Rainfall-Induced Landslide Stability for Variably Shaped Slopes: A Multi-Model Integration Approach Through Green-Ampt Theory and Numerical Validation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript entitled "Rainfall-Induced Landslide Stability for Variably Shaped Slopes: A Multi-Model Integration Approach Through Green- Ampt Theory and Numerical Validation", presents an interesting work.

A comprehensive analytical approach for examining rainfall-triggered slope instability mechanisms in various morphological configurations is presented in this paper. The relevant geological models for linear, concave, and convex slopes were created in this article, and the Green-Ampt infiltration model was used to derive the infiltration models of slopes with various forms under high and low intensity rainfall conditions. The stability calculation models of slopes under two rainfall situations were then created and the stability change laws of slopes were investigated in conjunction with the limit equilibrium analysis approach. Additionally, numerical modeling was used to evaluate and examine the infiltration law and stability of slopes of various shapes under situations of heavy and low rainfall.

In general, the manuscript should be acceptable for publication but some problems must be repaired prior to publication. It needs some significant improvement. Some suggestions are as follows:

-All three models—linear, concave, and convex—were examined in case studies, but only the linear and convex models were examined in the theoretical analysis of slope stability. The concave slope model must also be theoretically described.
-In addition, since it is a research study, the article lacks an introduction that includes the research's goals, hypothesis, and techniques. The purpose of this work should be more clearly stated.
-The authors' use of theoretical data rather than actual terrain slope data is the paper's worst flaw, or none of the chapters describe it, at the very least. True, precise information regarding the data used is lacking, such as a digital terrain model of a test location, how it was acquired, which methods were employed to build the terrain's slope, etc. The authors might utilize simulated data if they don't have actual data, however this is also not explained.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Major Comment

A major limitation of the manuscript is the lack of comparison with real landslide case studies. Additionally, the calibration parameters are not sufficiently justified.

Minor comment

Lines 82–90: The authors should clearly emphasize the main novelty and scientific contribution of the study in this section. Overall, the Introduction is well written, and the logical flow and consistency of the presented background information are acceptable.

Discussion Section:the discussion section is relatively weak and requires significant improvement. Specifically:The results are not adequately compared with findings from previous studies. A deeper physical interpretation of the results is needed. Practical engineering implications and real-world applications should be clearly discussed. 

 

The authors are encouraged to.compare model predictions with observed landslide events where possible.Provide stronger justification for parameter selection and calibration procedures. include statistical validation metrics (e.g., RMSE or similar quantitative error measures) to demonstrate model reliability.

Figure 1:The quality of Figure 1 is relatively weak. The symbols, labels, and text are difficult to read. The figure resolution and font size should be improved to ensure clarity. 

Line 189:The notation X∗X∗ and Z∗Z∗ used in the text is inconsistent with the indices shown in the corresponding figure. Please revise for consistency between equations and graphical representations.

Lines 197–216:Several equations presented in this section are not sufficiently referenced or explained within the text. Each equation should be clearly introduced and its physical meaning discussed.

Figure 8:The quality of Figure 8 is also insufficient. The resolution and readability should be improved, particularly the axis labels and annotations.

The reference list is not sufficiently up to date. Many cited studies are relatively old; therefore, the authors are encouraged to include more recent and relevant literature to better reflect current developments in the field.

 

 

Comments on the Quality of English Language

Line 43: English language editing is required. Several sentences are overly long, which reduces clarity. There are occasional grammatical inconsistencies, and some passive constructions obscure the intended meaning. Careful language revision is recommended to improve readability.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Dear Editor,

