Experimental Study on Mechanical Differences Between Prefabricated and Cast-In Situ Tunnel Linings Based on a Load-Structure Model

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In the context of active development of underground space of cities, fast and cost-effective tunneling is becoming a priority task. This paper examines the mechanical differences between precast and monolithic tunnel lining structures, which is especially important against the background of insufficient stability of precast structures in the area of ​​connections. The conducted bench experiments and numerical modeling showed that the strength of the precast lining is 15.3% lower, and the destruction zones are concentrated at the joints. However, the results also indicate the possibility of increasing the stability of the precast structure by optimizing the preload and stiffness of the joints. This allows achieving characteristics comparable to monolithic lining, while maintaining the advantages of precast construction. The work has practical value for the design and construction of tunnels using the open excavation method and contributes to improving the reliability and efficiency of modern underground structures.
At the same time, the article needs some revision.
1. Lines 50–52 rightly raise the issue of instability in the joint zone, but the causes of this instability are considered briefly. It would be useful to explain in more detail which geometric or design factors influence the reduction in joint stiffness.
2. Lines 118–130 provide data on the strength of the simulated material. However, deviations of up to 10% from real C50 concrete are not supported by a quantitative assessment of the sensitivity of the result to these deviations. It is necessary to explain how this affected the final conclusions.
3. Lines 167–188 describe the failure of the monolithic lining. However, the stated load values ​​(Fu = 340 kPa) are not explained in the context of engineering practice: are they realistic for tunnels under typical conditions? Clarification is needed.
4. The description of crack formation in lines 173–186 is quite detailed, but is not accompanied by images of stress zones. It would be useful to compare the cracks with the calculated zones of maximum bending moments or shear stresses. 5. Lines 243–254 show sharp changes in deformations. However, the paper does not explain whether these changes are related to critical material stresses or geometric features. It would be desirable to compare the data with the ultimate strength calculations.
6. Section 5.1 (lines 370–382) is devoted to the model parameters in ABAQUS. However, there is no justification for the choice of the friction model (coefficient 0.4), nor is there an analysis of the sensitivity of the result to this parameter. This is important given the key role of friction in the operation of the joints.
7. Lines 427–433 conclude that reducing the stiffness to 30 MN m/rad reduces the bending moment by 37.7%. However, it does not consider how this affects the safety and operational reliability of the tunnel as a whole — even with lower moments, unacceptable deformations may occur. 8. The conclusion presented in lines 434–456 is generally logical, but does not cover all the data presented: for example, neither crack width nor plastic deformation characteristics are mentioned.
9. The entire paper focuses on the physical and mechanical behaviour of the linings, but completely omits the issue of durability and reloading, especially in the context of fatigue cracks in the joint zone. It should be indicated what additional studies are planned.

Author Response

For research article

Comment 1: Lines 50–52 rightly raise the issue of instability in the joint zone, but the causes of this instability are considered briefly. It would be useful to explain in more detail which geometric or design factors influence the reduction in joint stiffness.

Response 1: Thank you for your suggestion, we agree with it and have made a change in the text in this area.

Comment 2：Lines 118–130 provide data on the strength of the simulated material. However, deviations of up to 10% from real C50 concrete are not supported by a quantitative assessment of the sensitivity of the result to these deviations. It is necessary to explain how this affected the final conclusions.

Response 2: Thank you very much for pointing this out and we discussed it. It is true that we did not consider the loss of actual performance of C50 concrete in our study. But We were mainly trying to compare the assembled tunnel lining with the cast-in-place lining, and the focus was on the structural study, and the material errors that may have occurred were not in the focus of the study.

Comment 3：Lines 167–188 describe the failure of the monolithic lining. However, the stated load values (Fu = 340 kPa) are not explained in the context of engineering practice: are they realistic for tunnels under typical conditions? Clarification is needed.

Response 3: We would like to thank the reviewers for their valuable comments, which are very important to improve the engineering application value and readability of this paper. The issues you point out are critical to ensuring the reliability of your models and conclusions. The load value Fu = 340 kPa is not arbitrary, but is based on the load test with a vertical load of Fu of 340 kPa (6.8 MPa in the real world).

Comment 4：The description of crack formation in lines 173–186 is quite detailed, but is not accompanied by images of stress zones. It would be useful to compare the cracks with the calculated zones of maximum bending moments or shear stresses.

Response 4: Thank you to the reviewers for their valuable suggestions. A series of crack pictures in Figure 5 in the text show the process of lining cracking during loading.

