Improved Theoretical Solutions for Estimating the Tunnel Response Induced by Overlying Excavation

Round 1

Reviewer 1 Report

This manuscript developed a new theoretical method for evaluating the tunnel response induced by overlying deep excavation. The paper is well written and well structured. The work contains interesting information and a worthy subject of investigation, with good contributions to the advancement in the study of estimating the influence of excavation on adjacent tunnel. This is an interesting work and the topic is also important for engineering practice. Thus, I suggest that the manuscript can be accepted for publication after the following comments are well addressed:

1.      Line 17-18: “The existing tunnel is idealized as an infinite beam resting on a three parameter Kerr-model…” What is reason of this hypothesis? This rationality needs to be explained. Meanwhile, please articulate the novelty of this manuscript.

2.      Line 60: “Although Pasternak-model and Vlazov-model…” The Vlazov-model should be corrected as Vlasov-model. Please carefully check the full text line by line about this.

3.      Line 106: When calculating the additional stress caused by adjacent excavation, the authors only consider the influence of foundation pit bottom unloading without the influence of foundation pit sidewall. Could the authors give an explanation about this?

4.      Line 113: “The unloading stress due to excavation is estimated by Mindlin’s formula”. The existing tunnel is not taken into consideration and the reasonableness should be presented.

5.      The authors should double-check the text and make the revisions; for example, the expression of the sentence in the section 3.2 in line 247 “... Fig. 7 indicates that the calculated results given by this study are closer to FEM results and the field measurements, and the rationality of this study is verified.” is complex.

6.      The conclusion part is supposed to point out the shortcomings of this study. Could the authors give some suggestion for future investigation?

7.      The reference in this paper should be double-check.

Author Response

This manuscript developed a new theoretical method for evaluating the tunnel response induced by overlying deep excavation. The paper is well written and well structured. The work contains interesting information and a worthy subject of investigation, with good contributions to the advancement in the study of estimating the influence of excavation on adjacent tunnel. This is an interesting work and the topic is also important for engineering practice. Thus, I suggest that the manuscript can be accepted for publication after the following comments are well addressed:

 

1. Line 17-18: “The existing tunnel is idealized as an infinite beam resting on a three parameter Kerr-model…” What is reason of this hypothesis? This rationality needs to be explained. Meanwhile, please articulate the novelty of this manuscript.

Response: Thank you for your suggestion. The explanation and innovation of the article have been refined in line 17: The shield tunnel is idealized as an infinite beam lying upon a three parameter Kerr-model and the vertical force equilibrium equation of tunnel element is established. Then the unloading stress along the tunnel is transferred as Fourier cosine series a theoretical solution is derived for capturing the soil-tunnel interaction subsequently.

 

2. Line 60: “Although Pasternak-model and Vlazov-model…” The Vlazov-model should be corrected as Vlasov-model. Please carefully check the full text line by line about this.

Response: Thank you for your suggestion. The Vlazov-model is corrected as Vlasov-model in all paper.

3. Line 106: When calculating the additional stress caused by adjacent excavation, the authors only consider the influence of foundation pit bottom unloading without the influence of foundation pit sidewall. Could the authors give an explanation about this?

Response: Thank you for your suggestion. Some explanations are added in line 98: According to the theory of Mindlin's formula [22] and the existing literature [19-21], the unloading stress q (x) along the tunnel is mainly induced by the unloading load at the excavation bottom, they can be described as below:

 

4. Line 113: “The unloading stress due to excavation is estimated by Mindlin’s formula”. The existing tunnel is not taken into consideration and the reasonableness should be presented.

Response: Thank you for your suggestion. Some explanations are added in line 115: ignoring the influence of the existing tunnel.

 

5. The authors should double-check the text and make the revisions; for example, the expression of the sentence in the section 3.2 in line 247 “... Fig. 7 indicates that the calculated results given by this study are closer to FEM results and the field measurements, and the rationality of this study is verified.” is complex.

Response: Thank you for your suggestion. This sentence is exchanged by in line 249: In general, Fig. 7 indicates that the calculated results given by this study are closer to FEM results and the field measurements. Therefore, the rationality of this study is verified.  

 

6. The conclusion part is supposed to point out the shortcomings of this study. Could the authors give some suggestion for future investigation?

Response: Thank you for your suggestion.According to your opinions, we add explanations in revision in conclusion in line 377: This improved theoretical solution cannot consider local separation in tunnel-soil interaction. The influence of ground water and the variation of soil properties are also ignored. These shortcomings will be taken more account in future studies.

 

7.The reference in this paper should be double-check.

Response: Thank you for your suggestion.According to your opinions, all reference in this paper is double-check.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments for author File: Comments.pdf

Author Response

Response: Thank you for your suggestion. The sentence marked by expert is rewritten as below:

1. The title is written as: Improved theoretical solutions for estimating the tunnel response induced by overlying excavation.
2. In line 25: the sentence is rewritten as: Results indicate that the increase in the bending stiffness and buried depth of tunnel, as well as the tunnel-excavation horizontal distance will significantly alleviate the tunnel deformation.
3. In line 39: the sentence is written as：and the safety and serviceability of existing tunnel would be threaten.
4. In line 353: The conclusion part is in a page.

