Investigation of the influence mechanism of rock damage on rock fragmentation and cutting performance by the discrete element method

Rock damage is one of the key factors in the design and model choice of mining machinery. In this paper, the influence of rock damage on rock fragmentation and cutting performance was studied using PFC2D. In PFC2D software, it is feasible to get rock models with different damage factors by reducing the effective modulus, tensile and shear strength of bond by using the proportional factors. A linear relationship was obtained between the proportion factor and damage factor. Furthermore, numerical simulations of rock cutting with different damage factors were carried out. The results show that with the increase of damage factor, the rock cutting failure mode changes from tensile failure to brittle failure, accompanied by the propagation of macro cracks, the formation of large debris and a notable decrease in the peak cutting force. The mean cutting force is negatively correlated with the damage factor. Besides this, the instability of cutting force was evaluated by the fluctuation index and the pulse number of unit displacement. It was found that the cutting force was quite stable when the damage factor was 0.3, which improves the reliability of cutting machines. Finally, the cutting energy consumption of rock cutting with different damage factors was analysed. The results reveal that an increase of damage factor can raise the rock cutting efficiency. The aforementioned findings play a significant role in the development of assisted rock-breaking technologies and the design of cutting head layout of mining machinery.

investigation they rely on primitive concepts of damage mechanics and commercial numerical software (PFC2d) to simulate the action of a single pick during rock cutting. Significant improvement of the use of the english language is required before the possible publication of the paper. Further comments are listed below: ⦁ In p. 1. The sentence "Two major working procedures are needed in mining: to excavate the mining channel and the ore body mining, as shown in Fig. 1. .." is not correct both in mining terms and with regards to its grammar or syntax . ⦁ In the Introduction and in the literature review the authors should mention the relevant paper regarding simulation of rock cutting with PFC and other methods by M. Stavropoulou, Modeling of small-diameter rotary drilling tests on marbles, International Journal of Rock Mechanics & Mining Sciences 43 (2006) 1034-1051, also with regards to rock damage the paper: Exadaktylos G. and Stavropoulou M., (2008) A Specific Upscaling Theory of Rock Mass Parameters Exhibiting Spatial Variability: Analytical relations and computational scheme, International Journal of Rock Mechanics and Mining Sciences, 45 (2008) pp. 1102-1125.
⦁ The damage influences the 7 parameters of the particle model of the rock that are involved in the simulation, namely the two stiffneses, UCS, UTS, friction angle. ⦁ In p. 3 the authors describe the cutting process but they do not mention the attack angle and the back rake angle..."7. The rock was cut by pickaxe cutter with an angle of 55 degrees, a cutting speed of 1 m/s and a cutting distance of 120 mm. The cutting depth is 5mm, 10mm and 15mm....". ⦁ Since the author have found from the simulations that the rock breakage is mainly performed through the creation of tensile cracks why did they have chose the Uniaxial Compression test (UCT) for the calibration of damage and for forming the ratio of SE over the energy expended in this test up to the point of failure instead of the uniaxial tensile test? The paper is concerned with a topic of appreciable practical significance, namely that of preconditioning the rock for subsequent action of a mechanical cutting pick that will result into more efficient cutting processes. However, the paper needs significant improvement before its publication.

Review form: Reviewer 3
Is the manuscript scientifically sound in its present form? Yes

Do you have any ethical concerns with this paper? No
Have you any concerns about statistical analyses in this paper? No

Recommendation?
Major revision is needed (please make suggestions in comments)

Comments to the Author(s)
This paper investigated the rock fragmentation induced by rock cutting via DEM with PBM. Some comments are the following: (1) The definition of parameter k was not clear, though it is a very crucial parameter in this paper.
(2) To my knowledge, the damage factor reflect the damage degree, i.e., the more the micro crack or bond damage is, the larger the damage factor is. Therefore, the DEM samples with different damage factors should be prepared according to their micro characteristics. However in this paper, only the different of E and UCS are provided for samples with different damage factors, whereas the description of the micro characteristic was not found.
(3) The macro parameters, e.g., the compressive and tensile strength, should be provided.
(4) The titles of sub-sections 4.1 and 4.2 were the same in the manuscript. (5) The investigation of influence of rock cutting on fragmentation should be more detailed, and more micro information, e.g. the force chain, the bond breakage, is expected to be provided. The content in section 4 was too little. (6) The English needs improvement. (7) "、"should be revised as "," at Line 48, first page. Major revision is needed.

