Scale Effect and Correlation between Uniaxial Compressive Strength and Point Load Index for Limestone and Travertine

Round 1

Reviewer 1 Report

The article contains valuable information, but in my opinion there should be some changes to it. Several editorial errors were also noted. My remarks I include below.

1. The article is very extensive, it contains numerous items of literature - 62 items. Some literature items could be reduced - especially those that are not cited in the analysis of the predictive models of uniaxial compressive strength from point load index, listed in Table 1 can be omitted.
2. The work includes many variables and abbreviations, which in many cases are not always explained or described.I suggest that you do this in the article - for example, the abbreviations ASTM and ISRM - the names of the standards in line 41. Also variables such as L, D, W and the abbreviation PLT in table 1 should be explained.Later in the work, especially in the formulas e.g. 28, 29 and 32, there are also variables not described, e.g. B, f_t, d_f, d_o, d_e, β_o, β_n, λ. I also suggest where the result of the formula has a unit, enter this unit, e.g. MPa, kN.
3. Table 1 is quoted on line 89 and appears after two pages. It should be placed after the paragraph after line 99. Then it makes sense to put formula No. 19 in the proposed order. Table 2, after the changes made, may remain after line 134. I suggest placing the tables so that their content will be on one page. This makes it easier to view their content.
4. Figure 1, 6, 9, and 10 have axes, a grid, and a description in grayscale. As a result, they are not very visible. I suggest changing the colour to black.
5. Figures 6 and 9 contain too many of the same markers that differ only in colour. For example, I suggest that the markers for ASTM should be in the shape of a star, Bieniawski in the shape of a circle, etc. This will make the chart easier to read.
6. On page 3 there are table no. 1 - line 227. The text refers to tables no. 3. The table should be renumbered. The same applies to the following tables no. 2 up to no 9, only table no. 12 is OK.
7. In line 252, reference should be made to formulas number 33-35, not 34 to 36.
8. Figures 4, 5, 13 and 14 do not have a description of the axes and the units. They need to be completed.
9. In the text, a single letter or a single word was noticed at the end of the line in several places. This should be avoided. For example lines 55, 66, 67, 79, 84, 88 etc. I suggest you correct this.
10. In addition, you should avoid separating values and units on two lines, e.g. lines 168 and 169 as well as 240 and 241.

Author Response

Dear reviewer,

 

 

First of all, we would like to thank you for your comments on the manuscript. Second, we answer you point by point:

 

 

1. The article is very extensive, it contains numerous items of literature - 62 items. Some literature items could be reduced - especially those that are not cited in the analysis of the predictive models of uniaxial compressive strength from point load index, listed in Table 1 can be omitted.

We think that the manuscript could have been separated into two parts, but that would be ideal if we had more experimental data (mainly results of uniaxial compressive strength at diameters of 45, 50, 54 mm, etc.). In this work, a first approximation of a more in-depth and detailed work is carried out, which will be published throughout 2021 or 2022 (if the pandemic let us work in the laboratory).

 

2. The work includes many variables and abbreviations, which in many cases are not always explained or described. I suggest that you do this in the article - for example, the abbreviations ASTM and ISRM - the names of the standards in line 41. Also variables such as L, D, W and the abbreviation PLT in table 1 should be explained. Later in the work, especially in the formulas e.g. 28, 29 and 32, there are also variables not described, e.g. B, f_t, d_f, d_o, d_e, β_o, β_n, λ. I also suggest where the result of the formula has a unit, enter this unit, e.g. MPa, kN.

We added the description of ASTM and ISRM in lines 42 to 44: “American Standard Test for Materials (ASTM) [1,2] and International Society for Rock Mechanics and Rock Engineering (ISRM) [3].”

 

The other abbreviations were defined in lines 189-192: “B and λ are the dimensionless constants of the material, f_t is the strength of a sample with an insignificant size, d is the diameter of the specimen, and d₀ is the maximum diameter of the aggregate.” They are not developed in detail because they are not used, since they are part of the fractal model of the scale effect, and the one studied in this work is the statistical one.

 

We added the units of Equations 28, 29 (lines 190 to 193): “where σN is the nominal resistance (MPa), B and λ are the dimensionless constants of the material, ft is the strength of a sample with an insignificant size (MPa), d is the diameter of the specimen (mm), and d0 is the maximum diameter of the aggregate (mm).”

 

We added the units of Equation 30 (line 201): “[…] Hawkins [44]. The intersection di is the diameter of the model-change (ascending to descending) in mm”.

 

At the end of Table 1 the following information was added: “Information in the literature about the geometry of the specimens/slumps used in the Point Load Test to determine the Point Load Index [3,22]. It must be taken into account that D is the height of the failure cross section, W is the width of the failure cross section, P is the failure load, L is the distance between the failure cross section and the two free faces parallel to it, d is the diameter of the cylindrical specimen and d_e is the equivalent diameter for blocks and slumps.”

 

3. Table 1 is quoted on line 89 and appears after two pages. It should be placed after the paragraph after line 99. Then it makes sense to put formula No. 19 in the proposed order. Table 2, after the changes made, may remain after line 134. I suggest placing the tables so that their content will be on one page. This makes it easier to view their content.

