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Peer-Review Record

Development of a More Descriptive Particle Breakage Probability Model

Minerals 2020, 10(8), 710;
Reviewer 1: Anonymous
Reviewer 2: Anonymous
Reviewer 3: Thomas Mütze
Minerals 2020, 10(8), 710;
Received: 8 June 2020 / Revised: 5 August 2020 / Accepted: 6 August 2020 / Published: 12 August 2020
(This article belongs to the Special Issue Comminution in the Minerals Industry)

Round 1

Reviewer 1 Report

AN interesting topic and potentially a useful contribution in terms of experimental data.

A little disappointing for lack of any underlying hypothesis to test - or even speculation about potential implications.

It seems to me that the underlying question is not simply the stress raisers (flaws or mineral grains) contained within a particular particle but also how those stress raisers are distributed across a sample of similar size/mass.

However, good empirical data is worthy of publication if sufficient detail is included to allow it to also be useful to other researchers. 

Perhaps the most serious weakness is that probability of breakage is based on a succession of similar impacts while tumbling mills apply a succession of different impact energies.

A recent paper 

Faramarzi, F., Napier-Munn, T.J., Morrison, R.D., Kanchibotla, S., The Extended Drop Weight Testing approach – What it reveals. Minerals Engineering, 2020, Article in Press.

suggests that particle resistance to impact breakage by drop weight testing  is itself a distributed property supporting the views of ref 17

This might explain why the probability of breakage apparently increases at less than unity for successive impacts (eqn 1). That is, the testing process is selecting for survivors which are harder on average.


Your definition "breakage" should be close to eqn 1

Fig 1 should be - after Bwaya (2015)

It should also specify if only one particle size or mass is being described.

Eqn 2 - to the power 0.76?

80 The main feature

84 after Bwaya and Moys - omit included in a later paper.

85 correlated with

87-92 The ULFC does provide a lot more information but you still need to input similar input energy

Typical UFLC results indicate a distribution of energy to first fracture which you are assuming is amenable to description with a single number/expression.

100 given by Shi (21)

108 successive impacts

110 Define rate of deterioration

112 Fig 2 Fig 2 seems to suggest that the increase in Pb decreases with each additional impact.

Is that what you actually are saying? Implications? for > and < unity?

124  15 not 24

130 the number of particles was increased

144 your definition of breakage should be provided with eqn 1

167 Table 3 - Cumulative breakage probability?

175 Table 4: Do the parameters caver all of the sizes/masses tested?

158/9 h sub 1 or 2

Is the DWT height adjusted for mass losses for each subsequent stage or kept the same?

Figures 4 to 8 At least one graph should be plotted as for Figure 1 for a different material

You should provide mass and nominal size for each set of tested particles

216 size relative to what?

226 Fig 10 might make you point better if plotted against J/g

Fig 11 ditto

Fig 12 with the exception of silica, the other materials appear to become more difficult to break.

The purple line lacks a caption.

262/4 the presence of grains of minerals also has a large effect.

271/76 Fig 13 would benefit from an example

297/8 The argument is that a larger particle can contain a larger flaw which provides a larger stress raiser making the particle easier to break - see ref 13

Ref 11 should not be a preprint now

Ref 23 - where was the conference held?

A general comment on modelling for DEM

This is for future papers - not this one

YOu might consider modelling the behaviour of the survivors. This avoids the need for exponentials and will allow you to test the null hypothesis that the probability of survival stays the same for each event.

The probability of survival after n events becomes the product of each probability and gets  rid of fractional powers of n.

You can explore weakening or strengthening factors in that context. If that approach works with your data, it can be extended to successive impacts of different intensities







Author Response

Thank you for your useful technical comments and suggestions on our manuscript. We have modified the manuscript accordingly

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper presents an improved method for the particle breakage probability model. The following are the comments prior to the acceptance of the paper:

  1. I understand that the Authors proposed an improved method for the particle breakage probability model. I suggest finding a proper word to replace "revision" in the title. In my opinion, this does not seem appropriate.
  2. I suggest the Authors double-check English. For example in Section 2: "Here we give a general procedure that was used .....". This sentence is OK but needs to be rewritten into a more academic writing sentence.
  3. It would be better to present the Figures in Table 2 in a Figure format instead of Table.
  4. The captions of Figure 3 are blurring. Please enhance the resolution.
  5. According to the present title, what the Authors would like to revise in the particle breakage probability model. Please indicate clearly in the paper.
  6. Please remove all grid in Figure 4 - 12. You can also provide some comparison Tables if you would like to highlight the comparison value from different models in Figure.
  7. Please add some content in the Conclusion Section that supported by the result.

Author Response

Thank you for your useful technical comments and suggestions on our manuscript. We have modified the manuscript accordingly

Author Response File: Author Response.pdf

Reviewer 3 Report

You have been working on a very intersting topic of (in my opinion) high relevance. Nevertheless, I found some point which have to be adressed before I can recommend the paper for publication. I summarized my recommendations in a seperate file.

Comments for author File: Comments.pdf

Author Response

Thank you for your useful technical comments and suggestions on our manuscript. We have modified the manuscript accordingly

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Dear Authors,

Thank you for providing the revised paper. I have no further comments.

Author Response



Development of a more descriptive Particle Breakage Probability Model


Dear Editor



Thank you for your useful technical comments and suggestions on our manuscript. We have modified the manuscript as follows:


  • Where the reviewers requested the authors to modify statements as per their suggestions, the statements were modified in the manuscript and the changes were tracked in the manuscript for the editors and reviewers to check.
  • All words, Tables and Graphs recommended to be removed were removed and tracked in the manuscript.
  • The references recommended to be included were included in Lines 106 to 108.
  • Figures 4 and 5 were swapped as per the reviewer’s suggestion, Lines 153 and 154.
  • The size ranges of particles shown in Figure 5 are those that are given in Table 1 and a statement confirming that has been added in Line 155.
  • Figure 7 in the previous manuscript is now Figure 6 in the revised manuscript. Previous Figure 6 was removed.
  • The reviewer requested the authors to represent size with the representative size of particles in each size class rather than weight in grams in previously Figures 12 and 13. The authors tried the reviewer’s suggestions and observed that there were no discernible trends to explain since when size replaces mass, the distinction is not the same. Thus, they opted to  plot this in terms of J/kg
  • The specific energy, in J/kg, was included in all figure captions as per the reviewer’s suggestion.
  • First person was changed to third person reporting in the manuscript.
  • Figure 15 was deleted from the manuscript and the models were fitted in Figures 12 and 13.
  • The statement “Apparently, the bigger particles are weaker at low energy input while at higher energy input, the opposite seems to be the case.” Was rewritten in Lines 284 – 286.
  • The sentence “This difference is due to the fact that some materials will tend to plastically deform and thus will require further breakage attempts before yielding.”– The authors have addressed that in Lines 311 to 312 and 341 to 342.
  • Reconsider the sentence, “The difference in cumulative damage beyond the threshold energy is attributed to plastic deformation of particles” having in mind comment on lines 294-296. The authors have addressed that in Lines 341 to 342.
  • The references were corrected as suggested by the reviewer.
  • The presentation of graphs was improved as per the reviewer’s recommendation.

The authors would like to thank you once more for the constructive comments that have helped to improve the quality of this work.


Kind regards,

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