Innovative Use of UHPC and Topology Optimization in Permeable Interlocking Pavers: Advancing Sustainable Pavement Solutions

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The study fosters intrinsic topic, where an innovative solution is cultivated for maintaining efficient water flow discharge as well as advanced structural capacity. However, multiple concerns must be addressed firstly before accepting for publication

• The parameters of equation 2 should be defined
• The assumed values for the software inputs, which are given in Table 1, should be based on findings of previous studies and should be referenced
• No logistic and objective correlation between the experimental and simulation works is given. The manuscript must be structured in the way that clarifies the contribution of both numerical simulation and experimental work in the scope of the study
• The result section seems to be very limited and particularly poor. Only one experimental finding is shown and no sensitivity or optimization analysis was conducted through the simulation work

Author Response

We sincerely thank the reviewers for their careful reading and constructive feedback on our manuscript. Please find below our point-by-point responses to each comment, with the corresponding revisions clearly indicated in the re-submitted version of the manuscript.

Comments 1: The parameters of equation 2 should be defined

Response 1: Thank you very much for your valuable comment. We agree with your observation. We have carefully revised the manuscript and included the definitions of the parameters of Equation 2 in the revised version. The definitions have been added in lines 252 to 254, as suggested.

Comments 2: The assumed values for the software inputs, which are given in Table 1, should be based on findings of previous studies and should be referenced

Response 2: Thank you for your insightful comment. We appreciate the opportunity to clarify this point. The parameters presented in Table 1 were taken from the Master's dissertation of Mesquita (2024), titled "Ultra-high Performance Concrete (UHPC) eco-efficient: Strategies to minimize mixing energy and binder consumption". This reference has now been properly included in the manuscript as reference number 21. The indication of the source has been added in the text in lines 290 to 292, as well as in the caption of Table 1.

Comments 3: No logistic and objective correlation between the experimental and simulation works is given. The manuscript must be structured in the way that clarifies the contribution of both numerical simulation and experimental work in the scope of the study

Response 3: Thank you for your constructive comment. We acknowledge the importance of clearly establishing the correlation between the experimental and numerical parts of the study. To address this, we have inserted an elucidative paragraph in the revised manuscript (lines 223 to 230), explaining that the numerical optimization techniques were employed as an initial approach to optimize the block design. This focused on creating openings that could provide sufficient drainage capacity while maintaining mechanical strength—two critical and often conflicting requirements for permeable pavers. Additionally, to further clarify the distinct contributions of each part of the study, we have modified the titles of the relevant subsections in lines 222 and 456. These changes aim to improve the manuscript's structure and make the relationship between the numerical simulations and experimental validation more explicit.

Comment 4: The result section seems to be very limited and particularly poor. Only one experimental finding is shown and no sensitivity or optimization analysis was conducted through the simulation work

Response 4: Thank you for your valuable comment. We acknowledge the need to strengthen the presentation of the results. In response, we have expanded the Mechanical Performance section by including the results of the dynamic modulus of elasticity, which have been incorporated in the revised manuscript in lines 532 to 549. Additionally, we have improved the presentation of the compressive strength results by including the standard deviation of the samples, providing a more comprehensive and rigorous description of the experimental findings. We believe these enhancements contribute to a more robust and detailed results section.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript presents an interesting approach to improving permeable pavers by combining UHPC with topology-optimized block geometries. The authors argue that integrating fluid channels into UHPC blocks can simultaneously enhance hydraulic conductivity and maintain—or even exceed—the compressive strength requirements for the composite.

Before publication, the following revisions should be addressed to improve clarity:

A dedicated section is needed to explicitly state the scope, objectives, and broader significance of this work. While the introduction motivates the problem, a concise “Research Scope and Significance” subsection would help readers investigate the study’s unique contributions to the field.

The long-term performance—particularly the influence of clogging on the UHPC microstructure and freeze–thaw durability—should be discussed or at least outlined as future work. Adding preliminary analysis or literature discussion would strengthen the argument that the design mitigates clogging over the service life.

Several abbreviations (e.g., “CP35” steel, “P1,” “P5,” “AG0614,” etc.) are introduced without full descriptions. Please provide a table of material properties—including density, specific surface area, chemical composition, and source—for all components. Additionally, express the mix proportions normalized to 1 m³ of UHPC to enable reproducibility.

The aggregate and binder quantities are given in grams, but it is unclear how these scale to field practice. Please convert these values to kg/m³ and clarify the characteristic (e.g., average vs. design) water-to-binder ratio and any admixture dosages.

