Review Reports - Numerical Modeling of Levee Failure Mechanisms by Integrating Seepage and Stability Processes

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This study employed numerical simulation methods, systematically comparing computational results with experimental data and observed phenomena to validate and calibrate the model. The results demonstrate that this model is suitable for investigating the seepage behavior and failure mechanisms of levees composed of materials with differing hydraulic conductivities under seepage conditions. The research focuses on the pre-failure weakening phase of levees and the influence of structural material composition, addressing critical gaps in existing studies. Its research direction features well-defined innovative elements and demonstrates strong theoretical significance and practical value. The literature review is comprehensive, providing a detailed and thorough analysis of prior research that effectively identifies and articulates the limitations of existing studies, thereby strengthening the work’s originality and real-world relevance. However, the following limitations impact the study's rigor and the persuasiveness of its findings: the methodological approach remains relatively monolithic, and the number of computational case studies is insufficient.

Based on the above analysis, the following specific recommendations are provided to enhance the study’s rigor and the credibility of its conclusions:

1.While the manuscript repeatedly highlights the crucial role of the boundary between saturated and unsaturated zones in structural stability under seepage erosion conditions and includes substantial analysis of the seepage front, the authors fail to adequately elaborate on why this conceptual definition is fundamentally critical for understanding structural instability mechanisms.

2.Section 3.2’s analysis of failure surface geometry relies on an insufficient number of comparative cases—only one dataset is presented. Visually, the correspondence between the presented numerical simulation results and the referenced experimental data in the analysis figures appears suboptimal. Consequently, the evidence within this section lacks the robustness required to conclusively support the statement that the "numerical model effectively predicts the geometry and extent of levee failure."

3.The presentation effectiveness of the comparative validation analysis between the numerical simulations and existing experiments is inadequate. The claimed consistency is not sufficiently substantiated, and the figures require significant improvement as they currently possess limited informational value. Recommendations include enhancing chart design for clarity and informational density.

4.The research methodology is relatively limited. Complementing the findings with rigorous theoretical analysis would substantially bolster the credibility and persuasiveness of the conclusions.

Author Response

Response to Reviewer 1

Respected Reviewer,

We are sincerely grateful for your thoughtful and constructive comments. Your insights helped us significantly improve the clarity, consistency, and presentation of our manuscript. Please find below our detailed responses to each of your comments. We have made the necessary changes in the manuscript highlighted in yellow.

Point 1: While the manuscript repeatedly highlights the crucial role of the boundary between saturated and unsaturated zones in structural stability under seepage erosion conditions and includes substantial analysis of the seepage front, the authors fail to adequately elaborate on why this conceptual definition is fundamentally critical for understanding structural instability mechanisms.

Response 1: Thank you for this insightful comment. We have added a concise theoretical explanation highlighting the critical role of the seepage front in governing pore pressure evolution, matric suction loss, and effective stress changes during instability development. This helps clarify why this interface is essential in understanding pre failure weakening in levees.

Revision Made In:

Section 2.5. Validation of Numerical Model through Experimental Studies (Lines 372-382).

Point 2: Section 3.2’s analysis of failure surface geometry relies on an insufficient number of comparative cases only one dataset is presented. Visually, the correspondence between the presented numerical simulation results and the referenced experimental data in the analysis figures appears suboptimal. Consequently, the evidence within this section lacks the robustness required to conclusively support the statement that the 'numerical model effectively predicts the geometry and extent of levee failure.

Response 2: We appreciate this important observation. We have revised Section 3.2 to clearly state that failure surface validation was only possible in the IO-E8-F4 case, as the other test scenarios did not exhibit failure within the modeled seepage phase. We also revised overgeneralized claims in Section 3.2 and the Conclusion, limiting the conclusion to this case specific validation. Additionally, we provided a clearer explanation of why IO-E8-F4 uniquely exhibited failure, owing to high hydraulic conductivity contrast and foundation dominant seepage.

Revisions Made In:

Section 3.2.3 (Lines 570-590): Clarified limitations and future directions.

Section 3.2.4 (Lines 604–631): Focused discussion on IO-E8-F4 as a single case validation.

