Slope Failure Risk Assessment Considering Both the Randomness of Groundwater Level and Soil Shear Strength Parameters
Round 1
Reviewer 1 Report
1. In the abstract and conclusion section, it is good to present the results quantitatively.
2. The research method should be explained in detail in the introduction section.
3. Explain about the time steps in the presented model.
4. Explain about the optimization of the proposed method as well as the algorithm by which the optimization is done.
5. Has the sensitivity analysis been done on the parameters?
6. Is it possible to use the lower bound method with the same method? And do we converge to the same results using lower band limit analysis?
7. The most important weakness of the current manuscript is the verification of the presented method. The presented method must have a proper validation.
The manuscript needs editing for grammar and spelling
Author Response
Comment 1: In the abstract and conclusion section, it is good to present the results quantitatively.
Response 1: Agree with the reviewer's opinion, the abstract and conclusions have been revised in the newly submitted revised manuscript. Thank you for your advice.
Comment 2: The research method should be explained in detail in the introduction section.
Response 2: Agree with the reviewer's opinion, the research method has been explained in detail in the introduction section in the newly submitted revised manuscript. Thank you for your advice.
Comment 3: Explain about the time steps in the presented model.
Response 3: Firstly, stochastic number of groundwater level is generated by Monte Carlo simulation method; then, using the midpoint method of Cholesky decomposition for stochastic field of shear strength parameters generation; afterwards, calculation of slope stability seepage field; after that, the overload coefficient and safety factor of the Tm-th shear strength parameters under the action of the Tw-th groundwater level are calculated.
Comment 4: Explain about the optimization of the proposed method as well as the algorithm by which the optimization is done.
Response 4: this paper establishes a stochastic programming model for slope reliability analysis, as follows:
The Tm-th shear strength parameters under the action of the Tw-th groundwater level are determined by using dual simplex method and bisection method based on the reduction of shear strength parameters, respectively. When solving above linear programming problems with more variables than constraints, the dual simplex method can reduce the number of iterations. Therefore, this method is adopted in this paper to solve the overload coefficient. The bisection method based on the reduction of shear strength parameters is the most commonly used method to solve the safety factor, which has wide applicability. Therefore, bisection method is used to solve the safety factor.
Comment 5: Has the sensitivity analysis been done on the parameters?
Response 5: In this paper, the sensitivity of the number of elements to the calculation results of slope stability is analyzed. Due to the length of the manuscript, the relevant content is not discussed. The following figure shows the relationship between the safety factor obtained by the upper and lower bound method and the number of elements. It is not difficult to see that the number of elements has a significant impact on the calculation results of slope. However, when the number of elements is greater than 950, the calculation results obtained by the upper and lower limit method tend to be stable. Therefore, on the basis of sensitivity analysis, this paper chooses the appropriate element to carry out relevant research.
Comment 6: Is it possible to use the lower bound method with the same method? And do we converge to the same results using lower band limit analysis?
Response 6: Due to the complexity of the research, this paper only studies the upper bound method. The lower bound method can also carry out similar research work, but it needs to solve this problem: the upper bound method can determine the failure area according to the element failure function, and how to solve this problem by the lower bound method will be the focus of subsequent research. In addition, the upper bound solution and lower bound solution can converge to the same result by trial calculation. Due to the length of the manuscript, the relevant content is not discussed. The following figure shows the relationship between the safety factor obtained by the upper and lower bound method and the number of elements. It is not difficult to see that the number of elements has a significant impact on the calculation results of slope. However, when the number of elements is greater than 950, the calculation results obtained by the upper and lower limit method tend to be stable.
Comment 7: The most important weakness of the current manuscript is the verification of the presented method. The presented method must have a proper validation.
Response 7: According to the proposed method, the UBM program is compiled, and a classic slope calculation example is calculated and analyzed. Comparing with the calculation result of LEM, verified the correctness of the calculation method. It should be noted that the proposed method is supported by rigorous mechanical theory. However, the lack of experimental verification is difficult to solve in a short time. In the follow-up research, I will devote myself to the research idea of combining experiment and numerical simulation. Thank you for your advice.