Comment 5： Lines 243–254 show sharp changes in deformations. However, the paper does not explain whether these changes are related to critical material stresses or geometric features. It would be desirable to compare the data with the ultimate strength calculations.

Response 5: We thank the reviewers for their valuable suggestions. We have added the necessary explanations and analysis in the original article

Comment 6：Section 5.1 (lines 370–382) is devoted to the model parameters in ABAQUS. However, there is no justification for the choice of the friction model (coefficient 0.4), nor is there an analysis of the sensitivity of the result to this parameter. This is important given the key role of friction in the operation of the joints.

Response 6: Thank you very much for this question, this proposal is very important. I have made a modification at the original text by adding a reference source for a friction coefficient of 0.4.

Comment 7：Lines 427–433 conclude that reducing the stiffness to 30 MN m/rad reduces the bending moment by 37.7%. However, it does not consider how this affects the safety and operational reliability of the tunnel as a whole — even with lower moments, unacceptable deformations may occur. Response 7: Thank you very much for pointing this out. Determining the lining safety factor as the stiffness of lining joints changes is essential, and it is one of the things our team is working on.

Comment 8：The conclusion presented in lines 434–456 is generally logical, but does not cover all the data presented: for example, neither crack width nor plastic deformation characteristics are mentioned.

Response 8: Thank you very much for your questions and suggestions. Our main research objective in this part of the paper is to adjust the joint stiffness in the finite element simulation to obtain a better design of the assembly tunnel. For the degree of crack opening, it is very difficult to analyse the cracks and plastic deformations under this model, which may be a follow-up research for our team.

Comment 9：The entire paper focuses on the physical and mechanical behaviour of the linings, but completely omits the issue of durability and reloading, especially in the context of fatigue cracks in the joint zone. It should be indicated what additional studies are planned.

Response 9: Thanks to the reviewers for their valuable and insightful comments on the research area of this article. You have rightly pointed out a significant limitation of the current research, which has not yet addressed the durability issues that are critical to the long-term service performance of the lining and the structural behavior under repetitive loads, in particular the critical challenge of fatigue cracks in the joint zone, which you have keenly highlighted. We would like to thank you for clearly pointing out this important research direction, which points a clear and important path for the expansion of our work in the future.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Good afternoon, colleagues! I have reviewed the results of the study. The material is presented in clear language. The review is presented in the material, as well as references to the literature. It is somewhat confusing that the sources of literature do not include European, American and other authors. The subject of the research is widely known in world practice and the absence of other works in the literature sources is somewhat unjustified. Next, it is necessary to describe the experimental setup in more detail. How was its rigidity and contribution to the measured values of frame compliance evaluated? Why doesn't the experiment provide for branches that include unloading the tested element? The question of reinforcement of the test sample remains open to me. Why was this particular formulation chosen in the numerical experiment? What explains the absence of a model of additional three-dimensional elements using the well-known Menetri-William or William-Warnke models?

Author Response

For research article

2. Point-by-point response to Comments and Suggestions for Authors

Comments 1:I have reviewed the results of the study. The material is presented in clear language. The review is presented in the material, as well as references to the literature. It is somewhat confusing that the sources of literature do not include European, American and other authors. The subject of the research is widely known in world practice and the absence of other works in the literature sources is somewhat unjustified. Next, it is necessary to describe the experimental setup in more detail. How was its rigidity and contribution to the measured values of frame compliance evaluated? Why doesn't the experiment provide for branches that include unloading the tested element? The question of reinforcement of the test sample remains open to me. Why was this particular formulation chosen in the numerical experiment? What explains the absence of a model of additional three- dimensional elements using the well known Menetri William or William-Warnke models?

Response 1: Thank you very much for your questions and suggestions. It is true that many countries have conducted in-depth research in this direction internationally, so I have added some international scholars' research progress in the introduction part. This paper considers the case of tunnel lining damage and does not consider the unloading condition; in the design of model test, for the problem that local tiny components are difficult to simulate accurately due to the limitation of craftsmanship or materials, non-geometric similarity method can be used to deal with the secondary structure (Luo Yunfei. Research on bearing performance of prefabricated assembled up-arch joints in tunnels [D].Chengdu: Southwest University of Science and Technology, 2023.); effectively regulating the stiffness of the joints, to a certain extent, can be analysed on the tunnel as a whole, and can effectively shorten the calculation time and improve the research efficiency.

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

I have read the manuscript and overall found it relevant and well written. Methods for the testing regimes and results with their discussions are fairly at the required standard. Conclusions are understandable and backed by results.

