Fatigue Performance of Tunnel Invert in Newly Designed Heavy Haul Railway Tunnel
Round 1
Reviewer 1 Report
The paper describes fatigue tests and fatigue assessment of a tunnel segment. Revision is necessary to improve the quality and clarity:
1. The title is misleading. Which mechanical characteristics are subject of the paper, except for listing some data? Also, the fatigue performance of simplified elements is investigated, not necessarily representing the real fatigue behavior of the tunnel itself.
2. What is meant with 'disease'? Do you mean damage?
3. Line 25: Do you really mean 2 metres?
4. Line 46: Explain Vc!
5. Line 60: How can a boundary become 2.5 MPa? Do you mean pressure?
6. Fig. 2 and Table 1: Where is 'flexible cushion'?
7. Table 6: The unit for density is wrong (mass/volume).
8. Eq. (1): Explain t.
9. Fig. 5 is vertically compressed (distorted)!
10. Fig. 6 is rather difficult to understand. No. 1 does not look like a spring. Is the specimen subjected to 3-point bending in addition to a horizontal force? Improve the drawing and explain better!
11. Where are rectangular and cube specimens used? Fig. 6 seems to show only a rectangular specimen. Explain better!
12. Line 139: Delta_S is usually called 'load/stress range', not 'level'.
13. Fig. 7: The notations differ from the equations given. Harmonize!
14. Table 6 is not understood. Why are two values for dynamic loads given in the lower part? Shouldn't it be 'predominantly static loading'?
15. Eq. (6): A graphical representation would be very helpful (S-N line). What is R? It is usually used for stress ratio in fatigue analyses!
The English grammar and wording are very poor. Dozens of elementary errors occur regarding singular or plural of verbs, which cannot be all listed here. The involvement of an interpreter or native speaker is madatory! Further typos observed by the reviewer:
- Line 2: near past => recent past. believe => have believed.
- General remark: Always insert spaces before brackets! Also insert spaces before and after '-' in line 14 and elsewhere when used.
- Line 18: Through => through.
- Line 20: Liu N. => Liu.
- Line 87: safty => safety.
- Line 97: strss => stress.
- Line 102: large relatively => relatively large.
- Line 106 & others: high static low dynamic => high static and low dynamic.
- Line 185: Strange symbols in line.
- Line 189: far greater => far longer.
- Line 194 & others: broken => fracture.
Author Response
The expert reviews the manuscript very carefully. Thank you very much for your professional opinions and timely review. Your suggestions are very helpful
Which mechanical characteristics are subject of the paper, except for listing some data? Also, the fatigue performance of simplified elements is investigated, not necessarily representing the real fatigue behavior of the tunnel itself.
Thanks for the helpful advices. The main purpose of this article is to study the fatigue performance of the tunnel invert, and the numerical simulation is used to identify the actual stress state of the tunnel invert, and served for the fatigue test. So the following title may be more suitable.
“Fatigue Performance of Tunnel Invert in Newly Designed Heavy Haul Railway Tunnel”
What is meant with 'disease'? Do you mean damage?
Yes, “disease” means damage, which will lead to obvious defect and affect the operation safety of the railway, such as structure fracture, rising soil, subsidence.
Line 25: Do you really mean 2 metres?
Yes, that’s right. The original is: “The width of the base void has a significant effect on the fatigue life of the structure of heavy - haul railway tunnels. Based on the operation requirement of 100-year service life, the ultimate void width is 2m.”
Line 46: Explain Vc!
According to the Chinese standard - Code for design of railway tunnel (TB10003-2016), Vc represent a kind of weak surrounding rock grade which based on the BQ (basic quality) rock classification method, Grade I is the best, Grade VI is the worst, Grade V: BQ (basic quality) ≤ 250.
Line 60: How can a boundary become 2.5 MPa? Do you mean pressure?
The boundary unit of normal stiffness has been modified, It should be .
Fig. 2 and Table 1: Where is 'flexible cushion'?
Flexible cushion lies between track plate and foundation plate (Figure 4).
