Numerical Simulation of Rockfill Materials Based on Fractal Theory

Round 1

Reviewer 1 Report

At the current state, the paper is not at a level to be published and needs major revision.

• Please focus more on presenting the novelty of the work, research gaps, and the way this paper can contribute to the literature.
• The results have not sufficiently justified the claims provided in the introduction. 
• English needs to be polished.
• Try to focus more on the physics behind the trends in the results

Author Response

Dear Editor/Reviewers,

Thank you for the comments on our manuscript (applsci-1440102). The comments on our manuscript are helpful in improving our paper. We appreciate deeply for your hard work. According to the reviewers’ reports, we have checked our paper carefully. We have replied the questions from the reviewers point by point, as follows. We hope the new version of our paper is suitable for publication in Applied Sciences.

With our best regards,

Hongxing Han

 

P.S. the following is the reply for the questions from the reviewers point by point.

Reviewer 1

Question 1: Please focus more on presenting the novelty of the work, research gaps, and the way this paper can contribute to the literature.

Response: Thank you very much for your valuable comments. There are three main innovations in this article. (1) A fractal model is established with the number of particles of different particle, which can reflect the changing trend of particle size distribution. (2) The fractal model provides a new method for studying the mechanical properties of rockfill materials. (3) The model establishes a relationship between fractal dimension and coordination number. As a research gap, we consulted the references about fractal dimension. At present, most scholars have studied the mechanical properties of rockfill materials using the quality fractal model proposed by Tyler, but the fractal model is not reported with the number of particles between different particle groups in the newspaper. The research results provide a new method for studying the mechanical properties rockfill materials. The following words have been added to the manuscript and marked in blue:

Most scholars have studied the mechanical properties of rockfill materials using the quality fractal model proposed by Tyler, but the fractal model is not reported with the number of particles between different particle groups in the newspaper.

The research results provide a new method for studying the mechanical properties rockfill materials.

Question 2: The results have not sufficiently justified the claims provided in the introduction.

Response: Thank you very much for your work, which is helpful to improve the quality of the article. We have made appropriate modifications in the introduction. The following words have been modified to the manuscript and marked in blue:

The original grading curve of rockfill materials is scaled in four conventional scales by the fractal model. Taking the fractal dimension of the scaled sample as the index reflecting its structural parameters, the relative density test and biaxial compression test under different fractal dimensions are carried out, and the physical and mechanical properties of rockfill materials under different fractal dimensions are studied.

Question 3: English needs to be polished.

Response: We have checked the manuscript carefully. Inappropriate terms have been corrected.

Question 4: Try to focus more on the physics behind the trends in the results

Response: Thank you very much for your work, which is helpful to improve the quality of the article. In Section 4.2 of the article, we added physical phenomena to explain the strain characteristics of rockfill materials. In Section 4.3 of the article, we have made appropriate modifications to the test results in Figure 6. The following words have been modified to the manuscript and marked in blue:

The more fine-grained soil in rockfill materials, the more obvious the shear dilatancy.

Fig. 6 shows that in the initial stage of loading, the finer particles are gradually filled between the coarse particles, the contact points between the particles are increasing, the corresponding coordination number is also increasing, and the sample is in a compressed state; After the coordination number reaches the maximum value, with the continuous increase of load, relative sliding occurs between some coarse particles, the number of contact points between particles decreases, the corresponding coordination number decreases, and the sample is in the state of shear expansion; The coordination number changes corresponding to the four fractal dimensions D are similar. The larger the fractal dimension D is, the larger the coordination number is, but it does not coincide, indicating that the influence of fractal dimension D on numerical simulation calculation is objective.

Author Response File: Author Response.pdf

Reviewer 2 Report

I have the following questions:
- Have the results obtained with the statistical method been experimentally verified?
- What are the planned further works related to the method presented in the article? It would be good to present this in the conclusions.

Author Response

Dear Editor/Reviewers,

Thank you for the comments on our manuscript (applsci-1440102). The comments on our manuscript are helpful in improving our paper. We appreciate deeply for your hard work. According to the reviewers’ reports, we have checked our paper carefully. We have replied the questions from the reviewers point by point, as follows. We hope the new version of our paper is suitable for publication in Applied Sciences.

With our best regards,

Hongxing Han

 

P.S. the following is the reply for the questions from the reviewers point by point.

Reviewer 2

Question 1: Have the results obtained with the statistical method been experimentally verified?

Response: Thanks for your comments, which is helpful for future research. The results obtained with the statistical method have been verified by numerical methods, but they have not been verified by laboratory tests.

Question 2: What are the planned further works related to the method presented in the article? It would be good to present this in the conclusions.