The criterion for selecting 105 channels and the 6 mm diameter constraint are reasonable, but a brief rationale (manufacturing limits, mold release considerations) should be added. Likewise, clarify what “CP35” stands for (e.g., steel grade) in Table 1.

Authors write about the hydraulic conductivity of the composite; however, no tests were performed regarding that property (or anti-clogging) for the proposed composite. This section should be added, especially regarding the rationale behind the amount and diameter of proposed holes.

Specific comments in the attached pdf.

Comments for author File: Comments.pdf

Author Response

We sincerely thank the reviewers for their careful reading and constructive feedback on our manuscript. Please find below our point-by-point responses to each comment, with the corresponding revisions clearly indicated in the re-submitted version of the manuscript.

Comment 1: A dedicated section is needed to explicitly state the scope, objectives, and broader significance of this work. While the introduction motivates the problem, a concise “Research Scope and Significance” subsection would help readers investigate the study’s unique contributions to the field.

Response 1: Thank you for your valuable suggestion. We agree with the importance of clearly defining the research scope and significance. In response to your comment, we have included a new section titled Research Scope and Significance in the revised manuscript, located in lines 79 to 89. This section clarifies that the primary focus of this article is on the structural performance of the optimized block, while the drainage potential will be comprehensively addressed in a separate publication.

Comment 2: The long-term performance—particularly the influence of clogging on the UHPC microstructure and freeze–thaw durability—should be discussed or at least outlined as future work. Adding preliminary analysis or literature discussion would strengthen the argument that the design mitigates clogging over the service life.

Response 2: Thank you for your insightful comment. We agree that the long-term performance, particularly related to clogging and freeze–thaw durability, is an essential aspect to be addressed. As mentioned in the revised manuscript (line 72), these issues, including the drainage capacity and clogging mitigation, will be comprehensively treated in a future publication specifically dedicated to the hydraulic performance of the proposed block design.

Comment 3: Several abbreviations (e.g., “CP35” steel, “P1,” “P5,” “AG0614,” etc.) are introduced without full descriptions. Please provide a table of material properties—including density, specific surface area, chemical composition, and source—for all components. Additionally, express the mix proportions normalized to 1 m³ of UHPC to enable reproducibility.

Response 3: We thank the reviewer for this important observation. In response, we have clarified all abbreviations and provided detailed information about the materials used in the study. Specifically, we have inserted:

• Table 1. Physical properties of the used materials;

• Table 2. Chemical characteristics of raw materials, obtained by XRF;

• Additionally, Table 3. Material consumption for the optimized mix design has been revised and now presents the mix proportions normalized to 1 m³ of UHPC, ensuring reproducibility.

All these additions and revisions have been incorporated in Section 4.2 – Materials and Mix Design, starting from line 313. We appreciate the reviewer’s constructive suggestion, which has significantly improved the completeness and transparency of the manuscript.

Comment 4: The aggregate and binder quantities are given in grams, but it is unclear how these scale to field practice. Please convert these values to kg/m³ and clarify the characteristic (e.g., average vs. design) water-to-binder ratio and any admixture dosages.

Response 4: Thank you for your valuable observation. We have revised the table to convert all quantities to kg/m³ and clarified the water-to-binder (w/b) ratio as well as the absence of chemical admixtures in this formulation. These corrections and clarifications have been incorporated into the revised manuscript in lines 363 to 370.

Comment 5: The criterion for selecting 105 channels and the 6 mm diameter constraint are reasonable, but a brief rationale (manufacturing limits, mold release considerations) should be added. Likewise, clarify what “CP35” stands for (e.g., steel grade) in Table 1.

Response 5: Thank you for your thoughtful comment. We agree with the importance of providing a clear rationale for the selection of the channel dimensions and quantity. In response, we have included a detailed justification in the revised manuscript, covering both safety considerations and manufacturing constraints. Specifically, the rationale regarding pedestrian safety and the use of 6 mm diameter openings, as well as the design decision to include 105 holes based on moldability and structural integrity, has been incorporated in lines 233 to 245. Additionally, we clarified that “CP35” refers to a commercially available permeable block with traditional characteristics commonly used in Brazil. Accordingly, the nomenclature was modified to “Commercial” to maintain consistency with the terminology used throughout the experimental analyses.

Comment 6: Authors write about the hydraulic conductivity of the composite; however, no tests were performed regarding that property (or anti-clogging) for the proposed composite. This section should be added, especially regarding the rationale behind the amount and diameter of proposed holes.

