Predicting Railway Slope Failure Under Heavy Rainfall Using the Soil Moisture Extended Cohesive Damage Element Method

Round 1

Reviewer 1 Report (Previous Reviewer 2)

Comments and Suggestions for Authors

1. The Introduction section requires to be reorganized. Most literatures are out of date. Several latest literatures can be involved. For example,

X Gu, WG Zhang, Q Ou, X Zhu, CB Qin. Conditional random field-based stochastic analysis of unsaturated slope stability combining Hoffman method and Bayesian updating. Engineering Geology,2024, 330: 107415.

X Gu, L Wang, Q Ou, WG Zhang*. Efficient stochastic analysis of unsaturated slopes subjected to various rainfall intensities and patterns. Geoscience Frontiers, 2023, 14(1): 101490.

2. Also, in the Introduction section, the current research progress of railway slope failure should be briefly reviewed.
3. How to validate the accuracy of the proposed equation (1).
4. Please discuss the numerical model accuracy, such as the effects of different mesh sizes, model boundary range.
5. It should be mentioned that the railway train load is simplified as a linearly distributed loading. Then, the disturbance from the train to the embankment will be overlooked.
6. In Tables 4 and 5: The unit for soil friction angle is missing.
7. The notations in all figures should be enlarged.

Author Response

Reviewer 1

“The Introduction section requires to be reorganized. Also, in the Introduction section, the current research progress of railway slope failure should be briefly reviewed.”

Response: Thanks for this comment. The introduction section has revised a paragraph to reflect railway slope failure analysis outcomes.

“Most literatures are out of date. Several latest literatures can be involved. For example,

X Gu, WG Zhang, Q Ou, X Zhu, CB Qin. Conditional random field-based stochastic analysis of unsaturated slope stability combining Hoffman method and Bayesian updating. Engineering Geology,2024, 330: 107415.

X Gu, L Wang, Q Ou, WG Zhang*. Efficient stochastic analysis of unsaturated slopes subjected to various rainfall intensities and patterns. Geoscience Frontiers, 2023, 14(1): 101490.”

Response: Thanks for this comment, recommended two papers are cited in the introduction section in the revised version.

“How to validate the accuracy of the proposed equation (1).”

Response: Thanks for this comment. Validation of equation 1 was done by verifying equation 2 using Table 1 as manuscript mentioned: Table 1 also shows the calculated values of soil moisture a using Eq. 2. The averaged error from Eq. 2 is about 3% compared to forecasted values of soil moisture, which indicates Eq. 2 is a good correlation for rainfall intensity and soil moisture based on the provided meteorological data at Kent region, UK, from March to May 2022.

 

“Please discuss the numerical model accuracy, such as the effects of different mesh sizes, model boundary range.”

Response: Thanks for this comment. Manuscript has amended one paragraph as below: The mesh density, as shown in Figure 11, varies with element sizes ranging from 0.1 to 0.25 meters for good accuracy. The proposed SMECDE element, consisting of four nodes, is used in the numerical mesh for the simulation. This element has very good iteration accuracy in a relatively wide range of mess densities. Its detailed mess independence can be seen in [20-27].  

“It should be mentioned that the railway train load is simplified as a linearly distributed loading. Then, the disturbance from the train to the embankment will be overlooked.”

Response: Many thanks for this comment. This suggestion is accepted in the revised version.

“In Tables 4 and 5: The unit for soil friction angle is missing.”

Response: thanks for this comment. It was added into the revised version now.

“The notations in all figures should be enlarged.”

Response: This comment was accepted by the revised version.

Reviewer 2 Report (Previous Reviewer 3)

Comments and Suggestions for Authors

This paper introduces the Soil Moisture Extended Cohesive Damage Element (SMECDE) method to predict railway slope failure under heavy rainfall, correlating rainfall intensity with soil moisture. It develops a soil moisture decohesion model (SMDM) and validates predictions using field data and FEM analysis, offering a new approach for slope failure forecasting.

 

The paper presents a new approach (SMECDE method) but does not explicitly justify why this method is superior to existing models beyond mentioning limitations of previous approaches. The transition from rainfall intensity to soil moisture correlation should be better explained, especially how curve fitting was performed for parameter determination.

While the study states that it predicts railway slope failures, it does not clearly outline how its results advance previous research beyond citing past limitations. The validation section is weak—there is an attempt to validate with past meteorological data, but the claim of validation using ABAQUS is partial, as it does not account for all failure mechanisms. The assumptions made in defining the correlation parameters (e.g., nn and kk) need further justification. The study assumes a linear correlation between soil cohesion and depth but does not account for non-homogeneous soil conditions or variations due to underground water presence. The conclusion suggests the model can be used for real-time forecasting, but it does not account for dynamic factors like soil compaction variations or long-term degradation.

The paper should better highlight gaps in previous studies and clearly state how its approach overcomes these limitations. Instead of just listing prior studies, a comparative discussion would improve coherence. The correlation models should be better explained with equations formatted more clearly. The figures need stronger captions that describe their relevance to the study. The conclusions should reflect the limitations of the model more explicitly.

Comments on the Quality of English Language

Many sentences are excessively long and complex. For example:

"It should be noticed that the points shown on the figure are tested data from previous experiment work [16 - 19] (same to Figs. 2 to 6)."

Incorrect use of words:

"Slope failure includes natural slope failure (landslides) and engineered slope failure, such as railway embankment slope collapse."

"Rainfall infiltration directly causes moisture changes in soil, which is a critical factor in soil cohesion reduction."

