Study on the Mechanical Characteristics of the Sleeper Slab Track on a Long-Span Steel Truss Bridge

Round 1

Reviewer 1 Report

The manuscript can be published after major revised.

I believe that the manuscript should be revised using the following points:

1) High-speed railway is not used in the abstract and the number of this phrase in the manuscript is very low, so, it is not a keyword and should be delete.

2) The English language of the article is very good and clear. But it needs to be revised in terms of grammar and writing.

3) In page 2 and line 3, the phrase "Ys Cheng et al" should change to "Ys Cheng". The Reference [1] has one author.

4) In page 2 and line 7, the phrase "Ping Lou et al" should change to "Ping Lou et al."

5) In general, from a grammatical point of view, you should put a dot after "et al" and only the surname of the first author should be written in the text and its first name should be removed. For example, "Podwmna M et al" should change to "Podwmna et al.".

6) please show the different components on the Figures 1 and 2.

7) I believe that the fatigue is a fracture by initiation and propagation crack under cyclic loading. so, do you study the crack initiation and propagation? I strongly recommend to write only sine cyclic loading and delete the phrase "fatigue".

8) In page 11, it is stated that "continuous increase in the fatigue loading numbers resultes in a gradual decrease in the displacement.", examine and rewrite the meaning of the sentence.

9) In figure 7, why the displacement increase in the fatigue loading cycle numbers of 1 million and decrease on the other cases? Describe the reason physically.

10) In figure 8, why the measurement of 1 million is less than 0 and 2 million cycles.

11) In section 3.3.1, it means that after 3 million load cycle numbers, the displacement decreases? is it true that by applying fatigue load cycle numbers, the strength raises?

12) In section 3.4, how do you check the damage in the component? what is the criteria for damage identification? how do you inspect the crack?

13) What is your purpose to show the figure 10? The details are not clear?

14) How do you calculate the stress in the test? it is stated that displacement and strain sensors installed on the component. But, the difference between experiment and analysis results is reported about 17.93% in the section 4.2.1.

15) Details of simulation should be described as type of element, element size, boundary conditions, loading, different steps, type of analysis etc.

16) In figures 11, 12, and 13, the numbers are not clear and not proper for publication.

17) it is clear that the mechanical properties of the material decreases by applying fatigue load cyclic numbers, but, some achievements of this research are contrary to this fact. So, it is necessary to describe more about this matter.

Author Response

A point-by-point reply to Reviewer #1

We wish to thank you immensely for the painstaking efforts towards reviewing our manuscript. We really find the comments valuable to improving the manuscript. The comments and our responses are as follows.

Comments for the author

The manuscript can be published after major revised.

I believe that the manuscript should be revised using the following points:

1. High-speed railway is not used in the abstract and the number of this phrase in the manuscript is very low, so, it is not a keyword and should be delete.

Response: The words “High-speed railway” in keywords have been deleted.

2. The English language of the article is very good and clear. But it needs to be revised in terms of grammar and writing.

Response: The revised manuscript has undergone English language editing by MDPI. The text has been checked for correct use of grammar and common technical terms, and edited to a level suitable for reporting research in a scholarly journal.

3. In page 2 and line 3, the phrase "Ys Cheng et al" should change to "Ys Cheng". The Reference [1] has one author.

Response: There are three authors in Reference [1], namely, Y.S. Cheng, F.T.K. Au, and Y.K. Cheung.

4. In page 2 and line 7, the phrase "Ping Lou et al" should change to "Ping Lou et al.".

Response: Similar errors have been corrected in the full text.

5. In general, from a grammatical point of view, you should put a dot after "et al" and only the surname of the first author should be written in the text and its first name should be removed. For example, "Podwmna M et al" should change to "Podwmna et al.".

Response: Similar errors have been corrected in the full text.

6. Please show the different components on the Figures 1 and 2.

Response: Annotations have been added to Figures 1 and 2.

7. I believe that the fatigue is a fracture by initiation and propagation crack under cyclic loading. so, do you study the crack initiation and propagation? I strongly recommend to write only sine cyclic loading and delete the phrase "fatigue".

