Research on the Flexural Capacity of Pre-Tensioned Prestressed Hollow Concrete-Filled Steel Tubular Piles with Consideration of Pile–Soil Interaction

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Prestressed Hollow Concrete-Filled Steel Tube Piles with Consideration of Pile-Soil Interaction”

 

To investigate the flexural behaviour of pre-tensioned SC pile with accounting for the effect of pile-soil interaction, this paper developed a refined finite element analysis model (FEM) and benchmarked against test data. Based on this, the mechanical performance of pre-tensioned SC pile was found superior compared to that of traditional reinforced concrete piles during foundation pit excavation. The available design codes presented a conservative prediction in flexural performance and deflection during excavation when compared with FEM results. This paper is well-organized and approaches the level of this journal. The comments are gived below:

1. The grammar of this paper is needed to be improved.
2. The size of font in figures is required to be increased to at least 10 font size.
3. The lateral displacement for excavation depth between 1500mm and 11500mm should be presented in figure 5 to demonstrate the displacement development during excavation.
4. More information for soil should be given in Table 2, such as friction angle and cohesion.

Author Response

To investigate the flexural behaviour of pre-tensioned SC pile with accounting for the effect of pile-soil interaction, this paper developed a refined finite element analysis model (FEM) and benchmarked against test data. Based on this, the mechanical performance of pre-tensioned SC pile was found superior compared to that of traditional reinforced concrete piles during foundation pit excavation. The available design codes presented a conservative prediction in flexural performance and deflection during excavation when compared with FEM results. This paper is well-organized and approaches the level of this journal.

Response: Thank you for this positive comment.

Q1: The grammar of this paper is needed to be improved.

Response: Thank you for this suggestion. The grammar has been carefully improved.

Q2: The size of font in figures is required to be increased to at least 10 font size.

Response: Thank you for this suggestion. The size of text in all the figures of this paper has been increased to at least 10 font size.

Q3: The lateral displacement for excavation depth between 1500mm and 11500mm should be presented in figure 5 to demonstrate the displacement development during excavation.

Response: Thank you for this suggestion. The cloud figure for the lateral displacement of soil as the excavation depth of 6500mm is presented in Figure 5b in the revised manuscript.

Q4: More information for soil should be given in Table 2, such as friction angle and cohesion.

Response: Authors agree with this suggestion. We have presented more mechanical information for soil in Table 2, including friction angle and cohesion.

Reviewer 2 Report

Comments and Suggestions for Authors

In my opinion, the paper is simplistic and lacks the technical depth or numerical rigor required for publication. My specific comments are as follows:

1. 
   The paper correctly identifies a gap in research regarding pre-tensioned prestressed hollow concrete-filled steel tube (SC) piles, specifically concerning pile-soil interaction. However, the work presented is a straightforward application of established finite element modeling techniques (in ABAQUS) to this specific pile type. The methodology—using concrete damage plasticity, Mohr-Coulomb soil, and interface models—is standard practice in geotechnical numerical analysis. The study does not introduce a new model, a novel analytical method, or a fundamental new insight into the behavior of composite piles. It merely applies existing tools to a different cross-section, resulting in a lack of significant scientific novelty.
2. The paper's key finding—that prestressed SC piles perform well in deep excavations—is severely undermined by a critical omission in the model. The study simulates a deep excavation (up to 14 meters) without any horizontal support system (e.g., struts, anchors). In real-world geotechnical engineering, a cantilever retaining system is almost never used for excavations beyond a few meters due to stability and deformation risks. This unrealistic scenario makes the results of limited practical relevance and questions the validity of the conclusions for actual "large deep foundation pit projects" that the paper aims to address.
3. While the authors claim their model is "verified," the reported deviations of 10-15% for key outputs like bending moment and deformation are substantial for a "refined" model intended for precise capacity prediction. A 15% error in horizontal displacement can be the difference between a safe and a failed design in geotechnical practice. The validation appears to be a qualitative "curve-matching" exercise rather than a rigorous quantitative analysis. Without stronger statistical validation against multiple, high-quality experimental datasets, the reliability of the model for predictive design purposes remains unproven.
4. The comparison with other pile types (cast-in-place and normal SC piles) is a core claim, yet the analysis is superficial. The discussion on why prestressed SC piles have higher bending moments is hand-wavy, attributing it vaguely to "the combined effect of the differences in the bending stiffness... and the bond-slip performance." This lacks a rigorous mechanical explanation. Furthermore, the comparison fails to address critical practical factors such as constructability, cost-effectiveness, and long-term durability, which are essential for engineers to select a pile type. The conclusion that it has a "promising future" is not supported by a holistic analysis.
5.  The paper's conclusions contain internal contradictions that highlight a lack of deep analysis. For instance, it states that prestressed SC piles have the smallest displacement (a positive trait) but also the highest bending moments (which could be a negative trait, indicating higher stress). The authors do not adequately reconcile this, nor do they discuss the design implications of these higher moments (e.g., potential for earlier yielding). Furthermore, the conclusion that standard design codes are "conservative" is trivial, as codes are inherently conservative for safety. The paper fails to provide a meaningful, calibrated recommendation for how designers could safely leverage the purported efficiency of SC piles within or in improvement of the existing code framework.

