Coupled Responses of Sewol, Twin Barges and Slings During Salvage

Korean Sewol is successfully lifted up with the strand jack system based on twin barges. During the salvage operation, two barges and Sewol encounter offshore environmental conditions of wave, current and wind. It is inevitable that the relative motions among the three bodies are coupled with the sling tensions, which may cause big dynamic loads for the lifting system. During the project engineering phase and the site operation, it is necessary to build up a simulation model that can precisely generate the coupled responses in order to define a suitable weather window and monitor risks for the salvage operation. A special method for calculating multibody coupled responses is introduced into Sewol salvage project. Each body’s hydrodynamic force and moment in multibody configuration is calculated in the way that one body is treated as freely moving in space, while other bodies are set as fixed globally. The hydrodynamic force and moment are then applied into a numerical simulation model with some calibration coefficients being inserted. These coefficients are calibrated with the model test results. The simulation model built up this way can predict coupled responses with the similar accuracy as the model test and full scale measurement, and particularly generate multibody shielding effects. Site measured responses and the responses only resulted from from the simulation keep project management simultaneously to judge risks of each salvage stage, which are important for success of Sewol salvage.


Introduction
The sinking of Sewol Ferry occurred on April 16, 2014, on route from Incheon to Jeju in South Korea. When submerged, the ferry's portside touched seabed. On March 24, 2017, Sewol was successfully recovered out of water by Shanghai Salvage Company through 20 months' effort of salvage planning, preparation and operation. Traditionally, the wreck is firstly turned up on seabed. Lifting slings are then passed through the wreck bottom. Finally, the whole wreck is lifted up out of water by the floating cranes. However, Sewol has to be lifted and kept as the same attitude as on the seabed, which is required by the client of this salvage project. It is aimed to maintain the disaster scene and keep positions of the victims and cargoes inside Sewol for investigation afterwards. However, if the portside is on the downside, the structure strength of the ferry is not strong enough with the method of lifting slings to embrace the portside, especially its super structure.
Considering conditions of Sewol lifting attitude and the structure strength of the portside, the supporting beams lifting method is introduced into the salvage project. More than thirty supporting beams are installed under the portside of Sewol. Lifting slings are connected to the ends of the supporting beams. When lifting, Sewol is sitting on all the beams. Thus, Sewol structure and sinking attitude can be maintained as it is. By offering the method of supporting beams, Shanghai Salvage Company won the Sewol recovery project in the competition with many world-wide famous salvage companies, such as Smit, Titan Maritime and so on.
Sewol has been lying on seabed for almost three years until lifting up. The light weight of Sewol is more than six thousand tons. After lifted out of water, Sewol could weight more than ten thousand tons, including remaining cargos, muds and sands. Some physical properties of Sewol are very difficult to be predicted accurately, especially centers of its weight and buoyancy. It is necessary to find a lifting plan with large redundancy. During the salvage planning stage, a twin barge lifting method is put on the table for engineering. Two big size deck barges are moored along the wreck longitudinally. Strand jack lifting system is arranged on the decks of the two barges. The top end of each lifting sling is connected into each strand jack. The wreck can be lifted up by synchronously pulling of all the strand jacks. High stability of the two barges can provide lifting operation on stable platforms. More than thirty strand jacks on each barge can offer big redundancy of the lifting weight capability.
The wreck site of Sewol is about 50 km off the main land of South Korea and 25 km offshore of the Jindo Island. The mean water depth is 44 m. During the lifting operation, two barges and Sewol suffered from the environmental conditions of wave, current and wind. It is inevitable that relative motions among the three bodies occur. In order to avoid big peak dynamic loads in the lifting slings, a tension controller is installed into the end of each sling. During the engineering stage, a reliable coupled responses simulation model is used to assess the relative motion levels of the three bodies, effectiveness of the tension controller, and dynamic loads in the lifting slings. Limited operational sea states are identified with comprehensive assessment simulations.
Multibody coupled responses simulation needs to consider hydrodynamic coupled effects of different bodies. It is very challengeable to obtain accurate results from the numerical calculation for this area in the marine and offshore industry today. Hydrodynamic model test is usually required for this kind of the operation project by many owners or classification societies. But there are also limitations for the model test, such as available ocean basins, a small number of testing cases and so on. In this article, a numerical simulation model is introduced. It includes some unconventional coefficients that are calibrated by the model test results. The simulation model after the calibration can predict the coupled responses with similar accuracy as the model test and particularly also generate multibody shielding effects. Site measured responses and the responses only obtained from the simulation keep the project management simultaneously to judge risks of each salvage stage, which are important for successful salvage of Sewol.

