Study on Dominant Frequency Attenuation of Blasting Vibration for Ultra-Small-Spacing Tunnel

Round 1

Reviewer 1 Report

This is an interesting paper which expands the understanding of blasting vibration in tunnel engineering, particularly the frequency distribution of blasting induced vibrations. The authors present the experimental study of blasting induced vibration propagation in two-track roadway tunnel with a small clearance between the tracks, as well as the analysis of experimentally obtained results. The presented experimental results and corresponding analysis represent an valuable asset to engineering practice. There is no theoretical analysis and comparison between the theoretical and experimental obtained results which lowers the paper scientific value, but as already said, the paper is useful for engineering practice. Like any paper, this paper can be made better to increase its readability and value for a potential reader.

The sections and subsections should be numbered.

Certain references are lost during conversion to PDF. The authors should correct the referencing.

The rock mass properties given in section Field test should be referenced or the authors should explain how they obtained the values for uniaxial compressive strength, mass integrity coefficient, correction value of the basic quality index and average longitudinal wave velocity. In principle as no theoretical analysis is given in the paper, I fail to comprehend why these values are important at all.

The paper structure should be improved, the new section Results should be included where all the results and frequency spectrum analysis should be given. The analysis of results and explanations from subsections Difference in dominant frequency distributions on primary support and secondary lining, Spectrum analysis of MS delay blasting and Spectrum analysis of each delay sequence waveform should be transferred to section Discussion. The section Discussion should be reformatted/extended in order to better support the three conclusions given at the end of the paper. The figure 12 should be broken to three figures (X, Y and Z) as it is hard to track relationship between ZCF and DF on a single figure with so many points. Based on their understanding, the authors should discuss the figure in order to support the conclusion 2 given in section Conclusions, and explain why the nonlinearity is more pronounced for certain directions and locations.

The paper lacks the explanation how these results would be further used and what would be the directions of further research.

Author Response

Dear reviewers and editor:

Thank you for your letter and for the reviewers’comments concerning our manuscript entitled“Study on dominant frequency attenuation of blasting vibration for Ultra-Small-Spacing Tunnel”(ID: applsci-1553977). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We revised the manuscript in accordance with the reviewers’ comments, and carefully proof-read the manuscript to minimize typographical, grammatical, and bibliographical errors.

Here below is our description on revision according to the reviewers’ comments.

 

Part A (Reviewer 1)

1. The reviewer’s comment: The sections and subsections should be numbered; and certain references are lost during conversion to PDF. The authors should correct the referencing.

The author’s answer: Thanks for reminding. The paper has been updated to the correct form.

2. The reviewer’s comment: The rock mass properties given in section Field test should be referenced or the authors should explain how they obtained the values for uniaxial compressive strength, mass integrity coefficient, correction value of the basic quality index and average longitudinal wave velocity. In principle as no theoretical analysis is given in the paper, I fail to comprehend why these values are important at all.

The author’s answer: Thank you for your careful review. Our intention was to describe the conditions of the tunnel surrounding rocks, which have been removed as they are not relevant to the later analysis. In addition, the relevant depth of burial has been added. The revised content is as follows:

In the blasting test area, the average burial depth of the soil above the structures of the left and right tunnels is 100m and 20m, respectively; and the main surrounding rock of the tunnel is moderately weathered dolomite, with broken rock mass and developed joints and fissures.

3. The reviewer’s comment: The paper structure should be improved:

• The new section Results should be included where all the results and frequency spectrum analysis should be given.
• The analysis of results and explanations from subsections Difference in dominant frequency distributions on primary support and secondary lining, Spectrum analysis of MS delay blasting and Spectrum analysis of each delay sequence waveform should be transferred to section Discussion.
• The section Discussion should be reformatted/extended in order to better support the three conclusions given at the end of the paper.

