# Development and Validation of Universal 3D Blast Fragmentation Model
## 1 Introduction
The Kuz-Ram model was modified to meet mines' requirements where blast fragmentation significantly affects overall production effectiveness. The model had limitations due to the problems related to determining rock factors, mean fragment size, and handling of the area where rock is broken due to the crater effect. Representation of the primary rock blocks was identified as an issue as well. It should be noted that sublevel caving ring blasting is a specific case since it is done in confined conditions. The presence of fragmented rock in front of the free surface limits the movement of the blasted rock. It reduces its subsequent fragmentation related to fragment interaction and ground impact, which are common in unconfined blasting conditions. Models developed by Julius Kruttschnitt Mineral Research Centre (JKMRC) are based on the Kuz-Ram model and tend to overcome its limitations regarding fines estimation. These are known as the \"Two component model\" [9] and \"Crush zone model\" [10; 11]. Further improvements in fragmentation assessment, especially in the estimation of fines content and optimization, were made by introducing the Swebrec function [12]. The Fragmento model within JKSimBlast v2 software [13; 14] made a step forward by providing capabilities to handle more complex blasting patterns used in underground mining. Aegis [15; 16] is a powerful tool used for blast design within underground mines focusing on ring blasting. Unlike other models, it analyzes not a single blast but the whole stope and provides optimal ring design considering all relevant factors. Its core is related to the breakage zone analysis around the explosive charges in 3D, making it possible to estimate the void space formed after the blasting and dilution while matching the desired fragmentation for the loading process. The models mentioned above provide analytical solutions with acceptable prediction accuracy. As discussed herein, geological setup in available models is not represented in the most usual manner. Available methodology such as discrete fracture networks (DFN) [17] provides an opportunity to capture geological setup as it corresponds to reality and, more importantly, to provide spatial insight into the distribution of primary rock blocks that are being blasted. The first point in blast fragmentation analysis is primary block distribution in size and space. Additionally, rock joint distribution varies in space, and available models do not adequately capture this property. This means that variation in spacing, size, and orientation of joints is taken into account only by a single average value, which significantly simplifies the system. Numerical methods such as discrete element method (DEM) or its derivates are excellent tools for blasting process modeling [18; 19; 20; 21]. These methods allow users to create detailed and complex models to obtain insight into the effects of specific blasts. Due to the modeling concept, the bonding of singular particles into macro objects, it is possible to simulate pressure wave propagation through the medium and analyze bond breaking over time. The downside of such an approach is an expensive simulation in the time and resources necessary to create and process those models. The model herein tends to overcome other models' issues and provide an efficient and reliable tool for blast fragmentation analysis. The model ground was set through the rock fracturing theory explaining blast-induced fracture formation mechanisms. Their interaction with preexisting joints in the rock mass and properties of the blasting process is herein considered.