# An Integrated Cellular Automata Model Improves the Accuracy of Secondary Fragmentation Prediction
## 3 Results  
### Original Model Results  
The flow simulations of vertical stresses 0.8 MPa, 3 MPa and 5 MPa were evaluated to obtain the final sizes for each of the pass-through percentages to be assessed (d\({}_{10}\), d\({}_{20}\), d\({}_{50}\) and d\({}_{80}\)) for comparison with the previously obtained experimental results. From this comparison, the fragmentation prediction capacity associated with the original model was determined. The characteristic sizes obtained by the numerical model correspond to the average value of the five simulations carried out for each vertical stress.  
As shown in Figure 8 (square marker), at 0.8 MPa, the final simulated d\({}_{10}\) was 0.59 cm, while the experimental value was 0.50 cm. At 3 MPa, the values were 0.46 cm and 0.43 cm, respectively, and at 5 MPa, the results were 0.40 cm and 0.39 cm. The associated errors decrease with increasing pressure, from 17.5% at 0.8 MPa to 7.5% at 5 MPa. This suggests that although the simulation tends to slightly overestimate fragment sizes, the model's accuracy improves at higher stresses.  
As for the d\({}_{20}\) particle size, as shown in Figure 8 (circular marker), at 0.8 MPa, the error was 18.1%. However, as the stresses increased, this error was markedly reduced, with only 2.9% of error at 5 MPa. These data demonstrate that errors are greater at low stresses and decrease as the confinement stress increases.  
Figure 8 (diamond marker) presents the results for d\({}_{50}\), where the values obtained in the simulation were slightly higher than those obtained experimentally at the three evaluated stresses (0.8, 3 and 5 MPa). The percentage errors between the simulation and experiments are relatively low for d\({}_{50}\) (6.2% at 0.8 MPa, 3.6% at 3 MPa and 2.3% at 5 MPa). This suggests that the simulation reproduces the behavior of the material under different levels of confinement quite well, with a better accuracy at higher stresses, where the discrepancy between the simulated and experimental results is minimal.  
Finally, the values of the d\({}_{80}\) fragment size, as illustrated in Figure 8 (triangular marker), show a decrease in both simulation and physical experiments as the confinement  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Vertical Stress [MPa]** & **Upper Block Density** & **Material Density [kg/m\({}^{3}\)]** \\ \hline
0.8 & 116,675.85 & \\
3 & 437,027.03 & 2620 \\
5 & 728,378.61 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Densities associated with confinement pressures, including the rock density of the material used in the physical model and the high densities used to replicate a high vertical load in the numerical model.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Maximum extraction & 40 \\ N & 6 \\ M\({}_{\rm v}\) & 3 \\ d\({}_{10}\) initial & 0.66 \\ d\({}_{20}\) initial & 0.75 \\ d\({}_{50}\) initial & 1.08 \\ d\({}_{80}\) initial & 1.56 \\ Number of simulations per vertical stress & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Input data for numerical simulations of gravity flow.  
pressure increases. The percentage error for d\({}_{80}\) is lower compared to the other sizes, with values of 4.4% at 0.8 MPa, 2.7% at 3 MPa and 1.8% at 5 MPa. These results indicate that the simulation model is quite accurate in predicting the d\({}_{80}\) size, especially at higher stresses, where the discrepancy between the simulated and experimental values is minimal.  
Overall, in this first iteration, better results were obtained in predicting medium to coarser sizes. Similarly, better accuracy was achieved at greater confinements. This suggests that the fragmentation model is better able to predict the compression mechanism but does not adequately replicate any shear mechanism that may be present, as it misses more in smaller sizes and low loads.