Performance of some distributions to describe rock fragmentation data

Ten functions (Weibull, Swebrec, Gilvarry, Grady and Lognormal, and their bi-component versions) are fitted to 448 sets of screened fragment size data from blasted and crushed rock. The ordinary least squares criterion has been used for the fits and two minimization techniques have been tested, in both cases running the problem repeatedly with different initial values of the unknown parameters in order to ensure a global minimum. There is a distinct behavior of errors across the passing range, which has been divided in four zones, coarse (>80%), central (80%–20%), fine (20%–2%) and very fine (<2%). The representation of fragmentation data by some of the distributions can be made with good accuracy in the coarse and central zones, with moderate accuracy in the fine zone and with considerably poor accuracy in the very fine zone. As expected, bi-component distributions generally perform better than the single-components, though there are important differences among them. Extended Swebrec is consistently the best fitting distribution in all zones, with maximum relative errors of less than 25% in the coarse, 15% in the central, and 50% in the fine zones. Bimodal Weibull, bimodal Gilvarry and bimodal Grady's errors are statistically equivalent to extended Swebrec's in the central and fine zones. In the very fine zone, relative errors have a high probability of being in excess of 100%, with maximum expected values being several times that, even for the best fitting functions in this zone. Swebrec is by far the best single component function in all zones, with errors comparable to the best bi-components in the coarse and central.

► A large amount of experimental fragmentation data is compiled.
► Five distributions' functions, and their bi-component versions, are assessed.
► Two non-linear minimization techniques are applied to size distribution fitting.
► Quality of the fits is carefully analyzed in different sections of the curves.
► Functions are ranked by their performance in representing the experimental data.