Dynamic Response of Bottom-Sitting Steel Shell Structures Subjected to Underwater Shock Waves

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this work, the authors adopt the ALE numerical model to investigate the dynamic response of bottom-sitting steel shell Structures. The topic is valuable and interesting. It can be accepted after the following questions or concerns are well addressed.

1. Standardize the reference format. In the Introduction section, please define the acronym UNDEX the first time the term “underwater explosion” appears. Ensure this acronym (UNDEX) is used consistently throughout the rest of the manuscript where appropriate. It was noted that after its potential introduction, the acronym was not used.
2. Section 2 currently only introduces basic parameters and simple equations for the explosive, water, air, and steel. More theoretical background is needed. For example, important principles should be included, such as the theory governing the propagation of underwater explosion shock waves in water and the governing equations for the fluid-structure interaction interface.
3. Section 3 only compares the shock wave pressure results from the ALE computational model with those from Cole's theoretical formula. However, the main research theme of this paper is the structural response to underwater explosion shock waves. Therefore, only comparing peak pressures seems insufficient to convincingly validate the model's capability for analyzing structural response.
4. In section 3, the error in the calculated shock wave loads decrease as the measurement point gets further from the source point. Could you provide a specific explanation for this observed phenomenon?
5. Some parts of the research only present the conclusions without providing an in-depth analysis of the underlying mechanisms.
6. Make the Abstract stronger by providing the main findings of the present work in quantitative form.
7. The Conclusion in section 5 is too long and should be appropriately simplified.
8. In order to enhance the novelty and completeness of this work, the following recent relevant work about the UNDEX investigations are suggested to be cited in the introduction part.

[1] Fully coupled model for simulating highly nonlinear dynamic behaviors of a bubble near an elastic-plastic thin-walled plate. Physical Review Fluids, 2021, 6, 013605.

[2] An h-adaptive local discontinuous Galerkin method for second order wave equation: Applications for the underwater explosion shock hydrodynamics. Ocean Engineering 264 (3) 2022.

[3] Interaction between shock wave and a movable sphere with cavitation effects in shallow water. Physics of Fluids, 2020, 016103(32).

[4] Numerical investigation on underwater explosion cavitation characteristics near water wave. Ocean Engineering, 2020 (205) 107321.

 

Author Response

Dear Prof. Drake Deng

Dear Editors and Reviewers,

RE: Manuscript ID: infrastructures-3642683

Title: Dynamic response of bottom-sitting steel shell structures subjected to underwater shock wave

We would like to extend our sincere appreciation for your professional and meticulous review of our manuscript. Your insightful comments have significantly helped us refine the research and improve the quality of our work. 

Upon accessing the review report through the submission system, our entire team promptly initiated a rigorous revision process even before receiving the editorial decision. We dedicated ourselves to addressing all 8 comments raised by you with utmost care. Each suggestion has been thoroughly discussed and systematically responded to in our point-by-point reply, which we hope demonstrates our commitment to enhancing the manuscript’s clarity and scientific rigor. 

Given the time-sensitive nature of my doctoral graduation assessment, timely publication of this research is of critical importance. We kindly request your understanding and support in expediting the review process. If you could complete the evaluation and provide feedback within approximately 7 working days, we would be immensely grateful. 

We assure you that any further revisions requested will be promptly addressed by our team, and we are fully committed to cooperating with the journal’s processes to ensure a smooth and efficient publication journey. 

Once again, thank you for your invaluable contributions to improving our manuscript. Your expertise has been instrumental in shaping the final version, and we hope to have the opportunity to share the revised work with you for further review. 

We revise the latest manuscript and highlight the changes by using yellow colored text.

We provide below with “Revision — Authors’ response” followed by our answers to the reviewers’ comments.

Best wishes,

Corresponding author:

Air Force Engineering University, Xi’an, 710038, China

Email: liuchaojia@163.com

May 19^th, 2025

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The reviewer would like to first of all thank the authors for their submission. The reviewer feels that the paper in its current form is not ready for publication. Please find bellow the list of comments to which the authors should look to address within a revised submission:

General concept comments
The main areas for improvement in this article is thoroughness of the investigation and discussion. Specific scenarios have been investigated for one parameter but then a change of scenario for the next - a full parametric study could be complete to understand the most influencing factors that have been considered etc. Then once this was done being able to discuss the benefits of these i.e maybe at a standoff distance of 9m no deformation was seen so therefore this could be omitted from the remainder of the study. With this lack of communication and discussion is why the authors decided certain things feel unfinished. 

