Experimental Study on Hydromechanical Behavior of an Artificial Rock Joint with Controlled Roughness
Round 1
Reviewer 1 Report
Give a reference for eq. 7
Line 366: L is with bigger font than w. Please correct.
Line 367: give the value of ρ. It is a critical parameter for the calculations? Make a comment
Line 407-410: make a comment what do you believe it happens if JCR and c are dependent variables
Author Response
Give a reference for eq. 7
Response: Thank you very much for your valuable comment. We added a reference in the manuscript.
Line 366: L is with bigger font than w. Please correct.
Response: Thanks for the comment. We corrected the term as you recommended.
Line 367: give the value of ρ. It is a critical parameter for the calculations? Make a comment
Response: Thanks for the comment. We added the properties of the fluid we used. The density itself was not critical in the whole calculation.
Line 407-410: make a comment what do you believe it happens if JCR and c are dependent variables
Response: Thanks for the comment. If those variables, JRC and c, were dependent, Equation 11 could be expressed by a single variable, which would be simpler. However, many references treated them as independent, for examples, Zimmerman and Bodvarsson (1996), Yeo (2001), Xiong et al. (2018).
Author Response File: 
Author Response.docx
Reviewer 2 Report
The manuscript is well written and the theme is well presented and discussed.
A suggestion - in discussion, some words should be directed towards the problem of Equation 11 retrieve values (37,5%) which are lower than the ones registered during experimentation (underestimation of values).
Corrections:
Use of expression 'geometric characteristics' for joints is confusing, since usually it refers to their attitude, persistence and spacing; here it refers to a 'mechanical characteristic' - rugosity description! This should be clarified;
Figures captions are unequal - Figures 6, 8 and 11 have a different presentation of Figures 2, 3, 4 and 13; and graphs relating only to joints J1 should specify that in the caption;
line 196 - xz should be in italic;
Author Response
A suggestion - in discussion, some words should be directed towards the problem of Equation 11 retrieve values (37,5%) which are lower than the ones registered during experimentation (underestimation of values).
Response: Thanks for the comment but we cannot fully understand what you stated. Please explain more about the retrieve values, especially the number 37.5%, and underestimation, which we cannot trace from the manuscript.
Use of expression 'geometric characteristics' for joints is confusing, since usually it refers to their attitude, persistence and spacing; here it refers to a 'mechanical characteristic' - rugosity description! This should be clarified;
Response: Thanks for the comment. As you recommended, we changed the expression ‘geometric characteristics’ to ‘surface geometry’ or ‘geometric property’ for avoiding confusion.
Figures captions are unequal - Figures 6, 8 and 11 have a different presentation of Figures 2, 3, 4 and 13; and graphs relating only to joints J1 should specify that in the caption;
Response: Thanks for the comment. We modified the graphs you had mentioned to have the same format in terms of caption and sub-numbering.
line 196 - xz should be in italic;
Response: Thanks for the comment. We modified the word in italic.
Author Response File: Author Response.docx
Reviewer 3 Report
General comments
This paper clearly represents the culmination of a long and detailed project and I commend you on the outcomes. As I read the manuscript, I found that many of the questions that arose in my mind were subsequently addressed to my satisfaction. However, several remained unaddressed, and I include them amongst my Specific Comments below.
As one general comment, I would like to see some discussion of the inherent uncertainties introduced at each stage of your procedure (for example, figure 8 and table 4 indicate that ‘c’ is independent of JRC but that ‘c’ is only determined to ±2–3 percentile points scattered around a mean. This represents ~10% uncertainty in 'c' that should be carried through subsequent calculations), and the cumulative uncertainty in the final inferred relationship (Eq 11).
I would also like to see the manuscript include a discussion of the implications of this work. How will the results be applied in practice? Will your work improve the accuracy and reliability of hydromechanical models? If so, how? Does your work on quantifying increases in joint contact area have implications for fluid-rock interaction or geothermal underground heat exchanger models? Can the aperture distributions in Figure 9 be generalized for assigning stochastic distributions of mechanical aperture to geo-mechanical models?
Many of the cited references appear very old, with an average publication date of 1996 (23 years ago!) This can give the impression that the work might already be outdated.
