Modeling the Dynamic Properties of the Polyurethane Mixture with Dense Gradation Using the 2S2P1D Model
, Wenbin Gao 3, Shiping Cui 1, Zhen Li 4, Peiyu Zhang 1, Lin Wang 1, Wensheng Zhang 5, Chunhua Su 1 and Shijie Ma 1,*
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsModeling the Dynamic Properties of the Polyurethane Mixture with Dense Gradation Using the 2S2P1D model
In the paper ttiled “Modeling the Dynamic Properties of the Polyurethane Mixture with Dense Gradation Using the 2S2P1D model” the authors have used Polyurethane mixture for replacing the traditionally used asphalt mixture. The characterization of linear visco-elastic (LVE) property of the PU mixture was done using the 2S2PID model to find its feasibility and comparison was made with SBS − modified asphalt mixture with the same aggregate gradation and binder content. Study showed that PU mixture exhibited higher elastic property and lower creep property, The 2S2P1D model exhibited higher prediction accuracy than the SCM model but should improve creep and dashpot elements for much more accuracy. Paper seems to be mathematical at some places. The authors shall address the following queries before considering the paper for acceptance.
Major Issues
1. The authors shall briefly explain the significance of seven parameters of the 2S2P1D model for the PU and SBS − modified asphalt mixtures. How do these parameters influence the visco-elastic behaviour? How does this method remain efficient over others?
2. The authors say that based on Table 4 and Fig. 4(c), comparing both models under the same conditions, the predicted values from the 2S2P1D model were closer to the line of equality with minimal deviation. On the other hand, the predicted values from the SCM model were slightly scattered from the line of equality compared to the 2S2P1D model. But the fitting accuracy is very close to each other. Why is this so?
3. What is the significance of the phase angle in this study?
4. The authors shall consider some new relevant papers to be referred, if applicable and available. Many of the paper are quite old (before 2020). This can show the advancement in the field.
5. How does this paper fit the scope of the journal coatings, The authors shall include this in the introduction part of the paper.
Comments on the Quality of English Language
Minor issues
Minor English correction is suggested. Few of them are shown below.
1. In Abstract Line No. 23 “of” needs to be omitted.
2. In Page No. 4, Line No. 168, it would be “It was originally calibrated and developed”….”
There are some more places to get corrected.
Author Response
I appreciate your suggestions and valuable advice. Based on the suggestions, I modified the manuscripts as follows.
Point 1: The authors shall briefly explain the significance of seven parameters of the 2S2P1D model for the PU and SBS-modified asphalt mixtures. How do these parameters influence visco-elastic behaviour? How does this method remain efficient over others?
Response 1: The seven parameters for the 2S2PID model correspond to viscous, elastic, and creep properties of the PU and SBS-modified asphalt mixtures by different elements. Fig. 1 and lines 177-193 show that these elements represent different properties and how the element or parameters of the 2S2PID model influence the viscoelastic properties of the PU and SBS-modified asphalt mixtures. In comparison to other models, the 2S2PID model has elements with clear physical meanings that reflect different properties of the PU and SBS-modified asphalt mixture and introduces the creep element to reflect the creep properties which is the obvious improvement.
Point 2: The authors say that based on Table 4 and Fig. 4(c), comparing both models under the same conditions, the predicted values from the 2S2P1D model were closer to the line of equality with minimal deviation. On the other hand, the predicted values from the SCM model were slightly scattered from the line of equality compared to the 2S2P1D model. But the fitting accuracy is very close to each other. Why is this so?
Response 2: In comparison to the SCM model, the 2S2PID model improved the prediction accuracy, but the improvement is not so significant. According to analysis, this result can be explained by that the creep and viscous properties of the PU mixture are different from that of the SBS-modified asphalt mixture, the 2S2PID model should be improved by adding the viscous elements and decreasing the creep elements.
Point 3: What is the significance of the phase angle in this study?
Response 3: The phase angle is also used to evaluate the prediction accuracy of the 2S2PID model, if the prediction of the 2S2PID model for a LVE material is high, the predicted and measured phase angle data would have a good agreement. By comparing the measured phase angle and predicted phase angle by the 2S2PID model, the results demonstrate that the 2S2PID model should be improved for the PU mixture.
