Effect of the mineral spatial distribution heterogeneity on the tensile strength of granite: Insights from PFC3D-GBM numerical analysis

The mechanical characteristics of crystalline rocks are affected by the heterogeneity of the spatial distribution of minerals. In this paper, a novel three-dimensional (3D) grain-based model (GBM) based on particle flow code (PFC), i.e. PFC3D-GBM, is proposed. This model can accomplish the grouping of mineral grains at the 3D scale and then filling them. Then, the effect of the position distribution, geometric size, and volume composite of mineral grains on the cracking behaviour and macroscopic properties of granite are examined by conducting Brazilian splitting tests. The numerical results show that when an external load is applied to a sample, force chains will form around each contact, and the orientation distribution of the force chains is uniform, which is independent of the external load level. Furthermore, the number of high-strength force chains is proportional to the external load level, and the main orientation distribution is consistent with the external loading direction. The main orientation of the cracks is vertical to that of the high-strength force chains. The geometric size of the mineral grains controls the mechanical behaviours. As the average grain size increases, the number of transgranular contacts with higher bonding strength in the region connecting both loading points increases. The number of high-strength force chains increases, leading to an increase in the stress concentration value required for the macroscopic failure of the sample. Due to the highest bonding strength, the generation of transgranular cracks in quartz requires a higher concentrated stress value. With increasing volume composition of quartz, the number of transgranular cracks in quartz distributed in the region connecting both loading points increases, which requires many high-strength force chains. The load level rises, leading to an increase in the tensile strength of the numerical sample.