Table 6: The unit for density is wrong (mass/volume).
Helpful advice. The original unit is usually used in soil mechanics, and the international unit is more suitable for concrete materials. Based on the SI system, the unit for density has been changed into kg/m3.
Eq. (1): Explain t.
In the numerical model, t represents the running time of the train in the model, that means the contact point between wheel and track is different at different t.
Fig. 5 is vertically compressed (distorted)!
The distortion in Fig. 5 has been corrected.
Fig. 6 is rather difficult to understand. No. 1 does not look like a spring. Is the specimen subjected to 3-point bending in addition to a horizontal force? Improve the drawing and explain better!
Yes, No.1 is a side support, not spring. This error has been corrected. Then further explanations have been added in the paper: The horizontal forces of the specimen is applied by digital hydraulic jacks (No. 3).
Where are rectangular and cube specimens used? Fig. 6 seems to show only a rectangular specimen. Explain better!
The cube specimens are used to reflect the static elastic modulus and compressive strength of C35 concrete, and the rectangular specimens are used to reflect the dynamic elastic modulus and bending strength of C35 concrete.
Line 139: Delta_S is usually called 'load/stress range', not 'level'.
Delta_S is a dimensionless variable, delta_S ranges from 0–1, load range is a dimensional variable. So Delta_S is called dynamic stress/load level.
Fig. 7: The notations differ from the equations given. Harmonize!
The notations in Fig. 7 has been modified.
Table 6 is not understood. Why are two values for dynamic loads given in the lower part? Shouldn't it be 'predominantly static loading'?
It will cause confusion to the readers, and table 6 has been modified.
Eq. (6): A graphical representation would be very helpful (S-N line). What is R? It is usually used for stress ratio in fatigue analyses!
Eq. (6) is a two - parameter fatigue life equation, there is no corresponding S-N curve in 2D plane graph, so two independent S-N curves are drawn in Fig. 11.
R is adjusted R square, not stress ratio, shown in following equation.
where: n is the number of samples, P is the number of variables.
where, is the residual sum of squares, is the total sum of squares.
The English grammar and wording are very poor. Dozens of elementary errors occur regarding singular or plural of verbs, which cannot be all listed here. The involvement of an interpreter or native speaker is madatory! Further typos observed by the reviewer:
- Line 2: near past => recent past. believe => have believed.
- General remark: Always insert spaces before brackets! Also insert spaces before and after '-' in line 14 and elsewhere when used.
- Line 18: Through => through.
- Line 20: Liu N. => Liu.
- Line 87: safty => safety.
- Line 97: strss => stress.
- Line 102: large relatively => relatively large.
- Line 106 & others: high static low dynamic => high static and low dynamic.
- Line 185: Strange symbols in line.
- Line 189: far greater => far longer.
- Line 194 & others: broken => fracture.
Thanks for the reviewer's valuable advice, which is very helpful to improve my writing level. Except the above errors, some other grammatical errors have been corrected after inspection, which are listed as follows:
- base diseases => basal diseases
- Line 36: is suffer => are experiencing.
- Fig.1 => Figure 1.
- Line 167: Simplified => simplified.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
1. I do not understand the layout of the paper. The authors presented the numerical model of the tunnel, but next, they did not show any results from the numerical analysis. The mechanical characteristics are a too small section to indicate as alone. It should be connected with others.
The fatigue testing is conducted separately from the numerical analysis. The authors should clearly indicate the connection between numerical analysis and lab test.
2. Please do not use "he", "we". Please use the passive voice.
3. What does the paper contribute to the knowledge (added value)? It should be clearly incorporated into the last paragraph of the introduction.
4. What is maximum train speed for this railway?
5. The authors used various dimensions in text and Figure 1.
6. The authors should describe what materials were used to construct inverted arch filing, initial and secondary linings, etc.
