Determining the Deformation Characteristics of Railway Ballast by Mathematical Modeling of Elastic Wave Propagation

Round 1

Reviewer 1 Report

1. The relevance of the study needs to be strengthened. At the moment it is very vague.

2. The analysis of literary sources on the topic of the study is very concise. This part of the article does not allow to identify the previously unresolved problem. Therefore, I recommend the authors to refine this part of the article.

3.The purpose and objectives of the research are missing.

4. In the section "Materials and methods" it is necessary to designate the main hypotheses of the research, to highlight its limitations and assumptions.

5. There is no reference to the formula (1) in the text of the article.

6. Figure 7 needs to be explained in the text of the article.

7. From the "Discussion" section, information should come out on how the research performed closes the previously unresolved problem. At the moment this is not clear.

8. The conclusions to the article are missing.

9. The list of literary sources is also very short.

Author Response

Dear Reviewer, please check the attached PDF file in which you can find a comparison document where all the changes are tracked. We hope that you can agree with our modifications and the revised manuscript.

Author Response File: Author Response.pdf

Reviewer 2 Report

1.    SUMMARY

The paper investigates changes in stiffness and deformation characteristics of railway ballast due to ballast degradation. The degradation or contamination is represented by local reduction in the deformation modulus of the ballast, while the mechanical response of the railway track to external loads is mathematically modeled as an elastic wave propagation. First, the model is validated by comparing the experimental measurements of stress from train movement with model calculated stress values at two levels of depth below the ballast surface. Then, model results are provided for deformation gradient in the ballast with contamination (reduced modulus) at different levels of depth. It is shown that the ballast deformation is most affected by contamination in the upper 15-20 cm layer of the ballast since the stresses are the highest in this area and they quickly decay with further depth. Finally, numerical results of the deformation modulus of the ballast and the sub-rail base are provided for different combinations of modulus values of individual ballast layers and the soil, which show that the overall track stiffness also depends on the quality of the soil on which the track is laid.

2.    CRITICAL EVALUATION AND COMMENTS

The paper is clear in its scope and objective, and it provides sufficient background to understand the context of the research. The reviewer appreciates the authors’ attention to detail in their efforts to provide proper model validation and comprehensible results that effectively express the model’s predictive abilities. There are no concerns with any material presented in the paper. However, just for clarity, the authors are recommended to provide the description of 'E_s' as the deformation modulus of the soil in Figure 8 caption.

1.  The last two paragraphs of section 1 (Introduction, lines 76-79 and 82-84) may be combined into a single paragraph. Also, the reviewer recommends improving the quality of language in lines 82-84.

2.  Improvement in the quality of language is recommended in lines 183 and 184 for clarity. For instance, the lines may be “….the deformation modulus can reduce to 80%, and in cases of significant contamination, to 60% of its original value.”

Author Response

Dear Reviewer, please check the attached PDF file in which you can find a comparison document where all the changes are tracked. We hope that you can agree with our modifications and the revised manuscript.

Author Response File: Author Response.pdf

Reviewer 3 Report

The manuscript presents a study on the use of mathematical modeling to determine the deformable characteristics of railway ballast. The dynamic model of the stress-strain state of the system based on the theory of elasticity is used to determine the general characteristics of the ballast layer, and the results can be applied as initial data for other railway track models.

I provide my comments and suggestion below for the authors to consider further improving the manuscript's quality.

·         Although I am impressed with the aim and objectives to carry out this study, I am not convinced on the innovation and original contribution that the study can offer, and I recommend the authors emphasise on this matter.

·         since there are already numerous literature results on the dynamic model of the stress-strain state of railway ballast, this study does not present any new mathematical techniques. Additionally, the authors appear to have overlooked several recent publications related to the research area. Therefore, I recommend that the authors conduct a more comprehensive and critical review to improve the chances of acceptance for the revised manuscript.

·         Figure 2 appears to be blurry, making it difficult to read the embedded text. It is recommended that the resolution of the Figure be increased to improve its clarity.

·         The authors should provide a more detailed explanation and context for Figure 3 to help readers understand how it was derived and its significance in the current research. Currently, there is a lack of data interpretation, which may make it difficult for readers to fully grasp the figure's meaning. It would be beneficial if the authors could elaborate on this matter in the revised manuscript.

·         To provide additional context for the measured data presented in Figure 6, it would be beneficial for the authors to compare their results with those from other available studies.

·         It would be helpful to include a separate conclusion section that summarizes the main outcomes and findings of the current study.

English is fine. 

Author Response

Dear Reviewer, please check the attached PDF file in which you can find a comparison document where all the changes are tracked. We hope that you can agree with our modifications and the revised manuscript.

Author Response File: Author Response.pdf

Reviewer 4 Report

The results of this article are useful for the interested reader of the current journal. Thus, the manuscript can be considered for publication after major revision

    1. Please shorten the title of the paper (if possible).

2. Provide more information about the technique used.

3. The introduction part of the manuscript should be improved.

4. Details on obtaining equation (1) are required.

5. The theoretical aspect of this research is weak and needs further development to illustrate the mathematical model.

6. In page (6), Figure 5., need more clarification about the Comparison of experimental and calculated stresses in ballast.

      7. In page (8), Figure 8., need more clarification about                Dependence of the general deformation modulus of the               sub-rail base on the characteristics of the ballast and soil.

Comments for author File: Comments.pdf

Moderate editing of English language

Author Response

Dear Reviewer, please check the attached PDF file in which you can find a comparison document where all the changes are tracked. We hope that you can agree with our modifications and the revised manuscript.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors took into account the indicated recommendations and comments. Thank you!

Reviewer 3 Report

The authors have adequately addressed the comments and suggestions provided by this reviewer. Therefore, I recommend the publication of the revised manuscript.

Reviewer 4 Report

The authors have completely replies to my questions, and they have followed my recommendations. The paper has been improved so I recommend it for publication, as it is.