I went through the manuscript titled “Rainfall-Induced Landslide Stability for Variably Shaped Slopes: A Multi-Model Integration Approach Through Green-Ampt Theory and Numerical Validation” which investigates rainfall-triggered slope instability for different slope morphologies (linear, concave, convex) using an analytical framework that integrates Green–Ampt infiltration theory with limit equilibrium stability analysis, supported by numerical verification. I had summarized an evaluation that would provide major issues, minor issues, and overall recommendation. I focused on scientific rigor, novelty, clarity, and methodological soundness. The topic is relevant because rainfall-induced landslides remain a major geohazard and analytical frameworks linking infiltration dynamics and slope geometry are valuable for hazard assessment, which is specially a common issue in China. However, while the study is technically sound in concept, the manuscript currently suffers from methodological ambiguity, insufficient validation, and limited novelty justification. Abstract is too general; it should include key quantitative findings. Discussion section should compare results with previous studies. Several sections need clarification before the work can be considered robust. The manuscript lacks a clear structure constructed as Datasets, Methods, Results and Discussion sections as all the mentioned presented are all mixed when they should be separated distinctly. Besides those, there are critical issues that need to be addressed, such as while the slope morphology models (linear, concave and convex) are presented initially why the numerical simulation of concave model merely was presented. I summarized the issues in more detail as below.

1. Major Issues

1.1 Novelty and contribution are not clearly established.

The manuscript claims a “multi-model integration approach” but similar approaches combining Green-Ampt infiltration with limit equilibrium slope stability analysis have been widely used. The authors should clearly explain what new theoretical contribution this work provides, how this differs from existing infiltration-stability coupled models, as whether the novelty lies : (1) the analytical derivation, (2) the treatment of slope curvature, (3) the integration procedure between infiltration and stability models, (4) the comparative analysis of slope morphologies or the numerical verification. Currently this distinction is weak. I recommendation add a paragraph in the introduction comparing with the existing rainfall infiltration–slope stability models studies analyzing slope geometry effects previous Green-Ampt based stability frameworks and explicitly state: (1) what gap in the literature the study addresses, (2) how the proposed framework differs from existing infiltration–stability models, (3) and what new insights the model provides for slope failure prediction.

1.2 Assumptions of Infiltration Model (Green–Ampt Model) are not discussed.

The Green–Ampt infiltration model assumes (1) homogeneous soil, (2) sharp wetting front, (3) constant hydraulic conductivity, and (4) uniform rainfall infiltration. These assumptions rarely present in natural slopes. Soil heterogeneity, layered structures, and preferential flow pathways often influence infiltration processes. The manuscript does not sufficiently discuss how these limitations influence slope stability predictions. My recommendation is to add discussion on heterogeneity effects, preferential flow and layered soils with anisotropic permeability conditions and provide a clearer discussion of the implications of these assumptions for slope stability prediction.

1.3 Validation strategy is insufficient.

The manuscript mentions numerical validation while it is not described clearly it appears to rely primarily on model comparison rather than empirical validation. However, the main problem is the terminology and related work related with the “theoretical calculations” used in comparison with numerical calculations that is not clear what the authors meant by that. Since all the numerical calculations are constructed on theoretical equations and their calculations that are set up for specific models, the authors should clearly state what they meant with the “theoretical calculations”. Besides that, the errors of the slope stability of models should be explained clearly. I am not sure what are these errors represent amongst what.

Important missing elements are no real field landslide case, experimental infiltration data nor monitoring datasets existing in comparison. This limits the confidence in the proposed analytical solution. My recommendation is to strengthen the validation using at least one of the followings; a real landslide case comparison, rainfall-induced failure monitoring, data laboratory infiltration tests or comparison with widely used numerical models (e.g., seepage FEM). Without validation, the model remains largely theoretical.

1.4 Slope geometry representation needs clarification.

The study analyzes linear, concave, and convex slopes, but several methodological questions remain as: How exactly is curvature incorporated into the analytical model? Are slopes represented using geometric functions? How does curvature influence infiltration depth mathematically? While the concept is interesting, the mathematical representation of slope curvature is not sufficiently explained. Specifically, the manuscript should clarify: (1) how slope curvature is parameterized, (2) how geometry influences infiltration depth, (3) and how curvature affects pore pressure distribution and stability calculations. The derivations are not always easy to follow. My recommendation is to add schematic diagrams of slope geometry, clearer parameter definitions, and step-by-step derivation explanations. Additional schematic diagrams illustrating the modelling framework would significantly improve clarity.

