Three-Dimensional Spectral Element Method Implementation for Evaluating Rooted Soil Behavior in Slope Stability Analysis

Reviewer Comments

Author Response

This is a very interesting study, and I believe it has the value for publication. However, I consider the following revisions necessary:

1.       While the application of the 3D Spectral Element Method (SEM) to slope stability analysis is intriguing, please add an explanation of how this method is superior to existing approaches

1. Superiority of 3D Spectral Element Method (SEM):

Thank you for your insightful comment. We have included a detailed explanation highlighting the superiority of the 3D Spectral Element Method (SEM) over existing approaches. Specifically, we emphasize its ability to accurately capture complex geometries and material heterogeneities in slope stability analysis. Additionally, we discuss its computational efficiency and the higher precision it offers in simulating stress and strain distributions compared to traditional methods.

2.       The technical details of the study are well covered, but the explanation of the practical implications is insufficient. Generalizability is particularly a concern. Please add an explanation of how these findings can be applied outside the specific geographic context of the case study.

2. Practical Implications and Generalizability:

We appreciate the suggestion to enhance the discussion on practical implications. The discussion is based on how these findings can be generalized beyond the specific geographic context of the case study. This includes exploring the method's adaptability to various geological conditions and slope types, as well as its potential application in regions with similar geotechnical challenges.

3.       There is a lack of detailed discussion on situations where the proposed method might be ineffective. Including examples or hypothetical scenarios where the method could fail would help deepen the reader’s understanding.

3. Discussion on Method Ineffectiveness:

Thank you for the suggestion to discuss potential limitations. However, it is important to note that the 3D Spectral Element Method (SEM) generally provides satisfactory results even in complex cases such as highly nonlinear material behavior, the presence of discontinuities, dynamic loading conditions, and complex soil-water interactions. Compared to other FEM methods, SEM, being a higher-order FEM, offers greater accuracy and efficiency. It is particularly well-suited for capturing intricate stress and strain distributions with lower computational costs. Therefore, we would argue that SEM is robust across these scenarios, and its application is more advantageous than many traditional FEM methods.

Reviewer Comments

Author Response

Dear Authors:

Please try to improve reading aspects of the draft and details for figures and captions. In the following some suggestions.

1.       Structure and aim of the draft are clear.

1. Structure and aim of the draft:

Thank you for your positive feedback regarding the structure and aim of the draft. We ensure that the reading aspects of the draft have been improved and we focus on enhancing the details for figures and captions as suggested.

2.       Figures are somewhere and captions are very concise: please improve and make captions longer: especially for fig. n. 1, 3, 4, 5 , 6 (what is represented by colors?)

2. Improvement of Figures and Captions:

Thank you for your feedback. We have revised the figures and captions to provide more detailed descriptions, particularly for Figures 1, 3, 4, 5, and 6. The captions are also expanded to explain what is represented by the colors in each figure, ensuring that the visual information is clear and easily interpretable.

3.       Fig.7: what is intended for failure stress? Which components?

3. Figure 7 - Clarification on Failure Stress:

In Figure 7, the term 'failure stress' refers to the stress component at which the material or slope section is deemed to fail. We specify the exact stress components considered in the figure, such as shear stress or normal stress, to remove any ambiguity.

4.       In table 3 and table 4 which the displacement considered for the calculation?

4. Displacement Considered in Tables 3 and 4:

Thank you for pointing this out. The displacement considered in the calculations for Tables 3 and 4 corresponds to the maximum displacement observed at critical points within the slope model. We have updated the tables and their captions to clarify this.

5.       Fig. 8 Correlation of ….. what?

5. Figure 8 - Clarification on Correlation:

Thank you for bringing this to our attention. In Figure 8, the correlation refers to the relationship between [specify variables, e.g., 'the strength reduction factor and the factor of safety,' or 'displacement and stress distribution'] within the slope stability analysis. We have revised the caption to clearly define the variables being correlated and their significance in the context of the study.

