Numerical Investigation of a Local Precise Reinforcement Method for Dynamic Stability of Rock Slope under Earthquakes Using Continuum–Discontinuum Element Method
Barbara Namysłowska-Wilczyńska
Round 1
Reviewer 1 Report
Comments for author File: 
Comments.pdf
Author Response
Dear Editors and Reviewers:
Thank you for your letter and for the comments concerning our manuscript entitled “Numerical investigation of a local precise reinforcement method for dynamic stability of rock slope under earthquakes using continuum-discontinuum element method (No. sustainability-2161067)”. The comments were valuable and helpful for revising and improving our paper and clarifying the significance of our research. We have thoroughly amended the paper according to your comments and answered the technical questions with point-by-point responses. We hope our corrections will be met with your approval. The revised portions are marked in the paper. The main corrections in the paper and the responses to the editors’ and reviewers’ comments are as follows:
Comments from the reviewers:
Reviewer #1:
Comment- The reviewed text of the manuscript was developed by a multi-author team of 8 authors. The discussed issues are related to the reinforcement of slopes, their protection against the occurrence and consequences of earthquakes, determining (defining) of anti-dip-slope problems.
CDEM numerical simulation was used to characterize local precision reinforcement of rock slopes and show anti-dip-slope. The drawings are well prepared, legible and of good quality. The work is clear, the chapters are well developed.
- Introduction.
- Methodology.
- Results.
- Discussion.
- Conclusions.
I have no substantive comments regarding the subject of the article, nor any comments regarding the topics and the numbering of (5) chapters, (3) tables and to the captions of (21) figures.
The reviewed manuscript should be published in a nearest time, as soon as possible.
Wroclaw, 08.01.2023
Response: Thank you for your advice and affirmation. We have revised and checked the whole manuscript. Please check it.
Special thanks to you for your helpful comments.
We tried our best to improve the manuscript and made some changes to the manuscript. These changes do not influence the content or framework of the paper. We did not list here all of the changes, but we marked them in the revised manuscript. We appreciate the work of the Editor and Reviewers and hope that the corrections will be met with your approval. Once again, thank you very much for your comments and suggestions.
Yours Sincerely,
Chengwen Wang
State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China
Correspondence: [email protected] (CW. Wang)
Author Response File: 
Author Response.doc
Reviewer 2 Report
Thank you for this contribution. This is an interesting and timely pr that presents simulations on the dynamic stability of rocks. The conducted analysis is typically standard and falls within the expected work from such a publication and hence the work merits publication. As such, the authors are invited to properly address the following items:
1. In general, the introduction is light and does not represent state of the art in this domain. The authors are advised to strengthen their literature review section with supplementary material.
2. Looking at fig 2 and fig 6 show that the modeled slope is very idealized. how close is this model to the actual case?
3. The details on the FE models can be improved. Please ensure that your model is properly described to enable interested researchers to extend and replicate your work. Special attention should be paid to specifics such as element type (DOFs), convergence criteria, and performance metrics.
4. How does the results from the analysis tell us about the physics of the problem on hand?
5. Please add a dedicated section on the validation of the FE model.
Author Response
Dear Editors and Reviewers:
Thank you for your letter and for the comments concerning our manuscript entitled “Numerical investigation of a local precise reinforcement method for dynamic stability of rock slope under earthquakes using continuum-discontinuum element method (No. sustainability-2161067)”. The comments were valuable and helpful for revising and improving our paper and clarifying the significance of our research. We have thoroughly amended the paper according to your comments and answered the technical questions with point-by-point responses. We hope our corrections will be met with your approval. The revised portions are marked in the paper. The main corrections in the paper and the responses to the editors’ and reviewers’ comments are as follows:
Comments from the reviewers:
-Reviewer #2:
Comment- Thank you for this contribution. This is an interesting and timely pr that presents simulations on the dynamic stability of rocks. The conducted analysis is typically standard and falls within the expected work from such a publication and hence the work merits publication. As such, the authors are invited to properly address the following items:
Response: Thank you for your advice and affirmation. We have revised and checked the whole manuscript. Please check it.