7. How did the authors model the interaction between tunnel and rock/soil media?
8. Why did the authors use two 30t axle loads? Is it the maximum acceptable load for this railway?
9. The authors should clearly add, how many cyclic loading for fatigue test used?
10. How many concrete specimens for fatigue test were used?
11. Why only two strain gauges were used?
12. There is no Eq. (7).
13. The conclusions should be reorganized.
Author Response
Thanks for the reviewer’s helpful suggestions, it is really important to improve the logic and readability of the paper.
I do not understand the layout of the paper. The authors presented the numerical model of the tunnel, but next, they did not show any results from the numerical analysis. The mechanical characteristics are a too small section to indicate as alone. It should be connected with others.
The fatigue testing is conducted separately from the numerical analysis. The authors should clearly indicate the connection between numerical analysis and lab test.
Yes, it’s really an important opinion. The numerical simulation is served for fatigue tests. Through numerical simulation, the stress state of the most unfavorable position of the tunnel invert is determined. The results of numerical simulation reveal that: Under the action of surrounding rock pressure, the static strain of the most unfavorable positon is 40.3 × 10-6, and its dynamic strain which caused by train load is 8.3 × 10-6. The strain caused by surrounding rock pressure is far greater than that caused by train load. According to the high static and low dynamic stress state, a set of bending fatigue test system and a series of test conditions were designed to study the fatigue lives of the specimens under different stress states. This connection information has been added to the beginning of Chapter 4.
The main purpose of this article is to study the fatigue performance of the tunnel invert, and the mechanical characteristics are a too small section which are served for tests, so the title has been changed to “Fatigue Performance of Tunnel Invert in Newly Designed Heavy Haul Railway Tunnel”.
Please do not use "he", "we". Please use the passive voice.
Thanks for the reviewer’s professional suggestion. After careful checks, the unprofessional language has been corrected.
Such as line 2: he found => the tests results reveal that
Modified sentence: and the tests results reveal that the floor is still intact after 6 million cycles.
Line 28: As we all know => Meanwhile.
What does the paper contribute to the knowledge (added value)? It should be clearly incorporated into the last paragraph of the introduction.
The contribution of this paper has been added to the last paragraph of the introduction. Shown as follows:
In this paper, three-dimensional (3D) numerical simulation and three-point bending fatigue tests were combined to investigate the fatigue performance of tunnel bottom structures along the new line. The stress state of the most unfavorable position of the tunnel invert was determined using numerical simulation, and the static stress caused by the surrounding rock pressure and the dynamic stress caused by the train were identified. Then, the fatigue test condition was designed according to the stress state of the most unfavorable position to identify the fatigue lives of the specimens under different stress states. This paper studied the fatigue performance of a heavy haul railway tunnel under the action of high surrounding rock pressure and large axle load train, and provide a reference for the durability design of heavy haul railway tunnel structures.
What is maximum train speed for this railway?
The maximum design speed is 120 km / h.
The authors used various dimensions in text and Figure 1.
The units in Fig. 1 and Fig.4 have all been changed to cm.
The authors should describe what materials were used to construct inverted arch filing, initial and secondary linings, etc.
C25 concrete is used for invert arch filling, C25 shotcrete is used for initial support, C35 concrete is used for secondary lining. (Figure 1 and Table 1)
How did the authors model the interaction between tunnel and rock/soil media?
Tie constraints are used to simulate the interaction between initial support and surrounding rock.
Why did the authors use two 30t axle loads? Is it the maximum acceptable load for this railway?
The design axle load of Haoji heavy haul railway is 30 t, which means that the design goal is to ensure that the structure does not need major repair within 100 years. The railway’s short-term bearing capacity exceeds 30 t.
On one hand, when a whole train passes through, the tunnel base structure is mainly impacted by two types of dynamic impact: The first and last wheel sets of the train are separate wheel sets impact, while all carriages in the middle are impacted by Bogies (two sets of adjacent wheel sets).
On the other, limited by computing power and model accuracy, therefore, the two 30 t axle load carriages are used to simulate the dynamic impact of the train, which includes the above two kinds of dynamic impact.
The authors should clearly add, how many cyclic loading for fatigue test used?
