ABSTRACT:

This paper presents the theoretical formulation and numerical implementation of an anisotropic damage model for materials with intrinsic transverse isotropy, e.g. sedimentary rocks with a bedding plane. The direction dependent mechanical response is captured by utilizing four types of equivalent strains, for tension and compression, parallel and perpendicular to the bedding plane. The model is calibrated against triaxial compression test data, for different confinement and loading orientations. The variations of uniaxial tensile and compressive strengths with the orientation of the loading relative to the bedding follow the trends and magnitudes noted in experiments. Anisotropic non-local equivalent strains were used in the formulation to avoid localization and mesh dependence encountered with strain softening. Two different internal length parameters are used to distinguish the non-local effects along and perpendicular to the bedding. An arc length control algorithm is used to avoid convergence issues. Results of three-point bending tests confirm that the nonlocal approach indeed eliminates mesh dependency. Results show that the orientation and size of the damage process zone are direction dependent, and that materials with intrinsic transverse isotropy exhibit mixed fracture propagation modes except when the bedding aligns with the loading direction. Further research towards a multiscale hydro-mechanical fracture propagation scheme is undergoing.Modeling fracture propagation in sedimentary rocks requires complex coupled constitutive equations to account for both intrinsic and stress-induced anisotropy, and regularized numerical methods to avoid mesh size dependence due to strain softening. Experiments revealed that rock maximum axial compressive strength is reached when weak planes are either parallel or perpendicular to the loading direction, and minimum strength is reached when weak planes are orientated 30° –60° with respect to the loading direction (

Donath, 1961; Niandou et al., 1997; Pietruszczak and Mroz, 2001

). In indirect tensile tests, the tensile strength is maximum when tensile stress is applied within the weak plane, and gradually decreases as the orientation angle between the tensile stress direction and the bedding plane increases (

Mahjoub et al., 2015

). State-of-the-Art constitutive models are either based on Continuum Damage Mechanics (CDM) or Micromechanics. In CDM, damage criteria and evolution laws for anisotropic materials depend on a second order fabric tensor to account for the direction dependency (

Pietruszczak et al., 2007

). In Micromechanics models, the expression of the free energy is obtained by solving a matrix-inclusion problem for a given set of crack families. Depending on the homogenization scheme, crack interaction may or may not be accounted for. Intrinsic anisotropy is accounted for by attributing different properties to crack families of different orientations (

Chen et al., 2012

). Once implemented in a Finite Element (FE) code, both CDM and micromechanics models suffer from mesh dependence if strain softening is considered for compression/tension. Several localization limiters can be used, e.g. the crack band theory, a non-local integration- based formulation or non-local differentiation-based formulation. However, the non-local effects of intrinsic anisotropy are usually not accounted for.

This content is only available via PDF.
You can access this article if you purchase or spend a download.