Using the Morgenstern–Price Method and Cloud Theory to Invert the Shear Strength Index of Tailings Dams and Reveal the Coupling Deformation and Failure Law under Extreme Rainfall
Round 1
Reviewer 1 Report
In this study, the sensitivity of the shear strength index to the safety factor of a tailings dam was evaluated. Compared with stable state, the cohesion C and internal friction angle φ of tailings earth-rock dam under unstable state are uncertain, and the Morgenstern–Price method is used for inversion. During parameter inversion, uncertainty reasoning is established based on cloud theory, which overcomes the problem that the fuzziness and randomness of the quantitative cohesion value are transferred to the qualitative concept of the safety factor. It provides a new idea and method for parameter inversion of the shear strength index of tailings dams and provides a reference for the disaster prediction and prevention of tailings dams subjected to extreme rainfall. The specific modification opinions are as follows：
1，In line 47-50, many accidents were caused, described in a little more detail.
2. The position of the dry tailings yard in Figure 1 should be clearly marked, such as a red dot rather than an arrow.
3. Formula should be aligned.
4. Reason why the internal friction angle φ is 21 and the cohesion C range from 7.8 to 9.4 kPa are given.
5. Please describe the grid division in detail. Change Figure 12 and draw a grid quality map.
6. Please explain why the rainfall time is one hour.
7. According to plastic strain nephogram and displacement nephogram, the evolution law of deformation and failure is summarized, and the relationship between rainfall time and deformation and failure is explained.
Author Response
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Author Response.docx
Reviewer 2 Report
In this paper, M-P method combined with cloud theory is used to invert the shear strength of tailings dam and reveal the failure law of rainfall condition. It has certain practical significance and provides a new idea for studying the deformation and failure law of tailings dam under extreme rainfall conditions. However, the paper has the following minor drawbacks.
1. In the introduction, it is described that there is a lack of research on the impact of rainfall and the inversion of cloud theory inversion.
2. In Section 3.1, as the internal friction Angle in the research background is 21°, this paper expands to about 21° to analyze the influence of the change of internal friction Angle on the minimum safety factor. However, the range of cohesion is 7.8-9.4 kPa, while the influence range of cohesion analyzed in this paper is 8-12kPa. The selection of the range of cohesion needs to be considered.
3. In Section 3.1, when using cloud theory to divide cohesion, the subjective direct division of each interval is 0.4, which lacks explanation or division basis.
4. In Section 3, the third point is not specific enough. It does not use the research results of this paper to draw conclusions directly.
Author Response
Response to Reviewer 2 Comments
Dear Reviewer:
Thank you for your effort and consideration for possible publishing our manuscript entitled “Using Morgenstern-Price method and cloud theory to inverse the shear strength index of tailings dam and reveal the coupling deformation and failure law under extreme rainfall” (Sustainability-2266099). All the raised comments are all valuable and very helpful for improving our manuscripts point-by-point which improves the quality of the revised manuscript. All the changes in the revision are highlighted as red font. The point-by-point responses for all major comments are listed below.
Major Scientific Points:
1.In the introduction, it is described that there is a lack of research on the impact of rainfall and the inversion of cloud theory inversion.
Response 1: Thanks for this careful comment. In Line 94-109, Page 2: Add “Wang et al. proposed a model of cloud theory combined with mathematical evaluation for various fuzzy and correlation indicators involved in slope stability evaluation, which better reflects the random fuzzy distribution characteristics of measured data in the interval, and is more accurate than one-dimensional normal model. Wang et al. established a new comprehensive evaluation and inversion model based on normal cloud theory for tunnels in karst areas. Through systematic analysis of multiple influencing factors of water inrush, it was found that the normal cloud model was more accurate and the risk classification of water inrush prediction was feasible. It can not only meet the requirements of tunnel engineering, but also be extended to various applications. Yao et al. established a multi-level fuzzy evaluation index system. The cloud model theory is introduced to improve the importance scale and membership degree involved in the evaluation process, and a multi-level fuzzy comprehensive evaluation method of landslide risk improved by the cloud model is proposed. The results show that the improved cloud model can solve the uncertainty problem in the process of landslide preparation and occurrence, and provide an effective reference for the prevention of landslide disasters.”
In Line 133-141, Page 3: Add “Xu et al. assessed the deformation damage of earth and rock dam slopes with vibration induced fissures by rainfall and found that the adverse phenomenon of soil dis-placement of earth and rock dam slopes containing fissures was more pronounced in the rainfall condition, with steeper bumps at the shoulder of the slope and larger land-slide accumulation areas due to rainfall erosion. Tian et al. conducted model experiments of upstream type tailings dam failure and found that the development of tailings earth and rock dam failure was mainly caused by longitudinal undercutting and horizontal expansion due to water erosion, and observed the evolution of tailings dam failure and tailings seepage flow.”
