Granular materials forming part of rockfill dams or the base of pavements are subjected to large compressive stresses. As a result of these stresses, the granular materials break into pieces of different sizes. The size distribution of the broken granular material has been found to be fractal in nature. However, there are few explanations to date about the mechanisms that cause a granular material to develop a fractal size distribution. In this study, a simulated compression test designed to crush granular materials is presented. The compression test was numerically simulated using the Discrete Element Method (DEM). The DEM simulation indicated that the particles developed a network of force chains in order to resist the compressive stress. These force chains did not have a uniform intensity but was found to vary widely through out the sample. The intensity of the force chains was found to be fractal in nature. Also, the force chains in the sample did not involve all the grains. Thus, the force chains did not cover the whole sample. Using the box method, it was determined that the distribution of the force chains in the sample was fractal in nature. Thus, the fractal nature of the intensity of the force chains and their distribution were found to be the main reason the granular materials developed a fractal size distribution when subjected to a compressive force.