Point 4: The authors shall consider some new relevant papers to be referred, if applicable and available. Many of the paper are quite old (before 2020). This can show the advancement in the field.
Response 4: I have collected and read about 22 papers about the 2S2PID model for asphalt mixture after 2020, only part of these papers could provide useful information, and a few of these papers are referred to in this paper.
Point 5: How does this paper fit the scope of the journal coatings, The authors shall include this in the introduction part of the paper.
Response 5: The journal coatings calls for papers about the surface material of the pavement, which is part of the study area of this paper.
Point 6: In Abstract Line No. 23 “of” needs to be omitted.
Response 6: The mistake has been corrected in the new manuscript.
Point 7: In Page No. 4, Line No. 168, it would be “It was originally calibrated and developed”….”
Response 7: The mistake has been corrected in the new manuscript.
Point 8: There are some more places to get corrected.
Response 8: I have rechecked the manuscript, and mistakes were corrected in the new manuscript.
Thank you again for your hard, meticulous work!
Best regards!
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors provided the materials and methods in Section 2 for experimental investigation. As they claim to have characterised the linear viscoelastic behaviour of the PU mixture at elevated temperatures and loading frequencies (particularly in the small strain domain and considering only a few applied cycles), they failed to include any experimental results in the manuscript.
Comments on the Quality of English LanguageThe English language is extremely difficult to understand/incomprehensible.
Author Response
I appreciate your suggestions and valuable advice. Based on the suggestions, I modified the manuscripts as follows.
Point 1: The authors provided the materials and methods in Section 2 for experimental investigation. As they claim to have characterised the linear viscoelastic behaviour of the PU mixture at elevated temperatures and loading frequencies (particularly in the small strain domain and considering only a few applied cycles), they failed to include any experimental results in the manuscript.
Response 1: I am sorry about the confusion about this paper. Limited by the length of this paper, not all the test data were provided. All the test results of the dynamic modulus and phase angle for the PU mixture and SBS-modified asphalt mixture were detailed in the reference ( https://doi.org/10.3390/coatings13071143).
Point 2: The English language is extremely difficult to understand/incomprehensible.
Response 2: I have rechecked the manuscript, sentences that caused confusion were rewritten.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsModeling the Dynamic Properties of the Polyurethane Mixture with Dense Gradation Using the 2S2P1D model
Recommendation: Publish after minor revisions noted.
Comments:
This is an interesting contribution, which overall meets the criteria for publication. The work performs an analysis of using the rheological 2S2P1D model to characterize the linear viscoelastic behavior of PU and asphalt mixtures presenting a similar aggregate gradation and binder concentration.
Authors conclude with this study that this model successfully predicts the dynamic modulus of PU mixture by the minimization method, showing a good correlation with the experimental values. Additionally, the 2S2P1D model presented more precise predictions than the SCM for predicting the dynamic modulus of the PU, being an interesting way of obtaining theoretical data.
However, the viscous property and high-temperature properties are not accurately predicted, being necessary to include some improvements in the method.
The 2S2P1D model presents room for improvement on the prediction of creep and dashpot for the PU mixture. Thus, this study provides relevant information for improving the response and performance of PU and asphalt mixtures.
This research has been carefully carried out, however, there are some critical weaknesses that should be addressed prior to its publication.
ABSTRACT
Please, provide the definition of each abbreviation before using it; SBS, SCM.
RESULTS AND DISCUSSION:
1) Check and correct the significant numbers in Table 2, 3, 4, and 5.
2) The quality of the presented Figures is poor. Axes are difficult to read in graphs, please, increase the size of numbers and magnitudes.
3) In my opinion, mixing the results and discussion sections would help the reader to understand instead of going up and down to see the graphs and data.
Comments on the Quality of English Language
Minor editing of English language required
Author Response
I appreciate your suggestions and valuable advice. Based on the suggestions, I modified the manuscripts as follows.
Point 1: Please, provide the definition of each abbreviation before using it; SBS, SCM.
