Stability Evaluations of Unlined Horseshoe Tunnels Based on Extreme Learning Neural Network

Round 1

Reviewer 1 Report

1. The authors mention in line 76 that the object of study is a plastic solution for drainage stability, but the second part deals with anhydrous formations.
2. There is an obvious syntax error on line 310.
3. This paper is based on the results of numerical simulation, and the results obtained from ANN must be consistent with it.
4. In Fig. 15,or ?
5. There are formatting errors in the text, such as the title of Table 2.
6. In Table 2, the value of has a negative value, please explain the specific meaning.
7. The author mentions 'The differences between the current UB and 186 LB solutions are quite modest (less than 1%). '. Is the upper bound (UB) and lower bound (LB) related to the active and passive instability of the tunnel face? If so, how can it be concluded that the difference is less than 1%?
8. What is the basis for setting the number of neurons in the hidden layer to 7? Is it possible to increase R² and decrease the Mean Absolute Error and Root Mean Squared Error by increasing the number of neurons in the hidden layer?
9. In the introduction, literature review is not sufficient, and some references about tunnels are suggested to be added. Such as " Evaluation of Tunnel Face Stability Subjected to Seismic Load Based on the Non-associated Flow Rule", " Influence of non-associated flow rule on face stability for tunnels in cohesive–frictional soils ", " Experimental investigation of mechanical characteristics for linings of twins tunnels with asymmetric cross-section "…

Author Response

1. The authors mention in line 76 that the object of study is a plastic solution for drainage stability, but the second part deals with anhydrous formations.

Ans: The authors are appreciative of the positive comments. Please see the revised manuscript for all changes made. The authors would like to apologize for the unclear sentences in the introduction part. We have changed those sentences to “In this study, the numerical solutions of the stability of horseshoe tunnels in cohesive-frictional soils (or sandy soils) under plane strain conditions are presented by employing the numerical technique of FELA to derive the UB and LB solutions.”.

 

2. There is an obvious syntax error on line 310.

Ans: The errors have been corrected.

 

3. This paper is based on the results of numerical simulation, and the results obtained from ANN must be consistent with it. In Fig. 15, or?

Ans: The reviewer is right! We used Fig. 15 to demonstrate the correctness of the proposed ANN model. It can be seen from Fig. 15 that the predicted solutions from ANN are on the 45 degree line indicating that the acceptable predicted solutions are in good agreement with those from FELA.

 

4. There are formatting errors in the text, such as the title of Table 2.

Ans: The authors would like to thank the reviewer for the comment. All errors have been corrected.

 

5. In Table 2, the value of has a negative value, please explain the specific meaning.

Ans: We have added more description regarding this issue as “Note that the sign convention for the dimensionless load factors presented in Table 2 is that a positive sign corresponds to the cases where the ground above the tunnel can support the compressive normal stress and the self-weight of soil masses. In contrast, a negative sign corresponds to the cases where only the tensile normal stress can apply on the ground surface. The later cases of the negative sign rarely happen in practice since compressive normal stress is mostly applied on the ground surface. Nevertheless, these cases can indicate that if there is no tensile normal stress applied on the ground surface, the soils around the tunnel will certainly collapse due to the driving force from the self-weight of soil masses”.

 

6. The author mentions 'The differences between the current UB and 186 LB solutions are quite modest (less than 1%). '. Is the upper bound (UB) and lower bound (LB) related to the active and passive instability of the tunnel face? If so, how can it be concluded that the difference is less than 1%?

Ans: In this study, we produced both UB and LB solutions for the stability of tunnels with active failure (soil collapsing inside the tunnel) using FELA. However, we only showed the average solutions from UB and LB solutions and used these Ave solutions as training data in the ANN model. We wanted to confirm that the Ave solutions are rigorous solutions and good enough to use in the ANN model, so we explained about the difference between both UB and LB values. If the difference between both UB and LB solutions is less than 1%, it means that the bound solutions can be accepted as rigorous solutions. We have added more descriptions to clarify this issue in Section 4.