 

Specific comments 

• Introduction
  • Generally, the introduction is written like a list of statements which lack coherence in the narrative up to around line 100. The reviewer recommends a restructure of this to ensure each reference is relevant and a proper discussion around the findings of each reference is required as currently fail to mention any of the findings and are therefore seldom relevant. Below I have given some examples but It happens on almost every reference.
  • Line 35: The statement here does not really correlate to the references given. It is a broad statement and references other papers which undertake other similar studies but does necessarily need a reference here unless it’s an article of a real-world event otherwise it comes across as hearsay.
  • Line 52-55: This reference [5] discusses the proportionality of shock and bubble effects on structural response from a given event and this is a good addition to include which follows on from Ref [4].
  • Line 56-58: Ref[6] gives details of what is done but with no results, it is important to overview findings to explain the thinking of the article and how you work develops. The statement of neglecting confinement etc is good and shows understanding of the context.
  • Lines 58-62: Ref 7 and 8, discussion of results and findings are needed, not just a statement of what is done.
  • Lines 117-143: Very specific information and statements provided without references, that could be included.
  • Line 144-145: The sentence needs to be re-written as in its current form is not grammatically correct. “The resultant shock wave from underwater explosive events are one of the main features of loading on a structure and is the primary focus of this research. Shock waves travelling through water are distinctly different in behaviour to those which travel through air and rock, with features such as….. “
  • Line 153-158: Very long sentence, this needs to be broken down.

 

• Numerical Configuration
  • Table 4: Q690 Steel J-C model is not clear on what parameters within the card have been included as there are certainly more than 5 within LS-DYNA and whilst Ref [30] also doesn’t detail any more than what has been presented in the article, it is important to be thorough on the information provided.
  • Line 190: This reference I think should be 30 rather than 3.
  • Line 198: Cole’s peak shock wave pressure is not theoretical; it is empirical and is derived from a series of underwater explosive tests with measurements across a range of distances.
  • Figure 1: Could dimensions be added for the radius and axial length – this just makes is easy to digest.
  • Line 203: “LS-DYNA” make sure its consistent throughout the paper.
  • Line 205: Explosive equivalent is selected as 200kg – I think rewording this to be explicit saying “a 200kg TNT spherical explosive is selected for this analysis”. I am assuming spherical here as it does not state it anywhere.
  • Lines 210-212: I would state that whilst the model has errors of 22.22% within close distances to the measurement point, the errors become negligible at further distances, relating directly to the lack of complex bubble dynamics.
  • Table 5: This is perfectly fine to present but a supplementary to this would be some graphical results of the simulations to show the actual output from the models. Without this the discussion does not feel robust enough.
  • Revisiting Line 205: The discussion of 200kg used, is this a mistype because throughout the rest of the paper 300kg is used and therefore makes little sense to validate the model for 200kg - Could this be explained?
  • There seems to be no discussion on mesh sensitivity, cell size, or run time – this could be included for the fullness of discussion.

 

• Numerical Model
  • Line 228: This is not correct, the effect of underwater shock is not shown in figure 3, instead it is just a schematic of the planned model for investigation
  • Figure 4: Can figures a and b be colour consistent, i.e water being blue in both images.
  • Figure 5: title needs to be more explicit for a) isometric, b) plan, c) cross section
  • Figure 6: needs more information in the same vein. Further Figure 6a is not a cylinder and needs correcting.
  • Line 260: Deformation is mentioned but not referring to any results.
  • Line 269: Missing here is a percentage difference to really emphasise the effect.
  • Should displacements in this section be in a more realistic unit i.e mm rather than m?
  • Line 254- 299: There is no comparison made between the two shaped shells and only between air and water is trivial and not contributing to scientific understanding. It is advised to make a comparison of the differences between the displacement and talk about why this happens.
  • Lines 300-327: The purpose of this section seems trivial, as we decrease distance the deformation increases because the load is higher. Whilst this satisfies the model validity I am not convinced how this adds to knowledge.
  • Fig14-15: it feel like this assessment could be better – rather than considering vertical displacement, a deformation from unloaded shape could have been considered across each theta value to show a more general deformation because there are areas with deformation that aren’t captured in these plots because only vertical is discussed.
  • Line 345-347: Is there any comments on why 5m, 7m and 9m distances behave very similarly but 3m is wildly different. Further why are there no comparisons to the hemi-spherical shape here.
  • Line 357-362: Equation 1, 2 and 3 do not refer to the correct things.
  • Section 4.4: This assessment of failure is interesting and shows different considerations which would need to made depending on which structure is chosen. The reviewer does however believe that it is as the majority of this paper – scratches the surface of an interesting finding but then seems to not talk about what it means, how this benefits the betterment of knowledge etc.
  • Line 439: repeated word “structuresstructures”
  • Section 4.5: The investigation into hydrostatics is an interesting one but I am unsure why only one charge mass and standoff distance has been chosen and why this one in particular. We know from the previous sections that the deformation behaviour of the structure changes dramatically when change both mass and standoff and therefore a full parametric study here would have been quite nice.
  • Section 4.6: following on from the previous point, we now do a different distance again. There just seems to be lacking a consistency throughout the paper and therefore making fair comparisons of parameters and determining which ones are more influential is difficult.

