## 5 Results
### The Effect of Lifting-Cable Breakage on the Salvage System  
Lifting cables are subject to corrosion and fatigue damage during the salvage process, which can result in cable breakage. The breakage of lifting cables is very dangerous, and the rupture of cables at certain positions may trigger the breakage of other cables simultaneously. This scenario can lead to the shipwck sinking back into the ocean, causing severe damage. Therefore, studying the specific conditions associated with cable breakage is important. During the salvage of a shipwck, [PERSON] [39] defined the minimum safety factor of lifting cables as 1.67. To comprehensively evaluate the situation following cable breakage at various positions, Table 6 presents six cable breakage modes. In this section, the shipwck is in the P2 stage, and the wave directions are 135\({}^{\circ}\) and 180\({}^{\circ}\). This section primarily investigates the occurrence of cable breakage at different positions, assessing whether the remaining lifting cables will break and if their safety factor is met. Figure 23 depicts the moment of cable breakage at different locations, the increase in the maximum tension value of the remaining lifting cables, and the safety factor. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Mode** & **Broken Cable Number for** & **Broken Cable Number for** \\  & **Lifting-Barge A** & **Lifting-Barge B** \\ \hline Mode 1 & \#1, \#15 & \#16, \#30 \\ Mode 2 & \#3, \#13 & \#18, \#28 \\ Mode 3 & \#5, \#11 & \#20, \#26 \\ Mode 4 & \#7, \#88 & \#22, \#23 \\ Mode 5 & \#1, \#24, \#15 & \#16, \#17, \#29, \#30 \\ Mode 6 & \#2, \#3, \#13, \#14 & \#17, \#18, \#28, \#29 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Modes for breakage of lifting cables. Figure 23: _Cont._In Figure 23, the histogram illustrates the increase in the maximum tensile magnitude of the remaining lifting cables when cables at different positions rupture. Pale yellow represents the increase induced by waves in the 180\({}^{\circ}\) direction, while light green indicates the increase caused by waves in the 135\({}^{\circ}\) direction. The safety factors of the lifting cables are depicted by red and blue curves. Generally, cables 16-30 show a higher growth rate than cables 1-15. Consequently, lifting cables situated farther from the transverse center of gravity of the wreck have more significant increments and greater fluctuations. From a safety factor perspective, lifting cables subjected to waves in the 135\({}^{\circ}\) direction typically have a higher safety factor than those under waves in the 180\({}^{\circ}\) direction. The safety factor curves of cables 1-15 and 16-30 in most modes exhibit a distribution characterized by a rising middle portion. However, the shape of the increase in tension for cables 1-15 and 16-30 may vary. Some cases present a \"middle part drooping\" shape distribution, such as in Modes 1 and 5. In other cases, the distribution shows a \"middle part uplifting\" shape, such as Mode 2, Mode 3, and Mode 4. This phenomenon arises because adjacent cables experience significant fluctuations when lifting cables at different positions rupture, while those located farther away encounter less fluctuation. Fractured lifting cables gradually approach the vessel's center from Modes 1-4 and Modes 5-6, leading to a diminished augmentation rate of the remaining cables, thus ensuring gradual cable safety enhancement. In Modes 5-6, the minimum safety factors for lifting cables under 180\({}^{\circ}\)-wave action are 1.14 and 1.21, while the corresponding minimum safety factors under 135\({}^{\circ}\)-wave action are 1.29 and 1.33, respectively. The data reveal that the breakage of lifting cables is more hazardous under waves in the 180\({}^{\circ}\) direction. Therefore, extra attention should be paid to the dynamic responses of lifting cables when performing salvage operations under waves in the 180\({}^{\circ}\) direction. It also indicates that exceeding four broken lifting cables on one side of the shipwck may fracture the remaining cables.