Tense Consistency is missing in the entire length of paper,

Author Response

Reviewer 2

“The paper presents a new approach (SMECDE method) but does not explicitly justify why this method is superior to existing models beyond mentioning limitations of previous approaches. While the study states that it predicts railway slope failures, it does not clearly outline how its results advance previous research beyond citing past limitations.”

Response: Thanks for all comments. Manuscript has revised the following sentence: In this paper, a novel approach is developed by incorporating the proposed soil moisture decohesion model (SMDM) into the extended cohesive damage element (ECDE) method to predict progressive slope failure under heavy rainfall. This prediction of slope failure under heavy rainfall filled the research gaps which was not done by previous investigation. The outcomes from this paper can be used for making decision by railway management sectors in terms of weather forecast.

“The transition from rainfall intensity to soil moisture correlation should be better explained, especially how curve fitting was performed for parameter determination.”

Response: The correlation between rainfall intensity and soil moisture was given by a proposed mathematical equation 1 and was verified using data in Table 1.

“The validation section is weak—there is an attempt to validate with past meteorological data, but the claim of validation using ABAQUS is partial, as it does not account for all failure mechanisms. “

Response: The example investigated in this paper is of course the past event. Predicted critical values for rainfall intensity and moisture should be compared with past meteorological data. ABAQUS large deformation analysis can only partially validate the numerical analysis of new methodology due to limit function in commercial software. Together with validated critical meteorological data, the slope failure mechanisms under heavy rainfall should be validated.

“The assumptions made in defining the correlation parameters (e.g., nn and kk) need further justification.”

Response: The manuscript has justified these parameters through Table 1 for the investigated slope site. These parameters would vary with different locations.

 

“The study assumes a linear correlation between soil cohesion and depth but does not account for non-homogeneous soil conditions or variations due to underground water presence. The conclusion suggests the model can be used for real-time forecasting, but it does not account for dynamic factors like soil compaction variations or long-term degradation.”

Response: This investigation focusses on the railway embankment slope, which consists of manually prepared engineering soil materials with aggregates. Follow the usual way in previous investigation to treat it as homogeneous slope material. Underground water presence would be usually ignored in the railway embankment slope scenario because it is not very deep in the underground water affected area.  For prediction of natural slope failure under heavy rainfall, it is rather complex case, it needs consider non-homogeneous slope materials, varied rainfall time period effects and fatigue effects including compaction variations or long-term degradation, but this would be the future work. Railway embankment slope would be mainly affected by rainfall intensity or soil moisture, soil depth and average rainfall time period.   

“The paper should better highlight gaps in previous studies and clearly state how its approach overcomes these limitations. Instead of just listing prior studies, a comparative discussion would improve coherence. The correlation models should be better explained with equations formatted more clearly. “

Response: Research gaps have been highlighted in the revised version. More explanation of correlation models are added in the revised version.  

The figures need stronger captions that describe their relevance to the study. The conclusions should reflect the limitations of the model more explicitly.

Response: caption to each figure has been revised for better review. The conclusion section mentioned the limit of the model will be covered by the future work.

Many sentences are excessively long and complex. For example:

"It should be noticed that the points shown on the figure are tested data from previous experiment work [16 - 19] (same to Figs. 2 to 6)."

Response: This sentence was changed in the new version as: It should be noted that the points shown in the figure are data from previous experiments [16-19] (the same as in Figs. 2 to 6). This sentence should be within reasonable length.

“Incorrect use of words: Slope failure includes natural slope failure (landslides) and engineered slope failure, such as railway embankment slope collapse."

Response: this sentence is changed in the new version as: Slope failure includes both natural slope failure (landslides) and engineered slope failure, such as the collapse of railway embankments.

"Rainfall infiltration directly causes moisture changes in soil, which is a critical factor in soil cohesion reduction."

Response: This sentence is revised as: Rainfall infiltration directly causes changes in soil moisture, which is a critical factor in the reduction of soil cohesion.

Reviewer 3 Report (Previous Reviewer 4)

Comments and Suggestions for Authors

Dear Authors

I went through the revision, but it seems that some of the outlined points have not been properly considered.

For example:

• fig 9 caption has not been ameliorated
• values of stiffness moduli, friction angle , poisson ratio in table 4-5 seem unrealistic in terms of precision: engineering approach cannot supporty with that level of precision
• the case presented seems to be affected by problems of design or construction and accpetance of as built; a  sophisticated  parametric  analysis can help but not when overhanging problems are present

Best Regards

Author Response

Reviewer 3

“I went through the revision, but it seems that some of the outlined points have not been properly considered. For example:

fig 9 caption has not been ameliorated.”

Response: This caption is revised as: Railway embankment slope with a weak surface (a) and a case of failure in Kent, UK (b).

“values of stiffness moduli, friction angle , poisson ratio in table 4-5 seem unrealistic in terms of precision: engineering approach cannot supporty with that level of precision.”

Response: Thanks for this comment. Table 4 has revised all parameters at the ground service values as integers. Table 5 keeps two decimals considering accuracy in numerical analysis.   

“the case presented seems to be affected by problems of design or construction and accpetance of as built; a sophisticated parametric analysis can help but not when overhanging problems are present”

Response: Thanks for this comment. Authors are dealing with the problem reported by industrial partners in the reference [17]. Certainly, the railway embankment slope was designed and built several decades ago. It would be failed only in the heavy rainfall conditions. Our investigation tries to explain its failure mechanisms under heavy rainfall.

