# Blasting Fragmentation Study Using 3D Image Analysis of a Hard Rock Mine
## 3 Results and Discussion  
The results of the particle size analysis of the piles of fragmented material from the five blasting tests, obtained using the MMPro platform, were compared with the particle size distribution curves obtained using the Kuz-Ram model, as shown in Figure 4A-E. This configuration is presented graphically using a logarithmic scale for a better perception of the results presented by blasting. \begin{table}
\begin{tabular}{c c} \hline
**Productivity (t/h)** & **Variables** \\ \hline \(P_{c}=U_{t}\frac{3600L}{a\left(exp^{i\text{th}\text{sg}_{0}}\right)+2I_{w}+L_ {d}}\) & \(P_{c}\): loading productivity; \(U_{c}\): physical use of (\%); \(L_{c}\): excavator payload; \(a\): lithology calibration coefficient; \(t_{sw}\): turnaround time (s); and \(t_{d}\): discharge time (s). \\ \hline \(P_{t}=U_{t}\frac{60L}{\left[a\left(exp^{i\text{th}\text{sg}_{0}}\right)+2I_{w}+ L_{d}/60\right]p+\left(t_{c}+t_{f}\right)}\) & \(P_{t}\): transportation productivity; \(U_{t}\): physical use of transport (\%); \(L_{t}\) : average transport load (t); \(p\): number of passes; \(t_{v}\): variable time (min); and \(t_{f}\): fixed time (min). \\ \hline \(P_{bpX_{80}}=P_{bp}e^{-0.002X_{80}}\) & \(P_{bpX_{80}}\): primary crushing productivity and \(P_{bp}\): real productivity (t/h). \\ \hline \end{tabular}
\end{table} 
Table 4: Productivity equations for the drilling and blasting, loading, transport, and primary crushing phases. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline
**Blasting** & \ \begin{tabular}{c} **No. of** \\ **Drills** \\ \end{tabular}  & **H (m)** & **B (m)** & **Y (m)** & **L (m)** & **St (m)** & **J (m)** & **Q (kg)** & \begin{tabular}{c} **Rc** \\ **(kg/m\$)** \\ \end{tabular}  \\ \hline Test 1 & 24 & 15.00 & 4.00 & 4.80 & 10.14 & 5.65 & 0.79 & 668 & 2.06 \\ Test 2 & 48 & 16.00 & 4.00 & 5.00 & 12.40 & 3.96 & 0.36 & 776 & 2.49 \\ Test 3 & 36 & 15.00 & 4.00 & 5.00 & 11.43 & 4.21 & 0.64 & 701 & 2.59 \\ Test 4 & 35 & 16.00 & 4.20 & 5.40 & 11.94 & 4.00 & 0.00 & 714 & 1.98 \\ Conventional Test & 114 Through the analysis of the particle size distribution curves and Table 5, the Kuz-Ram model for Tests 1-3 with new blasting designs shows that the size at which 80% of the fragments pass through (X80) should be approximately between 365 and 469 mm; for Test 4 and conventional blasting, the X80 values would be 457 and 556 mm, respectively. By considering the values measured using the MMPro platform, it was found that for conventional blasting, the X80 value was 398 mm, and for Test 4, it was 305 mm. Thus, it was understood that the proposal of a smaller blasting pattern led to better fragmentation since the values of X80 were lower for Tests 1-3, correctly planning the configuration of the blasting parameters and optimizing the fragmentation of the blasting parameters of very compact itabirites. Additionally, Test 4 was performed with a pattern of the same size as  
Figure 4: Kuz–Ram and MMPro particle size distribution for (**A**): Test 1, (**B**): Test 2, (**C**): Test 3, (**D**): Test 4, and (**E**): conventional test. conventional blasting with an increased load ratio. The results showed improvement in fragmentation relative to conventional blasting of the same pattern made with staggered explosive loading. By observing the particle size distribution curves of Figure 5, it was found that the particle size distribution curves of the Kuz-Ram model were slightly different from the particle size distribution curves generated in the MMPro platform of PortaMetrics. Although the curves of the Kuz-Ram model did not differ much from each other because the blasting planes of Tests 1-4 were very similar, the conventional blasting curve was different from the others, with large sizes for different P(x). In the PortaMetrics particle size distribution curves, the values measured in the field were different for each blasting performed.