Response 6: Thank you for your observation. We acknowledge the importance of assessing the hydraulic conductivity and anti-clogging performance of the proposed composite. However, as mentioned in the revised manuscript (line 72), these aspects will be comprehensively addressed in a future publication specifically dedicated to the hydraulic performance of the optimized block design. This article focuses primarily on the structural performance and the rationale behind the amount and diameter of the proposed holes has been thoroughly explained in lines 69 to 78.

All the comments and suggestions indicated in the annotated PDF have been carefully addressed and incorporated into the revised manuscript. We appreciate the reviewers’ thorough and constructive feedback, which has significantly contributed to improving the clarity, rigor, and overall quality of our work.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

INNOVATIVE USE OF UHPC AND TOPOLOGY OPTIMIZATION IN PERMEABLE INTERLOCKING PAVERS: ADVANCING SUSTAINABLE PAVEMENT SOLUTIONS

1. Page 2, Line 79 is the repeat sentence from previous paragraph
2. Literature review on Topology optimization is not included. Please detail a few past works on TO.
3. In Table 2, explain the materials used. Not sure what P1/P5 etc. are
4. Since we are talking about permeability, it would be beneficial to add an aggregate gradation chart in the paper
5. What is the water/cement ration used
6. How were the plastic tubes removed after concrete set
7. How was water absorbed by cardboard mold accounted for in the mix design
8. Was the specimen placed in water bath for 28 days after casting
9. Mechanical tests were performed but was any permeability test conducted on the specimens.
10. How could the clogging issue be addressed for in UHPC

Author Response

We sincerely thank the reviewers for their careful reading and constructive feedback on our manuscript. Please find below our point-by-point responses to each comment, with the corresponding revisions clearly indicated in the re-submitted version of the manuscript.

Comment 1: Page 2, Line 79 is the repeat sentence from previous paragraph

Response 1: Thank you for pointing this out. The sentence on page 2, line 79, which repeated content from the previous paragraph, has been removed to improve clarity and avoid redundancy.

Comment 2: Literature review on Topology optimization is not included. Please detail a few past works on TO.

Response 2: Thank you for your valuable suggestion. A literature review on Topology Optimization (TO) has been included in the revised manuscript, specifically in lines 143 to 170, providing an overview of relevant past works and contextualizing the application of TO in the present study.

Comment 3: In Table 2, explain the materials used. Not sure what P1/P5 etc. are

Response 3: Thank you for your comment. The materials originally presented in Table 2 are now listed in Table 4, as two additional tables were included to support a more comprehensive characterization of the materials. In the revised manuscript, we clarified that P1 and P5 refer to two different grades of limestone filler used as partial replacements for cementitious materials. Furthermore, detailed information about all components—such as the use of Ordinary Portland Cement (OPC, CPV – Holcim) and silica fume (Elkem 971U)—was added to enhance clarity and reproducibility. These updates are now presented in Section 4.2: Materials and Mix Design, specifically in lines 314 to 360.

Comment 4: Since we are talking about permeability, it would be beneficial to add an aggregate gradation chart in the paper

Response 4: Thank you for your valuable suggestion. In this study, the permeability is primarily determined by the geometric design, specifically the pre-defined linear ducts incorporated into the block, rather than by the gradation of the aggregates. Since the UHPC formulation results in a dense matrix with minimal intrinsic permeability, we focused on describing the engineered flow channels that control the hydraulic behavior. For this reason, an aggregate gradation chart was not included, but we appreciate your observation and consideration of this aspect.

Comment 5: What is the water/cement ration used

Response 5: Thank you for your observation. The water-to-cement ratio used in the UHPC formulation has been included in the revised manuscript, specifically in line 365, to provide greater clarity and completeness to the description of the mix design.

Comment 6: How were the plastic tubes removed after concrete set

Response 6: Thank you for your question. The procedure for removing the plastic tubes after the concrete set is described in the revised manuscript, specifically in line 401, to clarify the methodology employed in creating the internal flow channels.

Comment 7: How was water absorbed by cardboard mold accounted for in the mix design

Response 7: Thank you for your question. This aspect has been addressed in the revised manuscript, specifically in lines 394 to 396, where it is explained that the cardboard molds were coated with adhesive tape to act both as a release agent and as a barrier to prevent water absorption.

Comment 8: Was the specimen placed in water bath for 28 days after casting

Response 8: Thank you for your question. The procedures related to demolding and subsequent curing have been further detailed in the revised manuscript, specifically in lines 396 to 406, to provide a clearer description of the specimen preparation and curing process after casting.

