Evolution Model of Coal Failure Using Energy Dissipation under Cyclic Loading/Unloading
Round 1
Reviewer 1 Report
The manuscript is interesting and well-written. Scientific methodology is consistent. There is a good presentation of experimental, analytical and numerical results. The paper can be accepted as it is. My only comment regards Eq. 16 where the damage factor D is uncoupled in the system written by the authors whilst should be related to the other equations through Eq. 7.
Author Response
General comments:
The manuscript is interesting and well-written. Scientific methodology is consistent. There is a good presentation of experimental, analytical and numerical results. The paper can be accepted as it is. My only comment regards Eq. 16 where the damage factor D is uncoupled in the system written by the authors whilst should be related to the other equations through Eq. 7.
AW: Thank you very much for your suggestions. We have reviewed the article and carefully considered all the suggestions to make changes, and we have touched up the revised manuscript with care. We sincerely thank the reviewers for their enthusiastic work and hope that the revised manuscript will be approved. To address this problem of Equation. We revisited Eq. 16 and found the fact that the damage factor D in it is uncoupled in the system of this problem of the article and related it to the other equations by Eq. 7.
Reviewer 2 Report
The paper presents an evolution model describing the behaviour of coal failure using energy dissipation under cyclic loading/unloading. The damage variables of energy dissipation were defined, and a theoretical model was established. These parameters include the relationship between energy state, damage state and strength state according to the uniaxial cyclic loading/unloading test. The results show that there are energy excitation and inhibition effects in the process of coal fracture. The abrupt increase of dissipated energy can be regarded as the precursor of coal fracture. Based on the analysis of the characteristics of damage and failure state and dissipated energy, the discriminant equation for the stability of the coal energy state was constructed.
An interesting paper, with a big potential for novelty.
I recommend paying greater attention to the accuracy of the English language, which the authors must improve.
Author Response
General comments:
The paper presents an evolution model describing the behaviour of coal failure using energy dissipation under cyclic loading/unloading. The damage variables of energy dissipation were defined, and a theoretical model was established. These parameters include the relationship between energy state, damage state and strength state according to the uniaxial cyclic loading/unloading test. The results show that there are energy excitation and inhibition effects in the process of coal fracture. The abrupt increase of dissipated energy can be regarded as the precursor of coal fracture. Based on the analysis of the characteristics of damage and failure state and dissipated energy, the discriminant equation for the stability of the coal energy state was constructed.
An interesting paper, with a big potential for novelty.
I recommend paying greater attention to the accuracy of the English language, which the authors must improve.
AW: Thank you very much for your recognition of the work we have done. We have carefully read your comments and suggestions, which have been very useful to us, and for this reason we have revised the revised manuscript for linguistic accuracy. We sincerely thank the reviewers for their enthusiastic work and hope that the revised manuscript will be approved.
Reviewer 3 Report
See attached file.
Comments for author File: 
Comments.pdf
Author Response
General comments:
This paper prosed a new energy index to discuss the evolution of damage and energy. It is an important issue in rock engineering. From the model proposed, which shows a good correlation with the laboratory results. Therefore, I recommend to accept this paper since it is worth to publish and let more peers to read.
There are some comments I presents to improve the quality of the paper.
AW: Thank you very much for your suggestions. We have reviewed the article and carefully considered all the suggestions to make changes, and we have touched up the revised manuscript with care. We sincerely thank the reviewers for their enthusiastic work and hope that the revised manuscript will be approved.
Q1. SEM is always a good tool for us to observe the micro-fractures. However, the authors always forgot to introduce the important information what they got from the SEM images. Therefore, the figure 1 should be edited:
- The scale bar is not clear.
- And you should mark the micro-fractures on the pics.
- Where is the magnification area? You also need to mark.
- How do you get the conclusion that you observe the obvious brittle characteristics?
AW: Thank you very much for your suggestion, we have carefully considered this issue and have re-edited Figure 1 in the revised manuscript to describe the morphology of the microcracks in the figure, labeled the magnification in the caption of the image and marked the magnified area with a red box, in addition to describing and illustrating in detail how the conclusion that a distinct brittle feature was observed was obtained.
Q2. At 2.2, if possible, can you please present a pic of your equipment, better with the state of in testing. The measuring precision relate to which parameter? The loading forces? The displacements? How do you measure the displacement? Strain gauge?LVDT? please introduce it and attach a pic. If you just use the displacement of the rod measured by the loading machine, please stress that the stiffness of the machine can be guaranteed. This is very important for this study since the following energy calculations are all based on the measured data.
AW: Thank you very much for your suggestion, we have completed the images for the test state of the experimental loading device and explained the stiffness of the test.
Q3. In terms of the experimental method, there are two kinds of loading waves were selected. What kind of scientific questions you want to research from these two loading waves? You should introduce it in this section.
