Study on the Construction of Dynamic Modulus Master Curve of Polyurethane Mixture with Dense Gradation
, Wenbin Gao 3, Shiping Cui 1, Wensheng Zhang 4, Shijie Ma 1,*, Baoji Miao 4, Chunhua Su 1, Jincheng Wei 1, Shan Liu 1 and Fuxiu Liu 1Round 1
Reviewer 1 Report
Dear Authors,
The article is very interesting, the subject of designing asphalt mixes and the analysis of their durability is a current topic, which you confirm.
The article focuses mainly on different variants of data presentation and simulation of basic data. You analyze mechanical properties of mineral-asphalt mixtures at the difference in charging frequency and temperature. The temperature-related factor is already subject to thermodynamic changes, and these, in turn, are related to phase changes (especially with the crystallization of amorphous phases) - such information is missing in the article, for example, the oxide composition of the asphalt mix, on the basis of which, apart from physical and mechanical properties, durability can be analyzed and direction of crystallization (under the influence of temperature) of amorphous phases.
Are you willing to provide such data and information, or is the article based mainly on simulation data in terms of physical and mechanical properties?
Regards!
Author Response
I appreciate your suggestions and valuable advice, thank you for your hard work. Point 1: The article focuses mainly on different variants of data presentation and simulation of basic data. You analyze mechanical properties of mineral-asphalt mixtures at the difference in charging frequency and temperature. The temperature-related factor is already subject to thermodynamic changes, and these, in turn, are related to phase changes (especially with the crystallization of amorphous phases) - such information is missing in the article, for example, the oxide composition of the asphalt mix, on the basis of which, apart from physical and mechanical properties, durability can be analyzed and direction of crystallization (under the influence of temperature) of amorphous phases. Are you willing to provide such data and information, or is the article based mainly on simulation data in terms of physical and mechanical properties?
Response 1: The study investigated the construction of a dynamic modulus master curve for a polyurethane mixture with dense gradation, using five master curve models, five shift factor equations, and four error minimization methods. The results showed that the generalized logistic sigmoidal model and sigmoidal combined Christensen−Anderson−Marasteanu model with the WLF equation had the most accurate master curve fitting result, and recommended accurate error minimization methods, master curve model, and shift factor equation. The paper provides a detailed investigation into the construction of a dynamic modulus master curve for a polyurethane mixture with dense gradation, which can be a valuable contribution to the field of pavement design and material selection. The dynamic modulus test about the PU mixture was performed on the specimen with the dimension of 150 mm in height and 100 mm in diameter. The microstructure of the PU binder itself was not involved in this paper. Therefore, there was no information about the crystallization of amorphous phases of the PU binder which could be provided in the paper. But the idea about the crystallization of amorphous phases of the PU binder is an excellent idea for further studying the microstructure and the relationship between the mechanical property and the temperature of the PU mixture. Thank you for your advice again.
Author Response File: 
Author Response.docx
Reviewer 2 Report
The study investigated the construction of a dynamic modulus master curve for a polyurethane mixture with dense gradation, using five master curve models, five shift factor equations, and four error minimization methods. The results showed that the generalized logistic sigmoidal model and sigmoidal combined Christensen−Anderson−Marasteanu model with WLF equation had the most accurate master curve fitting result, and recommended accurate error minimization methods, master
Major Revisio
The paper provides an interesting and detailed investigation into the construction of a dynamic modulus master curve for a polyurethane mixture with dense gradation, which can be a valuable contribution to the field of pavement design and material selection. However, there are several areas that need improvement before the paper can be considered for publicatio
Firstly, the paper lacks a clear and concise introduction that provides background information and the significance of the study. It is essential to introduce the topic and highlight the main problem and objectives of the study in the introduction sectio
Secondly, the abstract needs to be revised to reflect the main findings of the study in a more concise and understandable way. The abstract should provide a brief overview of the study, including the main problem, methodology, and significant result
Thirdly, the paper needs to provide a more in-depth discussion and interpretation of the results. The paper should explain why certain models, shift factor equations, and error minimization methods were selected and how they contributed to the results. The paper should also compare the findings with previous studies in the literature and provide a more detailed analysis of the differences and similaritie
Fourthly, the paper should provide more details on the testing procedures, including the equipment used, the testing conditions, and the sample preparation. Providing these details will help readers understand how the tests were conducted and increase the reliability and reproducibility of the result
Finally, the paper should be revised for clarity and organization. The paper should be written in clear and concise language, with appropriate headings and subheadings to guide the reader. The paper should also follow a logical structure, with the introduction providing background information, the methodology explaining the testing procedures, the results presenting the main findings, and the discussion interpreting the results and comparing them with previous studie
Recommendation
Based on the above major revisions, I recommend that the authors revise the paper to address the issues mentioned above. Specifically, the authors shoul
Provide a clear and concise introduction that highlights the main problem and objectives of the stud
Revise the abstract to reflect the main findings of the study in a more concise and understandable way
Provide a more in-depth discussion and interpretation of the results, including the selection of models, shift factor equations, and error minimization methods, and a comparison with previous studies
Provide more details on the testing procedures, including the equipment used, the testing conditions, and the sample preparation
Revise the paper for clarity and organization, with appropriate headings and subheadings to guide the reader and a logical structure that follows the introduction, methodology, results, and discussion
Overall, I believe that with these revisions, the paper will be a valuable contribution to the field of pavement design and material selection, and I recommend it for publication after the revisions have been made.
