Review Reports - Numerical Simulation Study on Lining Damage of Shield Tunnel under Train Load

Round 1

Reviewer 1 Report

Dear Editor/Authors

I have assessed the manuscript "Numerical Simulation Study on Lining Damage of Shield Tunnel under Train Load (sustainability-1948911)" for possible original article.

I would like to draw attention to the following points for a better study;

1) The cause-effect relation was not expressed in the article clearly. The subject and purpose of the article should be expressed, and the cause-effect relation should be revealed more clearly.

2) What is the difference between this study from other studies in the literature. Because there are lost of similar studies in the literature and please make a comparison. Write the similar/non similar points and emphasize your originality.

3) More information about the numerical studies and ABAQUS should be given.

4) The introduction and literature review section should be improved. Bring along as much as you can the baseline scientific proof for the knowledge you are going to explore in further sections. The literature is better to be updated based on the most recent works. It would be better to include the following references and other references.

· An evaluation on effects of surface explosion on underground tunnel; availability of ABAQUS Finite element method

· Importance of numerical analyses for determining support systems in tunneling: A comparative study from the trabzon-gumushane tunnel, Turkey

· A comparison of support systems obtained from the RMR89 and RMR14 by numerical analyses: Macka Tunnel project, NE Turkey

5) The figures and tables should be more comprehensible.

6) The article should be controlled in terms of language, expression and grammar.

I believe that a more understandable article will be obtained when all these points are evaluated and added to the study. It is necessary to revise the article that I stated above and suggestions from other referees. I think that the paper needs revisions.

I wish success to the authors in their study.

Best regards

Author Response

Detailed Point-by-Point Replies to Reviewers’ comments on

“Numerical Simulation Study on Lining Damage of Shield Tunnel under Train Load”

We would like to present our great thanks to the reviewers for giving the important and effective comments in the review that provide a significant improve of the manuscript for publication. All points have been corrected seriously according to reviewers’ comments and the details of corrections are listed in Authors’ reply as bellow.The revised expressions according to the comments are marked in red in the revised manuscript.

Besides, the final revision has been carefully proofread by a native English speaker and many grammatical errors have been corrected.

Reply to Reviewer 1’ Comments

(Letters C & R denote comment and reply respectively)

We would like to thank the Editor and the reviewers for providing the useful comments, which certainly help us to improve the quality of this paper. We have considered them carefully and have revised the manuscript accordingly.

C1:The cause-effect relation wasn’t expressed in the article clearly. The subject and purpose of the article should be expressed, and the cause-effect relation should be revealed more clearly.

R1:Thank you for the comment, the author has revised the summary and introduction of the article in response to comments made by the reviewer.

“Under the long-term dynamic load of the train, ..., causing traffic accidents and casualties. Based on the finite element software ABAQUS, this paper analyses the change rule of tunnel lining damage under long-term train dynamic load and explores the influence of tunnel buried depth on the change rule of tunnel lining damage. The excitation force function is used to generate a series of dynamic and static loads superimposed by sine functions to simulate the dynamic loads of the train. Load is applied above the tunnel by writing Dload subprogram.”, “In this paper, based on the finite element analysis method, the excitation force function to generate a series of sinusoidal functions to superimpose dynamic and static loads to simulate the dynamic loads of trains. Through the analysis of damage variation law of shield tunnel lining under long-term dynamic loads under different buried depths, the empirical formula of accumulated damage of tunnel concrete structure under dynamic loads of trains is given. It provides theoretical reference for safety evaluation and safety protection research of shield tunnel under long-term train dynamic load.”

C2:What is the difference between this study from other studies in the literature. Because there are lost of similar studies in the literature and please make a comparison. Write the similar/non similar points and emphasize your originality.

R2:Thank you for your suggestions, the author has revised it according to the reviewer's comments. “According to this constitutive model, the dynamic response and accumulated damage of tunnel cross structure under different train operating years were analyzed. .... The above scholars didn’t consider the long-term train load in their studies on underground structures such as tunnels. Under the long-term action of train load, there is little research on damage degree variation law of tunnel lining at different buried depths. With the increasing number of train loads, the change law of tunnel lining damage needs to be further studied.”

C3:More information about the numerical studies and ABAQUS should be given.

R3:Thank you for the comment, The author adds a more detailed description of the ABAQUS calculation program.

