Simulation of the mineral breakage using a fractal approach

Abstract

Hukki's law is an empirical law, which does not take into account several events of energy loss during the mineral 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 the fracture and fragmentation processes with fractal geometry has been proposed some decades ago. Empirical laws along this context show basic features of fractal geometry, mainly self-affinity and the power law behavior. Thus, in this paper, a model to simulate the fragmentation process and to check the relationship between energy consumption and fragment sizes was developed. The model is represented on a regular lattice where links represent pathways for fracture processes. The energy of fragmentation events was modeled by a probability distribution function. In the proposed model there is no mass loss and the fracture propagation occurs as self-avoiding random walks on the regular lattice.