Reviewer 3 Report

Title: Improved theoretical solution to estimate the tunnel response due to overlying deep excavation

Manuscript ID: sustainability-2121232

This study devotes to develop a theoretical solution to estimate the effect of overlying excavation on tunnel response. The existing tunnel is idealized as a Euler-Bernoulli beam lying on infinite beam. The accuracy of this study is proved by an existing finite element method and a field measurement. Then, parametric analysis is conducted to investigate the effect on the existing tunnel. The research topic is meaningful in the practical engineering. In general, I found the work interesting and thorough, and the analysis and discussion are well thought out. I would recommend this manuscript to be published with minor revisions:

1) Page 3: The bottom of the existing tunnel is parallel to the bottom of the excavation pit, this should be indicated in the basic assumptions.

2) Page 4: The variables (X, Y) are undefined in Eqs. (2) and (3), the relation between the two coordinates, (X, Y) and (x, y), are not clear, it is recommended to show it with graph.

3) Page 4: ‘B’ should be ‘D’ in Fig. 2.

4) Page 5: ‘M’ is defined repeatedly. ‘dx’ should be the tunnel element length, and ‘D’ should be ‘dx’ in Fig. 3.

5) Page 6 line 152: ‘Fig. 1’ should be ‘Fig. 2’, ‘Eq. (4)’ should be ‘Eq. (1)’.

6) Page 8: Only one case is presented to verified the theoretical model with the existing FEM model, it is necessary to give more verification cases to prove the model’s robustness.

7) Variables of ‘w’ and ‘w’ in the equations and the text should be unified.

8) The language of the paper is not understandable in some places. For example, I do not understand what is written at line 153 "Two ends of can be idealized as are free because of the infinity of tunnel." Please check through thoroughly to ensure all the English expression are correct.

Author Response

This study devotes to develop a theoretical solution to estimate the effect of overlying excavation on tunnel response. The existing tunnel is idealized as a Euler-Bernoulli beam lying on infinite beam. The accuracy of this study is proved by an existing finite element method and a field measurement. Then, parametric analysis is conducted to investigate the effect on the existing tunnel. The research topic is meaningful in the practical engineering. In general, I found the work interesting and thorough, and the analysis and discussion are well thought out. I would recommend this manuscript to be published with minor revisions:

 

1) Page 3: The bottom of the existing tunnel is parallel to the bottom of the excavation pit, this should be indicated in the basic assumptions.

Response: Thank you for your attention. In this paper, the existing tunnel is not parallel to the bottom of the excavation pit, and the solution is solved by substituting Eq. (3) into Eq. (1).

 

2）Page 4: The variables (X, Y) are undefined in Eqs. (2) and (3), the relation between the two coordinates, (X, Y) and (x, y), are not clear, it is recommended to show it with graph.

Response: Thank you for your attention. In this paper, The variables (X, Y) is transition coordinate system, in which taking the relationship between two coordinate system, thank you for your suggestion.

 

3) Page 4: ‘B’ should be ‘D’ in Fig. 2.

Response: Thank you for your attention. B is rewritten as D.

 

4) Page 5: ‘M’ is defined repeatedly. ‘dx’ should be the tunnel element length, and ‘D’ should be ‘dx’ in Fig. 3.

Response: Thank you for your attention. According to your opinions, M is bending moment of the tunnel. dx is the tunnel element length. However, D is also the diameter of tunnel.

 

 

5) Page 6 line 152: ‘Fig. 1’ should be ‘Fig. 2’, ‘Eq. (4)’ should be ‘Eq. (1)’.

Response: Thank you for your attention. According to your opinions, Fig. 1 is rewritten as Fig. 2, Eq. (4) is rewritten as Eq. (1).

 

6) Page 8: Only one case is presented to verified the theoretical model with the existing FEM model, it is necessary to give more verification cases to prove the model’s robustness.

Response: Thank you for your suggestion. In this paper, a field measurement in Shanghai, and the results from a finite element study are collected here to compare with the calculation results given by this study. Based on this, the efficacy of this study is verified. This method of verifying the rationality of the proposed method is often used in existing literature, such as existing literature [19-21]. And we will take this suggestion in the future investigations.

 

7) Variables of ‘w’ and ‘w’ in the equations and the text should be unified.

Response: Thank you for your attention. w in the equations and the text is corrected by rulers in this magazine.

 

• The language of the paper is not understandable in some places. For example, I do not understand what is written at line 153 "Two ends of can be idealized as are free because of the infinity of tunnel." Please check through thoroughly to ensure all the English expression are correct.

Response: Thank you for your attention. This sentence is written as :Two ends of tunnel can be idealized as are free because of the assumption of the infinity of tunnel. The English expression in this paper is double-checked. Thank you for your suggestion.

Author Response File: Author Response.pdf