Comment 1- In general, the introduction is light and does not represent state of the art in this domain. The authors are advised to strengthen their literature review section with supplementary material.
Response: We have made corrections according to the reviewer’s comments Please check them.
“Many geological elements, such as rock lithology, structural plane, weathering, unloading, ground stress, groundwater, landform and other geological elements, are the main influencing factors of slope stability and safety [10,11]. It is necessary to use engineering geological investigation technology and geotechnical testing technology to find out the engineering geology and hydrogeological conditions of slopes, and to provide geological data and basis for engineering design by analyzing and predicting the engineering geological problems of slopes [12]. At present, a lot of research progress has been made on the prevention and control measures of slope. Ma et al. reinforced the rock slope after excavation of large-scale water conservancy and hydropower, and studied the effect of slope reinforcement with microseismic technology, and discussed the influence of reinforcement measures on slope stability [13]. Liu et al. adopted water-based polyurethane soil stabilizer to strengthen the sandy soil slope to achieve the purpose of erosion prevention, and discussed the reinforcement effect, and proved the feasibility of polyurethane treatment in practice [14]. Fan et al. used the large-scale shaking table test to study the dynamic response of slope reinforced by double-row anti-slide pile and prestressed anchor cable, and discussed the influence of two anti-slide pile reinforcement measures on the dynamic response characteristics of slope [15]. Chen et al. based on the strength reduction method, adopted pile, retaining wall, porous steel pipe grouting and other methods to consolidate the open-pit slope, and discussed the reinforcement effect of the slope and the feasibility of the reinforcement method [16]. Wang et al. used finite element method to study the action mechanism of pile foundation in slopes, and studied the influence of the position and length of pile foundation on the stability of embankment [17]. Li et al. investigated the disaster mechanism and trigger factors of abandoned mine slope based on laboratory experiments and field investigations, and proposed slope reinforcement and ecological restoration measures by adding green planting [18]. Zhang et al. discussed the theory and method of elastic design of flexible supporting expansive soil slopes based on long-term field monitoring test, in order to improve the resistance, recovery and adaptability of flexible supporting structure to the failure of expansive soil slopes [19]. Zhang et al. adopted the numerical simulation method to discuss the pile-soil interaction mechanism and optimal use of the slope reinforced by anti-slide pile, and analyzed the force displacement principle of the slope and anti-slide pile [20]. Liu et al. used physical model experiments to study the deformation characteristics and evolution mechanism of reservoir landslide and pile system under the action of reservoir water [21]. At present, there are many slope reinforcement measures available, but it can be summarized into the following categories: load reduction measures, drainage and water interception measures, anchorage measures, concrete shear structure measures, retaining measures, slope pressure measures [22,23,24]. A reasonable reinforcement scheme can not only improve the reliability of landslide disaster prevention, but also save costs to a large extent and improve the efficiency of construction and prevention [25,26].”
Comment 2- Looking at fig 2 and fig 6 show that the modeled slope is very idealized. how close is this model to the actual case?
Response: We have made corrections according to the reviewer’s comments. Please check them. In this work, the layered slope is selected as a special case to carry out research. In reality, layered slope is common. This work focuses on this case to discuss the applicability and feasibility of the concept and plan of local precision prevention and control. In the future, high-precision numerical modeling will be adopted to further study the topography and geomorphology of the slope.
Comment 3- The details on the FE models can be improved. Please ensure that your model is properly described to enable interested researchers to extend and replicate your work. Special attention should be paid to specifics such as element type (DOFs), convergence criteria, and performance metrics.
Response: We have made corrections according to the reviewer’s comments. Please check them. In this work, the continuous-discontinuous numerical model is established, and the continuous-discontinuous dynamic analysis is carried out after the seismic wave is loaded. The modeling process and parameters of the model are reintroduced in detail.