Conclusion (Lines 664-682): Adjusted language to avoid overgeneralization also included future works.

Point 3: The presentation effectiveness of comparative validation analysis between the numerical simulations and existing experiments is inadequate. The claimed consistency is not sufficiently substantiated, and the figures require significant improvement as they currently possess limited informational value. Recommendations include enhancing chart design for clarity and informational density.

Response 3: Thank you for this valuable feedback. We have revised the figure captions for Figures 4 to 6 (seepage front comparisons) to better explain what is being compared, highlight the blue experimental phreatic line, and point out specific areas of agreement or deviation. For Figures 7 and 8 (failure geometry), we added clearer descriptions of each plotted line (e.g., simulated, experimental at 14 and 18 minutes) and clarified visual comparison points.

Revisions Made In:

Captions of Figures 4-6: Improved explanation of seepage front agreement and discrepancies.

Figures and captions 7 & 8: Clarified what each line represents and emphasized the agreement/limitations.

Sections 2.5, 3.2.3 and 3.2.4: Additional narrative clarifying interpretation of visual comparisons.

Point 4: The research methodology is relatively limited. Complementing the findings with rigorous theoretical analysis would substantially bolster the credibility and persuasiveness of the conclusions.

Response 4: We appreciate your recommendation. We have strengthened the theoretical foundation by adding discussions linking the observed behavior to capillary barrier effects, suction dependent strength loss, and the physical basis of the Richards equation and van Genuchten model. These additions enhance the reader’s understanding of why certain seepage behaviors and failures occur under different hydraulic contrasts.

Revisions Made In:

Section 3.1.1 (Lines 430–435): Added explanation of capillary barrier effects from theoretical standpoint.

Section 3.2.1 and 3.2.4: Added theoretical references to explain how suction loss and pore pressure govern failure.Lines (543-548 and 604-631)

Section 2.2.1 (Lines 259–266): Clarified how the model integrates unsaturated flow theory with limit equilibrium principles.

Please let us know if any further clarification or revision is required. We are very thankful for your constructive review.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Editor,

Please find my review of a manuscript geohazards-3776952 titled "Numerical Modeling of Levee Failure Mechanisms by Integrating Seepage and Stability Processes" by Liaqat Ali , Shiro Konno , Yoshiya Igarashi , Norio Tanaka submitted to Geohazards for consideration for possible publication.

In this study, the authors implemented and calibrated a validated numerical model to investigate seepage front progression and failure mechanisms in levees under seepage flow conditions, focusing on varying hydraulic conductivity contrasts between levee body and foundation materials. Numerical simulations were performed using van Genuchten based soil water retention parameters and experimentally derived hydraulic conductivities, with results compared against a series of controlled physical model tests. The results of this study contribute to the understanding of failure processes in levees and can inform the design of effective countermeasures for flood resilience.

The topic of the manuscript appears suitable for Geohazards, and it could be accepted for publication after revision.

The following suggestions are to help improving readability.

43-44. However, as the frequency and intensity of hydrological events continue to rise due to climate change and rapid urban development, levee failures have become increasingly common and more devastating.

Suggest to modify this statement making emphasis on the frequency and intensity of extreme hydrological events which most likely could lead to levee failures.

However, as the frequency and intensity of extreme hydrological events continue to rise due to climate change and rapid urban development, levee failures have become increasingly common and more devastating.

47-49. The catastrophic impacts of Typhoon Hagibis in 2019 exemplify how well-maintained levees can be breached, resulting in loss of life, displacement, and widespread property damage.

Suggest adding information about impact of typhoon making it clear that Japan was impacted: The catastrophic impacts of Typhoon Hagibis on Japan in 2019 exemplify how well-maintained levees can be breached, resulting in loss of life, displacement, and widespread property damage.

You may also wish to revise it adding specific information that some areas of Japan suffered heavy flooding, 139 people have been confirmed dead, total economic losses across Japan were estimated at ¥1.88 trillion (US$17.3 billion).

55-57. Among these, seepage-induced failure is particularly insidious, as it progresses gradually and often without visible warning signs. It develops gradually and often without visible surface signs until a critical state is reached.