Author Response

Q1: The paper correctly identifies a gap in research regarding pre-tensioned prestressed hollow concrete-filled steel tube (SC) piles, specifically concerning pile-soil interaction. However, the work presented is a straightforward application of established finite element modeling techniques (in ABAQUS) to this specific pile type. The methodology—using concrete damage plasticity, Mohr-Coulomb soil, and interface models—is standard practice in geotechnical numerical analysis. The study does not introduce a new model, a novel analytical method, or a fundamental new insight into the behavior of composite piles. It merely applies existing tools to a different cross-section, resulting in a lack of significant scientific novelty.

Response: Thank you for this suggestion. Authors kindly understand the concern presented by reviewer. Despite of this, authors would like clarifying that the key creative point in this paper is the comparison in mechanical performance of prestressed SC pile to that of the normal SC pile and the traditional cast-in-place concrete pile. Such comparison for mechanical performance as these piles with the consideration of pile-soil interaction has not been revealed previously. To correctly analysis the mechanical performance of piles in the soil, authors have collected the real monitoring data for the variation of horizontal displacement at the concrete pile top as the function of the excavation depth, which was adopted in this paper as the benchmarking material for FEM development. The existing test data for prestressed SC piles with bending was also adopted. Due to the validation of FEM, the mechanical responses of piles placed in soil as excavation developing can be suitably simulated. This validated FEM analysis method can be used in the comparison between newly SC pile and traditional members, and the new/novel model may not necessary. Additionally, to correctly simulate the loss of prestress values in SC piles, the new method has been established in this paper to calculate the tensile stress of the prestressed steel bars after prestress application, which is not presented in previous standards.

 

Q2: The paper's key finding—that prestressed SC piles perform well in deep excavations—is severely undermined by a critical omission in the model. The study simulates a deep excavation (up to 14 meters) without any horizontal support system (e.g., struts, anchors). In real-world geotechnical engineering, a cantilever retaining system is almost never used for excavations beyond a few meters due to stability and deformation risks. This unrealistic scenario makes the results of limited practical relevance and questions the validity of the conclusions for actual "large deep foundation pit projects" that the paper aims to address.

Response: Thank you for this suggestion. Authors agree that the cantilever retaining system is not appropriately used in the foundation pit with a deep excavation; while the reason for establishing the deep excavation model is to explore the mechanical response of prestressed SC pile, normal SC pile and cast-in-place concrete piles under ultimate condition with accounting for the pile-soil interaction. The model could be adopted to reveal the behavior of all the cantilever retaining systems at both elastic and elastoplastic stages, which is meaningful for the design. Additionally, the FE model simulate the responses of piles during the whole excavation process, and thus the responses of cantilever retaining system in the realistic scenario with small excavation is also illustrated in the figures of this paper.

Due to the novel research of this paper, the prestressed SC piles are proved to having superior properties and economical efficiency, and hence has been adopted in the real practices in Guangdong, China. These practices reflect the meaning of the works in this paper.

 

Q3: While the authors claim their model is "verified," the reported deviations of 10-15% for key outputs like bending moment and deformation are substantial for a "refined" model intended for precise capacity prediction. A 15% error in horizontal displacement can be the difference between a safe and a failed design in geotechnical practice. The validation appears to be a qualitative "curve-matching" exercise rather than a rigorous quantitative analysis. Without stronger statistical validation against multiple, high-quality experimental datasets, the reliability of the model for predictive design purposes remains unproven.

Response: Thank you for this suggestion. The deviation of 10-15% for the prediction of capability in SC member is not large, which is near to the deviation in the previous research [1,2]. In the Fig.3 of the original manuscript, the shape of simulated moment-deflection curve is near to that of the test curve, and thus the flexural behavior of prestressed SC pile could be reliably predicted. In addition, the 15% deviation of deep or top horizontal displacement for pile is smaller than the deviation of limited displacement listed in the Chinese Standard “Technical standard for monitoring of building excavation engineering” (GB 50497-2019). For example, the limit of top horizontal displacement for cast-in-place concrete pile is 20–30mm in the standard, which has 33.3% self-difference, two times larger than the deviation induced by the refined model. Because of this, the 15% error may be acceptable.

