Prediction of Wave Forces on the Box-Girder Superstructure of the Offshore Bridge with the Influence of Floating Breakwater

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

An interesting multibody fluid-structure interaction with fixed and floating bodies is presented, which has practical application.

I found the content and presentation style satisfactory. However, I have one suggestion to improve figures and associated descriptions.

Figure 7 to 15 contains multiple plots under one heading. I strongly advise labelling these plots with appropriate subheadings (a, b, c etc.). Some of these plots are described with subheading numbers in the manuscript (e.g. Figure 8b), but those subheadings were not labelled in the figure. Although one can intuitively identify the different plots and match the associated description, labelling each plot separately with sub-headings and numbers (a,b,c etc.) is recommended.

Also, for Figures 8 to 10, the associated descriptions are difficult to follow as subplots are not properly identified and referred to in the descriptions. I suggest revising this portion to include references to appropriate plots from the figures. To fonts for these figures could also be increased as they are difficult to read with current sizes.

 

 

 

Comments on the Quality of English Language

English is fine. Authors might do a revision to avoid any typos.

Author Response

Response to the reviewers’ comments

Reviewer 1:

Comments and Suggestions for Authors:

An interesting multibody fluid-structure interaction with fixed and floating bodies is presented, which has practical application.

I found the content and presentation style satisfactory. However, I have one suggestion to improve figures and associated descriptions.

Authors’ response:

Thank you for your suggestion. We appreciate the time and effort you took to review this paper. We really appreciate it. The responses to your comments are presented as follows.

 

Comments:

1. Reviewer's comment:

Figure 7 to 15 contains multiple plots under one heading. I strongly advise labelling these plots with appropriate subheadings (a, b, c etc.). Some of these plots are described with subheading numbers in the manuscript (e.g. Figure 8b), but those subheadings were not labelled in the figure. Although one can intuitively identify the different plots and match the associated description, labelling each plot separately with sub-headings and numbers (a,b,c etc.) is recommended.Authors’ response:

Thank you for this comment. Your comments have greatly facilitated the improvements to the manuscript. As you correctly pointed out, it would be beneficial to include the number of each subgraph in Figures 7 through 15 for ease of read and reference. We have addressed this concern in the revised manuscript.

 

2. Reviewer's comment:

Also, for Figures 8 to 10, the associated descriptions are difficult to follow as subplots are not properly identified and referred to in the descriptions. I suggest revising this portion to include references to appropriate plots from the figures. To fonts for these figures could also be increased as they are difficult to read with current sizes.

Authors’ response:

Many thanks for your comment. According to your suggestion, we have rectified the ambiguous sections in Figs. 8 to 10, eliminated redundant numerical values, and augmented the legend for enhanced clarity of its numerals and labels in the revised manuscript.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript evaluates the effect of offshore waves interacting with a structure, attempting to calculate the applied force to the object. Navier-stokes coupled with volume of fluid method is applied to simulate the two-phase flow field. K-\epsilon turbulence modeling is applied. The fluid-structure interaction is modeled using overset grid which transfers information using interpolation between different grids.  OpenFOAM which is an open-source solver is used to solve the equations and it also has a built-in overset grid module. The simulation is performed for some input parameters and the available data are fed into a neural network to be able to perform a fast prediction for later combination of input variables.

 

In my view the manuscript can be considered for publication in JMSE only after addressing the following comments:

1 - The author should explain the reason to apply turbulence modeling. Based on the manuscript there is no turbulent flow in solution domain. It is very important to explain the logic behind considering the flow to be turbulent.

2-      The authors mentioned that they have combined the SIMPLE and PISO solvers together, which is PIMPLE solver in OpenFOAM. Is the PIMPLE solver used, or a new solver has been developed?

3-   In figure 1, and figure 2, the authors should define the variable \eta and S before demonstrating them.  

4-      There is no grid shown in the manuscript. The authors should provide a figure to explain grid refinement at different areas of the solution domain.

5-      The authors should perform grid dependency to make sure the solution is not grid dependent.

6-      Boundary conditions are not mentioned in the manuscript. The authors should provide all the boundary conditions applied in the simulation.

