Study on Cumulative Deformation of Silt Soil Under Traffic Loading Based on PSO-BP Neural Network

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper examines the cumulative deformations and plastic flow patterns of silt under cyclic loads using dynamic triaxial tests and the PSO-BP neural network model. Given increasing traffic loads and intensive construction in coastal and riverine areas of China, studying the behavior of silts under repeated dynamic stresses is of great engineering significance. The results show that increasing confining pressure reduces cumulative deformation, while increasing dynamic stress amplitude and moisture content, conversely, increases it. The developed PSO-BP model provides the most accurate prediction of cumulative plastic deformations compared to traditional empirical relationships, confirming the effectiveness of machine learning methods in geotechnical calculations. This study contributes to improved reliability in predicting the stability of road foundations and hydraulic structures built on silt soils and has important practical implications for the design of durable transport and infrastructure systems.
The paper requires some revision. 1. The formulation of the study objective is fragmented and stylistically inconsistent: first, it talks about "proposing an empirical model," then about a "new model" based on PSO-BP, and then about a comparison with Monismith and (non-optimized) BP. It would be advisable to provide a unified objective with clear tasks: experimentally characterize the dependence of εp on σd, σ3, and w; calibrate Monismith; train BP and PSO-BP; conduct comparative validation and sensitivity analysis. (lines 95–103)
2. The "Materials" section needs to be expanded: the initial sample preparation procedures are provided, but the initial physical indices with confidence intervals, granulometry distribution with descriptive statistics (D10, D50, coefficients of unevenness, curvature), moisture control protocol, and compaction reproducibility are missing. It is also worth explicitly stating the standard/regulation (ASTM/GB/T) for the wet compaction method and the tolerances for deviations (lines 104–112).
3. The "Results: Effect of σ3" section demonstrates the expected trends, but the stated "96%" reduction with an increase in σ3 from 60 to 150 kPa appears arithmetically incorrect: 3.3266% → 1.6981% is a reduction of approximately 49%, not 96%. (lines 150–154).
4. The PSO-BP formulation is presented in an overview; The following architectural details are missing: number of inputs/outputs, feature normalization, activations, initialization strategy, loss function, early stopping, variable scaling (e.g., taking the logarithm of N), overfitting control (dropout/L2), and a bias-variance rationale for choosing 4 neurons in the hidden layer. (lines 257–269, 300–317)
5. The description of the database (≈80,000 points with reduction "every 5 cycles") raises questions about the independence of observations and temporal autocorrelation. It should be explicitly stated how overestimation of accuracy due to high N-point density for a single sample was prevented, and how data was aggregated across runs. A sensitivity analysis to the N-sampling rate is needed. (lines 280–286).
6. The statement about "a ~400% reduction in the optimized model's RMSE" is incorrect: a reduction of more than 100% is mathematically impossible; the intended meaning is likely "4 times" (-75%). This statement requires correction, and the exact baseline and improved RMSE/MSE values ​​should be provided. This is critical for a clear understanding of the optimization effect. (lines 334–346).
7. Comparison of PSO-BP and Monismith: the mean R² values ​​(0.993 vs. 0.973/0.976) are impressive, but there is no statistical test of the significance of the differences (e.g., using a bootstrap analysis by series or k-fold analysis). It is recommended to provide 95% CIs for R²/MAE/RMSE and Bland-Altman plots or error bars, as well as separate analyses of "stable" and "damaged" regions. (lines 381–386)
8. The "Discussion" section partially repeats the results and contains stylistic and terminological inaccuracies (e.g., "soil mechanic confining pressure problems"). A more thorough interpretation is needed: link the identified trends to micromechanics (contacts, water lubrication, structural reorganization), compare them with shakedown theory, and describe the limits of PSO-BP applicability when extrapolated beyond the training range. (lines 392–401).
9. In "Conclusions," points (1)–(3) repeat the results without specifying limitations and practical implications (e.g., how to use the model for design calculations: input data, ranges, safety factors). It is recommended to add a section on practical application (the algorithm for calculating εp for given w, σd, σ3, N), and also list the limitations of scalability to other soils and frequencies. (lines 402–429).

Comments on the Quality of English Language

The text contains numerous grammatical, lexical, and stylistic errors: case inconsistency (Dynamic vs. dynamic), terminological variability (Moisture contents / water content), tracings and syntactic errors ("the specimen was first isobaric consolidated," "Monismith's model predicted effects," "soil mechani confining pressure problems"), punctuation errors, typos ("contect," "enclosure pressures" instead of "confining pressures"). Recommended: unification of terminology according to the glossary (stress amplitude, confining pressure, water content, accumulated/cumulative plastic strain); checking numerical formulations ("four-fold reduction," "49% decrease"); elimination of run-on sentences and comma-spaces.

Author Response

Manuscript Number: buildings-3972699

Re: “Study on cumulative deformation of silt soil under traffic loading based on PSO-BP neural network”

 

Dear reviewers:

I am pleased to submit the revised paper. All your comments and questions have been addressed below.