Author Response
I appreciate your suggestions and valuable advice. Based on the suggestions, I modified the manuscripts as follows.
Point 1: Provide a clear and concise introduction that highlights the main problem and objectives of the study
Response 1: The related part about the main problem and objective of the study were improved in the new manuscript from lines 100−126 to highlight the introduction.
Point 2: Revise the abstract to reflect the main findings of the study in a more concise and understandable way
Response 2: I have rewritten the abstract about the main problem part, methodology part, and significant result part. In the result section, the main result was reorganized for clear and concise representation.
Point 3: Provide a more in-depth discussion and interpretation of the results, including the selection of models, shift factor equations, and error minimization methods, and a comparison with previous studies.
Response 3: The result discussion section was rewritten and improved about the model's comparison, shift factor equation comparison and selection, error minimization methods graphical comparison, and statistic analysis, parts of the result discussion were compared with the previous studies.
Point 4: Provide more details on the testing procedures, including the equipment used, the testing conditions, and the sample preparation
Response 4: More information about the sample preparation, the test equipment, and the testing conditions were provided in the new manuscript in section 2.1 Material.
Point 5: Revise the paper for clarity and organization, with appropriate headings and subheadings to guide the reader and a logical structure that follows the introduction, methodology, results, and discussion
Response 5: The former headings and subheadings couldn’t provide clear and enough information about the study content, in the new manuscript, the headings, and subheadings were rechecked and revised based on the studying content for clarity and organization.
Author Response File: 
Author Response.pdf
Reviewer 3 Report
Manuscript ID: coatings-2342629
Title: Study on the Construction of Dynamic Modulus Master Curve of Polyurethane Mixture with Dense Gradation
Coatings-MDPI
The paper presents an interesting paper related to the determination of dynamic modulus of polyurethane mixture. The following notes were outlined:
1. Page 2: It is preferred to present a typical master curve for dynamic modulus.
2. Page 3: The following studies may be beneficial. You can also refer to them:
· Hilal, M.M.; Fattah, M.Y., (2022), “Evaluation of Resilient Modulus and Rutting for Warm Asphalt Mixtures: A Local Study in Iraq”, Applied Science, 12, 12841. https://doi.org/10.3390/app122412841.
· Kadhim, A.J., Fattah, M.Y. and Asmael, N.M., (2020), “Evaluation of the Moisture Damage of Warm Asphalt Mixtures”, Innovative Infrastructure Solutions 5, 54 (2020). https://doi.org/10.1007/s41062-020-00305-y.
3. Page 3: How did you select load frequencies ? You used high frequencies like 25, 15 and 10 Hz.
4. In all models mention the units of E*.
5. In Eq. (3), define fr and its unit.
6. In Fig. 5 b and d, how do you attribute the rapid increase in E* ?
7. In Table 1, all models revealed high values of R2.
How can you compare among them ?
Author Response
I appreciate your suggestions and valuable advice. Based on the suggestions, I modified the manuscripts as follows.
Point 1: Page 2: It is preferred to present a typical master curve for dynamic modulus.
Response 1: The most widely used and typical master curve of dynamic modulus of the asphalt mixture is the standard logistic sigmoidal−shaped (SLS) model, presented in lines 62-64.
Point 2: Page 3: The following studies may be beneficial. You can also refer to the:
- Hilal, M.M.; Fattah, M.Y., (2022), “Evaluation of Resilient Modulus and Rutting for Warm Asphalt Mixtures: A Local Study in Iraq”, Applied Science, 12, 12841. https://doi.org/10.3390/app122412841.
- Kadhim, A.J., Fattah, M.Y. and Asmael, N.M., (2020), “Evaluation of the Moisture Damage of Warm Asphalt Mixtures”, Innovative Infrastructure Solutions 5, 54 (2020). https://doi.org/10.1007/s41062-020-00305-y.
Response 2: Thank you for the supplied valuable references. The useful information from these two references was presented as references 50 and 51 in the renewed manuscript.
Point 3: Page 3: How did you select load frequencies ? You used high frequencies like 25, 15 and 10 Hz.
Response 3: The dynamic modulus test was performed according to the asphalt mixture performance tester (AMPT), the loading frequencies provided by the AMPT ranged from 25 Hz to 0.1 Hz, which are the settled loading frequency of the AMPT.
Point 4: In all models mention the units of E*.
Response 4: Thank you for pointing out the errors, all the errors were corrected in the renewed manuscript.
Point 5: In Eq. (3), define fr and its unit.
