Experimental and Simulation Studies on Protective Structures in Floating Dock

Abstract

In this research, two distinct designs of protective structures were developed to address structural damage caused by ships impacting the internal structures of floating docks during maintenance operations. The designed protective structures consist of support sections and load-bearing sections, with the load-bearing section comprising three frame sections. For ease of description, the front frame section, middle frame section, and rear frame section are referred to as Frame A, Frame B, and Frame C, respectively. A drop-weight test was conducted with a stern-shaped indenter impacting the structures at 3.89 m/s. This study also assessed varying impact speeds and positions. The results showed that Specimen 2 had localized indentations on Frame B, while Specimen 1 exhibited overall deformation of Frame B and additional deformations in Frame A. The simulations agreed with the experimental results, confirming the model’s accuracy. At speeds from 2.34 m/s to 5.45 m/s, Specimen 2 consistently showed localized deformations, while Specimen 1 showed comprehensive deformation of Frame B at 3.89 m/s due to lower rigidity. When the indenter impacted the specimens at different locations with a speed of 5.45 m/s, the two specimens exhibited varying degrees of damage. As the impact location shifted from the central area to the end, the maximum indentation depth of Specimen 1 decreased from 52.26 mm to 41.71 mm, while that of Specimen 2 decreased from 43.26 mm to 38.50 mm. The reduction in indentation depth and extent as the impact location approached the support frame can be attributed to the increasing involvement of the web plate beneath the frame in resisting the impact. Additionally, compared to Specimen 1, Specimen 2 exhibited a relatively smaller overall indentation depth, and the impact of location variation on indentation depth was also relatively minor.

1. Introduction

Floating docks, also known as floating dry docks, are versatile marine structures primarily used for salvage operations and transporting damaged vessels to safe areas [1]. Compared to traditional, permanently situated dry docks, floating docks offer enhanced mobility and adaptability, allowing for the maintenance of vessels of varying displacements and accommodating large ships through modular interconnection [2]. However, this flexibility also introduces higher risks of accidents, particularly in adverse weather conditions or due to operational errors. For example, structural failures or instability may occur during the operation of floating docks, leading to severe damage or even capsizing. [3].

In recent years, many researchers have focused on ballast control of floating docks to enhance their stability and safety. For example, Korotaev et al. [4] improved operational safety during loading and unloading by monitoring the deflection of floating docks. Zhang et al. [5] conducted a comprehensive numerical study of floating dock systems. They developed an internal code to simulate dock movements and studied ballast water distribution strategies. Wen et al. [6] further introduced an improved P-controller for ballast water system management, enhancing the stability of floating docks during ballasting and de-ballasting operations. However, to further reduce the risk of internal structural damage during vessel entry and exit, installing collision protection devices to mitigate structural damage and enhance safety has also become crucial [7].

Collision protection devices have been widely applied across various fields of ship collision protection, including pier protection devices [8], rubber fenders used in ship-to-ship resupply operations [9,10], and protective devices for floating wind turbines during maintenance processes [11]. These devices are generally categorized into rigid, flexible, and composite collision protection systems. Flexible devices such as airbags [12] and rubber fenders [13] exhibit notable flexibility but limited energy absorption capabilities. Composite collision devices combine various structures and materials to resist impacts [14,15,16]. For instance, Wang et al. [17] designed a flexible floating facility that combines rubber and steel, effectively reducing the impact force on ships. Similarly, Zhou et al. [18] introduced an innovative collision protection system made from ultra-high-performance concrete connected by high-strength bolts, enhancing its energy absorption properties. Yan [19] proposed using fiber-reinforced polymer laminate and structural optimization schemes like sandwich structures to enhance the impact resistance of large marine protective devices. Effective composite devices are often complex, costly, and bulky, generally suited only for large protective facilities. For low-speed, low-energy collisions within docks, these devices may not be applicable. In contrast, rigid collision protection devices primarily use steel materials to absorb impact energy through plastic deformation, reducing impact forces. Due to their low cost, simplicity in manufacturing, ease of replacement, and stable long-term performance, rigid devices capable of absorbing significant energy have been widely used [20,21]. Recent research has demonstrated the excellent impact resistance of steel structures. For example, Zheng and Xu [22] conducted an experimental and numerical study on the mechanical behavior of composite steel structures under explosion loads, revealing their significant impact resistance. Therefore, it is essential to install such steel-framed protective structures to address collision risks within floating docks.

