Application of the Improved Entry and Exit Method in Slope Reliability Analysis

Round 1

Reviewer 1 Report

Title: Application of the Improved entry and exit method in Slope Reliability Analysis

The paper presents a study on an improved entry and exit method in Slope Reliability Analysis by considering two different hypothetical slope models. The improved method is expected to reduce the computation cost of the stability analysis. Based on a thorough review of the manuscript, the reviewer suggests that the paper requires "Major Revision". Following are the detailed comments of the reviewer:

Major Comments:

1.       Introduction: In addition to the studies related to the determination of critical slip surface, authors should discuss the role of uncertainty of index characteristics and shear strength parameters of slope materials, and their effects on the FOS.

2.       Introduction: Apart for numerical simulations considering LEM and FEM based methods, authors should also briefly discuss some the emerging slope failure prediction methods based on model and field testing approaches, which are evolved in recent time. Author should consider including the following such studies:

Xie, J., Uchimura, T., Wang, G., Shen, Q., Maqsood, Z., Xie, C., ...
& Qiao, S. (2020). A new prediction method for the occurrence of
landslides based on the time history of tilting of the slope surface.
Landslides, 17, 301-312.

3.       Example Analysis: The authors clearly justify the selection of geometry of models and calculation parameters for the analysis. The geometries of the models are fairly simple, having only single type of soil material. It is lucrative to consider some practical examples of the past landslide events to verify the findings of this study.

4.       Random field modeling of spatially variable soil properties: Strain rate or loading rate is one of the crucial parameter which affects the strength and deformation response of the granular and bounded materials such as natural soils, rocks and cemented soil. This aspect has totally been ignored in this study, and the effects of strain/loading rate on the probability of failure should be highlighted. Authors should add some literature on this aspect as the results presented in the study did not consider the effects of viscosity (loading/strain rate). The reviewer also suggest to include the findings of other studies related to loading rate dependency of different geomaterials for instance:

Maqsood, Z., Koseki, J., Ahsan, M. K., Shaikh, M., & Kyokawa, H. (2020). Experimental study on hardening characteristics and loading rate
dependent mechanical behaviour of gypsum mixed sand. Construction and
Building Materials, 262, 119992.

Based on these comments, the reviewer suggests that the paper requires "Major Revision".

English language is satisfactory. 

Author Response

Response to Reviewer 1 Comments

Point 1: Introduction: In addition to the studies related to the determination of critical slip surface, authors should discuss the role of uncertainty of index characteristics and shear strength parameters of slope materials, and their effects on the FOS.

Response 1: The authors have considered this comment carefully and added the following discussion in the introduction:

Nguyen et al. [11] studied the role of spatial variability of the soil nature during rainfall infiltration on sandy slope steadiness, they discovered that the uncertainty in the effective friction angle parameter had a significant influence on the obtained safety factor and failure probability. Wang et al. [12] proposed a reliability exploration method for assessing the earth dam slope failure possibility based on Extreme Gradient Boosting (XGBoost), and by conducting parameter sensitivity analysis on case studies, they found that the parameter of variation and fluctuation scale of spatially variable soil properties significantly influenced the failure probability of earth dam slopes.

Point 2: Introduction: Apart for numerical simulations considering LEM and FEM based methods, authors should also briefly discuss some the emerging slope failure prediction methods based on model and field testing approaches, which are evolved in recent time. Author should consider including the following such studies:

Xie, J., Uchimura, T., Wang, G., Shen, Q., Maqsood, Z., Xie, C., ...
& Qiao, S. (2020). A new prediction method for the occurrence of
landslides based on the time history of tilting of the slope surface.
Landslides, 17, 301-312.