Please revise, removing the repetition "it progresses gradually and often without visible warning signs" is virtually identical to "It develops gradually and often without visible surface signs".

118-119. In recent years, the importance of a fully coupled modeling approach integrating unsaturated saturated seepage behavior with slope stability analysis …

Please revise as "unsaturated and saturated seepage behaviour".

245-248. The method calculates the factor of safety (Fs) by incorporating the increment in suction-induced shear strength, considering soil properties and hydraulic conditions (Eq.3) [30,31] (Feredlund & Rahardjo 1993; Hamid & Miller 2009). The governing equation used is given below.

You probably do not need the sentence "The governing equation used is given below" as you already introduced equation 3 in your previous sentence.

388-389. Subfigures 4(a) and (c) correspond to SE-S74, while 4.4(b) and (d) correspond to IO-E8-F4.

=> Subfigures 4(a) and 4(c) correspond to SE-S74, while 4(b) and 4(d) correspond to IO-E8-F4.

405. When the upstream level reached 0.375 m Fig. 4.4(d),

=> When the upstream level reached 0.375 m Fig. 4(d),

413-414. Figure 5(a), (c) compares seepage front development in IO-E7-F5 and Figure 5(b), (d) at half and full upstream water levels in SE-S85.

=> Figures 5(a) and (c) compare seepage front development in IO-E7-F5 and Figures 5(b) and (d) at half and full upstream water levels in SE-S85.

436-437. Figure 6 illustrates the SE-S87 case at half Figure 6(b) and full 6(a) upstream water levels.

Please revise this sentence starting with Figure 6a for a full upstream water level at and then with Figure 6b at half upstream water level.

References.

[1-5] (Costa, 1985; Kang et al., 2021; Kang et al., 2024; Ruiz, 2019; Dasgupta 52

et al., 2020).

My understanding that it should be either [1-5] or (Costa, 1985; Kang et al., 2021; Kang et al., 2024; Ruiz, 2019; Dasgupta et al., 2020) but not both. Please check journal's guidelines for authors.

Author Response

Response to Reviewer 2

Respected Reviewer,

Point 1: 43-44. However, as the frequency and intensity of hydrological events continue to rise due to climate change and rapid urban development, levee failures have become increasingly common and more devastating.

Suggest to modify this statement making emphasis on the frequency and intensity of extreme hydrological events, which most likely could lead to levee failures.

Response 1: Thank you for the suggestion, and we have revised the sentence as below.

Revised Lines 38-40

Point 2: 47-49. The catastrophic impacts of Typhoon Hagibis in 2019 exemplify how well-maintained levees can be breached, resulting in loss of life, displacement, and widespread property damage.

Response 2: Thank you for the suggestion. We have revised the sentence to specify Japan as the affected country and have included quantitative information on the human and economic impacts of Typhoon Hagibis in 2019. This strengthens the context and underscores the significance of improving levee performance under extreme weather events..

Revised Lines 42-46 in Section 1 - Introduction
The catastrophic impacts of Typhoon Hagibis on Japan in 2019 exemplify how even well-maintained levees can be breached, leading to extensive flooding in many regions. The event caused 139 confirmed deaths and resulted in estimated economic losses of ¥1.88 trillion, highlighting the urgent need for improved levee resilience.

Point 3: 55-57. Among these, seepage-induced failure is particularly insidious, as it progresses gradually and often without visible warning signs. It develops gradually and often without visible surface signs until a critical state is reached.

Please revise, removing the repetition "it progresses gradually and often without visible warning signs" is virtually identical to "It develops gradually and often without visible surface signs".

Response 3: Thank you for catching this redundancy. We have revised the sentence to remove repetition and present the point more concisely while maintaining its intended meaning.

Revised Sentence: Lines 51-53 in Section 1 - Introduction.
Among these, seepage-induced failure is particularly insidious, as it often progresses without visible warning signs until a critical state is reached.

This keeps the meaning but removes redundancy.

Point 4:118-119. In recent years, the importance of a fully coupled modeling approach integrating unsaturated saturated seepage behavior with slope stability analysis …

Please revise as "unsaturated and saturated seepage behaviour".