Response: The words “fatigue loading” have been replaced by “sine cyclic loading”. There was no obvious crack in the sleeper slab track structure after 3 million times of cyclic loading. In this research, the inspection fatigue test was carried out. The purpose was to investigate the variation of mechanical properties of the structures and materials under specified loads and cyclic numbers. The authors think that the fatigue is still one of the main contents in this research.

8. In page 11, it is stated that "continuous increase in the fatigue loading numbers results in a gradual decrease in the displacement.", examine and rewrite the meaning of the sentence.

Response: In lines 361-364, the sentence "continuous increase in the fatigue loading numbers result in a gradual decrease in the displacement." has been replaced by “with the growth of the sine cyclic loading numbers, the stiffness of the rubber fulcrum increased gradually. Consequently, the displacement of the whole steel beam began to decrease.” In order to describe the deformation trend of the steel beam in more detail, the contents in lines 356-376 have been rewritten.

9. In figure 7, why the displacement increased in the fatigue loading cycle numbers of 1 million and decreased on the other cases? Describe the reason physically.

Response: In the revised manuscript, the title “Figure 7” has been replaced by “Figure 10”. According to Figure 10, the displacement of the rail relative to the sleeper slab decreased during the loading process of 1 million times. Before the cyclic loading, the contact between the rail and fastener system was not tight enough. This resulted in large displacement of the rail under the vertical load of 625kN. Under the action of cyclic loading, the loose state was eliminated rapidly, and the displacement of the rail after 1 million times of sine cyclic loading was less than before. Moreover, the loading position was in the middle of the two fasteners, which is the most unfavorable position as discussed by Gao et al. [1]. When the vertical load was applied on the rail, because of its bending stiffness, the force at the front and end of the fasteners was not consistent, and the pad was not in uniform force. As a result, only part of the nominal contact area was effective, which led to the reduction in fastener supporting stiffness. The above discussion is similar to the research studied by Chen et al. as shown in Figure 1 [2]. With the growth of the sine cyclic loading numbers, the rail displacement increased gradually. This result may be explained by the fact that the reduction in the fastener clamping force and the supporting stiffness occurred under the action of cyclic loading.

The displacement variation of the sleeper slab is also described in Figure 10. As the sleeper slab, self-compacting concrete cushion, and steel beam are not a whole and there is the certain gap between the above components, the displacement of the sleeper slab relative to the steel beam had an increase during the initial 1 million loading cycles. With the gradual compaction between the components of the track structure, the relative displacement of the sleeper slab gradually decreased and tended to be stable in the later stage of the test.

1. Gao, L.; Zhao, W.; Hou, B. Research on vertical mechanical behavior of WJ-8 fastener under clamping force failure (in Chinese). Engineering Mechanics 2020, 37(11), 228-237.
2. Chen, Z.; Andrawes, B. A mechanistic model of lateral rail head deflection based on fastening system parameters. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 2017, 231, 999-1014.
3. In figure 8, why the measurement of 1 million is less than 0 and 2 million cycles.

Response: In the revised manuscript, the title “Figure 8” has been replaced by “Figure 11”. During the sine cyclic loading process, the deformation trend of the steel beam relative to the ground is shown in Figure 11. The displacement of the steel beam first increased and then decreased. A possible explanation for this might be that the track components did not have tight contact at the initial time and the structural integrity was not in the best condition, which led to the increase in the steel beam displacement after 1 million times of sine cyclic loading. After that, with the growth of the sine cyclic loading numbers, the stiffness of the rubber fulcrum increased gradually. Consequently, the displacement of the whole steel beam began to decrease. What can be clearly seen in Figure 11 is that the deformation law of the steel beam is almost the same during the loading process.

11. In section 3.3.1, it means that after 3 million load cycle numbers, the displacement decreases? is it true that by applying fatigue load cycle numbers, the strength raises?

Response: Section 3.3.1 mainly discussed the longitudinal resistance test and its results. The maximum longitudinal displacement of the sleeper slab under different sine cyclic loading numbers is shown in Table 4. After 3 million times of sine cyclic loading, the longitudinal displacement increased by 85%. The displacement of the sleeper slab increased obviously, which means that the longitudinal resistance of the sleeper slab had a decrease. When the sine cyclic loading number varied from 2 million to 3 million, the change rate of the longitudinal displacement was only 2%. During this cyclic loading process, the displacement varied slightly. It means that the longitudinal resistance of the sleeper slab remained stable.