Comment 8: Comments on the Quality of English Language. The manuscript needs editing for grammar and spelling
Response 8: Agree with the reviewer's opinion, the newly submitted manuscript has been checked for grammar and spelling. Thank you for your advice.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In this manuscript, a new method for slope failure risk assessment considering both the randomness of groundwater level and soil shear strength parameters was proposed, which is usful for engineering and interesting for academy. The article is clear, well-structured and innovative in its approach. I think the study can be a candidate for publication with full consideration of the following comments.
(1) Line 159 has a different font size, please keep the characters in the text in the same format as the characters in the equation.
(2) How were the dimensions of the triangular slopes in Section 5.1 determined, and does their size affect the simulation results?
(3) How were the data in Table 1 determined and what is the reference?
(4) With a mean groundwater level of 7.5m and a standard deviation of 2.25, are the resulting data too discrete?
(5) Why are the pore pressure values also so discrete?
(6) What is the basis for the selection of P1, P2 and P3 positions? Why was it chosen this way?
(7) The conclusions should be reorganized. Only the findings of this paper should be described, not the characteristics of the traditional methods.
(8) This paper introduces too much about the method and calculation principles, so if it is not an original method of this study, it is recommended to streamline the length significantly.
Author Response
Comment 1: Line 159 has a different font size, please keep the characters in the text in the same format as the characters in the equation.
Response 1: Agree with the reviewer's opinion, Due to the author's negligence, some of the equations were inconsistent in size, and the newly submitted manuscript has been revised to ensure that the equations are consistent in size with full-text proofing. Thank you for your advice.
Comment 2: How were the dimensions of the triangular slopes in Section 5.1 determined, and does their size affect the simulation results?
Response 2: Due to the length of the manuscript, the relevant content is not discussed. The following figure shows the relationship between the safety factor obtained by the upper and lower bound method and the number of elements. It is not difficult to see that the number of elements has a significant impact on the calculation results of slope. However, when the number of elements is greater than 950, the calculation results obtained by the upper and lower limit method tend to be stable.
Comment 3: How were the data in Table 1 determined and what is the reference?
Response 3: Agree with the reviewer's opinion, due to the author's negligence in Table 1 data and forgetting to give references, the newly submitted manuscript has been given specific references. Thank you for your advice.
Comment 4: With a mean groundwater level of 7.5m and a standard deviation of 2.25, are the resulting data too discrete?
Response 4: In this paper, the mean value of groundwater is determined to be 7.5m and the standard deviation is 2.25 on the basis of the measured groundwater in many projects.
Comment 5: Why are the pore pressure values also so discrete?
Response 5: Because the groundwater level corresponds to the pore water pressure of the key points one by one, the pore water pressure of each key point can be obtained through the steady seepage calculation of each groundwater level.
Comment 6: What is the basis for the selection of P1, P2 and P3 positions? Why was it chosen this way?
Response 6: The key point was selected in this paper mainly to determine the value of pore water pressure at the point relative to the pore water pressure at the right slope toe, whose groundwater level is 5m.
Comment 7: The conclusions should be reorganized. Only the findings of this paper should be described, not the characteristics of the traditional methods.
Response 7: Agree with the reviewer's opinion, the conclusion has been reorganized in the newly submitted manuscript. The following are the conclusions after modification:
This paper combines finite element discretization technique, related non-Gaussian stochastic field simulation method, upper bound method theory and stochastic planning theory to propose a new method for slope failure risk assessment considering both the randomness of groundwater level and soil shear strength parameters. The corresponding calculation program is compiled to acquire safety factor, failure mode, failure probability and failure risk. The major conclusions are:
(1) When the randomness of groundwater level and soil shear strength parameters are considered comprehensively, the traditional LEM method will ignore multiple failure modes, and may miscalculate the slope failure risk. However, all failure modes can be acquired by UBM for seeking the minimum value of the kinematically admissible velocity field. Thus, the result more consistent with real situation. In addition, the traditional LEM only judges the slope stability by safety factor, which only reflects the degree of IPF. Therefor the EFP method is used to calculate EFR of slope, which can not only reflect the degree of IFP, but also accurately acquire the failure risk of slope. It should be noted that this calculation method can greatly reduce the calculation cost.
(2) The IFP and EFR of slope are increasing from 1.40% to 3.30% and 0.829 m2 to 2.094 m2 with the rise of groundwater level respectively. The slope failure risk analysis method based on EFP can accurately obtain EFR of slope under the effect of groundwater level by using the location information and failure situation of the element. This will provide engineers with realistic reference value for the slope reinforcement design.