This study proposes two steel protective structures aimed at enhancing safety during ship docking and undocking processes by reducing collision risks. Within a wet dock environment, simulating floating dock collision scenarios, impact resistance tests were systematically performed on these structures. Utilizing LS-DYNA software, v.SMP S R11.1, finite element models of these collision protection structures under stern indenter impact loads were developed. This study meticulously analyzed the recorded impact forces and resultant local indentations to ascertain the dynamic responses and deformation behaviors of the two structures under various operational conditions. The investigation also extends to exploring the dynamic behavior of these structures across different impact positions and velocities, thereby delineating the influence of impact parameters on their structural integrity. Such insights are vital for optimizing docking procedures within floating docks to minimize potential structural damages and deformations.

2. Protective Structures

To investigate the structural response of protective structures within a dock under impact loads, two different types of specimens representing typical sections of internal dock protections were designed and fabricated. The global coordinate system defined in Figure 1 characterizes the orientation of the specimens.

As depicted in Figure 1, each specimen consists of a central carrying frame and two end support frames, welded together. The support frames are spaced 1200 mm apart, a dimension determined by the spacing of the bulkhead strong components. The carrying frame includes three panels and three webs, with each pair of web and panel forming a frame section. Each frame section is spaced 210 mm apart, referencing the spacing of the connected floating dock’s structural members. For ease of subsequent description, the front, middle, and rear frame sections are referred to as Frame A, Frame B, and Frame C, respectively. Additionally, the panels of each frame are 8 mm thick, while the webs and support frames are 6 mm thick.

Specimen 1 and Specimen 2 share identical dimensions for the support frames but differ in the configurations of their load-bearing frames. In Specimen 1, all three load-bearing frames are U-shaped, with specific dimensions provided in Figure 2. In Specimen 2, Frames A and C are U-shaped, as detailed in Figure 2b, while Frame B is O-shaped, with dimensions shown in Figure 2c.

3. Falling Weight Impact Test

The experiments were conducted in the Mechanics Laboratory at Jiangsu University of Science and Technology, utilizing a drop-weight test machine (Figure 3a), which could achieve a maximum lifting height of 3.7 m and a maximum impact velocity of 8.5 m/s. This setup was capable of simulating most collision scenarios encountered in the maritime field. The maximum weight of the impactor was 1.35 tons, designed to generate a maximum gravitational potential energy of 50 kJ. In these experiments, the total weight of the impact hammer was 969 kg. Figure 3b illustrates the sensors mounted on the hammer to capture the acceleration data during impact. Additionally, a laser rangefinder was positioned directly above the measuring point on the hammer to record displacement data during the tests. Both sensors began recording data synchronously before the hammer’s descent, with the data acquisition frequency set at 20 kHz. This configuration was intended to precisely measure and analyze the dynamic response of protective structures within the dock under simulated collision scenarios.

3.1. Test Specimens Employed in Experiments

Following the detailed designs for two types of dock specimens, Specimens 1 and 2 were constructed through welding, as illustrated in Figure 4. Specimen 1 is composed entirely of U-shaped frames. In contrast, Specimen 2 features Frame B in an O shape, while the remaining frames are U-shaped.

Both specimens are constructed from high-strength steel. The static mechanical properties of the protective structures were determined via quasi-static tensile tests, with the testing apparatus shown in Figure 5a. The tests were conducted according to the GB/T 228.1-2010 standard, with the specimens and their specific dimensions shown in Figure 5b,c [23]. The testing rate was 1.0 mm/min until fracture. The engineering stress–strain relationships are presented in Figure 6, and the mechanical properties of the specimens are listed in

Table 1. Mechanical properties of test piece.

Property	Value	Unit
Density ρ	7850	kg/m3
Young’s modulus Ε	212	GPa
Poisson’s ratio υ	0.26	-
Yield strength σY	355	MPa
Ultimate tensile strength σu	510	MPa

.

3.2. Indenter Used in Experimental Testing

To simulate a scenario where a vessel enters a wet dock and collides with the protective structure, the impactor used in the experiments was designed to resemble the stern of a boat (Figure 7a), with specific dimensions detailed in Figure 7b. The impactor was made from GCr15 material, known for its high hardness, which allowed us to disregard the deformation of the vessel itself during the collision.

