GPU-Accelerated Anisotropic Random Field and Its Application in the Modeling of a Diversion Tunnel

Round 1

Reviewer 1 Report

I have attached my comments.

Comments for author File: Comments.pdf

Author Response

Response to Reviewer 1 Comments

 

Point 1. There is a lot of repetition in the abstract. A bit polishing resolve this.

Response 1: Thanks very much for the valuable comments. We have polished the statement in the abstract.

 

Point 2. It is advisable to add an overview on the structure of the paper in the end of the introduction.

Response 2: This a really helpful suggestion. We have added an overview on the structure of the paper in the end of the introduction.

 

Point 3. Use capital lambda for the matrix of eigenvalues.

Response 3: Thanks for the valuable comments from the reviewer. We have revised this symbol.

 

Point 4. “Huge” is a difficult size to understand.

Response 4: Thanks for the valuable comments from the reviewer. We have added a graph to the article to compare the efficiency of CPU and GPU processing arrays to express our point of view, as show in Figure 3. Meanwhile, we compared the computing time of different array size in Table 1. In the actual modelling process, the number of meshes and nodes is in the tens of thousands, so the array size for the calculation is also in the tens of thousands.

 

Point 5. Are the covariance matrices dense? I think they are, meaning that any modern method can be used to accelerate the Cholesky decomposition.

Response 5: Thanks for the valuable comments from the reviewer. As the reviewer said, the covariance matrices are really dense due to the huge number of meshes and nodes when modelling. The method to generate random field by traditional improving Cholesky decom-position fields is good, but the computational efficiency is very low and there are few practical applications. Therefore, in this paper, we take advantage of the efficiency of GPU parallel computing and cyclic simulation as the size of the matrix increases.

 

Point 6. Pg 7. L 241. Mud-free, L 246 (caption) no mudstone — terminology is not consistent.

Response 6: Thanks for the kindly reminder of reviewer. We have carefully revised the terminology in the paper.

 

Point 7. FLAC is not cited — I cannot comment on its capabilities

Response 7: Thanks for the valuable comment of reviewer. At the end of the article, on the basis of the previous modelling theory and efficient random field generation theory, we use FLAC software to analyse the displacement and stress changes of the tunnel in the anisotropic random field with different rotation angles.

Reviewer 2 Report

It is suggested to revise the abstract of the article as well as the conclusion of the research.

Research background should be focused on the topic. There seems to be a scattering. At the end, it should be summarized.

How are the information in Table 2 selected in terms of possible error criteria?

It seems that the validation of modeling, especially for the investigation of anisotropic effects, requires further explanation and comparison with other research results.

 

 

Author Response

Response to Reviewer 2 Comments

 

Point 1. It is suggested to revise the abstract of the article as well as the conclusion of the research.

Response 1: Thanks for the kind reminder of the reviewer, we have revised the abstract and the conclusion in this paper.

 

Point 2. Research background should be focused on the topic. There seems to be a scattering. At the end, it should be summarized.

Response 2: Thanks for the valuable comment from the reviewer. We have summarised in the introduction and the conclusion.

 

Point 3. How are the information in Table 2 selected in terms of possible error criteria?

Response 3: Thanks for the kindly reminder of reviewer. We selected these random field parameters according to the geological report on the red-bedded soft rocks of central Yunnan.

 

Point 4. It seems that the validation of modeling, especially for the investigation of anisotropic effects, requires further explanation and comparison with other research results.

Response 4: Thanks for the valuable comment from the reviewer. We we have supplemented the analysis of the cavern excavation under isotropic field in Section 4.2.

Reviewer 3 Report

This paper deals with interesting topic on modeling of diversion tunnel. The authors conducted valuable research where an approach of producing big numerical model random fields is obtained by combining the benefits of GPU and CPU computation with MATLAB programming control. The approach demonstrated a good performance, but I suggest that the authors point out that the main contribution of the paper is the efficiency of the approach to reduce the time consumed in the modeling considering anisotropic fields. To improve the paper some suggestions are presented below:

 

·       Please describe with more details in the abstract the main contribution of the study and explain better this contribution on conclusions.

