This paper presents a novel framework of modeling crushable granular materials under mechanical loadings based on the discrete element method (DEM). The framework is featured with the construction of the one-to-one model in which every particle in a physical experiment has its own numerical twin and allows the modelling of irregularly shaped fragments during the continuous breakage process. The X-ray microtomography (CT) data of particle crushing in a miniature specimen of a quartz sand was incorporated into the DEM modelling in a statistical way. The DEM simulation results of both one-dimensional (1D) compression and triaxial shearing of sands demonstrate that the proposed framework can reproduce macroscopic and particle-level behavior that agree well with the experimental results.