[1]Tao Z, Wang Z B, Yu Q. Finite element modelling of concrete-filled steel stub columns under axial compression[J]. Journal of Construction Steel Research, 2013, 89: 121-131.

[2]Han Linhai. steel tube Concrete Structures: Theory and Practice. Science Press, 2022 (4th edition), Beijing.

Q4: The comparison with other pile types (cast-in-place and normal SC piles) is a core claim, yet the analysis is superficial. The discussion on why prestressed SC piles have higher bending moments is hand-wavy, attributing it vaguely to "the combined effect of the differences in the bending stiffness... and the bond-slip performance." This lacks a rigorous mechanical explanation. Furthermore, the comparison fails to address critical practical factors such as constructability, cost-effectiveness, and long-term durability, which are essential for engineers to select a pile type. The conclusion that it has a "promising future" is not supported by a holistic analysis.

Response: Thank you for this suggestion. The rigorous mechanical explanation has presented in the original manuscript, which is following the sentence "the combined effect of the differences in the bending stiffness... and the bond-slip performance.". To clarify this, the explanation is highlighted in yellow in the revised manuscript and statement has been rephrased to be better understandable.

As for the analysis of constructability and cost-effectiveness, the prestressed SC pile is proved to having superior mechanical performance than the traditional pile. Because of this, this kind of pile has been adopted in the real practices in China before this revision. These practices reflect the meaning of the works in this paper. The comparison of constructability and cost-effectiveness will be included in the next paper. In addition, the long-term durability could not be considered in this paper. This is because of foundation pit support project is a kind of temporary project, which is required to be demolished as the main building structure is constructing.

Q5: The paper's conclusions contain internal contradictions that highlight a lack of deep analysis. For instance, it states that prestressed SC piles have the smallest displacement (a positive trait) but also the highest bending moments (which could be a negative trait, indicating higher stress). The authors do not adequately reconcile this, nor do they discuss the design implications of these higher moments (e.g., potential for earlier yielding). Furthermore, the conclusion that standard design codes are "conservative" is trivial, as codes are inherently conservative for safety. The paper fails to provide a meaningful, calibrated recommendation for how designers could safely leverage the purported efficiency of SC piles within or in improvement of the existing code framework.

Response: Thank you for this suggestion. The prestressed SC pile has a higher flexural capacity than the normal SC pile and traditional concrete pile, thus the highest bending moments for prestress SC pile does not induce unsafety. This is clarified in the revised manuscript.

Besides, the research in this paper is a kind of pioneer work, which is intended to comparing the mechanical performance of different piles with a consideration of pile-soil interaction. This work has proven the prestress SC piles has a superior mechanical response than the other traditional piles, especially in the simulation of real scenario, which could recommend designers adopting this kind of members. The safe design method and improvement of existing code framework is not the purpose of this paper. These works will be included in the future papers after finishing the experiments and parametric study of prestress SC piles.

Reviewer 3 Report

Comments and Suggestions for Authors

The article (Research on the Flexrual Capacity of Pre-tensioned Prestressed Hollow Concrete-Filled Steel Tubu Piles with Consideration of Pile-Soil Interaction) focuses on the analysis of the flexural capacity of prestressed hollow steel-concrete piles (SC piles), taking into account the pile-soil interaction during excavation of construction pits. The authors present a numerical model based on the ABAQUS program, in which they apply the concrete plastic damage model (CDPM) and the Mohr-Coulomb soil model. They then verify the results based on monitoring data and experimental tests and compare the behavior of SC piles with traditional concrete and steel-concrete piles.

The topic of the article is topical and practically interesting, because combined prestressed piles are of increasing importance in the foundation of deep construction pits. The authors' contribution is the effort to include the pile-soil interaction in the FEM analysis. On the other hand, the article shows several methodological and formal shortcomings that would need to be eliminated before publication. I have some questions for the authors:

1. What experimental data were used to verify the FEM model? How many tests and from what sources did they come?
2. How was the “temperature drop” method for prestressing applied in ABAQUS and how was its accuracy verified?
3. You claim that no study has yet taken into account the interaction of the pile and the soil for this type of piles - can you support this claim with a broader review of the literature (including international)?
4. How do the results of the FEM model change when changing soil parameters (e.g. friction, stiffness)? Was a sensitivity analysis performed?
5. What was the reason for choosing only one geotechnical case (one location)? Are the conclusions generalizable to other conditions?
6. Can you state numerically by how many % the horizontal deformation of piles was reduced when using prestressed SC piles compared to conventional ones?

