Dear Dr. Zhang,

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This work was funded by the general project of Hubei Provincial Key Laboratory of Blasting Engineering(BL2021-11),National Natural Science Foundation of China(52274136,51904210), and Natural Science Foundation of Hubei Province(2024 AFB766). We thank the Wuhan University of Science and Technology for providing experimental sites and equipment.

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This work was funded by the general project of Hubei Provincial Key Laboratory of Blasting Engineering(BL2021-11),National Natural Science Foundation of China(52274136,51904210), and Natural Science Foundation of Hubei Province(2024 AFB766). We thank the Wuhan University of Science and Technology for providing experimental sites and equipment.

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This work was funded by the general project of Hubei Provincial Key Laboratory of Blasting Engineering(BL2021-11),National Natural Science Foundation of China(52274136,51904210), and Natural Science Foundation of Hubei Province(2024 AFB766). We thank the Wuhan University of Science and Technology for providing experimental sites and equipment.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

Reviewer #1: Partly

Reviewer #2: Yes

Reviewer #3: Yes

Reviewer #4: Partly

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2. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #1: N/A

Reviewer #2: Yes

Reviewer #3: Yes

Reviewer #4: I Don't Know

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3. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #1: No

Reviewer #2: Yes

Reviewer #3: Yes

Reviewer #4: No

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4. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #1: No

Reviewer #2: No

Reviewer #3: Yes

Reviewer #4: No

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Reviewer #1: General Comments

The manuscript presents an experimental framework for optimizing blasting delays with the aim of jointly reducing vibration and improving fragmentation. The topic is relevant for blasting science and surface mining engineering, and the integration of delay theory, the Swebrec function, and controlled laboratory experiments is conceptually valuable.

However, the study suffers from a critical limitation frequently encountered in small-scale blasting research: the difficulty of relating laboratory-scale concrete experiments to full-scale bench blasting operations in actual rock masses. Several aspects of the experimental design, scaling, charge type, and interpretation of results raise concerns regarding the generalizability of the conclusions. The manuscript would benefit significantly from clarifications, additional discussion, and corrections (e.g., proper attribution of the Swebrec function).

Substantial revisions are required before the contribution can be properly evaluated.

Major Issues

1. Limited Realism and Representativeness of Laboratory Experiments

The fundamental challenge in this study is the large gap between the controlled concrete-block experiment and real open-pit blasting conditions. In the field, tons of rock are fragmented, numerous blastholes interact dynamically, and the rock mass behavior is controlled by discontinuities and heterogeneities.

In contrast, the experiments use 20 × 20 × 20 cm homogeneous concrete blocks with no natural joints or weaknesses.

The manuscript should explicitly discuss the implications of this discrepancy and clearly articulate how the laboratory results can—or cannot—be extrapolated to realistic blasting conditions.

2. Experimental Setup Description Is Incomplete

Figure 1 presents a schematic diagram of the test site, but no actual photographs of the test arrangement are provided.

For transparency and reproducibility, photographs of the real experimental setup from several angles should be included.

Such visuals would help readers understand the test boundary conditions, instrumentation, and geometry.

3. Use of Electronic Detonators Inside Small Holes

The blast holes have a diameter of 10 mm and include electronic detonators with metallic shells.

The fragmentation resulting from the detonator casing itself may significantly influence breakage of the small concrete blocks. This issue is not acknowledged and may bias the fragmentation results.

The authors should discuss this limitation.

A more appropriate laboratory charge configuration might have been the use of detonating cord placed within the holes.

4. Practical Relevance of the Recommended Delay Times (3–4 ms)

The manuscript concludes that 3–4 ms inter-hole and 1–3 ms inter-row delays are optimal.

However, for example, typical field delay increments in shock-tube systems are 17, 25, 42, and 65 ms, with 25 ms and 42 ms commonly used in surface mining.

The authors must explain whether the experimentally determined micro-delays have any meaningful correlation to actual field practice.

Without such discussion, the practical significance of the findings remains unclear.

5. Reliability of Fragmentation-Related Conclusions

The fragmentation results presented in Conclusion – Clause 1 appear overinterpreted given the experimental limitations:

• The specimen is small, homogeneous, and free of discontinuities.

• Fragmentation behavior in real rock masses is strongly influenced by structural features.

• The recommended delay interval (tk = 3 ms, tp = 3 ms) may have no real-scale effect on fragmentation mechanisms.

The reliability and applicability of these fragmentation conclusions should be reconsidered and discussed in detail.

6. Incorrect Attribution and Referencing of the Swebrec Function

The manuscript incorrectly refers to the distribution as the “Swebrec et al. distribution,” and the references provided are irrelevant.

