## 5 Results
### Cable Stress  
The dynamic response of adjacent cables was extracted, and only the stress time history of adjacent cables is given due to the limitation of space, as shown in Figure 8. The initial stress S\({}_{0}\), peak stress S\({}_{\text{dyn}}\) and quasi-static stress S\({}_{\text{s}}\) of the cable were compared, and the stress increase and dynamic amplification factor (DAF\({}_{1}\)) of the cable were calculated, as shown in Figure 9.  
It can be seen from Figure 8 that the fluctuation amplitude of the cable stress after successive breaking was smaller than that of simultaneous breaking, but it was closer to the stress of simultaneous breaking. The stress of adjacent cables increased sharply due to the breaking of upstream cables, and reached the stress peak at 1.812 s and 1.982 s, respectively, and then increased sharply again due to the breaking of downstream cables, which shows that the breaking time point that caused the maximum vibration response of the structure could be obtained using dichotomy iterations, and the structural vibration caused by the continuous breaking of cables was not as severe as the simultaneous breaking.  
Figure 8: Stress response of the nearest cables: (**a**) #M23 cable stress after #M24 broke; (**b**) #S28 cable stress after #S29 broke. Note: D indicates a single cable breaking, T indicates that pairs of cables were broken at the same time, and J indicates that pairs of cables were broken one after another.  
Figure 7: Observation point position. Note: Observation points #1 and #15 were the most unfavorable position and the maximum displacement position of the main beam under dead load, respectively. Points #2–#8 were the main span bisector, and observation points #9–#14 were the cable tower, the middle span of each side span and the pier. The points b–d were the bifurcation, variable cross-section and the most unfavorable position of the straight tower, respectively.  
As shown in Figure 9, the closer to the broken cable position, the greater the stress increase of the cable, which shows obvious proximity. The DCR of the cable stress was less than 1.0, which shows that the residual cable strength met the dynamic stress requirement of cables breaking one after another. As can be seen from Figure 9a, the peak stress of #M23 cable was the largest, and the peak stress was 628.91 MPa. The peak increase and quasi-static increase were 51.04 MPa and 41.68 MPa, respectively, and the ratio between them was 1.224. With the number of stay cables decreasing, the \(\mathrm{DAF}_{1}\) gradually increased, both of which were within 1.10-1.27, and the \(\mathrm{DAF}_{1}\) of the #M19 cable was larger. It can be seen from Figure 9b that the peak stress of the #S20 cable was the largest, and its peak increase was 40.05 MPa, which was 1.135 times that of the quasi-static stress increase. The stress increase of the #S28 cable was the largest, and its peak increase was 48.96 MPa, which was 1.144 times that of the quasi-static stress increase. With the increase in the number of stay cables, the \(\mathrm{DAF}_{1}\) gradually increased, ranging from 1.13 to 1.15, and the \(\mathrm{DAF}_{1}\) values of the #S26 and #S27 stay cables were larger.