Continuum-based heterogenous models for capturing brittle damage and failure of hard rocks under loading and unloading conditions

Abstract

Grain-scale heterogeneities play a crucial role in the failure process of hard brittle rocks. Previous numerical investigations have often overlooked certain sources of heterogeneity and the inherent variability in laboratory test data during model calibration. This study aims to assess the impact of grain-scale heterogeneities on macro-property variability, internal stress variations, and unloading-induced brittle damage using continuum-based heterogeneous models. For this purpose, ten realizations of homogeneous (consisting of one mineral type) and heterogeneous (consisting of four mineral types) Voronoi Tessellated Models (VTMs) were generated. These models were calibrated to match the mean strength of undamaged Lac du Bonnet (LdB) granite. The heterogeneous VTM demonstrated a stronger agreement with LdB granite in terms of the shape of the strength envelope and peak strength variability compared to the homogeneous VTM. Analysis of internal elastic stresses revealed higher induced tensile stresses within the heterogeneous VTM than the homogeneous VTM during compressive loading. Furthermore, it was found that, in contrast to the homogeneous VTM, unloading-induced brittle damage in the heterogeneous VTM led to a reduction in its peak strength and Young’s modulus, aligning with laboratory test results. Therefore, the heterogeneous VTM is deemed a more representative model for hard rocks than the homogeneous VTM.