Multibody boundary problem
Sewol is lifted off the seabed by twin barges. The lifting configuration is shown in Fig. 1. The distance between Lifting Barge 1 and Lifting Barge 3 is 29 m. The hydrodynamic coupled effects among these two barges and Sewol are strong. The main hydrodynamic coupled effects are shielding effects, enlarged wave elevations in gap and wave diffraction/radiation of each body interacting with each other. These effects put traditional hydrodynamic calculation theory into difficulty.
The traditional hydrodynamic theory is based on the potential flow, which is incompressible, free of separation, irrotational and inviscid. Based on this potential flow theory, the hydrodynamic forces of each body can be overestimated and the wave elevation in the gap between bodies can be unrealistically high, as studied by Chen (2005). To solve the problem, an artificial lid is put on the water surface in the gap to damp down the unrealistic wave elevation. This method is included in some commercial softwares such as WAMIT, Inc. (2015) and Bureau Veritas (2007). The lid is considered to be an extension of the body surface and represented by an additional patch. The lid damping has to be set up before the hydrodynamic calculation, ranging from 0 to 1. Usually, the lid damping is calibrated from the model test results. With this lid method and other calibrated hydrodynamic parameters, the multibody coupled responses can be calculated and reached close to the model test results of Xu et al. (2016) and Jean-Robert et al. (2006).
In the Sewol lifting project, a different method is performed to solve the multibody hydrodynamic calculation based on the existing potential flow theory but with some different calibration coefficients.

Coordinate systems
As shown in Fig. 1, the original of each vessel local coordinate is at the intersection of the keel line and after perpendicular. A positive x-axis points toward the vessel bow for each body, and a positive y-axis points toward the portside for the two lifting barges while pointing toward the top deck for Sewol. A positive z-axis points toward the top deck for the two lifting barges while pointing toward the starboard for Sewol. The original of the global coordinate is at the mean water surface. A global z-axis is upwards. YAO Zong et al. China Ocean Eng., 2018, Vol. 32, No. 2, P. 226-235 227 2.2 Principles of multibody boundary value problem In Sewol's lifting configuration shown in Fig. 1, all the three bodies are in sea water. Lifting Barge 1 and Lifting Barge 3 are floating on the surface, while Sewol is full of sea water and submerged. These three bodies are all considered as rigid. Sea water is assumed as the potential flow. In the fluid, each of the three bodies can move in six degrees of freedom. When calculating the hydrodynamic properties of each body, the other two are considered as fixed globally. This special treatment is the extension of the single body hydrodynamic calculation, but multibody coupled effects such as wave shielding, enlarged wave elevations in gap and others are included. This method is correct for the wave diffraction analysis. When conducting the wave radiation analysis, the other two wet body surfaces are taken as obstacles, which are expected to have some deviations but close to the reality for small waves. Some hydrodynamic properties calculated for each body are then calibrated with the multibody model testing results.
For each body in calculation, the flow velocity can be defined as the gradient of the fluid velocity potential Ф i . In harmonic waves, the problem is linearized and the velocity potential Ф i can be decomposed into the radiation and diffraction components as follows: is total velocity potential for each body calculation, for Lifting Barge 1, for Lifting Barge 3 and for Sewol.
is the radiation velocity potential and is the diffraction potential.
where is the incident wave potential and is the scattering wave potential.
Each of these velocity potential components has to fulfill a number of requirements and boundary conditions in the fluid. Requirements of (1) to (4) are applied for the velocity potential component of and , while the requirement of (5) is only applied for .
(1) Laplace equation or continuity condition (2) Seabed condition and the wet surface of the vessel body which is considered as fixed globally on the wet surface of the vessel which is considered as fixed globally (3) Boundary condition at the fluid free surface where g is the gravity acceleration, and ω is the frequency.
(4) Boundary condition on the wet surface of the body that is for the hydrodynamic calculation on the wet surface of the vessel that is for the hydrodynamic calculation, where is the outward normal velocity of a point at the wet surface of the vessel in calculation.
(5) Radiation condition at infinity Dis where is the distance in fluid from the oscillating vessel.