The author’s answer: Thanks for your careful guidance. The structural framework of the paper has been adjusted with a new section 4 Results; and all mesurements data and frequency spectrum analysis is summarazed in a new Table 3. The new section 5 Data Analysis includes subsections 5.1 Difference in dominant frequency distributions on primary support and secondary lining, 5.2 Spectrum analysis of entire MS delay blast vibration, and 5.3 Spectrum analysis of each delay sequence vibration. Also, a new subsection 5.4 Nonlinear relationship between ZCF and DF is added. Further, the introduction, discussion, and conclusion of the paper have been rewritten. The revised discussion are as follows:

The most critical measure to control blast vibration is establishing a threshold for PPV, which can be selected according to the characteristics of frequency distribution in different areas. As shown in Fig.6, the dominant frequency of the blast vibration wave undergoes a fluctuating decrease at a certain distance, only the high frequency part decays rapidly with the distance, and the dominant frequency shifts from higher band to a lower one (upper bond shown in Fig.6). The main reason is that, for multi-sequences delay blast, the spectrum of the vibration waves is multi-structured (as shown in Fig.9); and varient delay sequences produce different frequencies of vibration waves (as shown in Fig.10); and different frequency components in the propagation with different attenuation rate decay (as shown in Fig.6). On the other hand, the abrupt change of the propagation medium leads to a significant difference in the distribution of the dominant frequencies of vibration on the lining and the primary support (as shown in Fig.7).

On the basis of Chinese Safety Regulations for Blasting (GB6722-2014), a safety PPV criterion for traffic tunnel considering dominant frequency has been proposed (as shown in Table 6 the bold line). Its definition of dominant frequency is corresponding to the maximum amplitude of the partical velocity, which means ZCF.

Table 6
Safety PPV for blasting vibration (GB6722-2014, China)

Structure type	f ≤ 10 Hz	10-50 Hz	f > 50 Hz
General civil buildings	1.5-2.0	2.0-2.5	2.5-3.0
Hydraulic tunnel	7-8	8-10	10-15
Traffic tunnel	10-12	12-15	15-20
Mine roadway	15-18	18-25	20-30

 

Therefore, the way to select the right critical PPV for the tunnel structure is to choose a frequency band based on frequency-based vibration criteria. For the range of SD greater than 5.0 kg/m³, a safe PPV less than 50 Hz band is recommended; while the SD is below 5.0 kg/m³, it is determined by experience; and a more stringent PPV is more secure for the structure. For a point at the lining is exceeds 20m away from the blast, because the distribution of the frequency is generally greater than 50Hz, the safe PPV can be selected appropriately larger compared to the primary support.

However, it should be noted that the ZCF and DF exhibits a non-linear relationship, and the blast vibration wave frequencies obtained by different methods may lead to a different selection for safe vibration frequency bands.

 

4. The reviewer’s comment: The figure 12 should be broken to three figures (X, Y and Z) as it is hard to track relationship between ZCF and DF on a single figure with so many points. Based on their understanding, the authors should discuss the figure in order to support the conclusion 2 given in section Conclusions, and explain why the nonlinearity is more pronounced for certain directions and locations.

The author’s answer: We feel sorry that we simply give pictures without detailed analysis. Now we have redrawn Figure 12 and make the following discussions:

 The relationship between the ZCF and the DF is not completely linear (as shown Fig.12), and the frequency determined by the different methods deviates considerably. Particularly, the DFs are widely distributed below 10 Hz, in which range the ZCFs are almost absent. In the range of DFs higher than 10Hz, it has a certain linear relationship with ZCFs. Obviously, the use of a single frequency value gives a poor description of the vibration frequency. As shown in Fig.11, although the frequencies obtained by different methods show a consistent law, there are different values of DF and ZCF when describing a specific vibration wave. This is because the DF describes the entire waveform, while the ZCF only describes the the frequency of the cycle with the maximum amplitude. The ongoing revision of Norwegian standard is considering an alternative approach by implementing a frequency-weighted filter that directly describes the damage potential at different frequencies [32].

 

5. The reviewer’s comment: The paper lacks the explanation how these results would be further used and what would be the directions of further research.

The author’s answer: We are really sorry that we have not discussed. We added how to use the distributions of the dominant frequency to choose an appropriate safety PPV in section 7 Discussion . The new additions can be found in the answer to comment 3. In addition, we also discussed the directions of further research in the Conclusion. The following additions were made:

Because of the fluctuated drop of the vibration dominant frequency with the distance, further discussion is needed on how the different frequency components are decayed. Since the selection of safe PPV depends on the dominant frequency of blast vibration, finding a frequency that is more appropriate than the above for engineering is still worthy of further research.

Thanks for your proposal.