 

Comments 1: The formulation of the study objective is fragmented and stylistically inconsistent: first, it talks about "proposing an empirical model," then about a "new model" based on PSO-BP, and then about a comparison with Monismith and (non-optimized) BP. It would be advisable to provide a unified objective with clear tasks: experimentally characterize the dependence of ε_p on σ_d, σ₃, and w; calibrate Monismith; train BP and PSO-BP; conduct comparative validation and sensitivity analysis. (lines 95–103).

Response 1: We thank the reviewer for the valuable comments and appreciation of our work, We partially modified the research objectives and determined that the main research objective was the effectiveness of PSO-BP neural network in predicting the cumulative deformation of silt soils, which was verified by comparing the Monismith model and the BP neural network model, respectively.

The change can be found (Page 3, lines109-117.)

Comments 2: The "Materials" section needs to be expanded: the initial sample preparation procedures are provided, but the initial physical indices with confidence intervals, granulometry distribution with descriptive statistics (D10, D50, coefficients of unevenness, curvature), moisture control protocol, and compaction reproducibility are missing. It is also worth explicitly stating the standard/regulation (ASTM/GB/T) for the wet compaction method and the tolerances for deviations (lines 104–112).

Response 2: We appreciate the reviewer’s valuable comment. We have specifically added reference specifications on the basic physical properties and the wet compaction method(JTG 3430-2020), as well as a more detailed description of the particle gradation, Specific values of Cu = 8 and Cc = 0.7 were given and the soil was judged to be poorly graded.

The change can be found (Page 3, lines120-127.)

Comments 3: The "Results: Effect of σ₃" section demonstrates the expected trends, but the stated "96%" reduction with an increase in σ₃ from 60 to 150 kPa appears arithmetically incorrect: 3.3266% → 1.6981% is a reduction of approximately 49%, not 96%. (lines 150–154).

Response 3: We sincerely appreciate the reviewer’s valuable comments and suggestions on our manuscript. In this paper, the calculation of the effect of the confining pressure on the cumulative deformation does mainly underestimate the effect of the confining pressure on the cumulative deformation, so the attenuation rate in this paper is changed to 49%.

The change can be found (Page 5, lines 163-166.)

Comments 4: The PSO-BP formulation is presented in an overview; The following architectural details are missing: number of inputs/outputs, feature normalization, activations, initialization strategy, loss function, early stopping, variable scaling (e.g., taking the logarithm of N), overfitting control (dropout/L2), and a bias-variance rationale for choosing 4 neurons in the hidden layer. (lines 257–269, 300–317)

Response 4: Many thanks to the reviewers for their suggestions on the details of the algorithmic architecture, and the unarticulated parts are highlighted in this revised manuscript, with emphasis on the theoretical basis and process of selecting four neurons in the hidden layer.

The change can be found (Page 12-13, lines 330-365.)

Comments 5: The description of the database (≈80,000 points with reduction "every 5 cycles") raises questions about the independence of observations and temporal autocorrelation. It should be explicitly stated how overestimation of accuracy due to high N-point density for a single sample was prevented, and how data was aggregated across runs. A sensitivity analysis to the N-sampling rate is needed. (lines 280–286).

Response 5: Thank you very much for your valuable suggestions, we have carried out an in-depth discussion of this issue, we first sampled every 3 cycles and then 7 cycles and 10 and 100 for a cycle were sampled and studied the accuracy of the problem, found that when the N to every interval of 5 to take a point when the point density will not be too high with the N resulting in the overestimation of the fit, the fit is almost no difference with N = 10, but with N = 3 there are 0.05 fitting gap, so this paper chose each 5 for a period of sampling.

The change can be found (Page 11, lines 297-308.)

Comments 6: The statement about "a ~400% reduction in the optimized model's RMSE" is incorrect: a reduction of more than 100% is mathematically impossible; the intended meaning is likely "4 times" (-75%). This statement requires correction, and the exact baseline and improved RMSE/MSE values ​​should be provided. This is critical for a clear understanding of the optimization effect. (lines 334–346).

Response 6: We thank the reviewer for the valuable comments and appreciation of our work, We partially modified the reduction and specified the RMSE and MSE values before and after the improvement.

The change can be found (Page 14, lines391-398.)

Comments 7: Comparison of PSO-BP and Monismith: the mean R² values ​​(0.993 vs. 0.973/0.976) are impressive, but there is no statistical test of the significance of the differences (e.g., using a bootstrap analysis by series or k-fold analysis). It is recommended to provide 95% CIs for R²/MAE/RMSE and Bland-Altman plots or error bars, as well as separate analyses of "stable" and "damaged" regions. (lines 381–386)

Response 7: Thank you very much for your constructive suggestions, we have added Bland-Altman plots of R²/MAE/RMSE in the revised draft, intended to show the errors and variations between PSO-BP, BP, and Monismith, and we found that for R², PSO-BP has the best fit, which is in the range of 0.98-0.999, BP is in the range of 0.96-0.98, and Monismith fluctuates up and down in the range of 0.95. Similarly, the change rule of RMSE can be obtained, the RMSE of PSO-BP is the smallest, which is floating up and down at 0.003, and BP is between 0.012-0.016, and for MSE, the RMSE of PSO-BP is the smallest, which is floating up and down at 6e-4, and BP is at 0.01-0.02.

The change can be found (Page 17, lines448-454.)