12-Feb-2019
Dear Dr Liu, The editors assigned to your paper ("Investigation for the influence mechanism of rock damage on rock fragmentation and cutting performance by discrete element method") have now received comments from reviewers. We would like you to revise your paper in accordance with the referee and Associate Editor suggestions which can be found below (not including confidential reports to the Editor). Please note this decision does not guarantee eventual acceptance.
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Comments to Author:
Reviewers' Comments to Author: Reviewer: 1 Comments to the Author(s) 1. I cannot find in this manuscript how to define the factor k, and how to relate the k and damage factor D. Please give an explanation. 2. The microparameters in PFC model are very important for the calculation to reveal the real mechanism of the coaling process. Though the authors has used the uniaxial tests to determine the parameters, however, I cannot find the proof such as the testing curves or test conditions. 3. 4.1 and 4.2 is the same title. 4. How to modeling the cutting depth in PFC 2D? Is the depth is firstly supposed as a value, and then a drilling rate is given on the rock? It is not real for the drilling process. And from the Fig 2  and Fig.7, the drilling processes are different. 5. Check the figure 4, the curves are linear, it is not correct. And also, in Fig.5 and Fig.6, the relationship of the k And D, D and E, why are the two parameters are equal? 6. The rock breakage is very complex because of rock properties, drilling process and corresponding factors, we should find the breakage process based on the clear mechanical parameters to reveal the breakage mechanism. The description in this manuscript gives no details.
Reviewer: 2 Comments to the Author(s) The authors investigate the effect of prior inherited damage by the rock on its resistance to mechanical cutting with cutting picks usually met on the cutting heads of roadheaders. For this investigation they rely on primitive concepts of damage mechanics and commercial numerical software (PFC2d) to simulate the action of a single pick during rock cutting. Significant improvement of the use of the english language is required before the possible publication of the paper. Further comments are listed below: ⦁ In p. 1. The sentence "Two major working procedures are needed in mining: to excavate the mining channel and the ore body mining, as shown in Fig. 1. .." is not correct both in mining terms and with regards to its grammar or syntax . ⦁ The damage influences the 7 parameters of the particle model of the rock that are involved in the simulation, namely the two stiffneses, UCS, UTS, friction angle. ⦁ In p. 3 the authors describe the cutting process but they do not mention the attack angle and the back rake angle..."7. The rock was cut by pickaxe cutter with an angle of 55 degrees, a cutting speed of 1 m/s and a cutting distance of 120 mm. The cutting depth is 5mm, 10mm and 15mm....". ⦁ Since the author have found from the simulations that the rock breakage is mainly performed through the creation of tensile cracks why did they have chose the Uniaxial Compression test (UCT) for the calibration of damage and for forming the ratio of SE over the energy expended in this test up to the point of failure instead of the uniaxial tensile test? The paper is concerned with a topic of appreciable practical significance, namely that of preconditioning the rock for subsequent action of a mechanical cutting pick that will result into more efficient cutting processes. However, the paper needs significant improvement before its publication.
Reviewer: 3 Comments to the Author(s) This paper investigated the rock fragmentation induced by rock cutting via DEM with PBM. Some comments are the following: (1) The definition of parameter k was not clear, though it is a very crucial parameter in this paper.
(2) To my knowledge, the damage factor reflect the damage degree, i.e., the more the micro crack or bond damage is, the larger the damage factor is. Therefore, the DEM samples with different damage factors should be prepared according to their micro characteristics. However in this paper, only the different of E and UCS are provided for samples with different damage factors, whereas the description of the micro characteristic was not found.
(3) The macro parameters, e.g., the compressive and tensile strength, should be provided.
(4) The titles of sub-sections 4.1 and 4.2 were the same in the manuscript. (5) The investigation of influence of rock cutting on fragmentation should be more detailed, and more micro information, e.g. the force chain, the bond breakage, is expected to be provided. The content in section 4 was too little. (6) The English needs improvement. (7) "、"should be revised as "," at Line 48, first page. Major revision is needed.

Recommendation?
Accept as is

Comments to the Author(s)
The corrections are acceptable.

Recommendation?
Accept as is

Comments to the Author(s)
The authors revised the manuscript according to the comments. All the comments were responded, and the revision was well done. I therefore recommend this paper to be published.

01-Apr-2019
Dear Dr Liu, I am pleased to inform you that your manuscript entitled "Investigation for the influence mechanism of rock damage on rock fragmentation and cutting performance by the discrete element method" is now accepted for publication in Royal Society Open Science.
You can expect to receive a proof of your article in the near future. Please contact the editorial office (openscience_proofs@royalsociety.org and openscience@royalsociety.org) to let us know if you are likely to be away from e-mail contact. Due to rapid publication and an extremely tight schedule, if comments are not received, your paper may experience a delay in publication.
Royal Society Open Science operates under a continuous publication model (http://bit.ly/cpFAQ). Your article will be published straight into the next open issue and this will be the final version of the paper. As such, it can be cited immediately by other researchers. As the issue version of your paper will be the only version to be published I would advise you to check your proofs thoroughly as changes cannot be made once the paper is published. drilling process. And from the Fig 2 and Fig.7, the drilling processes are different. Action: Done. In this paper, the depth is pre-determined and the pick is placed in the corresponding position. Then the pick is given a speed to cut the rock.
Regarding the relationship between Figures 2 and 7, we studied a single pick from multiple picks. Generally, the cutting pathway of a single pick can be simplified as a straight line, because a cutting unit of the arc pathway could be deemed as a line in experimental scale modeling.
Remark #5: Check the figure 4, the curves are linear, it is not correct. And also, in The factor k is a microscopic parameter and D is a macroscopic parameter. There is neither any quantitative relationship between microscopic parameters and macroscopic parameters in PFC nor any relevant report. The equivalence of k and D is acquired from the experimental results. Figure 6 shows the relationship between the energy density and the rock damage factor D.

Remark #6:
The rock breakage is very complex because of rock properties, drilling process and corresponding factors, we should find the breakage process based on the clear mechanical parameters to reveal the breakage mechanism. The description in this