## 3 Models and Assessment Methods
### Ship and Cable Models  
The lifting barges and shipw models used in this paper are based on the salvage of the Korean Sewol ferry. Owing to the Sewol's significant underwater weight and insufficient structural strength, additional supports are necessary on the shipw's underside. Two lifting barges are positioned side by side on the water's surface. This configuration prevents the shipw from breaking owing to inadequate structural strength, thus avoiding secondary submergence into the seabed [10]. The ship models employed in this paper are shown in Table 1. The shipw rests at a depth of 280 m on the seabed. Common semisubmersible barges are chosen as the lifting barges, while the selected shipw model is the Wigley ship, commonly employed by many scholars who specialize in studying ships. The schematic diagram of the three vessels is depicted in Figure 1.  
During numerical simulations, engineers assess sediment conditions within the shipw and evaluate the extent of the damage. After gathering this information, they determine the salvage weight of the shipw (shipwreck weight minus internal and external buoyancy) and its center of gravity. In Stage P1, when the shipw is on the seabed, salvage involves overcoming the shipw's weight and adhesive force between the shipw and seabed sediment. The adhesive force depends on the shipw's weight, hull-sediment contact area, and sediment material. This force is often included in the shipw's weight during salvage by applying a coefficient. Typically, a coefficient of 10% is used, resulting in a salvage weight that is 1.1 times the usual weight of the shipw in Stage P1. In Stage P3, a part of the shipw structure appears at the water's \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Lifting Barge A** & **Lifting Barge B** & **(Fully Submerged/Partially Out of Water)** \\ \hline Length (m) & 140 & 140 & 210 \\ Width (m) & 55.89 & 55.89 & 22.81 \\ Depth (m) & 13.3 & 13.3 & 20.85 \\ Draught (m) & 8.6 & 8.6 & 280/140/15.9 \\ Displacement (kg) & \(6.39\times 10^{7}\) & \(6.39\times 10^{7}\) & \(4.83\times 10^{7}/4.45\times 10^{7}\) \\ Center of & x = 71.26, & x = 71.26, & x = 70.56, \(y\) = \(-0.833\), \\ gravity (m) & y = \(-3.55\), z = 7.04 & y = 2.45, z = 7.04 & z = 6.53/6.36/6.05 \\ Salvage weight (kg) & — & — & \(1.17\times 10^{7}/1.06\times 10^{7}/1.09\times 10^{7}\) \\ I\({}_{\text{ox}}\) & \(2.18\times 10^{10}\) & \(2.13\times 10^{10}\) & \(3.52\times 10^{9}/3.31\times 10^{9}/3.13\times 10^{9}\) \\ I\({}_{\text{yy}}\) & \(1.24\times 10^{11}\) & \(1.24\times 10^{11}\) & \(1.33\times 10^{11}/1.31\times 10^{11}/1.22\times 10^{11}\) \\ I\({}_{\text{zz}}\) & \(1.41\times 10^{11}\) & \(1.40\times 10^{11}\) & \(1.33\times 10^{11}/1.31\times 10^{11}/1.21\times 10^{11}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the ship model. Figure 1: Schematic diagram of a twin-barge salvage system: (**a**) overall; (**b**) partial; (**c**) top view. Process 1 (P1) represents the initial state of the shipw recovery, during which the shipw starts to detach from the seabed. Process 2 (P2) indicates that half of the salvage operation has been accomplished. Process 3 (P3) signifies the stage where a portion of the shipw structure becomes visible at the water’s surface. surface. Shipwreck structural buoyancy and airbag buoyancy decrease slightly, which increase the salvage weight. Notably, for large-tonnage shipwrecks, minimizing the water exposure is preferable to avoid strong coupling motion among the vessels owing to waves. In the Korean Sewol salvage, the heavy shipwck made complete removal from the water challenging. Therefore, when the shipwck was partially raised, engineers employed a semisubmersible barge to dive underwater and provide support, eventually enabling the complete removal of the shipwreck. Mooring cables are arranged radially. Each lifting barge has eight mooring cables measuring 980 m long, resulting in a total of 16 cables. Fifteen lifting cables are evenly distributed on one side of the shipwck, amounting to 30 lifting cables in total.