# Prediction of Damage Level of Slab-Column Joints under Blast Load
## 5 Prediction Model
### Verification of Prediction Model  
In order to verify the prediction model proposed in this study, numerical analysis was additionally performed. As shown in Table 5, numerical analysis results for various concrete strength of slab and column, slab thickness, TNT weights, and scaled distances were compared with predicted values of the proposed equation. Comparing cases 1 to 7 with the same concrete strength and slab thickness as the numerical analysis conditions for deriving the prediction model, the model predictions were in good agreement with the verification numerical analysis results for various TNT weights and scaled distances. It is noteworthy that reliable predictions were shown in all cases of cases 1 to 4 with relatively small effective fracture volume and cases 5 to 7 with relatively large effective fracture volume. Interestingly, although the proposed equation was derived based on a small TNT within 30 kg, the predictions for cases 6 and 7 of TNT 40 kg and 50 kg, respectively, agreed well with the analysis result. In cases 8 to 13, the effects of variables not included in the prediction equation, such as concrete strength and slab thickness, on the effective fracture volume were examined. As the concrete strength increased, the effective fracture volume decreased. In cases 8, 9, and 2, as the column concrete strength increased to 30 MPa, 40 MPa, and 50 MPa, the effective fracture volume decreased to 1.72%, 1.63%, \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{3}{*}{**Case**} & **Column** & **Slab** & **Slab** & **TNT** & **Scaled** & \multicolumn{3}{c}{**Effective Fracture**} & \multirow{3}{*}{**Prediction**} \\  & **Strength** & **Strength** & **Thickness** & **Weight** & **Distance** & **Variification** & **Prediction** & **Differences** \\  & **(MPa)** & **(MPa)** & **(mm)** & **(kg)** & **(m/kg\({}^{13}\))** & **Variification** & **Prediction** & **(\%)** \\ \hline
1 & & & & 6 & 0.03 & 0.73 & 1.00 & 0.27 \\
2 & & & & 12 & 0.06 & 1.21 & 1.40 & 0.19 \\
3 & & & & 18 & 0.09 & 1.84 & 1.47 & 0.37 \\
4 & 50 & & & 24 & 0.12 & 1.55 & 1.38 & 0.17 \\ \hline
5 & & & 300 & & 24 & & 4.19 & 4.00 & 0.19 \\
6 & & & & 40 & 0.03 & 6.39 & 6.66 & 0.27 \\
7 & & & & 50 & & 8.07 & 8.33 & 0.26 \\ \hline
8 & 30 & & & & & 1.72 & & 0.32 \\
9 & 40 & & & & & 1.63 & & 0.23 \\ \hline
10 & 50 & 20 & & 12 & 0.06 & 1.92 & 1.40 & 0.52 \\
11 & & 40 & & & & 0.90 & & 0.50 \\ \hline
12 & & & & & & 1.41 & & 0.01 \\
13 & 50 & 30 & & 340 & & & 1.43 & 0.03 \\ \hline \end{tabular}
\end{table} 
Table 5: Verification analysis variables and results. Figure 8: Effective fracture volume per unit weight of TNT according to scaled distance. and 1.21%, respectively. In cases 10, 2, and 11, as the slab concrete strength increased to 20 MPa, 30 MPa, and 40 MPa, the effective fracture volume decreased to 1.92%, 1.21%, and 0.90%, respectively, showing a greater reduction than the column. This was in line with the preliminary analysis results in which the slab showed relatively larger displacement, pressure, and impulse than the column. In cases 12 and 13, which had the same concrete cover thickness and reinforcement details as in case 2, the effect of the slab thickness on the effective fracture volume was investigated. It was observed that the effective fracture volume slightly increased as the slab thickness increased, but the difference in cases 12 and 13 was only 0.02%. It seemed that the effective fracture volume was not significantly affected by column concrete strength and slab thickness. For cases 8 to 13, the proposed equation yielded a constant value of the effective fracture volume due to variables not included in the equation. Although the predictions did not show much difference from the analysis results in the range of variables of concrete strength and slab thickness used in the verification analysis, further research is needed to propose a prediction equation that can take all these variables into account. Figure 9 shows the failure shape for some notable cases.