Method to solve the multibody boundary value problem
Similar to single body, the multibody boundary value problem defined above can be solved by the integral equation method. The radiation velocity potential on the body boundary is obtained from the integral equation where is the boundary of the body in calculation, is the Green function and the velocity potential at Point in the fluid domain due to a point source of the strength located at Point on body boundary, the unit vector is normal to the body boundary and it is assumed that the normal vector points out of the fluid domain.
The Green function satisfies the free-surface and radiation conditions. Details of the Green function are stated in the book of Lee and Newman (2004).
The equation for the total diffraction velocity potential is The integral equation for the source strength corresponding to the radiation potential takes the form The integral equation for the source strength corresponding to the scattering potential is (1) and (2), the fluid velocity on the body boundary due to or is then obtained from ∇Φ i The fluid velocity due to the incident wave is evaluated 228 YAO Zong et al. China Ocean Eng., 2018, Vol. 32, No. 2, P. 226-235 Φ i I directly from the incident wave potential . Integral of Eq. (9) to Eq. (13) are solved by the panel method. The wet body surface is represented by all the quadrilateral panels. The unknowns are assumed to be constant over each panel and the integral equation is enforced at the centroid of each panel.

Hydrodynamic force and moment on each body
On each body in the calculation, the forces and moments due to waves can be integrated based on the pressure over the wet body surface.
The pressure on the body wet surface is given by Bernoulli's equation.
(1), total velocity potential can be decomposed into and . The hydrodynamic force and moment of each body can also be divided into three components: the hydrostatic stiffness part which refers to the second part in the right of Eq. (17), the linear wave exciting force which is the first part in the right of Eq. (17) due to , and the added mass and damping coefficients which are from the first part in the right of Eq. (17) due to .
The mean wave drift forces and moments are obtained by averaging the force and moment expressions in Eqs. (15) and (16) with time. There are two contributions to the mean wave drift forces and moments, which are the wave diffraction potential and wave radiation potential .

Multibody coupled response analysis model
The wave hydrodynamic force and moment of each body are obtained based on the methods described in Section 2. Incorporating with loads from current, wind, mooring lines, lifting slings and fenders, the multibody coupled response analysis model can be built up. [ where, represents different bodies the same as in Eq. (1); is the position vector of Body , referring to the origin of the body local coordinate and having six degrees of freedom; is the mass matrix of Body ; is the frequency-dependent added mass of Body and calculated by the potential theory as defined above; is a calibration coefficient of the added mass value referring to the multibody model test; is the frequency dependent potential damping of Body and calculated by the potential theory as defined above; is a calibration coefficient of the damping value referring to the multibody model test; is hydrostatic stiffness of Body ; is the wind force of Body , which can be obtained by empirical coefficients or wind tunnel test; is the current force of Body , which can be obtained by empirical coefficients or wind tunnel test; is the linear wave exciting force of Body and calculated by the potential theory as defined above; is a calibration coefficient of linear wave exciting force referring to multibody model test; is the mean wave drift forces and moments of Body and calculated by potential theory as defined above; is a calibration coefficient of the mean wave drift forces and moments referring to the multibody model test; are the connector forces of Body , such as mooring lines, lifting slings and fenders.
Irregular wave elevations are expressed with spectrum. Current and wind forces are treated as constant loads. Hydrodynamic force and moment of each body are calculated in the frequency domain. Time series in the time domain are generated by discretizing the variance spectrum into a finite number of finite-valued harmonic components and by sampling phases from a uniform distribution from 0 to 2π. Calculation of the responses for each time step during the analysis can be performed by summation of harmonic components (sin/cos series). The calculation is conducted for the instantaneous locations of each body.
Mooring line forces on the twin barges are calculated with a quasi-static method. Restoring forces of each barge mooring system are the sum of each catenary mooring line top force. Restoring forces table with different excursions are applied for each barge in the time domain for instantaneous barge locations.
3.1 Numerical calculation for the hydrodynamic force and moment on each body To perform this multibody coupled response analysis, the hydrodynamic forces and moments on each body have to be firstly calculated based the method described above. Wet surfaces of each body are discretized into panels. Considering the wet surface shape of Sewol is unusual as it is submerged with the portside towards the seabed, the triangular panels are generated on the surface. Triangular panel is a special type of quadrilateral panel where two vertices coalesce. Quadrilateral panels are generated for the surfaces of the two lifting barges. Although the surfaces of the two lifting barges in air are also discretized into panels, only panels on the wet surfaces are applied in the calculation. 3D panels of all the three vessels are shown in Fig. 2.
There are three steps to calculate the hydrodynamic force and moment on each body in the multibody configuration as follows: • Lifting Barge 1 is in the modes of six degree freedoms, while Lifting Barge 3 and Sewol are fixed globally.
• Lifting Barge 3 is in the modes of six degree freed-oms, while Lifting Barge 1 and Sewol are fixed globally.
• Sewol is in the modes of six degree freedoms, while Lifting Barge 1 and Lifting Barge 1 are fixed globally.
Velocity potentials, hydrodynamic force and moment of each body in each step above are calculated by the computing code of MOSES, which was developed by Ultramarine, Inc. After the three steps of the calculation, the hydrodynamic force and moment on each body are obtained. Sea states of Sewol lifting operation are selected as low as possible. When Sewol starboard is below the bottom of any lifting barge during the operation, the wave hydrodynamic loads on Sewol are very limited. For the coupled response analysis when Sewol is lifted above sea bed but below the bottoms of any lifting barge, the wave hydrodynamic loads on Sewol are assumed as zero. Constant drag coefficients and added mass are applied on the body of Sewol.
The hydrodynamic force and moment on each body are also affected by wave headings, draft of each body and configuration of the three bodies. On engineering stage of the Sewol lifting project, a great number of cases have to be calculated. One example situation is shown in this paper for reference in Table 1.
It is the first stage that Sewol is lifted above seabed but its starboard is still below the bottom of any lifting barge. In the example case, the portside of Sewol is 2 m above the seabed and wave is heading towards the starboard of Lifting Barge 1. Only the two floating barges are affected by waves. Since it is the beam sea condition, the wave frequency critical motions of each lifting barge are sway, heave and roll. Wave mean drift critical motion is sway. Added mass, potential damping and mean drift forces of the two floating barges are calculated based on the theory defined in Section 2. The calculation results are provided in Figs. 3 and 4. These results are the bases for the numerical model calibration of the next step.
3.2 Analysis model of the sling and hydraulic tension controller As shown in Fig. 1, the top end of each sling is connected to the piston of one tension controller. The tension controller is a hydraulic passive tension control device, which works as a spring to absorb some energy from the tension and thus reduce the tension peak. The initial pressure force on the piston in the hydraulic cylinder is 153 tons. When the sling tension is below this pressure force, the piston cannot be moved and the sling connection is very stiff. When the sling tension is above this pressure force, the piston is moved by the sling and the tension goes up softly. While the piston is reached to another end of the hydraulic cylinder, the sling connection becomes stiff again. Fig. 5 shows the tension variation curve.
In the analysis model, each sling is modeled with an element whose force depends only upon the distance between two connection ends of a sling and acts in the direction of the vector from one end to the other. The stress-strain behavior of the sling element is calculated from material of the sling itself. The nonlinear tension variation curve of the tension controller is treated as an additional nonlinear force-deflection spring added into the top end of the sling.