·       Adjust all the wrong citations in the text. Ex: lines 45-47-> the correct form is “Beacher and Ingra [18] chose the Taylor expansion…”

·       In the lines 59-61, the authors said that: “Based on the literature above, it is evident that the random field method is capable of describing the spatial variability of geotechnical material parameters more accurately.”, but the efficiency of using the method mentioned above was not evident. In the previous paragraph you only indicated the use of the method in some studies, but do not point to the efficiency of the method. Improve writing.

·       In the lines 63-64, the authors said that: “Less research has been done in the stability analysis of excavation in underground caverns or tunnels.”. About these few developed works, what did you observe? Describe a little about these works. Improve your introduction.

·       In the lines 79-80, the authors said that: “There are methods to generate random fields. Currently, two main types of random field generation methods are commonly used [25]”. What are these two methods? What is the difference between them?

·       Attention in the text to call all the equations, please, revise all the equations and the indentations. In the lines 157 and 158 the numbers of equations are wrong.

·       The authors need to improve the Figure 8. Insert the methodology used to set the random field parameters (this is an important contribution).

·       The main contribution of the paper is indicated in the lines 197-203. It would be interesting to indicate this contribution to the summary and point it in the conclusions.

·       The data shown on Table 1 are yours? Please, describe better the analysis conducted to obtain these data.

·       In the subsection 4.1, the authors describe the computing conditions. How did the authors define this modeling scenario? Is there any work in the literature that supports the hypotheses employed?

·       In the figures 9a-15a the authors shown the anisotropic random field. What is the parameter associated with the color map of these figures?

·       In conclusion the authors need to indicate the efficiency of the approach proposed, and the se of GPU.

·       In conclusion, lines 425-426 the authors say that: “The effects of different correlation functions and different correlation lengths on the cavern excavation are compared in the isotropic random field model”. However, in the paper no results of the tunnel analysis are presented considering isotropic fields. It would be interesting for the authors to perform the tunnel simulation with an isotropic field and compare the values. These results would point to the importance of considering an anisotropic field.

Author Response

Response to Reviewer 3 Comments

 

Point 1. Please describe with more details in the abstract the main contribution of the study and explain better this contribution on conclusions.

Response 1: Thanks for the valuable comment from the reviewer. Thanks for the kind reminder of the reviewer, we have revised the abstract and the conclusion in this paper.

 

Point 2. Adjust all the wrong citations in the text. Ex: lines 45-47-> the correct form is “Beacher and Ingra [18] chose the Taylor expansion…”

Response 2: Thanks for the kindly reminder of reviewer. We have carefully revised the citations in this paper.

 

Point 3. In the lines 59-61, the authors said that: “Based on the literature above, it is evident that the random field method is capable of describing the spatial variability of geotechnical material parameters more accurately.”, but the efficiency of using the method mentioned above was not evident. In the previous paragraph you only indicated the use of the method in some studies, but do not point to the efficiency of the method. Improve writing.

Response 3: Thank you very much for the suggestion. We have revised the statement in the paper.

 

Point 4. In the lines 63-64, the authors said that: “Less research has been done in the stability analysis of excavation in underground caverns or tunnels.”. About these few developed works, what did you observe? Describe a little about these works. Improve your introduction.

Response 4: Thanks for the valuable comment from the reviewer. We have supplemented description of this work in the paper. As mentioned in the paper, the method proposed enables us to analyse the deformation and stress distribution state of the tunnel after excavation in central Yunnan.

 

Point 5. In the lines 79-80, the authors said that: “There are methods to generate random fields. Currently, two main types of random field generation methods are commonly used [25]”. What are these two methods? What is the difference between them?