The Swebrec function was developed by Finn Ouchterlony, and the correct references are:

• Ouchterlony, F. (2005a). The Swebrec© Function: Linking Fragmentation by Blasting and Crushing. Mining Technology, 114(1), 29–44.

• Ouchterlony, F. (2005b). What Does the Fragment Size Distribution of Blasted Rock Look Like? In: Proc. 3rd EFEE World Conf. on Explosives and Blasting, Brighton, 189–199.

This must be corrected for scientific accuracy.

Reviewer #2: （1）The title of this manuscript is "Experimental study on the coupling control of rock blasting vibration and crushing fragmentation size", but why does the first paragraph of the Introduction only mention blasting vibration and not the crushing fragmentation size?

（2）The references in the first paragraph of the Introduction of this manuscript start from [4], not [1]. In addition, the text "Error! Reference source not found" appears multiple times in the Introduction.

（3）Fig. 6 was not cited in the text, and the reviewer was unaware of its function.

（4）The formats of the references are inconsistent, such as [1] and [2].

There are too many similar format issues in the manuscript. It is suggested that the authors make revisions and resubmit it.

Reviewer #3: This paper proposes an optimized control method based on the delay time interval, aiming to achieve the synergistic optimization of blasting vibration control and rock fragmentation effect, and provides a new technical path for vibration control and efficiency improvement in open-pit deep-hole blasting engineering. Combining theoretical derivation with experimental verification, the research content is closely aligned with industry needs, and the proposed coupled regulation method has certain engineering application valueThe logic of this paper remains somewhat unclear; it is recommended that revisions be made before resubmission:

1.The abstract only mentions the "interval-based delay optimization framework" but fails to briefly explain its core logic (e.g., how to achieve coupled control through intervals rather than fixed values). It is recommended to add 1-2 sentences about the core principle of the framework to enhance the completeness of the abstract.

2.Although the introduction reviews domestic and foreign studies, it does not clearly point out specific literature limitation cases of the current "single-factor focused research" (e.g., a scholar's study only focuses on vibration without involving fragmentation). It is recommended to supplement the limitation analysis of 1-2 typical literatures to strengthen the persuasiveness of the research gap.

3.In the experimental design of Section 2.1, it is mentioned that "vibration measurement points 5, 6, and 7 are arranged on the lateral side of the free face," but only the reverse and forward direction data of the free face are analyzed in Sections 4.1 and 4.2, with no mention of the processing results of the lateral data. It is recommended to supplement the analysis of lateral PPV changes, vibration attenuation rate, and fragment distribution to achieve the unity of experimental design and data processing/analysis.

4.When deriving the delay time based on Hanukayev's theory in Section 3.1, only formulas are provided without substituting experimental parameters (such as the longitudinal wave velocity C and minimum resistance line W of C50 concrete) to demonstrate the calculation process. It is recommended to add an example of substituting key parameters for calculation to make the derivation process more traceable.

5.Section 4.2 mentions "performing Fast Fourier Transform (FFT) on blast vibration data to derive the dominant frequency," but the frequency domain analysis method (such as FFT parameter settings and frequency resolution calculation) is not separately clarified in "3 Theoretical Derivation" or "4 Result Analysis." It is recommended to add a new subsection or supplementary paragraph titled "Frequency Domain Analysis Method" to improve the analysis logic.

6.The experiment uses C50 concrete instead of natural rock. Only the mix ratio and strength grade of the concrete are mentioned in Section 2.1, without explaining the basis for the similarity of its mechanical parameters (such as elastic modulus, Poisson's ratio, and compressive strength) to the target natural rock mass (e.g., limestone and granite commonly found in open-pit mines). It is recommended to add a comparison table of mechanical parameters between concrete and natural rock mass (literature data can be cited) to verify the rationality of the model.

7.Some figures (such as Figure 1, Figures 2-5) have low resolution and missing key unit labels. It is recommended to increase the resolution of all figures to 300 dpi, correct image display issues, and unify the units of figures and tables.

8.The "optimized interval of delay time (tk=3–4 ms, tp=1–3 ms)" is proposed in Section 5.3, but the advantages of the interval-based delay time determination method compared with the traditional fixed-value method are not reflected. It is recommended to supplement the explanation of the advantages to enhance the expression of innovation.

9.In Table 3 "Fragmentation Size Table for Inter-hole Delay" in Section 4.1, the Xmax (19.8 cm) of Group 3 is much higher than that of other groups, but the reason for the increased fragments caused by the delay time (tk=2 ms) of this group (such as insufficient superposition of stress waves and inadequate crack propagation) is not analyzed. It is recommended to add 1-2 sentences of mechanism analysis on abnormal data to improve the depth of result interpretation.