Response 2: The authors have considered this comment carefully and added the following discussion in the introduction:

However, in practice, it is unrealistic to conduct slope reliability analysis considering all influencing parameters. In such cases, the emerging methods based on model and field testing have been widely adopted for slope failure prediction in recent years. For example, Liu et al. [15] proposed an improved Markov chain model, which can accurately simulate soil boundary uncertainty and obtain more accurate reliability results based on limited site drilling information. Xie et al. [16] conducted a set of model experiments and field tests to examine the tilting actions of landslides, and than they proposed a novel method that can effectively predict the remaining time before slope failure occurs. He et al. [17] introduced a machine learning aided approach for the stochastic reliability analysis of spatially variable soil slopes, the model generated based on machine learning in this method not only accurately predict the safety factor, but also greatly reduce the computational workload.

Point 3: Example Analysis: The authors clearly justify the selection of geometry of models and calculation parameters for the analysis. The geometries of the models are fairly simple, having only single type of soil material. It is lucrative to consider some practical examples of the past landslide events to verify the findings of this study.

Response 3: Thanks for pointing this out. The author has carefully considered this opinion and believes that:

1. The use of actual landslide examples in heterogeneous soil can better demonstrate the method proposed in this paper.
2. The focus of this study is to verify that this method can significantly reduce the cost of numerical calculation while obtaining more accurate failure probability calculation results, thus achieving a fast and practical reliability analysis and evaluation of large-scale slopes when conducting many slope stability analyses in the design stage and geotechnical engineering construction technology planning stage. Therefore, this article uses simple examples.
3. The actual calculation example shows that the soil layer is complex, and the generation of random fields is relatively complex. The author will use actual landslide examples of heterogeneous soil in subsequent research to further verify the applicability of the method proposed in this paper.

 

 

Point 4: Random field modeling of spatially variable soil properties: Strain rate or loading rate is one of the crucial parameter which affects the strength and deformation response of the granular and bounded materials such as natural soils, rocks and cemented soil. This aspect has totally been ignored in this study, and the effects of strain/loading rate on the probability of failure should be highlighted. Authors should add some literature on this aspect as the results presented in the study did not consider the effects of viscosity (loading/strain rate). The reviewer also suggest to include the findings of other studies related to loading rate dependency of different geomaterials for instance:

Maqsood, Z., Koseki, J., Ahsan, M. K., Shaikh, M., & Kyokawa, H. (2020). Experimental study on hardening characteristics and loading rate dependent mechanical behaviour of gypsum mixed sand. Construction and Building Materials, 262, 119992.

Response 4: According to the suggestions of the reviewers, the author has added and discussed relevant literature in this regard in the introduction:

Furthermore, strain rate or loading rate [13] is also one of the key coefficient which affects the shear strength and deformation response of soil particles. Deng et al. [14] revealed the mechanism of toe loading through triaxial compression tests, verifying the important relationship between strain rate effect and slope sliding.

References

11.  Nguyen,T.S.;Likitlersuang, S. Reliability analysis of unsaturated soil slope stability under infiltration considering hydraulic and shear strength parameters. Bulletin Engineering Geology and the Environment 2019, 78, 5727-5743. DOI: 10.1007/s10064-019-01513-2.
12. Wang,L.;Wu, C.; Tang, L.; Zhang, W.; Lacasse, S.; Liu, H, et al. Efficient reliability analysis of earth dam slope stability using extreme gradient boosting method. Acta Geotechnica 2020, 15, 3135-3150. DOI: 10.1007/s11440-020-00962-4.
13. Maqsood,Z.;Koseki, J.; Ahsan, MK.; Shaikh, M.; Kyokawa, H. Experimental study on hardening characteristics and loading rate dependent mechanical behaviour of gypsum mixed sand. Construction Building Materials 2020, 262, 119992. DOI: 10.1016/j.conbuildmat.2020.119992.
14. 14. Deng,J.;Xu, Q.; Koseki, How the toe loading suppresses the movements of an instable slope: mechanisms revealed from triaxial compression tests under varied strain rate condition. Engineering Geology 2016, 209, 93-105. DOI: 10.1016/j.enggeo.2016.05.012.
15. 15. Liu,L.;Cheng, Y.; Pan, Q.; Dias, Incorporating stratigraphic boundary uncertainty into reliability analysis of slopes in spatially variable soils using one-dimensional conditional markov chain model. Computers and Geotechnics 2020, 118, 103321. DOI: 10.1016/j.compgeo.2019.103321.
16. 16. Xie,J.;Uchimura, T.; Wang, G.; Shen, Q.; Maqsood, Z.; Xie, C et al. A new prediction method for the occurrence of landslides based on the time history of tilting of the slope surface. Landslides 2020, 17, 301-312. DOI: 10.1007/s10346-019-01283-8.
17. 17. He,X.;Xu, H.; Sabetamal, H.; Sheng, Machine learning aided stochastic reliability analysis of spatially variable slopes. Computers and Geotechnics 2020, 126, 103711. DOI: 10.1016/j.compgeo.2020.103711.