Figure 9 is poorly visible.

The article has potential, but the language and conclusions need to be improved, and the methodology needs to be supplemented.

Author Response

The article (Research on the Flexrual Capacity of Pre-tensioned Prestressed Hollow Concrete-Filled Steel Tubu Piles with Consideration of Pile-Soil Interaction) focuses on the analysis of the flexural capacity of prestressed hollow steel-concrete piles (SC piles), taking into account the pile-soil interaction during excavation of construction pits. The authors present a numerical model based on the ABAQUS program, in which they apply the concrete plastic damage model (CDPM) and the Mohr-Coulomb soil model. They then verify the results based on monitoring data and experimental tests and compare the behavior of SC piles with traditional concrete and steel-concrete piles.

The topic of the article is topical and practically interesting, because combined prestressed piles are of increasing importance in the foundation of deep construction pits. The authors' contribution is the effort to include the pile-soil interaction in the FEM analysis. On the other hand, the article shows several methodological and formal shortcomings that would need to be eliminated before publication.

Response: Thank you for this positive comment.

Q1: What experimental data were used to verify the FEM model? How many tests and from what sources did they come?.

Response: The monitoring data for the a real project was adopted to validate the predicted horizontal displacement at the pile top, which is collected from BGRIMM Technology Group. The tested moment-deflection curve at the mid-span section for prestressed SC piles under pure bending from literature [1] was used in validation. This is aimed to benchmarking against the prediction for flexural behavior of prestressed SC pile. The above information is clarified in the revised manuscript.

• Kou Zhao, Yand Junfeng, Mao Yongping, et al. Study on bending resistance of prestressed centrifugal steel pipe concrete pipe pile[J]. Proceedings of Conference on Seismic Technology of Engineering Structures in 2024.

Q2: How was the “temperature drop” method for prestressing applied in ABAQUS and how was its accuracy verified?.

Response: In finite element analysis, the “temperature drop” method​ is a widely used technique to simulate prestress in reinforced concrete by leveraging the principle of thermal contraction. This approach involves modeling the prestressing elements and assigning them a coefficient of thermal expansion. A predetermined temperature drop is then applied to these elements, causing them to contract. This contraction is resisted by the surrounding concrete elements, effectively generating tensile stress in the elements and introducing a compensatory compressive stress in the concrete. The required temperature drop (ΔT) is typically calculated using the formula: ΔT = P/(α×E×A), where P is the desired prestressing force, α is the coefficient of thermal expansion, E is the elastic modulus of the tendon, and A is its cross-sectional area. Compared to other methods like the initial stress approach, the “temperature drop” method is often favored for its straightforward implementation within many finite element software packages (like ABAQUS) and its ability to account for prestress losses by adjusting the temperature load [1].

• Shi, S., Wang, S., Wang, P., & Bai, J. (2015). Seismic Performance Analysis of Self-Centering Steel Frame with Web Energy Consumption. Journal of Hebei University of Engineering (Natural Science Edition), 32(1), 1-4.

Q3: You claim that no study has yet taken into account the interaction of the pile and the soil for this type of piles - can you support this claim with a broader review of the literature (including international)?.

Response: Authors agree with this comment and add some international literatures.

Q4: How do the results of the FEM model change when changing soil parameters (e.g. friction, stiffness)? Was a sensitivity analysis performed?.

Response: The soil parameter is the same for different section of piles in this paper. The variation of soil parameter may change the responses of all the models; while the relative difference in flexural responses among those models may not have big changes. Furthermore, the aim of this paper is the comparison in mechanical performance of prestressed SC pile to that of the normal SC pile and the traditional cast-in-place concrete pile. In this context, we do not discuss a lot about the response variation by changing soil parameters. This discussion will be included in our future studies.

Q5: What was the reason for choosing only one geotechnical case (one location)? Are the conclusions generalizable to other conditions?.

Response: Thank you for this comment. According to the aim of this paper, the sensitivity analysis is not provided in this paper. The influence of geotechnical case will consider to be presented in future studies.

Q6: Can you state numerically by how many % the horizontal deformation of piles was reduced when using prestressed SC piles compared to conventional ones?.

Response: Thank you for this comment. The percentage of reduction is added in the revised manuscript.

Q7: The article has potential, but the language and conclusions need to be improved, and the methodology needs to be supplemented..