Comments 8: The "Discussion" section partially repeats the results and contains stylistic and terminological inaccuracies (e.g., "soil mechanic confining pressure problems"). A more thorough interpretation is needed: link the identified trends to micromechanics (contacts, water lubrication, structural reorganization), compare them with shakedown theory, and describe the limits of PSO-BP applicability when extrapolated beyond the training range. (lines 392–401).

Response 8: Thank you very much for your valuable comments on the discussion section. We have mainly investigated the feasibility of PSO-neural network for predicting cumulative deformation of silt soils and its advantages over other models. The revised version focuses on the PSO-BP neural network part of the Discussion section with more in-depth elaboration, which specifies its operation process and advantages. You propose to establish links between identified trends and micromechanical mechanisms (contact action, water lubrication effects, structural remodelling), to validate them against settlement theory, and to clarify the limitations of the applicability of the PSO-BP model when predictions are beyond the training range. However, due to the limitation of test conditions, test time, test environment and other factors, this time we did not carry out specific tests on the microscopic part of the silt soil, and the part you recommended is very helpful to us in the future, in the future, we will comprehensively consider linking the neural network with the micro-parameters obtained from micro-tests, such as SEM, and explore the limitations of the applicability of the PSO-BP model when the prediction is out of the training range.

Comments 9: In "Conclusions," points (1)–(3) repeat the results without specifying limitations and practical implications (e.g., how to use the model for design calculations: input data, ranges, safety factors). It is recommended to add a section on practical application (the algorithm for calculating εp for given w, σd, σ3, N), and also list the limitations of scalability to other soils and frequencies. (lines 402–429).

Response 9: Thank you very much for your valuable comments on the conclusions. (1)-(3) in the revised manuscript combine (1)-(2), and (2) summarises in more depth the effectiveness of PSO-neural networks in predicting the cumulative deformation of silt soils. (3) describes the model's use of the interpolated data can be used to make a more accurate prediction of the unknown data from within the range of my dynamic stress, moisture content, and confining pressure, but further research is needed for the unknown data outside the range. In addition, factors such as freeze-thaw cycles were not considered in this paper; therefore, future research should focus on databases with different factors (freeze-thaw cycles, wet and dry cycles).

The change can be found (Page 18, lines486-508.)

Reviewer 2 Report

Comments and Suggestions for Authors

The present study focuses on the development of permanent deformation in silt soil under varying conditions of confining pressure dynamic stress amplitude, and water content.

My recommendation and reviewer report are summarized as following:

- Overall, the content has fatal English mistakes along with different types of typos. I would like to recommend an English grammar service or a proof reading by native speaker.

- What is the justification of this study? Authors should provide a logical way to justify their studies for the scientific community.

- The abstract must include some explicit information about the results obtained rather than giving general statements.

- Authors should more clearly emphasis the novelty of their work in the abstract and introduction.

- The references should be updated in the introduction.

- Quality of figures needs to be improved.

- Page 3, L106: please provide the origin of silt soil.

- Page 3, L107, 108: please revise the sentence.

- Measurement errors are missing.

- 2.2 Testing methodology: this section must be rewritten due to the English mistakes along with different types of typos.

- Please avoid repetition of the unit of measurement. For example: 10 to 80 kPa.

- Figs 4 and 5: Figure 5 is not a partial enlargement of Figure 4. Please provide a correct enlargement.

- I recommend combining Figures 4 and 5 together and showing the enlarged portion.

- Authors must place the results in context by comparing them with the literature.

- In the text, write "dynamic" instead of "Dynamic”.

- Please use the same term inside the text: "Figure" or "Fig."

- Page 5, L166-168: please add the corresponding reference.

- Figure 6: Authors should explain why the parameters in Figure 6c (axial cumulative strain between 0 and 10% and dynamic stress between 170 and 250 kPa) are different from those in Figures 6a, b, d, and e.

- Please correct the title of Fig. 6 as follows: “Fig. 6. Variation of axial cumulative deformation with the number of cycles at different moisture contents: (a) 17.3 % moisture content; (b) 18.3 % moisture content; (c) 19.3 % moisture content; (d) 20.3 % moisture content; and (e) 21.3 % moisture content.

- 3.3 Effect of Moisture contents on cumulative plastic strain: Figures 6c, d, and e are not well interpreted.

- Page 6, L196-199: please add the corresponding reference of the paragraph.

- Page 8, L219: please add the corresponding reference of the Equation 1.

- I strongly recommend that the authors combine the figures into a single figure called “Fig. 8”.

- Page 13: 4.3.1 Comparison of BP and PSO-BP prediction performance: this section must be improved. A comparison with the literature is missing.

- Page 16: Discussion: this section must be re-written and improved.

Indeed, one discussion should be included instead of two.

Comments on the Quality of English Language

Overall, the content has fatal English mistakes along with different types of typos. I would like to recommend an English grammar service or a proof reading by native speaker.

Author Response

Manuscript Number: buildings-3972699

Re: “Study on cumulative deformation of silt soil under traffic loading based on PSO-BP neural network”

 

Dear reviewers:

I am pleased to submit the revised paper. All your comments and questions have been addressed below.

 

Comments 1: Overall, the content has fatal English mistakes along with different types of typos. I would like to recommend an English grammar service or a proof reading by native speaker.

