Influence of Blasting Disturbance on the Dynamic Stress Distribution and Fracture Area of Rock Tunnels

Round 1

Reviewer 1 Report

The topic of research is of interest, however, the study conducted is not strong enough. The manuscript is not up to the standard for publication. Following are some suggestions that the authors can consider to improve the manuscript:

1.     The language needs to be revised thoroughly. There are many grammatical and punctuation mistakes in the paper.

2.     “However, few studies have been conducted on dynamic stress distribution and fracture area of rock tunnels under blasting loads.” I don’t think this statement is true. There are plenty of studies that have investigated the dynamic stress distribution and fracture failure of rock tunnels under blast loading. In fact, few have already been mentioned by the authors themselves. Provide specific novelty of the manuscript.

3.     How is Figure 1 relevant to the study? There is no explanation for it. Plus, many phenomena are misrepresented in the figure.

4.     “In this study, the tunnel and blasting source in the actual project is simplified into a plane model at a ratio of 1:1.” What exactly does the ratio 1:1 mean and how was it arrived at?

5.     What does “common rock” mean?

6.     “the specific physical parameters were tested by SonicViewer-SX device”. How were all the properties obtained through this device? Please clarify.

7.     What was the mesh size and was there any mesh size convergence study conducted?

8.     No validation of the numerical model has been provided. This undermines the reliability of the study.

9.     What was the charge weight of the explosive?

English can be improved.

Author Response

Questions from the Reviewer 1

 

Q1. The language needs to be revised thoroughly. There are many grammatical and punctuation mistakes in the paper.

Reply：According to the reviewer’s suggestion, we have read repeatedly and revised the sentences in the revised manuscript.

 

Q2. “However, few studies have been conducted on dynamic stress distribution and fracture area of rock tunnels under blasting loads.” I don’t think this statement is true. There are plenty of studies that have investigated the dynamic stress distribution and fracture failure of rock tunnels under blast loading. In fact, few have already been mentioned by the authors themselves. Provide specific novelty of the manuscript.

Reply：According to the reviewer’s suggestion, we have made the following modifications and highlighted the novelty of the article as:

“However, not much studies have been conducted on dynamic stress distribution and fracture area of rock tunnels under different orientations of blasting disturbance.”

 

Q3. How is Figure 1 relevant to the study? There is no explanation for it. Plus, many phenomena are misrepresented in the figure.

Reply：Figure 1 is not strictly a layout diagram of mining tunnels, it is only used to illustrate the mutual influence of tunnels during the blasting process. According to the reviewer’s suggestion, we have added the explanation of Figure 1 in the revised manuscript as:

Resource extraction engineering involves the construction of underground mine tunnels, and the excavation operations of different buried levels of tunnels often involve cross tunnel mining, riding tunnel mining, etc. These cross and intersect underground tunnels will be subject to dynamic disturbance during the blasting and excavation operation process. The position relationship of different buried tunnels is shown in Figure 1.

 

Q4. “In this study, the tunnel and blasting source in the actual project is simplified into a plane model at a ratio of 1:1.” What exactly does the ratio 1:1 mean and how was it arrived at?

Reply：In the numerical modeling process, the size of the tunnel is set according to the actual tunnel size as shown in Figure 2, which means that the size of the tunnel and the propagation time of blasting stress waves in the numerical simulation software are the same as in reality.

In order to express the meaning of the article more clearly, we have added the explanation in the revised manuscript as:

In this study, the tunnel and blasting source in the actual project are simplified into a plane model at a ratio of 1:1, i.e. the size of the tunnel is set according to the actual tunnel size as shown in Figure 2, which means that the size of the tunnel and the propagation time of blasting stress waves in the numerical simulation software are the same as in reality. Three types of blasting source locations are designed respectively at the left side of the tunnel, roof of the tunnel and bottom of the tunnel. The simplified model size of the tunnel is shown in Figure 2.

 

Q5. What does “common rock” mean?

Reply：We used the word “common rock” here without a clear meaning. In fact, sandstone was used as the propagation medium. According to the reviewer’s suggestion, we have changed the “common rock” to “sandstone” here in the revised manuscript as:

“The propagation medium is sandstone, and the specific physical parameters were tested…”

 

Q6. “the specific physical parameters were tested by Sonic Viewer-SX device”. How were all the properties obtained through this device? Please clarify.

Reply：The P-wave and S-wave speeds of the sandstone were measured by Sonic Viewer-SX device, as shown in Figure 3, and according to the P-wave and S-wave speeds, the dynamic elastic modulus and the dynamic Poisson's ratio were obtained. The dynamic physical properties of rock is shown in Table 1.