 

• Conclusions
  • Conclusion 3 is obvious in the field of blast engineering, and I don’t think is one which can be claimed in this paper.
  • Conclusion 6 is another obvious one – increasing the thickness of a material will increase its structural robustness and thus its ability to deform.
  • There is a real lack of overall message at the end to round of the paper. 

Comments on the Quality of English Language

Quality of English used throughout the document is generally okay. There are a few typos and spelling issues pointed out in the overall comments. 

Author Response

Dear Prof. Drake Deng

Dear Editors and Reviewers,

RE: Manuscript ID: infrastructures-3642683

Title: Dynamic response of bottom-sitting steel shell structures subjected to underwater shock wave

We are deeply grateful for your thorough review and constructive feedback on our manuscript. Your comments have provided us with valuable perspectives to enhance the depth and clarity of our research.

As soon as we accessed the review report, our team began working day and night to revise the manuscript, even before receiving the official decision. We have carefully addressed all 36 comments you raised, providing detailed responses and revisions to ensure each point is adequately resolved. Our goal is to make the manuscript more robust and aligned with the journal’s standards. 

We understand that academic timelines can be challenging, and we respectfully request your assistance in expediting the review process due to my upcoming doctoral graduation assessment. Prompt feedback within 7 working days would greatly facilitate our progress and allow us to finalize the manuscript in a timely manner.

Please rest assured that we are fully prepared to make any additional revisions as needed and will promptly resubmit the updated manuscript for your review. Your continued support is sincerely appreciated. 

Thank you again for your dedication to reviewing our work. We hope the revised manuscript meets your expectations and look forward to your further guidance.

We revise the latest manuscript and highlight the changes by using yellow colored text.

We provide below with “Revision — Authors’ response” followed by our answers to the reviewers’ comments.

Best wishes,

Corresponding author:

Air Force Engineering University, Xi’an, 710038, China

Email: liuchaojia@163.com

May 19^th, 2025

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript examines the dynamic response of bottom-sitting steel shell structures to underwater shock waves through numerical models utilizing the Arbitrary Lagrangian-Eulerian (ALE) algorithm. It analyzes the impact of shock wave medium, explosive distance, explosive equivalent, hydrostatic pressure, and shell thickness on deformation. The results indicate that deformation increases with a higher explosive equivalent or a decreasing distance, while hydrostatic pressure affects deformation differently for semi-spherical and semi-cylindrical shells.

Although the study is intriguing and demonstrates significant potential, the current structure and presentation require greater clarity for publication. The authors should thoroughly address the following comments:

1) Line 43: The phrase "and so on" lacks specificity and formality for a technical manuscript.

2) While the introduction addresses the significance of assessing structural damage resulting from underwater explosions, the authors could strengthen their manuscript by incorporating a paragraph that reviews related studies on damage identification and dynamic response evaluation from other structural domains.For instance, research on damage assessment of various structures may provide additional insights into methodologies applicable to underwater structures subjected to explosive forces. I recommend that the authors consider including the following studies to broaden the scope of their discussion: • X. Li, M. Kurata, M. Nakashima, Evaluating damage extent of fractured beams in steel moment-resisting frames using dynamic strain responses, Earthq. Eng. Struct. Dyn. 44 (2015) 563–581, https://doi.org/10.1002/eqe.2536. • M. Razavi, A. Hadidi, F. Ashrafzadeh, Feature extraction based on dynamic response measurements for structural damage identification: a comparative study, Journal of Structural Integrity and Maintenance, 9 (2024) 2364125. https://doi.org/10.1080/24705314.2024.2364125 • K. Danai, S.A. Civjan, M.M. Styckiewicz, Direct method of damage localization for civil structures via shape comparison of dynamic response measurements, Computers & structures, 92 (2012) 297-307. https://doi.org/10.1016/j.compstruc.2011.10.016

3) Line 257: Please clarify the rationale behind selecting these specific values (7m explosive distance, 300kg explosive equivalent). Were they derived from real-world scenarios or experimental data?

