Review Reports - Nonlinear Regression Expansion Model for Fissured Highly Expansive Soils

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper presents a regression model to predict the amount of expansion of a highly expansive fissured soil as a function of the fissure ratio, dry density, initial water content and applied stress. A significant number of swell tests must have been carried out to provide the data for the regression analysis. The regression model fits the data well and the paper is of interest to the geotechnical community. The following comment is provided which the authors are requested to address:

A single soil type was used for this study and it is necessary characterise this soil more comprehensively. Please provide a detailed mineralogical composition of both the clay matrix and the infill material in the fissures. Also please provide background as to the geological setting, i.e. whether this is a residual soil or a transported soil, in which case the depositional environment and age needs to be provided. The material covered is also somewhat unique in that it appears that all fissures have been filled by infill, which is not applicable to all expansive soils. This means that the model may not necessarily be suitable to all expansive soils. This should be pointed out.
The paper refers throughout to "expansion rate" while it actually presents data on "final expansion magnitude" after swell tests, and not the rate at which expansion took place. This should be corrected in the paper by referring to "amount of expansion", "ultimate expansive" or "expansion magnitude" or a similar more descriptive term. The term "rate" where used inappropriately in the reviewer's opinion has been highlighted in many instances in the marked-up copy of the paper.
Line 83 makes reference to "expansion rate experiments". However, no detail is presented as to how the expansion tests were carried out. Please explain how the tests were carried out. Also, how was it determined that swelling was complete?
It is understood that the tests were carried out on remoulded samples which means that the original fabric in which fissuring would have played a part had been completely altered (line 88-90). How can it then be assumed that the behaviour is representative of fissured expansive soils? This aspects need to be comprehensively addressed. It may be necessary to change to title of the paper to apply to remoulded highly expansive clay.
An indication of scale will be valuable in Figure 1.
Line 70 states "Studies indicate that weakly expansive soils have 64.3% to 83.9% of fissures filled with gray-green clay." Please provide a reference to these studies or clarify whether these are the authors' own studies.
Line 77. The fissure ratio was determine from the volume of infill material to the volume of the matrix. How were these respective volumes determined?
Table 2: It is doubtful that expansion can be quoted in kPa to two decimal places. One decimal is adequate. Also look at the number of significant figures presented elsewhere in the paper. In civil engineering applications it is typically adequate to present 3 or 4 significant figures.
Sections 4.1, 4.2 and 4.3 present identical explanations for regressions carried out for various "fissure ratios". Sections 4.2 and 4.3 are therefore unnecessarily repetitive. Rather present the relevant coefficients determined for various fissure ratios in a suitable table, mentioning that the same procedure as in Section 4.1 was followed.
Figure 3: An exponential fit is presented for parameter fits which appear to the reviewer to be highly linear. Although the amount of expansion may be exponentially related to the fissure ratio, it is not clear why exponential fits were chosen for the parameters. Would linear fits also work? Some justification is requested.
Line 315-316 mentions factors influencing expansion, which includes the fissure ratio. However, this paper is exclusively applicable to clay in which the fissures which have been completed infilled with a specific material. Because samples were remoulded to various percentages of material taken from fissures relative to the matrix material, it considers different mixtures of materials and not really fissuring as such. It appears that the volume of infill significantly affects swell extent. This may not be the case in fissured clays where the amount of infill is less significant where fissuring would control the rate rather than the amount of swell. This should be clarified from the outset.
Some typographical correction is suggested in the marked up copy's Conclusion section.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

The standard of English used in this paper is reasonably good. However, the use of articles ("the" and "a") can be improved. It is recommended that a native English speaker be approached to assist in this regard.

Author Response

Comment 1

A single soil type was used for this study and it is necessary characterise this soil more comprehensively. Please provide a detailed mineralogical composition of both the clay matrix and the infill material in the fissures. Also please provide background as to the geological setting, i.e. whether this is a residual soil or a transported soil, in which case the depositional environment and age needs to be provided. The material covered is also somewhat unique in that it appears that all fissures have been filled by infill, which is not applicable to all expansive soils. This means that the model may not necessarily be suitable to all expansive soils. This should be pointed out.

Response:

Thank you for the helpful suggestion. We revised the manuscript to characterize the Nanyang soil more comprehensively:

Geological setting added. We now state that the tested soil is a transported Middle Pleistocene alluvial–proluvial clay (al-plQ2) from the Nanyang section. Field logging shows very dense small fissures with 2–5 mm gray-green clay infill; no groundwater was observed in the strong expansive layer (new text in Materials / Site description).