Response 4: Thank you for the correction. We have revised the sentence to read “unsaturated and saturated seepage behaviour” for clarity and grammatical accuracy.

Lines 123-125 in Section 1 – Introduction.

We also replaced behavior to behaviour in whole manuscript.

Point 5: 245-248. The method calculates the factor of safety (F_s) by incorporating the increment in suction-induced shear strength, considering soil properties and hydraulic conditions (Eq.3) [30,31] (Feredlund & Rahardjo 1993; Hamid & Miller 2009). The governing equation used is given below.

You probably do not need the sentence "The governing equation used is given below" as you already introduced equation 3 in your previous sentence.

Response 5: Thank you for pointing this out. We have removed the redundant sentence "The governing equation used is given below" to streamline the text, as the equation is already referenced in the preceding sentence.

Lines 248–249 in Section 2.2.1 – Slip Failure Analysis.

Point 6: 388-389. Subfigures 4(a) and (c) correspond to SE-S74, while 4.4(b) and (d) correspond to IO-E8-F4.

Subfigures 4(a) and 4(c) correspond to SE-S74, while 4(b) and 4(d) correspond to IO-E8-F4.

Response 6: Thank you for catching this typo. We have corrected the figure reference as suggested.

Section 3.1.4 -Comparison of Experimental and Simulated Seepage Fronts.

We also have checked and corrected the whole manuscript.

Point 7: 405. When the upstream level reached 0.375 m Fig. 4.4(d),

When the upstream level reached 0.375 m Fig. 4(d),

Response 7: Thank you for pointing out the formatting inconsistency. We have corrected the figure reference from Fig. 4.4(d) to Figure 4(d) as suggested.

Section 3.1.4 – SE-S74 and IO-E8-F4 Case Comparison.

Point 8: 413-414. Figure 5(a), (c) compares seepage front development in IO-E7-F5 and Figure 5(b), (d) at half and full upstream water levels in SE-S85.

Figures 5(a) and (c) compare seepage front development in IO-E7-F5 and Figures 5(b) and (d) at half and full upstream water levels in SE-S85.

Response 8: Thank you for this helpful suggestion. We have revised the sentence to properly reference the grouped subfigures and improve readability as recommended.

Lines 445–446 in Section 3.1.4 – Seepage Front Comparison (SE-S85 and IO-E7-F5).
Figures 5(a) and 5(c) compare seepage front development in IO-E7-F5, and Figures 5(b) and 5(d) show the same for SE-S85 at half and full upstream water levels.

Point 9: 436-437. Figure 6 illustrates the SE-S87 case at half Figure 6(b) and full 6(a) upstream water levels.

Please revise this sentence starting with Figure 6a for a full upstream water level at and then with Figure 6b at half upstream water level.

Response 9: Thank you for pointing this out. We have revised the sentence to start with Figure 6(a) and clarified the description of the upstream water levels for each subfigure.

Lines 471–472 in Section 3.1.4 – SE-S87 Seepage Front Comparison.
Figure 6(a) shows the SE-S87 case at full upstream water level, while Figure 6(b) illustrates the case at half upstream water level.

Point 10: References.

[1-5] (Costa, 1985; Kang et al., 2021; Kang et al., 2024; Ruiz, 2019; Dasgupta 52

et al., 2020).

My understanding that it should be either [1-5] or (Costa, 1985; Kang et al., 2021; Kang et al., 2024; Ruiz, 2019; Dasgupta et al., 2020) but not both. Please check journal's guidelines for authors.

Response 10: Thank you for this helpful reminder. You are correct, using both reference numbers and author names is redundant. We have followed the journal's referencing style and retained only the numerical citations (e.g., [1–5]) throughout the manuscript.

Line 52 and elsewhere as needed (entire manuscript citations updated per MDPI guidelines).

Please let us know if any further clarification or revision is required. We are very thankful for your constructive review.

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

Please check out the file attached.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

Moderate edits.