 

Thanks very much for the guidance of the reviewer. We eagerly hope that the above corrections and explanations could be recognized. It is hoped that our research could be affirmed to promote related research and engineering applications.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

The article addresses an important topic of the study on dominant frequency attenuation of blasting vibration for Ultra-Small-Spacing Tunnel, which is appreciated. The study include the experimental research. In this paper the dominant frequency attenuation in the preceding tunnel with the middle rock pillar spacing ranging from 4.0 m to 9.4 m was presented. The Reviewer appreciates the efforts done in this paper, however, the reviewer has some concerns regarding the introduction, results and conclusions. The English language should be improved for Native Speaker (from seismic area). In current version of the language in some parts are not clear. Furthermore, please use the template of this Journal. In opinion of Reviewer this paper should be subjected to major revision.

Other comments:

1. Please add more literature about similar research, because of the introduction is really poor and should be improved. My proposition to read and cited similar articles as your research (about Fourier analysis):

• https://doi.org/10.1016/j.soildyn.2018.05.036
• https://doi.org/10.1016/j.tust.2020.103808
• https://doi.org/10.1016/j.undsp.2018.09.007

2. The aim of this research is not clear. What is new based on previous research?
3. Please delete this sentence of all paper “[Error! Bookmark not defined.]”.
4. Please improve the Figure 3. Please add the high of soil cover above tunnel structure.
5. Some parts of the text are not clear/understand, you can see below:

“One aspect is the distribution of the dominant frequencies on the primary support is wider than that on the lining, which is evidently in zone II. For example, in Fig. 7a, in the range higher than 150 Hz of zone II, more data are distributed on the primary support than on the lining; moreover, in Fig. 7b, the range higher than 150 Hz of zone II distribute data of the primary support without any data of the lining. We believe that a portion of the frequency of the vibration wave has been wholly attenuated, and is related to the gap between the primary support and the secondary lining. The primary support is closely bonded with the surrounding rock mass and directly receives the seismic waves from the inside of the surrounding rock. However, there is a space between the lining and the primary support for installing a waterproof board and a geotextile (as shown in Fig. 3), which are not entirely close to the primary support but are nailed in a quincunx arrangement. In addition, the secondary lining is cast in situ by concrete, and there are inevitable cavities and gaps between it and the primary support. Thus, there is a notifiable interface for seismic wave propagation. On the other hand, blasting seismic wave is usually composed of body waves (P wave and S wave) and Rayleigh surface waves (R wave) [[34]]. The surface wave propagates on the free surface, and the body waves propagate inside the surrounding rock; body waves at a non-vertical incidence angle on a free surface will produce reflected and mode-converted body waves as well as surface waves [[35]]. Therefore, it can be considered that when the seismic waves are transmitted from the primary support to the lining, an abrupt change in the medium, causing a part of the blasting seismic waves (mainly body waves) not to pass through, thereby significantly reducing the transmission energy.”

Other

“As shown in Fig. 10, the ZCF is near the peak of each waveform and the DF is at the peak amplitude in the power spectrum. Overall, the ZCF and the DF increase as the delay sequence grows; however, it is not a completely linear trend. To better describe it, the MFs are calculated in Table 4, and three dominant frequencies (ZCF, DF, and MF) of each delay sequence are depicted in Fig. 11. It is seen that the global frequency of the entire vibration is close to the DF of the cutting blastholes in MS1. The charge structure has a significant influence on the dominant frequency of a vibration [Error! Bookmark not defined.]. Understandably, in this study, the change in the dominant frequency of each sequence is independent of the charge structure because all sequences have the same charge structure. There are two other theories for the propagation law of the dominant frequency. One is the blasting cavity theory [Error! Bookmark not defined.]: for the same free surface or the same blast shapes, a large equivalent blasting vibration source (EBVS) implies a low vibration frequency. The other is the free surface theory [Error! Bookmark not defined.]: multiple free surfaces cause superposition of blasting vibration waves and increase of frequency; for example, as the cutting blastholes are detonated under a confined boundary condition in the MS delay blasting, the dominant frequency of it is smaller than those of the subsequent blastholes. The abovementioned not-completely-linear trend of the dominant frequency with the increase in the delay sequence can be explained by the free surface theory. In contrast, the curve fluctuates for some sequences with the same blast shapes conforms to the blasting cavity theory. Based on the blasting parameters (as shown in Fig. 4), the EBVS at MS5 and MS7 have the same shapes but different sizes, and there is a negative correlation between the dominant frequency and the radius of the EBVS. This rule, which conforms to the blasting cavity theory, is also observed for MS9 and MS11.”

Please use the scientific English language with passive voice in all text.

