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