Response 5: Thank you for pointing out the error, all the error was corrected in the renewed manuscript.
Point 6: In Fig. 5 b and d, how do you attribute the rapid increase in E* ?
Response 6: I am sorry for the confusing expression, the expression about the changing of E* was rewritten in the new manuscript in section 4.1.
Point 7: In Table 1, all models revealed high values of R2.
How can you compare among them ?
Response 7: Thank you for reminding me. In the new manuscript, the trend line slope and SSR values which combined with the trend line R2 value were used to compare the difference between the master curves in section 4.4.1.
Author Response File: Author Response.pdf
Reviewer 4 Report
In this work, the dynamic efficiency of polyurethane has been evaluated by considering viscoelastic properties and density variations. For this purpose, various master curve models with different shift factors are used. The relevant parameters are obtained by the regression process.
1- The application of the results of the present research in the real industry field should be further explained.
2- The defects and advantages of the utilized method should be stated especially in comparison with neural network methods.
3- The presented figures have low quality, such as Figure 1. Also, the drawn curves in some figures are not clear, such as in Figure 8.
4- The presented results are stated without validation with theoretical or experimental results and are not reliable.
5- The literature review in the introduction section is not comprehensive. It is recommended that the following articles be explained in detail: DOI: 10.1016/j.polymertesting.2022.107516. DOI: 10.1016/j.carbpol.2021.118871.
6- The English written language of the article should be improved.
6- Provide valid references for the used mathematical formulas.
7- The explanations of some formulas such as formulas 17-18 are insufficient.
8- The innovation and scientific gap in the literature should be clearly explained for the present research.
Author Response
I appreciate your suggestions and valuable advice. Based on the suggestions, I modified the manuscripts as follows.
Point 1: 1- The application of the results of the present research in the real industry field should be further explained.
Response 1: The results of this study would supply information for the dynamic modulus of the PU mixture when the pavement structure consisted of the PU mixture layers and could help to get the optimum pavement layer thickness which could resist permanent deformation at higher temperatures. This study also makes it possible to design the pavement structure with the parameters at a higher temperature instead of parameters at 15 ℃ which is used in the current pavement structure design procedure, this change could improve the accuracy of the pavement structure design. That explanation about the application of the results in the real industry field was added in the new manuscript.
Point 2: The defects and advantages of the utilized method should be stated especially in comparison with neural network methods.
Response 2: In this paper, only five traditional mathematical equations introduced from the asphalt mixture master curve construction were compared and analyzed for the applicability of the equations for the dynamic modulus master curve of the PU mixture. This is only the first step to analyzing the dynamic modulus master curve of the PU mixture, the study of the dynamic modulus of the PU mixture is a complicated systematic work, and the next stop should be to use the neural network methods to develop new mathematical equations which are more suitable for the dynamic modulus master curve of the PU mixture. This explanation about the defects or drawbacks of this paper and the further study targets were added in the new manuscript.
Point 3: The presented figures have low quality, such as Figure 1. Also, the drawn curves in some figures are not clear, such as in Figure 8.
Response 3: All the pictures were plotted by using the software of Origin, the pictures could be enlarged to 10 times with high clarity. But the requirements of the Coatings were 6cm in length and height which restrict the clarity of the pictures. I am sorry about that.
Point 4: The presented results are stated without validation with theoretical or experimental results and are not reliable.
Response 4: This paper aimed to use the dynamic modulus master curve of the asphalt mixture to fit and construct the dynamic modulus master curve of the PU mixture, and to verify the applicability of the mathematical equations. The next step of the study would verify the results with more PU mixture dynamic modulus test results, e.g., stone matrix gradation, more aggregate types, and PU types. The dynamic modulus master curve study of the PU mixture is a new and complicated research topic, this paper is only the first step on the topic, more attention and effort should be applied.
Point 5: The literature review in the introduction section is not comprehensive. It is recommended that the following articles be explained in detail: DOI: 10.1016/j.polymertesting.2022.107516. DOI: 10.1016/j.carbpol.2021.118871.
Response 5: Thank you for providing two worthwhile articles, I have read two articles and added these articles as the new references for 52 and 53.
Point 6: The English written language of the article should be improved.
Response 6: Thank you for your advice, I have checked the manuscript and rewritten parts of the manuscript to improve the English written language.
Point 7: The explanations of some formulas such as formulas 17-18 are insufficient.
Response 7: I am sorry about the confusion in the article, more information about the formulas was added in the new manuscript.
Point 8: The innovation and scientific gap in the literature should be clearly explained for the present research.
Response 8: There were no studies about the suitable dynamic modulus master curve mathematical equation for the PU mixture, the innovation of this paper was to determine the suitable master curve models for the PU mixture and partially filled the gap of the dynamic mechanical study of the PU mixture. The explanation was added in the new manuscript in the conclusion section.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
All concerns are adressed in the revised version. Accept in its current form
Reviewer 4 Report
All the requested modifications have been made. The article is acceptable as it is and can be published in its current form.
