Modeling of Tensile and Compressive Damage in Layered Sedimentary Rock: A Direction Dependent Non-Local Model

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.