## 3 Material Constitutive Parameters and Verification
### Material Parameter Verification  
A series of blasting crater tests that used different blasting funnel depths were designed to verify the validity of the model parameters presented in this paper. The field test results were compared with the numerical simulation results to validate the reliability of the numerical simulations conducted in this study. Based on the actual production conditions of the mining site and the provided test site conditions, five groups of blasting funnel tests were designed. The specific test parameters are shown in Table 5.  
The processes of drilling, hole inspection, excavation, and measurement during the experiment are shown in Figure 4. The on-site measurement data of the blasting crater, obtained once the blasting crater experiment had been completed, are presented in Table 6.  
To save computational costs, a one-quarter numerical model was established based on the symmetry of the numerical simulation. The dimensions of the numerical simulation were 200 cm \(\times\) 200 cm \(\times\) 300 cm. Parameters such as the drill hole depth, hole diameter, and charge length in the numerical calculation were consistent with those in the on-site crater experiment. The specific numerical model is shown in Figure 5. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Hole**} & \multicolumn{2}{c}{**Explosive**} & \multirow{2}{*}{**Funnel**} & \multirow{2}{*}{**Funnel**} & \multirow{2}{*}{**Funnel**} \\  & **Bural** & & & & \\  & **Depth/m** & & & & \\ \hline
1 & 1.2 & 1.55 & 1.06 & 2.47 \\
2 & 1.3 & 2.01 & 1.08 & 2.46 \\
3 & 1.4 & 2.08 & 1.02 & 2.27 \\
4 & 1.5 & 2.16 & 0.96 & 2.08 \\
5 & 1.6 & 2.21 & 0.92 & 1.96 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Data obtained in blasting funnel field tests. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**\(\rho\)/(g/cm\({}^{3}\))**} & \multirow{2}{*}{**C**} & \multirow{2}{*}{**S\({}_{1}\)**} & \multirow{2}{*}{**S\({}_{2}\)**} & \multirow{2}{*}{**S\({}_{3}\)**} & \multirow{2}{*}{**\(\gamma_{0}\)**} & \multirow{2}{*}{**E\({}_{0}\)**} & \multirow{2}{*}{**V\({}_{0}\)**} \\ \hline
1 & 0.148 & 2.56 & \(-1.986\) & 0.227 & 0.5 & \(2.56\times 10^{-4}\) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Water material parameters. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Hole**} & \multicolumn{2}{c}{**Blast Hole**} & \multicolumn{2}{c}{**Blast Hole**} & \multirow{2}{*}{**Charge**} & \multirow{2}{*}{**Filling**} & \multirow{2}{*}{**Powder**} & \multirow{2}{*}{**Decoupling**} \\  & **Diameter/mm** & & & & & \\ \hline
1 & 120 & 1.2 & 0.45 & 0.75 & 3 & 1.33 \\
2 & 120 & 1.3 & 0.45 & 0.85 & 3 & 1.33 \\
3 & 120 & 1.4 & 0.45 & 0.95 & 3 & 1.33 \\
4 & 120 & 1.5 & 0.45 & 1.05 & 3 & 1.33 \\
5 & 120 & 1.6 & 0.45 & 1.15 & 3 & 1.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summary table of blasting funnel test parameters. After the calculation is completed, the damage results of the numerical model are analyzed and measured. The area with a damage factor of 0-0.1 is defined as the elastic vibration zone, and the damage in this area is ignored. The area with a damage factor of 0.1-0.9 is the crack zone, and the area with a damage factor of 0.9-1.0 is the crushing zone. The specific numerical simulation results of the blasting funnel test are shown in Figure 6.  
Figure 4: Blasting funnel test. Figure 5: Numerical model of blasting funnel. Once the numerical calculations had been completed, the data obtained from the blasting craters formed by explosives with five different burial depths were statistically analyzed and calculated. The numerical simulation results of the blasting crater experiments are presented in Table 7.  
A comparative analysis of the numerical simulation test results and the field test data was performed. The comparison results are shown in Figure 7.  
An analysis of Figure 6 shows that the numerical simulation results for the blasting crater exhibit the same patterns as those obtained in the field tests. There is good consistency between the two.