 

Author Response File: Author Response.docx

Reviewer 2 Report

Dear authors

In this study, the entry and exit method is a simple and practical method to determine the critical slip surface of slope. However, it has the drawback of sacrificing computational efficiency to improve search accuracy. To solve this problem, this paper proposes an improved entry and exit method to search for the critical slip surface. Based on the random fields generated by using Karhunen–Loève expansion method, the simplified Bishop’s method combined with the improved entry and exit method is used to determine the critical slip surface and its corresponding minimum factor of safety. Then, the failure probability is calculated by conducting Monte Carlo simulation. Two examples are reanalyzed to verify the accuracy and efficiency of the proposed method. Meaningful comparisons are made to demonstrate the calculating accuracy and calculating efficiency of the improved entry and exit method in searching for the minimum safety factor of slope, based on which the effect of the reduced searching range on slope reliability was explored. The results indicate that the proposed method provides a practical tool for evaluating the reliability of slopes in spatially variable soils. It can greatly improve

  The manuscript is well organized and has good content. In the opinion of the reviewer,
this manuscript note could be accepted after the major revisions and re-evaluation.

 1-     Authors are recommended to emphasis the novelty and significance of the study in more detail.

2-     Considering the importance of section “Discussion on reduced searching range”, it is recommended to provide more complete explanations in this section

3-     In the conclusions section, the description is provided in the form of numbering. It is recommended to remove the numbering system in the text of this section.

4-     The colors used in Figure 8 are not very clear when printing. It is recommended to use other colors to draw this shape to have a higher quality when printing.

5-     Authors are recommended to provide a more complete explanation in the “Example analysis” section.

6-     Some of the references provided are old. It is suggested that a number of related topics that are newer and have been published in the last five years be used in the article.

Minor editing of English language required

Author Response

Response to Reviewer 2 Comments

Point 1: Authors are recommended to emphasis the novelty and significance of the study in more detail.

Response 1: Thanks for pointing this out. In order to emphasize the novelty and significance of this study in more detail, the author has added the following content at the end of the “Discussion on reduced searching range”:

Regarding the research findings obtained in this discussion section: It is evident that the number of trial slip surfaces significantly affects on the accuracy of computed failure probability results. The proposed improved entry and exit method can significantly reduce the computational cost while obtaining more accurate result of calculating failure probability. This method is applicable for realizing rapid and practical reliability analysis assessments on a large number of slopes - both at the design stage and at the stage of planning the technology for the execution of geotechnical works.

Point 2: Considering the importance of section “Discussion on reduced searching range”, it is recommended to provide more complete explanations in this section.

Response 2: The authors have considered this comment carefully and added the following content at the beginning of the “Discussion on reduced searching range”:

This section provides the number of potential critical sliding surfaces (with the global minimum safety factor) that were omitted due to the reduced searching range during the second search. Its primary purpose is to discuss the fluctuation degree of the difference value in positions between potential critical sliding surfaces and critical sliding surfaces under two different search accuracies. This also fundamentally validates the result in the example analysis that a larger reduced searching range leads to a more accurate estimation of failure probability.

