Prior to performing collision-damage analysis, a comparative study was conducted with the results of the impact test for a stiffened cylinder model conducted by Do et al. (2018) to verify the numerical analysis technique. The impact test was conducted at the Structural Research Laboratory of the Department of Naval Architecture and Ocean Engineering, University of Ulsan. Fig. 1 shows the test facility. The test was conducted on a cylindrical model with both longitudinal stiffeners and ring stiffeners. This stiffener arrangement is common to most cylindrical floaters. The knife-edge geometry was adopted for to the striker, and the impact-test conditions are summarized in Table 1. Numerical analysis for the verification was conducted using Abaqus 6.22 software (2022). As for the constraints, fixed boundary conditions were imposed on the bottom of the cylinder end plate in the same manner as the impact test. In the study of Do et al. (2018), the element size of the finite-element model was determined via element-convergence verification, and the element size in the collision area was approximately 1.6 times the thickness. In this study, a finite-element model was constructed based on the above as shown in Fig. 2. The fine-element size (5 mm × 5 mm) was applied to the collision area, whereas the 20 mm × 20 mm size was applied to other areas.

The material properties obtained by conducting a tensile test on the specimen used in the experiment were secured from the literature (Do et al., 2018). The input data that exerted the most significant effect on the results of collision analysis were the material properties. However, the material properties may differ between the steel material used in the experimental model and that used in the floater design. Therefore, the results of the static and dynamic tensile tests conducted using tensile specimens from the steel material used in the actual structure are required to obtain accurate results. Normally, the yield strength can be known in the initial design phase of the actual structure. However, in this study, the ultimate strength and tensile strain were estimated from the yield strength of the material using Eqs. (1) and (2) proposed by Park (2017). Park derived the equations by the regression analyses of 7,737 mill sheets of mild and high-tensile steels. To calculate the plastic deformation caused by the impact load via numerical analysis, a true stress-strain curve that can consider the strain-hardening effect of the material is required. Thus, a true stress-strain curve was calculated using Eqs. (3)–(5). In this instance, 0.0218 was applied from the estimation formula of Park for the strain at the start of the strain hardening. In the numerical analysis, both the actual material properties and the material properties calculated from the estimation formulas were applied. Fig. 3 shows the true stress-strain curve. where

In addition, the stress-strain curve based on the strain rate was estimated by applying Eqs. (6)–(9) proposed by Park (2017) to consider the strain-rate effect of the material with instantaneous deformation. In this instance, 0.001, 1, 10, 30, 50, 80, 100, 200, and 1000 s⁻¹ were considered for the strain rate. Fig. 4 shows the stress-strain curve with consideration of the strain rate.

Collision analysis was conducted by applying the material properties defined above, and the displacement values at the point with the maximum displacement were compared. Fig. 5 shows the deformation history at the collision point of the numerical-analysis results. The average value of the section from 0.03 to 0.045 s after the spring-back was regarded as the final permanent deformation. Subsequently, the test and numerical-analysis results were compared, as shown in Table 2. The largest error of 22% occurred when the Cowper-Symonds equation was applied, and an error of 19% was observed even when the actual material properties were applied. Meanwhile, applying Park’s dynamic equation resulted in an error of 8% with respect to the test results. In addition, the numerical-analysis results obtained by applying Park’s estimation formula and the numerical-analysis results obtained based on the actual material properties derived from the tensile test were almost identical, that is, the difference in maximum deformation was only 0.2 mm. Fig. 6 shows the deformed model after the impact test and the numerical- analysis results. As shown in the figure, the deformed shape was almost identical. As for the collision analysis for the actual structure, numerical analysis was conducted in this study by applying Park’s material-property estimation formula and dynamic stress-strain curve equations. This is expected to yield more conservative results as compared with the damage to the actual structure.

The appropriate collision scenarios must be selected for the collision analysis of a floater. Dai et al. (2013) examined the risk of ship collision that may occur during the life cycle of an offshore wind turbine. They considered the ships that may approach the floater during its operation. In this study, installation waters were not selected, and thus, ships that operate along the routes under ALS scenarios were excluded. Among the ships that can be utilized during the life cycle, only working vessels with relatively high potential for collision damage were defined as targets. Table 3 summarizes the working vessels mobilized based on the operational stage and purpose of FOWTs. Vessels such as crew-transfer vessels (CTVs) were considered in ULS design. However, they were excluded from collision analysis owing to their insignificant impact on structures due to small displacement. As for colliding ships, multipurpose vessels (MPVs), service-operation vessels (SOVs), and anchor-handling tug ships (AHTSs), which are ships with different bow shapes, were considered (see Fig. 7). Additionally, 1,500 and 4,000 tons of displacement were applied considering the cargo loads. The hydrodynamic effect by fluid viscosity only considered the added mass and 0.25 was applied as the added-mass coefficient in accordance with DNV standards (2021). The DNV standards recommend collision velocities of 2 m/s or higher for the ALS. Therefore, collision velocities of 2 and 5 m/s were considered in this study. Analysis cases that do not involve fracture at a velocity of 2 m/s were excluded from the analysis cases for a velocity of 5 m/s. At a velocity of 2 m/s, only the cases with the highest collision energy were considered for each collision ship type. In this study, the collision between the bow of the ship and the outer column of the floater was considered, and collision angles of 0°, 30°, 60°, and 90° examined. In particular, angles of 0° and 90° represent collision cases with vertical girder members in the outer column, whereas angles of 30° and 60° represent collision cases with longitudinal stiffeners. Thus, 0° and 60° were selected as the final collision angles. Table 4 summarizes the collision-analysis conditions. The energy of the striker was calculated using Eq. (10).