Table 4. Maximum longitudinal displacement of sleeper slab (relative steel beam).

12. 1 In section 3.4, how do you check the damage in the component? what is the criteria for damage identification? how do you inspect the crack?

Response: Firstly, the transverse failure test was carried out on the sleeper slab, and the transverse thrust was continuously increased. At the same time, the transverse displacement of the sleeper slab was recorded to form a load-displacement curve. When the thrust was added to a certain value, the transverse displacement of the sleeper slab increased sharply, which indicated that the transverse failure occurred. Record the thrust value at this time as the transverse resistance limit of the structure. The longitudinal failure test is the same as the transverse failure test. In the horizontal failure test, the status of the structure components was observed, and the failure modes were recorded. The crack was observed by the combination of visual inspection and crack observation instrument.

13. What is your purpose to show the figure 10? The details are not clear?

Response: The function of Figure 10 in the original manuscript was to show a three-dimensional finite element model of the sleeper slab track structure. In the revised manuscript, Figure 10 has been deleted. The main purposes of the current research were to verify the applicability of the sleeper slab track on the long-span steel truss bridge and to investigate the mechanical characteristics during the fatigue process with an experimental method. The finite element model established in Chapter 4 was simplified to some extent, which is different from the actual working condition and cannot effectively represent the working status of the structure. The finite element model needs to be considered in more detail. Therefore, the authors decided to delete Chapter 4 without affecting the main content of the article. After this paper, further work about the finite element model will be done, considering the reviewers' suggestions.

14. How do you calculate the stress in the test? it is stated that displacement and strain sensors installed on the component. But, the difference between experiment and analysis results is reported about 17.93% in the section 4.2.1.

Response: In the revised manuscript, the contents of the concrete stress have been removed, and the results were discussed based on the strain data measured by the strain gauges. The finite element model established in Chapter 4 was simplified to some extent, which is different from the actual working condition and cannot effectively represent the working status of the structure. The finite element model needs to be considered in more detail. Therefore, the authors decided to delete Chapter 4 without affecting the main content of the article. After this paper, further work about the finite element model will be done, considering the reviewers' suggestions.

15. Details of simulation should be described as type of element, element size, boundary conditions, loading, different steps, type of analysis etc.

Response: In the revised manuscript, the Chapter 4 has been deleted. After this paper, further work about the finite element model will be done, considering the reviewers' suggestions.

16. In figures 11, 12, and 13, the numbers are not clear and not proper for publication.

Response: In the revised manuscript, the Figures 11, 12, and 13 have been deleted. After this paper, further work about the finite element model will be done, considering the reviewers' suggestions.

17. It is clear that the mechanical properties of the material decrease by applying fatigue load cyclic numbers, but, some achievements of this research are contrary to this fact. So, it is necessary to describe more about this matter.

Response: In lines 262-318, lines 328-376, and lines 381-445, the effect of the fatigue load cyclic numbers on the mechanical properties of the structures and materials has been discussed in more detail.

Author Response File: Author Response.doc

Reviewer 2 Report

I am afraid this paper presents quite regular studies. Experimental measurements of such structures, supported by FEM analysis are nothing new. The paper is very well written but it forms a good engineering work only. Research contribution must be shown more precisely and explained before publication in details. I expect from the Authors to highlight an important novelty of their work supported by a comparative study based on published results.

In case I am wrong, maybe the manner of presentation is just improper. Thus let's give a chance to improve the paper or provide a good rebuttal.

Author Response

A point-by-point reply to Reviewer #2

We wish to thank you immensely for the painstaking efforts towards reviewing our manuscript. We really find the comments valuable to improving the manuscript. The comments and our responses are as follows.

Comments for the author

I am afraid this paper presents quite regular studies. Experimental measurements of such structures, supported by FEM analysis are nothing new. The paper is very well written but it forms a good engineering work only. Research contribution must be shown more precisely and explained before publication in details. I expect from the Authors to highlight an important novelty of their work supported by a comparative study based on published results.