Reviewer 4 Report (New Reviewer)

Comments and Suggestions for Authors

In this paper, a soil moisture extended cohesive damage element (SMECDE) method is proposed to predict the occurrence of railway slope instability under intense rainfall conditions. In the article, the correlation between rainfall intensity and soil moisture is established, and the soil moisture decoupling model (SMDM) is combined with the extended cohesive damage element (ECDE) method to predict the instability process of railway slopes under different soil moisture and rainfall intensities, and the method is applied to carry out a case study of railway slopes in the Kent region of the UK. The manuscript can be accepted after a series of modifications. The following concerns should be addressed by the publication is considered:

1. Line 68 lacks punctuation at the end of the paragraph.
2. There are a number of misspellings in the literature. For example, in line 178, "Lomay" should be "Loamy", and "Young’s modules" should be "Young’s modulus". In line 240, "cab" should be "can", and in line 463, "models" should be "modulus". Please check carefully.
3. In Figure 5 and in line 226 the unit should be "kPa".
4. Does "Fig. 8b" in line 497 correspond? Please check.
5. Some formulas are not typographically consistent (e.g., variable symbols in Eq. 1 and Eq. 2) and need to be checked for consistency throughout the text.
6. The limitations of existing models (e.g. PFEM) need to be described more specifically in the article, e.g. by pointing out their shortcomings in the "prediction of rainfall triggering conditions".
7. The model assumptions section of the article mentions that the effect of groundwater on soil moisture and cohesion is ignored, and it is suggested that the authors further elucidate the effect of this assumption on the model predictions.
8. The physical significance of the parameters n and k in Eq. 1 needs to be further clarified, e.g. whether they are based on properties such as soil permeability or porosity, or whether they are only the result of mathematical fitting. The choice of values for n and k in Eq. 32 needs further elaboration.
9. The description of the integration process between SMECDE and ABAQUS is too brief, and it is recommended to provide the complete input parameters (e.g., mesh dimensions, boundary conditions) of the validation case to enhance reproducibility.
10. The article focuses only on railway slopes in the Kent region of the UK in the case study and is modelled with soil moisture and precipitation intensity data from selected sites. However, lacks an exploration of the wider applicability of the model to different regions or different types of soil conditions.

Author Response

Reviewer 4

Line 68 lacks punctuation at the end of the paragraph.

Response: It is added in the revised version.

“There are a number of misspellings in the literature. For example, in line 178, "Lomay" should be "Loamy", and "Young’s modulus" should be "Young’s modulus". In line 240, "cab" should be "can", and in line 463, "models" should be "modulus". Please check carefully.”

Response: many thanks for indications. All typos are corrected in the revised version.

In Figure 5 and in line 226 the unit should be "kPa".

Response: This typo is corrected in the revised version.

“Does "Fig. 8b" in line 497 correspond? Please check.”

Response: thanks for this comment. There is no Fig. 8b. In Fig. 9b is a picture showing a railway embankment slope failure in Kent region, UK.

“Some formulas are not typographically consistent (e.g., variable symbols in Eq. 1 and Eq. 2) and need to be checked for consistency throughout the text.”

Response: After checking, authors confirms that variable symbols in Eq. 1 and Eq. 2 are all correct.

“The limitations of existing models (e.g. PFEM) need to be described more specifically in the article, e.g. by pointing out their shortcomings in the "prediction of rainfall triggering conditions".

Response: manuscripts mentioned this as: However, the PFEM has limitations in forecasting initiation and the starting location of slope failure under heavy rainfall condition.

“The model assumptions section of the article mentions that the effect of groundwater on soil moisture and cohesion is ignored, and it is suggested that the authors further elucidate the effect of this assumption on the model predictions.”

Response: Thanks for this comment. This paper is dealing with railway embankment slope failure. Its geometry is not very deep to involve underground water effects. When considering natural slope failure, it should consider underground water effects on the correlation between soil moisture and depth, which would increase moisture in the underground water affected area.

“The physical significance of the parameters n and k in Eq. 1 needs to be further clarified, e.g. whether they are based on properties such as soil permeability or porosity, or whether they are only the result of mathematical fitting. The choice of values for n and k in Eq. 32 needs further elaboration.”

Response: Eq. 1 is purely mathematical way to present correlation between weather forecasted rainfall intensity and ground surface moisture. It does not relate to soil permeability or porosity. Soil physical property would affect correlation between soil moisture and depth.

“The description of the integration process between SMECDE and ABAQUS is too brief, and it is recommended to provide the complete input parameters (e.g., mesh dimensions, boundary conditions) of the validation case to enhance reproducibility.”

Response: thanks for this comment. Considering the length of this paper, manuscript has mentioned enough information about mesh density and boundary conditions as below: Fig. 11 depicts a basic SMECDE model of half of the railway embankment slope, with the following boundary conditions: symmetrical restraints applied at the left edge and fixed restraints applied at the bottom of the model. The mesh density, as shown in Figure 11, varies with element sizes ranging from 0.1 to 0.25 meters for good accuracy. The pro-posed SMECDE element, consisting of four nodes, is used in the numerical mesh for the simulation. This element has very good iteration accuracy in a relatively wide range of mess densities. Its detailed mess independence can be seen in [20-27].

“The article focuses only on railway slopes in the Kent region of the UK in the case study and is modelled with soil moisture and precipitation intensity data from selected sites. However, lacks an exploration of the wider applicability of the model to different regions or different types of soil conditions.”

Response: thanks for this comment. Authors hope to explore more application in the future work.  

Round 2

Reviewer 3 Report (Previous Reviewer 4)

Comments and Suggestions for Authors

No other issue.

