# Development and Validation of Universal 3D Blast Fragmentation Model
## 6 Conclusions  
The model's universal functionality is seen in its capability to model all blasting cases used in practice, which shows its robustness. Bench blasting is typical in surface and underground mining, where parallel boreholes are used. This simple situation means that all boreholes are parallel and equally distanced among themselves, resulting in even fragmentation within the blasted block. A much more complex case is ring blasting, where explosive charges are placed with different spacing between them within a single pattern. The model can capture this case accurately and has been tested against such cases in practice. Further, the model can provide estimates for complex blasting patterns, such as in tunneling or underground mining development. This case is specific since the spacing between boreholes changes during the firing sequence, and boreholes may be parallel or non-parallel among themselves. Besides those mentioned earlier, the model captures the influence of the previous blasts, borehole deviation, and misfires that significantly influence the overall fragmentation results. A case study is provided to validate the model where model prediction is compared with two ring blasts from the underground mine. The setup of the model is such that it captured the exact blasting pattern used for the stope blasting with the same firing sequence. At the same time, the primary block size was estimated by generating DFN from the available joint survey. Initial burden analysis showed that pressure estimation formulas used for the model resulted in much lower borehole pressures impacting the high difference between model and in situ burdens of explosive charges. For such reasons, the model was pre-calibrated to operate with borehole pressure that would result in the same 2 m burden that is found in stope blasting. The fragmentation survey was provided using the image processing software WipFrag v4 and following their sampling and analysis guides. The obtained results showed that the relative error for X50 values is 11.76% for the first blast, while the second blast and model X50 values are the same. X80 value-relative errors are 15.15% and 4.11%, respectively. This means that model prediction is accurate within this size range. The maximum error found for the size range between X10 and X80 is around 17%. Size prediction for the range of X80-X90 shows an increased error of 13% and 30%, respectively, for blasts B1 and B2, and the maximum predicted value is also significantly larger in the model than for the case of in situ tests. This issue is discussed, and several reasons are possible causes for this. First, the model was only pre-calibrated, and no post-calibration procedures were carried out to adjust the model to the obtained results. Therefore, the model could be recalibrated to provide the best fit for the specific location. However, the critical point here is to validate the general model functionalities and determine if the results fall within the reasonable scope of expected values that have been proven. Comparing obtained curves from the model and in situ tests, it was determined that R2 values are 89.97% and 92.48%, demonstrating the model's reliable estimate. At its prototype stage, the model shows a high level of agreement compared with full-scale in situ ring blasting tests and a simple pre-calibration procedure. With further development of the model, the main idea is to improve its computational speed and resource usage. This could provide the possibility of modeling complex scenarios with millions of fragments to be generated, considering complex DFNs, and using real-world drilling data. Also, a standardized calibration procedure utilizing modern AI or ML tools might be developed to decrease estimation errors for each size class by adjusting the model to certain conditions. [PERSON] and [PERSON] formulated and implemented fragmentation model; [PERSON], [PERSON] and [PERSON] designed in situ tests and collected and processed dana; [PERSON] wrote the paper.