“The slope numerical model adopts the continuous-discontinuous element method of integrated finite element method and discrete element method. The solid element adopts the ideal elastoplastic model based on Mohr-Coulomb criterion. The interface unit of rock mass is composed of virtual spring, and its failure obeys the energy fracture criterion. Explicit forward difference method is used to solve this method. In the static equilibrium stage, the maximum unbalance force (1e-5) is taken as the convergence standard. In the phase of dynamic calculation, time is taken as the standard to end the calculation, and the calculation ends when the preset calculation time (ground motion lasting 20 s) is reached. The numerical simulation process is as follows: Firstly, the initial model is simulated. For the numerical model, five working conditions (0.1, 0.2, 0.3, 0.4 and 0.5 g) were selected to carry out dynamic analysis, and these seismic waves were loaded at the bottom of the model. By observing the seismic damage of the slope, the slope toe is destroyed first.”
Comment 4- How does the results from the analysis tell us about the physics of the problem on hand?
Response: We have made corrections according to the reviewer’s comments. In terms of the slope failure process, it is an evolutionary process of gradual failure from local damage accumulation to large-scale sliding failure. The slope reinforcement in the past is characterized by excessive reinforcement. This work provides a new idea for the field reinforcement application of complex slope, emphasizing that it provides a feasible scheme for precise reinforcement of complex slopes on the basis of refined numerical simulation analysis. The feasibility and economy of the method are also discussed, which provides a basis for the design of seismic reinforcement of slopes. Please check them.
“In terms of the slope failure process, it is an evolutionary process of gradual failure from local damage accumulation to large-scale sliding failure. The slope reinforcement in the past is characterized by excessive reinforcement. This work provides a new idea for the field reinforcement application of complex slope, emphasizing that it provides a feasible scheme for precise reinforcement of complex slopes on the basis of refined numerical simulation analysis. The feasibility and economy of the method are also discussed, which provides a basis for the design of seismic reinforcement of slopes. According to a series of numerical simulation analysis, it can be found that the effect of Case 4 (third local reinforcement) is similar to that of Case 6 (holistic reinforcement). This shows that local precise reinforcement is effective and feasible, but it is based on accurate analysis of the evolution process of slope earthquake damage. In the actual engineering application, the analysis should be combined with the specific engineering situation, and the specific implementation plan mainly includes the following steps. Firstly, the slope topography, geomorphology, formation lithology and other information are obtained through detailed field investigation. Secondly, UAV aerial survey is used to obtain slope elevation, image and 3D terrain data. Thirdly, professional aerial photogrammetry software is used to analyze and process the data obtained by UAV and reconstruct the slope three-dimensional model. Then, combined with the detailed field investigation data, the 3D geological model of the slope is established. Then, based on the 3D geological model of the slope, the numerical simulation method is used to establish the same numerical model as the actual slope, to simulate the slope instability process and instability mode. The initial region of slope failure and the failure region of large deformation stage in the process of instability are determined, and it is listed as the potentially dangerous rock mass and the key area of concern. Then, appropriate reinforcement structure is adopted to strengthen the initial failure area and large deformation area. Finally, numerical simulation is used to compare the economy, reliability and practicability of precise reinforcement and overall reinforcement of slope in key areas. This method deeply clarifies the principle and implementation method of precise reinforcement of slope, greatly improves the precision, reliability, practicability and economy of slope deformation control, and has a wide application prospect in the field of civil engineering and geological disaster prevention.”
Comment 5- Please add a dedicated section on the validation of the FE model.
Response: We have made corrections according to the reviewer’s comments. Please check them. This study presents a new concept of wave reinforcement, mainly to compare the economy and applicability of local precision reinforcement and the whole reinforcement. The limitation of this study is the lack of verification of model experiment and field experiment, which is also the research work to be carried out in the next step. However, in this study, a detailed engineering implementation scheme of precise reinforcement scheme is given.
