Slope Crack Propagation Law and Numerical Simulation of Expansive Soil under Wetting–Drying Cycles

Round 1

Reviewer 1 Report

I have no fundamental comments on the article. I can conclude that the methodology used to solve the chosen problem is correct. I appreciate that the actual experiment is supported by numerical simulation and that an actual local problem has been solved. The results can be considered as expected, but the use of the methodology showed the authors' ability to solve other more complex problems in the future. The article would be enriched by discussion and confrontation with similar results. Please add it.

I have only one suggestion for editing the text - Figure 8 - unnecessary title, it is given below the figure - remove it.

Author Response

Dear Editors and Reviewers:

Thank you very much for your reply and help. Thanks a lot for the comments and suggestions on our manuscript entitled “Slope Crack Propagation Law and Numerical Simulation of Expansive Soil Under Wetting-Drying Cycles”. We have studied the reviewer’s comments carefully and have revised the article. We have tried our best to revise our manuscript according to the comments. Revised portions are marked in red on the paper. Besides, we have carefully examined the whole manuscript and corrected grammar mistakes. We provide this letter to explain, point by point, the details of our revisions in the manuscript and our responses to the reviewers’ comments as follows. We hope the revised paper would satisfy you. We would like to express our great appreciation to you for your comments on our paper. Looking forward to hearing from you soon.

Revisions list according to the comments

Reviewer:

 I have only one suggestion for editing the text - Figure 8 - unnecessary title, it is given below the figure - remove it.

Response:

Thank you for your suggestion. Thank you for your inquiry. We have made detailed modifications to the image as requested, including the removal of unnecessary captions and modifications to the X-axis coordinates.

We appreciate for Reviewers’ warm work earnestly and hope that the correction will meet with approval.

 Once again, thank you very much for your comments and suggestions.

Kind regards.

Authors: Xuanyi Chen, Xiaofei Jing*, Xiaoshuang Li, Junji Chen, Qiang ma, and Xiaohua Liu

Author Response File: Author Response.docx

Reviewer 2 Report

The paper is interesting and instructive. Hence, I recommend it for publication provided that the authors address in full the following comments:

1) Numbering of the cited reference does not match that in the reference list. Moreover, there are references missing from the list. 

2) Line 109: What is the free swelling rate or ratio. If it is the free swelling strain, then 51% free swelling strain indicates a very highly expansive soil, not weakly expansive.  

3) Line 138: Water content 45% during compaction seems very high. Is this value correct? 

4) Lines 176-178 and 180-183: Remove these sentences. The explanations given are not valid.

5) Show the locations of all the moisture sensors in a figure. 

6) Lines 302-304: The reasoning here is not well explained. Rephrasing is needed. 

7) The weakest point of the paper is the PFC analyses. In my opinion, PFC (discrete element method) is unsuitable for analyzing the problem at hand (which involves a fine grained soil) and arriving at sensible practical conclusions. Moreover, the proper way to assess the influence of the cracks on the safety of the slope is to calculate the Factor of Safety (FoS). I strongly suggest the authors perform again the calculations either in a finite element software (e.g. Plaxis), finite difference software (e.g. FLAC), or in a classical limit equilibrium program, so that FoS can be established and compared between the models, instead of comparing displacements.  

 

Author Response

Dear Editors and Reviewers:

Thank you very much for your reply and help. Thanks a lot for the comments and suggestions on our manuscript entitled “Slope Crack Propagation Law and Numerical Simulation of Expansive Soil Under Wetting-Drying Cycles”. We have studied the reviewer’s comments carefully and have revised the article. We have tried our best to revise our manuscript according to the comments. Revised portions are marked in red on the paper. Besides, we have carefully examined the whole manuscript and corrected grammar mistakes. We provide this letter to explain, point by point, the details of our revisions in the manuscript and our responses to the reviewers’ comments as follows. We hope the revised paper would satisfy you. We would like to express our great appreciation to you for your comments on our paper. Looking forward to hearing from you soon.

Revisions list according to the comments

Reviewer:

1. Numbering of the cited reference does not match that in the reference list. Moreover, there are references missing from the list.