In the collision analysis, a yield strength of 355 MPa was assumed for high-tensile steels frequently used in the marine structural design. Material properties that consider the true stress-strain curve and the strain-rate effect were estimated using the estimation formula of Park (2019). The same material properties were applied to both the shell and stiffener. Fig. 8 shows the stress-strain curves of the material applied to the numerical-analysis model. In addition, a shear-fracture model was applied to consider fracture deformation. Meanwhile, the shear criterion was set based on the studies of Ringsberg et al. (2018) and Park et al. (2023), who specified 0.23 to 0.27 as the shear criterion based on a parametric analysis for validation. In this study, a value of 0.25 was applied as the criterion for the shear-fracture model.

A 15MW semi-submersible type of UMaine VolturnUS-S was applied as the floater (Christopher et al., 2020). The internal stiffener of the floater was designed in accordance with DNV standards, and watertight bulkheads were installed at 5 m above the still water level (SWL) and 3 m below the SWL. Vertical displacement was restrained at the bottom of the floater. Except for the collision column, constrains for horizontal displacement were imposed on both sides of the column at the bottom. Collision ships were modeled as rigid bodies. A mesh size of 50 mm × 50 mm, which is 1.6 times the thickness of the column shell, was applied to the collision area, whereas 400 mm × 400 mm was applied to the other areas to reduce the analysis time. Fig. 9 shows the applied boundary conditions and the arrangements of the floater and collision ship. Fig. 10 shows the created finite-element model. Yoon and Choung (2023) demonstrated that collision occurs instantaneously. Thus, the effect of hydrodynamic force on damage is limited. In the collision analysis of this study, hydrodynamic force was considered only as the added mass of kinetic energy, whereas the damage range and the occurrence of fracture were examined based on the collision-area geometry.

The shell deformation results for the collision column were examined. Fig. 11 shows the maximum deformation distribution in the collision area under a collision angle of 0°. The maximum deformation of the shell was approximately 694 mm, which occurred during the collision of an SOV with a bulbous bow. Fig. 12 shows the x-direction displacement by case for a collision angle of 0°. As shown, the displacement distribution of the collision ship is consistent with the bow shape. Fig. 13 shows the maximum displacement at a collision velocity of 5 m/s. As presented, the displacement increased with the increase in the displacement of collision ship. This appears to be a valid result considering kinetic energy, and displacement more than doubled at a collision angle of 60°. Fig. 14 shows the displacement of the collision column in the xy-plane for Cases 3 and 4. The results indicate that a large deformation occurred at a collision angle of 60° due to the displacement of the entire column arising from the displacement of the floater pontoon. Table 5 summarizes the damage and fracture results for all collision cases. For the MPV and AHTS, the risk of flooding was low even after collision because the collision area and maximum deformation positions were above the sea level. In the case of SOV, the collision area and maximum deformation position were near the sea level, and damage occurred above and below the watertight bulkhead positions, as shown in Fig. 15. Therefore, when collision occurs, it is necessary to examine the occurrence of fracture in the shell and the flooding of the column.

The occurrence of fracture in the shell of the collision column was examined. If fracture occurs in the shell, then flooding occurs in the area below the SWL or in the splash zone, thus jeopardizing the floater’s stability. In accordance with the standards, the fracture occurrence was similarly examined at 2 m/s, which is the lowest collision velocity of the ALS. Fig. 16 shows the equivalent plastic strain results of SOV-collision analysis. For a collision angle of 0°, no fracture occurred even at a high displacement of 4,000 t. In the case of 60°, fracture occurred even at a low displacement of 1,500 t. Fine fracture occurred at a collision velocity of 2 m/s with the smallest kinetic energy. Furthermore, the occurrence of fracture differed depending on the collision angle, because the longitudinal girders attached at 90° intervals from 0° prevented the plastic deformation of the shell (Fig. 17). These results confirmed that the shell deformation caused by collision is proportional to the collision energy, whereas the shell can be fractured even by small collision energy, depending on the collision angle and internal stiffener arrangement. Fig. 18 shows the extent of damage. Because fracture occurs between the sea level and the watertight bulkhead at 3 m below the SWL, the flooding section caused by collision is the VOID section near the SWL. The results confirmed that collision with ships featuring a bulbous bow, including the SOV that was applied as a collision ship, may cause the flooding problem. Thus, the damage stability must be further examined to secure the safety of FOWT systems after collision occurs. If the damage stability cannot be secured, it can be made possible by designing the minimum flooding section of the VOID tank between watertight bulkheads or by applying foam-filling technology to prevent flooding of the damaged area (Shin et al.,2019).