Response: Thank you for this comment. We have improved the language and conclusions accordingly.

Reviewer 4 Report

Comments and Suggestions for Authors

This study investigated the flexural behavior and pile–soil interaction of pre-tensioned prestressed hollow concrete-filled steel tube (SC) piles using ABAQUS finite element modeling, validated against monitoring and experimental data. The topic is relevant for foundation engineering, and the focus on prestressed SC piles fills a practical niche. The paper demonstrates commendable modeling effort and provides comparative analyses with conventional piles. However, the manuscript still requires major revision before it can be considered for publication. Several aspects of novelty, validation, presentation, and discussion should be substantially improved.

1. The paper presents useful modeling of prestressed SC piles, but its scientific contribution remains ambiguous.

(1) The novelty is described mainly as “considering pile–soil interaction,” which has already been addressed in prior numerical and analytical studies of composite piles. The authors should clarify what is truly new—for example, whether the refinement lies in the specific prestress implementation method, validation approach, or comparison with standards.

(2) The introduction would benefit from a sharper research gap analysis, explicitly summarizing how this work differs from existing studies on composite or prestressed pipe piles.

-> The paper should better define the innovation and technical advancement beyond existing finite element simulations of pile–soil interaction.

2. The modeling framework is detailed but would benefit from stronger justification and discussion.

(1) Many material parameters (e.g., cohesion, friction angle, modulus) are adopted from “project exploration reports,” but no sensitivity analysis is performed to show how these parameters affect results.

(2) The prestress implementation via the “temperature drop method” should be validated or referenced with verification examples, as this approach can produce nonuniform stress states.

(3) The mesh size discussion is clear, but no convergence study results are shown. Adding a brief figure or table demonstrating mesh independence would strengthen the reliability claim.

(4) Boundary conditions and model dimensions should be clearly illustrated in a schematic figure with scale and labeled axes.

3. Although the model is compared with field monitoring and experimental bending tests (Figures 2 and 3), the validation remains limited.

(1) Only one project case and one laboratory test are used; thus, the model’s general applicability is uncertain.

(2) The reported deviations (10–15%) are acceptable, but it is unclear whether they are within experimental uncertainty or due to modeling assumptions.

(3) Please provide quantitative comparison metrics such as RMSE or mean percentage error and explicitly state how measurement errors were handled.

(4) The description “the model is in good agreement” should be supported with statistical evidence rather than qualitative statements.

4. Sections 3 and 4 provide lengthy qualitative descriptions but lack deeper physical interpretation.

(1) The observed differences in displacement and bending moment among pile types should be connected to mechanics (e.g., stiffness contrast, soil reaction modulus, composite action).

(2) The explanation of moment development with excavation depth (Figure 6) repeats basic soil mechanics principles rather than offering new insight. Consider simplifying and focusing on how prestress modifies the stress redistribution compared with ordinary SC piles.

(3) The analysis could be strengthened by including dimensionless comparisons (e.g., displacement-to-diameter ratios, normalized bending moments) to generalize the findings.

(4) A brief parametric study on prestress level or steel ratio would significantly enhance the paper’s value.

5. The comparison with the Chinese design code (JGJ 120-2012) is useful but rather brief.

(1) The study could be improved by including a table summarizing the predicted versus code-based results (bending moment, displacement) at key excavation stages.

(2) The authors should clarify whether the “elastic foundation beam” method was implemented analytically or via separate software.

(3) The conclusion that code predictions are “conservative” should be supported with quantitative ratios or error percentages.

6. Figures are informative but need clearer labels, consistent units (use “mm” and “kN·m” uniformly), and better resolution.

(1) Figure captions should be more descriptive; for example, Figures 4–9 should include boundary and loading conditions.

(2) Several sections (e.g., 2.4, 2.5) contain typographical errors or formatting artifacts such as equation spacing or broken sentences.

(3) The English language is generally understandable but requires professional proofreading for grammar, article use, and sentence flow.

(4) The numbering of conclusions appears inconsistent (jumping from point 3 to 5). Please renumber and merge overlapping conclusions for conciseness.

7. The study focuses entirely on numerical and comparative analysis; however, its engineering relevance would be clearer if:

(1) A short subsection discussed how prestressed SC piles can improve safety or economy in real projects (e.g., reduced displacement limits, construction cost benefits).

(2) Limitations of the current model (e.g., neglect of time-dependent effects or nonlinearity of soil modulus) were acknowledged.

Minor issues)

(1) Define all abbreviations at first use (e.g., SC pile, FEM).