Comment 9: Mechanical tests were performed but was any permeability test conducted on the specimens.

Response 9: Thank you for your question. The hydrological aspects and the evaluation of the drainage potential of the proposed design will be comprehensively addressed in a future publication, as the focus of the present study was primarily on the mechanical performance and structural feasibility of the optimized UHPC blocks.

Comment 10: How could the clogging issue be addressed for in UHPC

Response 10: Thank you for your question. In this study, the use of UHPC is fundamental to ensuring the durability and mechanical performance of the blocks, even with the incorporation of pre-defined holes that provide the desired drainage potential. The exceptional strength and low porosity of UHPC make it a valuable ally in addressing clogging concerns, as it maintains structural integrity while allowing for engineered drainage through the designed flow channels. These considerations have been incorporated into the conclusions of the revised manuscript to emphasize the material’s advantages in this context.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The article is interesting and holds significant potential. The central topic concerns the unsealed pavement concept made from UHPC concrete bricks. The main aim was to compare concrete bricks with and without an opening. Durability was also considered the main aspect of the following study.

The authors' determination to consider many variables is commendable. This study's relevance to a crucial area is evident, and its findings could profoundly impact it, inspiring further research and development in the field.

 

Your use of up-to-date references. It not only adds credibility to your work but also shows your respect for the current state of research in the field. The simplicity and directness of the article's construction further enhance its readability, making it a strong point of this paper.

 

Your article's thoughtful inclusion of images and charts enhances the readability of the text and aids in comprehending complex concepts, making it a valuable contribution to the paper. Your efforts in this regard are appreciated and recognized.

 

The English language is acceptable. Easy to read and understand.

 

 

Although the following article has multiple pros, it could be published after minor revisions.

 

All these efforts will improve clarity, scientific form, and consistency. The following remarks are presented below.

 

 

1. Lines 23-42 – It is strongly recommended in the abstract to present two things that are currently missing. First, the solution applied to your problem; second, the key findings achieved by this solution. Please fix it by adding one sentence to each point.
2. Lines 48-70 - it is recommended to highlight in the end of the introduction what the main problem of your study is and what methods you will apply. Do this by pointing out usage from the list. Moreover, you could link the introduction with the literature review. The article would be more complex then.

 

3. Lines 64-71 - using transparent bricks is common in most European countries like Poland. Your proposal and innovative idea is to use UHPC instead of regular concrete - emphasize it for complexity.
4. Lines 72-132 - add 2-3 recent references related to your topic. This field is not as new as it is presented. Moreover, in the end, it would be beneficial to state the problem clearly and outline how you plan to address it. - Fix it.

 

5. Lines 134 - 302 - You cite much literature initially. In the Materials and Methods section, you should clearly describe what you are doing and what you are using to perform your experiment. There is no time to present facts from the literature as references. (I mean that when I read this part, especially at the beginning, I thought you were continuing your review. Please rephrase your text there.)

 

6. Lines 372-409 - discussions and conclusions are okay, but in my opinion, two things are missing: First, you should highlight the main findings of your study from the list. Secondly, it is strongly recommended to emphasize the practical aspects of your research, including where it can be used and, in the end, what you will do next (because it is not the end of your study, am I right?).

 

Generally - good work.

Author Response

Comment 1: Lines 23-42 – It is strongly recommended in the abstract to present two things that are currently missing. First, the solution applied to your problem; second, the key findings achieved by this solution. Please fix it by adding one sentence to each point.

Response 1: We thank the reviewer for this valuable suggestion. In response, the abstract has been revised to explicitly include both the solution applied to the problem—namely, the design of interlocking permeable blocks using Ultra-High-Performance Concrete (UHPC) optimized through topology optimization—and the key findings, highlighting the achievement of high compressive strength and superior mechanical performance even with integrated drainage channels. These additions clarify the contribution and impact of the study.

Comment 2: Lines 48-70 - it is recommended to highlight in the end of the introduction what the main problem of your study is and what methods you will apply. Do this by pointing out usage from the list. Moreover, you could link the introduction with the literature review. The article would be more complex then.

Response 2: Thank you for your detailed and constructive feedback. To address these important points, we have included a new subsection titled "2. Research Scope and Significance" in the revised manuscript, specifically in lines 79 to 89. This addition clarifies the main problem of the study, outlines the methods applied, emphasizes the innovative use of UHPC over conventional materials, and better links the introduction with the literature review. We believe this revision improves the overall coherence and complexity of the article.