Add “Zhou et al. conducted a numerical simulation study of a rainfall-induced landslide of an earth and rock dam in Chongqing, and the results showed that the landslide accumulation of the earth and rock dam due to rainfall reacts violently under rainfall induction, and the occurrence of local collapse still exists after the landslide disaster, which can produce secondary landslides. Wu et al. used numerical simulation to analyze a shallow loess dam slope landslide disaster in Sichuan Province in 2020. The study found that the minimum rainfall that caused the landslide disaster was 177.2mm, and the infiltration of rainwater and ice and snow melt water was the main reason for inducing the dam slope landslide.”
- In Section 3.1, as the internal friction Angle in the research background is 21°, this paper expands to about 21°to analyze the influence of the change of internal friction Angle on the minimum safety factor. However, the range of cohesion is 7.8-9.4 kPa, while the influence range of cohesion analyzed in this paper is 8-12kPa. The selection of the range of cohesion needs to be considered.
Response 2: Thanks for this careful comment. The Cohesion range is 7.8-9.4 kPa, while the cohesion influence range analyzed in this paper is 8-12 kPa. This analysis is to compare the Cohesion and Internal Friction Angle which have greater influence on the safety factor. Through analysis, it can be found that by adjusting the cohesion of the four units, the safety factor increases by about 0.275, while by adjusting the internal friction angle of the four units, the safety factor changes by about 0.07. The purpose of selecting 8-12kPa is only to prove that increasing the Cohesion has a greater impact on the safety factor than the Internal Friction Angle under the same unit condition. It can be seen from Figure 7 that by adjusting the values of Cohesion and Internal Friction Angle of the same unit, the change degree of the safety factor of tailings dam is different, and the influence of Cohesion on the safety factor is greater, so it can be considered that the influence of Cohesion on the safety factor of tailings dam is more sensitive. That is to say, the change of Cohesion has a greater impact on the stability of tailings dam. Therefore, in disaster prevention and control work, we should focus on the impact of soil Cohesion change on slope stability, and focus on doing this work well.
In Line 340-347, Page 12: “As shown in the figure, the fitting degree is very high, and the fitting degree of the influence curve of cohesion C is 0.99648, and the fitting degree of the influence curve of internal friction angle φ is 0.99145. The relationship between the cohesion C and the safety factor Fs is: , and the relationship between the internal friction angle φ and the safety factor Fs is: . Based on the sensitivity of the tailings dam shear strength parameter, it can be seen that the cohesion C and the internal friction angle φ are positively correlated with the safety factor Fs of the tailings dam, but the change of cohesion C has a greater impact on the safety factor of the tailings dam.” revised as “ As shown in the figure, the fitting degree is very high, the fitting degree of the influence curve of cohesion C is 0.99648, and the fitting degree of the influence curve of internal friction angle φ is 0.99145. The relationship between the cohesion C and the safety factor Fs is , and the relationship between the internal friction angle φ and the safety factor Fs is . According to Figure. 7, cohesion C and internal friction angle φ It is positively related to the safety factor Fs of tailings dam. However, the change of cohesion C leads to more changes in the safety factor Fs, so the influence of cohesion C on the safety factor Fs of tailings dam is greater."
- In Section 3.1, when using cloud theory to divide cohesion, the subjective direct division of each interval is 0.4, which lacks explanation or division basis.
Response 3: Thanks for this careful comment. Expectation Ex describes the expected value of the cloud model. The most representative digital feature is represented as the center of gravity in the cloud image. According to the analysis in 3.1, the value of fixed Internal Friction Angle is selected and the value of Cohesion is changed to calculate the safety factor. 7.8-9.4kPa corresponds to a safety factor of 1.000-1.1.03. The earth-rock fill dam is in an unstable state. When the cohesion is 8.6kPa, the safety factor of the tailings dam is about 1.050. According to cloud theory calculation rule (Cao et al.2022, https://doi.org/10.3390/math10020266、Zhang et al.2019, https://doi.org/10.1016/j.ecolind.2019.105864) ，the calculated 8.6kPa should be an expected value in the interval. When the Cohesion is exactly 8.6kPa, the safety factor is 1.05, which is also near the middle value of the safety factor range. In order to simplify the calculation and improve the accuracy of calculation, an expected value is set in the range of 7.8-8.6kPa and 8.6-9.4kPa respectively. According to the formula, the expected value of each interval is 7.8kPa, 8.2kPa and 9.0kPa, and 9.4kPa respectively. Therefore, 0.4 is used as interval for division.
In Line 355-360, Page 12: Add “The cohesion range is 7.8-9.4 kpa, with a median of 8.6 kpa. According to the cloud model theory, in order to simplify the calculation, divide the possible value range, and divide an interval every 0.4kpa. The expected values of each interval are 7.8kpa, 8.2kpa, 8.6kpa, 9.0kpa, and 9.4kpa, respectively. These five values are within the cohesion range, including the internal boundary value and the median value. The interval distribution is average, which meets the demand of cloud theory computing. ”
- In Section 3, the third point is not specific enough. It does not use the research results of this paper to draw conclusions directly.
