A poromechanical framework for hydraulic fracturing processes in transversely isotropic rocks

We present a poromechanical framework for hydraulic fracturing processes in transversely isotropic rocks. We derive the conservation laws and effective stress formulation for the coupled solid deformation, damage evolution, and fluid flow processes in porous rocks based on the mixture theory and continuum thermodynamics. For the modeling of hydraulic fracture propagation in transversely isotropic rocks, a recently developed double-phase-field model is adopted that considers fracture initiation through the rock matrix and along the weak bedding planes. The finite element framework for the coupled processes is introduced in detail as a \(u-p-d\) formulation, and the staggered numerical solution scheme is adopted that updates the displacement and pore pressure fields first and then the phase-field variables. We then conduct element-level simulations to verify the proposed framework. Lastly, we investigate the hydraulic fracturing processes for both isotropic and transversely isotropic rocks. The impact of bedding plane orientations, strength ratios between the rock matrix and bedding planes, strength anisotropy levels of the rock matrix, and tectonic stress conditions on the initiation and propagation of hydraulic fractures in transversely isotropic rocks are studied.