(3) Groundwater level and earthquake are two important causes of slope instability and failure. However, this study does not consider the impact of earthquake on slope reliability. Therefore, relevant studies on seismic slope stability will be carried out in the future. In addition, according to the upper bound theory, the safety factor obtained belongs to the upper bound solution, which is inevitably greater than the true solution. Therefore, when the upper bound solution of safety factor is used to calculate the overall failure probability of slope, the failure probability will be underestimated. To solve this problem, it is necessary to study the calculation method of slope reliability based on the lower bound theory in the future research work. The lower bound solution and upper bound solution of slope failure probability can be obtained at the same time through the lower and upper bound analysis, so the interval range of the real failure probability can be accurately judged, and the reliability index of slope can be quantified more accurately.
Thank you for your advice.
Comment 8: This paper introduces too much about the method and calculation principles, so if it is not an original method of this study, it is recommended to streamline the length significantly.
Response 8: Agree with the reviewer's opinion, the method and calculation principles have been streamlined in the newly submitted manuscript. However, this paper combines relevant theories to carry out research of slope failure risk assessment considering both the randomness of groundwater level and soil shear strength parameters. In order to facilitate readers to better understand the relevant process, the article has only been partially streamlined. Thank you for your advice.
Author Response File: Author Response.pdf
Reviewer 3 Report
In this paper, the authors demonstrated the slope failure risk assessment considering both the randomness of groundwater level and soil shear strength parameters. The logic of this paper is clear and the structure is complete, however, there are still some questions in this manuscript. The following are the questions in this manuscript:
(1) The author selected groundwater levels of 1, 25, and 50 for analysis, but lacked explanation for the selection of groundwater level values.
(2) In page 11 line 331, the authors mentioned that “At lower groundwater level, the contour line of pore water pressure of slope is gentle with less areas of slope are in saturation. At higher groundwater level, the contour line of pore water pressure of slope is gentle with most areas of slope are in saturation”, but the range of slope saturation area in Figure 5 is not obvious.
(3) In page 12 line 350, the authors mentioned that “In addition, the soil cohesion and the angle of internal friction are negatively correlated in space”, but Figure 7 cannot intuitively reflect the negative correlation between the soil cohesion and the angle of internal friction.
(4) In Figures 14, the author divides the slope failure mode into 6 types based on the failure area, but there is no explanation for the rules for determining the failure area of each boundary..
(5) In Figures 15 and 17, the distribution maps of EFP and EFR have consistent representations except for different units, but there is a significant difference in the magnitude of their subsequent results. It is recommended to use different methods to draw the two maps.
(6) In page 3 line 102, the authors mentioned that “Similar to literature [32], stochastic groundwater level Hw is assumed to obey truncated normal distribution”, but in page 11 line 319, the author mentioned again that the truncated normal distribution is used for the groundwater level, and 50 random numbers are generated for verification, the two part are repetitive.
Author Response
Comment 1: The author selected groundwater levels of 1, 25, and 50 for analysis, but lacked explanation for the selection of groundwater level values.
Response 1: Agree with the reviewer's opinion, the explanation for the selection of groundwater level values has been added in detail in the newly submitted revised manuscript. The new description is “Figure 5 (a), (b) and (c)are the slope stable seepage fields when (Hw=6.8006m), (Hw=7.4848m) and (Hw=8.1951m) respectively.” Thank you for your advice.
Comment 2: In page 11 line 331, the authors mentioned that “At lower groundwater level, the contour line of pore water pressure of slope is gentle with less areas of slope are in saturation. At higher groundwater level, the contour line of pore water pressure of slope is gentle with most areas of slope are in saturation”, but the range of slope saturation area in Figure 5 is not obvious.
Response 2: Agree with the reviewer's opinion, this above part of the description has been revised in the newly submitted revised manuscript, in addition to adding the Steady seepage fields of slope when . The new description is “It can be seen that the saturated area inside the slope increases and the contours of pore water pressure become steeper with the increase of groundwater level.” Thank you for your advice.
Fig.5 Steady seepage fields of slope: (a) Tw=1
Comment 3: In page 12 line 350, the authors mentioned that “In addition, the soil cohesion and the angle of internal friction are negatively correlated in space”, but Figure 7 cannot intuitively reflect the negative correlation between the soil cohesion and the angle of internal friction.