Mineralogy added (Nanyang). Representative bulk XRD measurements for the strong expansive clay (al-plQ2) yield the following average composition (values rounded to one decimal place): smectite 53.0%, chlorite 4.0%, illite 3.0%, kaolinite 3.0%, quartz 40.0%, feldspar 1.0%, calcite ~0%. For context, the local medium-expansive silt clay shows lower smectite (~23.7%) and higher quartz (~53.8%) (new paragraph in Mineralogical composition).

Matrix vs. infill and scope. Separate XRD for the gray-green fissure infill was not performed; the infill was sampled from the same stratigraphic horizon and is clayey. Accordingly, the remoulded specimens are treated as volumetric mixtures of matrix and infill within the same mineral suite. We have also explicitly limited the applicability of the regression model to predominantly infilled fissure systems and cautioned against direct application to open or partially infilled fissures (added to the Abstract and Conclusions).

We believe these concise additions address Comment 1 while keeping the manuscript focused on the single Nanyang soil tested in this study.

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Comment 2

The paper refers throughout to "expansion rate" while it actually presents data on "final expansion magnitude" after swell tests, and not the rate at which expansion took place. This should be corrected in the paper by referring to "amount of expansion", "ultimate expansive" or "expansion magnitude" or a similar more descriptive term. The term "rate" where used inappropriately in the reviewer's opinion has been highlighted in many instances in the marked-up copy of the paper.

Response:

We agree and have corrected the terminology throughout. The manuscript now consistently uses “ultimate expansion (δ_ep, %)” or “expansion magnitude” to denote the final expansion measured at the end of the swell tests. The former “expansion rate” wording has been removed wherever it inappropriately referred to the final value. Corresponding updates have been made to the response-variable definition, figure axes, table headers, equation symbols (now using δ_ep), and relevant sentences (e.g., “expansion rate experiments” → “swell tests measuring ultimate expansion”). No changes to data or analysis were required—only terminology was standardized as requested.

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Comment 3

Line 83 makes reference to "expansion rate experiments". However, no detail is presented as to how the expansion tests were carried out. Please explain how the tests were carried out. Also, how was it determined that swelling was complete?

Response:

We have clarified the Methods. At line 83, “expansion rate experiments” was replaced with “swell tests measuring ultimate expansion (δ_ep, %)”. We also added a concise description of the procedure (end of Section 2, “Swell test procedure”): one-dimensional oedometer tests in accordance with ASTM D4546-14 under a constant vertical stress; specimens remolded to target ρ_d and w_i, inundated at room temperature, and deformation recorded versus time until the deformation–time curve reached a plateau (stabilized), at which point δ_ep was taken. No additional laboratory-specific numerical threshold was imposed. These edits make both the test procedure and the completion criterion explicit.

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Comment 4

It is understood that the tests were carried out on remoulded samples which means that the original fabric in which fissuring would have played a part had been completely altered (line 88-90). How can it then be assumed that the behaviour is representative of fissured expansive soils? This aspects need to be comprehensively addressed. It may be necessary to change to title of the paper to apply to remoulded highly expansive clay.

Response:

Thank you for raising this point. We have clarified the representativeness and scope of the specimens and model:

What we added. In Section 2, we inserted a new paragraph titled “Representativeness and scope of remolded specimens.” It explicitly states that the specimens were remolded volumetric mixtures of the matrix clay and the gray-green fissure infill taken from the same stratigraphic horizon in Nanyang. This design prescribes the fissure ratio K_r via mixture proportion and isolates the compositional effect (mineral suite and fines content), together with the state variables (ρ_d, w_i, σ_v), on the ultimate expansion δ_ep under confinement.

Why remolding is representative here. In the Nanyang field setting, fissures are predominantly infilled, and the infill shares the same clay-mineral assemblage as the matrix. Under one-dimensional inundation tests, the final expansion magnitude is therefore expected to be governed primarily by composition and state, rather than by intact macro-fissure geometry. The paragraph makes this rationale explicit.

Scope/limitation. We explicitly note that the regression does not address behaviors controlled by open or partially infilled fissures or by intact macro-fabric anisotropy (which mainly affect wetting paths and early-time kinetics). Applications to such cases should be made with caution. This scope statement is now also reflected in the manuscript text.

