Efficient Method for Calculating Slope Failure Risk Based on Element Failure Probability
Round 1
Reviewer 1 Report
The proposed EFP based slope failure risk analysis method is usable for avoiding the problem of stability coefficient in case of multi failure mode and it can accurately quantify the risk of failure.
Author Response
Comment 1: The proposed EFP based slope failure risk analysis method is usable for avoiding the problem of stability coefficient in case of multi failure mode and it can accurately quantify the risk of failure.
Response 1: Thank you very much. In this paper, an element failure risk method (EFR) for calculating soil slope failure risk is pro-posed based on element failure probability (EFP) acquired by the plastic limit analysis. The proposed method does not require any assumptions about the failure modes.
Author Response File: 
Author Response.docx
Reviewer 2 Report
The study on "Efficient method for calculating slope failure risk based on ele-2 ment failure probability is interesting, however major corrections should be made".
Properly represent the flow diagram in Figure 1, adding the appropriate symbology of the process operation.
The format of the publication of an article should be sectioned according to the format of the journal, delimiting, title, introduction, material and methods, results, discussion, conclusions and references.
The discussion section with support of references should be described.
Author Response
Comment 1: The study on "Efficient method for calculating slope failure risk based on element failure probability is interesting, however major corrections should be made".
Response 1: Thank you very much. The author will carefully complete the changes of the paper according to the comment of experts and improve the quality of the manuscript.
Comment 2: Properly represent the flow diagram in Figure 1, adding the appropriate symbology of the process operation.
Response 2: Agree with the reviewer's opinion, the author has properly represented the flow diagram in Figure 1 and adding the appropriate symbology of the process operation.
Thank you for your advice.
Comment 3: The format of the publication of an article should be sectioned according to the format of the journal, delimiting, title, introduction, material and methods, results, discussion, conclusions and references.
Response 3: Agree with the reviewer's opinion, the author has sectioned according to the format of the journal. The new section is as follows:
- Introduction
- Methodologies
2.1 Limit state function of slope
2.2 Stochastic programming model for slope failure risk
2.3 Solution strategy of stochastic programming model
2.4 Element failure probability of slope
- Calibration and Application
3.1 Case 1: A homogeneous slope
3.1.1 Homogeneous slope description
3.1.2 Result of homogeneous slope
3.2 Case 2: A heterogeneous slope
3.2.1 Heterogeneous slope description
3.2.2 Result of heterogeneous slope
4 Discussion
5 Conclusions
Appendix A
References
Thank you for your advice.
Comment 4: The discussion section with support of references should be described.
Response 4: Agree with the reviewer's opinion, the discussion section has been added with support of references should be described. The discussion section is as follows:
An efficient method for calculating slope failure risk based on element failure probability is proposed in this paper, which uses , and to judge the instability of slope, and uses velocity field obtain by UBM to locate each failure element. The problem of solving the failure probability and failure risk coefficient of each failure mode is transformed into the problem of solving the element failure probability and failure risk coefficient of discrete elements, which greatly simplifies the calculation process. In addition, according to the definition of limit state, the element failure function is established based on , and [18]. It can be seen from the calculation process of , and (As shown in Figure 1) that and are only solved once for large-scale linear programming problems, while usually involves solving and for many times, so the failure risk computational efficiency based on and are greatly improved.
The analysis of the two cases shows that the results obtained by UBM based on , and are very close, with a small error (<5%). Theoretically, the slope failure risk coefficient under each sample should be consistent, that is, the obtained results should be equal. However, the load distribution type, action form and calculation accuracy may affect the results. When using MATLAB calling Geo-studio software program for failure risk comparative analysis, the critical sliding surface obtained from the mean value of soil shear strength parameters is used to analyze all samples [5]. In addition, the LEM only considers one-dimensional spatial variability of the sliding surface, so its calculation results are worthy of discussion [20]. The most accurate result can be obtained by 8-node FEM method based on OptumG2 on the basis of the known soil constitutive relationship. However, unfortunately, the soil constitutive relationship is complicated, and the failure mode screening involves a lot of human factors [4,17]. It should be noted that the UBM computation program in this paper can implement parallel computation in Python, so the computation efficiency can be greatly improved.