“The schematic diagram of the shield tunnel model based on ABAQUS finite element software is shown in Fig. 1 and Fig. 2, and the section perpendicular to the center axis of the tunnel is 50 × 50m square, the length of the model along the axis of the tunnel is 30m, and the horizontal distance between the rail and the axis is 0.7175m. In the coupled dynamic finite element model, the formation is simplified as an isotropic, homogeneous elastic medium. The Mohr-Coulomb model is used for the soil mass of the tunnel. The soil mass with a density of 1860kg/m3, and the elastic modulus is 20MPa. The internal friction angle, cohesion and Poisson ratio of soils are 30 degrees, 0 kPa and 0.27 respectively. C50 concrete damage model (CDP model) is used for lining and ballast of tunnel in calculation model. The rail adopts an elastic model with a density of 7850kg/m3, and the elastic modulus is 210GPa. Poisson ratio of rails is 0.25. Elastic models are used for outsourcing polymers. The density of polymer material is 600 kg/m3, elastic modulus is 300 MPa and Poisson ratio is 0.35. The viscoelastic boundary is applied at the truncated boundary to eliminate the reflection effect of the boundary on the incident wave. Load application is achieved by writing DLOAD subprogram. The subprogram is used to simulate the long-term effects of train loads during calculation.”

C4:The introduction and literature review section should be improved. Bring along as much as you can the baseline scientific proof for the knowledge you are going to explore in further sections. The literature is better to be updated based on the most recent works. It would be better to include the following references and other references.

An evaluation on effects of surface explosion on underground tunnel; availability of ABAQUS Finite element method.

Importance of numerical analyses for determining support systems in tunneling: A comparative study from the trabzon-gumushane tunnel, Turkey.

A comparison of support systems obtained from the RMR89 and RMR14 by numerical analyses: Macka Tunnel project, NE Turkey.

R4:Thank you for the comment, seven references have been added by the author.

“19.Kanik M, Gurocak Z, Alemdag S. A comparison of support systems obtained from the RMR89 and RMR14 by numerical analyses: Macka Tunnel project, NE Turkey. Journal of African Earth Sciences, (2015) 109: 224-238. doi:10.1016/j.jafrearsci.2015.05.025.

20.Kanik M, Gurocak Z. Importance of numerical analyses for determining support systems in tunneling: A comparative study from the trabzon-gumushane tunnel, Turkey[J]. Journal of African Earth Sciences, (2018), 143: 253-265, doi:10.1016/j.jafrearsci.2018.03.032.

23.Yeau K Y, Sezen H, Fox P J. Simulation of behavior of in-service metal culverts. Journal of Pipeline Systems Engineering and Practice, (2014), 5(2): 04013016, doi:10.1061/(ASCE)PS.1949-1204.0000158.

24.Maleska T, Beben D. Behaviour of soil-steel composite bridge with various cover depths under seismic excitation. Steel and Composite Structures, (2022), 42(6): 747-764, doi:10.12989/scs.2022.42.6.747.

25.Maleska T, Beben D, Nowacka J. Seismic vulnerability of a soil-steel composite tunnel–Norway Tolpinrud Railway Tunnel Case Study. Tunnelling and Underground Space Technology, (2021), 110: 103808, doi:10.1016/j.tust.2020.103808.

26.Flener E B, Karoumi R. Dynamic testing of a soil–steel composite railway bridge. Engineering structures, (2009), 31(12): 2803-2811, doi:10.1016/j.engstruct.2009.07.028.

27.Hashash Y M A, Hook J J, Schmidt B, et al. Seismic design and analysis of underground structures. Tunnelling and underground space technology, (2001), 16(4): 247-293, doi:10.1016/S0886-7798(01)00051-7.”

C5:The figures and tables should be more comprehensible.

R5:Thank you for your suggestion, the author has optimized the pictures and tables in the article.

C6:The article should be controlled in terms of language, expression and grammar.

R6:Thank you for the comment, the author checks the grammar and expression carefully and corrects the whole text carefully.

Reviewer 2 Report

General considerations:

· In a society in need of an optimized and sustainable use of the subsoil. The general subject matter is interesting and relevant. However, in the context of the specific and concrete contributions in this field, as well as the applicability of the proposal, this should be much clearer. In this respect, the paper's proposal may be incomplete and inconsistent at present.

· The manuscript, which counts all its sections, has a total length of 8 pages. The writing of the document is basic, and sometimes short fragments of text from other sources are used. Despite the number of figures, the graphical work should be improved

· On a general level, a thorough proofreading of the document is recommended.