Specific comments
Line 21: Include your inferred hydraulic aperture function (ie Eq 11) in the abstract
Line 42: Not all joints are related to metamorphic processes
Line 44: “characterized” would be a better word than “affected” here
Line 46: It would be useful to introduce and define ‘hydraulic aperture’ at the same time as ‘mechanical aperture’ in this paragraph.
Line 67: “mathematically define” would be a better term than “generate” here
Line 91: “mathematically define” would be a better term than “make” here also
Line 97: “…and/or generating models of artificial joint surfaces.”
Line 106: Add more explanation of the images to the caption. Eg what are the upper, middle and lower images showing, and what is the difference between the left and right images?
Paragraph 109–120: I found this paragraph a bit confusing and/or ambiguous. I could not distinguish when you were referring to the samples in your companion paper [21] versus the samples related to this manuscript. I presume “those” at Line 114 refers to the examples reported in [21] and shown in Fig 1? It might be better to remove text referring to the earlier samples and only cite [21] as the source of figure 1.
Line 119: Figure 1 does not show hexahedrons. The images are of square samples.
Line 121: Reword to “The 3D printer used in this study was an ‘additive manufacturing’ type…”
Line 143: Explain in the caption what each component is, including what the red boxes highlight. Also, “…and its CAD drawing.”
Line 154: Define and state the purpose of the ‘MTS 816 system’.
Line 160: Use “…joint characteristics and dimensions…” instead of “…size and roughness…”
Line 162: 5 mm/s strain rate? Is that correct?
Paragraph 165–177: Please rewrite this paragraph to provide a clearer description of the experimental setup. Many items are labelled on Figure 3 without any explanation of their role in the setup. I was unable to identify the joint specimen or end caps in Figure 3a, or to understand where the Figure 3a assembly appears in Figure 3b. Is the ‘triaxial chamber’ truly triaxial, or uniaxial with confining pressure?
Line 167: My understanding is that a ‘confining pressure unit’ applies equal pressure on all sides of a sample. How, then, did you use this unit to apply differential stress normal to the joint?
Lines 172-173: The ‘two loading cycles’ play a very large role in the subsequent parts of the manuscript but are not described at all. Please add a paragraph in here to clearly describe the experimental sequence of events through the entire first and second loading cycles.
Line 186: Define all variables in Eq 1.
Line 190: You should justify your assertion that 2D parameterization of joint surfaces is more ‘practical’ than 3D
Line 199: Is averaging the roughness of the joint over several profiles a reasonable approach, given the non-linear relationship between roughness and hydraulic properties shown for example in Figure 10? Areas of greater roughness could dominate the flow characteristics of a joint, but such areas would not be properly represented by the average roughness of the joint. Please justify this approach.
Line 200: Label the x and z axes on the plots in Figure 4b.
Line 202: “(b) x-z profiles for three y-values as shown in (a)”
Line 217: How were weightings assigned and applied?
Line 222: “…those of roughness. We attributed this to the effect…”
Line 224: Express the relationship between mechanical aperture and JRC as a function
Line 231: Explain where the upper limit of JRC = 20 comes from. Is this a ‘hard’ physical limit, a limit of the original definition, or is there some other limiting factor?
Line 240: If mechanical aperture is generally log-normal, why have you fitted a normal distribution curve to Figure 5b?
Lines 250-251: “Also, we assumed that our material was more similar to sedimentary rocks than crystalline because of its texture of cemented grains.”
Line 253: Table 2 and most of the preceding paragraph seem irrelevant to this manuscript, which describes a largely empirical study of stress versus aperture. The rest of the manuscript does not mention or require quantitative knowledge of mechanical properties of the material. If it is not relevant then remove it. If it is relevant, then please explain why and define all variables in the table header.
Line 258: Define Δδj
Line 259: Replace “intact part” with “matrix component of deformation”
Line 260: Joint closure “…with respect to normal stress…”?
Lines 262-263: Maybe replace “…good agreements between them could be found” with “…good fits were achieved using each of them.”
Line 264: “…in Equation 4, showing good fits for normal stress > 3 MPa.”
Line 266: Quote and justify the assumed values of ‘a’ and ‘b’ for the Bandis lines on each plot.
Line 269: Could different values of ‘a’ and ‘b’ provide better fits for normal stress < 3 MPa?
Line 270: No part of any of these plots looks ‘linear’.