10.When using the Swebrec function to evaluate the fragment size in Section 3.2, only the formula is given without explaining the calculation process of the "fluctuation exponent b" (e.g., how to solve it with the least-squares method through sieving data). It is recommended to supplement the key steps of calculating the b value (such as sample size and goodness of fit R²) to enhance the repeatability of the method.

11.There are ambiguous expressions and grammatical errors in some sentences of the paper. It is recommended to recheck the grammar to make the expression professional and accurate.

12.The conclusion mentions that "PPV shows exponential attenuation in the free face direction and linear attenuation in the reverse direction," but it is not supported by specific data in the paper (such as the forward attenuation coefficient and reverse attenuation slope under a certain group of delays). It is recommended to supplement key data (e.g., the forward PPV of Group 4 decreases from X cm/s to Y cm/s, conforming to the exponential law y=ae^(-bx)) to enhance the credibility of the conclusion.

13.The format of references is inconsistent. Some references (such as [21], [25]) lack complete DOIs or journal names. It is recommended to unify and standardize the format according to "Author. Title[Document type identifier]. Journal name, Year, Volume(Issue): Pages. DOI." and supplement missing DOIs and journal names.

14.For the parameter settings of "inter-hole spacing of 100 mm and row spacing of 70 mm" in the experimental design, the basis for the similarity ratio between this size and the actual deep-hole blasting in open-pit mines (e.g., inter-hole spacing of 5-10 m) is not explained. It is recommended to supplement the design logic of the similarity ratio to illustrate the correlation between the model experiment and engineering practice.

15.When analyzing the dominant frequency law in Section 5.2, only "the dominant frequency attenuates with the increase of the blast center distance" is mentioned, without explaining the practical significance of the change in dominant frequency for "avoiding structural resonance" (e.g., the dominant frequency of a certain delay scheme is always higher than the resonance frequency of buildings). It is recommended to supplement the correlation analysis between the dominant frequency and engineering safety to strengthen the engineering value of the research.

Reviewer #4: Achieving both shock absorption and optimized fragmentation simultaneously poses a challenge in delay design for open-pit blasting. This paper proposes an intriguing interval-based delay optimization framework. The research provides important theoretical support for safe and efficient mining blasting operations. However, there are still some issues that need to be clarified before publication.

1. In the first paragraph of the introduction, references [1-3] are missing, and references [4-7] are cited improperly. Moreover, two citation errors also appear in the second paragraph of the introduction. This gives readers the impression that the research in this manuscript is not yet fully developed.

2. Figures 2-7 are presented as separate charts, but they actually form a set of images. It is recommended to consolidate them into a multi-panel chart module to enhance clarity and compactness. Furthermore, regarding the interpretation of Figures 2-7, presenting the impact patterns with concrete data would make the research findings more persuasive. Regarding Figure 8-11, the same recommendation applies.

3. The text in the images within the manuscript is not very clear and is difficult to read, requiring better design of the text within the images.

4. Figure 13 should provide references.

5. The interval-based delay optimization framework proposed in this manuscript is not clearly defined, preventing readers from systematically learning the underlying theory and methodology. Although the manuscript presents some experimental findings, its scientific contributions remain somewhat unclear.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

Reviewer #4: Yes: Jun YangJun YangJun YangJun Yang

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Submitted filename: Review comments.doc

Dear Dr. Zhang,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Apr 19 2026 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

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If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at . Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at . Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at . Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols....

We look forward to receiving your revised manuscript.

Kind regards,

Zhenhua Li

Academic Editor

PLOS One

Journal Requirements:

If the reviewer comments include a recommendation to cite specific previously published works, please review and evaluate these publications to determine whether they are relevant and should be cited. There is no requirement to cite these works unless the editor has indicated otherwise.

Additional Editor Comments:

You will see from the referees' comments that additional information needs to be provided, and we ask that this be provided, before we consider you manuscript further.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

Reviewer #1: (No Response)

Reviewer #2: (No Response)

Reviewer #3: (No Response)

Reviewer #4: (No Response)

Reviewer #5: All comments have been addressed

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2. Is the manuscript technically sound, and do the data support the conclusions??>

Reviewer #1: Yes

Reviewer #2: (No Response)

Reviewer #3: (No Response)

Reviewer #4: Partly

Reviewer #5: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #1: Yes

Reviewer #2: (No Response)

Reviewer #3: (No Response)

Reviewer #4: Yes

Reviewer #5: Yes

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4. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #1: Yes

Reviewer #2: (No Response)

Reviewer #3: (No Response)

Reviewer #4: Yes

Reviewer #5: Yes

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5. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #1: Yes

Reviewer #2: (No Response)

Reviewer #3: (No Response)

Reviewer #4: Yes

Reviewer #5: Yes

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Reviewer #1: (No Response)

Reviewer #2: In response to the issues raised by the reviewer previously, although the authors have made some revisions, there are still many formatting problems in the current manuscript. The reviewer have listed the more obvious problems as follows:

(1)Citation of references in the text: For multiple consecutive references, such as the first five references in the text, the citation format should be [1-5], rather than "[1][5]". Similarly, "[17]-[20]" in the manuscript is also not standard. Additionally, reference [7] in the Introduction is not cited.

