A model for fragmentation in bench blasting that originates from dimensional analysis of fragmentation in asteroid collision is presented. Percentiles of the size distributions are obtained in the basic model as the product of rock strength-to-explosive energy ratio, a bench shape factor, a scale factor or characteristic size and percentage passing-related factor. The parameters of the model are fitted to data from 169 bench blasts in different sites and rock types, bench geometries and delay times, for which the fragmentation of the muck pile was obtained by sieving. The basic model is found to significantly improve with an additional factor describing the rock mass structure in terms of the spacing and orientation of discontinuities, and another one describing the delay between successive contiguous shots; the latter is conveniently formulated as a function of the p-wave velocity and the holes spacing. The rock strength property chosen is the strain energy at rupture that, together with the explosive energy density (or energy powder factor), forms a combined rock strength/explosive energy non-dimensional factor. The model, called xP-frag, is applicable from 5 to 100 percentile fragment 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 a half to one third of the errors expected with the best prediction models available to date.