7-      In figures which include some subfigures, each subfigure should be independently sub-captioned.

8-      There are some typos in the manuscript and the authors should proof-read and make sure they are all addressed. For example, in subsection 4.1, line 15 and line 18, the “LS10” and ‘ “DC", "DC0.5", "DC1.5","DC2.5", respectively’ seems to be redundant. In subsection 4.1, in line 20, “when” should be “When”, some others which authors can find in the manuscript.

9-      All the variables should be shown on the figures to better understand them. For example, B, D, …. Just a schematic can be helpful.

10-   The authors should explain the definition of the maximum Fx and Fy in the manuscript, and since the problem is transient, how they have calculated these two variables?

11-   The results in figure 11 and 12 shows that by increasing Af, the force may increase and decrease. The authors should explain the logic that why this is reasonable.

12-   In table 1, the range of different variables are shown to be used in the NN model. The authors should elaborate on the number of data used for each variable and the amount of data between maximum and minimum value, if they have been selected uniformly or not.

13-   The authors should clearly explain why they have applied neural networks and what they have gained by using it.

14-   The authors should elaborate on the percentage and range of each variable which has been used for training and testing.

15-   In the text above figure 13, RSME of the horizontal force is mentioned to be 0.83017, but the figure shows R^2 to be that number.

16-   The authors should explain why the magnitude of the RSME is very large (in the order of 100) on the plots shown in figures 13 and 14.

17-   The authors should explain more detail about the neural network, what are the input variables and what are the output variables?

18-   The authors should explain if they have non-dimensionalized before training.

Comments on the Quality of English Language

-

Author Response

Response to the reviewers’ comments

 

Reviewer 2:

Comments and Suggestions for Authors:

The manuscript evaluates the effect of offshore waves interacting with a structure, attempting to calculate the applied force to the object. Navier-stokes coupled with volume of fluid method is applied to simulate the two-phase flow field. K-\epsilon turbulence modeling is applied. The fluid-structure interaction is modeled using overset grid which transfers information using interpolation between different grids. OpenFOAM which is an open-source solver is used to solve the equations and it also has a built-in overset grid module. The simulation is performed for some input parameters and the available data are fed into a neural network to be able to perform a fast prediction for later combination of input variables.

In my view the manuscript can be considered for publication in JMSE only after addressing the following comments:

Authors’ response:

Thank you for your suggestion. We appreciate the time and effort you took to review this paper. We really appreciate it. The responses to your comments are presented as follows.

 

Comments:

1. Reviewer's comment:

The author should explain the reason to apply turbulence modeling. Based on the manuscript there is no turbulent flow in solution domain. It is very important to explain the logic behind considering the flow to be turbulent.Authors’ response:

Thank you for this comment. Your comments have greatly facilitated the improvements to the manuscript. According to numerous previous studies, the estimation of wave force on offshore bridge superstructures can be more accurately achieved through the use of turbulence models. Additionally, in cases where waves interact with structures, such as gas-liquid interactions, wave runups and wave breaking simulations utilizing turbulence models will yield greater accuracy. Relevant literature provides further discussion and evidence supporting this claim:

Xu, G.; Cai, C.S. Numerical simulations of lateral restraining stiffness effect on bridge deck–wave interaction under solitary waves. Eng. Struct. 2015, 101, 337–351.

Qu, K.; Sun, W.Y.; Ren, X.Y.; Kraatz, S.; Jiang, C.B. Numerical Investigation on the Hydrodynamic Characteristics of Coastal Bridge Decks under the Impact of Extreme Waves. Journal of Coastal Research, 2020, 37(2).

Huang, B.; Hou, J.; Yang, Z.; Zhou, J.; Ren Q.; Zhu, B. Influences of the pile-restrained floating breakwater on extreme wave forces of coastal bridge with box-girder superstructure under the action of two-dimensional focused waves. Applied Ocean Research 2023, 134, 103508.

In order to reflect the above comments in the revised manuscript, we have added the following statements: “The introduction of turbulence model is instrumental in enhancing the precision of the calculation of wave forces on the offshore bridge superstructure and wave-structure interaction [3, 26].”

