A unified fractional breakage model for granular materials inspired by the crushing tests of dyed gypsum particles

Particle breakage of granular materials is a phenomenon of great importance in engineering practices. This paper presents a unified particle breakage model for granular materials, which is able to capture the evolution of the particle size distribution (PSD) of each size fraction of particles. A novel experimental technique using dyed gypsum particles (DGPs) to track the fractional particle breakage was first adopted in the one-dimensional compression tests. A unique path of the fractional particle breakage, regardless of whether the particles were in a polydisperse medium or in other different granular assemblies, was then experimentally identified. This result has inspired the introduction of the definition of a fractional breakage index, based on which the breakage-plastic work relationship for overall granular assemblies was extended to describe the fractional particle breakage. The established fractional particle breakage model differs from most existing particle breakage models in that it is able to capture both the evolution of the fractional and the overall PSDs of granular materials, even when the initial PSD of the granular material surpassed partially the theoretical fractal PSD. These results set a vision to predict and understand the particle breakage of granular materials in industrial activities.