Table 1 is too wide to fit all the information in the letter size of the journal. In a previous article they changed the orientation of the table (they rotated it 90º to the left) so that it was in the correct place, but we think that it should be done by the template designer of the journal.

Regarding Table 2, we totally agree, but we think the same, the journal designer should be commissioned.

 

4. Figure 1, 6, 9, and 10 have axes, a grid, and a description in grayscale. As a result, they are not very visible. I suggest changing the colour to black.

We fully agree, the color has been changed to black.

 

5. Figures 6 and 9 contain too many of the same markers that differ only in colour. For example, I suggest that the markers for ASTM should be in the shape of a star, Bieniawski in the shape of a circle, etc. This will make the chart easier to read.

The color criteria is the same for each reference in Figures 6 and 9. In addition, Excel only allows 4 types of markers, so we decided to assign a color to each point and only change the type of marker (from square to triangle) to highlight the experimental results.

 

6. On page 3 there are table no. 1 - line 227. The text refers to tables no. 3. The table should be renumbered. The same applies to the following tables no. 2 up to no 9, only table no. 12 is OK.

We apologize, we had not realized that we had a problem with cross references. Everything is corrected.

 

7. In line 252, reference should be made to formulas number 33-35, not 34 to 36.

Thank you. It is already changed (line 257).

 

8. Figures 4, 5, 13 and 14 do not have a description of the axes and the units. They need to be completed.

The axes in Figures 4, 5, 13 and 14 are dimensionless. The presentation of the normal probability plot is standard, while the histogram shows the distribution of the term β₁, corresponding to the simple linear regression coefficient for the origin or slope (which is also dimensionless).

 

9. In the text, a single letter or a single word was noticed at the end of the line in several places. This should be avoided. For example lines 55, 66, 67, 79, 84, 88 etc. I suggest you correct this.

We think that it does not depend on us, but on the designer of the journal. We will pay attention on it when the editor send us the proof.

 

10. In addition, you should avoid separating values and units on two lines, e.g. lines 168 and 169 as well as 240 and 241.

We think the same, but I think there are differences when viewing it on macOS and Windows (DOC format), since we did not find what you told us, that is, in all lines the unit of measurement accompanies the value of the magnitude in the same line. We understand that if there is one in the final version, we will correct it in the proof.

Author Response File: Author Response.docx

Reviewer 2 Report

Scale Effect and Correlation between Uniaxial Compressive Strength and Point Load Index for Limestone and Travertine

by

Solange Contreras, Manuel Saldaña, Ignacio Pérez-Rey, Manuel A. González, Norman Toro, and Javier González

 

General Comment

The manuscript deals with the measurements of the mechanical resistance of limestone and travertine. In particular, the authors did a review of the direct and indirect methods used for estimating the compressive strength on these two sedimentary rocks. The paper emphasizes the effect of specimen geometry on the magnitude of the value of compressive strength. I recommend this manuscript for publication in the journal.

 

Specific comments

The following sentences should be revised:

Lines 27-28: ‘The limestone model was ascending, while the travertine model was descending’ – Please, describe better the significance of matter.

Lines 40-41:  ‘using cylindrical specimens’ -  And the cubic specimens?

Line 135 and others: ‘dolomite’ - is an anhydrous carbonate mineral composed of calcium and magnesium carbonate (CaMg(CO3)2). The term is also used for a sedimentary carbonate rock composed mostly of the mineral dolomite, but alternative names are dolomite rock, dolostone or dolomitic rock.

Lines 199-206: Please, add some further information about limestone and travertine quarries.

Line 201: ‘quarry’ instead of ‘mine’.

Line 254: Please, add ‘The accuracy of volume determination is better than 0.02 % by vol. for specimens larger than 30 cm³ [Franzini, M.; Lezzerini, M. A mercury-displacement method for stone bulk-density determinations. Eur. J. Mineral. 2003, 15, 225-229].’

Line 279: Please, check the values of porosity and density. They seem to me that they do not correspond to each other.

Line 310: Please, check the values of porosity and density. They seem to me that they do not correspond to each other.

Tables 2-5. Please, check the significative digits. It seems to me that the significant figures are not always the same.

Line 400: How did the authors identify the presence of calcite and aragonite?

Author Response

Dear reviewer,

 

 

first of all, we would like to thank you for your comments on the manuscript. Second, we answer you point by point:

 

1. Lines 27-28: ‘The limestone model was ascending, while the travertine model was descending’ – Please, describe better the significance of matter.

Done. In line 28 “(strength increases as diameter increases)” was added and in line 29 “(strength decreases as diameter increases)”.

 

2. Lines 40-41: ‘using cylindrical specimens’ -  And the cubic specimens?

Both ASTM and ISRM only suggest the use of cylindrical specimens for uniaxial compressive strength (UCS) testing. The use of cubic specimens to determine UCS in rock mechanics dates back to the 1960s and 1970s, but not today.

Likewise, in order to plot the UCS from equations 11, 12 and 13, the equivalent diameter was calculated (0.25*Pi*d^2 = side*side).