Response 3: Agree with the reviewer's opinion, due to the author's negligence in drawing the angle of internal friction random field error, resulting in the graphic description of the situation is not rigorous, the newly submitted manuscript has been corrected. Below is the revised image and description:
In addition, there is a negative correlation between soil cohesion and the angle of internal friction in space.
Fig.7 Stochastic fields of slope shear strength parameters: (a) cr (500); (b) φr (500)
Thank you for your advice.
Comment 4: In Figures 14, the author divides the slope failure mode into 6 types based on the failure area, but there is no explanation for the rules for determining the failure area of each boundary.
Response 4: Agree with the reviewer's opinion, the newly submitted manuscript has explained for the rules for determining the failure area of each boundary. Detailed modification is as follows:
Based on 100000 Monte Carlo simulations of the slope, LEM defaults that only one failure mode exists (as shown in the LEM sliding surface in Figure 14); The biggest advantage of UBM compared with LEM in this paper is that it can capture all slope failure modes according to failure information of elements (as shown in the pink failure area in Figure 14), and then conduct the reliability index for slope. Similar to the method in reference 37, failure areas were used to classify failure modes, there are six failure modes of slope under 50 groundwater levels act (as shown in Figure 14). The failure probability and failure risk of the above six slope failure modes are list in Table 3. The failure probability and failure risk corresponding slope failure modes when , and are list in Table 4. Thank you for your advice.
Comment 5: In Figures 15 and 17, the distribution maps of EFP and EFR have consistent representations except for different units, but there is a significant difference in the magnitude of their subsequent results. It is recommended to use different methods to draw the two maps.
Response 5: Agree with the reviewer's opinion, the newly submitted manuscript has used different methods to draw the distribution maps of EFR. Detailed modification is as follows:
When , the frequency of EFR between 0 and 0.00062m2 is 675, the frequency of EFR between 0.00062 and 0.00124m2 is 36, the frequency of EFR between 0.00124 and 0.00186m2 is 58, the frequency of EFR between 0.00186 and 0.00248m2 is 69, the frequency of EFR between 0.00248 and 0.00310m2 is 140, the frequency of EFR between 0.00310 and 0.00372m2 is 11, and the slope failure risk is 0.829 m2. When , the frequency of EFR between 0 and 0.00082m2 is 670, the frequency of EFR between 0.00082 and 0.00164m2 is 32, the frequency of EFR between 0.00164 and 0.00246m2 is 54, the frequency of EFR between 0.00246 and 0.00328m2 is 56, the frequency of EFR between 0.00328 and 0.00410m2 is 165, the frequency of EFR between 0.00410 and 0.00492m2 is 12, and the slope failure risk is 1.302 m2. When , the frequency of EFR between 0 and 0.00150m2 is 666, the frequency of EFR between 0.00150 and 0.00300m2 is 41, the frequency of EFR between 0.00300 and 0.00450m2 is 48, the frequency of EFR between 0.00450 and 0.00600m2 is 62, the frequency of EFR between 0.00600 and 0.00750m2 is 158, and the frequency of EFR between 0.00750 and 0.00900m2 is 14. Under all potential groundwater levels act, the frequency of EFR between 0 and 0.04820m2 is 674, the frequency of EFR between 0.04820 and 0.09640m2 is 30, and the frequency of EFR between 0.09640 and 0.14460m2 is 57. The frequency of EFR between 0.014460 and 0.19280m2 is 59, the frequency of EFR between 0.19280 and 0.24100m2 is 157, the frequency of EFR between 0.24100 and 0.28892m2 is 12, and the slope failure risk is 2.094 m2.
Fig 17 EFR of the slope under Tw th groundwater level acts: (a) Tw =1; (b) Tw =25; (c) Tw =50;
Fig 18 EFR of the slope under all potential groundwater level act
Thank you for your advice.
Comment 6: In page 3 line 102, the authors mentioned that “Similar to literature [32], stochastic groundwater level Hw is assumed to obey truncated normal distribution”, but in page 11 line 319, the author mentioned again that the truncated normal distribution is used for the groundwater level, and 50 random numbers are generated for verification, the two part are repetitive.
Response 6: Agree with the reviewer's opinion, the repetitive parts have been removed from the newly submitted manuscript. Thank you for your advice.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
there is no comment.
there is no comment.