The propose method is mainly aimed at soil slope, but the failure of rock slope is mainly affected by the cohesion, friction angle and bulk density of the structural plane [4,35]. The study of efficient rock slope failure risk analysis will be the focus of subsequent work. In addition, earthquake and groundwater are the main causes of slope instability [5,21,27], so it is also urgent to study efficient failure risk analysis methods under the action of earthquake and groundwater.
Author Response File: Author Response.docx
Reviewer 3 Report
Please consider adding the following references:
- Cheng, H., Chen, J., Chen, R., Chen, G., & Zhong, Y. (2018). Risk assessment of slope failure considering the variability in soil properties. Computers and Geotechnics, 103, 61-72.
- Intrieri, E., Carlà, T., & Gigli, G. (2019). Forecasting the time of failure of landslides at slope-scale: A literature review. Earth-science reviews, 193, 333-349.
- Maxwell, A. E., Sharma, M., Kite, J. S., Donaldson, K. A., Thompson, J. A., Bell, M. L., & Maynard, S. M. (2020). Slope failure prediction using random forest machine learning and LiDAR in an eroded folded mountain belt. Remote Sensing, 12(3), 486.
- Chu, X., Li, L., & Cheng, Y. M. (2019). Risk assessment of slope failure using assumption of maximum area of sliding mass and factor of safety equal to unit. Advances in Civil Engineering, 2019.
- Kolapo, P., Oniyide, G. O., Said, K. O., Lawal, A. I., Onifade, M., & Munemo, P. (2022). An Overview of Slope Failure in Mining Operations. Mining, 2(2), 350-384.
- Apostu, I. M., Lazar, M., & Faur, F. (2021). A Suggested Methodology for Assessing the Failure Risk of the Final Slopes of Former Open-Pits in Case of Flooding. Sustainability, 13(12), 6919.
Mayor:
- A nomenclature is needed to understand the great number of variables.
- What is the meaning of the variables in bold? In Eq. (6) there is a sum of "bold variables" (We+Wd+WF), and these can be vectors or matrix, and it results in a non-bold variable "k".
Minor:
- Line 12: Please change "The" to "the".
- Line 14: Please change ";" to ".".
- Line 251: Please change "was prepared by Python" to "was prepared by Python".
- Line 268: Please change "、" to ",". Check this in the whole document.
- Line 462: Please change "calculation program is prepared by Python" to "calculation program is prepared in Python".
Author Response
Comment 1: Please consider adding the following references:
- Cheng, H., Chen, J., Chen, R., Chen, G., & Zhong, Y. (2018). Risk assessment of slope failure considering the variability in soil properties. Computers and Geotechnics, 103, 61-72.
- Intrieri, E., Carlà, T., & Gigli, G. (2019). Forecasting the time of failure of landslides at slope-scale: A literature review. Earth-science reviews, 193, 333-349.
- Maxwell, A. E., Sharma, M., Kite, J. S., Donaldson, K. A., Thompson, J. A., Bell, M. L., & Maynard, S. M. (2020). Slope failure prediction using random forest machine learning and LiDAR in an eroded folded mountain belt. Remote Sensing, 12(3), 486.
- Chu, X., Li, L., & Cheng, Y. M. (2019). Risk assessment of slope failure using assumption of maximum area of sliding mass and factor of safety equal to unit. Advances in Civil Engineering, 2019.
- Kolapo, P., Oniyide, G. O., Said, K. O., Lawal, A. I., Onifade, M., & Munemo, P. (2022). An Overview of Slope Failure in Mining Operations. Mining, 2(2), 350-384.
- Apostu, I. M., Lazar, M., & Faur, F. (2021). A Suggested Methodology for Assessing the Failure Risk of the Final Slopes of Former Open-Pits in Case of Flooding. Sustainability, 13(12), 6919.
Response 1: Agree with the reviewer's opinion, the above references have been added in the revised version.
Comment 2: A nomenclature is needed to understand the great number of variables.
Response 2: Agree with the reviewer's opinion, An Appendix A has been added in the revised version.