Response 1: The abbreviation of SBS and SCM in the abstract has been rechecked, and the initial definitions were provided.
Point 2: Check and correct the significant numbers in Table 2, 3, 4, and 5
Response 2: The numbers in Table 2-5 have been rechecked, decimal places of these numbers have been corrected.
Point 3: The quality of the presented Figures is poor. Axes are difficult to read in graphs, please, increase the size of numbers and magnitudes.
Response 3: The figures in this paper could be enlarged to 10 times without distortion, the poor quality is due to the size of the figure (6cm*6cm) required by the template. Figures in this paper have been replotted for reading.
Point 4: In my opinion, mixing the results and discussion sections would help the reader to understand instead of going up and down to see the graphs and data.
Response 4: The template requires that the test result should be in section 3, and the result discussion should be in section 4. I am sorry about the confusion in this paper.
Point 5: Minor editing of English language required.
Response 5: I have rechecked the manuscript, sentences which caused confusion were rewritten.
Reviewer 4 Report
Comments and Suggestions for AuthorsThe authors investigated the feasibility of using the 2S2P1D model to characterize the viscoelastic behavior of both Polyurethane (PU) and SBS-modified mixtures, by keeping both bitumen content and aggregate gradation fixed.
- I question how 9 authors can meaningfully contribute to one paper.
- Line 23: “The index η of cannot accurately characterize …” Please check and revise.
- Line 119: The authors state that “this study focuses on characterizing the linear viscoelastic behavior of the PU mixture under elevated temperatures and loading frequencies”. However, at line 33 they also stated that “at high temperatures … the asphalt mixture exhibits a nonlinear viscoelastic plastic behavior”. Is it correct to assume a LVE behavior when they are dealing with PU mixtures at high temperatures? Please explain.
- The introduction is a bit confusing. What is the main gap in the scientific literature the authors wanted to fill? It is not very clear by reading the introduction section.
- Line 149: is it “uε” intended to be “µε”? Please check and eventually revise.
- Line 149: “six recommended test temperatures … were utilized”. Please provide a scientific reference.
- Line 159: in addition to mathematical-empirical models, machine-learning (ML) models have been gaining massive popularity within the scientific community in recent years. Some of these have been able to provide accurate and simultaneous predictions in terms of dynamic modulus and phase angle, and it would be worth at least mentioning them:
https://doi.org/10.1016/j.conbuildmat.2021.123642
https://doi.org/10.1016/j.conbuildmat.2023.132709
https://doi.org/10.1016/j.conbuildmat.2023.133610
- Authors are strongly encouraged to standardize the formatting of equations as well as figures. They should carefully revise the text on Figures’ axes by using consistent notation (sometimes they write “variable/unit of measurement”, sometimes “variable (unit of measurement)” and so on.) Figure 4(c) is missing units of measurement both on x- and y-axis.
- Please use the same number of decimal digits to describe the results within the same Table (in Table 2, Table 3, Table 4, and Table 5). Furthermore, it is not necessary to go to 9 decimal places when describing errors (Table 2). 4 decimal digits are sufficient.
- Is it significant to say that 2S2P1D model better fits PU mixture than SBS-one when the difference in R2 metric can be read just at the 5th decimal digit? Please explain.
- is it meaningful to talk about the sixth (or even seventh) decimal place to describe the phase angle in Table 5? Please explain.
- Be careful that 35th reference is “!!!INVALID CITATION!!!”
Comments on the Quality of English LanguageEnglish language is overall fine: however, some improvements could be made.
Author Response
I appreciate your suggestions and valuable advice. Based on the suggestions, I modified the manuscripts as follows.
Point 1: I question how 9 authors can meaningfully contribute to one paper.
Response 1: All authors made significant contributions to this paper, they responded with Methodology, funding acquisition, test material providing, investigation, test performing, test result analysis, visualization, writing - the original draft, and writing review & editing, respectively.
Point 2: Line 23: “The index η of cannot accurately characterize …” Please check and revise.
Response 2: The mistake has been corrected in the new manuscript.
