Scaling laws for the size-dependent breakage force of brittle near-spherical particles under quasi-static loading

This study investigates the size-dependent breakage force of brittle, near-spherical particles under quasi-static compressive loading. A physically motivated analytical model is derived, predicting a power-law relationship between particle size and breakage force—specifically, a quadratic scaling with diameter and a 2/3-power scaling with mass. To validate this model, a multi-material experimental campaign using synthetically produced spherical specimens was conducted, followed by a numerical simulation campaign using the Discrete Element Method (DEM) with a bonded particle modelling (BPM) approach. The experimental results confirmed the proposed scaling law, with coefficients of determination (R2) exceeding 0.94 for a combined material consideration. The DEM simulations, calibrated using experimental data, reproduced breakage forces, and scaling patterns with high fidelity and enabled extension of the size range by a factor of more than two in diameter and four in mass, whilst also increasing statistical resolution through a higher number of replicates per size class. This numerical extension not only enabled broader parameter exploration but also mitigated experimental limitations, such as specimen variability, preparation inconsistency, and practical size constraints.Across analytical, experimental, and numerical approaches, consistent agreement was found, supporting the general applicability of the model. The findings provide a robust basis for defining breakage thresholds in DEM-based simulations—e.g. for replacement-based approaches—and offer a scalable alternative to physical testing. The validated framework facilitates improved prediction of breakage behaviour in slow compression systems such as jaw crushers and contributes to the broader understanding of particle-scale mechanics in brittle materials.