We believe these clarifications address the concern about remolded specimens and delineate the intended applicability of the model. If the editor prefers, we are open to adjusting the title to emphasize “remolded” more prominently, but with the above clarifications the current framing accurately reflects the study.

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Comment 5

An indication of scale will be valuable in Figure 1.

Response:

Thank you for the helpful suggestion. We have revised Figure 1 to include an indication of scale. The caption now specifies that the typical width of the filled fissure is approximately 10 cm, providing a clear sense of scale for the figure as requested.

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Comment 6

Line 70 states "Studies indicate that weakly expansive soils have 64.3% to 83.9% of fissures filled with gray-green clay." Please provide a reference to these studies or clarify whether these are the authors' own studies.

Response:

Thank you for the comment. The cited percentages (64.3–83.9%) describing the proportion of fissures filled with gray-green clay are taken from the geological survey and statistical results reported by Dai et al. (2020, Applied Sciences, 10(13), 4616; https://doi.org/10.3390/app10134616). To clarify this, we have added the corresponding citation at line 70 in Section 2. The sentence now reads:

“Studies indicate that weakly expansive soils have 64.3% to 83.9% of fissures filled with gray-green clay [11].”

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Comment 7

Line 77. The fissure ratio was determine from the volume of infill material to the volume of the matrix. How were these respective volumes determined?

Response:

We have clarified how the volumes were determined. In our remolded mixtures, the fissure ratio Kr is prescribed by the volumetric fraction of the gray-green infill. For each target Kr, we selected oven-dry masses of the infill and matrix and converted mass to volume by dividing by the measured particle (solid) density of each component (pycnometer), i.e., V=m/ρ_s. The materials were then mixed to the target w_i and compacted to the target ρ_d in the oedometer ring. Because the two components have similar mineral suites and comparable particle densities, the target K_r is very close to the corresponding dry-mass fraction used at mixing. This operational definition has now been added to the Methods near line 77.

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Comment 8

Table 2: It is doubtful that expansion can be quoted in kPa to two decimal places. One decimal is adequate. Also look at the number of significant figures presented elsewhere in the paper. In civil engineering applications it is typically adequate to present 3 or 4 significant figures.

Response:

Thank you for the suggestion. In Table 2, expansion is reported as ultimate expansion, δ_ep, in percent strain, while 0/25/50 kPa denote the applied vertical stress σ_v conditions. To avoid any ambiguity, we added an explicit note to the table caption clarifying this. We also rounded δ_ep to one decimal place and standardized significant figures across the manuscript.

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Comment 9

Sections 4.1, 4.2 and 4.3 present identical explanations for regressions carried out for various "fissure ratios". Sections 4.2 and 4.3 are therefore unnecessarily repetitive. Rather present the relevant coefficients determined for various fissure ratios in a suitable table, mentioning that the same procedure as in Section 4.1 was followed.

Response:

Thank you for the suggestion. Sections 4.1–4.3 indeed follow the same regression procedure under different fissure ratios (K_r = 35%, 50%, and 65%), which may appear repetitive. However, each subsection reports independent regression outputs (R, ANOVA, coefficients, and sensitivity rankings) that are essential for transparency and reproducibility. These results form the empirical basis for the generalized model presented in Section 4.4. To clarify this and improve readability, we added linking sentences: “Following the same regression procedure as in Section 4.1…” at the beginnings of Sections 4.2 and 4.3, and “According to previous analyses from Sections 4.1–4.3…” at the start of Section 4.4. These minor edits explicitly state that identical methods were applied while retaining the necessary statistical detail for each fissure ratio.

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Comment 10

Figure 3: An exponential fit is presented for parameter fits which appear to the reviewer to be highly linear. Although the amount of expansion may be exponentially related to the fissure ratio, it is not clear why exponential fits were chosen for the parameters. Would linear fits also work? Some justification is requested.

Response:

Thank you for the insightful comment. We have carefully examined both linear and exponential fittings between the parameters (a, b, c) and the fissure ratio (K_r). As the reviewer observed, the linear fits yield comparable coefficients of determination (R² differences < 0.01). Nevertheless, we retained the exponential form for two main reasons:

(1) Physical rationale: The effect of fissure ratio on the expansion characteristics of highly expansive fissured soils is inherently nonlinear. When K_r increases from low to moderate values, the contribution of fissures to volumetric deformation grows rapidly and then gradually approaches a saturation tendency as fissures become filled or closed. This nonlinear and asymptotic behavior is better captured by an exponential function.