 

2. Reviewer's comment:

The authors mentioned that they have combined the SIMPLE and PISO solvers together, which is PIMPLE solver in OpenFOAM. Is the PIMPLE solver used, or a new solver has been developed?

Authors’ response:

Many thanks for your comment. We are sorry for the lack of clarity. We directly used PIMPLE solver and did not develop new solvers. In view of this, we have emphasized in the revised manuscript: “The PIMPLE solver (SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) combined with PISO (Pressure-Implicit with Splitting of Operators)) is used to decouple the pressure and velocity component, and the algorithm can solve the simulation of transient flow fields with large time steps.”.

 

3. Reviewer's comment:

In figure 1, and figure 2, the authors should define the variable \eta and S before demonstrating them. Authors’ response:

Thank you for your comment. Descriptions of the variables have been added to the revised manuscript: “Figure 1 shows the results of comparing the numerical wave surface (η) with the theoretical result.” and “The numerical and theoretical wave spectra density (S) are in good agreement, and the energy distribution in the low-frequency and high-frequency parts is slightly higher than the theoretical wave spectrum, while the energy distribution in the peak-frequency part is slightly lower than the theoretical value, which is mainly due to the transfer of energy from the peak-frequency region to other regions due to the wave-wave interaction.”.

 

4. Reviewer's comment:

There is no grid shown in the manuscript. The authors should provide a figure to explain grid refinement at different areas of the solution domain.Authors’ response:

Thank you for your comment. The grid employed in this study has been incorporated into the revised manuscript, along with corresponding explanations: “The meshes were generated through the development of structured background meshes, which underwent refinement in the primary computational domain and further refinement near the girder model. A red nested mobile mesh is utilized at the breakwater location to monitor the movement of the floating breakwater. In the main computational domain, a range of mesh sizes were employed to assess mesh sensitivity. Figure 5(c) illustrates the variation in the maximum horizontal wave forces across different mesh sizes (indicated by total grid count) for the case with wave amplitude A_f = 4 m. It is evident that with a total of 6.2E06 grids, the numerical computation can be executed precisely and efficiently. After conducting a grid independence test, the optimal mesh size was determined as follows: A horizontal mesh size of 0.4 m was used in the near-inlet boundary zone, while a smaller mesh size of 0.1 m was employed in the main computational domain and an even finer mesh size of 0.03 m was utilized in the near-outlet boundary zone. In addition, vertical spatial distances of 0.4 m were applied to the atmosphere boundary region, whereas air-water interfaces and deeper water regions required more refined spacing with values of 0.1 m and 0.03 m respectively.”

(b) Grid mesh adapted in this paper

 

5. Reviewer's comment:

The authors should perform grid dependency to make sure the solution is not grid dependent.Authors’ response:

Many thanks for your comment. The grid dependency has been performed in the revised manuscript: “In the main computational domain, a range of mesh sizes were employed to assess mesh sensitivity. Figure 5(c) illustrates the variation in the maximum horizontal wave forces across different mesh sizes (indicated by total grid count) for the case with wave amplitude A_f = 4 m. It is evident that with a total of 6.2E06 grids, the numerical computation can be executed precisely and efficiently. After conducting a grid independence test, the optimal mesh size was determined as follows: A horizontal mesh size of 0.4 m was used in the near-inlet boundary zone, while a smaller mesh size of 0.1 m was employed in the main computational domain and an even finer mesh size of 0.03 m was utilized in the near-outlet boundary zone. In addition, vertical spatial distances of 0.4 m were applied to the atmosphere boundary region, whereas air-water interfaces and deeper water regions required more refined spacing with values of 0.1 m and 0.03 m respectively.”

(c) Grid independence test

 

6. Reviewer's comment:

Boundary conditions are not mentioned in the manuscript. The authors should provide all the boundary conditions applied in the simulation.Authors’ response:

Thanks for your comment. All the boundary conditions applied in the simulation have been added to the revised manuscript: “The numerical flume is bounded by inlet and pressure outlet boundaries on its left and right sides, respectively. Its structure surface serves as a wall boundary, while the bottom of the flume acts as a slip boundary. An empty condition is applied to the frontBack boundary, whereas an atmospheric boundary condition governs the top of the numerical wave flume.”.