 

Point 3: In the conclusions section, the description is provided in the form of numbering. It is recommended to remove the numbering system in the text of this section.

Response 3: According to the suggestions of the reviewers, the author has removed the numbering system from the conclusion text in the revised manuscript.

 

Point 4: The colors used in Figure 8 are not very clear when printing. It is recommended to use other colors to draw this shape to have a higher quality when printing.

Response 4: According to the suggestions of the reviewers, the author has already used other colors to draw Figure 8 in the revised manuscript.

 

Point 5: Authors are recommended to provide a more complete explanation in the “Example analysis” section.

Response 5: To make the manuscript more precise and readable, the authors have rephrased languages of this paper at the end of the “Example analysis” section in the revised manuscript. For example, the sentence that “Therefore, using the improved entry and exit method to search for the critical slip surface, the calculated failure probabilities are very close to the target value and greatly improve the calculation efficiency. The safety factor search method for improved entry and exit is an effective and suitable method to solve the low computational efficiency of traditional method in slope stability analysis.” has been revised as “These results indicate that when using improved entry and exit method to search for critical slip surfaces , even with a smaller reduced searching range (unilateral 2D or unilateral 4D), it is possible to calculate failure probabilities that are very close to the target value. Moreover, this method significantly enhances computational efficiency while providing more accurate estimates of failure probabilities. Therefore, the safety factor search method for improved entry and exit is an effective and suitable approach for addressing the contradiction between computational efficiency and search accuracy in traditional methods for slope reliability analysis.”

 

Point 6: Some of the references provided are old. It is suggested that a number of related topics that are newer and have been published in the last five years be used in the article.

Response 6: Thanks for pointing this out. The author has added some more recent relevant thematic literature published in the past five years to the introduction of the revised manuscript, including:

11.  Nguyen,T.S.;Likitlersuang, S. Reliability analysis of unsaturated soil slope stability under infiltration considering hydraulic and shear strength parameters. Bulletin Engineering Geology and the Environment 2019, 78, 5727-5743. DOI: 10.1007/s10064-019-01513-2.
12. Wang,L.;Wu, C.; Tang, L.; Zhang, W.; Lacasse, S.; Liu, H, et al. Efficient reliability analysis of earth dam slope stability using extreme gradient boosting method. Acta Geotechnica 2020, 15, 3135-3150. DOI: 10.1007/s11440-020-00962-4.
13. Maqsood,Z.;Koseki, J.; Ahsan, MK.; Shaikh, M.; Kyokawa, H. Experimental study on hardening characteristics and loading rate dependent mechanical behaviour of gypsum mixed sand. Construction Building Materials 2020, 262, 119992. DOI: 10.1016/j.conbuildmat.2020.119992.
14. 14. Deng,J.;Xu, Q.; Koseki, How the toe loading suppresses the movements of an instable slope: mechanisms revealed from triaxial compression tests under varied strain rate condition. Engineering Geology 2016, 209, 93-105. DOI: 10.1016/j.enggeo.2016.05.012.
15. 15. Liu,L.;Cheng, Y.; Pan, Q.; Dias, Incorporating stratigraphic boundary uncertainty into reliability analysis of slopes in spatially variable soils using one-dimensional conditional markov chain model. Computers and Geotechnics 2020, 118, 103321. DOI: 10.1016/j.compgeo.2019.103321.
16. 16. Xie,J.;Uchimura, T.; Wang, G.; Shen, Q.; Maqsood, Z.; Xie, C et al. A new prediction method for the occurrence of landslides based on the time history of tilting of the slope surface. Landslides 2020, 17, 301-312. DOI: 10.1007/s10346-019-01283-8.
17. 17. He,X.;Xu, H.; Sabetamal, H.; Sheng, Machine learning aided stochastic reliability analysis of spatially variable slopes. Computers and Geotechnics 2020, 126, 103711. DOI: 10.1016/j.compgeo.2020.103711.