 

3. Line 135 and others: ‘dolomite’ - is an anhydrous carbonate mineral composed of calcium and magnesium carbonate (CaMg(CO3)2). The term is also used for a sedimentary carbonate rock composed mostly of the mineral dolomite, but alternative names are dolomite rock, dolostone or dolomitic rock.

Thank you for this important detail, but "dolomite" is the name that the respective researchers wrote in their papers. For example, Deere and Miller (1966) speak of “dolomite (Oneota)” and “dolomite (Lockport)”, Al-Jassar and Hawkins (1979) speak strictly of “dolomite” and define it as “dolomite is micritic in texture with most of the grains showing a rhombic shape”, and finally, Cargill and Shakoor (1990) speak of “DeCew dolomite ”.

 

4. Lines 199-206: Please, add some further information about limestone and travertine quarries.

We do not consider that the relevance of the quarries beyond their location is necessary, because only the engineering properties of the rocks were studied. In fact, the name is not usually indicated if a specific work is not carried out together with the companies. Anyway, we can tell that the travertine quarry was abandoned when we caught the rock blocks (https://www.google.com/maps/@-22.4481964,-68.8246147,1779m/data=!3m1!1e3?hl=es-ES), and the limestone one is in operation, but we do not have more information because the specimens are remains of another work that has not yet been published (https://www.google.com/maps/@-20.8925933,-69.5085187,409807m/data=!3m1!1e3?hl=es-ES).

 

5. Line 201: ‘quarry’ instead of ‘mine’.

Yes, it is more accurate. It's already changed.

 

6. Line 254: Please, add ‘The accuracy of volume determination is better than 0.02 % by vol. for specimens larger than 30 cm³ [Franzini, M.; Lezzerini, M. A mercury-displacement method for stone bulk-density determinations. Eur. J. Mineral. 2003,15, 225-229].’

Thanks for the recommendation, it is an interesting article, but the work does not reside in determining the accuracy of the density, since the procedure of the ISRM (2007) was strictly followed, which only takes into account the accuracy to determine the masses (dry, satured and submerged), but not for density. ISRM (2007) indicates the following:

1. […] The sample is regarded as 'oven dry' when successive mass determinations at intervals of 4 hr yield values differing by less than 0.1% o of the sample mass.
2. […] The sample is then transferred underwater to a basket in an immersion bath. Its saturated-submerged mass (msub) is determined to an accuracy of 0.1 g from the difference between the saturated-submerged mass of the basket plus sample and that of the basket alone.
3. […] The sample is then removed from the immersion bath and surface dried with a moist cloth, care being taken to remove only surface water and to ensure that no rock fragments are lost. Its saturated-surface-dry mass (msat), is determined to an accuracy of 0.1 g.

 

4. Line 279: Please, check the values of porosity and density. They seem to me that they do not correspond to each other.

The experimental results are correct. In fact, you can check them in the corresponding publication González et al. (2019) [González, J .; Saldaña, M .; Arzúa, J. Analytical Model for Predicting the UCS from P-Wave Velocity, Density, and Porosity on Saturated Limestone. Appl. Sci. 2019, 9, 5265].

If you wish, we can share the experimental data with you.

 

5. Line 310: Please, check the values of porosity and density. They seem to me that they do not correspond to each other.

The experimental results are correct. In fact, you can check them in the corresponding publication Saldaña et al. (2020) [Saldaña, M .; González, J .; Pérez-Rey, I .; Jeldres, M .; Toro, N. Applying Statistical Analysis and Machine Learning for Modeling the UCS from P-Wave Velocity, Density and Porosity on Dry Travertine. Appl. Sci. 2020, 10 (13), 4565.].

If you wish, I can share the experimental data with you.

 

6. Tables 2-5. Please, check the significative digits. It seems to me that the significant figures are not always the same.

Yes, there are different levels of accuracy depending on the magnitude, since the tool used to measure is different. The goal is to simplify the results as much as possible, even though all decimals were used in the spreadsheet.

 

7. Line 400: How did the authors identify the presence of calcite and aragonite?

We do not know that, based on the book of Pentecost (2005) [Pentecost A. Travertine. Dordrecht: Springer, Germany, 2005] we understood that travertine could contain aragonite, and therefore the crystalline structure of the mixture could be important in the results of Uniaxial compressive Strength. As we do not have the means for an in-depth study (use of larger diameter cylindrical specimens, thin section of limestone and travertine, etc.), we suggest that there are two differentiated behavior between limestone and travertine:

1. Spatial distribution of irregular pores and irregular pore size inside travertine (we mainly based on the article by Soete et al. (2015) [Soete, J .; Kleipool, L .; Claes, H .; Claes, S .; Hamaekers, H .; Kele, S .; Swennen, R. Acoustic properties in travertines and their relation to porosity and pore types. Marine Petrol. Geol. 2015, 59 (1), 320–335.])
2. Difference in crystalline structure between limestone and travertine (mainly based on Pentecost (2005), although there are other papers).

 

 

 

Author Response File: Author Response.docx