Fracture-Induced Anisotropy of the Stress–Strain Response of Shale at Multiple Scales

Abstract

This paper investigates deformation and stiffness anisotropy induced by damage propagation in a rock brittle deformation regime. Specifically, a finite-element–based Continuum damage mechanics model is used to capture sample size effects and the influence of intrinsic anisotropy on the stress–strain response of shale. The differential stress-induced damage (DSID) model previously proposed by the authors is calibrated against triaxial compression tests performed on North Dakota Bakken shale samples. Laboratory tests simulated with the FEM reproduce deformation and damage localization phenomena and capture the increase of boundary effects expected in larger samples. Simulations performed for various initial states of damage are used to investigate the role of the dominant fabric anisotropy of the rock: bedding planes in shale are modeled by a smeared damage zone with the DSID model and by a discrete crack plane. The continuum approach successfully captures the development of microcrack propagation and energy dissipation at the early stage of the strain hardening process observed in triaxial compression tests. Additionally, using initial anisotropic damage can effectively account for various types of mechanical anisotropy in shale.