Line 271: Describe the effect strain hardening would have on the plots. Does “the last loading stage” refer to the second loading cycle, or to the maximum load applied during each of the two cycles?
Line 272: “…not large enough.” Is this an interpretation of your observation, or was it a theoretical prediction? If the latter, at what load would you expect to see strain hardening? Also, the ‘non-linear’ trend looks proportionally very similar between the first and second load cycles on all Figure 6 plots. Justify your assertion that the trend was smaller in the second cycle.
Line 288: Add x and y scale bars to the figure
Line 289: Confirm that red color represents the contact area
Line 299: Explain ‘contact ratio %’ in the caption
Line 300: Delete “However”
Line 303-304: It is oxymoronic to say the results are comparable but can’t be compared. Say instead that the results are similar and delete “…even though direct comparisons…to measure the contact area.” The methods used to measure the contact area are not really relevant if your point is only to illustrate that the results were similar.
Line 305: Perhaps quantify this point by providing linear regression equations through the 20 points on each graph to confirm that the average contact ratio on Figure 8b is larger than on Figure 8a for all normal stress values.
Line 306: State which sample demonstrated 3.8% increase.
Lines 307-309: The plots on Figure 8 would suggest that this observation is not significant and that the variation you observe falls well within the range of experimental uncertainty.
Paragraphs 310-327: I would like to see a discussion of the cumulative uncertainties in these calculations
Line 320: “possible” instead of “available”
Line 324: “…until the percentage or overlapping surface points equaled the…”
Line 328: Would log-normal curves fit these histograms better than normal-distribution? Also, increase the size/legibility of the scale bar beside the bottom plots.
Line 333: I don’t understand what was “10 times exaggerated”. Do you mean vertical-to-horizontal exaggeration on the plots? Such ‘exaggeration’ is meaningless when the vertical scale is expressed as colors as on the figure.
Equation (6): Define α and Pw
Lines 343-345: Cross plots of which two variables? Provide graphs of the cross plots. They might illustrate whether the coefficients for J1 (0.80), J2 (0.87), J3 (0.75) and J4 (0.82) are really different or actually the same value (0.81) with an experimental uncertainty (± 0.06).
Lines 347-349: How is Δh defined or measured? Is pore pressure the same as injection head, or are these controlled by different laboratory systems?
Lines 357-358: Delete the entire sentence, “It was because…level of normal stress.” Aperture size obviously influences the absolute flow rate, but there is no obvious reason why it should influence the percentage reduction with respect to normal stress.
Line 368: “…the effective bulk hydraulic aperture…”. Also, I am not clear on how you measured the flow rate and the uncertainty in the measurement. Perhaps describe the measurement procedure clearly in the experimental setup section of the manuscript.
Line 372: “…shown for J1 samples in Figure 11.”
Line 383: Maybe this is a typo but it states the opposite of what is presented in Figure 11.
Line 411: Why use the cube of (eh / em)? Why not the square, or just (eh /em)?
Line 413: “Section” instead of “Chapter”. Also, Section 3 does not seem to describe any relationship between (eh / em)3 and ‘c’.
Line 414: Given the point above, remove “…and contact area…”
Line 417: Delete “two”
Line 419: Delete “However” and replace “analyzed that they were” with “found to be”
Line 420: Replace “with” with “of”
Line 497: Your ‘Conclusions’ section can be much shorter. Most of what is written summarizes all the preceding sections but draws no conclusions. Only the last paragraph (lines 533-539) presents your conclusions.
Author Response
As one general comment, I would like to see some discussion of the inherent uncertainties introduced at each stage of your procedure (for example, figure 8 and table 4 indicate that ‘c’ is independent of JRC but that ‘c’ is only determined to ±2–3 percentile points scattered around a mean. This represents ~10% uncertainty in 'c' that should be carried through subsequent calculations), and the cumulative uncertainty in the final inferred relationship (Eq 11).
Response: Thanks for the comment. We consider it very important. However, error analysis and its propagation could not be done in some cases, since we do not have margin of error of some parameters. For instance, we have just best (point) estimations of contact area under specific normal stress, not the margin since we did not conduct multiple tests. Also, in your comment, you recommended to concatenate all ‘c’ values regardless of joint roughness, which is little bit away from our intention. Therefore, it is somewhat insufficient for us to make those kinds of calculation at this point but we will consider it in our further research.
