Study on the Impact Coefficient of Tied Arch Bridge Shock Effect Based on Vehicle-Bridge Coupling

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The article entitled “Study on the Impact Coefficient of Tied Arch Bridge Shock Effect Based on Vehicle-Bridge Coupling” focuses on the impact coefficient in concrete-filled steel tube tied-arch bridges under high-speed train loading. The study aims to investigate how train speed and track spacing influence stresses and deflection, particularly in the suspenders. The paper is interesting and relevant, but for publication the following issues should be addressed:

1. The introduction does not clearly state the unresolved problem or gap in the existing literature. Moreover, it should be emphasized how this work improves experimental validation compared to purely numerical studies.
2. The authors should provide an explicit description of the actual boundary conditions of the bridge during testing, details on sensor calibration (sensitivity factor, error, and sampling frequency), and the technical specifications of the hybrid 4G+GPS system (sampling rates, synchronization accuracy, and filtering methods).
3. The material properties of the structural components are not reported. The authors should specify the mechanical properties of all materials used in the model, supported by technical standards, laboratory tests, or bibliographic sources.
4. Why are the results compared against design code limits only at 152 km/h? Such comparisons should be presented for all simulated conditions.
5. The authors do not explain how the measured signals were filtered during data processing.
6. Fatigue and the cumulative effects of cyclic loading are not discussed, despite being highly relevant for suspenders subjected to repeated dynamic stresses.

After addressing these points, I recommend the manuscript for publication. The paper requires minor revisions.

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The article considers an impact effect on the shock effect in hangers when a high-speed train is going through on the tied-arch bridge. The results from the numerical model are compared with those obtained using real measurements. The presented approach is interesting, and can be considered for publication in Applied Science after including comments listed below:

1. Lines 23-34: “The bridge model is combined with the 21 CRH2 train model built by the multi-body dynamics software SIMPACK to realize the vehicle-bridge coupling and conduct joint simulation, and the reliability of the vehicle-bridge coupling vibration system is verified by comparing the simulation calculation results with the measured results under the same conditions, and on this basis, the simulation is carried out in the range of 4.2~5.4m (0.4m increment) under the single line driving of the main line spacing of 80~270km/h (10km/h). 270km/h (10km/h increments) under a total of 80 working conditions, the impact effect of the shock effect. The results show that: the vehicle-bridge coupling vibration system adopts ANSYS and SIMPACK joint simulation, the calculation results have the reliability; short shock effect compared with long shock effect, the stress impact coefficient is greater; shock effect impact effect with the increase of vehicle speed, showing a wave-shaped increasing trend; when 180~200km/h close to the bridge inherent frequency, the impact effect on the bridge components to reach the critical speed. Easy to trigger the resonance of the bridge;“ The text is incomprehensible and requires linguistic corrections. It doesn't reflect the content of the article. There are numerous repetitions. The sentences are too long, making it difficult to understand.  
2. What structural element does the symbol "A#" represent? Where exactly is it located? It is not specified in the text or visible in Figure 1.
3. Figure1 - it is also worth showing a cross-sectional view of the bridge and the arrangement of the tracks.
4. The description of the numerical model presented in section 3.1 is insufficient. The text lacks information on the cross-sections used for individual groups of elements, the parameters of the materials used during modeling process or the types of supporting the system. It is worth showing cross-sections of the main structural elements or specifying them in the text. There's no information about the types of connections between elements. The missing parts need to be completed. It would be helpful to provide an ANSYS screenshot of the bridge's numerical model and its basic parameters, such as the number of individual elements, the number of nodes, and the number of degrees of freedom. This would allow for an estimate of the model's complexity.
5. It is worth to add a column in Table 1 with the percentage difference between the results from the numerical model and the tests. This would make the results more readable.
6. The descriptions in Figure 3 are not visible and should be enlarged. It would be helpful to divide the figures into two groups: a) and b) and specify in the description of Figure 3 which ones come from the numerical simulation and which ones come from the tests. This will improve the presentation of the results.
7. A drawing or diagram of the vehicle's subsystem should be included to illustrate the description presented in lines 172-176. This would facilitate understanding of the analysis.
8. Table 2: The description of the middle column is incomplete and incomprehensible. It should be corrected.
9. Lines 187-190: „Through the FRMBS interface in SIMPACK, these components were integrated to form a flexible multi-body dynamics model, producing bridge flexible body files (.fbi) constrained by force elements between rail and vehicle subsystems.” What exactly does the term "force elements" mean? I suggest rephrasing the sentence to make it more understandable.
10. Line 228: There is a reference to equation 1 in the text, but the equations are not numbered, which should be completed.
11. Line 235: The introductory sentence before the equation is missing, it needs to be completed.
12. Figure 6: Why is only hanger 1# shown in the results? This hasn't been explained. What about hanger 7#, which is in the middle of the span?
13. Table 3: On what basis was the impact factor of sensitive components at critical velocities determined? There is no explanation in the article about this value.
14. Line 332-333: “…, and when the speed approaches the bridge’s natural frequency (within the 180–200 km/h range),….” This sentence isn't very accurate, as two different values—train speed and frequency—shouldn't be compared. It's worth considering changing the comment. In fact, the time-dependent excitation forces acting on the bridge at a train speed within range 180-200 km/h entered a resonance region with the bridge's natural frequency, which in turn caused an increase in displacement.
15. The conclusions are short, some additional general conclusions could have been drawn and summarized from the research conducted.