Response: Thanks for your comments. The next main work is establishing the relationship between fractal dimension, peak strength and confining pressure of rockfill materials by particle aggregate. The limit value of particle breakage is given by using fractal dimension. That is already present in the conclusion and marked in red:

The relationship between fractal dimension, peak strength and confining pressure of rockfill materials is established by the fractal theory, which is used to calculate the rockfill materials. The limit value of particle breakage is given by fractal dimension.

Reviewer 3 Report

The topic of the application of fractal analysis is of great interest in the context of construction applications.
The introduction to the article provides a full introduction to the topic of the article. The research is designed correctly and the research methods are described correctly. 
The research is presented clearly. The only remark concerns the analysis of the correctness of linear pattern matching with the obtained results. Due to the fact that there are only 4 points to guide this graph using R^2 is in my opinion insufficient. I suggest checking MAPE and other measures of goodness of fit. Additionally, I am missing from the graphs showing the data the standard deviation for the results obtained. 
Overall the article is very interesting and after taking into account the above comments in my opinion it can be published. 

 

Author Response

Dear Editor/Reviewers,

Thank you for the comments on our manuscript (applsci-1440102). The comments on our manuscript are helpful in improving our paper. We appreciate deeply for your hard work. According to the reviewers’ reports, we have checked our paper carefully. We have replied the questions from the reviewers point by point, as follows. We hope the new version of our paper is suitable for publication in Applied Sciences.

With our best regards,

Hongxing Han

 

P.S. the following is the reply for the questions from the reviewers point by point.

Reviewer 3

Question 1: The research is presented clearly. The only remark concerns the analysis of the correctness of linear pattern matching with the obtained results. Due to the fact that there are only 4 points to guide this graph using R^2 is in my opinion insufficient. I suggest checking MAPE and other measures of goodness of fit. Additionally, I am missing from the graphs showing the data the standard deviation for the results obtained.

Response: Thanks for your comments. The analysis of linear pattern matching and the obtained results, we use 5 points to guide this graph using R², As shown in Fig. 2. Because the particle breakage is not considered in the sample, the standard deviation has little effect on the experimental results. Therefore, the influence of the standard deviation on the results is ignored.

Reviewer 4 Report

The paper contains a numerical survey on the effects of scaling methods used for rockfill materials. Scaling methods consist of recreating with the rockfill material retrieved on site a sample with a representative grain size distribution without considering fractions exceeding the maximum size allowed by the test equipment. The authors explored the different grain size distribution created by four scaling method in terms of fractal dimension, density state and mechanical behaviour.

The two main issues emerge reading the paper:

1. The numerical model is not introduced. A description of the type of discrete element type and the contact laws adopted are certainly necessary, since the paper is based on the numerical results.
2. A comparison between the numerical results obtained with the scaled gradings and the ones obtained by the original grading is necessary to establish which scaling method has the least influence on the properties of the material.

Punctual comments:

3. The English should be revised, especially on the abstract and on pag3
4. The first part of the introduction requires references.
5. All the notations should be written in italic.
6. How is the fractal dimension of the designing grading curve?
7. About the contact stiffnesses and interparticle friction, how did you calibrate these values and are they used the same among the RD and bi-axial tests?
8. A discussion is needed on the reliability of mechanical properties obtained by two-dimensional analyses of discrete element. Eventually by comparing the results obtained with the experimental results reported in the reference [25].

Author Response

Dear Editor/Reviewers,

Thank you for the comments on our manuscript (applsci-1440102). The comments on our manuscript are helpful in improving our paper. We appreciate deeply for your hard work. According to the reviewers’ reports, we have checked our paper carefully. We have replied the questions from the reviewers point by point, as follows. We hope the new version of our paper is suitable for publication in Applied Sciences.

With our best regards,

Hongxing Han

 

P.S. the following is the reply for the questions from the reviewers point by point.

Reviewer 4

Question 1: The numerical model is not introduced. A description of the type of discrete element type and the contact laws adopted are certainly necessary, since the paper is based on the numerical results.

Response: Thank you very much for your work, which is helpful to improve the quality of the article. In this paper, a fractal model is proposed based on the particle number of particle group, and then the fractal dimension and the physical properties of rockfill materials are mainly analyzed. The discrete element types and the contact laws used are described in the main references[29-30]. The following words and reference have been added to the manuscript and marked in green.

In this paper, the linear stiffness model without considering particle breakage is adopted, and the calibration of meso parameters refers to references [29-30].

29. B. Zhou, H.B. Wang, W.F. Zhao, J.W. Li, and B.C. Zheng, Analysis of relationship between particle mesoscopic and macroscopic mechanical parameters of cohesive materials, Rock and Soil Mechanics. 33(10) (2012) 3171-3178.
30. H.X. Han, W. Chen, B. Huang, X.D. Fu, Numerical simulation of the influence of particle shape on the mechanical properties of rockfill materials, Engineering Computations. 34(7) (2017) 2228-2241.