4) Line 254: Please include an explanation of how shock wave attenuation in air and water results in differing structural responses. A more comprehensive discussion on the physical mechanisms of shock wave propagation in air and water (e.g., differences in density, sound speed, and energy dissipation) would enhance this section.

5) Line 303: Please justify the selection of explosive distances (3m, 5m, 7m, and 9m) in terms of real-world applicability. Are these values representative of typical underwater explosions, or were they chosen solely for computational convenience?

6) Line 309: While the trend is acknowledged, the physical explanation for the observed decrease in deformation with increasing explosive distance is not adequately addressed. Is this trend attributable to the shock wave losing energy over distance, or is it related to the geometry of the shell and its interaction with the shock wave?

7) Line 391: The rationale for choosing the specific values of explosive equivalents ranging from 50kg to 800 kg is unclear. Please briefly justify the selection of these explosive equivalents. Are they intended to represent typical underwater explosion scenarios, or were they chosen for computational purposes?

8) Line 396: The phrase "slightly increases" is somewhat ambiguous. Does "slightly" refer to a minor magnitude of deformation, or does it indicate a negligible effect on the overall structural response? Please consider providing quantitative results or specific data points to clarify this observation.

9) Line 399: The statement "significantly increases" is clear; however, the underlying reasons for this significant increase should be discussed. Is it attributable to the shell's higher energy absorption or the greater force exerted by the shock wave? Additionally, is there any comparison with deformation at lower explosive equivalents (e.g., 50kg, 100kg) to illustrate the progression of this increase?

10) Line 421: Please provide a quantitative comparison of the oscillatory frequencies between the two shell types. Is the frequency difference substantial or minimal? Consider discussing how this difference affects the resonance behavior of the structure.

11) Line 439: Please elaborate on how hydrostatic pressure interacts with shock wave loading to induce additional damage. Does hydrostatic pressure contribute to compressing the structure, resulting in greater plastic deformation, or does it influence the stress distribution in another manner?

12) Line 519: Please expand on the differences in stiffness between the two thicknesses. Increased shell thickness leads to enhanced stiffness, thereby reducing deformation. Additionally, elucidate the material science principles behind this behavior, specifically, how increased thickness improves resilience to dynamic loads.

Author Response

Dear Prof. Drake Deng

Dear Editors and Reviewers,

RE: Manuscript ID: infrastructures-3642683

Title: Dynamic response of bottom-sitting steel shell structures subjected to underwater shock wave

 

We wish to express our heartfelt thanks for your careful review and insightful comments on our manuscript. Your expertise has been invaluable in identifying areas for improvement and strengthening the overall quality of our research. 

Upon receiving your review report, our team immediately commenced the revision process, working diligently to address all 12 comments you provided. We have prepared detailed responses to each suggestion, incorporating necessary modifications to enhance the manuscript’s logical flow, data accuracy, and theoretical depth. 

Due to the time constraints associated with my doctoral graduation requirements, we kindly ask for your understanding and support in expediting the review process. Feedback within 7 working days would be tremendously helpful for us to meet our academic deadlines and finalize the manuscript accordingly. 

We are committed to promptly addressing any further comments and will ensure that the revised manuscript is resubmitted without delay. Your continued engagement in this process is sincerely appreciated. 

Once again, thank you for your significant contributions to this project. We hope the revised manuscript reflects our earnest efforts to address your concerns and look forward to your positive evaluation. 

We revise the latest manuscript and highlight the changes by using yellow colored text.

We provide below with “Revision — Authors’ response” followed by our answers to the reviewers’ comments.

Best wishes,

Sincerely,

Corresponding author:

Air Force Engineering University, Xi’an, 710038, China

Email: liuchaojia@163.com

May 19^th, 2025

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

My questions and concerns are well addressed. Now, it is in a good state to be accepted.

Reviewer 2 Report

Comments and Suggestions for Authors

The reviewer would like to thank the authors for their extensive revisions - it is clear that a lot of work has gone into improving the overall discussion and narrative of the paper. 

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript is recommended to be published in the journal.