Comment 3: What is the meaning of the variables in bold? In Eq. (6) there is a sum of "bold variables" (We+Wd+WF), and these can be vectors or matrix, and it results in a non-bold variable "k".
Response 3: This study is based on the previous study, which is actually a linearization process:
kFWF=We+Wd-WG
WF=1
So kF=We+Wd-WG
Comment 4:
- Line 12: Please change "The" to "the".
- Line 14: Please change ";" to ".".
- Line 251: Please change "was prepared by Python" to "was prepared by Python".
- Line 268: Please change "、" to ",". Check this in the whole document.
- Line 462: Please change "calculation program is prepared by Python" to "calculation program is prepared in Python".
Response 4: Agree with the reviewer's opinion. The above mistakes have been changed in the revised version.
Reviewer 4 Report
This work presents a novel efficient, upper-bound method for calculating the slope failure risk. The method was implemented in a parallel python code. The authors applied the proposed method (UBM) to two types of slopes, a homogeneous step and a heterogeneous step, and compared the solutions with two different methods, the rigid body limit equilibrium method (LEM) and the finite element method (FEM).
The manuscript is generally very-well written and the results are very well presented as well.
After reviewing thoroughly this manuscript, I recommend publishing this work in the journal. As the authors pointed out, the presented method is more efficient than the other methods and the discrepancies are minimum. However, I have the following questions and/or recommendations:
- Since one of the main results is that the method is more efficient with respect to the other methods, the authors should provide more details about the implementation of method in the python code for a better comparison with the other methods, e.g.: what type of parallelization is used? A strong and weak scaling study for the code parallelization should be also included, etc. Similarly, the authors should provide more information about the other method’s implementation (LEM and FEM) for a better comparison. Are the other codes implemented in parallel? etc.
- I would also like to give the following suggestion: Since sections 4.1 and 4.2 are very dense, would it be possible to split them into different subsections.
Author Response
This work presents a novel efficient, upper-bound method for calculating the slope failure risk. The method was implemented in a parallel python code. The authors applied the proposed method (UBM) to two types of slopes, a homogeneous step and a heterogeneous step, and compared the solutions with two different methods, the rigid body limit equilibrium method (LEM) and the finite element method (FEM).
The manuscript is generally very-well written and the results are very well presented as well.
After reviewing thoroughly this manuscript, I recommend publishing this work in the journal. As the authors pointed out, the presented method is more efficient than the other methods and the discrepancies are minimum. However, I have the following questions and/or recommendations:
Comment 1: Since one of the main results is that the method is more efficient with respect to the other methods, the authors should provide more details about the implementation of method in the python code for a better comparison with the other methods, e.g.: what type of parallelization is used? A strong and weak scaling study for the code parallelization should be also included, etc. Similarly, the authors should provide more information about the other method’s implementation (LEM and FEM) for a better comparison. Are the other codes implemented in parallel? etc.
Response 1: Agree with the reviewer's opinion. The proposed EFP based slope failure risk analysis method is usable for avoiding the problem of stability coefficient in case of multi failure mode and it can accurately quantify the risk of failure. It should be noted that the UBM parallel computing program was prepared in Python can make full use of the advantages of multi-threaded parallel computing on small work-station. Theoretically, it can call 64 threads at the highest for parallel computing of each sample, but only 42 threads are called due to other operational requirements. When GEO-studio software is called by MATLAB to calculate each sample, random fields need first to be generated through pre-processing, and then the calculation of each sample is carried out on this basis. The 8-node FEM method based on OptumG2 can only obtain the result of one sample each time, and cannot carry out large-scale parallel calculation. The description is detailed in the revised version. Thank you for your advice.
Comment 2: I would also like to give the following suggestion: Since sections 4.1 and 4.2 are very dense, would it be possible to split them into different subsections.
Response 1: Agree with the reviewer's opinion. The new sections have been split in the revised version.
- Calibration and Application
3.1 Case 1: A homogeneous slope
3.1.1 Homogeneous slope description
3.1.2 Result of homogeneous slope
3.2 Case 2: A heterogeneous slope
3.2.1 Heterogeneous slope description
3.2.2 Result of heterogeneous slope
Thank you for your advice.
Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
Accepted in its present form
