Mathematical Analysis of the Vibratory Pile Driving Rate
Round 1
Reviewer 1 Report
1) The Abstract should be rewritten. It should be presented in a clear way and easily understandable (what is not the fact at the moment). From the Abstract is unknown what exact results the Authors obtained in the research, so at least some of the most important exact results should be added in the Abstract. At the moment, the Abstract is too general and descriptive.
2) The Authors have tried to explain all abbreviations, symbols and markings used in the equations under each equation. I believe that it will be more clear and easier for reading and understanding that all abbreviations, symbols and markings are arranged at one place – in the Nomenclature. Therefore, the Nomenclature should be added in the paper.
3) In the paper is missing any kind of exact validation (direct comparison of numerical model results and results obtained in practice by measurements). In this research, the Authors have assumed that the presented numerical model will provide proper results, without any comparison to the experiment. There is no such numerical model which is universally applicable, without any kind of validation.
It seems that the presented numerical model results are correct, but that does not mean that numerical model can track real exploitation conditions, especially not with appropriate accuracy and precision. Without any validation and comparison to the measurements from exploitation, this research I consider only as a theoretical one which results may (or may not) be applicable in real exploitation conditions. Only theoretical calculations, without any connection to the real exploitation conditions are interesting, but they cannot be considered (at least in my opinion) as a proper and rounded scientific research.
4) In the paper is missing any kind of a numerical model error analysis – as there is no numerical model which did not have errors in comparison to the exploitation conditions, the presented results can be considered at least as debatable.
5) Figure 10 should be presented as equations, not a figure. Moreover, the title of this figure is completely wrong.
6) As the Abstract, the Conclusions section is too descriptive and general, without any details and exact results obtained in the presented analysis.
7) The English is understandable, but it should be improved in many sentences or whole paper parts.
8) The scientific novelty of this paper is not clear (at least to me). As the Authors have stated in the Introduction – many researches related to this topic can be found in the literature, so at the moment I did not find in this paper sufficient elements which will clarify research novelty. The Authors should add in the paper at least a discussion which will clarify the research novelty, its contribution to the existing research field as well as which will highlight novel and unique elements which are presented in this paper (which are currently missing in the existing literature).
Final remarks: This paper I can consider as a theoretical research only which connection to the actual exploitation conditions is non-existing. Also, a numerical model accuracy and precision is unknown. As there is no presented any exact validation, this paper I cannot consider as a proper and rounded scientific research and I cannot recommend its publication.
Author Response
Please see the attachment.
Author Response File: 
Author Response.docx
Reviewer 2 Report
The article presents a mathematical analysis of the vibratory pile driving rate. However, there are several significant revisions that need to be addressed to improve the manuscript before the second round of review.
Specific Comments:
The Abstract should be revised to be concise and informative. It should cover essential aspects such as the study's background, research question, hypothesis, methodology, key findings, and conclusions. Furthermore, it should highlight the primary implications and broader context of the research.
The methodology section needs to be strengthened to provide sufficient detail for other researchers to replicate the study. If the methodology has been previously published, a brief summary and citation of the source should be provided.
The introduction section requires a more detailed discussion leading to the problem statement and scope of the study. Additionally, it is necessary to include more relevant literature, citing specific references. For example:
Lines 152-154 please cite: https://doi.org/10.1016/j.soildyn.2022.107451
The manuscript highlights the key findings regarding the vibratory embedding rate of the pile. The relationship between the rate and factors such as static loading, dynamic load amplitude, vibration frequency, and pile driving depth is well-explained. The authors effectively discuss the underlying mechanisms, such as the increase in shear stresses and reduction in viscosity coefficient, which contribute to the observed trends. It would be beneficial to include specific numerical or graphical results to support the findings and enhance the clarity of the analysis.
Overall, addressing these revisions will enhance the clarity, accuracy, and scientific rigor of the manuscript
moderate
Author Response
Please see the attachment.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
The Authors have performed paper revision, but the main issues mentioned in my previous review still remain unsolved. These issues are:
1) In the paper is missing any kind of exact validation. In this research, the Authors have assumed that the presented numerical model will provide proper results, without any comparison to the experiment of any kind. There is no such numerical model which is universally applicable, without any kind of validation.
2) In the paper is missing any kind of a numerical model error analysis – as there is no numerical model which did not have errors, the presented results can be considered at least as debatable.
3) In the answers to my comments, the Authors have stated that: "the results are consistent with a literature". What does it mean? This kind of results explanation is too general. Does that mean that the obtained curves look like these in the literature? Please use exact, not general terminology during the results description.
4) The Authors have agreed (according to the answers to my comments) that the whole research is theoretical and that it did not have to be connected with real exploitation conditions of any kind. Such research is nice to see, but in my opinion scientific worthless.
5) The Authors have presented numerical calculation of one new parameter. What is the value of this calculation procedure if it cannot be confirmed in reality?
6) Theoretical calculation of one new parameter I cannot consider as a proper scientific novelty or contribution to the existing research field.
Author Response
Please see the attachment.
Author Response File: Author Response.docx
Reviewer 2 Report
Accept
Minor
Author Response
Thank you very much for the review and valuable comments on the manuscript.
Round 3
Reviewer 1 Report
Dear Authors,
To me, it is not clear why it was necessary to revise Your article three times to perform any kind of validation (on which I was insisting since my first revision). Lack of any validation was the reason why I have rejected this article two times.
I did not (and I cannot) specify on which way the validation should be performed - if You did not posses own measurements and data for validation, then the validation can be performed by direct comparison to the measurements from the literature.
Finally, after the third paper revision, the validation is presented (Figure 10 and 11). These two figures resolved any my concerns, from them it is obvious that the developed numerical model can properly track real systems in the exploitation.
Now, after proper and exact validation presentation, I have no more concerns related to this numerical model.
The only question is - why this validation was not presented after the first paper revision? I truly cannot find the proper answer on this question.
