Semi-Analytical Solution for the Vertical Vibration of a Single Pile Embedded in a Frozen Poroelastic Half-Space
Round 1
Reviewer 1 Report
The reviewed manuscript could be treated as a further advancement of the research from Ref. 30. In particular, the possible interaction of the vertical pile with a half-space substrate is considered within the simplified Winkler foundation model. With the derived analytical solution, the authors are analyzing the influence of the problem mechanical properties on the dynamical response of the single pile. To the reviewers opinion, the paper in its current form is not in a complete consistence with the scope of the Applied Sciences journal, since the the manuscript makes an impression of being a numerical exercise with minute applicability to real-world applications. Therefore, the authors are suggested either to resubmit their paper either to any journal in the field of mathematical physics or add more results concerning any realistic practical cases including, for instance, any comparison with experimental data.
Some more specific questions and comments:
1) From the Conclusions, it not clear at all what is the particular influence of a more complex model for pile-half-space interaction. All the obtained results are qualitatively consistent with the earlier presented data from Ref. 30
2) For clarity, the authors are strongly advised to directly compare their results from Figures 6 and 8 to the corresponding data from Figures 2 and 6 from Ref. 30.
3) How the bearing coefficient of pile bottom could be interpreted in terms of real-world materials for piles and soils?
4) Are all the results from Fig. 3 obtained by the authors?
5) Page 11, line 223. The physical meaning of the parameter b* is not clear
6) Page 11, lines 221-222. More details should provided related to the derivation of a relation for k_b
7) Eq. (7): Shear stresses, i.e., \tau_{rz} for solid and ice should be also added here.
8) The authors should clearly state for what frequency regimes and mechanical properties of piles and solids the assumptions regarding the considered model are valid (i.e., "The pile is represented in a simplified manner by an elastic and circular homogeneous one-dimensional rod", "the interaction between the overlying soil layer and half-space is simplified by the Winkler model").
Author Response
- The reviewed manuscript could be treated as a further advancement of the research from Ref. 30. In particular, the possible interaction of the vertical pile with a half-space substrate is considered within the simplified Winkler foundation model. With the derived analytical solution, the authors are analyzing the influence of the problem mechanical properties on the dynamical response of the single pile. To the reviewers opinion, the paper in its current form is not in a complete consistence with the scope of the Applied Sciences journal, since the the manuscript makes an impression of being a numerical exercise with minute applicability to real-world applications. Therefore, the authors are suggested either to resubmit their paper either to any journal in the field of mathematical physics or add more results concerning any realistic practical cases including, for instance, any comparison with experimental data.
Answer: Thank you very much for your positive comments on our paper. Before submitting the paper to Applied Sciences journal, we consulted the editors of Applied Sciences journal, who believed that our paper met the subject requirements of the journal.
- From the Conclusions, it not clear at all what is the particular influence of a more complex model for pile-half-space interaction. All the obtained results are qualitatively consistent with the earlier presented data from Ref. 30.
Answer: Thank you for your comments. In general, the biggest difference between this paper and Ref. 30 is that this paper is aimed at the vertical dynamic characteristics of non-end bearing piles, while Ref. 30 is aimed at end bearing piles. The solution in Ref. 30 cannot be extended to the analysis of non-end bearing piles, so this solution has certain limitations.
According to your comments, we rewrote the conclusions in the revised manuscript.
- For clarity, the authors are strongly advised to directly compare their results from Figures 6 and 8 to the corresponding data from Figures 2 and 6 from Ref. 30.
Answer: Thank you for your suggestions. To be honest, the authors did refer to the research ideas in Ref. 30 when analyzing the influence of temperature and shear modulus of pile surrounding soil. However, since this paper focuses on the analysis of the dynamic characteristics of non-end bearing piles, which is not consistent with the cases of Ref. 30, it is not convenient to directly compare our results from Figures 6 and 8 to the corresponding data from Figures 2 and 6 from Ref. 30. Meanwhile, Fig. 7 in our paper shows the influence of the temperature on the velocity response of pile top in the time domain. However, Ref. 30 only gives the frequency domain solution of the vertical vibration of piles in frozen soil, and cannot be used to discuss the vertical dynamic response of piles in the time domain.
- How the bearing coefficient of pile bottom could be interpreted in terms of real-world materials for piles and soils?