Author Response

Response to Reviewer 3

Respected Reviewer

Point 1: Abstract

Lines 12 and 73: high water conditions (or high-water level conditions in Line 42), any better

terminology for this? Intensive rainfall and flooding?

Line 19: Citation inconsistency in abstract.

Line 21: What are cases like SE-S74, SE-S85, IO-E8-F4, and SE-S87 in an abstract that has not

defined those abbreviations? Readers cannot understand what they are before reading the

details from your methodological chapter.

Lines 11-34: The abstract was written in a lengthy manner, so it needs to be condensed into a

concise, yet informative version, specifically less than 250-300 words. All testing codes and

unnecessary technical details should be omitted; instead, they should be presented to readers

in the methodological chapter.

Response 1: Thank you for these constructive comments on the abstract. We have revised it to improve clarity and conciseness, reducing the length to under 300 words.

The term high water conditions have been changed to “prolonged flooding and elevated upstream water levels and intensive rainfall and flooding” to better reflect the hydraulic context.
Citation style has been corrected to MDPI numeric format.
The experimental case codes (e.g., SE-S74, IO-E8-F4) have been removed from the abstract to avoid undefined abbreviations; they are now described in the methodology section and in Table 1. Technical detail is condensed, and the abstract now focuses on key findings and significance.

Revisions Made In:

Lines 11–29 – Abstract section revised considering above comments.

Technical codes shifted to Section 2 Experimental Cases for Model Validation and in Table 1: (Lines 212-224),also briefed in Section 3 Results and Discussion (lines 389-394) and Lines (519-521) for clarity and consistency.

Point 2: Introduction

Line 61, 70, and 75: Have you considered the transient effects or the so-called dynamic

nonequilibrium effects of soil suction in SWRC under highly transient seepage conditions? This

could serve to predict soil suction and moisture in Richards’ PDE and strength reduction in the

unsaturated MC criterion under extreme weathering conditions, such as intensive rainfall and

flooding [1].

Line 77: seepage line -> phreatic line. Please verify your terminology in English.

Line 81-82: In addition to unsaturated soil strength reduction caused by infiltration, are there

any literature reviews of rapid drawdown-induced instability?

Response 2: Thank you for these important observations. We have revised the Introduction section to incorporate above comments.

Acknowledged that the current model applies equilibrium based SWRCs and does not include dynamic nonequilibrium suction effects, which are known to influence infiltration under highly transient conditions also relevant references included.(Lines 70-77)
Replaced the term seepage line with phreatic line throughout the manuscript to reflect the correct definition.
Added a brief review of rapid drawdown induced instability and cited relevant literature, clarifying that this mechanism, although critical, is beyond the scope of the current study.(Lines 83-88)

Point 3: Methodology

Lines 182 and 192: The citation format is not in accordance with MDPI.

Line 187: x and z of K should be subscripted.

Line 208: I think this hydraulic boundary-dependent soil saturation variation matters with the

transient effect in reference [2].

Lines 208-213: It would be good to cite Figure 2a when you mention the setup of boundary

conditions.

Table 1: Are there any grain size distributions for samples in Table 1? The reason why I ask for

this is that the Ks of sample No. 4 reach the magnitude of the gravel’s Ks (e-3 m/s = e-1 cm/s).

Please confirm whether sample No. 4 is silica sand or gravelly sand or even sandy gravel.

Equation (3): You forgot to note i for the ith segment in the limit equilibrium analysis by using the

Janbu method.

Equation (4): You forgot to illustrate the lever arms for moment calculations.

Lines 308-324: A good visualisation of initial and boundary conditions can help you save many

words. You should cite Figure 3 in this part for all conditions you applied in this model.