Response 1: We are very grateful for some of your suggestions on grammar, and we have made some changes to the grammar in response to this, to standardise the nouns.

Comments 2: What is the justification of this study? Authors should provide a logical way to justify their studies for the scientific community.

Response 2: Thank you for your question. Traditional predictions of cumulative deformation of soils mainly rely on empirical formulations (e.g., Monismith model) or complex elasto-plastic constitutive models. These methods are either of limited accuracy or have complex and computationally expensive parameter determination. Neural network methods, on the other hand, provide a new data-driven paradigm that can predict the cumulative deformation of soil bodies more quickly and accurately.

Comments 3: The abstract must include some explicit information about the results obtained rather than giving general statements.

Response 3: We sincerely thank the reviewer for the valuable suggestion regarding the abstract. In the revised version, we have completely restructured the abstract. The revised version is now clearly articulated:

In order to study the cumulative deformation of silt soil in highway foundation engineering, dynamic triaxial tests were conducted to investigate the effects of dynamic stress, confining pressure and moisture content on the cumulative plastic strain of silt soil under traffic loading. Particle swarm optimisation is used to improve the prediction of cumulative plastic strain in silt soils, and the architecture is optimised for traditional BP neural network learning, with the introduction of weights for better control of the development and analysis of the prediction results. In addition, this neural network also provides more accurate prediction of multiple factors, which further improves the prediction results. The results show that.The cumulative deformation of the silt soil decreases gradually with increasing confining pressure. The cumulative deformation decreases from 3.32 percent to 2.82 percent when the confining pressure increases from 60 kPa to 150 kPa. With the increase of dynamic stress and moisture content, the cumulative deformation gradually increases. The cumulative deformation rate was obtained by the derivation of the cumulative deformation and the number of cycles, and it was found that the cumulative deformation rate decreased gradually with the increase of the number of cycles. When the moisture content is 17.4%, the cumulative deformation rate decreases from 0.3912 to 4.54e-5 when the number of cycles increases from 1 to 10000. Based on the cumulative deformation test data of silt soil, the Monismith model is used for the prediction of plastic deformation, and the cumulative plastic deformation model is constructed by learning from the PSO-BP neural network, which takes into account the multiple factors of the moisture content, the confining pressure, and the magnitude of the dynamic stress. Prediction model. Comparing the three cumulative deformation prediction models, the PSO-BP neural network has the best prediction effect. All of them are more than 0.99.

The change can be found (Page 1, lines25 to 48.)

Comments 4: Authors should more clearly emphasis the novelty of their work in the abstract and introduction.

Response 4: We sincerely thank the reviewer for the constructive suggestion regarding the introduction. In the revised version, we have refined and expanded the introductory section. pecifically, we have placed greater emphasis on the novelty of the research findings in the introduction and abstract. The details are as follows:

(1) Most previous studies have focused on static characteristics and single influencing factors, with more limited exploration of dynamic behaviour under multiple factors;

(2) Most of the previous predictions of cumulative deformation were based on various correction models, this paper combines BP neural networks and particle swarm optimisation algorithms to further predict the cumulative deformation of silt soils, the effect of neural networks in predicting cumulative deformation has not yet been fully investigated; Based on the research gaps identified above, we clearly define the purpose of this study: that is, to elucidate the cumulative deformation characteristics of silt soils and to accurately predict the cumulative deformation through the combination of dynamic triaxial tests and neural networks. This will provide a theoretical basis for engineering applications.

The change can be found (Page 3, lines110 to 117.)

Comments 5: Quality of figures needs to be improved.

Response 5: We thank the reviewer for the valuable comments and appreciation of our work, In this article, the pixel width of all images is increased from 10,000 to 15,000 to improve their clarity.

Comments 6: L106: please provide the origin of silt soil.

Response 6: We sincerely thank the reviewer for this valuable comment. We acknowledge that the source of the soil sample was not added and has now been added to the text.

The change can be found (Page 3, lines120.)

Comments 7:  L107, 108: please revise the sentence.

Response 7: We thank the reviewer for the valuable comments and appreciation of our work, In response to your suggestion, we have added additional clarification. In the revised version, we have described the test methods used in more detail.

The can be found (Page 3, lines120-127.)

Comments 8: 2.2 Testing methodology: this section must be rewritten due to the English mistakes along with different types of typos.

Response 8: Thank you very much for your careful reading and thoughtful feedback on our manuscript.

This paper has been modified for part 2.2, specifically to avoid duplicating units of measurement as much as possible.

The change can be found (Page 4, lines132-150.)

Comments 9: Figs 4 and 5: Figure 5 is not a partial enlargement of Figure 4. Please provide a correct enlargement.

Response 9: We thank the reviewer for the valuable comments and appreciation of our work, Fig. 5 of this paper can better see the effect of different confining pressure on the cumulative deformation, and it is not a partial enlargement of Fig. 4. Therefore, Fig. 5 is renamed as the variation of cumulative deformation with the number of cycles under different confining pressure, which has been modified in the revised draft.

The change can be found (Page 5-6, lines168-173.)

Comments 10: I recommend combining Figures 4 and 5 together and showing the enlarged portion.