6. The Reviewer appreciates the efforts done in Figure 7 but in my opinion is not clear. Please improve this figure, e.g. please used line on the figure (not point). Maybe this form of results presentation will be more clear and understandable for the other readers.
7. The Figure 8 in my opinion should be create as Figure 9 (will be more clear).
8. In the results please improve about:

• the most important tendency from your research etc.
• the reasons of these results etc.
• the impact of tunnel/or human etc.

9. The conclusions should be improve. Please add this sentence to conclusions “Therefore, finding a frequency that is more appropriate than the above for engineering is still worthy of further research.”. In addition, please add conclusions from my suggestions (point 8 from this review).

And the end I hope that my comments will be helpful for the authors.

Author Response

Dear reviewers and editor:

Thank you for your letter and for the reviewers’comments concerning our manuscript entitled“Study on dominant frequency attenuation of blasting vibration for Ultra-Small-Spacing Tunnel”(ID: applsci-1553977). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We revised the manuscript in accordance with the reviewers’ comments, and carefully proof-read the manuscript to minimize typographical, grammatical, and bibliographical errors.

Here below is our description on revision according to the reviewers’ comments.

Part B (Reviewer 2)

1. The reviewer’s comment:

• The English language should be improved for Native Speaker (from seismic area), In current version of the language in some parts are not clear.
• Please use the template of this Journal.

The author’s answer: We are sorry for any inconvenience caused to reviewers due to our English level. The paper has been updated to the correct form and the unclear description in the paper was revised.

2. The reviewer’s comment: Please add more literature about similar research, because of the introduction is really poor and should be improved. My proposition to read and cited similar articles as your research (about Fourier analysis):

• https://doi.org/10.1016/j.soildyn.2018.05.036
• https://doi.org/10.1016/j.tust.2020.103808
• https://doi.org/10.1016/j.undsp.2018.09.007

The author’s answer: After reading the above literatures, it has given me a lot of
new enlightenment. So these references has now been cited.

3. The reviewer’s comment: The aim of this research is not clear. What is new based on previous research?

The author’s answer: We are sorry for not describing the purpose of the study clearly. In order to compare more clearly with previous studies, a revised literature review is presented below:

In blasting engineering, a part of the explosion energy is used to break a rock and the remainder is transmitted to the surrounding rocks by the blasting vibration waves [1,2], which may be a significant threat to the safety of adjacent structure [3, 4]. In small-spacing tunnels, after the primary support and secondary lining of the preceding tunnel are completed, its structure and the middle rock pillar may be affected by the blasting vibrations of the succeeding tunnel, which are manifested as seismic cumulative effects [5]. For example, the repeated blast loading during tunnelling works cause the damages on jointed basalt rock masses [6]; and the cyclic blast excavations cause the critical damage PPV for the middle rock pillar drops significantly [7]. Meanwhile, the blast vibration waves may cause a decline in the bearing capacity of the rock [8,9] and some increases in the stress of the anchors [10], concurrently, the excavation damaged zone and deformation modulus of the surrounding rock is also influenced [11]. Recently, owing to the limited space in mountainous areas, small-spacing tunnels are becoming common, where the clearance between two tunnels is much shorter than the safe distance to alleviate vibration waves, such as Qishucao bifurcation tunnel [12], Liuyuetian bifurcation tunnel [13], Heshang three-lane tunnel [14], and closely spaced triple tunnels in Badaling [15]. The minimum clearance between these underground constructions is less than their span. Periodic non-uniform natural seismic wave excitation causes shear deformation in underground constructions [16]. And one of the biggest differences between blasting vibration waves and natural seismic waves is the difference in frequency characteristics, where the seismic waves is in low frequency ranges and the blast vibration waves frequency is higher, generally greater than 5 Hz. Therefore, it is necessary to analyze the characteristics of blast vibration waves propagating in the area very close to the tunnels so as to help protect the tunnel structure.

