Experimental and analytical assessment of fracture criteria for non-spherical sand grains

Particle shape affects the mechanical behavior of crushable granular media, especially in the context of phenomena such as impact and penetration. However, shape descriptors are rarely incorporated into fracture criteria for single grains, which focus instead on size effects and assume idealized spherical geometries. This study aims to extend multiple frameworks used to predict the crushing resistance of individual sand grains by incorporating the effect of particle shape. We conducted an experimental study for varying grain geometries, as revealed by x-ray tomography, and propose a series of analytical models incorporating the grains’ aspect ratio, computed by ellipsoidal approximation fitting. Specifically, non-spherical shape descriptors are incorporated into different contact laws, fracture criteria, and statistical failure models providing closed-form expressions of the strength of single particles as a function of their size and shape. We compare the performance of these models and assess their accuracy against a series of compression experiments on Ottawa sand grains. Experimentally, we find that elongated grains tend to break at lower compression stress than spherical particles of equal size and that their strength depends more on their shape than on their size. By comparing the performance of the proposed models, it was found that the modified Weibull model for non-spherical grains provides the best overall performance. However, the proposed centre crack model for ellipsoidal grains was found to have a similarly satisfactory ability to capture the experimental evidence, while requiring a simpler parameter calibration procedure. By providing criteria to rationalize and predict the effect of the shape on the crushing resistance of single particles, these results offer an analytical foundation to model shape-dependent particle strength in discrete and continuum models for particle crushing which require this quantity as an input for their analyses.

Graphical abstract