I would also like to see the manuscript include a discussion of the implications of this work. How will the results be applied in practice? Will your work improve the accuracy and reliability of hydromechanical models? If so, how? Does your work on quantifying increases in joint contact area have implications for fluid-rock interaction or geothermal underground heat exchanger models? Can the aperture distributions in Figure 9 be generalized for assigning stochastic distributions of mechanical aperture to geo-mechanical models?
Response: Thanks for the comment. We think results of this study can be utilized in many geomechanics engineering application. Especially, the analyses on rock mass scale, such as DFN (discreet fracture network), should be conducted based on the features of a joint. Several characteristics of a joint are required in DFN and among them, aperture is a critical parameter. So accurate understanding of the apertures is quite important and this is where our experimental works and prediction model can be applied to. We added some descriptions in discussion as you recommended.
Many of the cited references appear very old, with an average publication date of 1996 (23 years ago!) This can give the impression that the work might already be outdated.
Response: Thanks for the comment. Considering your comment, we added more references which are relatively new.
Specific comments
Line 21: Include your inferred hydraulic aperture function (ie Eq 11) in the abstract
Response: We included the equation in the abstract as you recommended
Line 42: Not all joints are related to metamorphic processes
Response: We changed the expression.
Line 44: “characterized” would be a better word than “affected” here
Response: We changed the word as you recommended.
Line 46: It would be useful to introduce and define ‘hydraulic aperture’ at the same time as ‘mechanical aperture’ in this paragraph.
Response: We changed the phrase as you recommended.
Line 67: “mathematically define” would be a better term than “generate” here
Response: We changed the word as you recommended.
Line 91: “mathematically define” would be a better term than “make” here also
Response: We changed the word as you recommended.
Line 97: “…and/or generating models of artificial joint surfaces.”
Response: We changed the phrase as you recommended.
Line 106: Add more explanation of the images to the caption. Eg what are the upper, middle and lower images showing, and what is the difference between the left and right images?
Response: We added more explanation regarding figure 1.
Paragraph 109–120: I found this paragraph a bit confusing and/or ambiguous. I could not distinguish when you were referring to the samples in your companion paper [21] versus the samples related to this manuscript. I presume “those” at Line 114 refers to the examples reported in [21] and shown in Fig 1? It might be better to remove text referring to the earlier samples and only cite [21] as the source of figure 1.
Response: Thanks for the comment. Figure 1 is an example to show how well the method controls the joint roughness and is excerpted from reference [21]. It is actually irrelevant to the experiments in this manuscript. We modified the paragraph to avoid confusion and deleted some texts regarding detailed comparison results about the reference.
Line 119: Figure 1 does not show hexahedrons. The images are of square samples.
Response: Thanks for the comment. We replaced the term ‘hexahedron’ to ‘rectangular parallelepiped’ upon your comment.
Line 121: Reword to “The 3D printer used in this study was an ‘additive manufacturing’ type…”
Response: We changed the phrase as you recommended.
Line 143: Explain in the caption what each component is, including what the red boxes highlight. Also, “…and its CAD drawing.”
Response: We changed the caption as you recommended.
Line 154: Define and state the purpose of the ‘MTS 816 system’.
Response: Thanks for the comment. We revised the paragraph 154-177 for better understanding.
Line 160: Use “…joint characteristics and dimensions…” instead of “…size and roughness…”
Response: We changed the phrase as you recommended.
Line 162: 5 mm/s strain rate? Is that correct?
Response: We are sorry for the typo. The correct unis is mm/s.
Paragraph 165–177: Please rewrite this paragraph to provide a clearer description of the experimental setup. Many items are labelled on Figure 3 without any explanation of their role in the setup. I was unable to identify the joint specimen or end caps in Figure 3a, or to understand where the Figure 3a assembly appears in Figure 3b. Is the ‘triaxial chamber’ truly triaxial, or uniaxial with confining pressure?
Response: Thanks for the comment. We rewrote paragraph 154-177 for clearer description.
Line 167: My understanding is that a ‘confining pressure unit’ applies equal pressure on all sides of a sample. How, then, did you use this unit to apply differential stress normal to the joint?