1. The abstract is clear, concise and reflect on key results of the research - which is good.
2. Line 46: Putting 7 references [1-7] in one place and after such a long paragraph is not healthy. Why not distributing the references across the paragraph to be able to tell which reference says what exactly?
3. Lines 57 - 79 and beyond: the references 11 to 18 are not in brackets and you may think they are numbers only. 
4. Lines 111-118: This is not a sentence (too long to be) and is not a paragraph. What is it and how can the reader understand this? Better to to break it down. Do the same wherever needed.
5. In Figure 8: How would you explain the jump in strains between approximately -20 and 0 at around 3.5 loading step for the left arch?
6. All Figures and Tables should be mentioned in the text before they can appear or be imbedded.

Comments on the Quality of English Language

English language needs improvement, especially avoiding the use of paragraph sentences - very long sentences that can annoy the reader or cause the reader to be lost before fully understanding the message.

Author Response

For research article

Comment 1: The abstract is clear, concise and reflect on key results of the research - which is good.

Response 1: Thank you reviewers for the clarity and conciseness of our abstract and the accuracy of its summary of the core findings of the study. We are very pleased that the abstract effectively communicates the main findings and implications of this study.

Comment 2：Line 46: Putting 7 references [1-7] in one place and after such a long paragraph is not healthy. Why not distributing the references across the paragraph to be able to tell which reference says what exactly?

Response 2: Thank you for your suggestion, we agree with it and have made a change in the text in this area.

Comment 3：Lines 57 - 79 and beyond: the references 11 to 18 are not in brackets and you may think they are numbers only. 

Response 3: Thank you for your suggestion, we agree with it and have made a change in the text in this area.

Comment 4：Lines 111-118: This is not a sentence (too long to be) and is not a paragraph. What is it and how can the reader understand this? Better to to break it down. Do the same wherever needed.

Response 4: Thank you for your suggestion, we agree with it and have made a change in the text in this area.

Comment 5：In Figure 8: How would you explain the jump in strains between approximately -20 and 0 at around 3.5 loading step for the left arch?

Response 5: Due to the applied load, the whole model is stressed and at 3.5 load step, cracks start to appear in the left arch, the test setup shows signs of subsidence, and the left and right sides show sudden changes in the strain values of uneven settlement.

Comment 6：All Figures and Tables should be mentioned in the text before they can appear or be imbedded.

Response 6: Thank you very much for pointing out the normative problem with the order of reference to the charts! We have strictly followed the principle that charts should be mentioned first in the text.

Comments on the Quality of English Language：English language needs improvement, especially avoiding the use of paragraph sentences - very long sentences that can annoy the reader or cause the reader to be lost before fully understanding the message.

Response: Thank you to the reviewers for their meticulous corrections to the language expressions! We fully agree that long compound sentences will affect readers' comprehension efficiency, and have systematically optimized the sentence structure of the whole text.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The article has been significantly improved: explanations, calculations, images have been added, and discussions have been expanded. However, important aspects — model sensitivity to material, operational safety, and durability — are not covered in sufficient detail. What the authors should improve:

Include a numerical assessment of the effect of strength deviation from C50 on the calculation results.

Introduce or at least qualitatively discuss safety factors when varying the stiffness of joints.

Summarize data on crack width and possible consequences for operational suitability.

Author Response

For research article

2. Point-by-point response to Comments and Suggestions for Authors

Comment 1: The article has been significantly improved: explanations, calculations, images have been added, and discussions have been expanded. However, important aspects — model sensitivity to material, operational safety, and durability — are not covered in sufficient detail. What the authors should improve:

Include a numerical assessment of the effect of strength deviation from C50 on the calculation results.

Introduce or at least qualitatively discuss safety factors when varying the stiffness of joints.

Summarize data on crack width and possible consequences for operational suitability.

Response 1: Thank you very much for your questions and suggestions. Numerical evaluation of the impact of strength deviation from C50 on the calculation results:​​ The influence of lining joint stiffness magnitude on structural behavior was the primary focus of this study. While concrete strength magnitude affects the structure's load-bearing capacity, it does not alter the locations of crack initiation. Therefore, a numerical evaluation of the impact of strength deviations from C50 on the calculation results was not performed.

​​Introducing, or at least qualitatively discussing, safety factors when modifying joint stiffness:​​ A discussion of safety factors has been added.

​​Summarizing crack width data and its potential consequences for serviceability:​​ A summary of crack widths and their potential implications for serviceability has been added.

Author Response File: Author Response.docx