The Effect of Materials Structure on the Features of Fracture Process in Rocks: Discrete Elements Modeling and Laboratory Experiment

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Abstract
—A computer model of fracture in heterogeneous materials (including rocks) is proposed to study evolution of the defect structure (cracks) during deformation process. The model is based on the Discrete Element Method (DEM), which, in contrast to the methods relying on continuum mechanics, naturally simulates the formation and evolution of cracks. We used the bonded particle model (BPM), which is widely used in various modifications to study the fracture process. The material is modeled by a set of spherical particles (simulating polycrystalline grains), connected by bonds placed at particle contact points, which simulate grain boundaries. In the BPM model, crack initiation is determined by the breakage of bonds, and its propagation is provided by the coalescence of a numerous set of broken bonds. Computer experiments were performed with different material parameters (different mechanical properties of grains and grain boundaries, different grain sizes) to determine their effect on the local stress patterns, defect formation, and fracture source nucleation and development. The calculations were performed in the open-source DEM simulation software MUSEN. Samples were modeled by cylinders filled with spherical particles of the same or different radii packed up to reaching the void ratio 0.35–0.37. The materials simulating grains and bonds (grain boundaries) were specified with mechanical parameters corresponding to granite, quartz, orthoclase, oligoclase, and glass. The sample was placed in a virtual press in which a bottom plate was fixed and a top plate was moved towards the lower plate at a constant rate until the sample failed. The maximum local stress calculations have shown that homogeneous materials yield more heterogeneous spatial distributions of local stresses and vice versa—material heterogeneity leads to more uniform stress distributions. Comparison with the results of laboratory rock deformation experiments has shown that the proposed model of polycrystalline materials realistically describes some features of fracture in these materials when the main processes occur along the grain boundaries. These features include the brittle type of fracture in homogeneous materials and the presence of nonlinear elasticity (plasticity) revealed for more heterogeneous materials based on the stress-strain diagrams, as well as the time behavior of “acoustic emission rate” (or acoustic activity)—the number of bonds broken per unit time. For heterogeneous materials, the model shows a two-stage pattern of the fracture process with uniform defect accumulation throughout the sample at the first stage and the formation and growth of fracture nucleation sites at the second stage.

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