According to the reviewer’s suggestion, we have added the explanation of the in the revised manuscript as:

“The propagation medium is sandstone, and the P-wave and S-wave speeds of the sandstone were measured by Sonic Viewer-SX device, as shown in Figure 3, and according to the P-wave and S-wave speeds, the dynamic elastic modulus and the dynamic Poisson's ratio were obtained. The dynamic physical properties of sandstone is shown in Table 1…”

 

Q7. What was the mesh size and was there any mesh size convergence study conducted?

Reply：We have set four sizes for the mesh size: 1.5 mm, 1 mm, 0.5 mm, and 0.25 mm. During the calculation process, the results of using the mesh size of 0.5 mm was convergent. Therefore, the mesh size used in the article is 0.5 mm, and we have included explanations in the article.

According to the reviewer’s suggestion, we have added the explanation in the revised manuscript as:

“Four kinds of sizes 1.5 mm, 1 mm, 0.5 mm, and 0.25 mm was conducted in the convergence study and size 0.5 mm was used in this study…”

 

Q8. No validation of the numerical model has been provided. This undermines the reliability of the study.

Reply：The finite difference code AUTODYN was employed in this numerical study. AUTODYN code has been applied widely in solving dynamic problems, and its effectiveness has been well validated. And the following references have conducted relevant research:

[1] Zhu ZM, Mohanty B, Xie HP. Numerical investigation of blasting-induced crack initiation and propagation in rocks. Int J Rock Mech Min Sci. 2007, 44(3): 412-424.

[2] Wang M, Zhu ZM, Dong YQ, Zhou L. Study of mixed-mode I/II fractures using single cleavage semicircle compression specimens under impacting loads. Eng Fract Mech. 2017, 177:33-34.

[3] Zhu ZM, Wang C, Kang JM, Li YX, Wang M. Study on the mechanism of zonal disintegration around an excavation. Int J Rock Mech Min Sci. 2014, 67(4):88- 95.

[4] Zhu ZM. Numerical prediction of crater blasting and bench blasting. Int J Rock Mech Min Sci. 2009, 46(6):1088-1096.

[5] Zhu ZM, Li YX, Zhou ZR, Ran X, Jin XX. Dynamic response of defected rock under blasting load. Chin J Rock Mech Eng. 2011, 30(6):1157-1167.

[6] Liu RF, Du YM, Zhu ZM. Effect of crack length on mode I crack propagation under blasting loads. Theoretical and Applied Fracture Mechanics, 2022, 118:103277.

In order to express the meaning of the article more clearly, we have added the explanation in the revised manuscript as:

“The finite difference code AUTODYN has been applied widely in solving dynamic problems, and its effectiveness has been well validated [7-11, 23, 25-26, 28]. With the help of the finite difference software AUTODYN, a numerical model 1:1 with the actual model is established to conduct dynamic numerical simulation research…”

 

Q9. What was the charge weight of the explosive?

Reply：Due to the fact that the numerical model is a planar model, the depth of the charge is consistent with the thickness of the model. The weight of the charge should be designed and calculated based on the cubic volume of rock and the level of surrounding rock in the tunnel, and then set in AUTODYN. The unit rock loss of general explosives ranges from 0.5 to 1.5kg.

Author Response File: Author Response.docx

Reviewer 2 Report

Considerations

 

Page 6.

Equation 1.

?(?) = k ( ?/?? − 1), If the densities are the same (? = ??, for liquids, incompressible), how to establish the pressure value?

 

A = 778.3 GPa, B = 7.071 GPa (Why were these values used for the constants A and B? GPa, it is sure?

 

Would it be possible to simulate also with the presence of aquifers?

What about gas tanks?

If  yes, What is the impact on the responses in figure 5?

 

Could equations 1 and 3 still apply?

 

I suggest associating the conclusions with some case study.

Author Response

Questions from the Reviewer 2

 

Q1. Page 6. Equation 1. (?) = k (?/?? − 1), If the densities are the same (? = ??, for liquids, incompressible), how to establish the pressure value? A = 778.3 GPa, B = 7.071 GPa (Why were these values used for the constants A and B? GPa, it is sure?

Reply：Equation 1 is based on the JWL equation in AUTODYN, where the parameters are preset and can be modified and adjusted according to one's own needs. Generally, the default values are used, so the numerical units of parameters A and B are GPa.

 

Q3. Would it be possible to simulate also with the presence of aquifers?

Reply：The JWL equation of state (EOS) for explosives is also applicable to aquifers, and the Euler - Lagrange coupling model can be used for the propagation medium.