Response 3: Thank you for the detailed suggestions on the Methodology section. We have revised the manuscript to address each point as follows:

Citation format in whole manuscript has been corrected to comply with MDPI’s numerical style.
The directional hydraulic conductivities are now expressed with proper subscripts.[Line 191]
A note has been added in Lines 334-337 acknowledging that boundary dependent saturation variations may reflect transient effects under rapidly changing seepage conditions. The reviewer’s comment mentioned a second reference; although it was not listed in the comment file, we have incorporated a relevant study on transient nonequilibrium SWRC behavior to support this point.
Figure 2(a) is now cited in the description of the boundary condition setup to improve clarity[.Lines 317-337]
In response to the comment on Table 1 now Table 2, Sample No. 4 is confirmed as Mikawa silica sand No.4, classified as a coarse uniform silica sand. The sieve analysis from the supplier (Mikawa Silica Co., Ltd.) (https://www.mikawakeiseki.co.jp/%E6%99%AE%E9%80%9A%E5%93%81), gives D₂₀ = 0.70 mm, D₅₀ = 0.875 mm, and D₆₀= 0.925 mm, with Cu = 1.42 and Cc = 0.94. The relatively high k (10⁻³ m/s) is consistent with this gradation and matches values reported in prior experimental studies (Ali & Tanaka, 2024).The measured k_s for Sample No. 4 (1.6×10⁻³ m/s) falls within the typical range for coarse uniform sands (10⁻³ - 10⁻²m/s) reported in standard references [Bear, 2013; USBR, 1987; Ali and Tanak 2024].
Equation (3) has been updated to include the subscript i on all slice dependent variables to match the Janbu method formulation.Lines 250-251.
Figure 2(c) has been updated to show representative lever arms for some forces not for all so save readability with point E identified as the assumed rotation center.
Figure 3 is now cited in Lines 317–337 to visually summarize the initial and boundary conditions.

Bear, J. (2013). Dynamics of fluids in porous media. Courier Corporation.

Reclamation, U. B. O. (1987). Design of small dams. Water Resources Technical Publication, 860p.United states department of the interior bureau of reclamation.

Ali, L., & Tanaka, N. (2024). Enhancing Levee Resilience Through Material Compatibility: A Comprehensive Study on Erosion Dynamics. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 1-15.

Point 4. Results and Discussions:

Lines 385-390: Those codes were not even mentioned in any former tables. Readers cannot be

aware of what those codes indicate in specific engineering cases. A similar issue appears in

your abstract as well. Please read through your own work from the readers’ viewpoint to ensure

that this manuscript reaches the standard level of readability.

Figures 4-6: Are there any better-quality simulation outputs? What is the unit of the contour bar?

Read it as a reader, please.

Table 2: The experimental cases are all assigned the corresponding codes in a table that

follows their first appearance in the previous figures. Could you please reorder them in the

correct presenting sequence?

Figure 7: In the legend, you did not note which line plot represents experimental observation

and which represents simulated outcomes.

Line 561: At the end of discussions, have you considered any criterion of FoS selection for limit

equilibrium analysis, such as FoS = 1.5 or 2 under specific cases (serviceability and durability

(short term and long term), if having seismic activities, etc.) according to any engineering

standard in any nation?

Response 4: Thank you for the constructive suggestions to improve the Results and Discussions section. We have addressed each point as follows:

Lines 212–224 : table 1 summarizing all experimental cases and their identifiers (SE-S74, IO-E8-F4, SE-S85,IO-E7-F5, SE-S87) has been added in the methodology section. This introduces the case codes in one place and ensures consistency when they first appear in the results. The abstract has also been revised to remove undefined codes and instead refer to the validation against five experimental cases.Results section at (lines 389-394) and Lines (519-521) has been updated.
The Tecplot outputs were generated directly from the seepage simulation and are already in high resolution added water level; the captions have been revised to describe each subfigure so they can be understood without cross referencing the main text. We have clarified the unit of the contours: Figures 4-6 show the degree of saturation (S_r) in %, derived from the van Genuchten model (Eq. 2). The captions now explicitly state the color scale units and identify the experimental phreatic line overlay.
Table 2 Now Table 3: The experimental cases in Table 3 have been reordered to match the sequence in which they are presented in Figures 4-6 and in the discussion text.
Figure 7: The legend has been updated to explicitly distinguish between simulated and experimental results, and the caption clarifies which curves correspond to each.
Line 610-621: We have added a note discussing practical design criteria for the Factor of Safety . While F_s = 1.0 was used in this study to identify failure initiation in the numerical model, engineering standards often adopt higher safety margins. For example, F_s ≥ 1.3–1.5 is common for static conditions, and F_s up to 2.0 may be required under seismic or long-term serviceability considerations [USACE, 1995; USBR, 1987]. This discussion has been added to highlight the potential for incorporating code-specific F_s thresholds in future applications of the model.