Response:

Thank you very much for your feedback! We have proofread the references and supplemented the missing ones. We have also added new references, increasing the total number of references to 41.

2. Line 109: What is the free swelling rate or ratio. If it is the free swelling strain, then 51% free swelling strain indicates a very highly expansive soil, not weakly expansive.

Response:

Thank you for your inquiry! The free swelling rate of expansive soil refers to the degree of swelling that occurs under unconstrained conditions after the expansive soil absorbs sufficient moisture in a dry state. Generally, the free swelling rate refers to the volume change caused by the free swelling of unit volume of expansive soil under unconstrained conditions. The free swelling strain is a specific manifestation of the free swelling rate, defined as the relative change in length of a unit length of expansive soil. According to the classification provisions for expansive soil in the "Technical Code for Construction of Expansive Soil Areas" (GBJ112-87):

	Non-expansive soil	Slightly expansive soil	Moderately expansive soil	Highly expansive soil
Free Swell Index	<40	40≤ <60	60≤<90	≥90

 

 

3. Line 138: Water content 45% during compaction seems very high. Is this value correct?

Response:

Thank you for your question. Firstly, to ensure the accuracy of this value, we did indeed raise the moisture content of the soil to 45% during the initial stages of the experiment, to observe the cracks generated by changes in moisture content. Indeed, such a high moisture content made the experimental process very challenging, but after adding water and stabilizing, the moisture content was ultimately measured to be 45% during the stacking process.

 

4. Lines 176-178 and 180-183: Remove these sentences. The explanations given are not valid.

Response:

Thank you very much for your suggestion. We have fully followed your proposal and deleted the content in lines 176-178 and 180-183.

 

5. Show the locations of all the moisture sensors in a figure.

Response:

Thank you very much for your suggestion! We have followed your proposal and buried the moisture content sensors at 5cm below the slope top surface and 0.4m away from the left, right, and rear walls of the experimental pool, where the center of the slope top is. The sensors were buried in the soil at 5cm intervals from top to bottom in a crisscross pattern to minimize the impact of multiple sensors on the same area. A total of 7 sensors were buried at a depth of 35cm. To minimize the impact of sensor cables penetrating the soil surface and affecting the experimental data, the cable ends of the sensors were led out from the rear wall of the experimental pool through drilled holes and sealed with glass glue at the drilling location. The experimental data were collected once the readings of the moisture content sensors were stable and did not change for several hours.

 

6. Lines 302-304: The reasoning here is not well explained. Rephrasing is needed.

Response:

Thank you very much for your suggestion! We have changed it to: The larger the contact area between soil and air, the faster the water loss. Without the presence of cracks, water needs to slowly rise from the bottom of the soil to the surface before it can be evaporated. However, after the occurrence of cracks, new evaporation surfaces are formed on the inner walls of the cracks, increasing the evaporative area. Water no longer needs to rise from the bottom to the very surface of the soil, as it can be evaporated directly from the soil to the inner wall of the crack. This shortens the distance of water evaporation, accelerating the change in water content. Therefore, this reduces the hydraulic gradient between the upper and lower layers of the soil, leading to a more uniform distribution of water content within the soil.

 

7. The weakest point of the paper is the PFC analyses. In my opinion, PFC (discrete element method) is unsuitable for analyzing the problem at hand (which involves a fine grained soil) and arriving at sensible practical conclusions. Moreover, the proper way to assess the influence of the cracks on the safety of the slope is to calculate the Factor of Safety (FoS). I strongly suggest the authors perform again the calculations either in a finite element software (e.g. Plaxis), finite difference software (e.g. FLAC), or in a classical limit equilibrium program, so that FoS can be established and compared between the models, instead of comparing displacements.

