Buckling Instability of Monopiles in Liquefied Soil via Structural Reliability Assessment Framework

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this paper, in order to tackle the gap of the insufficient studies in large-diameter monopiles to support railway bridges subjected to buckling instability and the lack of simplified tools to quickly assess the structural reliability of large-diameter monopile foundations for railway bridges, a simplified reliability analysis framework is formulated. The framework could quickly assess the structural reliability of large-diameter monopiles in fully liquefied soil. The process derivation of the proposed method is sufficient and the discussion for the monopile buckling instability results is detailed. However, this paper is not innovative enough and there is an obvious error in the analysis result, which makes it unsuitable for publication in the current situation. It needs to be revised based on the comments listed below:

1.       In the abstract, the innovation of the paper and the difficulties of the current research should be pointed out.

2.       The details of reliability analysis should be introduced in the body of the text instead of the abstract. The abstract should concisely summarize the content of the proposed methodology.

3.       In the introduction, the research progress on reliability analysis in the field of buckling instability should be added.

4.       Please verify that the data on earthquakes in China referred to table 1 is correct or not.

5.       The first order reliability method is used in the framework proposed in the paper, but the relevant details are not presented in section 3.4.

6.       The first-order reliability method is essentially a linear approximation method, so there will be a large error when applied to the buckling analysis. How does the framework take this into account?

7.       In section 5.3, “Conversely, buckling instability will likely not happen in monopiles with a diameter of 1.80m to 2.20m because the value is one”. The probability of failure being equal to one means that the structure is bound to break down. The conclusion given by the paper is opposite

8.       There are some spelling mistakes and editing errors in the article. For instance，“Lateral spreading because of liquefied soil in sloping and level ground are the leading cause of damage to the pile foundations”. There is a problem of incorrect use of the predicate verb. Please check it carefully.

9.       The recent advances on the topic of buckling should be reviewed. Efficient reliability-based design optimization of composite structures via isogeometric analysis; Stochastic isogeometric buckling analysis of composite shell considering multiple uncertainties; A new reliability-based design optimization framework using isogeometric analysis.

Comments on the Quality of English Language

The English should be further improved.

Author Response

In this paper, in order to tackle the gap of the insufficient studies in large-diameter monopiles to support railway bridges subjected to buckling instability and the lack of simplified tools to quickly assess the structural reliability of large-diameter monopile foundations for railway bridges, a simplified reliability analysis framework is formulated. The framework could quickly assess the structural reliability of large-diameter monopiles in fully liquefied soil. The process derivation of the proposed method is sufficient and the discussion for the monopile buckling instability results is detailed. However, this paper is not innovative enough and there is an obvious error in the analysis result, which makes it unsuitable for publication in the current situation. It needs to be revised based on the comments listed below:

1. In the abstract, the innovation of the paper and the difficulties of the current research should be pointed out. Thank you for pointing this out. Yes, we improved the abstract as requested. We highlighted that the development and application of a structural reliability assessment framework itself represent a significant innovation.
2. The details of reliability analysis should be introduced in the body of the text instead of the abstract.The abstract should concisely summarize the content of the proposed methodology. Thank you for pointing this out. Yes, we removed some in the abstract but not much because most of it is important information.
3. In the introduction, the research progress on reliability analysis in the field of buckling instability should be added. Thank you for pointing this out. Please consider as we added in Section 1.2 that a monopile illustrated in Figure 1(c) might experience pure buckling instability with a shear deformation effect. We believe that the Literature Review already shows the research progress on reliability analysis in the field of buckling instability. Also, kindly consider our response to your comment no. 3 is now incorporated in the Literature Review.
4. Please verify that the data on earthquakes in China referred to table 1 is correct or not. Thank you for pointing this out. We double-checked the data and corrected to 2008 instead of 2002. We added also a new reference, see Reference no. 11, to support the information.
5. The first order reliability method is used in the framework proposed in the paper,but the relevant details are not presented in section 3.4. Thank you for pointing this out. Yes, the first order reliability method is adopted in this research, as mentioned in Section 3.1. The method is also known as Hasofer-Lind Reliability Index. The relevant details for this method already explained in Reference no. 40: A. M. Hasofer and N. C. Lind, “Exact and Invariant Second-Moment Code Format,” Journal of the Engineering Mechanics Division, vol. 100, no. 1, pp. 111–121, Feb. 1974, doi: 10.1061/JMCEA3.0001848. Furthermore, the Section 3.4 of the current study illustrates the limit state function using the Hasofer-Lind Reliability Index as explained in Equation no. 2.
6. The first-order reliability method is essentially a linear approximation method,so there will be a large error when applied to the buckling analysis. How does the framework take this into account? Thank you for pointing this out. Yes, the current study focuses on linear approximation method. We believe that a large-diameter monopile can be analyze first by linear approximation method as simplified approach. The current study validated the results using an experiment and found in some portion we have in agreement.
7. In section 5.3, “Conversely, buckling instability will likely not happen in monopiles with a diameter of 1.80m to 2.20m because the value is one”. The probability of failure being equal to one means that the structure is bound to break down.The conclusion given by the paper is opposite Thank you for pointing this out. We double-checked our calculation and found out that we missed to consider the principle 1-p = Pf. We revised Figure 8 and added some statement. Also, the abstract and conclusion is updated.
8. There are some spelling mistakes and editing errors in the article. For instance，“Lateral spreading because of liquefied soil in sloping and level ground are the leading cause of damage to the pile foundations”.There is a problem of incorrect use of the predicate verb. Please check it carefully. Thank you for pointing this out. We revised accordingly, “Lateral spreading poses a significant risk to pile foundations when liquefaction affects the soil. The liquefied soil can no longer support the loads placed upon it, causing it to flow laterally. In sloping ground, this lateral movement can exert considerable force on pile foundations, potentially causing them to tilt, shift, or even fail”.
9. The recent advances on the topic of buckling should be reviewed. Efficient reliability-based design optimization of composite structures via isogeometric analysis; Stochastic isogeometric buckling analysis of composite shell considering multiple uncertainties; A new reliability-based design optimization framework using isogeometric analysis. Thank you for pointing this out. For large-diameter monopile, we believe that the structure itself is not complicated and can be analyze first with simplified approach such as linear approximation. We will consider your comments into our next paper related to monopiles analyzed with more advance analyses such as isogeometric. We will try to compare the outcome.