Model test and numerical model
There are some assumptions in the potential flow theory to solve the multibody hydrodynamic motion calculation as stated in Section 2. It is unavoidable that the accuracy of the theoretical calculation is decreased by these assumptions. Thus, some calibration parameters are particularly built into the multibody coupled response analysis model as defined in Eq. (18). These parameters have to be calibrated or adjusted according to the model test results to make the numerical model applicable to the real project in terms of accuracy.

Model test set-up
A model test for Sewol lifted in different heights and in many sea states is conducted in the State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University. The model test setup is shown in Fig. 6. The three vessel bodies, lifting slings and mooring lines are all modeled with the scale factor of 1:50.  A mechanism is designed to model the tension controller behavior in the model test scale, as shown in Fig. 7.
The total 33 supporting beams are designed to stay be-low Sewol. However, in the model test scale, there is no enough space on the barge model to accommodate 66 tension controller mechanisms. The number of the supporting  YAO Zong et al. China Ocean Eng., 2018, Vol. 32, No. 2, P. 226-235 231 beams and slings are reduced to one third of the original design, as shown in Fig. 9.

Model test results
The example case described in Section 3.1 is also performed in the model test. Sea state in this case is summarized in Table 2. The windage area of the two lifting barges is very small. The lifting operation window is located into a season of small wind. Thus, wind effect is not included into the model test.
In the example case in the model test, the vessels are under the beam sea condition. The most critical motion is the vessel sway. Sway time series of each vessel are shown in Fig. 8. This time series records the vessel sway movement away from its original static position. As Lifting Barge 1 is on the wave side, the wave frequency motion is the heaviest among the three vessels. For Lifting Barge 3, the major wave attacking area is shielded by Lifting Barge 1. Wave frequency motions of Sewol and Lifting Barge 3 are mainly transferred from Lifting Barge 1 by the lifting slings. Drift movement of Sewol is the biggest, Lifting Barge 3 is the second, and Lifting Barge 1 is the third. This is because Sewol itself has a big current area which produces a big drag load while Sewol is only vertically lifted. There are four mooring lines on the starboard of Lifting Barge 1, but only two on the starboard of Lifting Barge 3. Mooring restoring force of Lifting Barge 3 on the wave direction in the analysis is much smaller than that of Lifting Barge 1.