(2) Check all reference formatting for MDPI style consistency.

(3) Add recent international references on composite piles and soil–structure interaction.

(4) Ensure equations (1)–(10) are formatted properly with clear variable definitions.

(5) The “Patents” section at the end seems irrelevant unless an actual patent is cited; it may be omitted.

Comments on the Quality of English Language

The English language is generally understandable but requires professional proofreading for grammar, article use, and sentence flow.

Author Response

This study investigated the flexural behavior and pile–soil interaction of pre-tensioned prestressed hollow concrete-filled steel tube (SC) piles using ABAQUS finite element modeling, validated against monitoring and experimental data. The topic is relevant for foundation engineering, and the focus on prestressed SC piles fills a practical niche. The paper demonstrates commendable modeling effort and provides comparative analyses with conventional piles. However, the manuscript still requires major revision before it can be considered for publication. Several aspects of novelty, validation, presentation, and discussion should be substantially improved..

Response: Thank you for this positive comment.

Q1: The paper presents useful modeling of prestressed SC piles, but its scientific contribution remains ambiguous.

(1) The novelty is described mainly as “considering pile–soil interaction,” which has already been addressed in prior numerical and analytical studies of composite piles. The authors should clarify what is truly new—for example, whether the refinement lies in the specific prestress implementation method, validation approach, or comparison with standards.

(2) The introduction would benefit from a sharper research gap analysis, explicitly summarizing how this work differs from existing studies on composite or prestressed pipe piles.

-> The paper should better define the innovation and technical advancement beyond existing finite element simulations of pile–soil interaction.

Response: Thank you for this comment. The key creative point in this paper is the comparison in mechanical performance of prestressed SC pile to that of the normal SC pile and the traditional cast-in-place concrete pile. Such comparison for mechanical performance as these piles with the consideration of pile-soil interaction has not been revealed previously. To correctly analysis the mechanical performance of piles in the soil, authors have collected the real monitoring data for the variation of horizontal displacement at the concrete pile top as the function of the excavation depth, which was adopted in this paper as the benchmarking material for FEM development. The existing test data for prestressed SC piles with bending was also adopted. Due to the validation of FEM, the mechanical responses of piles placed in soil as excavation developing can be suitably simulated. This validated FEM analysis method can be used in the comparison between newly SC pile and traditional members, and the new/novel model may not necessary. Additionally, to correctly simulate the loss of prestress values in SC piles, the new method has been established in this paper to calculate the tensile stress of the prestressed steel bars after prestress application, which is not presented in previous standards.

The above clarification has been added in the introduction of revised manuscript.

Q2: 2. The modeling framework is detailed but would benefit from stronger justification and discussion.

(1) Many material parameters (e.g., cohesion, friction angle, modulus) are adopted from “project exploration reports,” but no sensitivity analysis is performed to show how these parameters affect results.

(2) The prestress implementation via the “temperature drop method” should be validated or referenced with verification examples, as this approach can produce nonuniform stress states.

(3) The mesh size discussion is clear, but no convergence study results are shown. Adding a brief figure or table demonstrating mesh independence would strengthen the reliability claim.

(4) Boundary conditions and model dimensions should be clearly illustrated in a schematic figure with scale and labeled axes.

Response: Thank you for this comment.

(1)The soil parameter is the same for different section of piles in this paper. The variation of soil parameter may change the responses of all the models; while the relative difference in flexural responses among those models may not have big changes. Furthermore, the aim of this paper is the comparison in mechanical performance of prestressed SC pile to that of the normal SC pile and the traditional cast-in-place concrete pile. In this context, we do not discuss a lot about the response variation by changing soil parameters. This discussion will be included in our future studies.

(2)In finite element analysis, the “temperature drop” method​ is a widely used technique to simulate prestress in reinforced concrete by leveraging the principle of thermal contraction. This approach involves modeling the prestressing elements and assigning them a coefficient of thermal expansion. A predetermined temperature drop is then applied to these elements, causing them to contract. This contraction is resisted by the surrounding concrete elements, effectively generating tensile stress in the elements and introducing a compensatory compressive stress in the concrete. The required temperature drop (ΔT) is typically calculated using the formula: ΔT = P/(α×E×A), where P is the desired prestressing force, α is the coefficient of thermal expansion, E is the elastic modulus of the tendon, and A is its cross-sectional area. Compared to other methods like the initial stress approach, the “temperature drop” method is often favored for its straightforward implementation within many finite element software packages (like ABAQUS) and its ability to account for prestress losses by adjusting the temperature load [1].