· The document contains a total of 21 references, of which 14 are publications written in the last 5 years (67%), 4 in the last 10 years (19%), and 3 have more than 10 years (14%). In this way, the total number could be considered poor, but their actuality is acceptable. Citations and references are recommended to be completed and enriched in a new version of the document. Some of the references are written in Chinese and should be replaced with others in English.

Title, Abstract and Keywords:

· The title “Numerical Simulation Study on Lining Damage of Shield Tunnel under Train Load” is ambitious but does not reflect what is written in the document. The concept expressed in the title on which the research is theoretically based is not explicitly defined and explained in the manuscript. Nor is there any mention of the case study, either in the title or even in the abstract.

· The text of the abstract may be too brief and incomplete. It does not address the importance of the subject matter, nor the degree of novelty and relevance of the research. There is no mention of the case study and the results can be considered inconsistent. Finally, there are no mention of conclusions that address the replicability of the method for preventive conservation of structures and tunnels.

· The selection of keywords seems to be appropriate, although acronyms of significant terms are recommended as well. Words like damage are so generic that they should be preceded by an adjective for a better description.

Section 1: Introduction

· Tunneling works should not only be concerned with damage and movements in tunnels but primarily with possible damage to the built environment, hence the great importance of assessing the movements and deformations caused, as well as the question of vibrations. This issue is not addressed in the introduction and could be an improvement of the paper. The introduction does not clearly present the work done afterward.

Section 2: Tunnel Numerical Model and Train Load

· This section should be completed with more information that clarifies in detail the characteristics of the working area: characteristics of the soil, it seems to have only one layer, the presence of the water table, detailing the physical-mechanical parameters of the subsoil, surface traffic overload. All this suggested information should be included to improve the research.

· The constitutive model for the soil is not explained at all and neither is the soil behavior. Parameters such as cohesion equal to 0 in a silty sand layer should be justified, the effective stress principle and the influence of the pore pressure or the void ratio are not included. The description is extremely vague and is not admissible for this kind of paper.

· Soil stiffness could vary with depth and this issue is not even mentioned. The deformation of the soil and the lining is not considered.

· Similarly, the layout of the tunnel in plan is not specified. The conditions of the urban context of the working area are not understood, and it is not known what kind of effects the monitored movements may cause on the built elements. What happens on the surface and in the upper layer?

Section 3: Calculation Results

· The pressure applied to the lining causes the tubing to move, and this is neither considered nor explained.

· To obtain reliable numerical solutions to the problems considered in this paper, the size of the grid spacing should be explained and taken into account. The figures of the model, numbers 1 and 2, should be better described.

· The inaccuracy caused by a too coarse mesh may lead to wrong conclusions.

· The tunnel-soil interaction problem is not adequately addressed in this study.

· The tubing parameters and the friction angles are not given.

· The boundaries between different materials are not described.

· A cross section of the soil layer and the water table should be included with a proper description.

· Due to the extremely poor definition of the model, the calculation results are not interesting, they do not provide useful information.

· There is no contribution of interest, only inconsistent assertions, based on a wrong model of the soil and the tunnel.

Section 4: Conclusions

· Some conclusions, are so generic that no calculations are required.

· The conclusions section should be devoted to specifying the degree of innovation and relevance of the method developed, as well as its validity and replicability.

Final evaluation

The manuscript in its current state can be considered inconsistent and unfinished and does not allow the real contributions of the research to be visualized. I encourage its authors to incorporate all recommended improvements.

Author Response

Detailed Point-by-Point Replies to Reviewers’ comments on

“Numerical Simulation Study on Lining Damage of Shield Tunnel under Train Load”

Reply to Reviewer 2’ Comments

(Letters C & R denote comment and reply respectively)

C1: General considerations:

In a society in need of an optimized and sustainable use of the subsoil. The general subject matter is interesting and relevant. However, in the context of the specific and concrete contributions in this field, as well as the applicability of the proposal, this should be much clearer. In this respect, the paper's proposal may be incomplete and inconsistent at present.

The manuscript, which counts all its sections, has a total length of 8 pages. The writing of the document is basic, and sometimes short fragments of text from other sources are used. Despite the number of figures, the graphical work should be improved

On a general level, a thorough proofreading of the document is recommended.

