## 2 Methods and Steps
### Sensitivity Analysis Method for the Influencing Factors of the Haeped-Up Bulk Characteristics
#### 2.4.1 Characteristic Variables and Related Dependent Variables  
According to the relevant definition of the characteristic variable and related factor variable, the controllable factor variable controlling the cast blasting target was taken as the dependent variable in this study and is denoted as \(x_{i}\) = (\(i\) = 1, 2, 3, \(\cdots\), \(n\)). Meanwhile, the parameter index representing the cast blasting effect was taken as the characteristic variable and is denoted as \(y_{i}\) = (\(i\) =1, 2, 3, \(\cdots\), \(m\)).  
Then, the sequence of the system correlation variables and system characteristic variables formed by each system's correlation factor variable \(x_{i}\) and characteristic variable \(y_{i}\) were obtained after s times of cast blasting. These were represented as follows:  
\[\left\{\begin{array}{l}X_{i}=\left[x_{i}(1),x_{i}(2),x_{i}(3),\cdots,x_{i}( k),\cdots,x_{i}(s)\right]\\ Y_{j}=\left[y_{j}(1),y_{j}(2),y_{j}(3),\cdots,y_{j}(k),\cdots,y_{j}(s)\right] \end{array}\right. \tag{19}\]  
where \(x_{i}(k)\) represents the sample data of the \(i\)th system's relevant dependent variable in the \(k\)th cast blasting test and \(y_{j}(k)\) represents the sample data of the \(j\) system characteristic variable tested in the \(k\) cast blasting.  
Considering that there are many factors affecting the effect of cast blasting, part of the cast blasting data is selected as the system variable sample in this study. The height of bench (\(x_{1}\)) represents the height of the rock step to be blasted; bench width (\(x_{2}\)) represents the width of the rock step to be blasted; unit explosive consumption (\(x_{3}\)) represents the amount of explosive used per unit of rock blasting; bench slope angle (\(x_{4}\)) represents the inclination angle of the rock step with blasting; row spacing (\(x_{5}\)) represents the distance between two adjacent rows of holes; hole spacing (\(x_{6}\)) represents the distance between two adjacent rows of holes; minimum burden (\(x_{7}\)) represents the minimum distance between the hole and the free surface; length of stemming (\(x_{8}\)) represents the filling length of the material inside the hole; delay blasting (\(x_{9}\)) represents the time interval of detonation of adjacent holes; expansion ratio (\(y_{1}\)) represents the ratio of the volume of loose rock to the natural volume of rock before blasting; casting ratio of coyote blasting (\(y_{2}\)) represents the ratio of the material quantity of rock directly into the goaf to the total volume of the blasting pile; and throw length (\(y_{3}\)) represents the farthest distance between the rock landing position and the explosion zone. Some parameters are shown in Figure 5. And, the variable samples of the partial cast blasting system are shown in Table 3 below.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline
**No** & \(x_{1}\) & \(x_{2}\) & \(x_{3}\) & \(x_{4}\) & \(x_{5}\) & \(x_{6}\) & \(x_{7}\) & \(x_{8}\) & \(x_{9}\) & \(y_{1}\) & \(y_{2}\) & \(y_{3}\) \\ \hline
1 & 36.2 & 85 & 0.69 & 65 & 6.8 & 12.1 & 7.2 & 7.4 & 9 & 1.24 & 32.2 & 93.4 \\
2 & 36.5 & 85 & 0.72 & 65 & 7.1 & 12.2 & 6.8 & 7.1 & 9 & 1.26 & 34.1 & 94.5 \\
3 & 36.8 & 85 & 0.73 & 65 & 7.1 & 12.3 & 6.9 & 7.6 & 9 & 1.24 & 33.6 & 96.1 \\
4 & 37.1 & 85 & 0.7 & 65 & 6.9 & 11.8 & 7.1 & 6.8 & 9 & 1.25 & 33.1 & 94.8 \\
5 & 37.4 & 85 & 0.69 & 65 & 6.8 & 12.3 & 6.9 & 7.2 & 9 & 1.24 & 34.7 & 96.4 \\
6 & 37.4 & 85 & 0.67 & 65 & 7.1 & 11.8 & 7.3 & 6.9 & 9 & 1.22 & 33.2 & 95.2 \\ \hline \end{tabular}
\end{table}
Table 3: Partial variable samples of the cast blasting system.