Investigation of granite fracture under three-point bending using the meso-modeling approach considering the random distribution of poly-crystals

A three-dimensional meso-modeling approach based on Weibull distribution for rock is proposed to study the fracture behavior of rock. And the macro-meso model of granite with random poly-crystals is developed for numerical studies. By controlling the kinetic energy of the model system and combining the erosion criterion, a method for accelerating the calculation of quasi-static problems is presented. Through the comparative analysis of numerical simulation and experimental test, the applicability and reliability of the modeling method in the study of spatial heterogeneity of rock materials are verified. Using finite element analysis, the fracture characteristics of granite at different loading rates are obtained. The effect of loading rate includes the following aspects: (1) the tensile strength and fracture toughness increase with the increase of loading rate; (2) the dynamic damage evolution process varies greatly under different loading speeds; (3) the increase of loading rate accelerates the crack propagation, and some cracks that originally propagate along the poly-crystals surface will propagate along the block. These studies offer a meso-scale strategy to study the fracture growth of rock.