Response: Figure 1 below shows a schematic diagram of the testing setup in earlier study. We adopted the same setup with the reference (Singh et al., 2015). Joint specimen with the endcaps was placed inside of the triaxial chamber (the cell in the figure). As you mentioned, the ‘confining pressure unit’ applies equal pressure on all sides of a sample, however, mechanical constraints along the axial (vertical) direction are imposed by the main frame (specifically by the actuator) in terms of stress or displacement. In this paper, axial stress of 0.1 MPa was applied to fix the specimen assembly and servo-controlled during the whole tests. Therefore, the ‘confining pressure unit’ could apply and control diametrical stress only, which acted as normal stress under this conditions.
Figure 1. Schematic diagram of the testing setup (Singh et al., 2015, Laboratory simulation of flow through single fractured granite)
Lines 172-173: The ‘two loading cycles’ play a very large role in the subsequent parts of the manuscript but are not described at all. Please add a paragraph in here to clearly describe the experimental sequence of events through the entire first and second loading cycles.
Response: Thanks for the comment. We added more description as you recommended.
Line 186: Define all variables in Eq 1.
Response: We added all definitions as you recommended.
Line 190: You should justify your assertion that 2D parameterization of joint surfaces is more ‘practical’ than 3D
Response: Thanks for the comment. In many references and applications, use of 2D parameters is quite exceeding that of 3D parameter mainly due to its simplicity. 3D parameters require much information about the joint surface and complicated procedure so that 2D parameters have been used more frequently in practical viewpoint.
Line 199: Is averaging the roughness of the joint over several profiles a reasonable approach, given the non-linear relationship between roughness and hydraulic properties shown for example in Figure 10? Areas of greater roughness could dominate the flow characteristics of a joint, but such areas would not be properly represented by the average roughness of the joint. Please justify this approach.
Response: Thanks for the comment. Like description in the manuscript, averaging is an alternative approach to consider both practicability of 2D and representativeness of 3D parameter and we think it is reasonable. Although the effect of areas of greater roughness in your comment may be weaken in averaging but still it seems more reasonable than using a profile. And in this case another problem arises on which profile should be selected. Regarding the comment about figure 10, roughness is not a sole factor that dominates fluid flow in a joint even though it is quite important. It should be considered the roughness as well as other joint properties, such as aperture.
Line 200: Label the x and z axes on the plots in Figure 4b.
Response: We changed the figure as you recommended.
Line 202: “(b) x-z profiles for three y-values as shown in (a)”
Response: We changed the caption as you recommended.
Line 217: How were weightings assigned and applied?
Response: We adopted a typical procedure for the weighted average
Line 222: “…those of roughness. We attributed this to the effect…”
Response: We changed the description as you recommended.
Line 224: Express the relationship between mechanical aperture and JRC as a function
Response: Thanks for the comment. We think the relationship you mentioned is between JRC and initial mechanical aperture. As we know, there is one relationship proposed by Bandis et al. (1983).
It is an empirical equation derived from many test results. The equation can broadly estimate the relationship but cannot give accurate results. We tried it but failed and concluded that making the relationship required wider database than we had and could not be expressed by one parameter.
Line 231: Explain where the upper limit of JRC = 20 comes from. Is this a ‘hard’ physical limit, a limit of the original definition, or is there some other limiting factor?
Response: Thanks for the comment. It is a limit of the original definition by Barton and Choubey (1977). JRC is somewhat qualitative parameter, only represented by the shape of joint profile so that there are no other factors but the shape.
Line 240: If mechanical aperture is generally log-normal, why have you fitted a normal distribution curve to Figure 5b?
Response: Thanks for the comment. Log-normal as well as normal distribution can be used to represent the distribution of mechanical aperture. Normal distribution is more suitable for Figure 5(b).
Lines 250-251: “Also, we assumed that our material was more similar to sedimentary rocks than crystalline because of its texture of cemented grains.”
Response: We changed the description as you recommended.
Line 253: Table 2 and most of the preceding paragraph seem irrelevant to this manuscript, which describes a largely empirical study of stress versus aperture. The rest of the manuscript does not mention or require quantitative knowledge of mechanical properties of the material. If it is not relevant then remove it. If it is relevant, then please explain why and define all variables in the table header.
Response: Thanks for the comment. Table 2 contains fundamental properties of the testing material but as you mentioned it is rather irrelevant with the following descriptions. So we removed the table and modified some paragraphs.