In case I am wrong, maybe the manner of presentation is just improper. Thus, let's give a chance to improve the paper or provide a good rebuttal.

Response: In the revised manuscript, the effect of the fatigue load cyclic numbers on the mechanical properties of the structures and materials has been discussed in more detail. The research contribution has been shown more precisely in the Conclusions. The novelty of this research is that it uses a new type of sleeper slab track structure as the research subject, which is rarely mentioned in previous studies. This track structure is planned to be applied to the long-span steel truss bridge to overcome the weaknesses of the traditional track structure on the open deck, such as poor integrity, difficult sustenance of track geometry, and heavy maintenance work. The sleeper slab track structure was designed by the authors and their departments. At present, there may be few researches on it, and its mechanical properties and fatigue performance are not clear. Therefore, the full-scale laboratory tests were carried out by authors. The fatigue test can simulate the long-term effect of cyclic train load, thereby allowing researchers to understand the fatigue performance of structures and materials in a short time. The horizontal resistance test can evaluate the horizontal bearing capacity of the sleeper slab track structure, which is very important for the track structure on the bridge. The experimental work can provide new insights into the track selection of the long-span steel truss bridge.

The finite element model established in Chapter 4 is simplified to some extent, which is different from the actual working condition and cannot effectively represent the working state of the structure. The finite element model needs to be considered in more detail. Therefore, the authors decided to delete Chapter 4 without affecting the main content of the article. After this paper, further work about the finite element model would be done considering the reviewers' suggestions. Future work to be performed by the authors will be focused on the precise numerical simulation of the track structure.

Author Response File: Author Response.doc

Reviewer 3 Report

The paper concerns a new type of sleeper-slab tracks. The Authors proposed a new modular system, in which sleepers are integrated with a track slab. The system is dedicated to be used in bridge engineering. Results of extensive experimental strength testing and numerical modelling were presented within the paper. The performed test required a lot of effort and can be interesting to other researchers. However, a form of results presentation is quite confusing and some interpretations are not clear enough. I have listed my main doubts. 

• The manuscript need an extensive language editing, the English is rather poor. 
• The quality of figures is poor also. E.g. some descriptions are very big and distorted, which does not look decent. The screenshot from Abaqus are very poor - the resolution is very low, legends are not visible. One can generate high quality screen shots using Abaqus (in vector or raster graphics). This system enables modification of legend style also.
• The introduction section is quite hard to follow, since the comments on other research are mixed with opinions of the authors. 
• It is not clear how the load was applied to the system in the tests with horizontal loading. 
• Was strength of concrete in the slab and in the cushion tested using small probes (cylinders or cubes)?
• In experiment, the strains were measured directly. How were they transformed into stresses? You have to assume constitutive relationship and stress state to make such calculation. Which assumptions were made? Was concrete tested to determine material mechanical parameters (especially Young modulus – the discrepancy between codes provisions and tested values can be significant)? 
• Fig. 7 - This plot is quite surprising, since it is not monotonical. Why the displacement is the biggest after 1 million and, then, it decreased. Could the author comment this trend?
• I think that it is not a good idea to model the rail with a beam elements and the fastening system with springs for the Authors purposes (experiment simulation). Value of the springs stiffness is probably not given in the manuscript. In analysed system the stress state is clearly complex. Moreover, the vicinity of fastening system is an area of stress concentration - it is important to model this part precisely. 
• The Authors compare stresses obtained within experimental test and numerical model. For this purposes, the mesh-dependency studies are very important, since the mesh size influence the values of strains and stresses predicted by the FE model a lot.  

Author Response

A point-by-point reply to Reviewer #3

We wish to thank you immensely for the painstaking efforts towards reviewing our manuscript. We really find the comments valuable to improving the manuscript. The comments and our responses are as follows.

Comments for the author

The paper concerns a new type of sleeper-slab tracks. The Authors proposed a new modular system, in which sleepers are integrated with a track slab. The system is dedicated to be used in bridge engineering. Results of extensive experimental strength testing and numerical modelling were presented within the paper. The performed test required a lot of effort and can be interesting to other researchers. However, a form of results presentation is quite confusing and some interpretations are not clear enough. I have listed my main doubts.