Response 10: Thank you very much for your careful reading and thoughtful feedback on our manuscript. Fig. 5 of this paper can better see the effect of different confining pressure on the cumulative deformation, and it is not a partial enlargement of Fig. 4. Therefore, Fig. 5 is renamed as the variation of cumulative deformation with the number of cycles under different confining pressure, which has been modified in the revised draft.

The change can be found (Page 5-6, lines168-173.)

Comments 11: Authors must place the results in context by comparing them with the literature.

Response 11: Thank you for your valuable suggestions. In this paper, the optimisation part of the PSO-BP neural network is compared with the existing literature to demonstrate the correctness of the laws and the feasibility of the PSO-BP neural network for the prediction of cumulative deformation.

The change can be found (Page 14, lines 391-398.)

Comments 12: In the text, write "dynamic" instead of "Dynamic”.

Response 12: Thank you very much for your careful reading and thoughtful feedback on our manuscript. The content has now been changed to dynamic.

Comments 13: Please use the same term inside the text: "Figure" or "Fig."

Response 13: We thank the reviewer for the valuable comments and appreciation of our work, In this document, the terminology has been changed to fig.

Comments 14: Page 5, L166-168: please add the corresponding reference.

Response 14: Many thanks to the reviewers for their questions about the references, which have been added in a revised version of this paper with specific relevant literature.(Ai Xihui. Research on cumulative deformation behaviour of loess improved by nano-SiO₂ based on stability theory[D]. Sichuan Agricultural.)

The change can be found (Page 20, lines586.)

Comments 15: Authors should explain why the parameters in Figure 6c (axial cumulative strain between 0 and 10% and dynamic stress between 170 and 250 kPa) are different from those in Figures 6a, b, d, and e.

Response 15: We thank the reviewer for the valuable comments and appreciation of our work, In Fig 6b, d and e of this paper, the dynamic stress should be 170-210 kPa for 18.4% moisture content, 130-170 kPa for 20.4% moisture content, and 100-150 kPa for 21.4% moisture content, and the diagrams have now been revised.

The change can be found (Page 7, lines 202-207.)

Comments 16: Please correct the title of Fig. 6 as follows: “Fig. 6. Variation of axial cumulative deformation with the number of cycles at different moisture contents: (a) 17.3 % moisture content; (b) 18.3 % moisture content; (c) 19.3 % moisture content; (d) 20.3 % moisture content; and (e) 21.3 % moisture content.

Response 16: We truly appreciate the reviewer’s constructive criticisms and detailed advice. We have made changed the title of Fig. 6 as follows: “Fig. 6. Variation of axial cumulative deformation with the number of cycles at different moisture contents: (a) 17.3 % moisture content; (b) 18.3 % moisture content; (c) 19.3 % moisture content; (d) 20.3 % moisture content; and (e) 21.3 % moisture content.

The change can be found (Page 7.)

Comments 17: 3.3 Effect of Moisture contents on cumulative plastic strain: Figures 6c, d, and e are not well interpreted.

Response 17: Thank you very much to the reviewers for their valuable comments on this issue, and we have more specifically described the changing law of cumulative deformation at different moisture contents in (a)-(e). When in different moisture contents, the dynamic stress required to achieve 5% damage of the specimens is gradually decreasing with the increase of the function rate, in which the dynamic stress required to achieve damage in (c), (d) and (e) has decreased to below 200 kPa. This has been added to the revised version.

The change can be found (Page 6, lines 202-206.)

Comments 18: Page 6, L196-199: please add the corresponding reference of the paragraph.

Response 18: Many thanks to the reviewers for their questions about the references, which have been added in a revised version of this paper with specific relevant literature.(Liu Songbiao. Experimental study on deformation characteristics and shear characteristics of loess under wet load[D]. Changan University, 2023)

The change can be found (Page 20, lines 588.)

Comments 19: Page 8, L219: please add the corresponding reference of the Equation 1.

Response 19: Many thanks to the reviewers for their questions about the references, which have been added in a revised version of this paper with specific relevant literature.(CHEN Kang, LIU Xianfeng, JIANG Guanlu, et al. Experimental study on the effect of moisture content on the dynamic properties of red bedded mudstone fill [J]. Geotechnics, 2024, 45(12): 3705-3716.)

The change can be found (Page 20, lines 590.)

Comments 20: I strongly recommend that the authors combine the figures into a single figure called “Fig. 8”.

Response 20: Valuable comments on the graphs are very much appreciated, as different graphs correspond to different water contents and their characteristic laws are not exactly the same, so this is not combined in this paper.

Comments 21: 4.3.1 Comparison of BP and PSO-BP prediction performance: this section must be improved. A comparison with the literature is missing.

Response 21: Very much your valuable comments, this paper indeed did not compare with the laws of the relevant literature, the revised draft added a comparison with the literature(Sun Y, Zhou S, Meng S, et al. Accumulative plastic strain of freezing–thawing subgrade clay under cyclic loading and its particle swarm optimisation–back-propagation-based prediction model [J]. Cold Regions Science and Technology, 2023, 214: 103946), the laws are basically the same, more can determine the feasibility of this neural network model.

The change can be found (Page 14-15, lines 392-398.)

Comments 22: Discussion: this section must be re-written and improved.