1.5 Sensitivity analysis is missing.

Slope stability predictions depend strongly on several parameters, including: (1) rainfall intensity, (2) hydraulic conductivity, (3) soil cohesion, (4) friction angle, (5) suction head. The manuscript would be significantly improved by a sensitivity analysis showing which parameters control failure most strongly. Such analysis would help identify the dominant controls on rainfall-induced slope failure.

2. Moderate Issues

2.1 Literature review needs expansion.

The literature review focuses heavily on analytical models but omits many recent landslide hydrology studies. Include references related to: (1) rainfall thresholds for landslides, (2) hydrological slope stability modeling, (3) coupled hydro-mechanical approaches

2.2 Clarity of equations and variable definitions are missing.

Several equations appear without sufficient explanation. Problems include (1) variables introduced without definition, (2) missing units, and (3) unclear boundary conditions. A nomenclature table would help readers as well as tables for all models and conditions and used units. In the table where the model parameters were described, why these values were used was not explained.

2.3 Numerical model description is too brief.

The numerical verification section lacks details, such as; (1) explanation of software used, (2) mesh configuration, (3) boundary conditions and (4) hydraulic parameters, (5) convergence criteria in the Methods section. Without this information the results are difficult to reproduce.

4. Minor Comments

The authors are recommended to improve English grammar in several sections (some sentences are overly long). Figures need clearer axis labels and units. There are also typos that should be corrected line in the conclusions section in page 22 line 594 with the word “results” and line 600 with “40 °” (delete the space between number and degree). Also please put space between the numbers and m, and define the acronyms such as d as day (d) in the paper in the beginning and similar with the others so on.

Despite the issues of strengths of the study, the paper has several positive aspects as; it is a relevant topic in geohazard research, it attempts to connect infiltration mechanics and slope morphology. Analytical framework may be useful for rapid hazard screening and multi-geometry comparison is interesting. In conclusion, I recommend a major revision of the manuscript for regarding the comments above for a second consideration of publication in the journal. The manuscript has potential but requires clearer novelty statement, stronger validation, improved methodological transparency, deeper discussion of assumptions. If these issues are addressed, the work could become a useful analytical contribution to rainfall-induced landslide modeling. 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Based on the feedback provided, the manuscript has been suitably improved. It has been conceptually developed. The article's methodological section has also been enhanced. I see that the rewritten manuscript's internal validity has also improved.

I would only suggest to the authors to correct the article regarding the references. Several problems are observed that the authors should correct:

The first is that in the added text in the introduction of the article, I assume that the automatic system for generating references has not worked properly and the text appears that an Error has occurred! Reference source not found.

The text's lack of a reference under serial number 16 is the second issue.

in line 204 there is a reference that is not according to the instructions for citing in the text of the article.

The final, and possibly most significant, issue is that the introduction chapter includes a list of all the references cited throughout the paper. Then, they are absent throughout the entire paper, particularly in the section that describes the process and makes extensive use of equations. This gives us the impression that the authors created and specified mathematical equations, even though many of them were undoubtedly used using sources that aren't mentioned in this case. It is recommended that the authors of the article go over the entire document and include the relevant references when necessary. Only the discussion and conclusion section at the end of the article contains references.

Author Response

1. Response to comment: The first is that in the added text in the introduction of the article, I assume that the automatic system for generating references has not worked properly and the text appears that an Error has occurred! Reference source not found.