Revisions Made In:

Methodology Section (Table 1 and separate section introducing cases)

Abstract (removal of undefined codes)

Figures 4–6 (resolution, units, revised captions)

Table 3 (reordered entries)

Figure 7 (legend and caption updated)

Lines 610–621 (added F_s design criteria discussion)

United States. Army. Office of the Chief of Engineers. (1995). Design and Construction of Levees: Engineering and Design (Vol. 1110, No. 2-1913). Department of the Army, Office of the Chief of Engineers.

Reclamation, U. B. O. (1987). Design of small dams. Water Resources Technical Publication, 860p.3rd edition, United states department of the interior bureau of reclamation.

Point 5. Conclusions

Lines 623-625: Before running into the research prospects for the next stage, you may want to mention a few limitations in a short self-reflection section very concisely, such as neglecting dynamic nonequilibrium suction in SWRC under extreme transient flow conditions (see [2]); that means the instantaneous equilibrium assumption has also been adopted in the current model. Other limitations include heterogeneity and sensitivity analysis of parameters, as you mentioned in the aims for the next stage.

Response 5: Thank you for this valuable suggestion. We have added a concise self reflection on the current model’s limitations at the end of the Conclusions section.

Acknowledged that the present model uses an equilibrium based SWRC and does not capture dynamic nonequilibrium suction effects under highly transient seepage conditions.
Noted the assumptions of material homogeneity and the lack of a full parametric sensitivity analysis as current limitations.
Connected these limitations to the future research plan, which includes incorporating soil heterogeneity, performing detailed sensitivity tests, considering transient SWRC behavior, and extending simulations to include fluctuating water levels and gradual erosion to better reproduce progressive failures.

Revisions Made In:
Lines 664–682 of the Conclusions section.

Please let us know if any further clarification or revision is required. We are very thankful for your constructive review.

Author Response File: Author Response.docx

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have addressed the issues in the last round of major revisions. Minor edits are needed before acceptance.

Line 409: Subfigures 4(a) and 4(c) -> Figures 4(a) and 4(c). Please check out the publication standard of the MDPI.

Any contour plots of FoS in addition to the contour plot of saturation (Figures 4-6) and post-failure line in levee profiles (Figures 7-8)?

Comments on the Quality of English Language

Minor edits.

Author Response

Respected Reviewer,

Point 1: Line 409: Subfigures 4(a) and 4(c) -> Figures 4(a) and 4(c). Please check out the publication standard of the MDPI.

Response 1: Thank you for pointing this out. As per the MDPI Geohazards formatting guidelines, we have revised all references to subfigures throughout the manuscript. Specifically, we replaced terms such as Subfigures 4(a) and 4(c) with Figure 4a and Figure 4c consistently. Parentheses and the prefix subfigure have been removed in accordance with the journal's style for referencing sub-panels.

Revisions Made In:
Throughout the entire manuscript, including figure captions and in-text references.

Point 2: Any contour plots of FoS in addition to the contour plot of saturation (Figures 4-6) and post-failure line in levee profiles (Figures 7-8)?

Response 2: Thank you for this insightful comment. The current modeling framework calculates the Factor of Safety (FoS) using limit equilibrium analysis (Janbu method) along critical slip surfaces extracted from the transient seepage results. While the model captures the evolution of FoS over time for these critical surfaces, it does not generate full-domain contour plots of FoS. We acknowledge this as a current limitation. As the reviewer suggested, incorporating FoS mapping across the entire domain could improve spatial interpretation and will be explored in future extensions. To address your comment, we have revised the Results section to explicitly clarify how FoS was evaluated, acknowledge the current limitation regarding full-field visualization, and suggest its integration as part of future model development.

Revisions Made In:
Lines 611–619 of Section 2.4

Please let us know if any further clarification or revision is required. We are very thankful for your constructive review.

Author Response File: Author Response.docx