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This paper proposes a phase field model (PFM) for describing hydraulicfracture propagation in transversely isotopic media. The coupling between thefluid flow and displacement fields is established according to the classicalBiot poroelasticity theory while the phase field model characterizes thefracture behavior. The proposed method uses a transversely isotropicconstitutive relationship between stress and strain as well as anisotropy infracture toughness and permeability. An additional pressure-related term and ananisotropic fracture toughness tensor are added in the energy functional, whichis then used to obtain the governing equations of strong form via thevariational approach. In addition, the phase field is used to constructindicator functions that transit the fluid property from the intact domain tothe fully fractured one. Moreover, the proposed PFM is implemented using thefinite element method where a staggered scheme is applied and the displacementand fluid pressure are monolithically solved in a staggered step. Afterwards,two examples are tested to initially verify the proposed PFM: a transverselyisotropic single-edge-notched square plate subjected to tension and anisotropic porous medium subjected to internal fluid pressure. Finally,numerical examples of 2D and 3D transversely isotropic media with one or twointerior notches subjected to internal fluid pressure are presented to furtherprove the capability of the proposed PFM in 2D and 3D problems.

Phase field modeling of hydraulic fracture propagation in transversely isotropic poroelastic media