 

7. What is the basis for setting the number of neurons in the hidden layer to 7? Is it possible to increase R2 and decrease the Mean Absolute Error and Root Mean Squared Error by increasing the number of neurons in the hidden layer?

Ans: The number of neurons should be carefully considered. There are many rules to choose to optimum number of neurons by using e.g. 2/3 the size of the input layer + size of output later, less than twice the size of the input layer etc. as a starting point. Then, trial and error can be used by increasing the number of hidden neurons until the model is overfitting. This can be observed when the R² tends to decrease or stable. This study starts by 1 neuron and keeps increasing until 10 and we observe the R² decrease and MAE and RMSE increase when the number of neurons is over 7.

 

8. In the introduction, literature review is not sufficient, and some references about tunnels are suggested to be added. Such as " Evaluation of Tunnel Face Stability Subjected to Seismic Load Based on the Non-associated Flow Rule", " Influence of non-associated flow rule on face stability for tunnels in cohesive–frictional soils ", " Experimental investigation of mechanical characteristics for linings of twins tunnels with asymmetric cross-section "…

Ans: The authors would like to thank the reviewer for the suggested references. These references have been added to the paper.

Reviewer 2 Report

This paper presents a very interesting effort to use the neural network to boost the numerical prediction of the stability of shallow horseshoe tunnels. The paper is well organised in a high quality. Before the acceptance, some minor revisions could be made as the followings.

 

 

1. Section 4. As a crucial part of data science, it should be clearly stated about the size of the generated FE results.

 

2. What is the reason for choosing a horseshoe tunnel? Provide a few real life examples.

 

3. The variations shown in Table 1 could not conduct their suitable meaning, kindly replace "/" with "," for more clarification.

 

4. Why 5000 elements in the FELA is considered at the very first step? 10000 elements were sufficient for simulation with adequate accuracy?

 

5. The fact that paper is focused only on the "unlined" tunnels probably should be mentioned in the title as well; it is a significant aspect of the study.

 

6. There are a lot of self-citations; most of them are not really necessary, just serving the purpose of bumping up statistics, it seems. Please either put more reference to works of other authors or delete some of the self-citations, so it is not too obvious.

 

Author Response

This paper presents a very interesting effort to use the neural network to boost the numerical prediction of the stability of shallow elliptical tunnels. The paper is well organised in a high quality. Before the acceptance, some minor revisions could be made as the followings.

Ans: The authors are appreciative of the positive comments. Please see the revised manuscript for all changes made.

 

1. Section 4. As a crucial part of data science, it should be clearly stated about the size of the generated FE results.

Ans: The details of the sizes of the generated FE results have been added in the paper in the section of numerical analysis.

 

2. What is the reason for choosing a horseshoe tunnel? Provide a few real life examples.

Ans: The authors would like to thank the reviewer for the comment. An example of the previous studies and cases of horseshoe tunnels has been added in the introduction part of the paper.

 

3. The variations shown in Table 1 could not conduct their suitable meaning, kindly replace "/" with "," for more clarification.

Ans: The authors would like to thank the reviewer for the comment. All "/" have been replaced by "," in Table 1.

 

4. Why 5000 elements in the FELA is considered at the very first step? 10000 elements were sufficient for simulation with adequate accuracy?

Ans: The authors would like to thank the reviewer for the comment. We used this setting by following our experience of using this scheme. If the number of elements is more than this setting, the computation time will be very long. Also, this setting can provide an adequate accuracy of the results since the differences between the UB and LB solutions are within 1% as mentioned in the manuscript.

 

5. The fact that paper is focused only on the "unlined" tunnels probably should be mentioned in the title as well; it is a significant aspect of the study.

Ans: The authors would like to thank the reviewer for the comment. We have added "unlined" in the title of the paper.

 

6. There are a lot of self-citations; most of them are not really necessary, just serving the purpose of bumping up statistics, it seems. Please either put more reference to works of other authors or delete some of the self-citations, so it is not to obvious.

Ans: The authors would like to thank the reviewer for the comment. We have deleted some of the self-citations.

Round 2

Reviewer 1 Report

The authors have made sufficient modification and explanation according to the

comments, so my opinion is: accept.