A Fractal Approach for Mineral Breakage

HukkiÆs law is an empirical law, which does not take into account several events of energy loss during the fragmentation processes. Since experimental results are very difficult to obtain, for a large range of fragment sizes, the verification of the law is very difficult. The relation between fractures and fragmentation processes with fractal geometry was proposed some decades ago. Empirical laws known in this context show basic features of fractal geometry, mainly self-affinity and power law behaviour. Thus, in this work a model was developed to simulate the fragmentation process and to check the relation between energy consumption and fragment sizes. The model is represented on a regular lattice. Links can represent pathways for fracture processes. The events of fragmentation have energy given by a probability distribution function. In the model there is no mass loss. Propagation of fractures occurs as self-avoiding random walks on the regular lattice.