Before initiating the drop-weight test, the specimen of the protective structure was positioned on the test stand, aligning the center of its carrying part with the midpoint of the impact hammer. The testing device then lowered the hammer until it touched the specimen’s carrying surface, at which point the displacement and load data were set to zero. To simulate a collision involving a vessel weighing 235 tons moving at a speed of 0.25 m/s against the protective structure, and to ensure energy equivalence in the simulation, the hammer was released from a height of 0.495 m above the contact point.

4. Test Results

4.1. Deformation Modes of Structure

The damage deformation directly reflects the dynamic response of the protective structure under the impact load of vessels entering the dock. This study observed and measured the overall deformation patterns and assessed the deformation mechanism of the cross-section of the load-bearing frame. The deformation distribution of the sandwich panel at the impact center area under an initial impact speed of 3.89 m/s is depicted. Figure 8a shows the overall deformation of Specimen 1, along with the maximum deformation in the Z-direction of Frames A and B; Figure 8b shows the overall deformation of Specimen 2 under the same impact conditions and the maximum deformation in the Z-direction of Frame B.

The maximum plastic deformation for both specimens occurred at the middle position of the load-bearing frame. The B panel of Specimen 1 exhibited local U-shaped indentations on both sides of the contact area, with a maximum depth of 32.4 mm; the entire Frame B showed downward deformation extending to the connection with the support frame. Additionally, due to the overall downward deformation of Frame B, the impact head made contact with one side of Panel A, causing slight deformation with a maximum depth of 5.6 mm. The contact area on both sides of Panel B in Specimen 2 showed local “saddle-shaped” deformation, with a maximum depth of 23.6 mm on one side and 14.7 mm on the other. Due to the strong rigidity of Frame B in Specimen 2, which is an enclosed “O”-type structure, the strong web effectively resisted the impact load, thus limiting deformation to a smaller area.

Observations of the damage deformation in Specimens 1 and 2 reveal that the maximum deformation on both sides of Panel B in the contact area with the impact head is not uniform. The reason is that the loading position of the vessel’s stern head is not completely horizontal, leading to the initial contact with the lower half of the panel, followed by the upper half. This phenomenon is more pronounced in Specimen 2.

4.2. Impact Load

The load–displacement curve (Figure 9) can be segmented into three phases: the initial stage, characterized by a gradual increase in load; the second stage, where the reaction force escalates rapidly and the majority of the impact kinetic energy is dissipated; and the final unloading stage.

As seen in Figure 9, at the initial impact stage, the edge of Panel B in Specimen 2, which has stronger stiffness, first makes contact with the impact head and undergoes local deformation. Subsequently, the lower half of the panel continues to bear the load and further deforms inward, with a rapid rise in load occurring after point A. Once the upper panel is compressed, the web also contributes to resisting deformation, leading to a gradual slowdown in the increase in impact load until the maximum deformation is reached. During the unloading stage, the frame overall releases some of the elastic deformation, marking the end of the collision process. In this phase, as the impact force decreases sharply, displacement slightly drops, releasing the stored elastic strain energy.

In contrast to Specimen 2, in the load–displacement curve of Specimen 1, during the second stage, the impact load gradually slows down and then rapidly rises until it reaches the maximum load. This occurs because the web and panels of Frame B jointly resist deformation; the frame has a relatively lower rigidity and adopts an open U-shaped structure. The web and panels of Frame B first deform locally and then collectively indent inward.

5. Numerical Simulations

5.1. FE Models

This section describes the finite element analysis of the dynamic response of dockside anti-collision structures using the LS-DYNA finite element software package. The analysis aims to complement the laboratory experiments and provide additional information not obtainable solely through experimental measurements. The geometric shapes used in the numerical simulation are the same as those in the experimental tests. The load-bearing and supporting frames are modeled using Belytschko–Tsay shell elements based on Mindlin’s theory, comprised of four-node shell elements and some three-node shell elements, with a mesh size of 10 mm. The Belytschko–Tsay shell element, with its default shell element formulation and in-plane single-point integration, offers high computational speed and is generally the most stable and effective formulation for deformation problems. A mesh sensitivity analysis was performed on both specimens to ascertain an appropriate mesh size. Mesh sizes of 20 mm, 15 mm, 10 mm, and 5 mm were selected. Figure 10 shows the peak collision force variation curves for Specimen 1 and Specimen 2 at these four different mesh sizes. It can be observed that these collision force curves exhibit good convergence, with minimal differences in the computed results when using mesh sizes of 5 mm and 10 mm. Therefore, a mesh size of 10 mm is adopted for both specimens in subsequent analyses.

