Bridging grain-scale heterogeneity and size-dependent tensile responses in granite: Computational insights into mineral arrangement and grain-boundary morphology

The tensile strength of crystalline rocks exhibits a pronounced size dependence, yet the contribution of different microstructural heterogeneities remains difficult to resolve because several sources of heterogeneity coexist in natural rocks. This study uses grain-based models of Lac du Bonnet granite to examine how mineral spatial distribution and grain-boundary morphology affect size-dependent tensile responses under Brazilian splitting and direct tension. At each specimen size, three Voronoi boundary realizations and three mineral-assignment realizations were combined in a crossed 3 × 3 design while the mineral proportions, prescribed grain-size distribution, specimen geometry, and constitutive parameters were held constant. A total of 72 simulations were performed in UDEC using a Cohesion Weakening-Friction Strengthening-Tensile Loss contact model for four specimen sizes ranging from 22.5 mm to 45.0 mm. The calculated peak strengths differ from the previous reported experimental results by approximately 7% for Brazilian splitting and 10% for direct tension. Brazilian splitting strength decreases from 10.8 MPa to 8.3 MPa with increasing specimen size, corresponding to a 23.1% reduction, whereas direct tensile strength exhibits a non-monotonic size-dependent response and size-dependent dispersion. Mineral redistribution modifies both local elastic stress transfer and the occurrence and connectivity of mineral-pair contacts. Within the adopted intergranular-fracture framework, grain-boundary morphology produces larger changes in stress localization, crack deflection, and fracture-path evolution. The contrast between the two tests is related to the loading configuration: Brazilian splitting restricts fracture to a narrow central region, whereas direct tension permits greater competition among potential initiation sites and fracture paths. The observed size-dependent tensile responses therefore result from the combined influence of specimen size, loading configuration, and grain-scale heterogeneity.