“In terms of the slope failure process, it is an evolutionary process of gradual failure from local damage accumulation to large-scale sliding failure. The slope reinforcement in the past is characterized by excessive reinforcement. This work provides a new idea for the field reinforcement application of complex slope, emphasizing that it provides a feasible scheme for precise reinforcement of complex slopes on the basis of refined numerical simulation analysis. The feasibility and economy of the method are also discussed, which provides a basis for the design of seismic reinforcement of slopes. According to a series of numerical simulation analysis, it can be found that the effect of Case 4 (third local reinforcement) is similar to that of Case 6 (holistic reinforcement). This shows that local precise reinforcement is effective and feasible, but it is based on accurate analysis of the evolution process of slope earthquake damage. In the actual engineering application, the analysis should be combined with the specific engineering situation, and the specific implementation plan mainly includes the following steps. Firstly, the slope topography, geomorphology, formation lithology and other information are obtained through detailed field investigation. Secondly, UAV aerial survey is used to obtain slope elevation, image and 3D terrain data. Thirdly, professional aerial photogrammetry software is used to analyze and process the data obtained by UAV and reconstruct the slope three-dimensional model. Then, combined with the detailed field investigation data, the 3D geological model of the slope is established. Then, based on the 3D geological model of the slope, the numerical simulation method is used to establish the same numerical model as the actual slope, to simulate the slope instability process and instability mode. The initial region of slope failure and the failure region of large deformation stage in the process of instability are determined, and it is listed as the potentially dangerous rock mass and the key area of concern. Then, appropriate reinforcement structure is adopted to strengthen the initial failure area and large deformation area. Finally, numerical simulation is used to compare the economy, reliability and practicability of precise reinforcement and overall reinforcement of slope in key areas. This method deeply clarifies the principle and implementation method of precise reinforcement of slope, greatly improves the precision, reliability, practicability and economy of slope deformation control, and has a wide application prospect in the field of civil engineering and geological disaster prevention.”
Special thanks to you for your helpful comments.
We tried our best to improve the manuscript and made some changes to the manuscript. These changes do not influence the content or framework of the paper. We did not list here all of the changes, but we marked them in the revised manuscript. We appreciate the work of the Editor and Reviewers and hope that the corrections will be met with your approval. Once again, thank you very much for your comments and suggestions.
Yours Sincerely,
Chengwen Wang
State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China
Correspondence: [email protected] (CW. Wang)
Author Response File: Author Response.doc
Reviewer 3 Report
1. The selected dynamic load is a simple harmonic load with a fixed frequency, which is not an actual ground motion. This is not reasonable for seismic analysis, and it is difficult to reflect the response of the slope under the earthquake loads. The author should give further explanation about this issue.
2. The author only uses the dynamic load with the PGA scaled to 0.5g. Please explain why 0.5g PGA is used.
3. For such rock slope in this study, long-duration ground motion is often more unfavorable. The author uses a 20s dynamic load. Whether the results can reflect the seismic damage state of the actual slope, please explain.
4. In lines 262-266, the author indicated that it is necessary to convert the acceleration time history curve into the velocity time history curve, then into the stress time history, and finally apply it on the viscous boundary. However, the process of integration will produce constant terms, resulting in drift error. How can the author deal with this problem?
5. The English writing needs to be improved.
Author Response
Dear Editors and Reviewers:
Thank you for your letter and for the comments concerning our manuscript entitled “Numerical investigation of a local precise reinforcement method for dynamic stability of rock slope under earthquakes using continuum-discontinuum element method (No. sustainability-2161067)”. The comments were valuable and helpful for revising and improving our paper and clarifying the significance of our research. We have thoroughly amended the paper according to your comments and answered the technical questions with point-by-point responses. We hope our corrections will be met with your approval. The revised portions are marked in the paper. The main corrections in the paper and the responses to the editors’ and reviewers’ comments are as follows:
Comments from the reviewers:
-Reviewer #3:
Comment 1- The selected dynamic load is a simple harmonic load with a fixed frequency, which is not an actual ground motion. This is not reasonable for seismic analysis, and it is difficult to reflect the response of the slope under the earthquake loads. The author should give further explanation about this issue.