1. The manuscript need an extensive language editing; the English is rather poor.

Response: The revised manuscript has undergone English language editing by MDPI. The text has been checked for correct use of grammar and common technical terms, and edited to a level suitable for reporting research in a scholarly journal.

2. The quality of figures is poor also. E.g. some descriptions are very big and distorted, which does not look decent. The screenshot from Abaqus is very poor – the resolution is very low, legends are not visible. One can generate high quality screen shots using Abaqus (in vector or raster graphics). This system enables modification of legend style also.

Response: The figures have been replaced with the high-quality versions. In lines 262-318, lines 328-376, and lines 381-445, the figures and data have been discussed in more detail.

3. The introduction section is quite hard to follow, since the comments on other research are mixed with opinions of the authors.

Response: In lines 37-129, the introduction section has been rewritten and some new references were cited. The sleeper slab track structure was designed by the authors and their departments. At present, there are few researches on it. In order to make the research subject proposed in this paper understood more comprehensively, the authors summarized the track structure forms applied to the long-span bridges, and then compared the characteristics of several types of track structures. Finally, the advantages of the sleeper slab track structure were highlighted.

4. It is not clear how the load was applied to the system in the tests with horizontal loading.

Response: The horizontal load was applied to the system with the jack and counterforce system as shown in Figure 6.

Figure 6. Loading devices used in horizontal resistance test.

5. Was strength of concrete in the slab and in the cushion tested using small probes (cylinders or cubes)?

Response: Due to the limitation of test conditions, the authors did not test the strength of concrete in the slab and in the cushion with small probes. In the revised manuscript, the contents of the concrete strength have been removed, and the results were discussed based on the strain data measured by the strain gauges.

6. In experiment, the strains were measured directly. How were they transformed into stresses? You have to assume constitutive relationship and stress state to make such calculation. Which assumptions were made? Was concrete tested to determine material mechanical parameters (especially Young modulus – the discrepancy between codes provisions and tested values can be significant)?

Response: Due to the limitation of test conditions, the authors did not test the material mechanical parameters. In the revised manuscript, the contents of the concrete stress have been removed, and the results were discussed based on the strain data measured by the strain gauges.

7. Fig. 7 - This plot is quite surprising, since it is not monotonical. Why the displacement is the biggest after 1 million and, then, it decreased. Could the author comment this trend?

Response: In the revised manuscript, the title “Figure 7” has been replaced by “Figure 10”. According to Figure 10, the displacement of the rail relative to the sleeper slab decreased during the loading process of 1 million times. Before the cyclic loading, the contact between the rail and fastener system was not tight enough. This resulted in large displacement of the rail under the vertical load of 625kN. Under the action of cyclic loading, the loose state was eliminated rapidly, and the displacement of the rail after 1 million times of sine cyclic loading was less than before. Moreover, the loading position was in the middle of the two fasteners, which is the most unfavorable position as discussed by Gao et al. [1]. When the vertical load was applied on the rail, because of its bending stiffness, the force at the front and end of the fasteners was not consistent, and the pad was not in uniform force. As a result, only part of the nominal contact area was effective, which led to the reduction in fastener supporting stiffness. The above discussion is similar to the research studied by Chen et al. as shown in Figure 1 [2]. With the growth of the sine cyclic loading numbers, the rail displacement increased gradually. This result may be explained by the fact that the reduction in the fastener clamping force and the supporting stiffness occurred under the action of cyclic loading.

The displacement variation of the sleeper slab is also described in Figure 10. As the sleeper slab, self-compacting concrete cushion, and steel beam are not a whole and there is the certain gap between the above components, the displacement of the sleeper slab relative to the steel beam had an increase during the initial 1 million loading cycles. With the gradual compaction between the components of the track structure, the relative displacement of the sleeper slab gradually decreased and tended to be stable in the later stage of the test.