The impactor head of the vessel’s impact hammer is modeled as rigid, only allowed to move in the impact direction (Z-direction). The entire finite element model is shown in Figure 11. The initial velocity was set to 3.89 m/s and applied to the impact hammer head using the “Boundary prescribed motion rigid” command. The termination time was set in this command to ensure that the kinetic energy of the hammer head at the moment of contact with the specimen matched that in the experiment. To simplify the simulation, the bottom nodes of the support frame were fully constrained to simulate the welded fixation at the bottom of the specimen in the experiment, accurately predicting the impact damage observed in the experiments. Additionally, the specimen’s material parameters were defined using the “mat piecewise linear plasticity” command, with specific parameters referenced from Table 1. The hammer head was defined using the “mat rigid” command, and its weight was matched to the actual hammer head by adding mass points.

In this analysis, the automatic surface to surface contact model provided by LS-DYNA was utilized to define the contact problem. Given that both the dockside anti-collision structures and the impact hammer are made of steel, the penalty function method was chosen to construct the contact algorithm. Following previous research, the friction coefficient was set at 0.3, and the failure strain was established at 0.25 [24,25].

5.2. Results and Comparisons

Numerical simulation results are compared with experimental measurements in terms of the deformation modes and impact load.

5.2.1. Deformation Modes

The comparison of damage deformations in the protective devices in the experiments and numerical simulations at an impact speed of 3.89 m/s is shown in Figure 12.

In the simulations, the deformation patterns of Specimens 1 and 2 are consistent with the experimental results. It was observed that the mid-section panel of Specimen 1 exhibited overall downward deformation, with the lowest point descending by 34.2 mm, and a slight indentation on one side of Section C, with a maximum descent of 6.7 mm. The section panel of Specimen 2 showed localized deformation, appearing saddle-shaped, with one side indenting downward by 25.8 mm and the other by 16.2 mm. Additionally, Section C of Specimen 2 did not make contact with the impact head; thus, no deformation occurred.

5.2.2. Impact Load

Comparing experimental results, the simulated load–displacement curves also showed a trend of gradually loading to a peak followed by rapid unloading (see Figure 13).

In the simulations, the displacement of Specimen 1 was 5.5% higher than the experimental results, while the displacement of Specimen 2 was 9.3% lower than the experimental results. Additionally, the peak load in the simulation for Specimen 1 was 3.9% lower than the peak experimental load, and for Specimen 2, it was 4.6% lower (see

Table 2. The peak load and maximum displacement in the test and in simulation.

Specimen	Maximum Displacement (mm)		Discrepancy	Peak Load (kN)		Discrepancy
	Experiment	FE		Experiment	FE
Specimen 1	32.4	34.2	5.5%	310.9	298.8	3.9%
Specimen 2	23.6	25.8	9.3%	327.0	312.1	4.6%

). These differences primarily arose because perfect fixed constraints were used in the simulations, whereas the bolt connections in the experiments could not achieve such perfect fixation. Overall, the simulation results effectively predicted the collision behavior between the anti-collision structures and the ship-stern-like impact head. The simulations captured most of the deformation modes observed in the experiments, including deformations in both sections of Specimen 1, the saddle-shaped deformation of the panel in Specimen 2, and the warping deformations of the web of Frame B in both specimens. These results indicate that the numerical simulation model established can accurately describe the impact response and the resulting damage states.

6. Parameter Sensitivity Analysis

6.1. Effect of Initial Impact Velocity

When vessels enter a dock, varying docking speeds occur due to factors such as wind and waves. To investigate the impact of collision speed on the resilience of anti-collision structures, this study selected five different impact speeds, with the point of impact consistent with the experimental setup (see

Table 3. Numerical simulation cases with different impact velocities.