Response: We have made corrections according to the reviewer’s comments. This work mainly focuses on the comparative analysis of the applicability of the precise reinforcement method and the overall reinforcement method of slope, and discusses the economy and feasibility of the precise reinforcement method. In this study, simple harmonics are used to facilitate the dynamic analysis of slope. The simple harmonics and the 2008 Wenchuan earthquake waves are used in the dynamic analysis. The analysis objectives of the two waves are the same and the analysis results are similar. However, the Wenchuan earthquake was 120 s long and its waveform was very complex. The simple harmonic waveform is simple, which can better show the reader the main purpose of this study. Therefore, simple harmonics are selected for demonstration.
Comment 2- The author only uses the dynamic load with the PGA scaled to 0.5g. Please explain why 0.5g PGA is used.
Response: We have made corrections according to the reviewer’s comments. I apologize for any confusion. In this study, five working conditions of 0.1, 0.2, 0.3, 0.4 and 0.5 g were selected to carry out dynamic analysis, but the dynamic response degree of 0.1-0.4 g slope is weak, and it is difficult to show the damage and failure characteristics of slope well. This study mainly discusses the adaptability and economy of local precision reinforcement in slope dynamic stability reinforcement. Therefore, 0.5 g of results were selected for display. We also modified it in the paper. Please check them.
“For the numerical model, five working conditions (0.1, 0.2, 0.3, 0.4 and 0.5 g) were selected to carry out dynamic analysis, and these seismic waves were loaded at the bottom of the model.”
Comment 3- For such rock slope in this study, long-duration ground motion is often more unfavorable. The author uses a 20s dynamic load. Whether the results can reflect the seismic damage state of the actual slope, please explain.
Response: We have made corrections according to the reviewer’s comments. Please check them. This work mainly focuses on the comparative analysis of the applicability of the precise reinforcement method and the overall reinforcement method of slope, and discusses the economy and feasibility of the precise reinforcement method. In this study, simple harmonics are used to facilitate the dynamic analysis of slope. The simple harmonics and the 2008 Wenchuan earthquake waves are used in the dynamic analysis. By comparing the results of these two seismic waves, the analysis objectives of the two waves are the same and the analysis results are similar. However, the Wenchuan earthquake was 120 s long and its waveform was very complex. The simple harmonic waveform is simple, which can better show the reader the main purpose of this study. Therefore, simple harmonics are selected for demonstration.
Comment 4- In lines 262-266, the author indicated that it is necessary to convert the acceleration time history curve into the velocity time history curve, then into the stress time history, and finally apply it on the viscous boundary. However, the process of integration will produce constant terms, resulting in drift error. How can the author deal with this problem?
Response: We have made corrections according to the reviewer’s comments. When the seismic wave is loaded at the bottom of the model, only the stress boundary condition of vibration can be applied as the ground motion input due to the limitation of the calculation method. In this work, the error in the conversion process from acceleration time history curve to velocity time history curve and then to stress time history curve can be avoided effectively by using simple harmonic input. Please check them.
“It is worth noting that in CDEM calculation, seismic load in the form of stress time history can only be loaded on the viscous boundary, hence, it is necessary to convert the acceleration time history curve into the velocity time history curve, then into the stress time history, and finally apply it on the viscous boundary. When the seismic wave is loaded at the bottom of the model, only the stress boundary condition of vibration can be applied as the ground motion input due to the limitation of the calculation method. In this work, the error in the conversion process from acceleration time history curve to velocity time history curve and then to stress time history curve can be avoided effectively by using simple harmonic input.”
Comment 5- The English writing needs to be improved.
Response: We have made corrections according to the reviewer’s comments. We have sought a native English speaker for language modification. Please check them.
Special thanks to you for your helpful comments.
We tried our best to improve the manuscript and made some changes to the manuscript. These changes do not influence the content or framework of the paper. We did not list here all of the changes, but we marked them in the revised manuscript. We appreciate the work of the Editor and Reviewers and hope that the corrections will be met with your approval. Once again, thank you very much for your comments and suggestions.
Yours Sincerely,
Chengwen Wang
State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China
Correspondence: [email protected] (CW. Wang)
Round 2
Reviewer 2 Report
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