Voronoi-Based Discrete Element Analyses to Assess the Influence of the Grain Size and Its Uniformity on the Apparent Fracture Toughness of Notched Rock Specimens

Abstract

The fracture toughness reflects the rock resistance to crack propagation, and therefore represents an important parameter for rock fracture assessments. From a strict point of view, the real fracture toughness (it {K}_{mathrm{it IC}}) corresponds to a cracked situation in which the notch radius is theoretically equal to zero. However, most of the defects in rocks have a finite radius and, therefore, should be studied as notch-type defects. Here, the notch effect is numerically studied together with the influence of the grain size and the sorting coefficient (grain size uniformity) on the apparent fracture toughness (it {K}_{mathrm{it IN}}). To this end, several four-point bending tests with different U-shaped notch radii, mean grain sizes and degrees of uniformity in grain size and shape have been simulated using the Discrete Element Method. In order to represent the grains of the rocks, the Voronoi tessellation is used to create randomly sized and distributed polygonal blocks. These Voronoi polygons have been defined, on the one hand, by an average edge length of 1, 2 and 3 mm, and, on the other hand, by a different number of iterations (n) in the relaxation process during the generation of the polygons, which defines the grain size uniformity. The numerical analyses performed and the interpretation of the results show a clear notch effect in all the studied cases, as the apparent fracture toughness (it {K}_{mathrm{it IN}}) increases with notch radius. Finally, the obtained stress fields at the notch tip have been compared to those obtained from the traditional finite element method.