Regards

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The study addresses an important topic with potential for meaningful contributions to the field. However, the manuscript currently faces several challenges that significantly hinder its clarity, rigor, and scientific value. Below, I provide detailed feedback on areas that require improvement. My comments are intended to assist the authors in refining their work to better meet the standards of scientific publication.

1.      Language and Terminology: The manuscript contains numerous language issues that make it difficult for the reader to follow. For example, there is inconsistent terminology when referring to meteorological data, with some instances mistakenly using "meteoritical" instead of "meteorological." I strongly recommend that the manuscript undergo a thorough review and editing by a native English speaker or a professional language editor. Enhancing the clarity and consistency of the language will significantly improve readability and help convey the authors’ contributions more effectively.

2.      Literature Review: While the literature review includes a wide range of sources, it lacks consistency and a clear structure, which makes it challenging to follow. Reorganizing this section—perhaps thematically or by addressing key research gaps—would help contextualize the study within the existing body of work and better highlight its contributions.

Additionally, some statements require clarification. For instance, in line 75, the statement, “Soil moisture content was determined by (Jim et al., 1999) [11],” is ambiguous. What is the authors’ intention here? Greater specificity would improve the reader’s understanding.

3.      Simplification of Soil Moisture Correlation: The authors’ approach of correlating soil moisture solely with rainfall intensity appears overly simplistic. While rainfall intensity is a key factor, soil moisture is influenced by many other variables, including rainfall duration and frequency, temperature, humidity, soil properties (e.g., texture, permeability, organic content), land cover, water table depth, and underlying geology. A more detailed discussion of these factors and the conditions under which this simplified approach might hold would significantly enhance the analysis.

4.      Correlation Analysis (Figures 5 and 6): The use of high-order polynomial equations to correlate two parameters based on a small dataset raises concerns about overfitting. This can lead to models that capture noise rather than meaningful relationships, limiting their generalizability. A more robust analysis would involve simpler models unless there is strong theoretical justification for using a high-order polynomial. If the latter is the case, the authors should provide clear theoretical support, demonstrate that overfitting is not occurring, and evaluate the model’s predictive performance through techniques such as cross-validation.

5.      Data Presentation (Figure 1 and Table 1): There are discrepancies between the data presented in Figure 1 and Table 1, yet it is implied that they refer to the same dataset. The authors should clarify this and specify whether the dataset is measured data or sourced from a weather forecasting agency. Additionally, λ is expressed in mm per hour but is given over a three-day interval. Is this the average over the period, or a single value within that range? Greater precision in describing the dataset is necessary.

 

6.      Relevance of Loamy Soil: In line 120, the authors state that the parameters can be determined by soil testing. However, the specific tests are not identified. It appears that the authors did not conduct these tests but instead relied on literature data for loamy soil.

 

Loamy soil, a mixture of sand, silt, and clay, is primarily used for plant growth and is generally not used for earthworks. Its use is prohibited by many design codes. The paper would benefit from more detailed characterization of the loamy soil properties (e.g., grain size distribution, void ratio) and justification of its relevance to the Kent railway embankment analysis. The material properties should align with those of the embankment under study to ensure that the analysis in Chapters 6 and 7 has practical relevance. Otherwise, the conclusions drawn from this analysis may be of limited value.

These issues compromise the validity and relevance of section 7. I recommend addressing the concerns and refine the analysis and conclusions.

Comments on the Quality of English Language

Please do a thorough review and editing by a native English speaker or a professional language editor.

Author Response

Reviewer 1

The study addresses an important topic with potential for meaningful contributions to the field. However, the manuscript currently faces several challenges that significantly hinder its clarity, rigor, and scientific value. Below, I provide detailed feedback on areas that require improvement. My comments are intended to assist the authors in refining their work to better meet the standards of scientific publication.

Response: thanks a lot for this comment.

1. Language and Terminology: The manuscript contains numerous language issues that make it difficult for the reader to follow. For example, there is inconsistent terminology when referring to meteorological data, with some instances mistakenly using "meteorological" instead of "meteorological." I strongly recommend that the manuscript undergo a thorough review and editing by a native English speaker or a professional language editor. Enhancing the clarity and consistency of the language will significantly improve readability and help convey the authors’ contributions more effectively.

Response: Many thanks for this comment and suggestion. We including a native speaker have carefully checked and corrected English in the whole manuscript.

2. Literature Review: While the literature review includes a wide range of sources, it lacks consistency and a clear structure, which makes it challenging to follow. Reorganizing this section—perhaps thematically or by addressing key research gaps—would help contextualize the study within the existing body of work and better highlight its contributions.

Response: Thanks for the comment. We have slightly modified the literature review section to be better in reflecting major features including contributions and research gaps in previous work.

Additionally, some statements require clarification. For instance, in line 75, the statement, “Soil moisture content was determined by (Jim et al., 1999) [11],” is ambiguous. What is the authors’ intention here? Greater specificity would improve the reader’s understanding.

Response: Thanks for this comment. The corresponding sentence is changed as: soil moisture content can be defined as a volumetric soil moisture content: the volume of water in the soil as a fraction or percentage of the total soil volume [11], in the updated version.

3. Simplification of Soil Moisture Correlation: The authors’ approach of correlating soil moisture solely with rainfall intensity appears overly simplistic. While rainfall intensity is a key factor, soil moisture is influenced by many other variables, including rainfall duration and frequency, temperature, humidity, soil properties (e.g., texture, permeability, organic content), land cover, water table depth, and underlying geology. A more detailed discussion of these factors and the conditions under which this simplified approach might hold would significantly enhance the analysis.

