# Development and Validation of Universal 3D Blast Fragmentation Model
## 4 Case Study
### Results  
In situ data were collected within the stope approximately one hour after the blasting and before loading the muckpile. Data were compiled using the latest-technology cellphone with a high-performance camera and pair of mobile LED reflectors. The lighting and camera positioning were fixed, as suggested by WipFrag's \"Sampling and Analysis guide\". Image processing was performed by qualified technicians using MailFrag service, and the obtained results from two underground blasts using a ring blasting pattern are shown in Figure 18. The fragmentation model was prepared as previously described and pre-calibrated for the burden used for stope blasting. A comparison between two in situ blasts and model results is given in Figure 19.  
As can be seen from Figure 19, fragment size distribution between the model and in situ blasts showed a high level of agreement between fragmentation curves. In the first 40% of the diagram, the model curve passes between two in situ curves, where excellent prediction is made for the given conditions. General agreement between the model and in situ data continues up to 80% of the diagram, with slight variations that have no significant importance for the overall result. Fragment size for the X50 values between the model and blast B2 are the same, while the same value compared with blast B1 has an 11.76% relative  
Figure 18: Survey results for blasts B1 and B2 using WipFrag image analysis software. error. In the case of the X80 values, the model prediction has higher values than those measured, where the relative error between the model and blast B2 is 4.11%, and between the model and blast B1, it is 15.15%. Considering these errors for the X50 and X80 values, it can be stated that the model prediction has high reliability (Table 3). The model generally agrees better with blast B2, where a relative error has a maximum value of 13.33% for a range between X10-X80. In the case of blast B1, relative errors are slightly higher than with a second blast, and for the size range of X10-X80, the maximum relative error is 17.39% for the X10 sizes. The size range above X80 shows that model prediction has increased relative error in both cases, where the comparison with blast B1 has a 31.58% difference, and B2 has only 13.64%. The maximum estimated value according to the model is significantly higher than those measured in situ. Even though this is only a small fraction of the total muckpile maximum size, this may imply the necessity for further scaling of the material. Reasons for this discrepancy may be found in the model and the image processing size distribution methodology. As with any other digital model, the first model may provide errors due to imperfections and inevitable simplifications of reality. In other words, capturing exact in situ conditions and representing them within models is still impossible. Also, due to its nature, the mining industry is one of the few where data variations are increased. Another possible reason for the discrepancy between the maximum sizes may be that by image processing methodology, one captures only one part of the muckpile that is available for photographs. This means that the actual fragment size may differ from the one that is  
Figure 19: Fragment size distribution comparison between model and in situ blasts. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Model (m)** & **Blast B1 (m)** & **Blast B2 (m)** & \ \begin{tabular}{c} **Relative Error** \\ **M=B1 (\%)** \\ \end{tabular}  & \begin{tabular}{c} **Relative Error** \\ **M=B2 (\%)** \\ \end{tabular}  \\ \hline X0 & 0.00 & 0.00 & 0.00 & - & - \\ X10 & 0.19 & 0.23 & 0.18 & 17.39\% & 5.56\% \\ X20 & 0.26 & 0.31 & 0.24 & 16.13\% & 8.33\% \\ X30 & 0.34 & 0.37 & 0.30 & 8.11\%  
determined, and some fragments are not shown, as they are found within the deeper part of the mucgpile. In means of an agreement between fragmentation curves, it can be said that R\({}^{2}\) values are 89.97% between the model and blast B1 and 92.48% between the model and blast B2.