Response 22: We are very grateful for some of your suggestions on discussion, In our revised manuscript, for the discussion section we only address the feasibility of PSO-BP neural networks for the prediction of cumulative deformation of silt soils, revolving around PSO-BP neural networks and discussing their superiority.

The change can be found (Page 17, lines 461-472.)

Reviewer 3 Report

Comments and Suggestions for Authors

This paper proposes a neural network model based on particle swarm optimization algorithm, which aims to accurately predict the cumulative deformation of silt soil under the action of different factors, providing an important reference for the research in this field, which is innovative but has the following deficiencies:

 

1:

The title could be more specific by clarifying the intended application scope. For instance, specifying whether the findings are applicable to highway subgrades or the transport infrastructures would enhance its relevance.

 

2:

The abstract should be restructured to clearly address the scientific question and include quantitative results. The editorial board recommends using the following structured format:

• Background: Place the research in context and state the objective.
• Methods: Briefly describe the experimental and modeling approach.
• Results: Summarize key findings with quantitative data.
• Conclusion: State the main conclusions and implications.

 

3:

The manuscript uses multiple English expressions for the same technical term (e.g., “perimeter pressure” and “confining pressure”). It is recommended to adopt a consistent terminology throughout the paper. For instance, “confining pressure” is the standard term in geotechnical engineering and should be used uniformly.

 

4:

In Section 4.2.3, grey correlation analysis is mentioned to evaluate the influence of dynamic stress amplitude, water content, and confining pressure on cumulative plastic strain. However, the specific calculation procedure is not provided. Please include a detailed description of the grey correlation analysis method and the computational steps applied in this study.

 

5:

What do the grey correlation degree and characteristic parameters of cumulative deformation factors represent? A correlation value of approximately 0.7 is considered high, but the evaluation criteria or threshold for such interpretation are not explained. Please clarify the meaning and benchmark values used for assessing the correlation strength.

 

6:

The authors mention using three characteristic parameters derived from grey correlation analysis as inputs to a PSO algorithm, with specific parameter settings (e.g., inertia weight = 0.9, learning factors c₁ = c₂ = 4.494, etc.). Please explain the rationale behind selecting these parameter values and the optimization process involved.

 

7:

When the applied dynamic stress amplitude is small, the material exhibits plastic creep behavior. Please specify the evaluation criteria for identifying plastic creep and describe the transitional process from elastic to plastic creep stages.

 

Author Response

Manuscript Number: buildings-3972699

Re: “Study on cumulative deformation of silt soil under traffic loading based on PSO-BP neural network”

 

Dear reviewers:

I am pleased to submit the revised paper. All your comments and questions have been addressed below.

 

Comments 1: The title could be more specific by clarifying the intended application scope. For instance, specifying whether the findings are applicable to highway subgrades or the transport infrastructures would enhance its relevance.

Response 1: Thank you very much for your constructive suggestions on the title.The original title 《Study on cumulative deformation of silt soil under cyclic loading based on PSO-BP neural network》aims to emphasize the cumulative deformation behaviour of silt soil under cyclic loading and to study the cumulative deformation in combination with PSO-BP neural network. Now the title is changed to 《Study on cumulative deformation of silt soil under traffic loading based on PSO-BP neural network》, which aims to emphasise the cumulative deformation characteristics of silt soil under simulated traffic loading, and to provide experience for engineering applications.

The change can be found (Page 1, lines 1.)

Comments 2: The abstract should be restructured to clearly address the scientific question and include quantitative results. The editorial board recommends using the following structured format:

Background: Place the research in context and state the objective.

Methods: Briefly describe the experimental and modeling approach.

Results: Summarize key findings with quantitative data.

Conclusion: State the main conclusions and implications.

Response 2: We sincerely thank the reviewer for the constructive suggestion regarding the abstract. In the revised manuscript, we have refined and expanded the introduction section. Specifically, We systematically summarise existing research advances in the field of cumulative deformation of silt soils and highlight the following innovations and summaries of this paper:

Background-study the cumulative deformation of silt soil in highway foundation engineering

Methods-dynamic triaxial tests were conducted to investigate the effects of dynamic stress, confining pressure and moisture content on the cumulative plastic strain of silt soil under traffic loading.

Results- Advantages of PSO-BP neural network model regarding the effect of moisture content, confining pressure, and dynamic stress on the cumulative deformation of silty soils.

Conclusion- Elucidation of cumulative deformation characteristics and the effectiveness of PSO-BP neural network in predicting cumulative deformation of silty soil.

This revised abstract highlights more of the innovations in this paper.

Where in the recised manuscript this change can be found(Page 1, lines25 to 48.)

Comments 3: The manuscript uses multiple English expressions for the same technical term (e.g., “perimeter pressure” and “confining pressure”). It is recommended to adopt a consistent terminology throughout the paper. For instance, “confining pressure” is the standard term in geotechnical engineering and should be used uniformly.

Response 3: We sincerely thank the reviewer for carefully identifying the language, It is true that there is no consensus on the formulation of confining pressure in this paper, which has now been expressed as confining pressure.

Comments 4: In Section 4.2.3, grey correlation analysis is mentioned to evaluate the influence of dynamic stress, moisture content, and confining pressure on cumulative plastic strain. However, the specific calculation procedure is not provided. Please include a detailed description of the grey correlation analysis method and the computational steps applied in this study.

