# An Integrated Cellular Automata Model Improves the Accuracy of Secondary Fragmentation Prediction
## 2 Materials and Methods
### Physical Experiment  
The experiments carried out by [11; 12] were used as a reference. These experiments were developed in a laboratory-scale experimental system that simulates a confined flow under different stresses of 0.8, 3 and 5 MPa, considering an initial and final granulometry for different fragment sizes as detailed in Table 1.  
The experimental design, previously presented by [12], details the use of a steel cylinder with an internal diameter of 340 mm and a height of 700 mm, capable of holding between 60 and 70 kg of material (Figure 1a). This cylinder is designed to apply a maximum pressure of 14 MPa, and at its base is a trough with two extraction points on a scale of 1:75. The drawbell is in the center of the model to minimize the interaction of the flow zones with the cylinder walls. The fragmented material flows through a rectangular opening of 53 mm by 96 mm, simulating the conditions of a confined flow (Figure 1b).  
These experiments were selected to study secondary fragmentation in a controlled environment, incorporating the effect of confinement during material extraction. In addition, input and output data were available, which were then used for comparison with the simulated numerical results. Each experiment was performed in duplicate, and the reported fragmentation values are the mean value for each experiment pair.  
The gravity flow in block caving mainly involves the forces of gravity, friction and cohesion. Electrostatic forces are a source of cohesion. These forces exist in all material, independent of its chemical nature [23]. Electrostatic forces are stronger than gravity for particle diameters below 100 \(\upmu\)m [24]. In the case of the material tested, however, gravity  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Initial Size**} & \multicolumn{4}{c}{**Final Size**} \\ \hline
**Stress** & **d\({}_{10}\)** & **d\({}_{20}\)** & **d\({}_{50}\)** & **d\({}_{80}\)** & **d\({}_{10}\)** & **d\({}_{20}\)** & **d\({}_{50}\)** & **d\({}_{80}\)** \\
**[MPa]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** \\ \hline
0.8 & & & & & 5.02 & 6.24 & 9.12 & 14.18 \\
3 & 6.65 & 7.47 & 10.8 & 15.6 & 4.03 & 5.14 & 8.59 & 12.66 \\
5 & & & & & 3.72 & 4.86 & 8.41 & 12.28 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Initial and final sizes of material in experiment.  
Figure 1: (a) Cylindrical model in a pressing machine to apply different vertical stresses. (b) Extraction point within the physical model [12].  
forces are stronger than electrostatic forces for 100% of the total mass. The kinematic similitude must include geometrical similitude, friction angle, bulk density and time. In the physical model, the geometry is at a scale of 1:75 in the drawbell dimension and in the particle size distribution of the material using the parallel gradation method [25]. The load is directly applied through the press machine. For the sake of simplicity, the scaling effect of material strength is omitted in this study; future work on this point may benefit this study.