Load Calculation and Strength Analysis of Prefabricated Floating Dock

Abstract

This paper proposes a multi-module assembly floating dock, which is assembled by a pin-jointed hinge structure between modules. Based on the design wave method, the three-dimensional potential flow theory is used to calculate the loads and analyze the strength of the assembly floating dock, and the configuration is optimized and analyzed. The results show that the longitudinal torque load in the wave load of the floating dock is the largest, and the maximum stress area is the connection between the platform and the column. Based on numerical results, structural strengthening design and analysis were carried out for multiple high-stress areas, which significantly reduced structural stress, with a maximum reduction of 54%, making the structural strength meet the design requirements. The research results of this paper can provide a reference for the design and strength optimization of floating dock configurations in the future.

1 Introduction

With the development of maritime production and transportation industries in the South China Sea, the construction of offshore and deep-water ports and wharves on islands and reefs has become increasingly important. Designing and constructing a simpler, more convenient, and cost-effective floating dock is crucial. Compared to traditional fixed docks, floating docks require less sand, stone, and steel materials, which reduces construction costs and makes them more economically viable. Moreover, floating docks are more flexible and mobile, better able to adapt to changes in the marine environment and the varying needs of ships. However, the marine environment where prefabricated floating docks are located is very complex and subjected to long-term wave loads, which may lead to a combination of various external forces such as shear and torsion, resulting in significant stress on local structural components and making them prone to failure. Once the entire structure of a floating dock fails, it will cause significant economic losses and pose a threat to the life safety of workers on the platform. Therefore, it is essential to study the overall strength of large offshore floating structures and ensure their safety.

Currently, research on the structural performance of floating docks and large floating structures has been conducted both domestically and internationally. Shahrabi and Bargi [1] provided optimal dimensions for different float widths that meet design constraints based on various modes and loads acting on the floating dock. Tajali [2] found that the response of a floating bridge is largely dependent on the size of the floating bridge, connector stiffness, wave conditions, and characteristics of the interaction between the floating bridge. Ji Chunyan et al. [3] analyzed the ultimate strength of a typical semisubmersible platform’s critical structures using the progressive failure method and finite element calculation. They predicted the design wave that the platform faced based on the theory of wave loads and computed the overall strength of a typical semisubmersible platform using the direct calculation method. Zheng Zhiguo [4] found that the wave resistance of the container combination floating body was poor due to its shape not being a double-curved surface by calculating the motion response of a single floating dock and different container combination floats. Kim [5] improved the vertical motion performance of the floating dock structure and optimized the structure’s shape to adapt to the coastal environment of Korea. Lin Sinan [6] designed a large floating dock with an asphalt deck surface and conducted a mechanical response study. Zhang Jingyi [7] calculated the strength of two configurations of ultra-large floating structures using the direct calculation method and obtained different high-stress regions. Based on the structural characteristics of these high-stress regions, they proposed improvement schemes. Lee et al. [8] calculated the overall strength of a traditional semisubmersible platform based on the theory of wave loads and found three main high-stress regions: the connection between the column and the float, the connection between the column and the cross-brace, and the connection between the column and the lower float. Lin Sinan [6] designed a large floating dock with an asphalt deck and conducted a mechanical response study. Zhang Jingyi et al. [7] proposed various improvement schemes based on the structural characteristics of the high stress areas of longitudinal and transverse large floating boxes and compared the results of three schemes to obtain the optimal configuration. Su Changnan[9] conducted a detailed study on the horizontal fixed tilt center height and freeboard height of the buoyancy tank through numerical simulation to ensure the reliability of the lateral stability of the buoyancy tank.

From the research of the scholars mentioned above, it can be seen that there is currently limited research on the strength of floating dock structures, and most studies focus on analyzing a single module of a floating dock. In this paper, we design a multi-module floating dock connected by hinge structures. This design is cost-effective and can be quickly assembled according to different needs. Using three-dimensional potential flow theory and DNV’s SESAM software, we establish a numerical model of the floating dock and analyze its wave load and structural strength. The results of this study can provide reference for future floating dock configuration design and strength optimization analysis.

2 Theoretical Basis

2.1 Three-Dimensional Potential Flow Theory

Wave loads on marine structures can be divided into three types: diffraction forces, inertia forces, and drag forces. Diffraction forces are generated by the diffraction effect of water flow on the structure, while inertia forces consist of added mass forces and added damping forces. Drag forces are generated by the disturbance of the structure on the water flow.

For different structural configurations and sizes, the proportion of wave load components can vary greatly. For small structures, drag forces and inertia forces are equally important. However, for large floating structures, inertia forces and diffraction forces are more important. Therefore, when calculating wave loads, it is necessary to first determine which calculation method is more appropriate based on the scale of the structure. Generally, three-dimensional potential flow theory is used to calculate the first-order wave load of large structures such as some large floating platforms. The size of the floating dock designed in this paper can reach 60 m, and the structural scale is relatively large, so three-dimensional potential flow theory is used for calculation.