 

7. Reviewer's comment:

In figures which include some subfigures, each subfigure should be independently sub-captioned.Authors’ response:

Many thanks for your comment. As you correctly pointed out, it would be beneficial to include the number of each subgraph in Figures for ease of read and reference. We have addressed this concern in the revised manuscript.

 

8. Reviewer's comment:

There are some typos in the manuscript and the authors should proof-read and make sure they are all addressed. For example, in subsection 4.1, line 15 and line 18, the “LS10” and ‘ “DC", "DC0.5", "DC1.5","DC2.5", respectively’ seems to be redundant. In subsection 4.1, in line 20, “when” should be “When”, some others which authors can find in the manuscript.Authors’ response:

Thanks for your comment. We apologize for the inadvertent grammatical, spelling, and presentation errors in the original manuscript. We have thoroughly reviewed and corrected the revised manuscript to ensure its accuracy. For instance, we have rectified the error you mentioned: “For convenience of description, the first type of breakwater is referred to as fixed breakwater, denoted by "S", and the second type of breakwater is referred to as elastically restrained breakwater, denoted by "LS", where "LS10", "LS50" and "LS100" represent three groups of restraint stiffness k = 10 kN/m, 50 kN/m and 100 kN/m, respectively, and the third type of breakwater is referred to as displacement restrained breakwater, denoted by "DC", where "DC0.5", "DC1.5" and "DC2.5" represent three groups of displacement limits of ± 0.5 m, ± 1.5 m and ± 2.5 m, respectively.”.

 

9. Reviewer's comment:

All the variables should be shown on the figures to better understand them. For example, B, D, …. Just a schematic can be helpful.Authors’ response:

Thanks for your comment. Your comments have greatly facilitated the improvements to the manuscript. We try to include variables that are easy to show in the Figure. As shown below:

(a) Model size and layout (Unit: m)

Figure 5. Arrangement diagram and grid settings of the numerical wave flume.

 

10. Reviewer's comment:

The authors should explain the definition of the maximum Fx and Fy in the manuscript, and since the problem is transient, how they have calculated these two variables?Authors’ response:

Thank you for your comment. The maximum horizontal (F_x⁺) and vertical wave force (F_y⁺) in this study represents the maximum value of the time history of wave forces on the box-girder superstructure under a certain case. The following statements have been added to the revised manuscript: “Additionally, the maximum horizontal (F_x⁺) and vertical wave force (F_y⁺) in this study represent the peak values of the time history of wave forces acting on the box-girder superstructure under a specific wave case.”.

 

11. Reviewer's comment:

The results in figure 11 and 12 shows that by increasing Af, the force may increase and decrease. The authors should explain the logic that why this is reasonable.Authors’ response:

Thanks for your comment. The reasons behind this phenomenon have been added in the revised manuscript: “A very interesting phenomenon is noted here, that is, with the increase of the wave amplitude, the horizontal wave force on the box girder does not increase linearly, but decreases after the wave amplitude reaches 4.5 m (as shown in Figure 11(a)). The elevated state of the box-girder superstructure may account for this phenomenon. When wave amplitude falls within a certain range, the majority of waves exert force on the web of the box-girder superstructure, leading to an increase in horizontal wave forces. However, with the continuous increase of waves, excessive wave amplitude leads to excessive wave runups when most of the waves interact with the box-girder superstructure, which consumes the energy of the wave action. On the contrary, the horizontal wave force on the box-girder superstructure is reduced.” and “It can be observed that the weakening of wave force on the box-girder superstructure by the floating breakwater is not directly proportional to the amplitude of waves. Generally, the most effective reduction in force is achieved when wave amplitudes are around 3.5 m. As the wave amplitude continues to increase, the interaction between the waves passing over the floating breakwater and the waves between the floating breakwater and the box-girder superstructure may lead to the increase of the speed of the water particles acting on the box-girder superstructure, thereby augmenting wave forces exerted on the box-girder superstructure.”