Impact Cases	Impact Velocity (m/s)	Impact Energy (kJ)	Drop Height (mm)
V-0.15	2.34	2.6	278
V-0.20	3.11	4.7	495
V-0.25	3.89	7.3	773
V-0.30	4.67	10.1	1114
V-0.35	5.45	14.4	1518

). In the simulations, all parameters remained constant except for the differing impact speeds of the ram. Table 3 shows the deformations of the load-bearing and mid-structure sections under varying impact speeds.

As observed in

Table 4. Deformation of Frame B in specimens at various impact speeds.

Impact Energy Cases	Final Deformation of Frame B in Specimen 1	Final Deformation of Frame B in Specimen 2
V-0.15
V-0.20
V-0.25
V-0.30
V-0.35

, at a docking speed of 0.15 m/s, only minor deformation occurs on Panel B of Specimen 1; however, as the speed increases, Panel B progressively indents downwards. When the speed reaches 0.25 m/s, Panel A of Specimen 1 also begins to indent. At the maximum impact speed (0.35 m/s), the panel and web of Frame B in Specimen 1 deform downward as a whole, with significant stress concentration occurring at the junction between the load-bearing and supporting frames. For Specimen 2, at all five speeds, Panel B exhibits localized downward indentation, and Frame B’s web shows localized “saddle-shaped” indentation at the joint with the panel. Due to its robust structure, no deformation is observed in Frame A of Specimen 2 at any of the impact speeds, nor does Frame b show overall sinking. Notably, as the speed increases, the area of deformation damage at the junction of the load-bearing and supporting parts in Specimen 1 gradually enlarges, while the corresponding area in Specimen 2 shows no significant changes. This indicates that the “O”-shaped closed structure of Specimen 2 possesses superior resistance to collision-induced deformation.

Figure 14 shows the load–displacement curves of the anti-collision structures under different impact speeds. The initial impact speed significantly affects the impact load on the structures. From the load–displacement curve of Specimen 1, it is evident that at speeds of 0.15 m/s and 0.2 m/s, there is no rapid increase in load after a gradual slowdown. This indicates that at lower speeds, Frame 1 only undergoes localized indentation deformations, and the mid-section does not experience overall sinking, which is also confirmed by the deformation contour maps. In contrast, the load–displacement curve of Specimen 2 shows that within the two phases, the load initially increases rapidly and then gradually slows down until reaching maximum displacement, followed by the unloading phase. As the speed increases, the duration of the load reduction in the second phase of Specimen 2 extends. The deformation contour maps reveal that the closed “O”-shaped structure effectively resists the impact of the ram, resulting in localized indentation deformations across all five speeds.

6.2. Effect of Initial Impact Locations

Experimental studies have shown that the impact ram is typically located in the middle area of the anti-collision structure. To further explore the deformation modes and dynamic responses of the anti-collision structures, this study examined the effects of impact locations on the dynamic performance of these structures. In real ship docking processes, the contact points between the ship and the anti-collision structures can become more uncertain due to variations in speed and the effects of wind and waves. Therefore, the experiment was conducted with a ship entering the dock at a speed of 0.3 m/s, testing four different positions on the anti-collision structure (see Figure 15).

In Case C-0, the impact ram is positioned at the transverse center. In Case C-150, the ram is positioned 150 mm outward from the mid-span. In Cases C-300 and C-450, the ram is located 300 mm and 450 mm outward from the mid-span, respectively. Considering the minimal change in the ship’s draft during docking, which results in minimal variation in the height at which the ship’s stern contacts the dock’s anti-collision structure, the simulations disregarded longitudinal (Y-direction) variations in the contact area between the ram and the anti-collision structure.

The responses of Frame B’s cross-sectional structures to collisions at four different positions, using two different construction types of anti-collision structures, are presented in

Table 5. Final deformation of specimen frames at various impact locations.