Response:

Thank you very much for your suggestion! FLAC3D and Plaxis are both excellent finite element software, with FLAC3D being particularly suitable for simulating the behavior of rock and soil under various stress states, including strength, deformation, seepage, and thermodynamic responses, while Plaxis provides rich material models and boundary conditions for different types of analysis, such as static analysis, dynamic analysis, and steady-state flow analysis. However, I believe that both of these software emphasizes continuity and deformation, simulating continuous variables such as stress, strain, and displacement. The main problem explored in this manuscript is the study of fine cracks, which are the effects of changes in soil moisture on the slope. PFC can model fine cracks on slopes and study their impact on slope stability. Although FLAC3D can also be used for slope stability analysis, its modeling approach and research focus are different from PFC. PFC is a discrete element simulation software based on particle flow theory, which focuses on the interaction between particles and their effects on overall mechanical behavior, especially suitable for studying processes such as particle flow, formation, extension, and closure of rock and soil cracks at the micro level. Taking FLAC3D as an example, it is a continuum simulation software based on the finite difference method, which is suitable for simulating the deformation and failure process of rock and soil and can be used to calculate macroscopic mechanical parameters such as the safety factor of rock and soil. In comparison, PFC can more intuitively represent the effect of cracks on slopes under gravity.

 

We appreciate for Reviewers’ warm work earnestly and hope that the correction will meet with approval.

 Once again, thank you very much for your comments and suggestions.

Kind regards.

Authors: Xuanyi Chen, Xiaofei Jing*, Xiaoshuang Li, Junji Chen, Qiang ma, and Xiaohua Liu

 

Author Response File: Author Response.docx

Reviewer 3 Report

The paper provides an important and comprehensive overview of the Slope Crack Propagation Law and its numerical simulation of expansive soil under wetting-drying cycles. Overall, this paper provides an invaluable resource for researchers and practitioners who are interested in understanding and applying the Slope Crack Propagation Law. This research also provides important information regarding the behavior of expansive soil slopes under drying-wetting conditions.

Even while I consider the paper to be of high quality, I do have a few comments:

1, It appears that 5 references in the Introduction are not included in the References section. It is important to ensure that all of the references used in the paper are properly cited, so any references missing from the References section should be added.

2, Why only three time cycles has been investigated? Are three cycles enough for the deep analysis?

I recommend the minor revision of the paper.

Author Response

Dear Editors and Reviewers:

Thank you very much for your reply and help. Thanks a lot for the comments and suggestions on our manuscript entitled “Slope Crack Propagation Law and Numerical Simulation of Expansive Soil Under Wetting-Drying Cycles”. We have studied the reviewer’s comments carefully and have revised the article. We have tried our best to revise our manuscript according to the comments. Revised portions are marked in red on the paper. Besides, we have carefully examined the whole manuscript and corrected grammar mistakes. We provide this letter to explain, point by point, the details of our revisions in the manuscript and our responses to the reviewers’ comments as follows. We hope the revised paper would satisfy you. We would like to express our great appreciation to you for your comments on our paper. Looking forward to hearing from you soon.

Revisions list according to the comments

 

Reviewer:

1. It appears that 5 references in the Introduction are not included in the References section. It is important to ensure that all of the references used in the paper are properly cited, so any references missing from the References section should be added.

Response:

Thank you for your valuable suggestions! We have carefully checked and revised the references in the paper, added missing references, and increased the total number of references to 41.

2.Why only three time cycles has been investigated? Are three cycles enough for the deep analysis?

Response:

Thank you for your valuable suggestion! Conducting three cycles of tests is not a random decision, but is based on the experience gained from multiple preliminary tests. After three cycles of wet-dry cycles, the morphology of crack development no longer changes, and the values of crack depth and area tend to stabilize. The growth rate of crack depth and the area gradually decreases under three cycles, and the trend of crack development in the third cycle is significantly lower than that in the second cycle, which is consistent with the experiments conducted by many scholars, such as Yao, Z., Chen, Z., and Tang, who also used three cycles as the number of wet-dry cycles. TANG obtained the same results after five cycles of experiments, which showed that the geometric structure of cracks basically stabilized after three cycles of wet-dry cycles.

The article mainly focuses on the study of the failure pattern and mechanism of expansive soil cracks. Three cycles of wet-dry cycles can explain the failure pattern and development mechanism of cracks, but further experiments and analysis are needed for predicting models of expansive soil cracks. Due to the limitations of funding, experimental materials, and time, only three cycles of wet-dry cycles were conducted in this study.

[4] Tang, C. S.; Cheng, Q.; Leng T. et al. Effects of wetting-drying cycles and desiccation cracks on mechanical behavior of an unsaturated soil[J]. CATENA, 2020, 194: 104-116.

