Grain breakage in rockfill in civil engineering structures is the major cause responsible for settlement and collapse. It is inherently due to large grain size and angular shape of the grains. To model these features, a three-dimensional discrete element model of a breakable grain is presented hereafter. The model is able to reproduce grain breakage into rigid irregular fragments with conservation of the mass of the initial grain. Polyhedral shapes are chosen to represent the grains, and are divided into irregular tetrahedral fragments joined together by a cohesive law to enable breakage. This model is implemented in a Non-Smooth Contact Dynamics code. Single grain crushing tests are first conducted to capture the influence of mechanical and geometrical parameters of the model. The intra-granular cohesion defines the grain strength. The grain size and the size and geometrical disposition of subgrains can act in a competitive way, thus contributing to the definition of the grain strength, and in the validation of the scale of effect observed in this type of material: the bigger the grain, the lower its strength. The same grain model is then used to generate multi granular samples subjected to oedometric compression, where grains interact via contact and friction processes, with a uniform initial grain size distribution. The effects of grain breakage are investigated through the analysis on the macroscopic and microscopic scales, with a comparison with unbreakable grains samples. The ability of the model to reproduce physical laboratory tests is confirmed through the simulations.