The document contains a total of 21 references, of which 14 are publications written in the last 5 years (67%), 4 in the last 10 years (19%), and 3 have more than 10 years (14%). In this way, the total number could be considered poor, but their actuality is acceptable. Citations and references are recommended to be completed and enriched in a new version of the document. Some of the references are written in Chinese and should be replaced with others in English.

Title, Abstract and Keywords:

The title “Numerical Simulation Study on Lining Damage of Shield Tunnel under Train Load” is ambitious but does not reflect what is written in the document. The concept expressed in the title on which the research is theoretically based is not explicitly defined and explained in the manuscript. Nor is there any mention of the case study, either in the title or even in the abstract.

The text of the abstract may be too brief and incomplete. It does not address the importance of the subject matter, nor the degree of novelty and relevance of the research. There is no mention of the case study and the results can be considered inconsistent. Finally, there are no mention of conclusions that address the replicability of the method for preventive conservation of structures and tunnels.

The selection of keywords seems to be appropriate, although acronyms of significant terms are recommended as well. Words like damage are so generic that they should be preceded by an adjective for a better description.

R1: Thank you for the comment, the author has modified the summary, introduction, key words, references and charts of the article accordingly.

Under the long-term dynamic load of the train, the shield tunnel structure is damaged. With the increase of operating number, the cumulative damage gradually increases. When cumulative damage increases to a certain value, the tunnel lining will produce cracks and lose tensile strength, and lead to tunnel deformation, damage, etc. In serious cases, the tunnel will stop operation, causing traffic accidents and casualties. Based on the finite element software ABAQUS, this paper analyses the change rule of tunnel lining damage under long-term train dynamic load and explores the influence of tunnel buried depth on the change rule of tunnel lining damage. The ex-citation force function is used to generate a series of dynamic and static loads superimposed by sine functions to simulate the dynamic loads of the train. Load is applied above the tunnel by writing DLOAD subprogram. The results show that the damage of tunnel lining mainly occurs at the arch foot and the structural damage in other places can be neglected. Under the same loading condition, the greater the tunnel lining damage is. Under the same loading conditions, the tunnel lining damage increases with the increase of buried depth. According to the test results, the mathematical expressions of cumulative damage value versus loading times at the location prone to fatigue damage. It provides theoretical reference for safety evaluation and protection of tunnel structure under long-term train load.

Keywords: Long-term load; Dynamic load; Shield tunnel; Accumulated damage; Numerical simulation

C2: Section 1: Introduction

Tunneling works should not only be concerned with damage and movements in tunnels but primarily with possible damage to the built environment, hence the great importance of assessing the movements and deformations caused, as well as the question of vibrations. This issue is not addressed in the introduction and could be an improvement of the paper. The introduction does not clearly present the work done afterward.

R2:Thank you for the comment, the author revised the introduction of the article, added some references, and introduced the work done in more detail.

Kanik et al.[19,20] selected the best tunnel support scheme by using rock mass rating (RMR), rock mass quality (Q) and rock mass index (RMi) evaluation indexes. Under the long-term action of train load, little research has been done on the regularity of damage degree of tunnel lining at different buried depths. With the increase of loading times, the change rule of tunnel lining damage needs to be further studied. Ma et al.[21] tested the dynamic behavior of tunnel basement structure with axial load. By analyzing the dy-namic response and the influence law of fatigue life of heavy-duty train under different base conditions (complete, damaged, and repaired), the adaptability of railway tunnel equipment to freight truck axle load is clarified. Yan et al.[22] proposed an improved constitutive model of concrete under uniaxial cyclic load considering fatigue rigidity degradation, fatigue strength degradation, and fatigue residual strain increment of concrete. According to this constitutive model, the dynamic response and accumulated damage of tunnel cross structure under different train operating years were analyzed. Maleska et al.[23,24] explored the influence of different cover depths on stress and strain of underground culvert structure based on finite element method. The above scholars did not consider the long-term train load in their studies on underground structures such as tunnels. Under the long-term action of train load, there is little research on damage degree variation law of tunnel lining at different buried depths. With the in-creasing number of train loads, the change law of tunnel lining damage needs to be further studied.

In this paper, based on the finite element analysis method, the excitation force function to generate a series of sinusoidal functions to superimpose dynamic and static loads to simulate the dynamic loads of trains. Through the analysis of damage variation law of shield tunnel lining under long-term dynamic loads under different buried depths, the empirical formula of accumulated damage of tunnel concrete structure under dy-namic loads of trains is given. It provides theoretical reference for safety evaluation and safety protection research of shield tunnel under long-term train dynamic load.