In the case of large structures, serious reflection and diffraction phenomena will occur when incident waves are present, so they cannot be ignored when calculating wave loads. Using potential flow theory to describe the motion state of the floating body can simplify the problem. When the ratio of wave height to wavelength is small, linear theory can further simplify the problem. Three-dimensional potential flow theory assumes that the fluid is an ideal fluid with no viscosity, no vorticity, and incompressibility. According to potential flow theory, the velocity potential satisfies the Laplace equation in the flow domain:

$$ \nabla^2 \Phi = 0 $$

(1)

The velocity potential can be further decomposed linearly into:

$$ \left. {\begin{array}{*{20}c} {\phi = \phi_O + \phi_R + \phi_D } \\ {\phi_O = \frac{iAg}{\omega } \times \frac{{\cosh k\left( {z + H} \right)}}{\cosh kH}e^{ - ik\left( {x\cos \beta + y\sin \beta } \right)} } \\ {\phi_R = i\omega \mathop \sum \nolimits_{j = 1}^6 \xi_j \phi_j } \\ \end{array} } \right\} $$

(2)

In the formula, $\phi_O$ represents incident potential; $\phi_R$ represents radiated potential; $\phi_D$ represents diffracted potential; $A$ represents wave amplitude; $\omega$ represents circular frequency of the wave; $\beta$ represents wave direction angle; $k$ represents wave number; $H$ represents water depth; $\xi_j$ represents the amplitude of motion in the six degrees of freedom of the object; $\phi_j$ represents unit radiated potential.

The diffraction potential and the radiation potential are satisfied:

$$ \frac{\partial \phi_j }{{\partial n}} = n_j ,\frac{\partial \phi_D }{{\partial n}} = 0 $$

(3)

By determining the velocity potential of the flow field through the distribution of sources and sinks on a wet surface, and solving the boundary conditions using Green’s formula, the total velocity potential can be obtained. Then, using numerical discretization, the pressure distribution acting on the floating dock can be calculated, and the wave forces and moments acting on the floating dock can be determined.

2.2 Finite Element Analysis Process

The finite element analysis process for a floating dock is shown in Fig. 1. The assembly-type floating dock is modeled, analyzed for hydrodynamics, and long-term forecasted using the GeniE, Wadam, and Postresp modules of the ship and ocean engineering large-scale finite element analysis software SESAM. The quasi-static analysis method is used to transmit the calculated wave loads and design wave parameters to the floating dock in the form of pressure loads through the Sestra module, and the overall structural stress information can be obtained in the Xtract module.

Fig. 1.

Finite element analysis process of prefabricated floating dock

3 Design Scheme for Floating Dock

3.1 Design of the Main Structure of a Floating Dock

As shown in Fig. 2, a single assembly-type floating dock is a floating structure composed of three parts: platform, column, and float. The platform adopts a box-type structure design, made of steel plate, and has strong bearing capacity and stability. The lower float is composed of four floating cylinders with a closed structure, and eight columns are used as supporting structures to connect the platform with the lower float, making the entire floating dock have strong durability and stability. For easy connection and disassembly, adjacent two single-section floating docks are assembled using a two-pin hinge connection structure. As shown in Fig. 3, it includes a bearing ring and a pin shaft, with a simple form, and the connection and release of the float can be achieved by inserting and pulling the pin shaft into and out of the bearing ring. Table 1 shows the relevant parameters of a single assembly-type floating dock.

Fig. 2.

3D Rendering of an assembled floating dock

Fig. 3.

Shaft pin connection structure

Table 1. Main parameters of a single floating dock

4 Coordinate System of Floating Dock

Taking a three-connected floating dock as an example, as shown in Fig. 4 (a), the coordinate system of the floating dock is set with the X-axis pointing from the stern to the bow as the positive direction, the Y-axis pointing from the centerline to the port side as the positive direction, and the Z-axis satisfying the right-hand coordinate system with the upward direction as the positive direction. Figure 4 (b) is a top view of the floating dock. When the waves propagate along the X-axis in the positive direction, the wave direction is 0°, and when the waves propagate along the Y-axis in the positive direction, the wave direction is 90°. When the waves change from the X-axis in the positive direction to the Y-axis in the positive direction in a counterclockwise direction, the wave angle gradually increases from 0° to 90°.

Fig. 4.