(2)Generally, a space should be added between numbers and units throughout the text, but the authors have not consistently followed this rule, such as "0.5m" and "45-75 Hz".

(3)For the references listed at the end of the manuscript, the format is still not uniform (e.g., [1], [4]) and not standard (e.g., [5]). The reviewer have provided examples of both Chinese and English reference lists as follows:

[1]Yang Z., Tao M., Memon M.B., Zhuang D.D., Zhao Y. Microwave irradiation-induced deterioration of rock mechanical properties and implications for mechanized hard rock excavation [J]. Journal of Rock Mechanics and Geotechnical Engineering, 2024, 24: 00308.

[2]Li X.B., Zhou J., Wang S.F., Liu B. Review and practice of deep mining for solid mineral resources [J]. The Chinese Journal of Nonferrous Metals, 2017, 27(06): 1236-1262. (in Chinese)

Regarding the above-mentioned problems existing in the manuscript, the reviewer did not list them one by one. It is suggested that the authors carefully revise the entire text.

Reviewer #3: (No Response)

Reviewer #4: The reviewers' comments have not been adequately addressed. The authors are requested to carefully revise the manuscript in accordance with the feedback provided.

Reviewer #5: 1. The similarity ratio of the experimental model is used as a reference, reducing the rationality of the article.

2. The reviewer has pointed out that the effect of the electronic detonator shell on the fragmentation effect is not sufficiently discussed. The author responded that it "does not affect the selection of the optimal delay combination." However, from the perspective of academic rigor, it is recommended to clearly state in the 'Limitations' section: the detonator shell in small-sized specimens may have an additional impact on fragmentation, and the differences in charge structures need to be considered during field applications.

3. The text mentions using the least squares method to fit parameter b, but the b values and goodness of fit R² for each group are not provided. It is recommended to supplement the b values and R² in Tables 4 and 5 to demonstrate the reliability of the fitting.

4. It is recommended to try to understand the issues raised by the reviewers and refine the details of the article. Latest research work related with this topic can be referred in the introduction. Probabilistic stability analyses of two-layer undrained slopes. Fracture evolution and mechanical deterioration of granite under cyclic thermal and liquid nitrogen cryogenic impact.

5. The text points out that the optimal delay is a range (tk=3-4 ms, tp=1-3 ms) but does not explain how the boundaries of this range are determined, such as whether it is based on empirical summaries of experimental results or some theoretical threshold. It is suggested to add a theoretical explanation of the range boundaries in the 'Discussion' section or propose a general principle for determining the range.

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what does this mean?). If published, this will include your full peer review and any attached files.). If published, this will include your full peer review and any attached files.). If published, this will include your full peer review and any attached files.). If published, this will include your full peer review and any attached files.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

Reviewer #4: Yes: Yang JunYang JunYang JunYang Jun

Reviewer #5: No

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Attachments

Attachment

Submitted filename: comments.docx

Experimental study on the coupling control of rock blasting vibration and crushing fragmentation size

PONE-D-25-62535R2

Dear Dr. Zhang,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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Kind regards,

Zhenhua Li

Academic Editor

PLOS One

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

Reviewer #2: All comments have been addressed

Reviewer #5: All comments have been addressed

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2. Is the manuscript technically sound, and do the data support the conclusions??>

Reviewer #2: Yes

Reviewer #5: Yes

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3. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #2: Yes

Reviewer #5: Yes

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4. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #2: Yes

Reviewer #5: Yes

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5. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #2: Yes

Reviewer #5: Yes

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Reviewer #2: (No Response)

Reviewer #5: This study takes this as an entry point to fill this academic gap, and proposes an optimal delay time selection method to achieve the coupled control of reducing blasting hazards and optimizing blasting effect, which provides a solid upport for the optimization of the development of blasting engineering.

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what does this mean?). If published, this will include your full peer review and any attached files.). If published, this will include your full peer review and any attached files.). If published, this will include your full peer review and any attached files.). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our For information about this choice, including consent withdrawal, please see our For information about this choice, including consent withdrawal, please see our For information about this choice, including consent withdrawal, please see our Privacy Policy..-->

Reviewer #2: No

Reviewer #5: No

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