C3:Section 3: Calculation Results

The pressure applied to the lining causes the tubing to move, and this is neither considered nor explained.

To obtain reliable numerical solutions to the problems considered in this paper, the size of the grid spacing should be explained and taken into account. The figures of the model, numbers 1 and 2, should be better described.

The inaccuracy caused by a too coarse mesh may lead to wrong conclusions.

The tunnel-soil interaction problem is not adequately addressed in this study.

The tubing parameters and the friction angles are not given.

The boundaries between different materials are not described.

A cross section of the soil layer and the water table should be included with a proper description.

Due to the extremely poor definition of the model, the calculation results are not interesting, they do not provide useful information.

There is no contribution of interest, only inconsistent assertions, based on a wrong model of the soil and the tunnel.

R3: Thank you for your suggestion, the author revised the comments made by the reviewer. In this paper, the reasonable grid size is selected. Under various grid partition methods, the one with faster calculation speed and higher accuracy is selected. The parameters of the tunnel are based on C50 and no friction angle is set. Because this paper explores the cumulative damage of lining under long-term load, no specific parameters of tunnel structure are given. The influence of water level on tunnel structure is not considered in this paper. The interaction between tunnel and soil is reflected by the coefficient of friction.

“The schematic diagram of the shield tunnel model based on ABAQUS finite element software is shown in Fig. 1 and Fig. 2, and the section perpendicular to the center axis of the tunnel is 50 × 50m square, the length of the model along the axis of the tunnel is 30m, and the horizontal distance between the rail and the axis is 0.7175m. In the coupled dynamic finite element model, the formation is simplified as an isotropic, homogeneous elastic medium. The Mohr-Coulomb model is used for the soil mass of the tunnel. The soil mass with a density of 1860kg/m3, and the elastic modulus is 20MPa. The internal friction angle, cohesion and Poisson ratio of soils are 30 degrees, 0 kPa and 0.27 respectively. C50 concrete damage model (CDP model) is used for lining and ballast of tunnel in calculation model. The rail adopts an elastic model with a density of 7850kg/m3, and the elastic modulus is 210GPa. Poisson ratio of rails is 0.25. Elastic models are used for outsourcing polymers. The density of polymer material is 600 kg/m3, elastic modulus is 300 MPa and Poisson ratio is 0.35. Friction coefficient between tunnel and soil is 0.55. The viscoelastic boundary is applied at the truncated boundary to eliminate the reflection effect of the boundary on the incident wave. Load application is achieved by writing DLOAD sub-program. The subprogram is used to simulate the long-term effects of train loads during calculation.”

C4:Section 4: Conclusions

Some conclusions, are so generic that no calculations are required.

The conclusions section should be devoted to specifying the degree of innovation and relevance of the method developed, as well as its validity and replicability.

Final evaluation

R4: Thank you for your suggestion, the author revises the conclusions of the article according to the comments made by the reviewer.

Conclusions

In this paper, the dynamic load of train is simulated by establishing excitation force function. Based on ABAQUS finite element software, the development law of shield tunnel lining damage under long-term train load is calculated and analyzed. Based on the test results, the cumulative damage development law at the locations prone to fatigue failure is fitted by empirical formula, and the variation law of cumulative damage of tunnel lining under different tunnel burial depths is compared and analyzed. The main conclusions are as follows:

With the increase of loading times, the accumulated damage value of lining located at the arch foot and the arch waist of the tunnel shows an increasing trend, and the ac-cumulated damage growth rate of lining at the arch foot is the highest. Damage to tunnel lining at arch foot occurs when loading times reach 1.16 million;

Under long-term train load, the tunnel lining at the arch foot is most prone to fatigue damage, followed by the arch waist. The accumulated damage value at the tunnel arch foot exceeds 0.9 and the tunnel arch waist exceeds 0.5 under different buried depths when loading times reache 1.16 million. Accumulated damage at other locations is negligible;

The cumulative damage value of lining at arch foot and arch waist of shield tunnel increases exponentially with the increase of loading times. The fastest change rate of accumulated damage value of tunnel lining at arch foot;

Under the same loading conditions, the cumulative damage of the tunnel lining is proportional to the buried depth of the tunnel. Under the action of train load, the ac-cumulated damage of tunnel lining decreases continuously as the buried depth of tunnel decreases. The corresponding tunnel structure with smaller buried depth has a longer service life. For deeply buried tunnels, the number of routine tunnel inspections and maintenance should be increased to ensure the normal and safe operation of the tunnel.

