# Development and Validation of Universal 3D Blast Fragmentation Model
## 3 Three-Dimensional Fragmentation Model
### Range of Application  
The model can capture fragmentation by blasting in most common blasting scenarios and therefore has general applicability. The range of applicability covers blasting of different scales and pattern complexity.  
Even if not used besides in research, the first application case is the possibility of modeling fragmentation of specimen-sized monolith rocks blasted in a laboratory environment. Such cases are reported in the literature [26] and are used for blasting process optimization where laboratory results are scaled up to the in situ application. Figure 13 illustrates an example on a laboratory-scale rock specimen blasted with a single explosive charge along the specimen's long axis.  
The fragmentation model's general applicability is further explained by its ability to model blasting with parallel and non-parallel explosive charges. For the model capability explanation's sake, each explosive charge may be of different explosive types and sizes. The most common blasting situation in both surface and underground conditions is bench blasting, i.e., a case where explosive charges are parallel. Also, spacing between explosive charges is uniform in this case, and the resulting fragmentation has even spatial distribution with minor or no variations.  
In underground mining, many blasting scenarios are used, especially with ring blasting, where highly complex cases may occur. This relates to cases with sublevel open stoping mines where single sublevel drift ring designs may vary depending on ore body morphology. Ring blasting scenarios have already been discussed in more detail within previous chapters, and examples were given.  
Figure 13: Specim blasting on a laboratory scale.  
The development of underground mines in hard rock conditions differs from typical production blasts due to pattern complexity and initiation sequence. These blasts start with closely spaced cut boreholes, usually spaced by 20 cm, in order to open additional free surfaces. The cut is followed by additional boreholes placed around it. Still, the spacing between those boreholes is subsequently increased until the final spacing (burden) is reached, or the contour of the underground opening is reached. In such cases, the fragmentation of blasted material is different in each blasting sequence only because of spacing between boreholes, which creates an extremely difficult case for fragmentation estimation. The practice has shown that most such blasts result in fine fragmentation where explosive usage is increased above the optimal level. The jointing conditions of the rock mass may influence oversized fragmentation and difficulties with the loading process if such a case is not predicted and adequately solved.  
Currently, available models do not provide such capabilities for fragmentation estimate in tunneling; therefore, herein, this capability is presented for the case of underground mine development. Figure 14 illustrates the blasting pattern used for model capability illustration. As seen, there are different zones where the spacing between boreholes and their spacing away from the free surface is different, and therefore, the fragment size will differ in each zone (Figure 15).  
Figure 14: Blasting pattern with initiation and fracturing sequence.  
Figure 15: Model before and after processing.