The nonuniform seismic excitation, similar to blast vibration waves, has great influence on the acceleration amplification in soil and the strain and displacement of the long deep buried pipeline [17]. In a tunnel affected by blast vibration waves, the dynamic stress of the structure is directly related to the peak vibration velocity (PPV) [18]. Xu [19] and Zhang [20] analyzed the effect of blast vibration waves on the safety of tunnel structures without considering the vibration frequency. However, the adverse effect of blast vibration waves is not only related to the vibration amplitude but also to the relationship between the dominant frequency of a blast vibration and the structural natural frequency. Evidently, Lv [21] found that the PPV at a tunnel wall is amplified compared to that of the incident vibration wave, and the amplification coefficient is positively correlated to the frequency of the blast vibration waves. Therefore, it is necessary to study the frequency distribution range of blast vibration waves. In the tunnel construction, Tian [22] found that the frequency range of blast vibrations is within 0–175 Hz, and the minimum distance between the blast source and the ground measurements point in the study was 30 m. However, the distance has an effect on the signal characteristics of the blast vibration wave. Koteleva [23] found that the frequency range is closely correlated with the distance values. Additionally, Zhou [24] established a mathematical relationship between the blast dominant frequency and its principal influencing factors. Triviño [25] found significant differences in the amplitude and spectrum of blast vibration signals collected separately at the surface and underground mines. Nevertheless, these studies on blast vibration frequencies in tunnel do not compared the characteristics of the frequency distribution on the primary support and the lining. In open-pit mines blast, Sun [26] compared the differences in the attenuation laws of three types of dominant frequencies caused by different blast charge structures. Blair [27] analyzed the frequency range of ground vibrations in detail in terms of the instantaneous frequency and by a time–frequency analysis. Yang [28] and Liu [29] compared the frequency characteristics for the blast-induced vibration velocity signal at different delay sequence from a millisecond (MS) delay blast. These studies on the propagation law of blast vibration waves in open-pit mines provide useful guidance for the analysis of tunnelling blast vibration waves. Furthermore, Fourier variation is the most common method to analyze the characteristics of seismic waves [30], and these studies also provide a reference to analyzing blast vibration waves. Based on the above investigations, there is still a lack of research on blast vibration frequency distribution the tunnels with a small clearance; and a theoretical study on the prediction and distribution law of the dominant frequencies of blast vibrations still needs a large amount of engineering data for validation, particularly for the two-track tunnel that the distance between two tunnels less than a tunnel span.

4. The reviewer’s comment: Please delete this sentence of all paper “[Error! Bookmark not defined.]”.

The author’s answer: Thanks for reminding. The paper has been updated to the correct form.

5. The reviewer’s comment: Please improve the Figure 3. Please add the high of soil cover above tunnel structure.

The author’s answer: Thanks for your carefully reminding. The relevant depth of burial has been added. The added content is as follows:

In the blasting test area, the average burial depth of the soil above the structures of the left and right tunnels is 100m and 20m, respectively;

6. The reviewer’s comment: Some parts of the text are not clear/understand, you can see below:

• “One aspect is the distribution …reducing the transmission energy.”
• “As shown in Fig. 10, the ZCF is near the peak …is also observed for MS9 and MS11.”
• Please use the scientific English language with passive voice in all text.

The author’s answer: We are sorry for the inconvenience to the reviewers due to our English writing level, and have changed the tense of the entire text to passive voice.

7. The reviewer’s comment: The Reviewer appreciates the efforts done in Figure 7 but in my opinion is not clear. Please improve this figure, e.g. please used line on the figure (not point). Maybe this form of results presentation will be more clear and understandable for the other readers.

The author’s answer: Thank you for the reminder. In order to better illustrate the difference of dominant frequency distribution on lining and primary support, the new Figure 7 have been plotted the lining and the primary support separately. The redrawn Figure 7 has been re-uploaded.

8. The reviewer’s comment: The Figure 8 in my opinion should be create as Figure 9 (will be more clear).

The author’s answer: Thanks for your kind suggestions. The spectrum analysis of both vibration curves in Figure 8 has been carried out, and the redrawn Figure 9 has been re-uploaded.

9. The reviewer’s comment: In the results please improve about:

• the most important tendency from your research etc.
• the reasons of these results etc.
• the impact of tunnel/or human etc.

The author’s answer: We appreciated the heads up. First, the structural framework of the paper has been adjusted with a new section 4 Results; and all mesurements data and frequency spectrum analysis is summarazed in a new Table 3. Second, the new section 5 Data Analysis includes subsections 5.1 Difference in dominant frequency distributions on primary support and secondary lining, 5.2 Spectrum analysis of entire MS delay blast vibration, and 5.3 Spectrum analysis of each delay sequence vibration. Also, a new subsection 5.4 Nonlinear relationship between ZCF and DF is added. Finnally, the introduction, discussion, and conclusion of the paper have been rewritten. The revised conclusions are as follows:

Based on the the framework of this research, the following conclusions can be drawn. The dominant frequencies of blast vibration has a wide range of distribution in areas relatively close to the blast, which are mainly distributed within 200 Hz. There is a clear difference in the distribution of the dominant frequency on the primary support and the lining: (1) The distribution of the dominant frequencies on the primary support is broader than that on the lining, and (2) the dominant frequencies on the lining are concentrated in the range when the lining is far from the blast face beside a specific value. The main reasons are the cavities and gaps between the primary support and the lining have the characteristics of vibration damping and filtering, hindering the propagation of the blasting vibration waves with some frequencies. Additionnally, the vibration waves is more affected by characteristics of blast design in areas relatively close to the blast,, while atlarger distances the propagating medium dominates the vibration response.