Reviewer 3 Report

The article addresses an important and very interesting topic of the numerical simulation study on lining damage of shield tunnel under train load, which is appreciated. The study includes the numerical research. In this paper was based on the current research status of the mechanical influence of tunnel structure under train load, the finite element software is used to study the lining damage variation of shield tunnel under long-term train dynamic load under different burial depth, and an empirical formula for cumulative damage of tunnel concrete structure under train dynamic load is given. The Reviewer has some concerns regarding the abstract, introduction, numerical models, results, conclusions and references. Generally, in this paper the English language is should be improved (some sentence should be more clearly, thus please check the text of Native Speaker. In opinion of Reviewer this paper should be subjected to major revision.

Other comments:

1. Introduction

Generally, the introduction should be improved in opinion of Reviewer and should be added the description/impact of seismic, dynamic loads, soil cover height of tunnel/soil-steel bridge, where the aspect of Soil-Structure Interaction was analysed.

Below you can find some papers about dynamic loads and SSI analysis

· https://doi.org/10.12989/scs.2022.42.6.747

· https://doi.org/10.1061/(ASCE)PS.1949-1204.0000158

· https://doi.org/10.1016/j.engstruct.2009.07.028

· https://doi.org/10.1016/j.tust.2020.103808

· https://doi.org/10.1016/S0886-7798(01)00051-7

2. Please check in all paper the passive voice.

3. Which boundary condition was used in numerical model? Please show on the numerical model.

4. Please show the dimension of numerical model.

5. How numerical model was verified?

6. How to applied the load in numerical model?

7. Please improve conclusions. In current version are really poor. The Reviewer cannot see the most important conclusions from your paper (please use bullets) about the impact of loads/SSI on the bridge.

8. The References should be improved. Generally, the scientific paper should be based on the literature from all world. You can use the suggestions papers from point # 1of this review. In addition, you can check other papers about dynamic loads of bridge and SSI effect.

Finally, I hope that my comments will be helpful for the authors.

Author Response

Detailed Point-by-Point Replies to Reviewers’ comments on

“Numerical Simulation Study on Lining Damage of Shield Tunnel under Train Load”

Besides, the final revision has been carefully proofread by a native English speaker and many grammatical errors have been corrected.

Reply to Reviewer 3’ Comments

(Letters C & R denote comment and reply respectively)

Other comments:

C1:Introduction

Below you can find some papers about dynamic loads and SSI analysis

https://doi.org/10.12989/scs.2022.42.6.747

https://doi.org/10.1061/(ASCE)PS.1949-1204.0000158

https://doi.org/10.1016/j.engstruct.2009.07.028

https://doi.org/10.1016/j.tust.2020.103808

https://doi.org/10.1016/S0886-7798(01)00051-7

R1:Thank you for your suggestion, in response to the suggestions made by the reviewers, the author added references on the impact of earthquake, dynamic load and soil height on the tunnel structure.

C2:Please check in all paper the passive voice.

R2:Thank you for the comment, the author checks the grammar and expression carefully and corrects the whole text carefully.

C3:Which boundary condition was used in numerical model? Please show on the numerical model.

R3:Thank you for your suggestion, viscoelastic boundary is used in this paper. The specific method is to apply viscoelastic boundary at the truncated boundary to eliminate the reflection effect of the boundary on the incident wave.

C4:Please show the dimension of numerical model.

R4:Thank you for the comment, the author added a picture introducing the size of the numerical calculation model.

C5:How numerical model was verified?

R5:Thank you for your suggestion, in this paper, only the simulation research has been carried out, and the simulation results conform to the general rules. However, it hasn’t been verified against the background of actual project.

C6:How to applied the load in numerical model?

R6:Thank you for the comment, load application is achieved by writing dload subprogram. The subprogram is used to simulate the long-term effects of train loads during calculation.

C7:Please improve conclusions. In current version are really poor. The Reviewer can’t see the most important conclusions from your paper (please use bullets) about the impact of loads/SSI on the bridge.

R7:Thank you for your suggestion, the author re-summarizes the conclusions of the article and revises the conclusions.