Response: many thanks for this comment. We agree with reviewer’s comment. The following sentences are added into the updated version: The soil moisture is mainly affected by rainfall intensity and soil depth. Other variables including rainfall duration and frequency, temperature, humidity, soil properties, land cover, water table depth, and underlying geology would also have influence. This is a rather complex topic, one investigation would be difficult to cover all variables. Progressively investigating different variables is a practical approach. This investigation focusses on the major factors, e.g. rainfall intensity and soil depth in a selected site with determined soil properties. Other variables’ effects, including rainfall duration, on soil moisture can be studied in the future work.

4. Correlation Analysis (Figures 5 and 6): The use of high-order polynomial equations to correlate two parameters based on a small dataset raises concerns about overfitting. This can lead to models that capture noise rather than meaningful relationships, limiting their generalizability. A more robust analysis would involve simpler models unless there is strong theoretical justification for using a high-order polynomial. If the latter is the case, the authors should provide clear theoretical support, demonstrate that overfitting is not occurring, and evaluate the model’s predictive performance through techniques such as cross-validation.

Response: Thanks for this comment. In general, soil properties vary with different soil types at different sites. Authors think it is hard to use theoretical formulas to express them due to uncertain parameters which need verification using different soil samples at different sites and variable moistures. This investigation used previous experimental test data to work out high-order polynomial equations which is better to reflect real tested features of investigated soil type in the selected site. We think this correlation based on experimental work is a realistic way.   

5. Data Presentation (Figure 1 and Table 1): There are discrepancies between the data presented in Figure 1 and Table 1, yet it is implied that they refer to the same dataset. The authors should clarify this and specify whether the dataset is measured data or sourced from a weather forecasting agency. Additionally, λ is expressed in mm per hour but is given over a three-day interval. Is this the average over the period, or a single value within that range? Greater precision in describing the dataset is necessary.

Response: Thanks for this comment. Figure 1 is exactly extracted from weather forecast provided by European Centre for Medium-Range Weather Forecasts (ECMWF) in the investigated period. In Table 1, λ (mm/h) is given over a three-day interval which is better to capture significant changes in the investigated period, and to avoid unnecessary numerous data treatment.     

6. Relevance of Loamy Soil: In line 120, the authors state that the parameters can be determined by soil testing. However, the specific tests are not identified. It appears that the authors did not conduct these tests but instead relied on literature data for loamy soil.

Response: Thanks for this comment. Manuscript mentioned this investigation used previous experimental work to conduct soil correlation. Actually, our industrial partners completed relevant test work before out investigation. Especially for investigating loamy soil in the selected site, we thank for previous work to let us enable further investigation. We have provided references [16-19] for readers interests on specific tests, detailed discussion of specific tests would be out of the scope of this investigation.     

Loamy soil, a mixture of sand, silt, and clay, is primarily used for plant growth and is generally not used for earthworks. Its use is prohibited by many design codes. The paper would benefit from more detailed characterization of the loamy soil properties (e.g., grain size distribution, void ratio) and justification of its relevance to the Kent railway embankment analysis. The material properties should align with those of the embankment under study to ensure that the analysis in Chapters 6 and 7 has practical relevance. Otherwise, the conclusions drawn from this analysis may be of limited value. These issues compromise the validity and relevance of section 7. I recommend addressing the concerns and refine the analysis and conclusions.

Response: Many thanks for this comment. Manuscripts presented figure 9 of the Kent railway embankment slope, consisting of basic three layers. The main layers are fillings and foundation, The materials used in these layers are manually prepared slope engineering materials. They would be local loamy soil mixed with others including aggregates. The following sentence is added into the manuscript to clearly present the slope materials: It should be noticed that embankment filings and foundation are the main body of the slope structure with manually prepared slope engineering materials. These materials would be local loamy soil mixed with others including natural aggregates. They are certainly not pure loamy soil but named as loamy soil in this paper for a simple classification. More detailed information of these engineering slope materials can be referred to the given reference in the paper. But discussion of detailed characterization of the loamy soil properties (e.g., grain size distribution, void ratio) and justification of its relevance to the Kent railway embankment analysis would be not the the scope of this paper.  

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript addresses the critical issue of predicting railway slope failure under heavy rainfall conditions by proposing the Soil Moisture Extended Cohesive Damage Element (SMECDE) method. It demonstrates academic innovation by incorporating the influence of soil moisture into cohesive damage modeling, presenting a mathematical framework, and validating it with finite element analysis using ABAQUS. The work is thorough and introduces valuable insights into slope failure mechanisms.

This paper can be accepted after some minor revision, including linguistic clarity, better explanation of model assumptions, and more comprehensive validation of results. Below are my detailed comments.

1.       Language and Clarity

The introduction contains repetitive information about slope failure due to rainfall (e.g., Page 1, Lines 30–42). Consider condensing these descriptions to improve readability and focus.

Some sentences are overly long, making it difficult for readers to follow. For instance, the sentence on Page 2, Lines 77–80, should be split into two sentences, separately discussing the soil moisture model and its integration into the extended cohesive damage element method.ve

The author can refer those paper to modify this manuscript：

Liu, S., Wang, L., Zhang, W., Sun, W., Wang, Y., & Liu, J. (2024). Physics informed optimization for a data-driven approach in landslide susceptibility evaluation. Journal of Rock Mechanics and Geotechnical Engineering. https://doi.org/10.1016/j.jrmge.2023.11.039

Dethier, E.N., Silman, M., Leiva, J.D. et al. A global rise in alluvial mining increases sediment load in tropical rivers. Nature 620, 787–793 (2023). https://doi.org/10.1038/s41586-023-06309-9

WANG Yun-hao, WANG Lu-qi, ZHANG Wen-gang, LIU Song-lin, SUN Wei-xin, HONG Li, ZHU Zheng-wei. A physics-informed machine learning solution for landslide susceptibility mapping based on three dimensional slope stability evaluation [J]. Journal of Central South University, 2024. DOI: https://doi. org/10.1007/s11771-024-5687-3.

