By means of the contact dynamics method together with a particle fracture model, in which the particles are cohesive aggregates of irreducible polygonal fragments, we investigate the evolution of particle size distribution in the process of uniaxial compaction of granular materials. The case of single particle breakup under compressive stress is used to test the method and the influence of discretization (number of irreducible fragments). We show that the breaking threshold of the granular assembly scales with the internal cohesion of the particles but it depends also on the initial size distribution and irregularity of polygonal particle shapes. The evolution of size distribution proceeds by consecutive periods of intense particle crushing, characterized by local shattering instability, and periods of little breaking activity. Starting with either monodisperse or power-law distribution of particle sizes, the latter evolves towards a broad distribution of the fragmented particles with a nearly power-law distribution in the range of intermediate particle sizes. Interestingly, a finite number of large particles survive despite ongoing crushing process due to the more homogeneous distribution of forces in the presence of small fragmented particles filling the pores between larger particles.