A Distribution-Free Description of Fragmentation by Blasting Based on Dimensional Analysis

A model for fragmentation in bench blasting is developed from dimensional analysis adapted from asteroid collision theory, to which two factors have been added: one describing the discontinuities spacing and orientation and another the delay between successive contiguous shots. The formulae are calibrated by nonlinear fits to 169 bench blasts in different sites and rock types, bench geometries and delay times, for which the blast design data and the size distributions of the muckpile obtained by sieving were available. Percentile sizes of the fragments distribution are obtained as the product of a rock mass structural factor, a rock strength-to-explosive energy ratio, a bench shape factor, a scale factor or characteristic size and a function of the in-row delay. The rock structure is described by means of the joints' mean spacing and orientation with respect to the free face. The strength property chosen is the strain energy at rupture that, together with the explosive energy density, forms a combined rock strength/explosive energy factor. The model is applicable from 5 to 100 percentile sizes, with all parameters determined from the fits significant to a 0.05 level. The expected error of the prediction is below 25% at any percentile. These errors are half to one-third of the errors expected with the best prediction models available to date.