 

Q4. What about gas tanks? If yes, what is the impact on the responses in figure 5? Could equations 1 and 3 still apply?

Reply：In this paper, the effect of the stress wave on the tunnel is considered firstly, and the distance between the blast source and the tunnel exceeds the influence range of the blasting gas, and its effect can be basically ignored. Therefore, the influence of detonation gas is removed from the EOS of explosive, which can be set in the JWL equation.

In order to express the meaning of the paper more clearly, we have added the explanation in the revised manuscript as:

“Since no stemming and no coupling were applied to the borehole, the blast-induced gas products would leak out, that means the gas products did not play any role in the crack propagation. Only the shock wave action in this numerical study was simulated…”

 

Q5. I suggest associating the conclusions with some case study.

Reply：According to the reviewer’s suggestion, we have re-written the conclusions in the revised manuscript as:

4. Conclusion

In this paper, AUTODYN finite difference method software is used to numerically simulate the stress distribution and fracture area of a tunnel under blasting disturbance. Through preliminary research, the following conclusions are obtained:

(1) Under the condition of the same blasting loads, it can be seen from the stress and displacement of the tunnel, the stress and displacement of the tunnel is relatively small when the blasting disturbance source is located above the roof, i.e. the stress state of the tunnel is relatively stable, and the fracture area around the tunnel is minimal.

(2) From the uniaxial stress around the tunnel and the tunnel peripheral displacement, it can be seen that the displacement caused by horizontal direction stress of the tunnel is the largest, and the deformation is mainly concentrated above the floor and at the shoulder, while the vertical wall part has almost no deformation.

(3) For brittle materials such as rock, the arch shaped stress bearing surface is more likely to disperse stress, while the straight wall and flat floor of the tunnel cannot well disperse stress, resulting in uneven stress on the stress bearing surface, uncoordinated deformation and ultimate failure…

Therefore, when blasting construction in tunnels is carried, it is particularly important to pay attention to the mutual disturbance between horizontal tunnels and a strengthen support in advance is necessary, e.g. the arch shoulder and bottom plate of the tunnel.

 

Author Response File: Author Response.docx

Reviewer 3 Report

The paper presents a set of numerical simulations of the effects of blasting on a tunnel. A finite-difference model was used, considering non-reflecting boundary conditions. The failure model of the rock material assumes element deletion when the maximum tensile or shear stresses are reached. The results are interesting, showing the different effects on the tunnel stresses and the failure modes obtained with 3 different blast locations. The paper is suitable for publication, but a language revision is necessary (see below).

A language revision is necessary. The discussion of the results in section 3 of the text is fairly clear. However, the conclusions 1 and 2 (also stated in the Abstract) are difficult to understand and should be re-written. In particular, blast location #2 should be described as “above the roof” and not “at the roof”. The expression “single direction stress around the tunnel” is not clear, maybe “hoop stress” or “uniaxial stress around the tunnel”. Also the expression “displacement caused by the unit stress of the horizontal tunnel” needs to be improved.

Author Response

Questions from the Reviewer 3

 

Q1. A language revision is necessary. The discussion of the results in section 3 of the text is fairly clear. However, the conclusions 1 and 2 (also stated in the Abstract) are difficult to understand and should be re-written. In particular, blast location #2 should be described as “above the roof” and not “at the roof”. The expression “single direction stress around the tunnel” is not clear, maybe “hoop stress” or “uniaxial stress around the tunnel”. Also the expression “displacement caused by the unit stress of the horizontal tunnel” needs to be improved.

Reply：According to the reviewer’s suggestion, we have re-written the abstract and conclusions in the revised manuscript as:

Abstract: In order to study the dynamic stress distribution and the fracture area of rock around the tunnel under different orientations of blasting disturbance, AUTODYN finite difference method software was used to conduct corresponding numerical simulation research. Gauge monitoring points are set around the numerical model of the tunnel to conduct real-time monitoring of the stress distribution, displacement, and fracture area of the rock material tunnel. Based on the analysis of the stress wave propagation law, the following conclusions are obtained: 1. Under the condition of the same blasting loads, it can be seen from the stress and displacement of the tunnel, the stress and displacement of the tunnel is relatively small when the blasting disturbance source is located above the roof, i.e. the stress state of the tunnel is relatively stable, and the fracture area around the tunnel is minimal; 2. From the uniaxial stress around the tunnel and the tunnel peripheral displacement, it can be seen that the displacement caused by horizontal direction stress of the tunnel is the largest, and the deformation is mainly concentrated above the floor and at the shoulder, while the vertical wall part has almost no deformation; 3. For brittle materials such as rock, the arch shaped stress bearing surface is more likely to disperse stress, while the straight wall and flat floor of the tunnel cannot well disperse stress, resulting in uneven stress on the stress bearing surface, uncoordinated deformation and ultimate failure….