Conclusions

With the increase of loading times, the accumulated damage value of lining located at the arch foot and the arch waist of the tunnel shows an increasing trend, and the accumulated damage growth rate of lining at the arch foot is the highest. Damage to tunnel lining at arch foot occurs when loading times reach 1.16 million;

Under the same loading conditions, the cumulative damage of the tunnel lining is proportional to the buried depth of the tunnel. Under the action of train load, the accumulated damage of tunnel lining decreases continuously as the buried depth of tunnel decreases. The corresponding tunnel structure with smaller buried depth has a longer service life. For deeply buried tunnels, the number of routine tunnel inspections and maintenance should be increased to ensure the normal and safe operation of the tunnel.

C8:The References should be improved. Generally, the scientific paper should be based on the literature from all world. You can use the suggestions papers from point # 1of this review. In addition, you can check other papers about dynamic loads of bridge and SSI effect.

R8:Thank you for the comment, seven references have been added by the author.

26.Flener E B, Karoumi R. Dynamic testing of a soil–steel composite railway bridge. Engineering structures, (2009), 31(12): 2803-2811, doi:10.1016/j.engstruct.2009.07.028.

Round 2

Reviewer 1 Report

Dear Editor/Authors

I have assessed the manuscript "Numerical Simulation Study on Lining Damage of Shield Tunnel under Train Load" for a possible original article.

The author(s) have/has made all the previously mentioned revisions.

I believe that the manuscript can be published now.

I wish success to the author(s).

Best regards

Author Response

We would like to present our great thanks to the reviewer for giving the important and effective comments in the review that provide a significant improve of the manuscript for publication. The author revised the article according to the opinions of the reviewers, which made it more complete, precise and reliable.

Reviewer 2 Report

Title, Abstract and Keywords:

The title “Numerical Simulation Study on Lining Damage of Shield Tunnel under Train Load” hasn´t been changed and there isn´t any mention of the case study, either in the title or even in the abstract.

This section has been improved as required.

Section 1: Introduction

The references have been improved as required.

Section 3: Calculation Results

I´m really sorry but I cannot agree with the expression “the reasonable grid size is selected” used in the response number 3, in a technical paper the size must be perfectly described, and neither the sentence “this paper explores the cumulative damage of lining under long-term load, no specific parameters of tunnel structure are given”. It is obvious the damage of the lining is related with the structure of the tunnel, and this should be included, considered and described.

I can see “The schematic diagram of the shield tunnel model based on ABAQUS finite element software is shown in Fig. 1 and Fig. 2” but a little effort could be done in order to improve the quality and definition of both figures and a description of the soil is really in need. It can be said that properties of the soil don´t affect the result of the calculations.

This section still needs to be improved. The following issues are still unsolved:

· To obtain reliable numerical solutions to the problems considered in this paper, the size of the grid spacing should be explained and taken into account.

· The inaccuracy caused by a too coarse mesh may lead to wrong conclusions.

The pressure on the lining at different depths should be included, in order to be compared with the damage

Section 4: Conclusions

It is said that with the increase of loading times, the accumulated damage value of lining located at the arch foot and the arch waist of the tunnel shows an increasing trend. This assertion should be related with the pressure in those points, and the depth of the tunnel.

The corresponding tunnel structure with smaller buried depth has a longer service life, this assertion is so obvious that should be improved.

Final Conclusion

After a thorough review of the work, I have to say most of the questions addressed have been solved, but there are a couple of things still unsolved as mentioned above. I encourage its authors to include all recommended improvements.

Author Response

Reply to Reviewer 2’ Comments

(Letters C & R denote comment and reply respectively)

C1: Section 3: Calculation Results

This section still needs to be improved. The following issues are still unsolved:

To obtain reliable numerical solutions to the problems considered in this paper, the size of the grid spacing should be explained and taken into account.

The inaccuracy caused by a too coarse mesh may lead to wrong conclusions.

The pressure on the lining at different depths should be included, in order to be compared with the damage

R1: Thank you for your suggestion, the author revised the article for grid division, soil description and other issues.