Definition of coordinate system

5 Calculation of Load and Stress Analysis for Floating Dock

5.1 Hydrodynamic and Structural Model

The strength analysis of the structure was carried out using SESAM software, and the finite element model included hydrodynamic finite element model and mass finite element model. The length of a single floating dock model is 60 m, width 20 m, designed water depth 20 m, seawater density 1.025 × 10³kg/m³, displacement 1949 t, and draft 4 m. The wet surface model includes the lower floating body and column, and the wave load is calculated using diffraction theory. The wet surface as a whole adopts a 0.8 m × 0.8 m grid, with a total of 3452 nodes and 3378 elements. Figure 5 shows the structural model consisting of three docks connected together, and the corresponding hydrodynamic model is shown in Fig. 6.

Fig. 5.

Structural model

Fig. 6.

Wet surface model

5.2 Motion Response and Analysis of Floating Dock

To investigate the effects of wave direction and period on the motion response and profile load transfer function of the modular floating dock, while referencing DNV regulations and considering the structure’s symmetry about the X and Y axes, a range of wave directions from 0 to 90° with a step size of 15° was selected. A total of 7 wave directions were chosen. The wave period range was from 1 to 40 s with an interval of 1 s, resulting in a total of 40 periods.

Fig. 7.

Motion response amplitude of modular floating docks

The motion response amplitude of the floating dock is shown in Fig. 7. It can be seen from the graph that the heave motion response reaches the maximum amplitude when the wave heading angle is 0°, and the sway motion response reaches the maximum amplitude when the wave heading angle is 90°. The pitch and roll motion responses reach the maximum amplitude at a period of 14 s, while the yaw motion response reaches the maximum amplitude at a period of 5 s. Compared to other motion responses, the motion response amplitude of the bow yaw is the smallest.

5.3 Sectional Load Transfer Function

The assembly-type floating dock is a new type of marine floating structure, and the industry currently does not have unified standards or regulatory references for its strength calculation. Therefore, it is necessary to refer to relevant structural strength analysis specifications for offshore platforms and determine the wave parameters of dangerous working conditions to conduct a comprehensive strength analysis. Firstly, the Wadam module of SESAM is used to conduct an overall structural analysis of the floating dock, selecting typical sections and predicting wave loads on these sections. Typical working conditions for offshore platforms are referenced to determine the design wave. Nine transverse sections between the two floats are selected, as shown in Fig. 8. SESAM is used to calculate the longitudinal force, transverse force, vertical force, longitudinal torque, vertical bending moment, and horizontal bending moment for the nine sections, and the design wave is finally determined based on the predicted wave loads.

Fig. 8.

Select the cross-section location

Fig. 9.

Different sectional forces and sectional bending moments

As shown in Fig. 9, the longitudinal force shows a decreasing trend, reaching its maximum at cross-Sect. 1. The transverse force shows a symmetrical trend, reaching its maximum at cross-Sect. 1 and its minimum at cross-Sect. 4. The vertical force is distributed more evenly and reaches its maximum at cross-Sect. 3. The longitudinal torque increases and then decreases, with a clear trend of growth and decline, reaching its maximum at cross-Sect. 5. The vertical bending moment shows a symmetrical trend and is distributed relatively evenly, reaching its maximum at cross-Sects. 3 and 7. The horizontal bending moment shows an overall decreasing trend and reaches its maximum at cross-Sect. 1. Therefore, the maximum wave load is the longitudinal torque, which reaches a maximum of 1.49 × 10⁸ N·m, and should be a focus in the strength analysis of the assembled floating dock.The maximum loads for different profiles are shown in Table 2.

Table 2. Maximum loads for different profiles

5.4 Long-Term Forecast for Floating Dock

The significant wave height in the working water area of the floating dock is 4 m, with a peak wave period of 7.64 s. For long-term forecasting, the Jonswap spectrum is used to fit the long-term sea conditions, with a peak enhancement factor of 2. According to DNV regulations, the long-term forecast values for each profile load are selected for a return period of 50 years to calculate the design wave parameters. The long-term forecast values for each profile load are shown in Table 3.

Table 3. Long-term forecast value of profile load.

5.5 Determine Design Wave Parameters

The design wave amplitude is the long-term forecast value of profile load divided by the corresponding profile load response function’s extreme value. The wave height is twice the wave amplitude, and the wave direction, period, and phase are the same as the maximum value of the corresponding profile load transfer function. The design wave parameters for various typical working conditions are calculated and shown in Table 4.

