Granular materials, due to their huge amount of industrial applications (from food industry to astrophysics), have been the object of an increasing number of studies throughout the last couple of decades. Much of the physical description concerning the behaviour of this kind of material, however, still eludes scientists, turning this field of research into a particularly rich one. Among the unsolved questions in this area there are some of growing interest, such as the mechanisms of grains transport and flux, which describe phenomena like correlated diffusion and the formation of shear bands, for example. By means of phenomenological and mathematical models, this work tries to improve the understanding of these phenomena and the mechanisms behind them, particularly the fundamental role of arches of forces created by the grains. Using a relatively simple phenomenological model and computer simulations, the role of arches becomes evident when it is observed, in the simulations, the characteristic behaviour of shear bands formation, reproducing experimental results and the predictions of theoretical models found in the literature. Simultaneously, a theoretical mathematical model was developed to describe granular correlated diffusion, a phenomenon we believe is based on the same principle of transportation by means of arches, reproducing the qualitative behaviour of computer simulations.