Author Response File: Author Response.docx

Reviewer 3 Report

Main remarks:

The article presents a modification of the entry and exit method for slope stability analysis. The title method concerned the selection of the location and shape of the failure surface, and the corresponding value of the stability coefficient was analysed using the Bishop method. A random lognormal distribution of subsoil properties was assumed (characterized by strength parameters: cohesion, angle of internal friction or undrained shear strength). The presented method makes it possible to significantly reduce the costs of numerical analyzes, which are measured by the number of calculated cases, with no greater impact on the accuracy and reliability of the obtained results. The presented method may be of significant practical importance when it is necessary to perform many slope stability analyzes - both at the design stage and at the stage of planning the technology for the execution of geotechnical works.

 Critical Remarks:

The presented method is certainly a significant modification that allows to reduce the calculation time, however, the authors should supplement their considerations with an answer to the question whether the choice of the primary slip surface, as well as the scope of the analyzes carried out, will not result in the omission of a certain shape of the surface, which will be had a worse stability factor. It would also be worth knowing the answer to the question of how the failure surface could be selected in the case of heterogeneous soil, e.g. stability analysis of the embankment, where the material of the embankment is different from the subsoil.

 Detailed remarks:

Line 167: instead of “gravity” should be “gravity force”, instead of “cohesive” should be “cohesion”

Line 357: instead of “assessment” should be “Assessment”,

Line 359: instead of “2-d” should be “2-D”,

Line 384: no author’s first name,

Line 403: instead of “slo pes” should be “slopes”. 

Author Response

Response to Reviewer 3 Comments

Point 1: Critical Remarks:

The presented method is certainly a significant modification that allows to reduce the calculation time, however, the authors should supplement their considerations with an answer to the question whether the choice of the primary slip surface, as well as the scope of the analyzes carried out, will not result in the omission of a certain shape of the surface, which will be had a worse stability factor. It would also be worth knowing the answer to the question of how the failure surface could be selected in the case of heterogeneous soil, e.g. stability analysis of the embankment, where the material of the embankment is different from the subsoil.

Response 1: Thanks for pointing these out. Because the entry and exit method used in this study has good robustness, each trial circular sliding surface generated by this method is independent of each other. Therefore, for the selection of failure surfaces in heterogeneous soil, this method can also select the sliding surface with the lowest safety factor calculated from a large number of trial sliding surfaces as the failure surface. In addition, using practical examples of heterogeneous soil can better demonstrate the method proposed in this paper. The author will use actual landslide examples of heterogeneous soil in subsequent research to further verify the applicability of the method proposed in this paper.

 

Point 2: Line 167: instead of “gravity” should be “gravity force”, instead of “cohesive” should be “cohesion”.

Response 2: According to the suggestions of the reviewers, the author has replaced “gravity” with “gravity force” and “cohesive” with “cohesion” in the revised manuscript.

 

Point 3: Line 357: instead of “assessment” should be “Assessment”.

Response 3: According to the suggestions of the reviewers, the author has replaced “assessment” with “Assessment” in the revised manuscript.

 

Point 4: Line 359: instead of “2-d” should be “2-D”.

Response4: According to the suggestions of the reviewers, the author has replaced “2-d” with “2-D” in the revised manuscript.

 

Point 5: Line 384: no author’s first name.

Response 5: Thanks for pointing this out. The author has added this author’s first name in the revised manuscript.

 

Point 6: Line 403: instead of “slo pes” should be “slopes”.

Response 6: According to the suggestions of the reviewers, the author has replaced “slo pes” with “slopes” in the revised manuscript.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors have satisfactorily responded to all the comments, and modified the manuscript accordingly.

Reviewer 2 Report

The desired corrections have been made. In my opinion, the article can be accepted.

Minor editing of English language required