Natural rock formations are anisotropic materials due to geological bedding planes and existing natural fractures. Modeling the fracturing process of anisotropic natural rocks remains a challenging issue because of numerical difficulties in dealing with the discontinuity of fractures. In this study, a phase-field method based on a variational approach with consideration of elastic displacement field and Griffith damage criteria is developed to simulate fracture initiation and propagation in transversely isotropic rocks. The capability of the proposed method is illustrated by reproducing experimental tests where rocks in a type of homogenous and transversely isotropic materials consisting of several bedding planes with a rotation angle was concerned. The simulation result regarding the fracture propagation pattern matches the experimental results. The finding of this study may help understand the fracturing process in anisotropic rocks and provide a feasibility study on modeling fracture problem in natural anisotropic rocks.
Modeling rock fracture pattern is an important topic for many rock engineering projects, such as extraction of geothermal and enhanced oil and gas recovery by hydraulic fracturing. Natural rocks are typically anisotropic brittle materials and often contain pre-existing fractures. Numerous experimental studies have been conducted to investigate the material properties and fracture propagation patterns in anisotropic rocks (Chen, Chen, et al., 2007, Mousavi Nezhad, Fisher, et al., 2018, Wang, Li, et al., 2017). To predict the fracture initiation and propagation in anisotropic brittle rocks, various anisotropic damage initiation and propagation criteria have also been developed. And fracture processes implemented in different numerical methods including the finite element method (Boone, Wawrzynek, et al., 1987), the extended finite element method (Jia, Nie, et al., 2016, Gao, Liu, et al., 2017), the discrete element method (Duan and Kwok, 2015), to name a few.
Despite these contributions, numerical modelling of fracture initiation and propagation remains a challenge due to difficulties in dealing with the discontinuity of fractures. Recently, phase-field model has been developed to model the fracture problems. To overcome the numerical difficulties associated with the discontinuities, the phase-field model replaces the discrete, discontinuous fractures by a continuous diffused/smeared damage field through the introduction of a scalar parameter, identifying the degree of damage in solid media. This technique permits the use of traditional continuum approaches, such as the finite element method to model the fracturing process.