# Development and Validation of Universal 3D Blast Fragmentation Model
## 5 Discussion  
The fragmentation model presented herein is based on theoretical work that describes the rock fracturing mechanism by blasting [22]. This work has been previously applied for estimating blast-induced damage of underground openings [34], and its further applicability was continued by constituting a 3D fragmentation model with general applicability, which is the subject of this manuscript. As explained in previous chapters, the model has general applicability in considering different blasting patterns and variations of both rock, explosive, and geometrical parameters of the blasting. It reflects the variation of input parameters as expected, meaning that the model constitution may be considered valid since it incorporates all essential parameters, and results are affected by their variability in an expected manner. This means that pressure increase will lead to finer fragmentation, as is the case with decreasing rock strength. Also, the same is true considering the influence of the previous blasts, DFN parameter change, and geometry variation of the slope and blasting patterns. It is important to state that model is in its prototype stage of development, and further improvement and capability development is expected. In terms of comparison with other available models, the model presented herein has the potential of application to any blasting scenario used in practice, whether it is bench, ring, or tunneling blast; even arbitrary blasting patterns could be analyzed. Other models are case-specific and usually work with one of the possible scenarios, while their modifications to work in more general applications did not provide significant results. Being developed in 3D space, it can handle the spatial variability of rock mass structural and mechanical properties in space and handle borehole deviations, misfires, and different explosive properties. All these capabilities contribute to the universality of the proposed model. Further development should consider the efficient handling of complex blasting patterns with a large number of boreholes, and this is a code-wise improvement. Core capabilities will consider blasting in different crustal stress conditions and its influence on blast-induced fracture length and orientation, which is especially important for deep underground mines. Blasting in confined conditions, such as in sublevel caving mines, is one of the research topics where the model could provide new insights, especially if coupled with gravity flow models, to assess the fragmentation influence on the recovery and dilution of ore. Due to the geometrical foundation of the model, fragmentation results are easily exported to the discrete element codes where each fragment can be modeled at its place of formation. Also, this relates to panel caving mines, where undercutting operations rely on ring blasting and where optimal ring blasting may influence cost reduction and overall productivity improvement. Regarding model validation against real-world data, several full-scale ring blasts were carried out to compare model results. The model generally agrees with in situ blasts, where R\({}^{2}\) values are around 90% for both cases. If X50 and X80 values are compared, the maximum error between the model and tests is around 15%, which is, in practical means, excellent prediction. A higher discrepancy between the model and tests is seen in values above X90 and in determining the maximum fragment size. This may be for different reasons associated with model and fragmentation survey methodology. As said, the model was only simply pre-calibrated by burden analysis, and no post calibration was carried out. Since the model creates fragments in the form of geometrical solids, there is the capability to identify fragments or areas of the model where the discrepancy is found and then to treat that area differently to match in situ data. Other options may include calibration of the model in depth to match the specific location in a best-fit manner by adjusting the model core parameters.