Statistical description of fracture pattern from single particle crushing test

The spatial distribution of fractures inside sand particles are highly influenced by loading condition, external morphologies and internal microstructures, i.e., initial cracks and voids. To understand this relationship, it is important to obtain quantitative measurements of the spatial distribution of fractures. In this study, the two-point correlation function was utilized to measure fractures. This function was implemented in three different ways, i.e., sample method, exponential method, and point-by-point method. These methods were applied to analysis the fracture of natural Leighton Buzzard Sand (LBS) particle obtained by an in-situ X-ray CT test on single particle crushing. It is found that the fractures are mainly parallel to the loading direction. While the sampling method generates almost the same results as those from the point-bypoint method, the exponential method could only reflect the pattern of the main direction.