Point 3: Line 119: The authors state that “this study focuses on characterizing the linear viscoelastic behavior of the PU mixture under elevated temperatures and loading frequencies”. However, at line 33 they also stated that “at high temperatures … the asphalt mixture exhibits a nonlinear viscoelastic plastic behavior”. Is it correct to assume a LVE behavior when they are dealing with PU mixtures at high temperatures? Please explain.
Response 3: The properties of the PU mixture at high temperature are assumed to a LVE behavior in this paper, and this paper tried to verify this assumption by the 2S2PID model.
Point 4: The introduction is a bit confusing. What is the main gap in the scientific literature the authors wanted to fill? It is not very clear by reading the introduction section.
Response 4: The PU mixture is a new engineering material for pavement paving, very little research is focused on its LVE properties, especially about the 2S2PID model. Therefore, the introduction introduced the literature about the application of the 2S2PID model for the asphalt mixture and provided information about the 2S2PID model to readers.
Point 5: Line 149: is it “uε” intended to be “µε”? Please check and eventually revise.
Response 5: The mistake has been corrected in the new manuscript.
Point 6: Line 149: “six recommended test temperatures … were utilized”. Please provide a scientific reference.
Response 6: The recommended test temperatures were selected according to the test range of the asphalt mixture performance tester (AMPT).
Point 7: Line 159: in addition to mathematical-empirical models, machine-learning (ML) models have been gaining massive popularity within the scientific community in recent years. Some of these have been able to provide accurate and simultaneous predictions in terms of dynamic modulus and phase angle, and it would be worth at least mentioning them:
https://doi.org/10.1016/j.conbuildmat.2021.123642
https://doi.org/10.1016/j.conbuildmat.2023.132709
https://doi.org/10.1016/j.conbuildmat.2023.133610
Response 7: Thank you for providing these valuable references about the machine learning method, these references are added in lines 63-69 in the new manuscript. The machine learning method is the most effective method to solve the problem for predicting the dynamic properties of the asphalt mixture. I would thoroughly study the machine learning method to predict the dynamic properties of the PU mixture.
Point 8: Authors are strongly encouraged to standardize the formatting of equations as well as figures. They should carefully revise the text on Figures’ axes by using consistent notation (sometimes they write “variable/unit of measurement”, sometimes “variable (unit of measurement)” and so on.) Figure 4(c) is missing units of measurement both on x- and y-axis.
Response 8: All the equations and figures were rechecked and corrected in the new manuscript.
Point 9: Please use the same number of decimal digits to describe the results within the same Table (in Table 2, Table 3, Table 4, and Table 5). Furthermore, it is not necessary to go to 9 decimal places when describing errors (Table 2). 4 decimal digits are sufficient.
Response 9: The numbers in Tables 2-5 have been rechecked, decimal places of these numbers have been corrected.
Point 10: Is it significant to say that 2S2P1D model better fits PU mixture than SBS-one when the difference in R2 metric can be read just at the 5th decimal digit? Please explain.
Response 10: The 2S2P1D model is better to fit the PU mixture than the SBS-modified asphalt mixture, this result is proved by the index of R2 combined with Se/Sy, Error2, and SSE.
Point 11: is it meaningful to talk about the sixth (or even seventh) decimal place to describe the phase angle in Table 5? Please explain.
Response 11: The numbers in Table 5 have been rechecked, decimal places of these numbers have been corrected.
Point 12: Be careful that 35th reference is “!!!INVALID CITATION!!!”
Response 12: Thank you for the reminder, I have rechecked all the references and corrected the mistakes.
Thank you again for your hard, meticulous work!
Best regards!
Author Response File: Author Response.pdf
Reviewer 5 Report
Comments and Suggestions for AuthorsComments in the attachment.
Comments for author File: Comments.pdf
Author Response
I appreciate your suggestions and valuable advice. Your suggestion about this paper is very worthwhile, many mistakes or details with confusion have been pointed out. Based on the suggestions, I modified the manuscripts.
Thank you again for your hard, meticulous work!
Best regards!
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsNA
Comments on the Quality of English LanguageNA
Reviewer 4 Report
Comments and Suggestions for AuthorsThe authors have properly replied to all the statements made. The paper can be considered suitable for publication