[13] Yao, Z.; Chen, Z. Experimental study on meso-structure change of remolded expansive soil during drying and wetting [J]. Journal of Underground Space and Engineering, 2009,5(03):429-434.

[14] Chen, Z.; Fang, X.; Zhu, Y. et al. Study on mesostructure and Evolution of expansive soil and loess [J]. Rock and Soil Mechanics, 2009,30(01):1-11.

[40] Tang, Chao-sheng.; SHI, Bin.; LIU, Chun. et al. Experimental characterization of shrinkage and desiccation cracking in thin clay layer[J]. Applied Clay Science, 2011, 52(1-2): 69－77.

 

 

We appreciate for Reviewers’ warm work earnestly and hope that the correction will meet with approval.

 Once again, thank you very much for your comments and suggestions.

Kind regards.

Authors: Xuanyi Chen, Xiaofei Jing*, Xiaoshuang Li, Junji Chen, Qiang ma, and Xiaohua Liu

 

Author Response File: Author Response.docx

Reviewer 4 Report

This paper shows a very interesting investigation on the slope crack propagation law and numerical simulation of expansive soil under wetting-drying cycles. This paper can be considered for publication after a minor revision.

(1) The author should show some quantitative data in the revised manuscript.

(2) For meeting the scope of Sustainability, the author should highlight the sustainable topic of this paper. The following one reference may be helpful for this paper “Characterization of sustainable mortar containing high-quality recycled manufactured sand crushed from recycled coarse aggregate” (https://doi.org/10.1016/j.cemconcomp.2022.104629).

(3) The error bar should be given in Fig. 7.

(4) The conclusions should be listed one by one. Besides, the innovations and findings should be further highlighted in the revised manuscript.

Author Response

Dear Editors and Reviewers:

Thank you very much for your reply and help. Thanks a lot for the comments and suggestions on our manuscript entitled “Slope Crack Propagation Law and Numerical Simulation of Expansive Soil Under Wetting-Drying Cycles”. We have studied the reviewer’s comments carefully and have revised the article. We have tried our best to revise our manuscript according to the comments. Revised portions are marked in red on the paper. Besides, we have carefully examined the whole manuscript and corrected grammar mistakes. We provide this letter to explain, point by point, the details of our revisions in the manuscript and our responses to the reviewers’ comments as follows. We hope the revised paper would satisfy you. We would like to express our great appreciation to you for your comments on our paper. Looking forward to hearing from you soon.

Revisions list according to the comments

 

Reviewer :

1. The author should show some quantitative data in the revised manuscript.

Response:

Thank you very much for your comments! We have added Tables 5 and 6 to the attachment:

Table5. Relationship between rainfall period and crack depth

Depth of crack(cm)	Period
1.26	Drying time
2.65
3.52
3.93
1.86	Rain heals and cracks again
2.25
3.88
4.45	Drying time
4.75
5.53
5.93
3.64	Rain heals and cracks again
4.56
5.33
6.23	Drying time
6.450
6.710
6.970

Table6. Number of drying-wetting cycles and water content, crack, and soil mass data

Number of drying-wetting cycles	Crack area(m2)	Crack rate%	Soil area ratio%	water content%
1	0.0848	10.6	89.4	31.8
2	0.1128	14.1	85.9	32.1
3	0.1264	15.8	84.2	32

 

2. For meeting the scope of Sustainability, the author should highlight the sustainable topic of this paper. The following one reference may be helpful for this paper “Characterization of sustainable mortar containing high-quality recycled manufactured sand crushed from recycled coarse aggregate” (https://doi.org/10.1016/j.cemconcomp.2022.104629).

Response:

Thank you very much for your suggestion! This reference has greatly inspired me in the field of sustainable development, and I have cited it in my work. Research on the cracks in expansive soil helps to enhance our understanding of slope stability, which is important for planning and designing infrastructure and buildings and reducing environmental damage and economic losses caused by slope instability.