AW: Thank you very much for your suggestion, the coal specimens were tested to experience cycles loading/unloading with two different stress loading paths under axial equivalent stress in the lab. Mode 1 is a graded cyclic loading/unloading test, which is mainly used to analyze the influence of loading/unloading behavior on the rupture behavior and rupture mode of coal samples under different loading conditions, as well as the mechanical response characteristics and energy distribution state of coal samples under different stress gradients. Mode 2 is the square equal amplitude cyclic loading and unloading test, which is mainly used to explore the influence of continuous cyclic loading and unloading on the damage state of coal samples under different stress levels, and to analyze the difference of the influence of different cyclic loading and unloading times on the fatigue damage state of coal samples under the same stress level. We have included this note in the latest revision of the manuscript.
Q4. Does the failure faults have difference between monotonic and fatigue compression? Please provide the pics and analyze it.
AW: Thank you very much for your suggestion, we think that the main object of study in this paper is for repeated loading/unloading pressure specimens, so the uniaxial compression damage curve is not compared and explained in detail，we hope this way can be approved by you.
Q5. I compared the stress-strain curves in details. Why the hysteresis loop is not obvious for constant amplitude in same unloading level? Generally, we always connect the damage inside the rock with the hysteresis loop. From my point of view, for the AC1 and AC2, the unloading elastic modulus were not same as the loading process. For BC1 and BC2, the unloading process almost followed the same path with the loading. Please explain it in the study.
AW: Thank you very much for your suggestions and explanations. After we reviewed the manuscript, your explanations and additions to the hysteresis loop for constant amplitude can make our manuscript more informative in this regard, and we have added this explanation to the revised manuscript.
Q6. Section 3.2, how to calculate the and ??? Two kinds of loading waves selected, and it must be two different calculation methods. Please provide the details.
AW: Thank you very much for your suggestion, the way we calculation of the energy and is usually based on the computer's calculus processing of the energy density of the picture, so the calculation method is not indicated in the manuscript. We explain this point in our revised manuscript.
Q7. Figure 7 is useless.
AW: Thank you very much for your suggestion, we noted this issue in Figure 7 and removed Figure 7 from the revised manuscript.
Q8. Line 188, the energy input is not the same process as the accumulation, dissipation and release. The energy input is always accompanied with the whole process. Please rephrase this sentence.
AW: Thank you very much for your suggestion, we found this expression, which was adjusted in the revised manuscript, that the loaded coal undergoes accumulation, dissipation, and release of energy throughout the deformation and destruction of the energy input.
Q9. Line 228-229, what is energy transfer? What is transformation?
AW: Thank you very much for your suggestion, we noted the semantically ambiguous statement and reworked it in a revised manuscript that the process of deformation and destruction of materials is essentially a state instability phenomenon driven by energy dissipation and release.
Q10. Line 221-223, I don' understand why the decrease of energy storage will reduce the ability of damage resistance.
AW: Thank you very much for your suggestion, we noted this unclear expression, the reduction of stored energy does not reduce its ability to resist injury. As stated in the text, due to the increasing input energy, the higher the elastic energy, the worse its state of stored elastic energy, the more unstable the coal sample is, and therefore the less resistant the coal is to injury and the easier it is to damage, probably due to the inaccurate presentation, we have modified and embellished this aspect in the revised manuscript.
Q11. Figure 9. What the meaning of the green line OP?
AW: Thank you very much for your suggestion, the implication of the green line op is that it is used as a reference for the conventional method of calculating the energy growth rate, which can be compared with the method of energy growth tangential factor, as a way to visualize more the superiority of the newly proposed calculation method.
Q12. What is self-inhibiting effect? You should explain it here.
AW: Thank you very much for your suggestion. We believe that the self-repression effect refers to the existence of a process of energy aggregation before the rupture of the coal sample in the critical case, in order to aggregate the energy and cause the final damage, thus slowing down the growth rate of dissipated energy, which we explain in the revised manuscript.
Q13. Why not the results of BC1 and BC2 are not discussed based on the model proposed.
AW: Thank you very much for your suggestion, we mainly carried out the exploration and analysis of the energy state of coal samples loaded in two ways: equal amplitude cyclic loading and unloading of coal samples and graded cyclic loading and unloading of coal samples, through which the influence of the number of cyclic loading and unloading of coal samples on the damage degree of coal samples can be analyzed. The energy states of coal samples at different stress stages can be analyzed by the graded cyclic loading and unloading of coal samples, and then the energy evolution model of coal samples at different stress stages under cyclic loading condition can be proposed.
Under the equal amplitude cyclic loading and unloading, the coal sample is subjected to repeated cyclic loading and unloading at the same stress level, which will have a non-negligible effect on the damage characteristics and deformation characteristics of the coal sample, and then affect the energy state and stability degree of the coal sample. From the previous analysis, it is clear that there is a closer relationship between the dissipative energy state inside the coal sample and the stability degree of the coal sample. Therefore, we explore the relationship between the damage change pattern of coal samples under the same stress level and the number of its cycles based only on the dissipative energy change characteristics of coal samples under repeated cyclic loading conditions. We have clarified in the revised manuscript.
