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 Widerstande. 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 firactal 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. (C) 2002 Elsevier Science B.V. All rights reserved.