# Several Tree-Based Solutions for Predicting Flyrock Distance Due to Mine Blasting
## 3 Case Study
### Collected Dataset  
To provide a dataset to construct predictive tree-based models, 234 blasting events were considered, and all features, including hole length, spacing, burden, powder factor, specific drilling, and flyrock, were recorded for these events. Figure 6 shows the relationships between the parameters of the database. The upper part of this figure shows the R\({}^{2}\) between the dataset parameters, and the lower part shows the trend between every two parameters  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Geological/Geometrical Properties** & **Value** \\ \hline Geological reserve of the deposit & 796 MT \\ Proved reserve & 410 MT \\ Average grade & 0.67\% \\ Height of the working benches & 12.5 m \\ Slope of the working benches & 68\({}^{\prime}\) \\ Angle of the overall pit slope & 37\({}^{\prime}\) \\ Width of the ramp & 30 m \\ Slope of the ramp & 5\({}^{\prime}\) \\ Age of the mine & about 32 years \\ Overall stripping ratio (W/O) & 1.7 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Geological and geometrical features of Sungun Copper Mine [85; 86].  
Figure 5: Sungun Copper Mine.  
of the dataset. As shown in Figure 6, flyrock shows an inverse relationship with hole depth, spacing, burden, and stemming; however, its relationship with the powder factor is direct. It is important to note that the powder factor has the highest correlation with flyrock, among others. Considering the upper part of Figure 6, it can be observed that the powder factor does not have an appropriate R\({}^{2}\) with other influential parameters on flyrock. This low R\({}^{2}\) value may indicate an inefficient blasting design. Hence, it would be better to study the design procedure for blasting in future studies to reach efficient models from an economic point of view because of blasting powder's high price.  
Table 3 presents the basic descriptive statistics of all parameters (input and output). These statistical indices show an acceptable range and distribution for each of the parameters, which are also observable in the histograms of Figure 6. Meanwhile, one parameter that was mentioned as an important parameter in the prediction of flyrock is the ratio of Stemming over Burden [88,89]. However, the R\({}^{2}\) between this parameter and flyrock in these datasets was calculated as 0.005, which does not show any meaningful relationship between this parameter and flyrock. To have a better overview of the used data, a number of ten data samples that were randomly selected are presented in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Category** & **Parameter** & **Unit** & **Min** & **Max** & **Avg** & **Median** & **St Deviation** \\ \hline Input & Hole Depth & m & 10 & 14 & 12.31 & 12.5 & 1.18 \\  & Spacing & m & 2 & 6.5 & 4.53 & 4.50 & 0.90 \\  & Burden & m & 2 & 5 & 3.69 & 4 & 0.82 \\  & Stemming & m & 1.8 & 4.5 & 3.66 & 4 & 0.76 \\  & Powder Factor & kg/m\({}^{3}\) & 0.2 & 0.93 & 0.46 & 0.4 & 0.20 \\ Output & Flyrock & m & 10 & 100 & 68.68 & 73.5 & 17.42 \\ \hline \end{tabular}
\end{table}
Table 3: Statistical description of parameters used in this study.  
Figure 6: Scatterplot matrix of flyrock parameters’ dataset with determination coefficient.