Answer: Thank you for your comments. Scholars usually simplify the supporting effect of pile end soil on the pile as a spring or a series of springs, and the bearing coefficient of pile bottom refers to the value of the spring model.
- Are all the results from Fig. 3 obtained by the authors?
Answer: Thank you for your comments. Yes, all the results from Fig. 3 were obtained by the authors. In order to compare the present model with the results in Ref. 15, we used Matlab to program the solution of Ref. 15 and obtained Fig. 3.
- Page 11, line 223. The physical meaning of the parameter b* is not clear.
Answer: Thank you for your comments. We already explained the physical meaning of b* in the revised manuscript.
- Page 11, lines 221-222. More details should provided related to the derivation of a relation for k_b
Answer: Thank you for your comments. In combination with theoretical derivation and experimental data inversion, Zeng and Rajapakse [15] obtained the empirical expression of kb. In order not to make the paper seem lengthy, we cited the origin of kb, and did not give its corresponding derivation process in the manuscript. In order to make readers better understand kb, we have added relevant descriptions in the revised manuscript.
- Eq. (7): Shear stresses, i.e., \tau_{rz} for solid and ice should be also added here.
Answer: Thank you for your suggestions. We added the description on shear stresses in the revised manuscript.
- The authors should clearly state for what frequency regimes and mechanical properties of piles and solids the assumptions regarding the considered model are valid (i.e., "The pile is represented in a simplified manner by an elastic and circular homogeneous one-dimensional rod", "the interaction between the overlying soil layer and half-space is simplified by the Winkler model").
Answer: Thank you for your suggestions. We made relevant modifications according to the suggestions of the reviewer.
Reviewer 2 Report
The paper is adequated to publish
Author Response
- The paper is adequated to publish.
Answer: Thank you very much for your positive comments on our paper.
Reviewer 3 Report
1- English language must be improved.
2- Some of review paper conclusions must be put in the introduction.
3-The review must contains a very recent papers deals with considered problem and must be more extended.
4- The range of considered variables must be put in the Abstract.
5- More recent references must be added.
6- Conclusions must be re-written as a clear points.
7-The originality points and the practical applications of this work must be added
8-The numerical approach needs to be clarified more
9-units must be included in nomenclature
10-Conclusions must be re-written as a clear points.
11-The discussion of results need improvements and must be divided into subsections
12-A correlations must be suggested based on the computed results
13-Increasing and decreasing in variables need to be clarified as a ratio ( %) in conclusions
14-Some figures are not clear and needs to be re-graph again
15-any equations not for authors need to be referenced
Author Response
- English language must be improved.
Answer: Thank you for your comments. We already asked experts whose native language is English to revise our paper. Please check the revised manuscript for the revision.
- Some of review paper conclusions must be put in the introduction.
Answer: Thank you for your comments. According to your suggestions, we described the conclusions of the main references in the revised manuscript as, ‘Li et al. [30-31] adopted Leclaire’s frozen porous media and Biot’s porous media models to simulate frozen and unfrozen soil layers, respectively, which realizing the dynamic analysis of end bearing piles in single- and double-layer frozen porous media. They found that the properties of frozen soil have a great influence on the dynamic response of pile foundation. Cao et al. [32] assumed that the water in soil gradually condenses into ice when the temperature is close to the freezing point and analyzed the influence of the change in ice content on the cementation effect between solid particles and the dynamic characteristics of pile foundation.’
- The review must contain a very recent papers deals with considered problem and must be more extended.
Answer: Thank you for your comments. We already added some papers related to the same topics which were published in 2021 and 2022.
- The range of considered variables must be put in the Abstract.
Answer: Thank you for your comments. We already revised the description of the Abstract according to your suggestions.
- More recent references must be added.
Answer: Thank you for your comments. We already added some papers related to the same topics which were published in 2021 and 2022.
- Conclusions must be re-written as a clear points.
Answer: Thank you for your comments. We already re-written the conclusions.
- The originality points and the practical applications of this work must be added.
Answer: Thank you for your comments. We already explained the innovation and practicality of this work in the revised manuscript.
- The numerical approach needs to be clarified more.
Answer: Thank you for your comments. We already described the programming process of the present solutions in the revised manuscript.
- units must be included in nomenclature.
Answer: Thank you for your comments. We already corrected the descriptions on the unit.
