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A simple, yet complete framework is introduced with the aim of modelling grain breakage in soils and crushable granular materials. The evolution of grain breakage is measured using a specific parameter of the grain-size distribution. The evolution of this new breakage parameter is related to the applied mechanical work, which allows the predictions to be independent of the stress paths. The correlation function proposed is trilinear, and is capable of describing the initiation, development, and stabilization of breakage. The initial state, coupled with three additional parameters, is used to calibrate this function. The three parameters are related to a grain specific quantity representing the strength of the particles that form the granular medium. The theory of fractal fragmentation is adopted, and the final state is considered to be unique and described by a single parameter: the fractal dimension. When tested against experimental results, this model was able to correctly predict the crushable behavior of a sand. [ABSTRACT FROM AUTHOR]

The authors reply to a comment on the their paper "Particle breakage in granular material -- A conceptual framework." Topics discussed include the effect of grain-size distribution (GSD) on particle breakage, the engineering applications of the breakage mechanics framework, and a proposed way to include the effect of soil density in the conceptual model.