 

12. Reviewer's comment:

In table 1, the range of different variables are shown to be used in the NN model. The authors should elaborate on the number of data used for each variable and the amount of data between maximum and minimum value, if they have been selected uniformly or not.Authors’ response:

Thanks for your comment. We have revised Table 1 to include all relevant input parameters in order to more clearly explain the parameters used in the neural network prediction model.  

Table 1 The range values of the relevant parameter for the wave force prediction model

Parameter	value
Maximum wave amplitude Af  (m)	3、3.5、4、4.5、5
Breakwater width B (m)	5、10、15、20、25
Breakwater height H (m)	2、4、6、8、10
Distance from the girder L (m)	10、50、100、150、200
Constrained stiffness K (kN/m)	0、10、50、100、106
Constrained displacement S (m)	0、0.5、1.5、2.5、5

 

13. Reviewer's comment:

The authors should clearly explain why they have applied neural networks and what they have gained by using it.Authors’ response:

Thanks for your comment. The specific reasons are added as follows in the revised manuscript: “In this study, the wave force acting on the box-girder superstructure is influenced by multiple factors, such as wave amplitude and the size and characteristics of the floating breakwater. This results in a nonlinear correlation law. Furthermore, due to its ability to automatically learn input-output samples, neural networks can approximate any complex nonlinear mapping with arbitrary precision. Therefore, a neural network is employed in this study to forecast the maximum wave forces acting on the box-girder superstructure under varying wave parameters and characteristics of the floating breakwater.”.

 

14. Reviewer's comment:

The authors should elaborate on the percentage and range of each variable which has been used for training and testing.Authors’ response:

Many thanks for your comment. We apologize for missing important information, the percentage and range of each variable which has been used for training and testing have been added to the revised manuscript: “It is worth noting that out of the 10 datasets, 7 are designated as training sets while the remaining 3 serve as test sets.”.

 

15. Reviewer's comment:

In the text above figure 13, RSME of the horizontal force is mentioned to be 0.83017, but the figure shows R^2 to be that number.Authors’ response:

Thanks for your comment. We are very sorry for the error in the original manuscript, this should refer to the R² of the horizontal force, not RMSE. Therefore, corrections have been made in the revised manuscript: “The R² of horizontal force and vertical force are 0.83017 and 0.84240, respectively,”.

 

16. Reviewer's comment:

The authors should explain why the magnitude of the RSME is very large (in the order of 100) on the plots shown in figures 13 and 14.Authors’ response:

Thanks for your comment. These two figures investigate the impact of different batch sizes and learning rates on the accuracy of a neural network prediction model. When the learning rate is set too high, the root mean square error (RMSE) can reach nearly 80, leading to a decline in prediction accuracy. However, after careful selection of the batch size and learning rate, the adopted prediction model achieves an RMSE less than 100 with only about 10 for horizontal wave forces and 30 for vertical wave forces.

 

17. Reviewer's comment:

The authors should explain more detail about the neural network, what are the input variables and what are the output variables?Authors’ response:

Thanks for your comment. The detail explanation about the input and out variables have been added to the revised manuscript: “The BP neural network model outputs the maximum horizontal and vertical forces, with input parameters including the maximum wave amplitude A_f, breakwater width B, breakwater height H, breakwater spacing L, constraint stiffness k, and constraint displacement S.”

 

18. Reviewer's comment:

The authors should explain if they have non-dimensionalized before training.Authors’ response:

Thank you for your comment. I deeply apologize for the lack of dimensionless processing in the training data utilized in this study, which is a critical issue that was overlooked. Future research will prioritize non-dimensionalized processing as you have suggested, with the aim of enhancing both accuracy and applicability of neural network predictions. The corresponding statements have been added to the conclusion part: “However, it should be noted that this study did not take into account the non-dimensionalization of training data, and the existing neural network prediction model is limited to the parameter range examined in this study. The accuracy and applicability of the model will be further expanded in future research.”.

 

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors fully addressed the comments