# Numerical Simulation on Dynamic Behavior of Slab-Column Connections Subjected to Blast Loads
## 3 Numerical Analysis
### Modeling of Blast Loads  
In this study, a preliminary analysis was performed to select the analysis method between multi-material arbitrary Lagrangian-Eulerian (MME) and load-blast enhanced (LBE). The concrete walls, which have the same characteristics as the main analysis including  
Figure 2: Process of the negative volume.  
materials and element size, were analyzed. As in the main analysis, 4 kg of TNT was placed at a vertical distance of 300 mm from the center of the structure surface. The surfaces for LBE were defined as the front of a wall that was directly affected by the explosion. Table 1 and Figure 3 show the analysis results from both methods of MME and LBE. The maximum pressures of MME and LBE were 3.97 \(\times\) 10\({}^{-7}\) MPa and 3.33 \(\times\) 10\({}^{-7}\) MPa, respectively. The area of the pressure curve of MME was larger than that of LBE, as shown in Figure 3. For the LBE method, the explosive pressure was directly applied to the element surfaces. For the MME, however, since the explosion load at the origin was transmitted through the atmosphere elements, the residual pressure was transmitted through the atmosphere after the maximum explosion pressure. Therefore, as shown in Figure 3, the pressure curve area of the MME was larger than the pressure curve area of the LBE, although the maximum pressure did not show a large difference. Table 1 compared the duration time of both analysis methods. The LBE method could be regarded as a more efficient explosion analysis method since the analysis time of MME was about 90 times longer than that of LBE. As a result, it is considered that the MME method is suitable for understanding the flow and progress of the explosive pressure, and the LBE method is suitable for understanding the effect of the maximum pressure on the structure under the explosive load. Therefore, in this study, the LBE method was chosen considering that the maximum pressure is similar to MME and it is more efficient in terms of analysis time. Moreover, many research studies showed that the LBE method is more efficient than the MME method considering analysis results and time [59; 60; 61].  
Based on empirical formulas of blast loads, the Protective Design Center (PDC) of US ARMY releases the Conventional Weapons Effects (ConWep), which could perform a variety of conventional weapons effects from TM 5-855-1 [58; 62]. The LS-DYNA applies the ConWep system to LBE. The blast loads of TNTs were located 300 mm from the column and  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multicolumn{4}{c}{**Number of Elements**} & \multirow{2}{*}{**Analysis Time**} & \multirow{2}{*}{**Duration of Analysis**} \\ \cline{2-2} \cline{4-6}  & **Structures** & & & & \\ \hline LBE & 800 & - & - & 129 s & \\ MME & 800 & 56075 & 125 & 11,075 s & 100 ms \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of analysis time of MME and LBE.  
Figure 3: Comparison of pressure histories of MME and LBE.  
slab. The variables for the amount of TNT were 4 kg and 12 kg. The mass of TNT used in this analysis represents the small and large briefcase bomb, as shown in Table 2 [63]. When 4 kg of TNT was used, which is equal to the amount used in a small briefcase, the blast resistance behavior could be well observed because the slab was not completely destroyed. On the other hand, when 12 kg of TNT was used, which is equal to the amount used in a large briefcase, a significant portion of the slab where the explosive load was placed was destroyed. Table 3 summarized the descriptions of the specimens including blast loads.