(2) Model consistency and generalization: The exponential relation ensures consistency with the nonlinear form of the unified regression model (Eq. 10) and with previously reported trends in expansive clay studies. It also provides a more realistic extrapolation beyond the three K_r levels tested.

To clarify this choice, a note has been added in Section 4.4 explaining that exponential fitting was selected to better reflect the nonlinear and asymptotic influence of fissure ratio, while linear fitting offers a similar statistical fit.

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Comment 11

Line 315-316 mentions factors influencing expansion, which includes the fissure ratio. However, this paper is exclusively applicable to clay in which the fissures which have been completed infilled with a specific material. Because samples were remoulded to various percentages of material taken from fissures relative to the matrix material, it considers different mixtures of materials and not really fissuring as such. It appears that the volume of infill significantly affects swell extent. This may not be the case in fissured clays where the amount of infill is less significant where fissuring would control the rate rather than the amount of swell. This should be clarified from the outset.

Response:

Thank you for this valuable clarification. We have emphasized from the outset that the present study considers mixtures of matrix and infill materials rather than intact fissure geometry. The Abstract now explicitly states that the regression model is applicable to fissure systems that are largely infilled, while extrapolation to open or partially infilled fissures should be made with caution. In Section 2, we also clarified that K_r represents the volumetric fraction of gray-green infill relative to the matrix clay, determined from the oven-dry masses and particle densities of the two components. These edits ensure that the study’s scope and definitions are clearly distinguished from open-fissure cases.

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Comment 12

Some typographical correction is suggested in the marked up copy's Conclusion section.

Response:

Thank you for pointing this out. We have carefully proofread and corrected all typographical and formatting issues in the Conclusion section, including punctuation, spacing, and symbol consistency.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

This paper addresses the adverse effects of moisture-induced swelling and shrinkage of fissured expansive soil on the stability of dam engineering, and develops a BP Neural Network prediction model with fissure ratio, dry density, initial moisture content, and overburden pressure as input parameters. The model is implemented in MATLAB and compares the performance of the gradient descent with momentum method and the Fletcher–Reeves conjugate gradient method. The results indicate that the latter converges about 30 times faster while maintaining similar prediction accuracy. Moreover, the model predictions are highly consistent with the measured values, demonstrating good generalization ability and providing a reliable tool for predicting expansive soil deformation and controlling risks in dam engineering. However, the paper still has some shortcomings. The specific review comments are as follows:

The number of references in this paper is relatively limited, which does not sufficiently reflect the current research status and academic background in this field. It is recommended that the authors supplement recent research achievements in this area to enhance the academic depth and persuasiveness of the paper.
The swelling behavior of expansive soil is influenced by multiple factors, and soil properties can vary significantly depending on origin and formation conditions. In this paper, it is not clearly stated whether the validation data for assessing generalization performance come from the same batch of expansive soil as the training data. If both are from the same batch, the model’s predictive capability mainly reflects in-sample generalization, and its applicability and reliability for expansive soils from other sources remain uncertain. It is recommended that the authors clarify the data sources or validate the model using test data from expansive soils of different origins to enhance the credibility of its wider application.

Author Response

Comment 1

The number of references in this paper is relatively limited, which does not sufficiently reflect the current research status and academic background in this field. It is recommended that the authors supplement recent research achievements in this area to enhance the academic depth and persuasiveness of the paper.

Response:

Thank you very much for this helpful suggestion. We fully agree that the literature in the original submission was too limited to reflect recent developments in this area. Accordingly, we have carefully revised the Introduction and added several recent studies (2023–2025) on machine learning and nonlinear regression modeling of expansive soils to strengthen the context and academic depth of the paper.

The following representative works have now been cited and briefly discussed in the revised version:

Taherdangkoo et al. (2023), Computers and Geotechnics – Neural-network-based prediction of swelling pressure.
Elakiya and Keerthana (2024), Archives of Current Research International – Application of artificial neural networks in soil science.
Mohammed et al. (2025), Modeling Earth Systems and Environment – Machine-learning prediction of soil swelling.
Li et al. (2024), Journal of Rock Mechanics and Geotechnical Engineering – Multi-algorithm ensemble modeling for small-sample geotechnical datasets.
Yao et al. (2024), Frontiers in Materials – Nonlinear regression modeling of swelling in cracked expansive soils.
Li et al. (2024), Geotechnical and Geological Engineering – In-situ creep behavior of expansive soils.
Alnmr et al. (2024), Applied Sciences – Machine-learning-based optimization for swelling mitigation.