2.       Model Assumptions

The correlation model between soil moisture and cohesion (Equations 3 and 4) references experimental data, but the selection criteria for the data and the confidence level of the curve fitting are not sufficiently detailed. Include more information about the data source and explain the physical significance of the fitted parameters.

The definition of "shallow soil" (e.g., depth range) is unclear. Clarify the assumed soil depth in the model and discuss its potential impact on the results.

3.       Figures and Tables

Table 5 (Page 12) presents soil parameters at different depths, but the trends in these values are not analyzed in the text. Add a discussion about how depth influences soil modulus and cohesion.

Figure 12 (Page 13) illustrates the predicted initial damage surfaces for different soil moisture levels but lacks specific numerical data or annotations highlighting the extent of the damage. Consider labeling key data points or adding explanations to the legend.

4.       Validation

The validation relies primarily on displacement contours from ABAQUS simulations (Figure 14, Page 14). While the critical rainfall intensity (66 mm/h) aligns with reported meteorological data, the absence of experimental or field-based validation reduces confidence in the model's accuracy. Include additional experimental data or real-world case studies to strengthen the validation.

The shear crack propagation under heavy rainfall is only theoretically described. Incorporate laboratory experiments or high-resolution simulations to validate the predicted crack paths.

5.       Future Directions

The conclusion mentions future research on "time-dependent effects of soil moisture on cohesion" but does not specify how this will be conducted. Provide concrete plans, such as incorporating dynamic soil moisture monitoring or experimental simulation, to make the future work more actionable.

Author Response

Reviewer 2

This manuscript addresses the critical issue of predicting railway slope failure under heavy rainfall conditions by proposing the Soil Moisture Extended Cohesive Damage Element (SMECDE) method. It demonstrates academic innovation by incorporating the influence of soil moisture into cohesive damage modeling, presenting a mathematical framework, and validating it with finite element analysis using ABAQUS. The work is thorough and introduces valuable insights into slope failure mechanisms. This paper can be accepted after some minor revision, including linguistic clarity, better explanation of model assumptions, and more comprehensive validation of results. Below are my detailed comments.

Response: many thanks for this comment. Authors have made a revision to address the mentioned points.  

1. Language and Clarity

The introduction contains repetitive information about slope failure due to rainfall (e.g., Page 1, Lines 30–42). Consider condensing these descriptions to improve readability and focus.

Response: Thanks for this comment. The introduction has been revised in terms of comment.

Some sentences are overly long, making it difficult for readers to follow. For instance, the sentence on Page 2, Lines 77–80, should be split into two sentences, separately discussing the soil moisture model and its integration into the extended cohesive damage element method.ve

Response: thanks for this comment. We have changed the long sentences in the updated version.

2. Model Assumptions

The correlation model between soil moisture and cohesion (Equations 3 and 4) references experimental data, but the selection criteria for the data and the confidence level of the curve fitting are not sufficiently detailed. Include more information about the data source and explain the physical significance of the fitted parameters.

Response: Thanks for this comment. Previously reported experimental data have been given in Figures 2 to 4 to support investigating correlation. Authors think that soil properties vary with different soil types at different sites. It is hard to use theoretical formulas to express them due to uncertain parameters which need verification using different soil samples at variable moistures. This investigation used previous experimental test data to work out high-order polynomial equations which is better to reflect real tested features of investigated soil type in the selected site. We think this correlation based on experimental work is a realistic way. The correlation between soil cohesion and moisture would be self-explained by their fitted curves based on tested data.    

The definition of "shallow soil" (e.g., depth range) is unclear. Clarify the assumed soil depth in the model and discuss its potential impact on the results.

Response: soil depth in the model can be seen clearly from Tables 4 and 5 relating to the depth of railway embankment slope.

3. Figures and Tables

Table 5 (Page 12) presents soil parameters at different depths, but the trends in these values are not analyzed in the text. Add a discussion about how depth influences soil modulus and cohesion.

Response: The manuscript mentioned on the corresponding page: Material parameters given in Table 5 at soil moisture 35% are used in SMECDE modelling prediction. Table 5 directly shows how depth influences soil modulus and cohesion.

Figure 12 (Page 13) illustrates the predicted initial damage surfaces for different soil moisture levels but lacks specific numerical data or annotations highlighting the extent of the damage. Consider labeling key data points or adding explanations to the legend.

Response: Thanks for this comment. Authors checked figure 12 to be sure it shows enough information of predicted damage initiation and damage belt forming process when increasing soil moisture. This figure illustration would be better than numerical data presentation. 

4. Validation

The validation relies primarily on displacement contours from ABAQUS simulations (Figure 14, Page 14). While the critical rainfall intensity (66 mm/h) aligns with reported meteorological data, the absence of experimental or field-based validation reduces confidence in the model's accuracy. Include additional experimental data or real-world case studies to strengthen the validation.

Response: Thanks for this comment. Section 8 in the paper mentioned that validation includes existing a real field-survey, reported meteorological data and ABAQUS modeling simulations.

The shear crack propagation under heavy rainfall is only theoretically described. Incorporate laboratory experiments or high-resolution simulations to validate the predicted crack paths.

Response: this paper mentioned it focuses on the investigation of the first failure stage: damage initiation, damage belt forming and damage scale under heavy rainfall. Prediction of shear crack propagation is mentioned as the future work and will be published in a different paper considering the length of the paper.      

