This paper represents a grain-based discrete element model for simulating the quasi-brittle failure of polycrystalline rocks considering the grain-scale geometrical and material heterogeneities of geo-material fabric. A rock material is represented by an assembly of polygonal grains bonded through their cohesive contacts. As a result, the micro-fracturing process can be simulated explicitly by development of crack along grain boundaries. Micro-mechanical parameters of the model is calibrated to Lac du Bonnet granite such that the model reproduces the physics similar to those of the rock during compression and tension. The calibration procedure is based on categorizing a set of input parameters that controls the elastic and fracture behavior of the model. The relation between macro-properties such as strength, friction and cohesion of the model and input micro-mechanical properties assigned to grains and interfaces is investigated by simulating a series of compressive triaxial and Brazilain tensile tests. The numerical experimentations demonstrate the capability of discrete element-Voronoi model to mimic the pre- and post-failure responses of brittle materials. The calibrated model very accurately predicts, in a quantitative sense, the macroscopic properties of real granite such as elastic properties, damage thresholds (crack initiation and interaction stresses), peak strengths (tensile and compression strengths), triaxial strength envelope (friction angle and cohesion). Results demonstrate the importance of considering the microstructural heterogeneity of rock fabric for successful modelling of brittle rock fracture.
The process of brittle rock fracture during compression and tension is a result of the initiation, growth, and coalescence of multiple individual micro-cracks which eventually leads to formation of some clustered regions of macro-fractures in rock. As the compressive, or tensile stress applies across the boundaries of a rock sample, a complex heterogeneous stress system will be distributed through the rock in which the tensile and shear stresses will be concentrated at pre-existing flaws (i.e. micro-cracks, grain boundaries, cavities, cleavages) . If the localized tensile stress exceeds the local strength of the microstructure some micro-cracks start to form at the point on the boundary of pre-existing flaw where tensile stress concentration is greatest. These axially aligned extensional micro-cracks occur during the early loading stages of compression tests. As the applied deviatoric stresses increase in the specimen, the density of compression-induced tensile cracks increases, and eventual interaction and coalescence of these cracks result in formation of some localized and macroscopic damaged zones in the material. It is the presence and creation of such micro-fractures that cause the compressional stress-strain curve of rock to deviate from true elastic (linearity) in the pre-failure region .