These updates ensure that the paper reflects the current research landscape more comprehensively and places the proposed nonlinear regression model within a clearer academic framework.

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Comment 2

The swelling behavior of expansive soil is influenced by multiple factors, and soil properties can vary significantly depending on origin and formation conditions. In this paper, it is not clearly stated whether the validation data for assessing generalization performance come from the same batch of expansive soil as the training data. If both are from the same batch, the model’s predictive capability mainly reflects in-sample generalization, and its applicability and reliability for expansive soils from other sources remain uncertain. It is recommended that the authors clarify the data sources or validate the model using test data from expansive soils of different origins to enhance the credibility of its wider application.

Response:

Thank you very much for this thoughtful comment. We completely agree that the origin and representativeness of the data are important for evaluating the model’s generalization. To clarify this point, we have expanded the description of the geological background and sample preparation in the revised manuscript.

The tested soils were collected from the Nanyang section of the South-to-North Water Diversion Project, belonging to the lower part of the Middle Pleistocene alluvial–proluvial deposits (al–plQ₂). The strong expansive layer is light-yellow to light-brown with gray-green streaks, and its fissures are dense but mostly filled with gray-green clay. XRD analysis confirms a smectite-dominated mineral composition (smectite 53%, chlorite 4%, illite 3%, kaolinite 3%, quartz 40%), indicating that both the matrix and the fissure infill share the same mineral suite.

For this reason, all specimens were remolded as controlled volumetric mixtures of matrix and infill materials from the same stratigraphic horizon. This approach allows the fissure ratio K_r to be precisely prescribed while keeping the composition and state variables (ρ_d,w_i,σ_v) consistent. The model therefore reflects the intrinsic composition–state–expansion relationship, rather than the geometric effects of open or partially filled fissures.

We have also added a note to emphasize that the current model applies mainly to fully filled fissured expansive soils, and that future work will extend the validation to open-fissure conditions and soils from other regions. These clarifications should make the data source and applicability of the model much clearer in the revised version.

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

Dear authors!
In my opinion, high-quality work has been done.
The work submitted for review is devoted to a relevant topic. Monitoring and forecasting the expansion parameters of fissured expanding soils allows us to solve safety issues of objects. The environmental aspect is also important.
A well-known mathematical apparatus has been applied.
There are no comments on the quality of the research.
But similar studies are being conducted by research teams in many countries around the world. And I would recommend conducting a review of similar studies in recent years in different countries.
I repeat that there are no comments on the quality of the study itself. But the publication of an article in a respected international publication implies a full literature review in the area under study. And this will only increase the value of this work.
I wish you success in your further research.

Author Response

Comment:

Response:

Thank you very much for your positive and encouraging feedback. We truly appreciate your suggestion to include a broader international perspective. In the revised version, we have added several recent studies (2023–2025) from different regions, including China, India, Australia, Africa, and the Middle East, to briefly reflect the global progress on expansive soil research. These additions make the Introduction more balanced and help place the present work within the context of ongoing international studies.

Author Response File: Author Response.docx

Reviewer 4 Report

Comments and Suggestions for Authors

This study investigates a nonlinear regression model for fissured, highly expansive soils, highlighting fissure ratio, dry density, initial water content, and overburden stress as the primary factors influencing expansion. Experimental results reveal linear relationships between the expansion rate and water content, dry density, and overburden stress, alongside an exponential relationship with fissure ratio.

Although the paper is generally well written, there are several issues in the Introduction. The state of the art is not sufficiently developed, which is crucial when presenting a new study. A well-developed state-of-the-art helps readers understand the topic, the problems being addressed, and the solutions proposed by the authors. In the current version, this aspect is not adequately addressed.

Moreover, the paper lacks a "Materials and Methods" section. The experimental setup is not described. For example, in line 86, it is stated that samples “had their physical properties analyzed.” I assume the data in Table 1 were measured by the authors. It would be helpful if the authors could include details on the experimental setup or explain how the data were obtained. How were the measurements presented, for instance, in Figure 2, conducted?

