*4.2. Cable*

Table 8 presents the maximum displacement and maximum effective stress of each scenario when a blast load was applied to each cable selected in this study (see Figure 2). The displacements and effective stresses on the cables increased with the blast load. In scenario D of Cable no. 53, a momentary stress was found to exceed the static tensile strength (fpu) of the cable (1765 MPa); however, no damage or breakage was observed, owing to the strain rate effect of the material. Furthermore, when the initial stress was excluded, the stresses resulting from the blast load only were found to be approximately 531–1292 MPa for Cable no. 37, 824–1258 MPa for Cable no. 53 and 646–1095 MPa for Cable no. 68 depending on the scenario. Cable no. 37 is observed to have the largest stress variation compared to the initial stress of the design. The reason for this is that Cable no. 37 has a maximum diameter, or maximum blast load reception area. In addition, the maximum displacement and the maximum effective stress occurred on Cable no. 53, which has a minimum cable diameter. These results suggest that the diameter of the cable has a greater influence on the behavior of stay-cables under blast load, or a cable with a small diameter is more vulnerable to blast load. Figures 13 and 14 show the displacement and effective stress contours resulting from the blast load. The fringe range of the displacement contour was set as 0–400 mm, and that of the effective stress contour was set to 0–1765 MPa, considering the tensile strength of the cable. The result output time was 0.18 s and 0.05 s, at which point the maximum displacement and effective stress have occurred.

**Figure 13.** Displacement contours of cables: (**a**) Cable no. 37, (**b**) Cable no. 53, and (**c**) Cable no. 68 (fringe level unit: mm).

**Figure 14.** Effective stress contours of cables: (**a**) Cable no. 37, (**b**) Cable no. 53, and **(c**) Cable no. 68 (fringe level unit: GPa).


**Table 8.** Summary of blast analysis results for the cables.

#### *4.3. Pylon*

– – – Table 9 presents the damage type, rebar stress, and transverse displacement of the pylon under the different blast load scenarios. The damage range of the pylon column was found to increase with the blast load, and the uppermost crossbeam of the pylon was also considerably damaged by the continuous compression. In Scenarios A and B, the concrete element was not eroded, though damage was observed. In Scenario C, partial spalling of the pylon column occurred near the blast load application point and on the underside of the pylon crossbeam. In Scenario D, concrete failure occurred in the portion of the pylon column level with the explosion; at that location the rebar was exposed. The rebar stress was examined based on a yield strength (fy) of 400 MPa, and the rebars in which the stress exceeded the yield strength are marked in red. In Scenarios A and B, very few rebars yielded at the position of the largest blast load. In Scenario C, numerous rebars began to yield and the damage range was increased. The rebars were fractured in Scenario D. It is believed that the rebar in the uppermost crossbeam of the pylon received a relatively small impact from the blast load; however, it yielded owing to the continuous compression of the pylon. The maximum transverse displacements

of the pylon are as follows: in Scenario A, local displacements of 9.2 and 18.7 mm occurred at the top of the pylon and at the height of the deck surface, respectively; in Scenarios B and C, local displacements of 19.1 and 59.1 mm at the pylon top and 32.8 and 78.6 mm at the height of the deck surface were observed, respectively; and in Scenario D, displacements of 636.6 and 649.7 mm occurred at the pylon top and the height of the deck surface, respectively, along with a partial fracture of the pylon. Thus, the blast affected the local behavior of the pylon in Scenarios A–C; however, in Scenario D, it affected the overall behavior of the pylon and was even predicted to result in its collapse. Figures 15–17 show the damage contours, axial stress contours, and displacement contours caused by the blast load. The measurement range of the axial stress contours was set to 0–400 MPa considering the yield strength of the rebar, and the measurement range of the displacement contours was set separately, considering the displacement for each scenario. The resulting output time was 1 s, at which point the analysis was terminated. ← → ← → ← → → ←

**Figure 15.** Damage contours of the pylon: (**a**) Scenario A, (**b**) Scenario B, (**c**) Scenario C, and (**d**) Scenario D.

**Figure 16.** Axial stress contours of the pylon rebars: (**a**) Scenario A, (**b**) Scenario B, (**c**) Scenario C, and (**d**) Scenario D (fringe level unit: GPa).


**Table 9.** Summary of blast analysis results for the pylon.

**Figure 17.** Displacement contours of the pylon: (**a**) Scenario A, (**b**) Scenario B, (**c**) Scenario C, and (**d**) Scenario D (fringe level unit: mm).

## **5. Conclusions**

The performances of key components in a cable-stayed bridge (deck, cable, and pylon) were evaluated via numerical analysis, and all responses for the components and damage type were examined for a range of strategically targeted blast events. The main findings of this study are as follows:


–

–

observed on Cable no. 37. However, the maximum displacement and effective stress occurred on Cable no. 53, which had a minimum cable diameter. Therefore, in the case of cables, a blast near the cable with a small diameter tends to have a large impact on the behavior of the cable-stayed bridge.

• For evaluating pylon characteristics, the case wherein a blast occurred on the hard shoulder was examined. The results show that the damage range of the pylon increased with the blast load, and the concrete and rebars were fractured in some scenarios. The damage and rebar yield occurred primarily in the pylon column and the upper cross beams, wherein the applied blast load was largest. The significant damage in the upper crossbeams was considered to be due to the continuous compression of the pylon. Furthermore, the maximum transverse displacement caused by the blast load was examined, and it was found to have an impact on the local behavior of the pylon for Scenarios A–C; however, for Scenario D, it was found to affect the overall behavior of the pylon, with displacements of 636.6 and 649.7 mm being observed at the top of the pylon and at the deck height in the column, respectively. Therefore, the pylon may be severely damaged under Scenario D.

These results indicate that the blast analysis method introduced in this study will be useful for evaluating the blast load performances of the individual components of cable-stayed bridges. If a performance evaluation of the entire bridge system can be conducted alongside this method, it will become possible to conduct a detailed review of the structural performances of bridges during operation.

**Author Contributions:** Conceptualization, methodology, writing—review and editing, and supervision, J.L.; methodology, formal analysis, investigation, and writing—original draft preparation, K.C.; conceptualization and supervision, C.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by a Korea Agency for Infrastructure Technology Advancement (KAIA) grant, funded by the Ministry of Land, Infrastructure, and Transport (Grant No.20SCIP-B119963-05); it was also supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF-2018R1A6A1A07025819).

**Conflicts of Interest:** The authors declare no conflict of interest.