[1]Shi, S., Wang, S., Wang, P., & Bai, J. (2015). Seismic Performance Analysis of Self-Centering Steel Frame with Web Energy Consumption. Journal of Hebei University of Engineering (Natural Science Edition), 32(1), 1-4.

• The mesh independence analysis has been adopted in the study.Through mesh analysis, the mesh size for the soil in the area near the support structures and the mesh size of the support structures are set at 1/4 of the pile diameter. For the regions far from the pile (about 3 times the pile diameter from the center), the mesh size is set at 1/12 of the selected width of soil. When the mesh size is smaller than these values, the influence induced by the mesh size on the mechanical performances during the excavation is less than 5%. The above information has been clarified in the revised manuscript.
• In the model, the width of soil is 10m, and the horizontal displacement of the soil side in the normal direction is restricted (Uy=0). The normal direction of soil in the pit is set as symmetrically boundary. The clarified label has been added accordingly.

Q3: 3. Although the model is compared with field monitoring and experimental bending tests (Figures 2 and 3), the validation remains limited.

(1) Only one project case and one laboratory test are used; thus, the model’s general applicability is uncertain.

(2) The reported deviations (10–15%) are acceptable, but it is unclear whether they are within experimental uncertainty or due to modeling assumptions.

(3) Please provide quantitative comparison metrics such as RMSE or mean percentage error and explicitly state how measurement errors were handled.

(4) The description “the model is in good agreement” should be supported with statistical evidence rather than qualitative statements.

Response: Thank you for this comment.

Authors agree the limitation of benchmarking test data. However, due to the pioneering work as we did, we have adopted all the test/monitoring data which can be collected. The monitoring data for the a real project was adopted to validate the predicted horizontal displacement at the pile top, which is collected from BGRIMM Technology Group. The tested moment-deflection curve at the mid-span section for prestressed SC piles under pure bending from literature [1] was used in validation. This is aimed to benchmarking against the prediction for flexural behavior of prestressed SC pile. The above information is clarified in the revised manuscript. More experimental works will be conducted in the future to make a further validation.

[1] Kou Zhao, Yand Junfeng, Mao Yongping, et al. Study on bending resistance of prestressed centrifugal steel pipe concrete pipe pile[J]. Proceedings of Conference on Seismic Technology of Engineering Structures in 2024.

(2) The experimental uncertainty is difficult to determine due to the limitation of test data, which will be further studied in our future works.

(3) RMSE and mean deviation has added in revised manuscript.

(4) Authors agree with this, and thus the statement is deleted.

 

Q4: Sections 3 and 4 provide lengthy qualitative descriptions but lack deeper physical interpretation.

(1) The observed differences in displacement and bending moment among pile types should be connected to mechanics (e.g., stiffness contrast, soil reaction modulus, composite action).

(2) The explanation of moment development with excavation depth (Figure 6) repeats basic soil mechanics principles rather than offering new insight. Consider simplifying and focusing on how prestress modifies the stress redistribution compared with ordinary SC piles.

(3) The analysis could be strengthened by including dimensionless comparisons (e.g., displacement-to-diameter ratios, normalized bending moments) to generalize the findings.

(4) A brief parametric study on prestress level or steel ratio would significantly enhance the paper’s value.

Response: Thank you for this comment. Further explanation and discussion of mechanical responses has been added in the revised manuscript accordingly.

 

Q5: The comparison with the Chinese design code (JGJ 120-2012) is useful but rather brief.

(1) The study could be improved by including a table summarizing the predicted versus code-based results (bending moment, displacement) at key excavation stages.

(2) The authors should clarify whether the “elastic foundation beam” method was implemented analytically or via separate software.

(3) The conclusion that code predictions are “conservative” should be supported with quantitative ratios or error percentages.

Response: Thank you for this comment. Due to the uncertainty of mechanical responses for the members adopted in the foundation project, the standard design method does not account for the beneficial interaction between the pile and soil or the active equilibrium state of the soil, which results in significant bending moments and deformations. Because of this assumption, the differences between the prediction by FEM and design methods in the force and deformation responses are large. The further information on the difference is added in the revised manuscript.

 

Q6: Figures are informative but need clearer labels, consistent units (use “mm” and “kN·m” uniformly), and better resolution.

(1) Figure captions should be more descriptive; for example, Figures 4–9 should include boundary and loading conditions.

(2) Several sections (e.g., 2.4, 2.5) contain typographical errors or formatting artifacts such as equation spacing or broken sentences.

(3) The English language is generally understandable but requires professional proofreading for grammar, article use, and sentence flow.