Response 4: We sincerely thank the reviewer for raising this important point. I really did not provide a detailed description of the grey correlation calculation, details of the calculation have been added to this paper. (Matlab programming tool was used to calculate the grey correlation for silt loam for all the different factors).

The change can be found (Page 11-12, lines 297-308.)

Comments 5: What do the grey correlation degree and characteristic parameters of cumulative deformation factors represent? A correlation value of approximately 0.7 is considered high, but the evaluation criteria or threshold for such interpretation are not explained. Please clarify the meaning and benchmark values used for assessing the correlation strength.

Response 5: We sincerely thank the reviewer for raising this important point. The characteristic parameters of grey correlation in this paper represent the three influencing factors of confining pressure, moisture content and dynamic stress, respectively.Grey correlation analysis is a method for analysing multi-factor correlations. It is generally stipulated that a correlation is considered high when the grey correlation exceeds 0.6, a criterion that has been added to this paper.

The change can be found (Page 11-12, lines 299-305.)

Comments 6: The authors mention using three characteristic parameters derived from grey correlation analysis as inputs to a PSO algorithm, with specific parameter settings (e.g., inertia weight = 0.9, learning factors c₁ = c₂ = 4.494, etc.). Please explain the rationale behind selecting these parameter values and the optimization process involved.

Response 6: We sincerely appreciate the reviewer’s insightful comments. In this paper, the inertia weights, learning factor population update times, population size, maximum speed, minimum speed, etc. are obtained through iterative operations to obtain the optimal weights and thresholds for neural networks, and optimised by constantly debugging the values of inertia weights, learning factor population update times, population size, maximum speed, minimum speed. For example, when the inertia weight is adjusted from 0.492 to 0.494, its RMSE is reduced from 0.018 to 0.012, which is better.

In this paper, the specific optimisation process is added.

The change can be found (Page 14-15, lines 391-398.)

Comments 7: When the applied dynamic stress is small, the material exhibits plastic creep behavior. Please specify the evaluation criteria for identifying plastic creep and describe the transitional process from elastic to plastic creep stages. In this paper, the cumulative deformation increases rapidly from 1.76% to 3.22% and then tends to stabilise, indicating that the specimen shows plastic creep phenomenon.

This paper has been revised by adding the criteria for determining plastic creep and the process of its development to the revised version.

The change can be found (Page 6, lines 176-183.)

 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Overall, the authors have made progress and corrected some key issues (the arithmetic for the influence of σ₃, expanded the "Materials," described the selection of nodes in the hidden layer, added cross-validation/N sampling, and refined the metrics and model comparisons). However, a number of requirements have only been partially met: the study's objective remains vague; the PSO-BP architecture is described with internal inconsistencies; the statistical significance of differences between models is not demonstrated (there are no 95% CI/bootstrap and no true Bland-Altman plots); stylistic/terminological inconsistencies and notational inconsistencies remain.

The study's objective in its current form remains too general and does not provide clear guidelines for the reader. Authors should specify what exactly they are testing and how the achievement of the goal is measured: state the subject of the study, formulate the ultimate goal in concrete terms (e.g., developing and verifying the PSO-BP model for predicting plastic deformations), and briefly outline the main stages of the work.

The description of the PSO-BP architecture requires clarification. The text contains inconsistencies between the number of neurons in layers and the number of weights, as well as duplicate formulas and unclear notations. The network structure needs to be agreed upon, the exact number of neurons at each layer is specified, the loss function used, the data normalization method, and the PSO parameters described.

The comparison of models has not yet been statistically validated. Differences between PSO-BP, BP, and Monismith are assessed only by mean metric values, without confidence intervals or significance testing. Authors should calculate 95% confidence intervals or use bootstrap estimation, and supplement the results with Bland-Altman plots showing the error distribution and systematic biases.

The text contains some stylistic and terminological inaccuracies, as well as inconsistent notations. All parameters and symbols must be standardized, inaccurate translations of technical terms must be corrected, and the captions for figures and tables must be verified.

Comments on the Quality of English Language

The text contains some stylistic and terminological inaccuracies, as well as inconsistent notations. All parameters and symbols must be standardized, inaccurate translations of technical terms must be corrected, and the captions for figures and tables must be verified.

