*4.2. Support Rotation*

Figure 5 shows the support rotation calculated by the displacement of the slab. According to the criteria, the limit of support rotation to effectively resist the moment is 2 degrees [9,10]. As shown in Figure 5, in all cases, except that the scaled distance between 0.026 m/kg1/<sup>3</sup> and 0.037 m/kg1/<sup>3</sup> for TNT 30 kg explosive loads, the support rotation was less than the American Society of Civil Engineers/Structural Engineering Institute (ASCE/SEI) and DoD criteria limit of 2 degrees [9,10]. However, as shown in Figure 6, the top and bottom surfaces of the slab suffered severe fracture damage at all scaled distances for the 30 kg TNT. Similar phenomena were observed in all specimens with 20 kg of TNT. This means that even if the support rotation is smaller than the criteria limit, substantial destruction can occur in the member. In order to properly evaluate the blast-resistant performance of the joint, other evaluation factors besides support rotation are required.

**Figure 5.** Support rotation of slab.

**Figure 6.** Failure shapes (30 kg, Z = 0.067 m/kg1/<sup>3</sup> ); (**a**) Top surface; (**b**) Bottom surface.

## *4.3. Fracture Volume*

In general, support rotation and displacement are used as criteria for evaluating the blast-resistant performance of RC members, but as shown in the previous analysis, the support rotation and displacement alone were not sufficient to accurately evaluate the performance of the slab-column joint. Moreover, it was difficult to use the support rotation or displacement to predict the blast-resistant performance of the slab-column joint because the support rotation and displacement according to the blast load condition did not have a certain tendency. Therefore, it is necessary to examine additional factors to evaluate the performance of the joint subjected to a blast load.

In this study, fracture volume was analyzed from the analysis results as an additional evaluation factor. Fracture volume was expressed as a percentage of the volume lost due to the explosive load relative to the total volume for the joint region within a scaled distance of 0.1 m/kg1/<sup>3</sup> in Figure 3. It should be noted that this fracture volume is the effective volume of joint excluding the concrete cover.

Figure 7 shows the effective fracture volume of the joint according to the scaled distance for each TNT weight of 10 kg, 20 kg, and 30 kg. Not surprisingly, as the weight of TNT increased, more damage occurred in the joint region. Interestingly, in all cases, the effective fracture volume decreased almost uniformly as the scaled distance increased.

**Figure 7.** Effective fracture volume.

#### **5. Prediction Model**

#### *5.1. The Suggestion of Prediction Model*

In this study, the effective fracture volume was used to predict the blast-resistant performance of the slab-column joint. Based on the trends identified in Figure 7, the correlation between the effective fracture volume per unit weight of TNT and the scaled distance was derived. As shown in Figure 8, regardless of the total amount of TNT applied, the effective fracture volume per unit weight of TNT showed almost similar value at any scaled distance and showed a certain tendency to decrease with increasing scaled distance. The trend line equation is shown in Figure 8, and the coefficient of determination (R<sup>2</sup> ) of the equation for the entire data was 0.870.

As a result, Equation (2) was proposed to predict the damage level of the slab-column joint subjected to blast load through the weight of the explosive material and the standoff distance.

$$\text{Effective fracture volume} = \text{W} \times (0.2375 \times 10^{-5} \text{.}^{1374 \text{Z}}) \tag{2}$$

where Effective fracture volume: Effective fracture volume percentage of slab-column joint (%). W: TNT weight (kg). Z: scaled distance (m/kg1/<sup>3</sup> ).

−

**Figure 8.** Effective fracture volume per unit weight of TNT according to scaled distance.

#### *5.2. 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.


**Table 5.** Verification analysis variables and results.

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%, 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.

**Figure 9.** Failure shape for some verification analysis cases; (**a**) Case 3; (**b**) Case 6; (**c**) Case 7; (**d**) Case 8; (**e**) Case 10; (**f**) Case 13.
