The objective of our research is to define a new Discrete Element Method (DEM) that can describe the processes involved in particle breakage and the resulting macroscopic behaviour of the particulate assembly, by directly observing and characterizing breakage mechanisms. To this aim, an oedometer compression test is performed on a dry granular assembly of zeolite, while acquiring 3D images of the specimen at several strain levels with an x-ray computed tomography device. We construct a DEM model that reproduces experimental observations, mainly: axial splitting is the main breakage mode; fragments are subjected to further breakage; very few fragments pass through the breakage plane. A fragment size limit is defined to reduce the computational cost associated with large numbers of breakage generations. We simulate the oedometer test for the same initial microstructure as in the lab test and with realistic particle mechanical properties, and compare the results to the 3D images. The numerical results show that our proposed model can capture the size evolution, shape change and mechanical response of the tested specimens.