Question 2: A comparison between the numerical results obtained with the scaled gradings and the ones obtained by the original grading is necessary to establish which scaling method has the least influence on the properties of the material.

Response: Thank you very much for your comments. There is no comparison between the numerical results obtained with the scaled gradings and the ones obtained by the original grading of rockfill materials, mainly including the following two points: First, the maximum particle size of the original grading is 600mm and the sample diameter is 300mm, which does not meet the requirement that the ratio of the maximum particle size to the sample diameter is less than 1:5. Second, if the maximum particle size of the original grading is 600mm, the sample diameter should be greater than or equal to 600mm. The number of particles in the numerical sample is large, and the calculation speed is too slow.

Question 3: The English should be revised, especially on the abstract and on pag3.

Response: We have checked the manuscript carefully. Inappropriate terms have been corrected.

Question 4: The first part of the introduction requires references.

Response: Thank you very much for your work, which is helpful to improve the quality of the article. The following words and reference have been added to the manuscript and marked in green.

Since its introduction [16], fractal theory has made some valuable achievements in the aspects of rock fracture [17], soil particle morphology [18-19], and rockfill materials breakage [20-22]. Fractal geometry theory was drawn into the gradation of rock-fill materials. It is found that the truncation error is one of the main factors affecting the density scale effect of rockfill materials [23].

21. Y. Xiao, M.Q. Meng, A. Daouadji, Q.S. Chen, Z.J. Wu, and X. Jiang, Effects of particle size on crushing and deformation behaviors of rockfill materials, Geoscience Frontiers. 11(2) (2020) 375-388.
22. L.Q. Wu, S. Zhu, Y.M. Wang, K.M. Wei, and C.Y. Lu, A modified scale method based on fractal theory for rockfill materials, European Journal of Environmental and Civil Engineering. 18(1) (2014) 106-127.
23. L.Q. Wu, S. Zhu, K.M. Wei, and C.Y. Lu, The fractal properties of scale effect on the density of rock-fill materials, Advanced Materials Research. 706-708 (2013) 520-525.

Question 5: All the notations should be written in italic.

Response: Thank you very much for your comments. We have changed all the notations to italics. Words that change italics are marked in green.

Question 6: How is the fractal dimension of the designing grading curve?

Response: Thank you very much for your comments. The maximum particle size of rockfill material is 600mm and the sample size is 300mm. The original grade distribution fractal dimension is not calculated.

Question 7: About the contact stiffnesses and interparticle friction, how did you calibrate these values and are they used the same among the RD and bi-axial tests?

Response: Thank you very much for your comments. We calibrate it through the following references[1-2]. The contact stiffness and friction coefficient are different in RD and biaxial tests.

1. B. Zhou, H.B. Wang, W.F. Zhao, J.W. Li, and B.C. Zheng, Analysis of relationship between particle mesoscopic and macroscopic mechanical parameters of cohesive materials, Rock and Soil Mechanics. 33(10) (2012) 3171-3178.
2. H.X. Han, W. Chen, Z.F. Qiu, and X.D. Fu, Numerical simulation of two-dimensional particle flow in broken rockfill materials, Chinese Journal of Geotechnical Engineering. 38 (S2) (2016) 234-239.
3. H.X. Han, W. Chen, B. Huang, X.D. Fu, Numerical simulation of the influence of particle shape on the mechanical properties of rockfill materials, Engineering Computations. 34(7) (2017) 2228-2241.

Question 8:A discussion is needed on the reliability of mechanical properties obtained by two-dimensional analyses of discrete element. Eventually by comparing the results obtained with the experimental results reported in the reference [25].

Response: Thank you very much for your work. The fractal dimension established in this paper mainly focuses on the relationship between fractal dimension and physical properties of rockfill materials, while reference [25] focuses on the relationship between scaling method and compactness, as well as the relationship between dry density and gradation.

Round 2

Reviewer 1 Report

The authors have addressed all the comments very well. The current version of the paper can be considered for publication.

Reviewer 4 Report

1. The core of this paper is based on results obtained by numerical simulations of relative density and bi-axial tests on four different grain size distributions obtained by scaling an original grading curve of rockfill material. The polydispersity of the grain size distribution is quantified by the fractal dimension evaluated by means of the number of particles (assumed spherical) and it is used as an intrinsic property of the material. The description of the model adopted is not provided, apart from two references added in the last revision. A punctual description about the type of element adopted, the contact models, the reliability of discrete element method to quantitatively evaluate physical and mechanical properties of a granular material should be provided.
2. the aim and especially the novelty of the work does not emerge. However, the fractal method combined with discrete element method simulations is potentially a good tool to evaluate the goodness of the scaling methods in respect to the original grading...
3. The main issues reported in the first review have not been solved.