3. The error bar should be given in Fig. 7.

Response:

Thank you for your question. Figure 7 in the paper represents the "Relationship between drying-wetting cycles and crack area ratio". Currently, there is no completely mature method for measuring crack area, so it is difficult to determine the exact measurement error between the measured value and the actual value. We used binary processing to calculate the crack area, which is based on the calculation of black and white pixels. The calculation of the crack area ratio is based on the comparison between the black pixels of the crack and the white pixels of the non-crack area.

4. The conclusions should be listed one by one. Besides, the innovations and findings should be further highlighted in the revised manuscript.

Response:

Thank you very much for your valuable feedback! We have listed out the conclusions one by one and provided further summarization of each conclusion.

(1) With increasing wetting-drying cycles, the rainwater infiltration rate into the lower layers of the soil was much higher than that of the soil without multiple cycles.

(2) A self-made binary image processing system was used to quantify the crack area of the soil, and the crack depth of the slope was measured using a crack depth detector. It was concluded that the greater the number of wetting-drying cycles, the larger the crack area and crack depth, but the smaller the growth trend of the crack area and depth.

(3) By using the PFC numerical calculation software and taking the quantitative results as the simulation parameters, it was found that the number of cracks and the crack location significantly influenced slope failure. The greater the number of wetting-drying cycles, the greater the number of cracks, resulting in significant changes to the slope, an obvious slip, slope instability, and a slip surface that moves backward.

 

 

We appreciate for Reviewers’ warm work earnestly and hope that the correction will meet with approval.

 Once again, thank you very much for your comments and suggestions.

Kind regards.

Authors: Xuanyi Chen, Xiaofei Jing*, Xiaoshuang Li, Junji Chen, Qiang ma, and Xiaohua Liu

 

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

The authors have adequately addressed the review comments.

Author Response

Additional concerns to deal with:
- the justification to use PFC (instead of FLAC3D or otherS) in the numerical simulation should be provided in the manuscript;

Review：

Thank you very much for your question! FLAC is a software based on finite element method, which discretizes complex structures into a finite number of elements and solves local equations within each element, and then combines them to solve the overall equation. In FLAC, the simulation area is divided into a grid, and the stress and strain on each grid are calculated through finite element analysis. Compared with discrete element method, finite element method is suitable for dealing with structures with smooth boundaries and complex geometric shapes.

However, compared with FLAC, discrete element method has many advantages in studying rock mechanics. First, the data simulated by discrete element method can comprehensively present from the micro to macro scale, providing strong support for the study of the properties, internal structure, and macroscopic behavior of rock and soil bodies. Moreover, discrete element method can study strongly random rock and soil, and can simulate well the progressive failure phenomena such as crack development and occurrence, spalling, and collapse. In addition, discrete element method can express well the development and influence of cracks, not only limited to stress, displacement, safety factors and other parameters. In reality, slope soil is composed of countless small particles, and using discrete element method can better approach the influence of cracks on the slope, thereby more accurately expressing the impact of cracks on the slope. In the introduction of our manuscript, we cited previous research on discrete element slopes.

42.Gao, W.; Yang, H.; Hu, R. Soil–rock mixture slope stability analysis by microtremor survey and discrete element method[J]. Bulletin of Engineering Geology and the Environment, 2022, 81(3): 121.

43.Lv, Y.; Li, H.; Zhu, X. et al. Discrete element method simulation of random Voronoi grain-based models[J]. Cluster Computing, 2017, 20: 335-345.

44.Jin, L.; Zeng Y. Refined simulation for macro-and meso-mechanical properties and failure mechanism of soil-rock mixture by 3d dem[J]. Chin J Rock Mech Eng, 2018, 37(06):1540–1550

45.Xu, Gj.; Zhong, Kz.; Fan, Jw.et al.Stability analysis of cohesive soil embankment slope based on discrete element method.[J]. Cent. South Univ.27, 2020, 1981–1991. https://doi.org/10.1007/s11771-020-4424-9.

- A general conclusion of the study and the relevance to the construction sector and to the sustainable development are missing;

Review：

Thank you very much! We have made modifications for engineering and sustainability issues, and marked the modified part, marking this part of the text in red.

- English writing still needs revision;

Review：

Thank you very much! We have made detailed modifications to the original manuscript, including changes in grammar, wording and sentence structure. We have marked the modified statement in red font.

 

 

Author Response File: Author Response.docx