Line 258: Define Δδj
Response: We added the definition as you recommended. (‘Δδj is the deformation of joint or joint closure.’)
Line 259: Replace “intact part” with “matrix component of deformation”
Response: We changed the description as you recommended.
Line 260: Joint closure “…with respect to normal stress…”?
Response: We changed the description as ‘joint closure due to normal stress’.
Lines 262-263: Maybe replace “…good agreements between them could be found” with “…good fits were achieved using each of them.”
Response: We changed the description as you recommended.
Line 264: “…in Equation 4, showing good fits for normal stress > 3 MPa.”
Response: We changed the description as you recommended.
Line 266: Quote and justify the assumed values of ‘a’ and ‘b’ for the Bandis lines on each plot.
Response: Thanks for the comment. ‘a’ and ‘b’ are fitting constants that vary with material properties and joint properties. The number itself does not have significant meaning since it cannot apply to other material or other geometry so that we think providing the number is not essential.
Line 269: Could different values of ‘a’ and ‘b’ provide better fits for normal stress < 3 MPa?
Response: Thanks for the comment. Of course different combinations of ‘a’ and ‘b’ could give better fits for a specific part. But we did not consider the local fitting.
Line 270: No part of any of these plots looks ‘linear’.
Response: Thanks for the comment. Under compressive stress, rock joint usually shows non-linear strain behavior at the beginning due to mating displacement and joint closure. After that portion, the strain behavior is usually regarded as linear as described in the manuscript.
Line 271: Describe the effect strain hardening would have on the plots. Does “the last loading stage” refer to the second loading cycle, or to the maximum load applied during each of the two cycles?
Response: Thanks for the comment. The ‘last loading stage’ meant the latter in your comment at both loading cycles. ‘Strain hardening’ may cause confusion so we changed the phrase.
Line 272: “…not large enough.” Is this an interpretation of your observation, or was it a theoretical prediction? If the latter, at what load would you expect to see strain hardening? Also, the ‘non-linear’ trend looks proportionally very similar between the first and second load cycles on all Figure 6 plots. Justify your assertion that the trend was smaller in the second cycle.
Response: Thanks for the comment. Regarding the ‘strain hardening’, what we wanted to express was non-linear deviation at around failure or after yield point. Compared with the material strength (48 MPa), maximum applied stress (10 MPa) was too small to observer that behavior. For clear understanding, we modified relevant phrases. Also, ‘non-linear trend’ in the second loading cycle was replaced with ‘non-linear deformation at the early stage’
Line 288: Add x and y scale bars to the figure
Response: Since there is limited space in the figures, we added the description.
Line 289: Confirm that red color represents the contact area
Response: We changed the caption as you recommended.
Line 299: Explain ‘contact ratio %’ in the caption
Response: We changed the caption as you recommended.
Line 300: Delete “However”
Response: We changed the description as you recommended.
Line 303-304: It is oxymoronic to say the results are comparable but can’t be compared. Say instead that the results are similar and delete “…even though direct comparisons…to measure the contact area.” The methods used to measure the contact area are not really relevant if your point is only to illustrate that the results were similar.
Response: Thanks for the comment. We changed the description as you recommended.
Line 305: Perhaps quantify this point by providing linear regression equations through the 20 points on each graph to confirm that the average contact ratio on Figure 8b is larger than on Figure 8a for all normal stress values.
Response: Thanks for the comment. Linear regression will confirm that the contact area of second cycle is larger than that of the first cycle. However, we think it is better to maintain the original format considering the scope and aim of this study.
Line 306: State which sample demonstrated 3.8% increase.
Response: There is a typo. We are sorry for your confusion. The maximum increase was 7.6% (J3 specimen under 7.5 MPa). We revised the description.
Lines 307-309: The plots on Figure 8 would suggest that this observation is not significant and that the variation you observe falls well within the range of experimental uncertainty.
Response: Thanks for the comment. It is an important comment and you may be right on this matter. Unfortunately, data regarding Figure 8 were not sufficient to conduct error analysis so that it is somewhat insufficient for us to make that kind of conclusion at this point.