1. Gao, L.; Zhao, W.; Hou, B. Research on vertical mechanical behavior of WJ-8 fastener under clamping force failure (in Chinese). Engineering Mechanics 2020, 37(11), 228-237.
2. Chen, Z.; Andrawes, B. A mechanistic model of lateral rail head deflection based on fastening system parameters. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 2017, 231, 999-1014.
3. I think that it is not a good idea to model the rail with a beam elements and the fastening system with springs for the Authors purposes (experiment simulation). Value of the springs stiffness is probably not given in the manuscript. In analysed system the stress state is clearly complex. Moreover, the vicinity of fastening system is an area of stress concentration - it is important to model this part precisely.

Response: In the revised manuscript, the Chapter 4 has been deleted. The main purposes of the current research were to verify the applicability of the sleeper slab track on the long-span steel truss bridge and to investigate the mechanical characteristics during the fatigue process with an experimental method. The finite element model established in Chapter 4 was simplified to some extent, which is different from the actual working condition and cannot effectively represent the working status of the structure. The finite element model needs to be considered in more detail. Therefore, the authors decided to delete Chapter 4 without affecting the main content of the article. After this paper, further work about the finite element model will be done, considering the reviewers' suggestions.

9. The Authors compare stresses obtained within experimental test and numerical model. For these purposes, the mesh-dependency studies are very important, since the mesh size influence the values of strains and stresses predicted by the FE model a lot.

Response: The mesh-dependency studies are very important in the finite element analysis. Based on these, the minimum mesh size that can be calculated by computer was adopted in the finite element model. In the revised manuscript, the Chapter 4 has been deleted. The finite element model established in Chapter 4 was simplified to some extent, which is different from the actual working condition and cannot effectively represent the working status of the structure. The finite element model needs to be considered in more detail. Therefore, the authors decided to delete Chapter 4 without affecting the main content of the article. After this paper, further work about the finite element model will be done, considering the reviewers' suggestions.

Author Response File: Author Response.doc

Round 2

Reviewer 1 Report

The authors tried to response all the comments and their responses are acceptable, but it was a pity that they deleted the fourth part, i.e., simulation, and it was better to complete this part.

Author Response

We are sorry to delete the fourth part. By this means, this paper can be more consistent with the Applied Sciences. Preparation of numerical model demands a lot of effort. The finite element model proposed in this paper was simplified to some extent and more detailed work is needed. The authors believe that the deletion of the finite element part does not have too much influence on the main content of the paper, which is also approved and supported by other reviewers. We will continue to do further work in numerical simulation.

Author Response File: Author Response.doc

Reviewer 3 Report

• I think that the decision to remove the numerical part and change stresses to strains was right and I fully support it. Preparation of numerical model demands a lot of effort. Moreover, the analysed system is highly non-linear, so validation of the model will not be an easy task.
• In my opinion, the lack of material strength tests is a serious drawback of the studies, and because of it, validation of the model is quite hard. On the other hand, deleting information went little too far and e.g. information about concrete class (even declared by prefabrication plant) should be included within the paper.
• I think that application of the force in longitunal and lateral load lacks of physical justification and does not represent the actual work of the structure built into the bridge. The force was applied to the one point and to the small area. Longitudinal and lateral forces will be transmitted from a boogie to a slab by rails. Could the authors comment this issue?
• Line 244 - the heading is inappropriate, since "modal tests" are tests using modal hammers, which are widely used in railway engineering too. The paper is about strength tests.
• 0 million means before cyclic loads? The phrase "0 million" looks quite strange.
• I would like to thank the authors for the English correction and explanation of the trends in plots. However, we cannot find such trends in the paper by Chen and Andrawes [28]. I think that small preload should have been applied before the displacement measurements, which eliminates effects of gaps between elements of the system. Was preload applied in the present studies?
• I have one more general doubt about dynamic properties of bridge-track system. Due to reduction of a track mass, the fundamental frequency increases. Does it not cause the amplification of the vibrations? Were dynamic properties of the structure studied?

Author Response

1. In my opinion, the lack of material strength tests is a serious drawback of the studies, and because of it, validation of the model is quite hard. On the other hand, deleting information went little too far and e.g. information about concrete class (even declared by prefabrication plant) should be included within the paper.