Hydrodynamic coefficients calibration in the numerical model
Based on Eq. (18), it is numerically built up that Sewol is lifted by the two lifting barges. As shown in Fig. 9, three vessels, lifting slings and mooring lines are all in the model and the same as in the model test. For the example case, the     multibody coupled response analysis is performed numerically in the time domain too.
As stated in Eq. (18), some parameters are calibrated according to the model test results. In Table 3 Table 4. It can be concluded that the calibrated numerical model can perform these three bodies coupled analysis with the same accuracy level as that of the model test.
Looking deeply into the motion time series of the three bodies, wave shielding effect in numerical model is also generated as shown in Fig. 10. Wave frequency motion of Lifting Barge 1 is much higher than that of Lifting Barge 3 because major waves are shielded by Lifting Barge 1.
Motion responses of twin floating barges and Sewol are heavily coupled in the waves. Coupled motions of the three bodies are also interacted with the sling tensions. Fig. 11 provides the sling tension comparison between the model test and numerical model with the static and maximum dynamic values. The comparison results show the sling tension responses in the numerical model agree well with the model test and be slightly conservative. The maximum dynamic tension of all slings covers the model test results.
According to the comparison results stated above, the accuracy and conservatism of the calibrated numerical model achieve a confident level for real project practice. This numerical model is applied into the design and assessment of the sling, tension controller and strand jack lifting system. These lifting devices are proven to work well at the salvage duration in terms of function and safety.

Site measurement and numerical simulation
Sewol lifting operation is selected at the neap tide period of March, 2017. Current is quite small at that period. Wind and waves are slight. The sea states when Sewol is just lifted above the seabed are measured and given in Table 5. Although Sewol's weight is estimated as accurate as possible at the salvage designing stage, the actual weight is necessarily measured again when it is lifted away from the seabed. Weight information is provided in Table 5.
Measured weight of Sewol and sea states at site are updated in the numerical model set up above. Coupled response is simulated with these measured data again.
Parameters measured and recorded at each salvage stage are the maximum roll and pitch of the three bodies, and the maximum sling tensions. Comparing responses from the measurement and simulation shown in Table 6, it is found that the results are very close and the numerical simulation is slightly conservative. It can conclude that this multibody simulation method is applicable in salvage project practice. The coupled response comparison between the measurement and simulation is important to assess the accuracy of the numerical model. Vessel motion and the maximum sling tension from the simulation are slightly larger than those of the measurement. One reason is that the calibrated numerical model can result in higher vessel motion and especially the sling tension than the model test as described in Section 4.3. The second reason is that the potential boundary method stated above can also induce larger hydrodynamic force and moment than reality, especially for multi-bodies adjacently. There is still some overestimations for waves in the gaps between the bodies. However, the deviation in numerical model is rewarding in terms of a conservative salvage plan design.
The accuracy of the potential boundary method to calculate each body's hydrodynamic force and moment in the multibody configuration is expected to be low when waves become large. The hydrodynamic coefficient calibration can be also hard for bigger waves. If this method is applied into the project opening in big waves, more studies should be conducted.
The numerical model with some input from the site measurement is run in the beginning of each salvage stage. Some coupled responses which are not measured can be obtained from the simulation. Based on the measured data and response only obtained from the simulation, the project management can judge risks of each salvage stage. Re-sponse measurement and simulation of each salvage stage are proven to be significant for successful Sewol salvage.

Conclusions
In Sewol salvage project, a special method for multibody coupled responses simulation is introduced and applied for the project practice. This special method needs the multibody hydrodynamic force and moment calculation with the wave potential flow theory and corresponding model test. To calculate each body's hydrodynamic force and moment in the multibody configuration, the body is treated with six degrees of freedom in space while the other bodies are set as fixed globally. Model test results are provided as a base for the coefficient calibration. After the model test validation and full scale application, some conclusions can be arrived on this multibody coupled response analysis method.
(1) It is an effective way to calculate each body's hydrodynamic force and moment in the multibody configuration for small waves after the body is treated as freely moving in space while the other bodies being fixed globally. Each body's hydrodynamic data base built up with this method can figure out the special multibody phenomenon such as the shielding effects.
(2) Hydrodynamic calibration coefficients are specially defined in the multibody coupled response analysis model. After these coefficients are calibrated with the model test results, the numerical model can generate coupled responses which are slightly conservative with respect to the model test and full scale measurement.
(3) Site measured responses and responses only obtained from the simulation keep the project management simultaneously to judge risks of each salvage stage, which