Reviewer 2 Report

Comments and Suggestions for Authors

Please see the attached file.

Comments for author File: Comments.pdf

Author Response

The paper focuses on pile failure mechanisms during seismic liquefaction, particularly buckling instability with shear deformation. The study highlights gaps in research on large-diameter monopiles for railway bridges and the lack of simplified tools for structural reliability assessment. For this, the authors proposes a simplified framework to evaluate the structural reliability of these monopiles in fully liquefied soils. Furthermore, the text emphasizes the that assessing structural reliability to understand the probability of buckling failure in liquefied soils is crucial. Therefore, this work constitutes a significant contribution in this regard. The authors provide a literature review on the subject. Furthermore, they introduce the mathematical formulation framework, present a case study of a high-speed railway bridge model, and conduct numerical validation and probability of failure analysis. While the reviewer is not qualified to assess the quality of English in this paper, they acknowledge that the manuscript is well-written and logically structured, both in organization and cohesion. The introduction clearly presents the research problem and the objectives of the study, and the conclusions are consistent with the evidence and arguments presented. The reviewer finds the results presented in the manuscript correct and recommend that the paper is accepted for publication, with some minor comments

and remarks.ratra

Some comments

1. To ensure better clarity for the reader, it might be more appropriate to transform Section 2 (Literature Review) into a subsection (1.3 Literature Review) of the introduction. Additionally, introduce a new subsection (1.4 Text Structure) before line 111.

For example:

1.4 Text Structure

“The outlines of the review are as follows: ...”

Thank you for pointing this out. Please consider that in a typical research paper the Literature Review always mention as second part. We would like to maintain Section 2 for the Literature Review. On the other hand, we incorporated the suggestion to add new subsection which is 2.2. Text Structure.

2. I suggest that Table 2 be presented as an appendix. Thank you for pointing this out.
3. Could you please center the titles of all the figures? Perhaps this is more suitable for the

structure of the text. Thank you for pointing this out. We centered the titles of all the figures as commented.

Some remarks

1. On Page 4, line 222: I think Equation 6 is not presented in the text. Thank you for pointing this out. We added now the Equation 6.
2. Please check the correct indentation on lines 401, 409 and 443. Thank you for pointing this out. We updated and implemented correct indentation.

Reviewer 3 Report

Comments and Suggestions for Authors

            The present work reports on pure buckling, with shear deformation and reliability assessment on monopile failure probability in fully liquefied soils concerning bridge foundations subjected to earthquake effects. A first order reliability method (FORM) – the Hasofer-Lind Reliability Index - has been used to conduct the evaluation followed by Normal and Gaussian distribution checks. The present article offers novelty regarding the use of a hybrid approach concerning buckling instability assessment in large diameter monopiles with respect to shear deformation effect.

            The present form of the manuscript is relatively well organized. The writing is very clear, the section definition is correct, and the English language is used accordingly to required standard.

            At a certain extent, the reviewer would recommend, if possible, the shortening of certain paragraphs, due to the traditional synthetic form of such an article.

            The reviewer would suggest that some of so called “state of the art” elements from the abstract should be moved in the “Introduction” section for a crisper, more straightforward first contact with the article. Then it would be of greater impact some brief considerations on nonlinear buckling domain using probabilistic measure of structural safety versus present complex mathematical formulation (Euler-Bernoulli vs. Timoshenko model).

Author Response

  The present work reports on pure buckling, with shear deformation and reliability assessment on monopile failure probability in fully liquefied soils concerning bridge foundations subjected to earthquake effects. A first order reliability method (FORM) – the Hasofer-Lind Reliability Index - has been used to conduct the evaluation followed by Normal and Gaussian distribution checks. The present article offers novelty regarding the use of a hybrid approach concerning buckling instability assessment in large diameter monopiles with respect to shear deformation effect.

            The present form of the manuscript is relatively well organized. The writing is very clear, the section definition is correct, and the English language is used accordingly to required standard. Thank you very much for the comment.

            At a certain extent, the reviewer would recommend, if possible, the shortening of certain paragraphs, due to the traditional synthetic form of such an article. Thank you for the recommendation. We believe that all information we put are all important. Please consider keeping all of them because are important information.

            The reviewer would suggest that some of so called “state of the art” elements from the abstract should be moved in the “Introduction” section for a crisper, more straightforward first contact with the article. Then it would be of greater impact some brief considerations on nonlinear buckling domain using probabilistic measure of structural safety versus present complex mathematical formulation (Euler-Bernoulli vs. Timoshenko model). Thank you for the suggestion. The suggested topic will be our next paper.