Blast-Fragmentation Prediction Derived From the Fragment Size-Energy Fan Concept

Abstract

The size-energy fan concept formulation is developed into a prediction model of the fragment size distribution from blast design and rock mass variables. The fragment size is scaled with a characteristic size of the blast and the rock mass discontinuity spacing and orientation. The energy is scaled with the rock strength and the cooperation degree between adjacent holes. A cooperation function is introduced that modifies the energy with the in-row delay, non-dimensionalized with the P-wave velocity and the holes spacing. The cooperation increases as the delay increases up to a certain value, beyond which the cooperation decreases and the fragmentation is coarser. Several prediction models are presented, using the Swebrec-based fan slopes function of the percent passing as starting point, with subsequent improvements involving alternative formulations of that function, that encompass a non-Swebrec underlying distribution of the fragment size. The models include 12 to 14 parameters, controlling the effect on fragmentation of the variables describing the rock mass, the explosive and initiation sequence, and the blast geometry. The parameters are determined from fits to the data base that was used for the xP-frag model, expanded with seventeen additional blasts. All fragmentation data used are mass size distributions determined by sieving and weighing of blasted muckpiles. The different models are introduced sequentially and discussed. The models presented improve the performance of xP-frag, while including a much smaller number of parameters and, unlike xP-frag, keeping the physically sound size-energy fan pattern, effectively extending its nature from a descriptive frame of the fragmentation-energy relations, to a predictive tool.