The high-frequency part of the vibration waves attenuates rapidly on the primary support under the damping effect of the rock, whereas the Z-direction (transverse) dominant frequency decays gradually. The power function of the upper and lower bounds of the dominant frequency on the primary support with the SD were proposed..

Multiple delay sequences blast contributes to a multi-structured amplitude spectrum of blast vibration waves. There are distinct differences between the global frequency of the entire vibration time series and the dominant frequencies at different delay sequences. The global frequency determined in all delays of the vibrations is close to the dominant frequency detonated in the cutting blastholes. The dominant frequencies in different sequences correspond to two parameters of the different delay sequence. Multiple free surfaces cause the overall trend of dominant frequency increase, and a large EBVS implies a low vibration frequency.

The ZCFs and DFs exhibit a nonlinear relationship. This is because the DF describes the entire waveform, while the ZCF only describes the the frequency of the cycle with the maximum amplitude. Nevertheless, the distribution of dominant frequencies in the different scaling distances obtained in this paper can be used to guide the selection of a suitable safe PPV.

Because of the fluctuated drop of the vibration dominant frequency with the distance, further discussion is needed on how the different frequency components are decayed. Since the selection of safe PPV depends on the dominant frequency of blast vibration, finding a frequency that is more appropriate than the above for engineering is still worthy of further research.

 

10. The reviewer’s comment: The conclusions should be improve. Please add this sentence to conclusions “Therefore, finding a frequency that is more appropriate than the above for engineering is still worthy of further research.”. In addition, please add conclusions from my suggestions (point 8 from this review).

The author’s answer: The answer to this comment was mentioned in the answer to comment 9.

 

We appreciate for Editors/Reviewers’ warm work earnestly，and hope that thecorrection will meet with approval. Once again, thank you very much for your comments and suggestions

 

Author Response File: Author Response.pdf

Reviewer 3 Report

The topic discussed in the work is up-to-date and very important from the point of view of assumptions for the construction of the tunnel. As the Applied Sciences Journal the topic of the work at hand would appear to be an appropriate one. 

The authors took up an interesting issue, the diagnosis of blasting vibrations at an stage of the building operation of tunnel has always been a research challenge from many aspects. The authors pay special attention to the safety of structures directly adjacent to the explosion areas. The applied research method, including the frequency analysis of the Fourier dominant, is commonly used to analyze the vibrations of building structures.

In general, when assessing the work, it is written in a very good scientific style, the technical vocabulary used is appropriate, the developed drawings are very carefully presented directly referring to the description in the text.

The work does not have any significant imperfections, nevertheless, I would like to convey to the authors a few comments that they should pay attention to, even not necessarily in the area of the work being assessed.

The editing form and text formatting raise doubts, it is very likely that it is caused by the translation to a pdf file. However, the author should pay attention to it before uploading the work. There are no defined chapters in the thesis, while reading the text the consistency of individual sections is preserved, but it will be necessary to introduce the appropriate editing form of the chapters.

The authors have included a number of illustrations and charts, they are neat and legible. However, it is necessary to place the drawing in the area of one side and not to divide it - as in Figures 2, 6, 7, this also applies to table placement. It will significantly improve the readability of the work.

Figure 9 shows the power spectrum of vibration waveform shown in Fig. 6b. However, figure 6b does not refer to this, maybe it is referring to figure 8b?

I would also like to highlight the Introduction section. The number of literature items cited in the text is appropriate, however, the way of working with literature is very poor here. The authors very succinctly and correctly refer to other studies, there is a certain insufficiency here - assigning several items of literature to one sentence is a certain abbreviation that should not be used. Very brief conclusions and the discussion relate to the results obtained, it is still under the question to include citations in the discussion? It is better to discuss the results obtained, and it is better to place comments relating to other studies in the main chapters of the work.

The article can be published after minor revisions. There is no need to re-review the work.