Impact Location Cases	Final Deformation of Frame B in Specimen 1	Final Deformation of Frame B in Specimen 2
C-0
C-150
C-300
C-450

. Due to the relatively high impact energy, the web of Frame B in both specimen types exhibited varying degrees of warping deformation under all conditions. The maximum indentation depth of Frame B’s panel decreases as the ram’s distance from the mid-span increases; that is, the maximum indentation is smaller when the ram is closer to the support frame (see Figure 16). This suggests that the distance from the support frame has a certain impact on the damage state of the anti-collision structure. Comparing the damage differences between the two specimen types, under higher impact energy, the stiffer Specimen 2 only deformed in Frame B, whereas Specimen 1 exhibited varying degrees of deformation in both Frames B and A in the cases of C-0, C-150, and C-300. However, in Case C-450, because the support portion absorbed some of the impact energy, the ram did not further contact Frame A. Notably, in the furthest condition from the mid-span, C-450, both types of specimens exhibited varying degrees of warping deformation at the junction between the load-bearing and support frames; Specimen 1 showed more significant warping, while Specimen 2, although warping to a lesser extent, had a broader range of deformation.

Comparing the load–displacement curves at different collision positions (Figure 17), it is observed that as both specimen types approach the boundary, the peak load values increase, while the maximum indentation depths decrease. The curves also visually demonstrate the impact of the support frame on the specimens’ impact resistance capabilities. As shown in Figure 17a, as the distance from the mid-span increases, the timing of the second peak rise in collision force advances, and the duration of impact shortens. This indicates that the collaborative resistance to the impact by the panel and web of Frame B is occurring sooner, with the duration of impact continually shortening. Similarly, Figure 17b reveals that as the distance from the mid-span increases, the duration of impact by the ram shortens. This demonstrates that as the location moves further from the mid-span, approaching the support frame, the anti-collision structure’s impact resistance significantly improves.

7. Conclusions

This research delineates the development and assessment of two distinct anti-collision structures designed for floating docks, focusing on their behavior under low-speed collision scenarios. By conducting both experimental drop hammer tests and detailed numerical simulations using the LS-DYNA software, this paper evaluates the structural integrity and dynamic responses of the anti-collision systems. The analysis covers deformation patterns and changes in impact forces, providing a comparative insight into the performance of the two structures. Furthermore, the influence of impact speed and location on the resilience of the structures is methodically explored. The principal findings of this study are summarized as follows:

• At an impact speed of 3.89 m/s, Specimen 1 exhibited indentation deformation in the mid-section contact area and overall sinking of the frame. Additionally, the middle position of the upper section panel of Specimen 1 also showed slight deformation due to the deeper impact depth, with the ram impacting the upper section again. Deformation in Specimen 2 occurred only on Frame B, exhibiting indentation deformation, with no other areas contacting the ram. Moreover, the localized deformation in Specimen 2 was “saddle-shaped”.
• The finite element analysis accurately predicted and captured the deformation modes of the two anti-collision structures. The maximum indentation depth and peak load in the mid-section contact area were very close to the experimental results. Specifically, the maximum indentation depth error for Specimen 1 was 5.5%, and for Specimen 2 it was 9.3%. The peak load errors for both specimens were also below 5%, demonstrating the accuracy of the finite element predictions.
• As the impact speed increased within the range of 2.5 m/s to 3.5 m/s, Specimen 1 exhibited overall structural deformation, with a maximum indentation depth of 52.26 mm. In contrast, Specimen 2 showed localized indentation deformation at all five speeds, with a maximum indentation depth of 43.26 mm. Both the damage deformation patterns and the maximum indentation depth data indicate that Specimen 2 has superior impact resistance.
• Finite element simulations of collisions at different positions showed that the dynamic responses of the two specimens with different structures were slightly affected by the impact location. As the impact location moved from the center to the end, the maximum indentation depth of Specimen 1 decreased from 52.26 mm to 41.71 mm, while that of Specimen 2 decreased relatively less, from 43.26 mm to 38.50 mm. This indicates that the O-shaped structure is less sensitive to impact location compared to the U-shaped structure. Additionally, the trend shows that for both specimens, as the impact location moves further from the midspan, the indentation depth decreases due to the increasing involvement of the support part in resisting the impact.

However, this study has certain limitations. Firstly, the experimental conditions employed may not fully replicate the complexities encountered in real-world operational environments. Secondly, although the study offers valuable preliminary data, further research should address the following areas: evaluating the performance of protective structures constructed from a variety of materials to identify more optimized material combinations, and conducting simulations and experiments under a broader range of impact conditions, including varying impact angles and velocities, to achieve a comprehensive assessment of the protective structures’ efficacy.