Granular materials are ubiquitous in one's daily life. They can be found in the cereal you eat, the sugar you put in your coffee or the sand you walk on in the beach. The study of granular materials has a rich history dating back to the 17th century where Kepler studied the packing of particles. The compaction of granular materials is a problem that is studied by using theory, experiments and simulations. While these studies have yielded some important results, there still are many details about the mechanisms of granular compaction that are unknown.

In this thesis, the density relaxation phenomenon is modeled using both Monte Carlo and discrete element simulations to investigate the effects of regular taps applied to a vessel having a planar floor filled with monodisperse spheres. Results suggest the existence of a critical tap intensity which produces a maximum bulk solids fraction. A key result that is found in this thesis is the mechanism responsible for the relaxation phenomenon is an evolving ordered packing structure propagating upwards from the plane floor.