4. Conclusion

In this paper, AUTODYN finite difference method software is used to numerically simulate the stress distribution and fracture area of a tunnel under blasting disturbance. Through preliminary research, the following conclusions are obtained:

(1) Under the condition of the same blasting loads, it can be seen from the stress and displacement of the tunnel, the stress and displacement of the tunnel is relatively small when the blasting disturbance source is located above the roof, i.e. the stress state of the tunnel is relatively stable, and the fracture area around the tunnel is minimal.

(2) From the uniaxial stress around the tunnel and the tunnel peripheral displacement, it can be seen that the displacement caused by horizontal direction stress of the tunnel is the largest, and the deformation is mainly concentrated above the floor and at the shoulder, while the vertical wall part has almost no deformation.

(3) For brittle materials such as rock, the arch shaped stress bearing surface is more likely to disperse stress, while the straight wall and flat floor of the tunnel cannot well disperse stress, resulting in uneven stress on the stress bearing surface, uncoordinated deformation and ultimate failure…

Therefore, when blasting construction in tunnels is carried, it is particularly important to pay attention to the mutual disturbance between horizontal tunnels and a strengthen support in advance is necessary, e.g. the arch shoulder and bottom plate of the tunnel.

Author Response File: Author Response.docx

Reviewer 4 Report

In my opinion, the model covers too small an area - 50 x 50 m. I suggest repeating the test cycle for the model, e.g. 100 x 100 m. The location of the explosion site at a distance of 5 m from the model boundary causes that the obtained results are contaminated by the influence of the model support on its edges. This is suggested, for example, in Fig. 5 and 6, where one can get the impression that the explosion wave is reflected from the edge of the model and propagates towards the tunnel. In fact, proportional wave propagation in all directions is to be expected, and the existence of the tunnel will undoubtedly affect the picture of wave propagation. The presented model is a theoretical model, there is no reference to mining practice (e.g. drilling of an excavation parallel to the existing one). Did the authors study this phenomenon "in situ"?

Author Response

Questions from the Reviewer 4

 

Comments and Suggestions for Authors

Q1. In my opinion, the model covers too small an area - 50 x 50 m. I suggest repeating the test cycle for the model, e.g. 100 x 100 m. The location of the explosion site at a distance of 5 m from the model boundary causes that the obtained results are contaminated by the influence of the model support on its edges. This is suggested, for example, in Fig. 5 and 6, where one can get the impression that the explosion wave is reflected from the edge of the model and propagates towards the tunnel. In fact, proportional wave propagation in all directions is to be expected, and the existence of the tunnel will undoubtedly affect the picture of wave propagation. The presented model is a theoretical model, there is no reference to mining practice (e.g. drilling of an excavation parallel to the existing one). Did the authors study this phenomenon "in situ"?

Reply：Thank you for the reviewer’s suggestion, we have not explained the meaning of “Transmit boundary” clearly in the paper. “Transmit boundary” means the stress wave does not reflect after encountering the boundary but dissipates directly through the boundary. Therefore, model covers an area 50 * 50 m is reasonable. In order to express the meaning of the paper more clearly, we have added the sentences in the revised manuscript as:

“Therefore, the “Transmit boundary” condition i.e. the transmission boundary is adopted which means the stress wave does not reflect after encountering the boundary, but dissipates directly through the boundary…”

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors have not addressed the suggestions provided.

The language has been improved.

Author Response

Thank you for taking the time to review the manuscript after your busy schedule and the quality of this paper has been greatly improved according to your suggestions. In the first round of revisions, we provided point-to-point responses and revisions based on your suggestion. In the second round, the comments of "The authors have not addressed the suggestions provided." were given. If you have any doubt about the response to the questions, please provide point-to-point review comments to us for future revisions. Thank you  for your suggestion.

Reviewer 2 Report

Corrected modifications.

Author Response

Thank you for taking the time to review the manuscript after your busy schedule and the quality of this paper has been greatly improved according to your suggestions.

Reviewer 4 Report

The changes made make the article more understandable for readers. In the future, I suggest research on a larger model.

Author Response

Thank you for taking the time to review the manuscript after your busy schedule and the quality of this paper has been greatly improved according to your suggestions. Based on your suggestion, we will adopt a larger model in subsequent related research, striving to achieve the expected results.