Response: The components of the sleeper slab track were produced in the prefabrication plant, and the cube compressive strengths under the same conditions have been measured by the prefabrication plant. As a result, the cube compressive strengths of C60 and C40 concrete are 70.1 MPa and 48.4 MPa, respectively. In addition, it should be noted that the information which has been deleted in chapter 4 was contained in chapter 2.

2. I think that application of the force in longitudinal and lateral load lacks of physical justification and does not represent the actual work of the structure built into the bridge. The force was applied to the one point and to the small area. Longitudinal and lateral forces will be transmitted from a boogie to a slab by rails. Could the authors comment this issue?

Response: The horizontal load generated by train operation is transferred from the rail and fastener to the sleeper slab, and finally borne by the high-strength bolts. Based on the longitudinal and transverse resistance tests (Single Tie Push Test) of the ballast bed [1], the horizontal equivalent load was directly applied to the sleeper slab in the horizontal resistance tests. This loading method is different from the actual work of the structure built into the bridge, but the effect is similar.

Figure 1. longitudinal and transverse resistance tests.

1. Liu, J.; Wang, P.; Liu, G.; Dai, J.; Xiao, J.; Liu, H. Study of the characteristics of ballast bed resistance for different temperature and humidity conditions. Construction & building materials 2021, 266. Response: In line 155, the heading "modal tests" has been replaced by “Specimen Geometry and Materials”.Response: In the revised manuscript, the words “0 million” have been replaced by “before cyclic loads”.Response: Chen et al. proposed that due to the rotation of the rail base, the rail pad is not in uniform shear, and only part of the nominal contact area is effective. We used this viewpoint for reference when analyzing the displacement of rail relative to sleeper slab. In the test, the loading position was in the middle of the two fasteners which led to the uneven deformation of the rail and the rail pads in the longitudinal direction. As a result, the stiffness provided by the rail pads is not uniform, either. During the loading process, the stiffness provided by the rail pad decreased gradually due to the decrease of the effective contact area, which led to the increase of the rail displacement. In fact, there was a preloading test before the displacement measurements. However, the test results showed that the preloading test is not enough to eliminate the gap between the system components completely. In the first 1 million times of sine cyclic loading, the trends of mechanical properties were unstable.Response: After this paper, further work about the dynamic characteristics will be done by authors. For the long-span steel truss bridge, the traditional ballasted track and ballastless track have some problems due to the limitation of open deck and secondary dead load. In contrast, the sleeper track structure can greatly reduce the deck load, and has been applied in many countries, e.g., composite sleeper track used in railway steel bridges in Japan and Yangtze River bridges in Dashenguan, China. The sleeper slab track is superior to the composite sleeper track in stability, resistance and mass which shows that this track structure is reasonable. We approve the viewpoint that the mass reduction of the track structure will lead to the increase of the fundamental frequency and amplification of the vibration. In addition, we think that the stiffness is also an important factor. This problem can be improved by using the rail pad and self-compacting concrete cushion. It should be noted that the structure proposed in the paper is not the final product. The optimization will be done if the dynamic characteristics of the sleeper slab track are found to be unreasonable in the further work. For instance, adjust the stiffness of the rail pad or apply the vibration isolation pad under the cushion.
2. 6. I have one more general doubt about dynamic properties of bridge-track system. Due to reduction of a track mass, the fundamental frequency increases. Does it not cause the amplification of the vibrations? Were dynamic properties of the structure studied?
3. 5. I would like to thank the authors for the English correction and explanation of the trends in plots. However, we cannot find such trends in the paper by Chen and Andrawes [28]. I think that small preload should have been applied before the displacement measurements, which eliminates effects of gaps between elements of the system. Was preload applied in the present studies?
4. 4. 0 million means before cyclic loads? The phrase "0 million" looks quite strange.
5. 3. Line 244 - the heading is inappropriate, since "modal tests" are tests using modal hammers, which are widely used in railway engineering too. The paper is about strength tests.

Author Response File: Author Response.doc

Round 3

Reviewer 3 Report

The authors respond to all my comments and questions in reasonable way. I would like to thank them for all amendments. I believe the manuscript was improved significantly. There are some details of testing which are questionable, but nobody is perfect. In general, presented results can be interesting for other researchers.

I would like to wish the authors good luck in developing their product.