Additionally, the section on statistical methods (lines 155–174) is not particularly informative, as the methods are standard and familiar to the general reader. If the authors wish to include this section, they should introduce and discuss all theoretical variables, explaining any non-standard applications that help interpret the experimental results. Otherwise, the section does not add value.

The Conclusion section should also be expanded to provide a deeper discussion of the results achieved.

Other minor remarks:

Line 103: I suggest combining Sections 3.1, 3.2, and 3.3 to improve readability.

Line 137: Please specify which statistical analysis software was used.

Line 243: From the data, the relationships appear more linear than exponential. Moreover, assessing the goodness of fit with only three points is highly questionable.

Author Response

Comment 1

Response:

We have significantly expanded the Introduction by adding a comprehensive review of recent international studies (2023–2025) on data-driven and nonlinear modeling of expansive soils, including ANN, ensemble learning, and fissure-coupled regression frameworks [11–17]. This addition clarifies the scientific background and positions our work within the current research frontier.

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Comment 2

Response:

The previous manuscript lacked a clear experimental description. In the revised version, Section 2 has been thoroughly rewritten. It now includes the geological context, mineralogical composition, preparation of remolded specimens, fissure-ratio definition, and the detailed one-dimensional swell test procedure following ASTM D4546-14.

These additions comprehensively clarify how the data in Table 1 and Figures 2–3 were obtained and ensure experimental reproducibility.

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Comment 3

Response:

Thank you very much for this helpful suggestion. We have carefully revised the statistical methods section to make it clearer and more focused on the needs of this study.

The revised text keeps the essential equations (Eqs. 1–4) to maintain transparency while removing lengthy textbook-style explanations. We now define all theoretical variables (R², βⱼ, Yᵢ, Ŷᵢ, n, p, lⱼⱼ) directly after their corresponding formulas for clarity. The statistical analyses were performed using SPSS 26.0 (IBM, USA) with a 95% confidence level (p < 0.05).

In addition, we explained how these methods were applied in our specific context. The enter method was used so that all independent variables (w₀, ρ_d, ln(1 + σ)) were included simultaneously for each fissure ratio K_r. This ensured model completeness and allowed us to evaluate the relative influence of each factor before developing the nonlinear regression model.

We believe these changes make the section more concise, informative, and directly relevant to the interpretation of the results.

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Comment 4

The Conclusion section should also be expanded to provide a deeper discussion of the results achieved.

Response:

We appreciate this thoughtful suggestion. The Conclusion has been carefully rewritten to provide a fuller and more meaningful discussion of the study outcomes. Rather than only summarizing the main findings, the revised version now explains the underlying mechanisms and practical implications in greater depth.

In particular, we expanded the discussion of how fissure ratio governs the swelling behavior of expansive soils, clarified the interactive effects among water content, dry density, and overburden stress, and emphasized the important role of gray-green clay infill in amplifying deformation. We also added a paragraph on the predictive performance and engineering relevance of the nonlinear regression model.

The final part of the section retains our original future work, which involves validating the model in different geological formations and in soils with open or partially filled fissures. It also extends the outlook to include time-dependent swelling and stress–path coupling effects. We believe the revised conclusion now gives a clearer sense of the scientific and engineering value of this work.

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Comment 5

Line 103: I suggest combining Sections 3.1, 3.2, and 3.3 to improve readability.

Response:

Thank you very much for this helpful comment. We carefully reviewed the structure of Section 3 and decided to keep Sections 3.1, 3.2, and 3.3 as separate parts. Each subsection focuses on a different influencing factor that affects the expansion behavior, including fissure ratio (K_r), dry density (ρ_d), and initial water content (w₀). Each variable represents a distinct physical mechanism, and separating them allows readers to better understand their individual contributions before these factors are combined in the regression model.

To make the text easier to follow, we refined the transition sentences and adjusted the paragraph flow between the subsections. We believe the revised version now reads more smoothly while maintaining a clear and logical discussion of each parameter.

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Comment 6

Line 137: Please specify which statistical analysis software was used.

Response:

We appreciate this helpful suggestion. The revised manuscript now specifies the software used for the statistical analysis. All regression and significance tests were performed with SPSS 26.0 (IBM, USA), as stated in Section 4. This clarification has been added to ensure transparency and reproducibility of the results.

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Comment 7

Line 243: From the data, the relationships appear more linear than exponential.

Moreover, assessing the goodness of fit with only three points is highly questionable.