- The discussion of results need improvements and must be divided into subsections
Answer: Thank you for your comments. We already revised the discussion according to your comments.
- A correlations must be suggested based on the computed results.
Answer: Thank you for your comments. We already added the descriptions on the correlations based on the numerical analysis.
- Increasing and decreasing in variables need to be clarified as a ratio ( %) in conclusions.
Answer: Thank you for your comments. We already revised the descriptions of variables according to your suggestions.
- Some figures are not clear and needs to be re-graph again.
Answer: Thank you for your comments. We already improved the quality of the figures.
- any equations not for authors need to be referenced.
Answer: Thank you for your comments. We already made corresponding modifications according to your comments.
Reviewer 4 Report
This paper presents a closed form solution of a specified problem. The presented solution is slightly different from already known ones. The paper consists mainly from equations with some analysis of solution sensitivity.
There is nothing to correct except some minor typos I pointed out.
It's not crucial paper - just a new solution for an old problem - a small step which might be useful for some specific cases. But we need also such a small steps for making the progress in science. That is why I recommend to print it as it is.
Minor editorial errors are highlighted in yellow in attached file.
Comments for author File: 
Comments.pdf
Author Response
- This paper presents a closed form solution of a specified problem. The presented solution is slightly different from already known ones. The paper consists mainly from equations with some analysis of solution sensitivity. There is nothing to correct except some minor typos I pointed out. It's not crucial paper - just a new solution for an old problem - a small step which might be useful for some specific cases. But we need also such a small steps for making the progress in science. That is why I recommend to print it as it is.
Answer: Thank you very much for your positive comments on our paper。
- Minor editorial errors are highlighted in yellow in attached file.
Answer: Thank you for your comment. We already corrected the errors in the revised manuscript according to your comments.
Round 2
Reviewer 1 Report
By the unknown reason, the authors have unfortunately ignored the following comment:
9. The authors should clearly state for what frequency regimes and mechanical properties of piles and solids the assumptions regarding the considered model are valid (i.e., "The pile is represented in a simplified manner by an elastic and circular homogeneous one-dimensional rod", "the interaction between the overlying soil layer and half-space is simplified by the Winkler model").
Their answer was that "relevant modifications according to the suggestions of the reviewer" were made. However, I was not able to find any of them. Without clear and thorough response to this comment in the manuscript text, the usability of the obtained results in real-world engineering practice is strongly questionable.
Author Response
Comments: By the unknown reason, the authors have unfortunately ignored the following comment:
- The authors should clearly state for what frequency regimes and mechanical properties of piles and solids the assumptions regarding the considered model are valid (i.e., "The pile is represented in a simplified manner by an elastic and circular homogeneous one-dimensional rod", "the interaction between the overlying soil layer and half-space is simplified by the Winkler model").
Their answer was that "relevant modifications according to the suggestions of the reviewer" were made. However, I was not able to find any of them. Without clear and thorough response to this comment in the manuscript text, the usability of the obtained results in real-world engineering practice is strongly questionable.
Answer: Thank you for your comments. Please forgive me for forgetting to add the revised content when revising the manuscript for the first time. The corresponding description are summarized:
Lines 97-99--- According to the previous research results of pile dynamics [2, 3, 10, 27], for most concrete solid piles with large slenderness (i.e. the slenderness of pile is greater than 10), the pile can be assumed to be an elastic and circular homogeneous one-dimensional rod.
Lines 110-113--- As shown in Fig. 1 (b), the interaction between the overlying soil layer and half-space is simplified by the Winkler model whose parameters can be obtained by inverse analysis of soil properties at the interface [40-42]. The soil surface is free, and the pile top is subject to an arbitrary exciting force...
Lines 191-195--- It should be noted that, the complex dynamic stiffness of pile top is mainly utilized for the dynamic design of pile foundation and the velocity response of pile top is used for the nondestructive testing of piles by mechanical impedance method. Therefore, the concerning frequency range may be 0~40 Hz in the design process of dynamic foun-dation and nondestructive testing of piles by mechanical impedance method.
Please check the corresponding content in red words in the revised manuscript.
Reviewer 3 Report
accept
Author Response
- Moderate English changes required
Answer: Thank you for your comments. We already asked experts whose native language is English to revise our paper. Please check the revised manuscript for the revision.
Round 3
Reviewer 1 Report
The authors have introduced suggested corrections. The paper could be accepted.