Response: Thank you very much for your valuable comment and careful review. We sincerely appreciate your pointing out this issue. We have thoroughly checked the automatic reference generation system and found that it malfunctioned when generating references for the newly added text in the introduction, which led to the abnormal prompt "Error has occurred! Reference source not found". We have promptly fixed the system fault, deleted the abnormal prompt, and re-verified the reference sources and citation formats of the newly added text in the introduction to ensure that all references are accurately cited, the sources are reliable, and the formats are standardized. We apologize for the inconvenience caused by this mistake and will strictly check the entire manuscript again to avoid similar problems.

2. Response to comment: The text's lack of a reference under serial number 16 is the second issue.

Response: hank you very much for your valuable comment and careful review. We sincerely appreciate your pointing out this issue. We have carefully checked the reference list and confirmed that the reference under serial number 16 is indeed missing. We have promptly supplemented the complete information of the 16th reference, including the author, title, journal name, publication year, volume, issue and page numbers, to ensure the completeness and standardization of the reference list. We apologize for the oversight in the previous revision and will conduct a comprehensive check of the entire reference list.

3. Response to comment: in line 204 there is a reference that is not according to the instructions for citing in the text of the article.

Response: Thank you for your suggestions. We have checked the citation format of the reference in line 204 and revised it in strict accordance with the citation guidelines required by the article to ensure that the citation format is consistent with the rest of the article.

4. Response to comment: The final, and possibly most significant, issue is that the introduction chapter includes a list of all the references cited throughout the paper. Then, they are absent throughout the entire paper, particularly in the section that describes the process and makes extensive use of equations. This gives us the impression that the authors created and specified mathematical equations, even though many of them were undoubtedly used using sources that aren't mentioned in this case. It is recommended that the authors of the article go over the entire document and include the relevant references when necessary. Only the discussion and conclusion section at the end of the article contains references.

Response: Thank you very much for this valuable and constructive comment. We highly appreciate your careful review and rigorous academic attitude.

We fully agree with your concern about the citation of references and the theoretical source of equations. We apologize for the inappropriate citation arrangement in the original manuscript, which may lead to misunderstanding.

In fact, all the analytical models and mathematical equations proposed in this paper are derived by the authors based on the classic Green–Ampt infiltration model (Ref. [16]) and the Mein–Larson model (Ref. [18]), rather than being put forward arbitrarily. The core theoretical framework comes from the above two classical literatures, and our contribution is to extend them to variably shaped concave and convex slopes and establish a new coupled infiltration-stability analytical solution.

In the revision, we will carefully check the full text and add necessary citations in the corresponding positions, especially:

Add citations of Ref. [16] when introducing the basic Green–Ampt model and deriving the fundamental infiltration equations.

Add citations of Ref. [18] when describing rainfall infiltration regimes and improving the model for sloping surfaces.

Supplement relevant citations in the process of formula derivation and theoretical analysis to clearly indicate the source of basic theories.

We will ensure that every key theoretical basis and formula derivation process is supported by formal references, so as to improve the standardization and academic rigor of the manuscript.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

No further comments.

Comments on the Quality of English Language

Line 43: English language editing is required. Several sentences are overly long, which reduces clarity. There are occasional grammatical inconsistencies, and some passive constructions obscure the intended meaning. Careful language revision is recommended to improve readability.

Author Response

1. Response to comment: Line 43: English language editing is required. Several sentences are overly long, which reduces clarity. There are occasional grammatical inconsistencies, and some passive constructions obscure the intended meaning. Careful language revision is recommended to improve readability.

Response: Thank you for your valuable suggestion on English language editing.

We have carefully revised the entire manuscript to shorten overly long sentences, correct grammatical issues, and optimize sentence structures for better clarity and readability.

In addition, we have used the professional English language editing service provided by MDPI to further polish the language of the paper. We believe the readability and academic presentation of the manuscript have been significantly improved.

We believe these revisions have substantially strengthened the manuscript and addressed all concerns raised. We are grateful for your guidance and hope that the revised version now meets the standards for publication in Geosciences.

Author Response File: Author Response.pdf