Investigation of Virtual Bimrocks to Estimate 3D Volumetric Block Proportions from 1D Boring Measurements

Round 1

Reviewer 1 Report

Please find the comments, questions and suggestions to improve the paper in the accompanying file.

Author Response

Th authors thank the reviewer for his/her revision work.

Best regards

Reviewer 2 Report

This paper proposed an estimation method for 3D volumetric block proportions from 1D Boring Measurements. Based on the method, the chart on the estimation of VBPs is revised for accuracy. The topic is interesting and useful in the engineering. However, the research can still be further improved in some aspects

(1) Obviously, the proposed method cannot be applied to all rock formations. Please highlight the scope of application of this method. Make sure that this method is applicable in specific circumstances.

(2) Although the uncertainty is analyzed in the methods from 1D measurements to estimate the information of 3D volumetric block proportions, the variation of the rock properties is not considered, the effect of different rock properties, such as shape and size of the rock block, on the accuracy of results needs to be further explained. At the same time, other limitations of the proposed method are supposed to be emphasized.

(3) The parameters investigation is not enough, parameters involved in the proposed method are required to be further explained for their sensitivity to results.

Author Response

The authors thank the Reviewers for the time spent in reviewing the manuscript and for his/her comments.

Revising the manuscript according to the suggestions proposed certainly increased the quality of the paper.

The answers to the points raised by the Reviewer are reported in the attached file.

Best regards

Author Response File: Author Response.pdf

Reviewer 3 Report

This paper aimed to improve the uncertainty factors for estimating the volumetric block proportions VBPs from linear block proportions LBPs, which can be easier obtained by analyzing exploration drilling in the engineering. This study is quite interesting, with an important engineering significance. However, some major revisions should be made to increase the readability of the paper, especially for some abbreviations and figures.

1. This study mainly updates and extends the data from Medley’s study, as such, some irrelevant studies need to be simplified in the description, especially the researches of Lu et al. [42] and Napoli et al. [4] presented in the Section 1.1.   

2. Although a lot of references are mentioned in this manuscript, some representative references related to the soil-rock mixtures S-RMs are also recommended to be reviewed. Because this paper is also very useful for the estimation of VBP of S-RMs, not only bimrocks.

[1] Zhang Han, Daniela Boldini, Wang Lehua, Deng Huafeng, Liu Chang (2022) Influence of block form on the shear behaviour of soft soil–rock mixtures by 3D block modelling approaches. Rock Mechanics and Rock Engineering, 55, 1-22.

[2] Zhang Han, Hu Xinli, Boldini Daniela, He Chuncan, Liu Chang, Ai Chuanjing (2020) Evaluation of the shear strength parameters of a compacted S-RM fill using improved 2-D and 3-D limit equilibrium methods. Engineering Geology, 269, 105550.

[3] Xu Wenjie, Xu Qing, Hu Ruilin (2011) Study on the shear strength of soil-rock mixture by large scale direct shear test. International Journal of Rock Mechanics and Mining Sciences, 48(8), 1235-1247.

3. Page 4 Line 145, what is the meaning of the abbreviation of Vv? Is it the VBP? If it is, I suggests the use of Vv in the description and the Fig2(a) should be replaced by the VBP, just like the Fig2(b).

4. What is the meaning of the label of Y-axis of Fig. 3, CV(Lb)? Dose the Lb represent the unit of CV?

5. Page 6 Line 213, why the ABP is difficult to be determined while the LBP is easily to be measured? For a bimrock, the LBP can be obtained by drilling, however, the ABP can be obtained easier by digital image analysis of a photo of the bimrock surface. This is also an important question why the VBP of a bimrock is estimated by 1D LBP, rather than 2D ABP?

6. For the validation of Medley’s findings, the virtual bimrock models were generated with spherical blocks. Obviously, the effect of block shape was neglected, however, as described in the Page 2 Line 74, the block shape and orientation were demonstrated that affect the estimation of VBP from ABP and LBP. It should be discussed in the validation.

7. Page 7 Line 256, the uncertainty factors UF is defined as standard deviation/mean, what is the meaning of the mean? While the uncertainty factors in the Medley researches is defined as standard deviation/VBP, why not use the same factor for the comparison?

8. As shown in Fig.6, the data obtained by the virtual bimrock models is very close to that obtained by the physical bimrock models with different block shapes, does it mean that block shape has no effect on the estimation of VBP?

9. Page 8 Line 294, what is the meaning of maximum number of randomizations?

10. For my opinion, the Fig.7 is unnecessary, the data is also shown in the Fig.8.

11. In the Fig. 8, some data of Medley is missing, e.g. the VBP of 13% with the N less than 10. Why the data obtained by the λ of 40 is significant different from the Medley’s? In the validation(Fig.6), the data obtained by the λ of 40 is very close to the Medley’s.

12. In the Application example, the VBP of bimrock located in the Scott Dam was considered as 31%, please describe the determination approach of the VBP, although may have been described in other researches, it is very important for demonstrating the validity of the improved data.

Author Response

The authors thank the Reviewer for the time spent in reviewing the manuscript and for his/her valuable comments.

Revising the manuscript according to the suggestions proposed certainly increased the quality of the paper.

The answers to the points raised by the Reviewer are reported in the attached file.

Best regards

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

I only has the last one comment on the author's work.

The author aims to develope a specialized Matlab code and perform virtual drilling programs through 3D computer-generated bimrock models. However, we can see that the model looks too simplifed which only use spherical particles to represent blocks. Many studies have develope realistic reconstruction of 3D/2D numerical model of rock soil mixture or rock blocks, which can help the authors to improve their prediction make it more realistic. Some references are listed as following and would be suggested to help the literature review part in the introduction.

Stochastic numerical model of stone-based materials with realistic stone-inclusion features

A novel approach of random packing generation of complex-shaped 3D particles with controllable sizes and shapes

Three-dimensional reconstruction of realistic stone-based materials with controllable stone inclusion geometries

Author Response

The authors thank the reviewer for this comment. Of course there have been proposed more sophisticated methodologies and approaches in the literature to create less simplified (more realistic) bimrock models. However, the implementation of these approaches is not an easy task. Since the aim of the work was to investigate the uncertainty in the estimation of bimrock VBPs and since previous studies have pointed out that the influence on VBPs of block shapes is apparently minor, the authors have used spherical particles to simulate the rock blocks. To clarify this aspect, a sentence (and a suggested reference) has been added on page 7:

“That there was a difference between Medley’s [43] ellipsoidal blocks and our spherical blocks may not have much influenced our findings, which is fortuitous given the difficulties involved in modelling populations of oriented ellipsoids or irregular-shaped blocks in virtual bimrocks [52,53]. Also: Lu et al. [45] and Ramos-Cañón et al. [6] discovered that the influence on VBPs of block shapes is apparently minor.”

Since it could be of interest to investigate the difference in the results from virtual bimrocks with different (and more realistic) block shapes, the last sentence of the Conclusion section has been also modified as follows:

Further research could investigate the variations in the UF values when geomaterials with different block-size distributions and (more realistic [53]) block shapes are considered.

Reviewer 3 Report

The paper can be accepted for publication.

Author Response

Thank you