the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 13 Nov 2023
Analysis of three-dimensional slope stability combined with rainfall and earthquake
Jiao Wang
Zhangxing Wang
Guanhua Sun
Hongming Luo
Abstract. In the current context of global climate change, geohazards such as earthquakes and extreme rainfall pose a serious threat to regional stability. We investigate a three-dimensional slope dynamic model under earthquake action, derive the calculation of seepage force and the normal stress expression of slip surface under seepage and earthquake, and propose a rigorous overall analysis method to solve the safety factor of slopes subjected to combined with rainfall and earthquake. The accuracy and reliability of the method is verified by two classical examples. Finally, the effects of soil permeability coefficient, porosity and saturation on slope stability under rainfall in a project located in the Three Gorges Reservoir Area are analyzed. The safety evolution of the slope combined with both rainfall and earthquake is also studied. The results indicate that porosity has a greater impact on the safety factor under rainfall conditions, while the influence of permeability coefficient and saturation is relatively small. With the increase of horizontal seismic coefficient, the safety factor of the slope decreases significantly. The influence of earthquake on slope stability is significantly greater than that of rainfall. The corresponding safety factor when the vertical seismic action is vertically downward is smaller than that when it is vertically upward. When considering both horizontal and vertical seismic effects, slope stability is lower.
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Jiao Wang et al.
Status: open (until 25 Dec 2023)
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RC1: 'Comment on nhess-2023-181', Anonymous Referee #1, 20 Nov 2023
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The authors presented an analytical approach to quantify the stability of slopes combined with rainfall and earthquake. Different from the existing studies, the present study considered the effect of rainfall on the phreatic surface within a slope, which directly relates rainfall to groundwater. Based on this, the effect of seepage and seismic is assessed, and two practical cases are provided to validate the presented method. In general, the manuscript is nicely written and the mathematical logic is well established. The authors provide an interesting work that extends previous studies. The results are reasonable and useful for practicing engineers. I recommend this work after the following comments have been addressed:
- In the introduction, only a few lines are mentioned about landslides, slope, rainfall and earthquake, and the background of the research is quickly mentioned. The introduction part should be explored more deeply.
- Line 74. Scientific gaps about these models need to be further highlighted.
- Line 258. Please insert figure reference to ease reading the slope elements.
- The quality of the Fig.12 is low.
- Line 313. Here, the authors have given no information on the geological context of the area studied, a brief geological background indicating the lithology affected, etc.
- Line 347. The paper discusses a phreatic surface, but no phreatic surfaces are presented in the paper.
- The topic of landslides and the effects of slope, rainfall and earthquake should be discussed more deeply in the conclusion section.
Citation: https://doi.org/10.5194/nhess-2023-181-RC1 -
AC1: 'Reply on RC1', Jiao Wang, 23 Nov 2023
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Dear Referee #1:
Thank you for the comments concerning our manuscript entitled “Analysis of three-dimensional slope stability combined with rainfall and earthquake” (Manuscript nhess-2023-181). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. According to the comments, we have made extensive modifications to our manuscript. The main correction in the paper and the responds to the comments are as following:Responds to the Referee #1’s comments:
1. Response to the comment: In the introduction, only a few lines are mentioned about landslides, slope, rainfall and earthquake, and the background of the research is quickly mentioned. The introduction part should be explored more deeply.
Response: We sincerely appreciate the valuable comments. We have rewritten the beginning of the Introduction, discussed more about the relationship between landslides, slopes and rainfall, and added more about the background of the research.
2. Response to the comment: Line 74. Scientific gaps about these models need to be further highlighted.
Response: Thanks for your suggestion. We have added scientific gaps about these models. In summary, although previous researches have provided significant insights into landslides triggered by earthquakes, there remain inadequacies in fully considering the vertical effects of seismic activity, extending analysis from 2D to 3D, and comprehensively integrating the effects of both earthquakes and rainfall.
3. Response to the comment: Line 258. Please insert figure reference to ease reading the slope elements.
Response: Thanks for your careful checks. We add figure reference at the beginning of the paragraph.
4. Response to the comment: The quality of the Fig.12 is low.
Response: Thanks for your suggestion. We are very sorry for our poor quality of Fig.12. To make it clear, we have redrawn Fig.12.
5. Response to the comment: Line 313. Here, the authors have given no information on the geological context of the area studied. a brief geological background indicating the lithology affected, etc.