Minor comments:

1. Lines 19-23: There are two sentences with the same meaning, one of them should be deleted.
2. Line 103-104: The title of Figure 1 was placed twice. One should be removed.
3. The font size of the descriptions in Figure 2 is insufficient, it should be increased.
4. Line 226: there is a typo in Figure 5 description in word “simulation”.

Comments on the Quality of English Language

The text requires linguistic revision to ensure the correct use of phrases and technical terms, especially in the abstract. Some comments are listed below:

1. Lines 23-34: The text needs rephrasing (see main comment no 1.).
2. Line 38: The sentence: “single line traffic will cause the train to be biased…” should be rephrased. The text is informal, technical language should be used.
3. I suggest replacing the word “suspenders” with “hangers” or “suspension cables”.
4. Line 96: “the arch rib has a planar rise of 25.6 m…” should be rephrased.
5. Line 216: It is better to use “good compatibility” rather than “strong agreement”.
6. Figure 7: The term "boom number" should be replaced by "hanger number".

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript examines the impact factor of a CFST tied arch bridge subjected to high-speed train loading through field testing and coupled vehicle–bridge simulations. Using ANSYS and SIMPACK models validated by dynamic load tests, the study shows that impact effects increase with train speed and exhibit resonance around 180-200 km/h. The results also reveal significant differences in impact between the near and far sides of the bridge, while single-line train operation further enhances asymmetrical responses and stress effects.

The manuscript presents a study with a defined methodological framework, but its structure and presentation require further refinement to ensure clarity and coherence. To enhance the clarity, depth, and practical contribution of the work, the revised version should provide explicit answers to the following questions:

1. The introduction should more critically discuss the limitations of previous studies, particularly regarding side-to-side comparative impact effects on suspenders and track spacing variations. The study’s unique contribution should be clearly emphasized, and the introduction should conclude with a brief overview of the manuscript’s structure. The reference list could be updated to include recent work on vehicle–track–bridge interaction that examines parameters influencing the structural response, such as https://doi.org/10.3390/buildings13092296
2. The current title of Section 2, “Engineering Overview”, does not accurately reflect the section’s content, which focuses on the description of the case study bridge and the associated experimental test setup. It is therefore recommended that the title be revised to more precisely represent the material presented. A more appropriate option could be “Case Study: Bridge Description and Experimental Configuration” or a similar formulation.
3. All figures should have a minimum resolution of 300 DPI, and the font size of labels, annotations, and legends should be increased where necessary to ensure clarity and readability. In particular, Figure 1 should be revised to present a complete layout of the bridge, explicitly including the piers and a representative cross-section, so that the figure provides a comprehensive and accurate depiction of the studied structure. Furthermore, the caption of Figure 1 should be correctly positioned directly below the figure, in line with standard formatting practice.
4. Section 2.2 gives only a general overview of the testing equipment and monitoring system. The authors should provide a more detailed explanation of the rationale for selecting the specific sensors (e.g., accelerometers, vibrometers, strain gauges), including their ranges, sensitivity, and suitability for capturing bridge dynamics, as well as clarify the criteria and methodology used to determine sensor placement and measurement points to ensure data reliability.
5. The manuscript should provide a more detailed description of the track structure and its modeling. In particular, the authors should clarify how the rails are represented (e.g., continuously welded or with expansion joints), whether the track stiffness and structural properties are accounted for in the bridge dynamic model, and how these aspects influence the overall bridge-track-vehicle interaction and the resulting dynamic responses.
6. The manuscript reports that the impact coefficients for suspenders 1# and 1## (0.185 and 0.307, respectively) exceed the limits specified in the Code for Design of Steel Structures of Railway Bridges [22]. While the text notes the particular susceptibility of short suspenders and the need to assess asymmetry, the discussion should be expanded to explicitly explain the engineering significance of these exceedances and how the results could inform the development of design, evaluation, and maintenance strategies for large-span tied-arch bridges.
7. The manuscript should clarify how eccentric train loads are modeled, including the definition of train position relative to the bridge centerline. It should also specify whether the loads are applied directly to the bridge or transmitted via the track, and explain the track’s role in load transfer and its influence on the bridge’s dynamic response.
8. The manuscript should include a clear summary of the key findings and practical implications of the study. Specifically, the authors should explicitly highlight the main insights regarding critical structural components, asymmetry of load effects, and the influence of track spacing on dynamic responses, and provide recommendations for bridge design, safety assessment, and operational practices.
9. The conclusions should explicitly acknowledge the limitations of the study and propose directions for future research. In particular, the authors should discuss potential extensions of the work regarding vehicle-bridge interaction under varying track conditions, train types, and operational scenarios, to provide guidance for broader applicability and further validation.

