Breakage Indices for Constitutive Models to Track the Evolution of Particle Crushing Under Continuous Shearing

Researchers have developed numerous breakage indices, predominantly relying on comparisons between pre- and post-test Grain Size Distribution (GSD) curves determined through conventional sieve analysis. Although these indices enable a precise estimation of particle breakage extent, a significant limitation arises when attempting to integrate them into constitutive models, especially when those models cannot consider GSD as an input. This paper addresses the need for tailored breakage indices designed to suit the specific requirements of different families of constitutive models. The new indices have been developed based on stress and strain tensor invariants or combinations thereof, ensuring the future ease of implementation into various constitutive models. The proposed equations have been validated using five different sets of experiments performed on rockfill material, calcareous, and quartz sands. The comparison between the available experimental data and the estimated degree of particle breakage using the suggested indices demonstrates their adequate performance. The novel indices can be integrated into different constitutive models, including hypoplastic, elastoplastic, and thermodynamically consistent approaches, as well as tested for their practical applicability for boundary value problems.