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

• Published in: Acta geotechnica Vol. 15; no. 9; pp. 2599 - 2618
• Main Authors: Zhou, Shuwei, Zhuang, Xiaoying
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2020; Springer Nature B.V
• Subjects: Anisotropy; Civil engineering; Complex Fluids and Microfluidics; Computational fluid dynamics; Constitutive relationships; Crack propagation; Displacement; Engineering; Finite element analysis; Finite element method; Fluid flow; Fluid pressure; Foundations; Fracture mechanics; Fracture toughness; Geoengineering; Geotechnical Engineering & Applied Earth Sciences; Hydraulic fracturing; Hydraulics; Isotropic media; Localization; Mathematical analysis; Mechanics; Notches; Permeability; Poroelasticity; Porous media; Pressure; Propagation; Research Paper; Soft and Granular Matter; Soil Science & Conservation; Solid Mechanics; Square plates; Tensors; Toughness; Phase field model; Porous media; Transverse isotropy; Fracture propagation; Hydraulic fracturing; Staggered scheme
• ISSN: 1861-1125; 1861-1133
• DOI: 10.1007/s11440-020-00913-z

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 applies a transversely isotropic constitutive relationship between stress and strain as well as anisotropy in fracture toughness and permeability. We add an additional pressure-related term and an anisotropic fracture toughness tensor 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 to solve the displacement, fluid pressure, and phase field sequentially. Afterward, two examples are used 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.