Comment 3: Lines 64-71 - using transparent bricks is common in most European countries like Poland. Your proposal and innovative idea is to use UHPC instead of regular concrete - emphasize it for complexity.

Response 3: Thank you for your observation. This aspect has been emphasized in both the introduction and the conclusions of the revised manuscript to better highlight and reinforce the innovative proposal of using UHPC instead of conventional concrete, thereby enhancing the complexity and originality of the study.

Comment 4: Lines 72-132 - add 2-3 recent references related to your topic. This field is not as new as it is presented. Moreover, in the end, it would be beneficial to state the problem clearly and outline how you plan to address it. - Fix it.

Response 4: Thank you for your constructive feedback. The requested information has been incorporated into the revised manuscript, specifically in lines 204 to 214, to clearly articulate the engineering solution proposed, its alignment with resilient infrastructure principles, and its relevance in addressing urban challenges related to climate change and stormwater management.

Comment 5: Lines 134 - 302 - You cite much literature initially. In the Materials and Methods section, you should clearly describe what you are doing and what you are using to perform your experiment. There is no time to present facts from the literature as references. (I mean that when I read this part, especially at the beginning, I thought you were continuing your review. Please rephrase your text there.)

Response 5: Thank you for your valuable observation. This section has been carefully revised, with the literature-related content being relocated to the Section 3. Literature Review. This restructuring ensures that the Materials and Methods section now focuses exclusively on the experimental procedures and materials used, thereby improving the clarity and organization of the manuscript.

Comment 6: Lines 372-409 - discussions and conclusions are okay, but in my opinion, two things are missing: First, you should highlight the main findings of your study from the list. Secondly, it is strongly recommended to emphasize the practical aspects of your research, including where it can be used and, in the end, what you will do next (because it is not the end of your study, am I right?).

Response 6: We thank the reviewer for this valuable feedback. In response, Section 6 – Conclusions has been revised to address both points raised. Specifically, a new paragraph summarizing the main findings of the study was added between lines 559 and 568, emphasizing the key outcomes related to structural performance, numerical modeling techniques employed in this research and the potential of UHPC for permeable pavement applications. Additionally, a paragraph highlighting the practical aspects of the research, including potential applications and future research directions, was incorporated between lines 589 and 596. These additions reinforce the relevance and applicability of the study, while also clarifying that this work is part of a broader ongoing research effort.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The current new version is worse than the first one. It does not address the comments given in the first review round. The text is greatly increased without, while the output is still limited. The text of the manuscript must be reduced and optimized. The previous comments must be addressed. The figures need to be polished and re-organized. The titles must be revised and must be clearly distinguishable. omments 3 and 4 in the first revise round are the ones that are not adequately addressed in the new version.

Author Response

We appreciate this important observation. In this revised version, we made significant efforts to reduce and optimize the manuscript. Specifically, the Literature Review section was substantially condensed, with redundant or overly detailed content removed to enhance clarity and focus.

It is important to highlight, however, that in response to earlier review suggestions — including those related to methodology and results, and particularly those raised by other reviewers — additional data and descriptions were incorporated in the last revision to strengthen the scientific rigor and robustness of the study. These additions were essential to meet the initial requests for greater clarity, justification of procedures, and completeness in the presentation of findings. Therefore, while the total length of the manuscript has slightly increased, this expansion was necessary to provide the depth of analysis expected for a solid scientific contribution, while still maintaining conciseness in the contextual sections.

Comment 3

Response: We have added a specific paragraph (lines 242–251) to clarify the role of numerical modeling in the development process. This addition explains how the topological optimization guided the geometric design, drainage sizing, and selection of mechanical properties. It also outlines how this modeling phase provided a rational basis for prototype development and informed the subsequent experimental phase. Additionally, to ensure a clearer transition and improve the manuscript’s structure, we inserted the subsection titles "Experimental Validation" in lines 252 and 424, explicitly marking the beginning of the experimental stages. This helps reinforce the connection between the numerical modeling and the subsequent laboratory testing.

Comment 4

Response: To address it, we have inserted a new paragraph (lines 472–483) in the Results section to complement our findings with relevant references from the literature. This addition provides a comparative perspective on the mechanical performance tests we conducted, reinforcing the interpretation of our results and situating them within the broader context of similar studies. We believe this enhances the scientific consistency and credibility of the reported outcomes.

We hope that the revisions and clarifications provided in this new version of the manuscript adequately address the concerns raised and are now in accordance with the suggestions made in the previous review rounds. We remain at your disposal for any further adjustments that may be necessary.

Thank you once again for your careful and constructive feedback.

Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

can be accepted