Response 4: Thanks for this careful comment. I have added to the third point of the third section. In Line 460-478, Page 18: Add “In order to analyze the deformation and failure of tailings dam under rainfall conditions, a fluid-structure coupling model of tailings pond is established based on the finite element method as shown in the figure. To simplify the operation, use CAD software to build the model, and then import it into COMSOL Multiphysics software for finite element calculation and analysis. The tailings pond section is selected as the simulation object, with a length of 14m, a height of 6m and an area of 68.8m2.
In order to better simulate the deformation and failure characteristics of tailings dam under short-term extreme rainfall conditions, the mechanical boundary conditions of the numerical model are set as follows: the upper part is set as a free boundary, the bottom is set as a fixed constraint, both sides of the dam body were supported by rollers, and the normal displacement is 0, but sliding can occur along this surface, and the rest are permeable boundaries except the bottom. The rainfall intensity is set at 92.16mm/h and the rainfall time was set to 1h. Based on the above simulation conditions, a numerical model was established as shown in the figure. The mesh size of the numerical model was set to be extremely fine. Except the mesh generator of the dam foundation is set to map, the rest were set to be free quadrilateral mesh. The number of cells was 3207, the number of mesh vertices was 3345, and the minimum cell mass was 0.5523. The maximum cell size was 0.141m, the minimum was 2.82×10-4m, the maximum cell growth rate was 1.1, and the curvature factor was 0.2”
In Line 539-552, Page 21: Add “Affected by short-term extreme rainfall, the maximum displacement is concentrated at the outer dam toe, followed by the dam abutment. The displacement tends to spread from the dam toe to the dam abutment. The plastic strain area is concentrated at the dam toe and continuously diffuses to the interior with time, seriously damaging the stability. At the beginning of rainstorm, rainwater washes away dam abutment continuously, earth and rock are lost continuously, and deformation and destruction take place preferentially. With the development of rainfall, the dam foot becomes the rainwater collection area. After humidification and softening, the structural stability becomes worse and plastic strain begins to appear. Finally, the entire dam surface is covered by deformation and destruction. The evolution law of deformation and destruction can be roughly divided into three stages: natural state, surface erosion and gully. The initial stage of rainfall is the key period of deformation, destruction and development. With the increase of rainfall time, the impact of deformation and destruction will increase.”
The cohesion parameter of tailings dam obtained in this study is 8.6901kPa. In actual working conditions, the tailings dam has been compacted. Considering the impact of compactness on cohesion is about 1/10, the setting of cohesion in numerical simulation is 9.56kPa after the inversion parameter is increased by 1/10. This is to be closer to the actual situation and make the numerical simulation results more accurate. In Line 485-487, Page 19: Add “The earth-rock fill dam has been compacted with high degree of compaction. In order to meet the actual situation of the project, the cohesion and internal friction angle parameters have been improved,”
Author Response File: Author Response.docx
Reviewer 3 Report
The manuscript comprises two content parts, i.e., uncertainty analysis and hydro-mechanical coupling simulation. The background and result analysis are provided sufficiently or even verbosely. However, the reviewer didn't find any connections between these two parts, and also the original idea proposed in each part. Additionally, the presentation of this work is primitive fulling of many typos or errors. Here are some examples, just mentioned a few:
(1) Line 49-50, this paper did nothing for avoiding the deformation of tailing dams.
(2) The sentence in Line 155-156 is unreadable.
(3) What is pore stress ratio Ru in Line 183?
(4) Many quantities in Sec 2.3-2.5 are undefined or easily misunderstood, for example, $h$ in Eq. 2, $_{i+1}$ in Eq. 8, Fn in Line 195. C in Eq. 16 is the so-called volume but also treated as cohesive in following content.
(5) What is membership in Fig . 4?
(6) The rainfall data is acquired according to the investigation in 1984 as mentioned by the author in Line 223, which is out-of-date.
(7) Typos in Line 264, 284,...
(8) The mechanical constitutive model is not presented in coupling analysis in Sec. 3.3.
(9) Is it right that the strength of the tailing material is lower than the tailing dam as presented in Table. 8?
Author Response
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Author Response File: Author Response.docx
Round 2
Reviewer 3 Report
Thanks for your reply. My final suggestions are:
(1) Add a reference for Eq. 16.
(2) Make the symbols self-consistent from Eq. 8 to Eq. 21, and explain each symbol when it is introduced. . For example, another C and K are introduced in Eqs. 20 and 21 which have been definitely used as other quantities.
(3) The effect of the volumetric strain is decoupled (Eq. 17) from the pressure equation (Eq. 16). Then how does the mechanical process (or deformation) affect the evolution of the pressure field? Please explain the coupling behavior more clearly in Line 306-308.
Author Response
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Author Response File: Author Response.docx