Table 4. Typical design wave parameters for operating conditions

6 Overall Strength Calculation and Result Analysis of Floating Dock

6.1 Overall Strength Calculation of Floating Dock

In order to carry out the strength analysis of floating structures, it is necessary to select the most dangerous working condition as the calculation condition. Calculation conditions can be divided into two categories: static water and wave conditions, according to the wave situation. Static water condition refers to the force situation when the floating body is in calm water surface, while wave condition refers to the force situation when the floating body is under the action of waves. At this time, the force on the floating body is not only gravity and buoyancy, but also the impact force and inertial force of the waves. In actual marine environment, floating structures will produce complex dynamic response under the action of waves, which will cause deformation and stress concentration of the structure. Therefore, in order to accurately calculate the strength of floating structures, it is necessary to consider the combined effect of static water condition and wave condition. The wave combination conditions are shown in Table 5.

Table 5. Wave combination working conditions

Figure 10 shows the stress cloud diagram of the floating dock under the most dangerous working condition, and Fig. 11 shows the intensity stress cloud diagram of the high stress area. Table 6 shows the maximum Von Mises stress values at key locations of the dock under various working conditions, and Table 7 shows the location and maximum stress values of the high stress area.

Fig. 10.

Overall maximum Von Mises stress contour plot of the structure

Fig. 11.

Von Mises stress contour plot of high stress areas

Table 6. Maximum Von Mises stress of critical parts of the structure

Table 7. Location and Maximum Value of High Stress Area

Table 8. Ocean Structure Allowable Stress Balance Standard

The study adopts the equivalent stress Von Mises for overall strength evaluation. According to ABS MODU2008 specifications, the allowable stress for Von Mises stress is shown in Table 8, and the allowable stress for combined working conditions should be 338.09 MPa. From the above charts, it can be seen that:

• 1) The stress distribution of the assembled floating dock is generally uniform, but there are still some high stress areas, which are the connection between the float and the column, the connection between the platform and the column, and the float.

• 2) High stress area 1 is located at the float on both sides, with a maximum value of 628 MPa for Von Mises stress; high stress area 2 is located at the connection between the column and the float, with a maximum value of 435 MPa for Von Mises stress; high stress area 3 is located at the connection between the platform and the column, with a maximum value of 726 MPa for Von Mises stress, all of which are greater than the maximum allowable stress;

• 3) These high stress areas are the hotspots most likely to experience fatigue fracture in the future, and the structure of these parts must be strengthened and improved to improve the reliability and safety of the structure.

6.2 Configuration Improvement and Analysis

According to the calculation results of the overall strength of the floating dock, reinforcement structures such as stiffeners and thicker wall panels should be added in the high stress areas to enhance the strength and stiffness of the floating dock. The specific improvement measures are shown in Fig. 12, and the improvement plan for structural strengthening in the high stress areas mentioned above is shown in Table 9. The maximum overall Von Mises stress cloud diagram of the improved structure is shown in Fig. 13.

Fig. 12.

Specific Improvement Measures

Table 9. Improvement Measures for High Stress Areas

Fig. 13.

Improved Structure Maximum Overall Von Mises Stress Cloud Map

Table 10. Maximum Von Mises Stress in Key Areas After Structure Improvement

The calculation results in Table 10 show that the overall strength of the improved floating dock structure is significantly better than the original design, with a notable decrease in stress values in high-stress areas. However, areas with relatively high stress values still exist, such as the connection between the float and column, the connection structure intersecting with the y-axis, and the float on both sides of the connection. In terms of the overall strength of the float, the maximum Von Mises stress value of the float is 324 MPa, the maximum stress value of the platform’s outer edge is 332 MPa, and the maximum stress value of the connection between the platform and the column is 335 MPa. The overall structural strength meets the design requirements.

7 Conclusion

This paper presents a new type of modular floating dock structure assembled using a pin connection system. Based on the design wave method, three-dimensional potential flow theory is used to calculate the wave loads and perform strength analysis on the floating dock. Based on numerical results, the configuration is optimized and analyzed. The following conclusions are drawn from numerical calculations and theoretical analysis:

• 1) The external load calculation results show that the longitudinal torque under the condition of a wave period of 7 s and a wave direction of 30° is the most critical condition for the floating dock, with a maximum stress of 726 MPa. This condition should be given attention in future research.

• 2) The overall stress distribution of the floating dock is reasonable, and some high-stress areas exist mainly at the connection between the platform and the column, the outer edge of the platform, and the floatation tank on both sides. The maximum stress is at the connection between the platform and the column, and these areas are prone to structural failure due to excessive stress.

• 3) The overall strength of the floatation body is improved by adding reinforcing ribs and thickening the wall after structural improvement of high-stress areas. The maximum stress at the connection between the platform and the column is reduced by 54% compared with the maximum stress before improvement, from 726 MPa to 335 MPa, due to structural reinforcement of the column. The maximum stress values at the outer edge of the platform and the floatation tank decrease by 23% and 48%, respectively, with a maximum decrease of 54%. The overall strength of the structure meets the design requirements. The research results of this paper have certain reference and guiding significance for the configuration design and strength optimization design of floating dock structures.