Implementation of Hyperbolic Tangent Function to Estimate Size Distribution of Rock Fragmentation by Blasting in Open Pit Mines

Rock fragmentation is one of the desired results of rock blasting. So, controlling and predicting it, has direct effects on operational costs of mining. There are different ways that could be used to predict the size distribution of fragmented rocks. Mathematical relations have been widely used in these predictions. From among three proposed mathematical relations, one was selected in this study to estimate the size distribution curve of blasting. The accuracy of its estimates was compared to that of the RR (Rosin-Rammler), SveDeFo (The Swedish Detonic Research Foundation), TCM (Two Component Model), CZM (Crushed Zone Model), and KCO (Kuznetsov – Cunningham - Ouchterlony) relations. The comparison included assessing the accuracy (Regression, R) and precision (Mean Square Error, MSE) of the best possible fit between the mathematical relations to estimate the cumulative distribution of fragmented rocks that result from rock blasting in open pit mines (Miduk Copper Mine, Sirjan Gol-e-Gohar, and Chadormalu Iron Mines) using image analysis technique. The results showed that the power hyperbolic tangent function can estimate size distribution of hard rock fragmentation with more uniformity in fine and coarse-grained sizes (unlike soft and altered rocks with the non-uniform distribution in these regions), more accurately and with higher precision. Also, unlike the KCO, the absence of a second turning point for the largest block dimensions (Xm) in the proposed function, can guarantee the accuracy of estimations related to any range of inputs. Finally, due to the ability of the proposed relation to accurately estimate rock fragmentation distribution caused by blasting, the uniformity coefficient required for the relation is provided by a linear combination of the geometric blasting parameters, where R=0.855 and MSE=0.0037.