*3.2. Blast Load Cases*

The blast load cases defined in this study are illustrated in Figure 8; they were set by considering the positions of the target components and lanes. For the superstructure case, it was assumed that the vehicle explodes in the second lane, either between crossbeams or immediately above one. For the pylon and cable case, explosions were assumed to occur on the shoulder, where the vehicle is closest to the target component. In blast load modeling, the load was applied after calculating the explosion pressure using the scaled distance, which was calculated from the TNT quantity and the distance from the explosion location to the target structure. This method allows the load of CONWEP to be applied indirectly using the \*LOAD\_BLAST\_ENHANCED and \*LOAD\_SEGMENT\_SET commands provided in LS-DYNA. Therefore, we applied the blast load using these commands. Because the blast load is reflected from the deck at the moment of detonation, the shock wave was assumed to propagate hemispherically. Table 5 summarizes the blast load cases in terms of the target components and scaled distances.



**Table 5.** *Cont*.

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**Figure 8.** Blast load position: (**a**) cross-sectional view and (**b**) plan view.

#### **4. Blast Analysis Results**

Numerical blast simulations were performed to evaluate the explosion resistance performances of major components of the cable-stayed bridge. The stress, displacements, and damage levels of the components were examined. The numerical analysis results show that the response sizes and damage ranges of all components increase with the blast load. The blast analysis results of the major components are described below for different scenarios. In addition, Table 6 summarizes the time step and CPU time utilized for the analysis of each numerical model. The numerical analysis of this study was all performed with a single CPU.


**Table 6.** Summary of utilized time step size and CPU time.

#### *4.1. Deck*

Table 7 summarizes the damage types and maximum stresses of the steel girder in each scenario, for a blast load applied between and above the crossbeams of the superstructure. The slab's displacement and response to rebar stress were not examined, because the analysis results included the occurrence of perforation. In blast analysis between the superstructure crossbeams, the damage range of the slab was found to increase with the blast load; however, the main damage occurred only between the crossbeams. In the damage assessments for each scenario, scabbing of the slab was observed in Scenario A, and slab perforations were observed in Scenarios B–D. When the effective stress and degree of damage of the steel girder were examined, the effective stress was found to increase with the blast load. Furthermore, the maximum stresses in Scenarios A–D were 434, 452, 479, and 509 MPa, respectively, and deformation occurred in the upper flange of the crossbeam. The ultimate strength (fu) of the steel girder was 520 MPa; hence, it was concluded that the steel girder plastically deforms but does not fracture when a blast load is applied between the crossbeams of the superstructure.

**Table 7.** Summary of blast analysis results of the deck.


In the analysis of a blast above the superstructure crossbeam, the damage range of the slab was found to increase with the blast load and was wider than that seen for the blast between the crossbeams. The damage types of each scenario were identical to those of the previous case. When the effective stress of the steel girder was examined, a stress of 602 MPa (exceeding the ultimate strength (fu) of the steel girder (520 MPa)) occurred momentarily in the upper flange and web of the crossbeam in Scenario A; however, it appears that no damage occurred owing to the strain rate effect of the material. In Scenarios B–D, the crossbeam was damaged, and the damage range increased with the blast load. This suggests that in the case of the superstructure, a blast load applied to the crossbeam causes greater damage (and has a larger effect on the structural behavior of the cable-stayed bridge) than the blast load applied between the crossbeams.

Figures 9–12 show the damage and effective stress contours generated by the blast load. The fringe range of the effective stress contour was set to 0–520 MPa, considering the ultimate strength of the steel girder; the resulting output time was 0.05 s, at which point the analysis was terminated.

**Figure 9.** Damage contours of the deck (between the crossbeams): (**a**) Scenario A, (**b**) Scenario B, (**c**) Scenario C, and (**d**) Scenario D.

**Figure 10.** Effective stress contours of the steel girder (between the crossbeams): (**a**) Scenario A, (**b**) Scenario B, (**c**) Scenario C, and (**d**) Scenario D (fringe level unit: MPa).

**Figure 11.** Damage contours of the deck (above the crossbeam): (**a**) Scenario A, (**b**) Scenario B, (**c**) Scenario C, and (**d**) Scenario D.

**Figure 12.** Effective stress contours of the steel girder (above the crossbeam): (**a**) Scenario A, (**b**) Scenario B, (**c**) Scenario C, and (**d**) Scenario D (fringe level unit: MPa).

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