Comments on the Quality of English Language

The manuscript should be carefully reviewed and revised to ensure that the English language usage aligns with standard scientific and technical terminology. Attention should be given to clarity, grammar, and consistency of terms, particularly those related to bridge engineering, vehicle-track-bridge interaction, and structural dynamics, to enhance readability and professional presentation.

Author Response

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Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

I would like to thank the Authors for the revised version of the article and for responding to the comments contained in the review. In the new version, the quality of the article has significantly increased thanks to the changes introduced by the Authors.

I have two comments regarding the previous comments:

1. Line 262-263 in the new version of the manuscript – The description of the middle column is still incomplete “ Vehicle body rotational iner-”. There should be probably a second row, which unfortunately isn't visible. This should be corrected before publication. Please verify the word “nutation” - in my opinion there is a mistake in translation.
2. Figure 10 – there is still “boom number” on the figure. It supposed to be replaced by the “hanger number”.

Minor comments:

1. Figure 1: line 131. Please, correct the location of the captions so that they are below the appropriate figures. The font size of the captions at the top of the bridge cross-section should also be increased, as they are invisible.
2. Line 151 , there should be a dot not semicolon “….to stream and record data in real time. All data…”
3. Figure 2: line 172 – Please, correct the description to be one line.
4. Table 1, line 189: The description does not match the table contents, it should be corrected. Please complete also the unit of dimensions included in the table.
5. Starting on line 219, the article contains references to incorrect numbers of figures and tables in the text. This is probably due to the inclusion of additional elements in the revised version of the manuscript and should be corrected.
6. Line 229, Figure 4: Correct the position of the caption under the figure so that it is on one line.
7. Lines 239- 245: figure 5 – mode shapes presented on the figure in the new version of the article are too small. I suggest to increase them.
8. Line 288: I think it should be “…where s denotes…”.
9. Line 289: Please verify the correctness of the equation at the end of the sentence. Shouldn’t it be „yt=±st/2”?
10. Line 330 : I suggest to write “ In Eq.(1)…”
11. All figure captions should be on the same page as the figures.

Comments on the Quality of English Language

I suggest to consider proofreading the text for correct punctuation. Some sentences are very long and separated by commas or semicolons, and they could be divided into shorter sentences to make the content easier to understand.

Author Response

 Please find the attachment enclosed

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

1. General Comment (regarding overall structure and language):
   The manuscript requires additional attention to improve the overall structure and organization. Sections should be logically arranged, with clear connections between the introduction, methodology, results, and conclusions. Furthermore, the manuscript needs a careful revision of spelling, grammar, and overall use of the English language to ensure clarity, readability, and consistency. Addressing these issues will significantly enhance the quality and professionalism of the manuscript.
2. Please correct Figure 3. The figure currently shows only the appearance of a single rail, while the caption states that it represents a track model. The figure and its description must be consistent. It is recommended to present the complete track calculation model (rails, sleepers, and supporting structure) to align with the caption.
3. The title of Table 1, “Bridge frequency and vibration type”, does not correspond to the actual content of the table. Please revise the table title so that it accurately reflects the data presented.
4. Figures presenting the results, as well as figures of the calculation models, must be improved in terms of quality and readability. In particular, Figure 1(c) does not adequately represent what is stated in its caption. The figure lacks sufficient clarity and detail to properly convey the intended information. We kindly request that the authors provide a revised version that accurately and clearly illustrates the described content.

Comments on the Quality of English Language

The manuscript needs a careful revision of spelling, grammar, and overall use of the English language to ensure clarity, readability, and consistency.

Author Response

 Please find the attachment enclosed

Author Response File: Author Response.docx

Round 3

Reviewer 3 Report

Comments and Suggestions for Authors

Table 1. CRH2 train key parameters does not correspond to the content of the table. The table presents the geometric and material properties of the rail.

The correct title of Figure 3 should be Simplified Track Calculation Model.

Author Response

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Author Response File: Author Response.docx