Response 5: Thanks for the kind reminder of the reviewer, we have added the description of these two main types of random field generation methods and compared the two methods in Section 2.1.

 

Point 6. Attention in the text to call all the equations, please, revise all the equations and the indentations. In the lines 157 and 158 the numbers of equations are wrong.

Response 6: Thanks for the kindly reminder of reviewer. We have revised the equations and the indentations in the paper.

 

Point 7. The authors need to improve the Figure 8. Insert the methodology used to set the random field parameters (this is an important contribution).

Response 7: Thanks for the kind reminder of the reviewer. We selected these random field parameters according to the geological report on the red-bedded soft rocks of central Yunnan.

 

Point 8. The main contribution of the paper is indicated in the lines 197-203. It would be interesting to indicate this contribution to the summary and point it in the conclusions.

Response 8: This a really helpful suggestion. We have revised and polished the statement in the conclusion.

 

Point 9. The data shown on Table 1 are yours? Please, describe better the analysis conducted to obtain these data.

Response 9: Thanks for the valuable comment from the reviewer. We have revised the description in Section 2.3. Meanwhile, we also added a figure to display the difference of computing time between CUP and GPU with the increase of matrix array size. When the operation matrix array gradually becomes larger, the advantages of GPU acceleration gradually appear, and its operation speed and efficiency far exceed that of CPU. When doing multiple loop calculations to calculate probability problems, it will save a lot of time and cost.

 

Point 10. In the subsection 4.1, the authors describe the computing conditions. How did the authors define this modeling scenario? Is there any work in the literature that supports the hypotheses employed?

Response 10: Thanks for the kind reminder of the reviewer. We modelled it based on the diversion tunnel in central Yunnan, and determined the calculation conditions based on the examples in the FLAC user manual.

 

Point 11. In the figures 9a-15a the authors shown the anisotropic random field. What is the parameter associated with the color map of these figures?

Response 11: Thanks for the kind reminder of the reviewer. The parameter of these figure is the cohesion in different anisotropic random fields. We have added the description in these figures.

 

Point 12. In conclusion the authors need to indicate the efficiency of the approach proposed, and the se of GPU.

Response 12: Thanks for the kind reminder of the reviewer. As suggested by reviewer, we have revised the statement and supplemented the description of the efficiency of the approach proposed in the conclusion.

 

Point 13. In conclusion, lines 425-426 the authors say that: “The effects of different correlation functions and different correlation lengths on the cavern excavation are compared in the isotropic random field model”. However, in the paper no results of the tunnel analysis are presented considering isotropic fields. It would be interesting for the authors to perform the tunnel simulation with an isotropic field and compare the values. These results would point to the importance of considering an anisotropic field.

Response 13: Thanks for the valuable comment from the reviewer. As suggested by reviewer, we have supplemented the analysis of the cavern excavation under isotropic field in Section 4.2.

Round 2

Reviewer 1 Report

The authors have submitted a substantially improved paper. However, there has been a misunderstanding on my Comment 7: FLAC is not cited — I cannot comment on its capabilities"

It is not clear if this is their own implementation, research code, or a commercial product. Please clarify this and provide an adequate explanation or citation for further reference.

Author Response

Response to Reviewer 1 Comments

Point 1. It is not clear if this is their own implementation, research code, or a commercial product. Please clarify this and provide an adequate explanation or citation for further reference.

Response 1: Thanks very much for the valuable comments. The GPU-accelerated anisotropic random field generation method mentioned in this article is implemented by ourselves through Matlab code, as shown in the figure below.

Reviewer 3 Report

The authors conducted valuable research where an approach of producing big numerical model random fields is obtained by combining the benefits of GPU and CPU computation with MATLAB programming control. The approach demonstrated a good performance. I consider that the authors have made all the corrections and suggestions indicated. Thus, that the paper can be accepted.

Author Response

Thank you for your recognition and appreciation of our work.