The accurate fatigue lives of the tests are listed in Table 9.
How many concrete specimens for fatigue test were used?
The bending fatigue test in this paper has 8 test conditions, and each condition contains 3 tests, so the total cost of fatigue test is 24 specimens.
Why only two strain gauges were used?
Because in the three-point bending test, the maximum tensile strain is at the bottom of the mid span section of the specimen, and the maximum compressive strain is at the top of the mid span section of the specimen.
There is no Eq. (7).
Yes, it should be Eq. (6).
The conclusions should be reorganized.
The conclusions have been reorganized, shown in follows:
The top center is the fatigue vulnerable position in the tunnel invert of the new line which suffering high static and low dynamic stresses. Its static maximum principal strain is 40.3 × 10-6 which is caused by surrounding rock pressure, while the dynamic maximum principal strain caused by train load is 8.3 × 10-6. The tests results reveal that the fatigue life decreasing as dynamic load and static load increasing. Combined with the expression of the two-parameter S-N, an evolution model is proposed to character the fatigue behavior of the tunnel invert specimens. For the new line’s tunnel invert, fatigue failure would not occur within 2 million cycles. If invert fracture emerged in the design service life, the main reason can be attributed to geological reasons or the bedrock defects, rather than fatigue failure caused by dynamic train load.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors have thoroughly revised the paper resulting in much-improved English and in consideration of most of the reviewer's comments.
Some minor remarks:
Fig. 6 is still difficult to understand. Mentioning of 'combination of 3-point bending and axial loading' in the text would help much. Table 6 is still puzzling. The reviewer thinks that 'constant loads' and 'static loads' in the same heading are the same. And why is the dynamic load a constant load? Please clarify! Fig. 11, which improves the clarity of the paper, shows an S-N diagram with linear vertical axis. Usual is logarithmic scale to obtain a straight S-N line. Is this usual for concrete? Line 77: boogie => bogie. Line 109: are => is. Line 132: ad => and. In some cases present tense instead of past would be appropriate. E.g. in the last paragraph of the Introduction (maybe you should start with 'In the investigation described in this paper'; last sentence: This paper studies ...) and in Line 98 (focused => focuses).Author Response
Thanks for the reviewer’s efficient and professional review. The reviewer is really responsible.
Fig. 6 is still difficult to understand. Mentioning of 'combination of 3-point bending and axial loading' in the text would help much.The second paragraph of chapter 4.1 has been modified as follows:
The bilateral horizontal forces of the specimen were applied using digital hydraulic jacks (No. 3 in Figure 6); the vertical load of the specimen was applied using MTS815 (No. 4 in Figure 6).
Table 6 is still puzzling. The reviewer thinks that 'constant loads' and 'static loads' in the same heading are the same. And why is the dynamic load a constant load? Please clarify!
Bilateral loads in all test conditions are 1.5 kN to reflect the horizontal confinement of the tunnel invert specimens;
In dynamic load conditions (case 1–4): The static loads are the same represent the tunnel is under the same surrounding rock pressure, the dynamic loads are different to investigate the influence of different axle load train.
In static load conditions (case 5–8): The dynamic loads are the same represent the tunnel is under the action of the same axle load train, the static loads are different to study the influence of different pressure of surrounding rock.
Fig. 11, which improves the clarity of the paper, shows an S-N diagram with linear vertical axis. Usual is logarithmic scale to obtain a straight S-N line. Is this usual for concrete?
Yes, the straight S-lgN line and expression are often used to characterize the fatigue performance of concrete.
Line 77: boogie => bogie.
Line 109: are => is.
Line 132: ad => and.
In some cases present tense instead of past would be appropriate. E.g. in the last paragraph of the Introduction (maybe you should start with 'In the investigation described in this paper'; last sentence: This paper studies ...) and in Line 98 (focused => focuses).
The errors have been corrected.
Reviewer 2 Report
The paper revision is well done. I recommend to publish the revised version of the paper.
Author Response
Reviewer 2 has no comments.