Comments for author File: Comments.pdf

Author Response

Dear reviewers and editor:

Thank you for your letter and for the reviewers’comments concerning our manuscript entitled“Study on dominant frequency attenuation of blasting vibration for Ultra-Small-Spacing Tunnel”(ID: applsci-1553977). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We revised the manuscript in accordance with the reviewers’ comments, and carefully proof-read the manuscript to minimize typographical, grammatical, and bibliographical errors.

Here below is our description on revision according to the reviewers’ comments.

 

Part C (Reviewer 3)

1. The reviewer’s comment: The editing form and text formatting raise doubts, it is very likely that it is caused by the translation to a pdf file. However, the author should pay attention to it before uploading the work. There are no defined chapters in the thesis, while reading the text the consistency of individual sections is preserved, but it will be necessary to introduce the appropriate editing form of the chapters.

The author’s answer: Thanks for reminding. The paper has been updated to the correct form.

2. The reviewer’s comment: The authors have included a number of illustrations and charts, they are neat and legible. However, it is necessary to place the drawing in the area of one side and not to divide it - as in Figures 2, 6, 7, this also applies to table placement. It will significantly improve the readability of the work..

The author’s answer: We appreciated the heads up. The Figures 2, 6, 7 have been redrawn.

3. The reviewer’s comment: Figure 9 shows the power spectrum of vibration waveform shown in Fig. 6b. However, figure 6b does not refer to this, maybe it is referring to figure 8b?.

The author’s answer. Thanks for careful inspection. The figure name has been corrected.

4. The reviewer’s comment: I would also like to highlight the Introduction section. The number of literature items cited in the text is appropriate, however, the way of working with literature is very poor here. The authors very succinctly and correctly refer to other studies, there is a certain insufficiency here - assigning several items of literature to one sentence is a certain abbreviation that should not be used.

The author’s answer: We are sorry that the introduction in this paper was too brief, the revised introduction is as follows:

In blasting engineering, a part of the explosion energy is used to break a rock and the remainder is transmitted to the surrounding rocks by the blasting vibration waves [1,2], which may be a significant threat to the safety of adjacent structure [3, 4]. In small-spacing tunnels, after the primary support and secondary lining of the preceding tunnel are completed, its structure and the middle rock pillar may be affected by the blasting vibrations of the succeeding tunnel, which are manifested as seismic cumulative effects [5]. For example, the repeated blast loading during tunnelling works cause the damages on jointed basalt rock masses [6]; and the cyclic blast excavations cause the critical damage PPV for the middle rock pillar drops significantly [7]. Meanwhile, the blast vibration waves may cause a decline in the bearing capacity of the rock [8,9] and some increases in the stress of the anchors [10], concurrently, the excavation damaged zone and deformation modulus of the surrounding rock is also influenced [11]. Recently, owing to the limited space in mountainous areas, small-spacing tunnels are becoming common, where the clearance between two tunnels is much shorter than the safe distance to alleviate vibration waves, such as Qishucao bifurcation tunnel [12], Liuyuetian bifurcation tunnel [13], Heshang three-lane tunnel [14], and closely spaced triple tunnels in Badaling [15]. The minimum clearance between these underground constructions is less than their span. Periodic non-uniform natural seismic wave excitation causes shear deformation in underground constructions [16]. And one of the biggest differences between blasting vibration waves and natural seismic waves is the difference in frequency characteristics, where the seismic waves is in low frequency ranges and the blast vibration waves frequency is higher, generally greater than 5 Hz. Therefore, it is necessary to analyze the characteristics of blast vibration waves propagating in the area very close to the tunnels so as to help protect the tunnel structure.