In a silty sand layer, the inner diameter of the shield tunnel is 6m, and the lining thickness is 0.3m. The width of the tunnel track bed is 5.2m, and the maximum thickness is 1.5m. In the tunnel calculation model, the rail section is simplified to a rectangle with a height of 0.2m and a width of 0.11m. In order to explore the influence of tunnel buried depth on tunnel lining damage, two independent shield tunnel models with 15m and 20m buried depth are established respectively. The schematic diagram of the shield tunnel model based on ABAQUS finite element software is shown in Fig. 1 and Fig. 2, and the section perpendicular to the center axis of the tunnel is 50 × 50m square, the length of the model along the axis of the tunnel is 30m, and the horizontal distance between the rail and the axis is 0.7175m. Higher grid accuracy results in lower calculation efficiency and lower accuracy results in large errors in calculation results. In this paper, the mesh type of tunnel soil is Hex (hexahedron) mesh element. The tunnel soil unit adopts C3D8 unit, and the lining unit adopts C3D8RI unit. The specific division method is as follows: 40 seeds are evenly distributed on the tunnel circle with a diameter of 6m; On a square around the tunnel with the tunnel center as the center of the quad-rangle, 20 seeds are distributed on each side. The closer to the tunnel center, the denser the seeds are distributed. The other positions are distributed with the unit precision of 1m side length. 75 seeds are evenly distributed along the length of the tunnel to divide the grid. In the coupled dynamic finite element model, the formation is simplified as an isotropic, homogeneous elastic medium. The Mohr-Coulomb model is used for the soil mass of the tunnel. The soil mass with a density of 1860kg/m3, and the elastic modulus is 20MPa. The internal friction angle, cohesion and Poisson ratio of soils are 30 degrees, 0 kPa and 0.27 respectively. The influence of soil parameters on tunnel structure is small and does not affect the calculation results. C50 concrete damage model (CDP model) is used for lining and ballast of tunnel in calculation model. The rail adopts an elastic model with a density of 7850kg/m3, and the elastic modulus is 210GPa. Poisson ratio of rails is 0.25. Friction coefficient between tunnel and soil is 0.55. The viscoelastic boundary is applied at the truncated boundary to eliminate the reflection effect of the boundary on the incident wave. Load application is achieved by writing DLOAD sub-program. The subprogram is used to simulate the long-term effects of train loads during calculation.

C2: Section 4: Conclusions

The corresponding tunnel structure with smaller buried depth has a longer service life, this assertion is so obvious that should be improved.

R2: Thank you for your suggestion, according to the suggestions made by the reviewers, the author has revised the conclusion of the article.

“When the buried depth and load of the tunnel are fixed, the cumulative damage value of the lining at the arch foot and the arch waist of the tunnel increases with the increase of loading times, and the accumulated damage growth rate of the lining at the arch foot is the highest. Damage to tunnel lining at arch foot occurs when loading times reach 1.16 million;

Under the same loading conditions, the cumulative damage of the tunnel lining is proportional to the buried depth of the tunnel. Under the action of train load, the accumulated damage of tunnel lining decreases continuously as the buried depth of tunnel decreases. For deeply buried tunnels, the number of routine tunnel inspections and maintenance should be increased to ensure the normal and safe operation of the tunnel.”

Reviewer 3 Report

Thank you for your improving. The Reviewer has still concern to this paper:

"C5:How numerical model was verified?

What is mean general rules? Please explain and add this aspect in the text.

In addition, please improved the references, because in my opinion are still poor.

Finally, I hope that my suggestions were really helpful for Authors.

Author Response

Reply to Reviewer 3’ Comments

(Letters C & R denote comment and reply respectively)

"C5:How numerical model was verified?

C: What is mean general rules? Please explain and add this aspect in the text.

In addition, please improved the references, because in my opinion are still poor.

Finally, I hope that my suggestions were really helpful for Authors.

R: Thank you for your suggestion, the "general rule" here refers to the calculation result obtained by the author that "the lining damage mainly occurs at the arch foot under train load" is consistent with the result obtained by other scholars. The author has revised the references in the article, deleted some documents that have been published for a long time, and added some relevant documents in recent years.

3.Liu, H., Liu, H., Zhang, Y., Zou, Y., & Yu, X. Coupling effects of surface building and earthquake loading on in-service shield tunnels. Transportation Geotechnics, (2021), 26, 100453.

7.Cheng X, Zhou X, Liu H, et al. Numerical analysis and shaking table test of seismic response of tunnel in a loess soil con-sidering rainfall and traffic load. Rock Mechanics and Rock Engineering, 2021, 54(3): 1005-1025.

10.Zhang, J., Yan, Q., Yang, K., & Sun, M. Experimental modeling of adjacent parallel shield tunnels subjected to train-induced vibration loads. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 235(9), (2021).1132-1142.

11.Sekiya, H., Masuda, K., Nagakura, S., & Inuzuka, S. Determination of shield tunnel deformation under train load using MEMS accelerometers. Tunnelling and Underground Space Technology, (2022), 126, 104535.