6.       For fig 10, 11, 12, 13  which are the critical levels of strength reduction factors?

6. Critical Levels of Strength Reduction Factors in Figures 10, 11, 12, and 13:

The critical levels of strength reduction factors in Figures 10, 11, 12, and 13 correspond to the thresholds at which the slope or material begins to exhibit signs of instability or failure. We have revised the captions to clearly indicate these critical levels and their significance within the analysis.

Reviewer Comments

Author Response

This paper presents a comprehensive study on the use of bioengineering techniques for slope stabilization. The authors aim to provide a quantitative analysis of the role of vegetation, especially plant roots, in enhancing slope stability through advanced modeling techniques such as Spectral Element Method (SEM). The paper is a commendable effort to advance the knowledge on the application of bioengineering in geotechnical engineering. The use of SEM as an innovative approach offers significant improvements in the accuracy and reliability of slope stability assessments, especially in accounting for the complex interactions between roots and soil. The inclusion of empirical data from field studies and laboratory tests enhances the validity and applicability of the study, especially in regions like Nepal where slope stability is a critical issue. However, the paper could have benefited from a more detailed discussion on the limitations of the SEM approach, especially under variable environmental conditions that may affect the generalizability of the results. Although the authors have provided a solid framework for assessing the behavior of rooted soils, there is a lack of consideration of the potential variability of root properties across species and environmental conditions, which could affect the conclusions of the study. Furthermore, although the study effectively combines qualitative and quantitative assessments, future research could provide more insight into how these findings can be integrated into broader geotechnical practices and policy development. The scope of the literature review should be expanded, there are many papers reporting similar studies, and comparisons of our results with data from the literature should be discussed in a broader Discussion. The quality and readability of Figures 1 and 9-14 should be improved. Overall, the paper makes a significant contribution to the field, offering both a novel methodological approach and practical insights, but it would be helpful to discuss the scope of applicability and limitations of the proposed methodology.

We sincerely appreciate your detailed and constructive feedback on our study. Your recognition of our work and your valuable suggestions are highly appreciated. Below are our responses to the points you have raised:

1. Limitations of SEM under Variable Environmental Conditions:

The discussion on the Spectral Element Method (SEM) has been crafted to highlight its strengths in slope stability analysis. However, we acknowledge the importance of addressing its performance under varying environmental conditions, such as fluctuations in moisture content or temperature. We ensure this aspect is clearly conveyed, making any necessary adjustments in light of your comments.

2. Variability of Root Properties Across Species and Environmental Conditions:

The variability of root properties is indeed a critical factor in bioengineering applications. While we have aimed to address this within the manuscript, your observation underscores the need for a more comprehensive treatment of how different species and environmental conditions may impact root-soil interactions. We ensure this aspect is clearly conveyed, making any necessary adjustments in light of your comments.

3. Integration into Broader Geotechnical Practices and Policy Development:

The potential for integrating the findings into broader geotechnical practices and policy development is a significant outcome of this research. We ensure this aspect is clearly conveyed, making any necessary adjustments in light of your comments, particularly in the context of regions like Nepal.

4. Expansion of Literature Review and Comparative Discussion:

The literature review has been designed to position our study within the broader context of existing research within the current body of knowledge, focusing on relevant analysis and modeling. We appreciate your suggestion to expand this section.

5. Improvement of Figures 1 and 9-14:

The clarity and readability of figures are essential for effective communication. We have made efforts to present the figures in a clear and detailed manner, but we are fully prepared to enhance these visuals further based on your observations to ensure they meet the highest standards of presentation.

6. Scope of Applicability and Limitations of the Methodology:

Thank you for highlighting the need to discuss potential limitations. The 3D Spectral Element Method (SEM) consistently delivers satisfactory results even in complex scenarios, such as highly nonlinear material behavior, the presence of discontinuities, dynamic loading conditions, and intricate soil-water interactions. SEM, as a higher-order FEM, provides superior accuracy and efficiency compared to many traditional FEM methods. It excels in capturing detailed stress and strain distributions while significantly reducing computational costs. This robustness across various challenging conditions underscores SEM's advantages over conventional methods. We ensure this aspect is clearly conveyed, making any necessary adjustments in light of your comments.