5. Future Directions

The conclusion mentions future research on "time-dependent effects of soil moisture on cohesion" but does not specify how this will be conducted. Provide concrete plans, such as incorporating dynamic soil moisture monitoring or experimental simulation, to make the future work more actionable.

Response: Thanks for this comment. In general, future work would be briefly introduced as further investigations with simple objectives considering the length of the paper. 

Reviewer 3 Report

Comments and Suggestions for Authors

Please address the following shortfalls in the paper:

The paper encompasses a wide range of topics; however, its presentation is overly complex and difficult to understand.

The methods for determining properties such as cohesion, modulus, etc., are not clearly explained.

Also, the figures are not adequately addressed, and the labels for the X-axis and Y-axis need to be clearly specified.

The conclusions are superficial and fail to effectively address the key outcomes of the paper.

Additionally, updating the references would strengthen the overall quality and credibility of the work

Comments on the Quality of English Language

The consistency of language is complex and need modification.

Author Response

Reviewer 3

Please address the following shortfalls in the paper:

The paper encompasses a wide range of topics; however, its presentation is overly complex and difficult to understand.

Response: Authors understand this comment. Indeed, slope failure mechanisms are rather complex. Many factors have influence. However, authors try our best to focus on the investigation of the main factors: soil moisture or rainfall intensity and soil depth. It is an interdisciplinary topic which needs multiple knowledge from computational damage mechanics, geotechnics and soil-hydraulics and weather forecasting informatics to help reviewing. 

The methods for determining properties such as cohesion, modulus, etc., are not clearly explained.

Response: Authors understand this comment. Cohesion and modulus are basic soil properties which can be found in many soil mechanics textbooks.

Also, the figures are not adequately addressed, and the labels for the X-axis and Y-axis need to be clearly specified.

Response: Thanks for this comment, Authors have checked all figures and tables to be sure there are enough information provided.

The conclusions are superficial and fail to effectively address the key outcomes of the paper.

Response: Authors checked the conclusion section and confirmed that the introduced new methodology in predicting slope failure under heavy rainfall has been clearly validated. Correlations between soil cohesion and moisture, and depth are explored well. The key parameters of moisture or rainfall intensity to cause railway embankment slope failure has been explored in case studies.   

Additionally, updating the references would strengthen the overall quality and credibility of the work.

Response: thanks for this comment. Authors checked all necessary references have been cited accordingly.

Reviewer 4 Report

Comments and Suggestions for Authors

Dear Authors

interesting topic, but structure of the draft seems unbalanced for theoretical and experimental issues.

Some comments below.

regards

1) In chapter 3 it is not clear the physical basis of the correlation between cohesion and moisture: in other words that is not a novelty that high water content is disturbing consistency of fine particles thus reducing strength properties.

2) Fig.5 legend of vertical axis seems not correct.

Values of the modules are so close each others that it seems quite unrealistic from the lab point of view to scatter those differencies , 2 kPa (fig. 5 a). In fig 5b there is a difference of about 20 MPa but it is not clear the field condition  and the natural range that such measures demonstrate.

3) Data shown in fig 5 and 6 are original or processed from elsewhere?

4) Theoretical approach at ch 5 is impressive, but quite difficult to follow from a technical point of view: which are the links with soil mechanics behaviour (adhesion, capillarity, clay minerals absorption etc). There is a discrepancy between theory and practical case validation.

5) Case presented in fig 9 seems quite due to a careless design of the embankment  rather than a novel and unexpected event in geotechnics. Data of the construction materials are provided in table 4 but without explanation.

6) Line 417 is moisture and not moiture

7) Values of modules presented in tables 4 and 5 seem not realistic from an experimental point of view. In particular, precision on modules values is hard to be justified.

 

Author Response

Reviewer 4

Dear Authors

This is an interesting topic, but structure of the draft seems unbalanced for theoretical and experimental issues.

Response: thanks for the comment. The investigation in this paper is prediction based on computational damage mechanics and geotechnics using weather forecast information and previous soil experimental test data. It mainly focuses on theoretical prediction.     

Some comments are given below.

1) In chapter 3 it is not clear the physical basis of the correlation between cohesion and moisture: in other words that is not a novelty that high water content is disturbing consistency of fine particles thus reducing strength properties.

Response: The physical basis of the correlation between cohesion and moisture can be seen exactly from previous physical experimental work given by [17, 18] and shown in Fig. 3 in this paper. There are also theoretical equations to express the correlation between cohesion and moisture. This way was not selected by authors considering uncertainty of parameters, which need many varied soil samples in test work to determine. Instead, we used previous experiment data for conducting correlations. More relevant information can be seen from the following textbooks:

"Geotechnical Engineering: Soil and Foundation Principles and Practice" by Richard L. Handy and Marian T. Spangler: This comprehensive textbook covers soil properties, including cohesion, and discusses how moisture content and depth influence these characteristics.

"Soil Mechanics" by T. William Lambe and Robert V. Whitman: A foundational text that delves into the principles of soil behavior, examining how moisture variations and depth affect soil cohesion and overall stability.

"Principles of Geotechnical Engineering" by Braja M. Das: This book provides an in-depth analysis of soil properties, including cohesion, and discusses the impact of moisture content and depth on soil behavior.

"Soil Engineering" by M. G. Spangler and R. L. Handy: This resource offers insights into soil cohesion and examines how factors like moisture and depth influence soil properties.

