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A simple, yet complete framework is introduced with the aim or modelling gram breakage in sous and crusnabie 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. Key words: particle breakage, granular media, grain crushing, fractal, particle strength, grain size distribution. Un cadre mecanique a la fois simple et complet est introduit dans le but de modeliser la rupture des grains dans les sols et autres milieux granulaires broyables. L'evolution de la rupture des grains est mesuree en utilisant un parametre caracteristique de la distribution granulometrique. L'evolution de ce nouveau parametre de rupture est reliee au travail mecanique applique, ce qui rend les predictions independantes du chemin des contraintes. La fonction de correlation proposee est trilineaire, et donc capable de decrire l'initiation, le developpement et la stabilisation de la rupture. L'etat initialainsi que trois autres parametres servent a calibrer cette fonction. Les trois parametres sont relies a une quantite propre au grain, et qui represente la resistance des particules qui forment le milieu granulaire. La theorie de la fragmentation fractale est adoptee, et l'etat final est donc suppose comme etant unique, et decrit par un seul parametre : la dimension fractale. Lorsque le modele est teste et les resultats compares a des travaux experimentaux, il devient possible d'apprecier la capacite du modele a simuler le comportement d'un sable. Mots-cles: rupture des particules, milieu granulaire, broyage des grains, fractal, resistance des particules, distribution granulometrique., Introduction Granular materials are of particular interest for civil engineers and soil mechanics specialists. Over time, the integrity of these materials varies depending on the mechanical conditions, the nature of [...]

We are grateful for the interest in our paper (Konrad and Salami 2018). The discussers reviewed the conceptual model for particle breakage in granular materials, and proposed ways to improve [...]