Response: We sincerely appreciate the valuable comments. We have added some information on the geological context according to the Referee #1’s suggestion in section 5.
6. Response to the comment: Line 347. The paper discusses a phreatic surface, but no phreatic surfaces are presented in the paper.
Response: Thanks for your suggestion. We apologize for the lack of an explanation of the phreatic surface, and we have added an explanation where the phreatic surface first mentioned according to the Referee #1’s suggestion. The phreatic surface is the interface between the saturated and unsaturated zones within the slope. Physical and mechanical parameters of the sliding below the phreatic surface adopt saturated, while above the phreatic surface adopt naturally. Based on the known initial phreatic surface, the rainfall-induced changes in the phreatic surface, and consequently the evolution of slope stability, are investigated.
7. Response to the comment: The topic of landslides and the effects of slope, rainfall and earthquake should be discussed more deeply in the conclusion section.
Response: Thanks for your suggestion. We have added an in-depth discussion of landslides and the effects of slope, rainfall and earthquake combined with the calculation results of the actual slope in the Three Gorges reservoir area in the conclusion section.Citation: https://doi.org/10.5194/nhess-2023-181-AC1
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RC2: 'Comment on nhess-2023-181', Anonymous Referee #2, 26 Nov 2023
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The manuscript entitled "Analysis of three-dimensional slope stability combined with rainfall and earthquake" by Jiao Wang et al. presents a slope stability analysis based on a 3D slice-free method under combined actions of rainfall and earthquake activity.
This is an original and well written work with a good mathematical sequence, validated by several cases, at different working conditions. The 3D slope stability analysis was applied to a case study at the Three Gorges Reservoir Area (China), considering the effects of rainfall and earthquake conditions.This is a quite innovative work that introduces new knowledge to slope stability analysis.
Nevertheless, there are some issues that should be considered.
Additionally, the figures can be improved, improving their resolution, and increasing the font.Thus, I recommend the work after considering some comments, referring to the line number on the original submitted work:
a) L. 244-245:
Do you have any reference slope gradient? Probably, I misunderstood, but the reference sliding surface is it 45º?b) L. 281:
Was the peak ground acceleration (0.05g) taken from any specific earthquake event or return period? Could you clarify?c) L. 318:
Could you state the gradient (º) or the range of gradient values?d) L. 322-323:
Perhaps this information about PGA could come earlier in L. 281, to better understand from where comes the data.e) L. 369:
Would soil porosity have the same effect on the phreatic surface, under rainfall conditions, with higher slope gradients?f) L. 369-371:
Since permeability coefficient and saturation vary directly with porosity, wouldn't be expected that all these factors could have correlative impact on slope stability?g) L.388-389:
Besides 0.05, the horizontal earthquake coefficients you refer to, are they assigned to any specific earthquake magnitude or return period? Could you state which?h) Probably you could better highlight the role of slope gradient combined with both rainfall and earthquakes, since slope is an important conditioning factor that amplifies their effects.
FIGURES:i) Figure 11:
A geographical map with the general setting of the area, i.e., a map with the geographic location of the site should be included in Fig. 11. This would help readers from abroad to better locate the area.j) Figure 12:
Please, improve the resolution of the figure and increase the font, which is too small.k) Figures 13, 14, 15, 16, and 17:
Please, increase the font.Citation: https://doi.org/10.5194/nhess-2023-181-RC2 -
AC2: 'Reply on RC2', Jiao Wang, 30 Nov 2023
reply
Dear Referee #2:
Thank you for the comments concerning our manuscript entitled “Analysis of three-dimensional slope stability combined with rainfall and earthquake” (Manuscript nhess-2023-181). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our research. According to the comments, we have made some modifications to our manuscript. The main correction in the paper and the responds to the comments are as following:Responds to the Referee #2’s comments:
a) L. 244-245: Do you have any reference slope gradient? Probably, I misunderstood, but the reference sliding surface is it 45º?
Response: We are sorry for our misleading expression. The sliding surface is not 45º. The slip surface of this wedge consists of two structural planes, ABC and OAB, and the sliding direction of the wedge sliding body is assumed to be parallel to the intersection line AB. The coordinates of the vertices have been listed in Figure 8, so the slope gradient is not specifically given. We have added some explanations for the slope in the revised manuscript.
b) L. 281: Was the peak ground acceleration (0.05g) taken from any specific earthquake event or return period? Could you clarify?
d) L. 322-323: Perhaps this information about PGA could come earlier in L. 281, to better understand from where comes the data.
