Percentile Fragment Size Predictions for Blasted Rock and the Fragmentation–Energy Fan

Abstract

It is shown that blast fragmentation data in the form of sets of percentile fragment sizes, xP, as function of specific charge (powder factor, q) often form a set of straight lines in a log(xP) versus log(q) diagram that tend to converge on a common focal point. This is clear for single-hole shots with normal specific charge values in specimens of virgin material, and the phenomenon is called the fragmentation–energy fan. Field data from bench blasting with several holes in single or multiple rows in rock give data that scatter much more, but examples show that the fragmentation data tend to form such fans. The fan behavior implies that the slopes of the straight size versus specific charge lines in log–log space depend only on the percentile level in a given test setup. It is shown that this property can be derived for size distribution functions of the form P[ln(xmax/x)/ln(xmax/x50)]. An example is the Swebrec function; for it to comply with the fragmentation–energy fan properties, the undulation parameter b must be constant. The existence of the fragmentation–energy fan contradicts two basic assumptions of the Kuz-Ram model: (1) that the Rosin–Rammler function reproduces the sieving data well and (2) that the uniformity index n is a constant, independent of q. This favors formulating the prediction formulas instead in terms of the percentile fragment size xP for arbitrary P values, parameters that by definition are independent of any size distribution, be it the Rosin–Rammler, Swebrec or other. A generalization of the fan behavior to include non-dimensional fragment sizes and an energy term with explicit size dependence seems possible to make.