Paragraphs 310-327: I would like to see a discussion of the cumulative uncertainties in these calculations
Response: Thanks for the comment. In equations you mentioned, for example , mechanical aperture under normal stress (em) is the most important parameter. Though initial mechanical aperture (em0) has margin of error, however, it does not vary according to the normal stress since it is a kind of reference value. Also, as joint closure (delta term) is measured value, its margin of error equals a half of measuring unit, which also does not vary. Therefore, error of em would be constant throughout the whole compression.
Line 320: “possible” instead of “available”
Response: We changed the word as you recommended.
Line 324: “…until the percentage or overlapping surface points equaled the…”
Response: We changed the description as you recommended.
Line 328: Would log-normal curves fit these histograms better than normal-distribution? Also, increase the size/legibility of the scale bar beside the bottom plots.
Response: Thanks for the comment. It would be better to remove the fitting curves for avoiding confusion. We changed the figure and also remove the scale bar. Instead some description for the bottom figure was added.
Line 333: I don’t understand what was “10 times exaggerated”. Do you mean vertical-to-horizontal exaggeration on the plots? Such ‘exaggeration’ is meaningless when the vertical scale is expressed as colors as on the figure.
Response: Thanks for the comment. What was exaggerated was the magnitude of mechanical aperture (z coordinate in the bottom plot of figure 10) for clear comparison. Without the exaggeration, it was ambiguous to visually compare at where larger aperture located and contact area. We added more description regarding it.
Equation (6): Define α and Pw
Response: We added the definition as you recommended.
Lines 343-345: Cross plots of which two variables? Provide graphs of the cross plots. They might illustrate whether the coefficients for J1 (0.80), J2 (0.87), J3 (0.75) and J4 (0.82) are really different or actually the same value (0.81) with an experimental uncertainty (± 0.06).
Response: We added graphs and descriptions as you recommended.
Lines 347-349: How is Δh defined or measured? Is pore pressure the same as injection head, or are these controlled by different laboratory systems?
Response: Thanks for the comment. Δh was measured value based on the water pressure. Since we knew the inlet pressure and outlet pressure (discharged so 0 MPa), Δh could be calculated from the Δp.
Lines 357-358: Delete the entire sentence, “It was because…level of normal stress.” Aperture size obviously influences the absolute flow rate, but there is no obvious reason why it should influence the percentage reduction with respect to normal stress.
Response: We deleted the phrase as you recommended.
Line 368: “…the effective bulk hydraulic aperture…”. Also, I am not clear on how you measured the flow rate and the uncertainty in the measurement. Perhaps describe the measurement procedure clearly in the experimental setup section of the manuscript.
Response: Thanks for the comment. We think ‘bulk hydraulic aperture’ is not a familiar expression so we would like to maintain the original expression. Flowrate was measured by an electronic balance as described in section 2.
Line 372: “…shown for J1 samples in Figure 11.”
Response: We changed the phrase as you recommended.
Line 383: Maybe this is a typo but it states the opposite of what is presented in Figure 11.
Response: We corrected the typo as you recommended, replacing ‘smaller’ with ‘larger’
Line 411: Why use the cube of (eh / em)? Why not the square, or just (eh /em)?
Response: Thanks for the comment. It is because of the cubic law. Using cubic of (eh/em) is more convenient than other expressions so that many references have adopted the term like a convention.
Line 413: “Section” instead of “Chapter”. Also, Section 3 does not seem to describe any relationship between (eh / em)3 and ‘c’.
Response: Thanks for the comment. We changed the word as you recommended. Relationship between (eh/em)3 and contact area could be implicitly deduced since contact area increased with the increase of normal stress, which hampered fluid flow, saying decrease in (eh/em)3.
Line 414: Given the point above, remove “…and contact area…”
Response: As explained right above, relationship between them could be deduced so we would like to maintain the original expression.
Line 417: Delete “two”
Response: We deleted the word as you recommended.
Line 419: Delete “However” and replace “analyzed that they were” with “found to be”
Response: We changed the descriptions as you recommended.
Line 420: Replace “with” with “of”
Response: We changed the word as you recommended.
Line 497: Your ‘Conclusions’ section can be much shorter. Most of what is written summarizes all the preceding sections but draws no conclusions. Only the last paragraph (lines 533-539) presents your conclusions.
Response: Thanks for the comment. We wrote the conclusion section to summarize preceding experimental results and prediction model followed by the implications of the study, of which the format is common in many other papers.
Author Response File: Author Response.docx