(4) The numbering of conclusions appears inconsistent (jumping from point 3 to 5). Please renumber and merge overlapping conclusions for conciseness.

Response: Thank you for this comment.

 

Q7: The study focuses entirely on numerical and comparative analysis; however, its engineering relevance would be clearer if:

(1) A short subsection discussed how prestressed SC piles can improve safety or economy in real projects (e.g., reduced displacement limits, construction cost benefits).

(2) Limitations of the current model (e.g., neglect of time-dependent effects or nonlinearity of soil modulus) were acknowledged.

Minor issues)

Response: Thank you for this comment. (1) Due to the novel research of this paper, the prestressed SC piles are proved to having superior properties and economical efficiency, and hence has been adopted in the real practices in Guangdong, China. These practices reflect the meaning of the works in this paper. The economy analysis for real project is complicated and this is not the key creative point in this paper, which will be presented in our future work for case studies.

• The limitation of the current model is added to the revised manuscript.

 

Q8: (1) Define all abbreviations at first use (e.g., SC pile, FEM).

(2) Check all reference formatting for MDPI style consistency.

(3) Add recent international references on composite piles and soil–structure interaction.

(4) Ensure equations (1)–(10) are formatted properly with clear variable definitions.

(5) The “Patents” section at the end seems irrelevant unless an actual patent is cited; it may be omitted.

The English language is generally understandable but requires professional proofreading for grammar, article use, and sentence flow.

Response: Thank you for this comment. All the above grammar issue has been revised and improved in the revised manuscript.

 

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors Too be accepted

Author Response

Many thanks for your valuable comments and suggestions on our manuscript.

Reviewer 3 Report

Comments and Suggestions for Authors

The article (Research on the Flexrual Capacity of Pre-tensioned Prestressed Hollow Concrete-Filled Steel Tubu Piles with Consideration of Pile-Soil Interaction) focuses on the analysis of the flexural capacity of prestressed hollow steel-concrete piles (SC piles), taking into account the pile-soil interaction during excavation of construction pits. The authors present a numerical model based on the ABAQUS program, in which they apply the concrete plastic damage model (CDPM) and the Mohr-Coulomb soil model. They then verify the results based on monitoring data and experimental tests and compare the behavior of SC piles with traditional concrete and steel-concrete piles.

The topic of the article is topical and practically interesting, because combined prestressed piles are of increasing importance in the foundation of deep construction pits. The authors' contribution is the effort to include the pile-soil interaction in the FEM analysis. 

The authors have incorporated my comments. At this time, I have no further notes on this version. And I recommend this article for acceptance. 

Author Response

Many thanks for your valuable comments and suggestions on our manuscript.

Reviewer 4 Report

Comments and Suggestions for Authors

The authors have made substantial and meaningful revisions in response to the first-round comments. The clarity of the manuscript has improved, the novelty is better articulated, and additional quantitative validation metrics have strengthened the technical credibility of the study. The discussion on mechanical behavior—including pile–soil interaction, displacement patterns, and bending moment redistribution—has been expanded and is now more persuasive.

Although several presentation issues remain, the scientific content is sound, and the revised manuscript is close to being ready for publication after minor adjustments.

1) Improve figure quality (resolution and readability).

2) Enhance figure captions with brief boundary/load descriptions.

3) Perform a final proofreading pass for grammar and formatting.

4) Consider shortening some long paragraphs in the discussion for readability.

Author Response

The authors have made substantial and meaningful revisions in response to the first-round comments. The clarity of the manuscript has improved, the novelty is better articulated, and additional quantitative validation metrics have strengthened the technical credibility of the study. The discussion on mechanical behavior-including pile–soil interaction, displacement patterns, and bending moment redistribution-has been expanded and is now more persuasive.

Although several presentation issues remain, the scientific content is sound, and the revised manuscript is close to being ready for publication after minor adjustments.

Response: Thank you for this positive comment.

Q1: Improve figure quality (resolution and readability).

Response: Thank you for this comment. Several figures have been revised and improved. The revised figures have been marked in Red.

Q2: Enhance figure captions with brief boundary/load descriptions.

Response: Thank you for this comment. We have already enhanced the figure captions with boundary and load descriptions.

Q3: Perform a final proofreading pass for grammar and formatting.

Response: Thank you for this comment. Authors have already performed a final proofreading pass for grammar and formatting. The revised part of this paper has been marked in red.

 

Q4: Consider shortening some long paragraphs in the discussion for readability.

Response: Thank you for this comment. Several long paragraphs in the discussion have been shortened for readability.