"Soil Mechanics in Engineering Practice" by Karl Terzaghi, Ralph B. Peck, and Gholamreza Mesri: A classic reference that explores the fundamentals of soil mechanics, including the relationships between cohesion, moisture content, and depth.

2) Fig.5 legend of vertical axis seems not correct.

Response: Thanks for this comment, Authors checked units in vertical axis in Fig. 5 and confirmed they are correct because different units used for Young’s modules in fillings and foundation due to different scales.

Values of the modules are so close each others that it seems quite unrealistic from the lab point of view to scatter those differencies, 2 kPa (fig. 5 a). In fig 5b there is a difference of about 20 MPa but it is not clear the field condition  and the natural range that such measures demonstrate.

Response: Please refer to the response to the above comment. They are correct and extracted from previous experimental work [28, 29]. More detailed data can be seen in tables 4 and 5. 

3) Data shown in fig 5 and 6 are original or processed from elsewhere?

Response: The points shown in Figures 5 and 6 are original data provided by previous experimental work [28, 29].

4) Theoretical approach at ch 5 is impressive, but quite difficult to follow from a technical point of view: which are the links with soil mechanics behaviour (adhesion, capillarity, clay minerals absorption etc). There is a discrepancy between theory and practical case validation.

Response: Authors have checked chapter 5 to be sure that all soil parameters varying with soil moisture and depth are clearly presented by figures and tables 4 and 5 as inputs to the predictive modelling.  

5) Case presented in fig 9 seems quite due to a careless design of the embankment  rather than a novel and unexpected event in geotechnics. Data of the construction materials are provided in table 4 but without explanation.

Response: Our industrial partner stated that the railway embankment slope shown in Fig. 9 was designed well in terms of design codes and used for several ten years. It was failed only at some local areas when unexpected heavy rainfall and long periods occurs.    

6) Line 417 is moisture and not moiture

Response: Thanks for this comment. The typo is corrected in the updated version.

7) Values of modules presented in tables 4 and 5 seem not realistic from an experimental point of view. In particular, precision on modules values is hard to be justified.

Response: Authors carefully checked Tables 4 and 5 and confirmed all values of parameters are calculated using the fitted equations based on the curves using data from previous experimental reports including industrial partners’ report for their designed railway embankment slope.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Thank you for your revisions and responses to the comments raised. While I appreciate your efforts to address the concerns, the revised manuscript and accompanying responses fall short in addressing key issues meaningfully and comprehensively. I have outlined my main concerns below for your consideration:

1. Correlation Analysis

Your reliance on experimental data for deriving high-order polynomial equations is noted. However, the concern regarding overfitting remains unaddressed. High-order polynomials, while potentially fitting the data well, may capture noise rather than meaningful relationships, limiting the generalizability of your findings.

To improve the robustness of the analysis, I recommend exploring simpler models, such as a linear correlation for the data presented in Figure 5a and a bi-linear correlation for Figure 5b. If a bi-linear model is used, it is crucial to justify the conditions leading to the transition point and discuss their physical significance. Additionally, a discussion of the limitations and applicability of the proposed polynomial models to other datasets or conditions would greatly enhance the credibility of your analysis.

2. Characterization of Embankment Materials

The additional details provided about the embankment’s composition are helpful, but referring to the material as "loamy soil" for simplicity is misleading and risks misinforming the reader. A more detailed characterization of the slope materials (e.g., grain size distribution, permeability, and compactness) is essential to ensure the analysis aligns with the actual conditions of the Kent railway embankment.

For example, you model the filling material with a Young’s modulus of 100 kPa. This value is exceptionally low for a manmade, compacted material used in embankment filling and would typically only apply to very soft or unconsolidated soils, or materials at a near-liquefaction state. Furthermore, there are discrepancies in the modeling: while two materials are presented (one for the filling with E≈100kPa down to 4.5 m in depth and one for the foundation with E=7MPa), Table 5 indicates that the filling material extends to a depth of 8 m (or possibly 6 m—this is unclear). Such ambiguities make it difficult for the reader to follow the analysis or assess its validity.

 

It is critical for the reader to clearly understand the materials and conditions at the Kent embankment, particularly given the unique and uncommon properties presented. If a detailed characterization is beyond the scope of the study, consider explicitly reframing the analysis to acknowledge this limitation and outline how it may impact the reliability of the conclusions drawn.

 

Comments on the Quality of English Language

Language is improved in the revised version

Reviewer 3 Report

Comments and Suggestions for Authors

The following points are to be addressed before publication:

While the topic is relevant, there is a lack of comprehensive references to state-of-the-art research.

The paper relies on a simplified mathematical model and assumptions (e.g., rainfall-soil moisture correlation), which might limit its applicability to real-world scenarios, particularly in heterogeneous terrains. It may be addressed.

The validation of the SMECDE method lacks sufficient experimental or field data, reducing the credibility of its predictive accuracy.

Conceptually, it overly simplifies complex phenomena like rainfall-soil interaction without adequately considering other critical factors like rainfall duration.

Figures like soil cohesion vs. depth lack proper legends and axis explanations, reducing clarity. Methodologically, the reliance on limited field data (Kent region) questions the universality of its findings.

The novelty claim is vague; prior models (e.g., PFEM) addressing similar issues are insufficiently contrasted.

Comments on the Quality of English Language

There are grammatical errors, repetitive phrasing, and poorly structured sentences, which detract from the readability and professionalism of the manuscript.

The paper suffers from inconsistent language and poor grammar (e.g., "rainfall intensity effect is changed to investigation of soil moisture effects shifts").

Reviewer 4 Report

Comments and Suggestions for Authors

Dear Authors

I do not have further comments.

Regards