A New Hyperbolic Function Approach of Rock Fragmentation Size Distribution Prediction Models

It is well known that the first stage of mine-to-mill optimization is rock fragmentation by blasting. The degree of rock fragmentation can be expressed in terms of average grain (X50) size and size distribution. There are approaches in which exponential functions are used to estimate the size distribution of the pile that will be formed before blasting. The most common of these exponential functions used to estimate the average grain size is the Kuz–Ram and KCO functions. The exponential functions provide a curve from 0% to 100% using the mean grain size (X50), characteristic size (XC), and uniformity index (n) parameters. This distribution curve can make predictions in the range of fine grains and coarse grains outside the acceptable error limits in some cases. In this article, the usability of the hyperbolic tangent function, which is symmetrical at origin, in the estimation of the size distribution as an alternative to the exponential distribution functions used in almost all estimation models is investigated. As with exponential functions, the hyperbolic tangent function can express the aggregated size distribution as a percentage with reference to the variables X50 and XC. It has been shown that the hyperbolic tangent function provides 99% accuracy to the distribution of fine grains and coarse grains of the pile formed as a result of blasting data for the characteristic size (XC) parameter and the uniformity index (n).