Three-Dimensional Stability Analysis of Ridge Slope Using Strength Reduction Method Based on Unified Strength Criterion

Round 1

Reviewer 1 Report

In view of the slope stability of ridge slope, the authors conducted a three-dimensional stability analysis using the strength reduction method based on unified strength criterion, revealed the deformation law of slope, and discussed the influence of the geometric parameters on the stability of slope. The study can be used for reference for engineering activities in similar terrain areas. However, the following issues need to be considered by the author:

(1)    What slope does “Rigid slope” mean in abstract? Is it an input error?

(2)    In the manuscript, the title of “2.2 Geometric parameters of natural ridge slope model” is repeated.

(3)    The proper nouns need to be unified, e.g. “Flank slope angle β” (line 114) and “side slope foot β” (line 138), “the strength reduction method” (line 139) and “the strength discount method” (line 144).

(4)    Line 120, the “so” in sentence of “ …exist, so the combination of …” is not used properly.

(5)    In the numerical model, how to describe the constitutive relationship of the slope materials? And how to deal with the truncated boundary conditions of the numerical model?

(6)    Which direction is the displacement in Figures?

(7)    The authors are requested to verify whether the calculation results are reasonable? From the figure 4, the total height of the slope is 10m, and the calculated result is 5m. I doubt the rationality of this result. Under normal circumstances, the slope at this time should have already been damaged. The author should indicate what case are these graphical results based on?

(8)    Figure 6 (b) and Figure 6 (c) seem to have little difference, please check.

(9)    Line 348, where can we get the “plastic displacement of the ridge slope”？

(10) According to the article, the front side of the slope is a straight elevation. How does this slope behave in the calculation?

(11) It seems inappropriate to choose the displacement at the top of the slope for analysis. As we know, the vertical displacement of the slope must be the largest at the top under the action of gravity. The vertical displacement cannot show the stability of the slope.

Author Response

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Reviewer 2 Report

1. You have organized the section of "Introduction" very well but you have not highlighted the main challenge(s) and your contribution to fixing it/them. If it is possible add some more newly published papers such as (Please cite them in the section of "References"): A: DOI: 10.3390/w14223743 B: DOI: 10.1007/s12665-022-10603-6 C: DOI: 10.1016/j.enggeo.2019.105349 2. The quality of Figures 6, 9, 12, and 16 is not suitable. 3. You could have compared your obtained result with the previous works. Please kindly provide a comparison table and try to evaluate the obtained results with the results of some of the papers that you presented in the section "Introduction". 4. The presented article and its topic are so interesting but you could not have addressed the contents of the paper properly. I mean you gathered some different sections in a single headline. Please separate them into different sections. 5. Please introduce the proposed model/contribution in a detail (its parameters, functionality, advantage, and so on).

Comments for author File: Comments.pdf

Author Response

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Reviewer 3 Report

An interesting topic about three-dimensional stability analysis of a ridge slope is presented by the authors. Moreover, a simple wedge model is constructed to simulate three-dimensional natural ridge slope (including its excavation model). The work done by the authors is very helpful to the construction of road slope. However, the authors only use conventional numerical simulation methods to carry out the analysis, and the work has not been verified to be reliable (e.g., it is doubtful that the displacement of the slope with a slope height of 10m can reach about 4m in the model established by the authors). Hence, it is not recommended to publish this paper in Journal of the Applied Sciences.

 

Some specific comments are given as follows:

(1) Please replace “unified intensity theory” with “unified strength theory”.

(2) Please replace “strength discount method” with “strength reduction method”.

(3) Please give the full name of the abbreviation “UMAT”.

(4) How did come about for the conclusion “When the ridgeline angle was small, the most vulnerable area of the ridge slope was near the front of the slope and prone to tensile fracture”.

(5) How did come about for the conclusion “When the ridgeline inclination angle was large, the most vulnerable area of the slope was at the rear edge of the slope, and many shear failures occurred”.

(6) The conclusions could be abbreviated.

Author Response

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Round 2

Reviewer 1 Report

I don't think the revised version has been improved. The authors first need to clarify the following aspects: (1) the relationship between the purpose of this study and the demonstration of the methods used. (2) the reasonable results of numerical simulation depend on the establishment of the model, the selection of material constitutive relations, the selection of parameters and the treatment of boundary conditions. (3) the selection of failure modes, criteria of failure and characterization variables of slope failure. Therefore, the authors should consider the following aspects:

(1)    The description in the introduction needs to be further condensed, and some attention should be paid to the logical relationship between the descriptions.

(2)    Line 119-120, the sentence of “In the model, the truncated boundary conditions in the model are set as fixed boundary conditions” needs to be checked, because such treatment may lead to problematic results.

(3)    According to the slope studied in this paper, as shown in Figure 3, the slope has three slopes. The article focuses on two sides, and does not mention the situation of the slope inclined to the x-direction. It is unknown whether this surface is a real slope or an artificially truncated virtual surface. If the slope is artificially truncated, how is this surface treated in the numerical value?

(4)    In Line 170, “This paper selects the displacement cloud image of the slope when the reduction coefficient is 30. At this time, the ridge and slope have become unstable, so the ridge slope will undergo a large displacement.” According to this description, all figures in this article are the slope state after instability. As we know, the finite element method can only deal with small deformation, and the large deformation after instability is not necessarily reliable. It is not reasonable to choose this working condition for discussion in this paper.

(5)    In Figure 16, the “PEMAG” should be plastic strain? So, where is the plastic displacement of “2.89cm” in Line 402 obtained?

(6)    The characterization parameters should be selected according to the failure mode of the slope for analysis.

Author Response

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Reviewer 2 Report

1. You should have compared the obtained result with the results of the previous works (numerical analysis/comparison). Please kindly provide a comparison table and try to evaluate the obtained results with the results of some of the papers that you presented in the section "Introduction". How do you claim that the proposed method is one of the best models? 2. As you know the main idea of the proposed model is based on the concept of "three- dimensionality". If it is possible, please focus on the differences between two-dimensional models the three- dimensional models and try to distinguish the differences between them. Also, highlight the reliable, and claimable viewpoints. 3. The quality of "Figure 18" is not proper. 4. Please list information about the hardware tools and software programs that you have used to simulate and implement the proposed model.

Comments for author File: Comments.pdf

Author Response

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Reviewer 3 Report

The work done in the paper is relatively simple. The authors have made a detailed reply to the review comments, and it may consider publishing this paper.

Author Response

Thank you very much.