks as an external boundary, which makes them difficult to apply to general settings. Here, the effective crack response model enables us to treat the initial crack simply as a nonsingular damaged zone within the computational domain, thereby allowing for easy and general computations.