## 5 Numerical Simulation
### Analysis Results for Each Stemming Model  
In the analysis of the shock chamber model, we focused on two stemming methods: sand and \"STF + sand\" stemming. We also looked at three types of stem plug devices used with STF. Following the explosion, the initial ejection of the stemming area began at 0.2 ms for sand and 0.3 ms for STF, with the STF initial ejection velocity being slower at 73% compared to sand stemming. The use of plug devices caused a delay in the time of ejection for the stemming part when compared to the \"STF + Sand\" model without a plug. For spike- and cone-type stemming materials, the initial ejection time was observed to be 0.32 ms after the explosives initiation, which was a delay of 0.02 ms compared to combined STF and sand stemming models without a plug device. In cases where twist plugs were used in combination with STF, the start time of stemming part ejection was measured at 0.36 ms post detonation, indicating better resistance performance compared to analyzed scenarios. To track pressure changes over time, a pressure gauge was placed on one side of the shock chamber cylinder, corresponding to half of all stemming components. The maximum pressures recorded at this location are listed in Table 7.  
At 0.1 ms after the explosion, the pressure peaked at the location, showing a 15% increase when using STF stemming material instead of just sand. The twist-type plug device recorded a pressure of 395 MPa. The shock wave from the blast initially compacted the stemming structure, pushing it towards the opening until all stemming structures were ejected during the blasting process. In blasting procedures, a common method is to use a stemming ejection model at the opening, determining the velocity of stemming material based on momentum and \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Stemming Material** & **Initial Ejecting Time** & **Initial Ejecting Velocity** & **Peak Pressure (m/s)** & **Quantum (M-s)** & **Relative Blockage** \\ \hline Only Sand & 0.20 & 450 & 300 & 60.6 & 1.00 \\ \hline STF + Sand & 0.30 & 330 & 350 & 44.6 & 1.35 \\ \hline STF + Cone Plug + Sand & 0.32 & 280 & 351 & 37.8 & 1.60 \\ \hline STF + Spike Plug + Sand & 0.32 & 260 & 353 & 35.1 & 1.72 \\ \hline STF + Twist Plug + Sand & 0.36 & 220 & 395 & 29.7 & 2.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Numerical analysis results of each stemming model. Figure 17: Stemming effect and comparison models for the (**a**) existing and newly designed plugs, (**b**) twist, and (**c**) spike. energy-conservation principles. The effectiveness of stemming was evaluated by calculating momentum for each case and comparing it to a baseline momentum value of 60.6 N-s in a sand stemming setup. A value above 1.0 signifies good performance in stemming blockage. Figure 18 analyzes the ejection velocity over time at the tip of the sand stemming component inside the blasting hole. The initial ejection speed is the rate at which the outermost material starts coming out of the blast hole. When sand was used as stemming material, it quickly moved out once the material began to be ejected from the hole. However, in cases with STF stemming, the movement of ejection showed an increase. Using a plug device caused a notable decrease in the speed of the stemming material's ejection. The slope on the velocity time graph indicates how fast the stemming material accelerates when it begins moving. In physics, acceleration is defined as how velocity changes over time for an object. The acceleration direction of the stemming material depends on the gas pressure acting on it. When STF was used as stemming material, acceleration dropped by around 30% compared to using sand. Introducing a plug device with STF stemmed materials led to a reduction in ejection acceleration. The use of the plug notably decreased the speed of ejection by 32% when compared to the \"STF + sand\" stemming method. Figure 19a,b exhibit the pressure patterns for the models using \"sand\" and \"STF + sand\" as stemming materials, respectively.