Response:

Thank you for raising this important point. The three representative fissure ratios (K_r = 35%, 50%, and 65%) were selected to represent distinct structural states of fissured expansive soils under controlled laboratory conditions. Each data point corresponds to the mean value of multiple parallel tests rather than a single observation, ensuring the reliability of the measured trend.

We have clarified this issue in Section 4 by adding the following explanation:

“Although linear fitting gives a similar coefficient of determination within the tested K_r range, the exponential form was retained because it better represents the nonlinear and asymptotic influence of fissure ratio on the expansion parameters.”

This revision explains that both linear and exponential forms were examined, and the exponential relationship was retained because it better reflects the theoretical expectation that the influence of fissure development gradually approaches an asymptotic limit. In addition, the nonlinear regression model presented in Section 5, which uses the full dataset, further validates this selection and confirms that the adopted exponential form is consistent with both the experimental observations and the physical mechanism of fissure-controlled swelling.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Thank you for addressing my comments. In terms of comment 4, please note that it is not standard English to refer to the "scope of remolded specimens". I would rather just refer to the "representativeness of remolded specimens" and remove the word "scope".

Comments on the Quality of English Language

The standard of English is good, but there is some room for improvement.

Author Response

Comment:
Thank you for addressing my comments. In terms of comment 4, please note that it is not standard English to refer to the "scope of remolded specimens". I would rather just refer to the "representativeness of remolded specimens" and remove the word "scope".

Response:
Thank you for the helpful linguistic suggestion. We have revised the heading to "Representativeness of remolded specimens."

Reviewer 3 Report

Comments and Suggestions for Authors

Dear authors,

I am completely satisfied with your response and the additions you made to the manuscript.

Once again, congratulations on a wonderfully conducted study!

Good luck!

Author Response

Thank you very much!

Reviewer 4 Report

Comments and Suggestions for Authors

In this second revision of the manuscript, the authors have made some minor adjustments, but unfortunately; however, the core concerns raised in the previous round remain largely unaddressed. The experimental study still lacks a clear and comprehensive description of the methodology, which is essential for reproducibility and scientific credibility. Without this, the results cannot be properly evaluated or validated.
Additionally, the inclusion of a generic section on standard statistical procedures does not substantially enhance the manuscript. These methods are well-known and their presentation here does not offer new insight or tailored analysis relevant to the study’s objectives.

Author Response

Comment 1
In this second revision of the manuscript, the authors have made some minor adjustments, but unfortunately; however, the core concerns raised in the previous round remain largely unaddressed. The experimental study still lacks a clear and comprehensive description of the methodology, which is essential for reproducibility and scientific credibility. Without this, the results cannot be properly evaluated or validated.

Response:
We are sorry that the previous revision did not fully address your concern. Thank you for pointing out the need for a clearer and more reproducible description of the experimental method. Section 2 has now been substantially revised to include all information necessary for full reproducibility. A new paragraph, “Specimen preparation and test conditions,” has been added at the end of the section to specify specimen size (61.8 mm × 20 mm), applied stresses (0, 25, 50 kPa), target dry densities (1.45, 1.50, 1.55 g/cm³), initial water contents (20%, 25%, 30%), number of replicates, temperature (20 ± 2 °C), displacement accuracy (0.001 mm), and the stability criterion for terminating the test (deformation rate < 0.01 mm/h for 24 h).

The revised section now explicitly states that the procedure followed ASTM D4546-14, with specimen geometry and test parameters based on the Chinese Specification of Soil Test Methods (SL 237-1999). These additions make the test process transparent and reproducible and address your concern about methodological completeness.

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Comment 2

Additionally, the inclusion of a generic section on standard statistical procedures does not substantially enhance the manuscript. These methods are well-known and their presentation here does not offer new insight or tailored analysis relevant to the study’s objectives.

Response:

Thank you for this constructive comment. In the revised manuscript, the statistical analysis section has been completely rewritten to emphasize its relevance to the experimental results rather than presenting general statistical procedures. The revised text now specifies that the regression analysis was performed to evaluate the effects of w₀, ρ_d, and ln(1+σ) on the ultimate expansion (δ_ep) under different fissure ratios (K_r). The description directly links the F- and t-tests to the verification of these influencing factors and integrates the statistical significance results with the observed physical trends in Figure 2. These revisions remove redundant textbook-style explanations and make the analysis concise, data-driven, and directly aligned with the study’s objectives.

Author Response File: Author Response.docx