A multifractal comminution approach for drilling scaling laws

The drilling comminution is theoretically and experimentally analyzed by a multifractal approach. A generalization of the three classical comminution laws Rittinger, P.R., 1867. Lehrbuch der Aufbereitungskunde. Berlin; Kick, F., 1885. Das Gesetz der Proportionalen Widerstände. Leipzig; Bond, F.C., Min. Eng. 193 (1952) 484] has been performed to evaluate the energy dissipation in the process and to compute the mass distribution of the particles. A transitional fractal exponent of the fragment size distribution is experimentally demonstrated to exist. As a consequence, a multifractal scaling law for the partial mass of fragments and its physical interpretation is consistently proposed.In addition, we show, both theoretically and experimentally, that the drilling strength is strongly size-dependent and cannot be considered a material constant, as classically supposed. Consequently, a multifractal scaling law for the drilling strength is also proposed.