# Development and Validation of Universal 3D Blast Fragmentation Model
## 1 Introduction  
Hard rock mining relies on drilling and blasting technology as the dominant method for rock breaking and further mineral extraction. The methodology assumes that several drill holes are drilled in a specific pattern, filled with explosives, and initiated in a precisely defined order. Explosive detonation generates pressure wave and forms numerous fractures in the rock mass that intersect with preexisting rock joints and newly formed blast-induced fractures, eventually forming rock fragments of different sizes and shapes. Rock fragments form a muckpile that is loaded and carried to the mineral processing plant for further scaling and chemical treatment. Different sizes and shapes of rock fragments are generated depending on the blasting pattern, type of explosives, and rock properties. Loading such rock is difficult if fragmentation is coarse, and further on-site scaling is required. This requires additional mining equipment, workforce, time to perform operations, and, from a business point of view, operational cost increases that could be avoided by better engineering. Difficulties also arise in processing plants where coarser fragmentation leads to faster wearing of the equipment and increased maintenance costs of crushing and grinding equipment, resulting in overall time and cost increase for production. On the other hand, finer fragmentation may result in losses if brittle minerals are extracted. Their improper blasting will result in a dust-like consistency that is hard to load and transport to a processing plant. Different mining methods utilize different blasting patterns. Open-pit mining dominantly uses blasting patterns with parallel blast holes, and in such situations, fragmentationis easier to control by pattern adjustments. Also, the size distribution of rock fragments is much more uniform since the spacing between blast holes is uniform. Underground mining methods rely on various blasting patterns for rock breaking, where development openings are excavated using complex blasting patterns to achieve the desired shape of the opening. Yet, there is ring or fan blasting where blast holes in the pattern are differently spaced along their length. These situations result in nonuniform fragment size distribution and loading difficulties, and additional scale requirements may result in much more complex problems for mining production. A typical case is a sublevel caving, where ring patterns are the base of the method and where fragments form gravity flow highly dependent on fragment size and spatial size distribution. Fragmentation in sublevel caving is one of the critical parameters and may compromise the whole method if blasting is not carried out with care. Geology significantly impacts fragment formation since the structural setup of rock mass defines conditions in which fragments are formed. The spacing and orientation of rock joints have a significant impact since those joints prevent the propagation of blast-induced fractures [1; 2; 3]. Therefore, the primary rock blocks' size, shape, and spatial distribution dominate fragment formation and are only partly considered by available models. Estimating blast fragmentation has been essential in mining engineering practice and research, where different methodologies have been developed over a long time. The Kuz-Ram model is widely used for predicting blast fragmentation in mining operations. Based on Rosin-Rammler distribution [4; 5; 6; 7], it is still the dominant methodology for blast fragmentation assessment, considering geological, drill, and blast properties. The model has been widely validated through field trials and found to be an acceptable predictor of blast fragmentation in various mining operations. The model can predict fragmentation using parallel blast holes, while ring blasting cases are not as extensively investigated [8]. Application of the Kuz-Ram model for ring blasting was investigated within the Kiruna and Malmberget mines in Sweden, with large-scale sublevel caving operations [8].