The nonuniform seismic excitation, similar to blast vibration waves, has great influence on the acceleration amplification in soil and the strain and displacement of the long deep buried pipeline [17]. In a tunnel affected by blast vibration waves, the dynamic stress of the structure is directly related to the peak vibration velocity (PPV) [18]. Xu [19] and Zhang [20] analyzed the effect of blast vibration waves on the safety of tunnel structures without considering the vibration frequency. However, the adverse effect of blast vibration waves is not only related to the vibration amplitude but also to the relationship between the dominant frequency of a blast vibration and the structural natural frequency. Evidently, Lv [21] found that the PPV at a tunnel wall is amplified compared to that of the incident vibration wave, and the amplification coefficient is positively correlated to the frequency of the blast vibration waves. Therefore, it is necessary to study the frequency distribution range of blast vibration waves. In the tunnel construction, Tian [22] found that the frequency range of blast vibrations is within 0–175 Hz, and the minimum distance between the blast source and the ground measurements point in the study was 30 m. However, the distance has an effect on the signal characteristics of the blast vibration wave. Koteleva [23] found that the frequency range is closely correlated with the distance values. Additionally, Zhou [24] established a mathematical relationship between the blast dominant frequency and its principal influencing factors. Triviño [25] found significant differences in the amplitude and spectrum of blast vibration signals collected separately at the surface and underground mines. Nevertheless, these studies on blast vibration frequencies in tunnel do not compared the characteristics of the frequency distribution on the primary support and the lining. In open-pit mines blast, Sun [26] compared the differences in the attenuation laws of three types of dominant frequencies caused by different blast charge structures. Blair [27] analyzed the frequency range of ground vibrations in detail in terms of the instantaneous frequency and by a time–frequency analysis. Yang [28] and Liu [29] compared the frequency characteristics for the blast-induced vibration velocity signal at different delay sequence from a millisecond (MS) delay blast. These studies on the propagation law of blast vibration waves in open-pit mines provide useful guidance for the analysis of tunnelling blast vibration waves. Furthermore, Fourier variation is the most common method to analyze the characteristics of seismic waves [30], and these studies also provide a reference to analyzing blast vibration waves. Based on the above investigations, there is still a lack of research on blast vibration frequency distribution the tunnels with a small clearance; and a theoretical study on the prediction and distribution law of the dominant frequencies of blast vibrations still needs a large amount of engineering data for validation, particularly for the two-track tunnel that the distance between two tunnels less than a tunnel span.

 

5. The reviewer’s comment: Very brief conclusions and the discussion relate to the results obtained, it is still under the question to include citations in the discussion? It is better to discuss the results obtained, and it is better to place comments relating to other studies in the main chapters of the work.

.The author’s answer: Thanks for your kind guidance. We have revised the discussion section and discussed issues that were not clearly stated in the previous section. The revisions are as follows:

The most critical measure to control blast vibration is establishing a threshold for PPV, which can be selected according to the characteristics of frequency distribution in different areas. As shown in Fig.6, the dominant frequency of the blast vibration wave undergoes a fluctuating decrease at a certain distance, only the high frequency part decays rapidly with the distance, and the dominant frequency shifts from higher band to a lower one (upper bond shown in Fig.6). The main reason is that, for multi-sequences delay blast, the spectrum of the vibration waves is multi-structured (as shown in Fig.9); and varient delay sequences produce different frequencies of vibration waves (as shown in Fig.10); and different frequency components in the propagation with different attenuation rate decay (as shown in Fig.6). On the other hand, the abrupt change of the propagation medium leads to a significant difference in the distribution of the dominant frequencies of vibration on the lining and the primary support (as shown in Fig.7).

 

We appreciate for Editors/Reviewers’ warm work earnestly, and hope that the correction will meet with approval. Once again, thank you very much for your comments and suggestions.

 

 

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The Reviewer appreciates the efforts done in this paper, however, the reviewer has some concerns regarding the references.  

Please add a few articles about similar researches from this area but please concentrate on the most interesting papers from over the world (not only China). In current version around 20 article are from China. In my opinion should be less than 50% of all articles, because of your paper is a scientific paper based on the papers from whole world not only paper for China. Of course you can also check other papers from authors which were cited in the current version.

Author Response

Dear reviewers and editor:

Thank you for your letter and for the reviewers’comments.

 

The reviewer’s comment: Please add a few articles about similar researches from this area but please concentrate on the most interesting papers from over the world (not only China). In current version around 20 article are from China. In my opinion should be less than 50% of all articles, because of your paper is a scientific paper based on the papers from whole world not only paper for China. Of course you can also check other papers from authors which were cited in the current version.

The author’s answer: Thanks for your reminder. We have replaced two references, Ref. [1] and Ref. [3], added Ref. [12]; and added one small-spacing tunnel case from Istanbul, Turkey [14] and one in Cairo, Egypt [15] to the list of engineering cases. The revised Reference has 17 articles from China, which is less than 50% of all articles.

 

We appreciate for Editors/Reviewers' warm work earnestly, and hope that the correction will meet with approval.

Author Response File: Author Response.pdf

Round 3

Reviewer 2 Report

Thank you for your improving. I accept this paper in current form.