Response: We sincerely appreciate the valuable comments. We now combine our answers to these two comments. According to your suggestion, we have explained earlier how the peak ground coefficient is taken. We refer to the peak ground acceleration at the place where the Three Gorges reservoir slope is located, and therefore take consistent with the actual slope in Section 5.
c) L. 318: Could you state the gradient (º) or the range of gradient values?
Response: We sincerely appreciate the valuable comments. We have added the general gradient of Woshaxi slope.
e) L. 369: Would soil porosity have the same effect on the phreatic surface, under rainfall conditions, with higher slope gradients?
Response: Thanks for your suggestion. As noted by the Referee #2, it is clear from Eq. 1 that the change in the phreatic surface under rainfall is indeed closely related to both soil porosity and slope gradient. In this actual slope, the slope gradient is determined, and the gradient of the surface element corresponding to each slip surface element is different, so our analysis does not specifically address changes in different gradients.
f) L. 369-371: Since permeability coefficient and saturation vary directly with porosity, wouldn't be expected that all these factors could have correlative impact on slope stability?
Response: Thank you for your insightful comments and question regarding the interrelationship between permeability coefficient, saturation, and porosity, and their collective impact on slope stability. In our study, we employed a controlled variable method to individually analyze the impact of permeability coefficient, saturation, and porosity on slope stability. This approach allowed us to clearly understand the influence of each individual parameter without the confounding effects of their interactions. We recognize that permeability coefficient, saturation, and porosity are interrelated in real-world scenarios and that their combined effect could present a more complex influence on slope stability. However, to simplify our analysis and to better understand the independent role of each parameter, we chose to study them separately. We acknowledge that this might limit the comprehensive understanding of the combined effects of these factors and could potentially lead to an overestimation or underestimation of their impact on slope stability in certain situations. Future research will consider the interrelation of these parameters and explore their combined effect.
g) L.388-389: Besides 0.05, the horizontal earthquake coefficients you refer to, are they assigned to any specific earthquake magnitude or return period? Could you state which?
Response: Thanks for your suggestion. We have added a statement in the revised manuscript. In this research, we employed three different horizontal earthquake coefficients: 0.05, 0.1, and 0.15. The coefficient of 0.05 is based on the seismic zoning map of China, corresponding to the seismic characteristics and expected level of seismic activity in the study area. As for the other two coefficients, 0.1 and 0.15, they are not directly associated with any specific earthquake magnitude or return period. These values were set based on engineering requirements and safety considerations, aiming to assess the variation in slope stability under stronger seismic actions. This approach allows us to understand the response of the slope under different seismic intensities and provides a safety margin for seismic activities that may exceed expectations.
h) Probably you could better highlight the role of slope gradient combined with both rainfall and earthquakes, since slope is an important conditioning factor that amplifies their effects.
Response: We think this is an excellent suggestion. You have aptly noted that the role of slope gradient is indeed crucial in amplifying the effects of rainfall and earthquakes on slope stability and should be more prominently highlighted. In the current study, our focus was predominantly on the impacts of soil permeability coefficient, porosity, and saturation on slope stability, without explicitly considering slope gradient as a variable factor. This was primarily due to our study was based on predetermined slope conditions rather than treating the gradient as a changing parameter. The slope gradient is determined for a real slope, so the change in gradient is not taken into account. However, we acknowledge that slope gradient is a key conditioning factor that can significantly magnify the effects of rainfall and earthquakes when combined. As such, we plan to incorporate the impact of slope gradient in our future research endeavors to explore how it interacts with rainfall and seismic activities to influence slope stability.FIGURES:
i) Figure 11: A geographical map with the general setting of the area, i.e., a map with the geographic location of the site should be included in Fig. 11. This would help readers from abroad to better locate the area.
Response: We sincerely appreciate the valuable comments. We have added the geographic location of the site in Fig. 11.
j) Figure 12: Please, improve the resolution of the figure and increase the font, which is too small.
k) Figures 13, 14, 15, 16, and 17: Please, increase the font.
Response: Thanks for your suggestion. We have modified Figs. 12-17 according to your suggestion.Citation: https://doi.org/10.5194/nhess-2023-181-AC2
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AC2: 'Reply on RC2', Jiao Wang, 30 Nov 2023
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Jiao Wang et al.
Jiao Wang et al.
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