Author Response

Comments 1: The study's objective in its current form remains too general and does not provide clear guidelines for the reader. Authors should specify what exactly they are testing and how the achievement of the goal is measured: state the subject of the study, formulate the ultimate goal in concrete terms (e.g., developing and verifying the PSO-BP model for predicting plastic deformations), and briefly outline the main stages of the work. Response 1: We thank the reviewers for their valuable comments and acknowledgement of our work and have elaborated the research directions of this paper and future research directions in the revised manuscript in conjunction with the conclusion section. this study constructs a cumulative plastic deformation prediction model using the PSO-BP neural network, which is trained on experimental data and incorporates multiple influencing factors (i.e., moisture content, confining pressure, and dynamic stress). Compared with the BP neural network model and the Monismith model, the PSO-BP model exhibits more excellent fitting performance. Through interpolation, the model can achieve high-precision prediction of unseen data within the defined ranges of dynamic stress, moisture content, and confining pressure; however, predictions for data beyond this parameter range require further investigation. In addition, factors such as freeze-thaw cycles were not incorporated in the current study. Future research should focus on expanding the scope to construct a comprehensive database encompassing diverse influencing factors, thereby improving the model’s universality and applicability. The change can be found (Page 19, lines527 to 542.) Comments 2: The description of the PSO-BP architecture requires clarification. The text contains inconsistencies between the number of neurons in layers and the number of weights, as well as duplicate formulas and unclear notations. The network structure needs to be agreed upon, the exact number of neurons at each layer is specified, the loss function used, the data normalization method, and the PSO parameters described. Response 2: Thank you very much for your constructive comments, we have detailed the PSO-BP architecture in the revised draft as follows: 1. Determine the number of nodes (4x4x1) in the input layer, hidden layer, and output layer by hyperparameter optimisation. Calculate the weight between the input layer and the hidden layer by multiplying the number of nodes in the input layer by the number of nodes in the hidden layer (16). The weight between the hidden layer and the output layer is calculated by multiplying the number of nodes in the hidden layer by the number of nodes in the output layer (4). 2. MSE is selected as the loss function of this paper and the remaining two evaluation criteria (MAE, RMSE) are obtained through MSE. It is obtained through the following equation: 3. Data normalisation normalises the training input P-train to the training output T-train by saving the parameter ps-input and adopting the same parameters; meanwhile, the test input P-test is normalised to the test output T-test by saving the parameter ps-output and adopting the same parameters. 4. Selection of PSO-BP parameters, select the appropriate population size, calculate the final loss value by selecting different size of population size and find that the loss value is minimum when the population size is 10, so as to obtain the optimal training parameters. Finally determine the inertia weights, the number of population iterations, the learning factor and other specific parameters. The change can be found (Page 13-14, lines339 to 401.) Comments 3: The comparison of models has not yet been statistically validated. Differences between PSO-BP, BP, and Monismith are assessed only by mean metric values, without confidence intervals or significance testing. Authors should calculate 95% confidence intervals or use bootstrap estimation, and supplement the results with Bland-Altman plots showing the error distribution and systematic biases. Response 3: Thank you for your question. In response to the absence of confidence intervals or significance tests, we supplemented the results by adding 95% confidence intervals to all prediction curves. The change can be found (Page 17-19.) Comments 4: The text contains some stylistic and terminological inaccuracies, as well as inconsistent notations. All parameters and symbols must be standardized, inaccurate translations of technical terms must be corrected, and the captions for figures and tables must be verified. Response 4: Thank you very much for your constructive comments. In this revised version of the thesis, several corrections have been made to the terminology and symbols and to some issues; the terminology relates mainly to the terms confining pressure, dynamic stress and moisture content.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Thank you for your work in revising your manuscript according to the indicated comments. 

The revised paper is well improved but additional corrections must be made.  

• It is not necessary to repeat the unit of measurement (60 to 150 kPa, 3.3266 to 1.6981 %, 1.76 to 3.22 %, 170 to 210 kPa,...)
• - Page 4: the two figures 2 and 3 can be grouped together in the same figure.
• - Page 5: 3.1.1 Effect of Confining pressure on cumulative plastic strain: the paragraph must be revised because the word "Fig.4" has been repeated several times.
• - Fig 13, 14, 15, 16, . PSO-BP flowchart: the quality of figure must be improved.
• - the subtitle "4.Discussion" has been repeated twice: the second title on page 17 must be deleted and the paragraph must be kept.

 

Author Response

Manuscript Number: buildings-3972699

Re: “Study on cumulative deformation of silt soil under traffic loading based on PSO-BP neural network”

 

Dear reviewers:

I am pleased to submit the revised paper. All your comments and questions have been addressed below.

 

Comments 1: It is not necessary to repeat the unit of measurement (60 to 150 kPa, 3.3266 to 1.6981 %, 1.76 to 3.22 %, 170 to 210 kPa,...)

Response 1: We are very grateful for some of your suggestions on grammar, We have reduced the number of duplicate units of measurement.

The change can be found (Page 6-7, lines175 to 209.)

Comments 2: Page 4: the two figures 2 and 3 can be grouped together in the same figure.

Response 2: We sincerely thank the reviewer for the constructive suggestion regarding the introduction. In the revised version, We have merged the two charts.

The change can be found (Page 6)

Comments 3: 3.1.1 Effect of Confining pressure on cumulative plastic strain: the paragraph must be revised because the word "Fig.4" has been repeated several times.

Response 3: We thank the reviewer for the valuable comments and appreciation of our work, We have reduced this description of Fig 4. in the revised version.

Comments 4:  Fig 13, 14, 15, 16, . PSO-BP flowchart: the quality of figure must be improved.

Response 4: Thank you very much for your questions about the quality of the figure, we have made some adjustments in the revised version for Figures 13, 14, 15 and 16 to make them clearer.

Comments 5: the subtitle "4.Discussion" has been repeated twice: the second title on page 17 must be deleted and the paragraph must be kept.

Response 5: We sincerely thank the reviewer for the constructive suggestion regarding the discussion. We have deleted the second heading on page 17 and merged it with the conclusion in the revised version

The change can be found (Page 20, lines527 to 542.)

Author Response File: Author Response.docx