Seismic Fragility Analysis of Retaining Walls Dependent on Initial Conditions
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe manuscript titled as “Seismic Fragility Analysis of Retaining Walls Dependent on Initial Conditions” condected non-linear time history analyses, through the 2D Finite Element simulation method for the determination of damage potential of retaining walls. In the work, fragility curves for cantilever retaining walls of three different heights were obtained considering cohesionless soil materials using the vertical ground displacement of the backfill soil and permanent horizontal displacement of the wall’s base. Paper needs revisions and some important topics to be addressed in the manuscript as stated below:
1. The study discusses about the permissible horizontal/vertical displacements levels or damage states for the retaining walls proposed by different researchers/studies. Finally, horizontal displacements were determined as function of height, and constant values for vertical displacement. However, depending on the soil type (cohession, cohessionless etc) these values can be still altered. Accordingly, it is advised to address the uncertainties associated with the damage states on the fragility. Following study can be beneficial and quatod to mention about this issue in the manuscript. https://doi.org/10.1007/s10518-021-01292-w.
2. The study lacks of giving adequate details about the record selection which is one of the uncertain issue in the manuscript since displacements are affected from the selected records. Seismic hazard depending on the location of retaining wall have important topic and earthquake records selected considering and other multi objectives such as Mw, soil type, target spectrum etc. Accordingly, authors should mention about this issue in the manuscript. See also the attached file for more info.
3. Related with the previous question, authors claimed that they scaled the earthquakes basedn on target PGAs equal to 0.1g, 0.2g, 0.3g, 0.4g and 0.5g. According to selected earthquake Pga provided in the table 5, some earthquake should be scaled more than 20 which is so high!. Authors should also give some necessary information about this referencing literature studies. Some suggested studies regarding the issue for further reference are provided below (not limited to given studies)
https://doi.org/10.1016/j.istruc.2023.03.040 and https://doi.org/10.1002/eqe.3173
4. In lines 292-298, authors inform about the the evalution approaches such as efficiency, practicality and proficiency. According to claim of authors low ratio of proficiency is more proficient. However, this should reversed !. Assume that you have a 45o correlation line which is equal to y=x, this means R2 is 1 and slope is then equals to 1. Which means proficiency is 1 which is more proficient. Needs clarification!
5. The calculation behind the equation 5 is not clear! If authors use standart lognormal distribution then Btot can be calculated by the least sqaures method (LSM) or maximum likelihood estimation (MLE) method. Accordingly, mean and standart deviation which Btot in this study, is calculated. Did authors used some constant values for (βds), (βC), and (βD)? Needs clarification.
6. Combination of Ux+Uy is not clear. It would be beneficial to provide some information how did authors combined vertical and horizantial displacement in the evaluation process.
7. In the manuscript, intensity measures are called for example, PGA and some PGAFF. The difference is not explanied or no information is provided. If they are same, then unique notation should be used. If not, explanation is needed.
8. Limitations of the study can be also discussed to clarify open issues for future studies.
Additional comments and revisionsa re provided in the attached file.
Comments for author File: 
Comments.pdf
The use of language is fine in general. Just Minor editing of English language required.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsDear authors,
The present manuscript describes seismic fragility curves of retaining walls, with the novelty of adding a hydrostatic water table behind the wall. In general, the paper is clearly written and understandable. The scientific methodology is consistent. However, the main aim of the research paper (effect of water) is not enough detailed/discussed. What are the implication of water behind a retaining structure. A comparative figure could help to illustrate this impact.
In addition to the general comment above, the authors can find below major comments, minor comments as well as typos. Some of them might even be linked with the main (major) comment.
Major comments:
Lines 343-353: Verifying the validity of the plaxis nonlinear model based on the comparison with linear results does not seem correct. Please update the validation of the model with any other possibility (comparison with existing non-linear model / comparison with experiments / … )
Section 3.3: The selected IMs may not be independent. Therefore, the reviewer suggests applying classical methods to differentiate them. In addition, since the IMs are not dimensionless, the practicality is also not dimensionless, which certainly prevents a faire comparison between the different IMs. For instance, the reviewer thinks that it is better to use a efficient IM (Arias intensity) with a reasonable practicality as the linear regression is much more reliable. The selected IMs mostly exclude the effect of frequency and duration of the motion, while it is known to have an effect on the response of geotechnical structures. Could the authors explain why they limited your analyses to these intensity measures ?
Section 3.5: The methodology to extract fragility curves must be better explained in the light of the present data set of numerical results.
Figure 12: the relatively large differences (quantitative and qualitative) between the present results and the one from the literature is not enough explained.
Minor comments:
Lines 87-109: The reviewer suggests specifying the software used by the research studies in the literature. Possibly, studies focused on other type of retaining walls (masonry gravity walls or flexible steel retaining structures) could also be briefly described. It would help the reader to get that such approaches are done in each field of retaining structures.
Line 143: The choice of the multilayer soil profile (with the limit being 1m below the wall) should be detailed.
Line 146: The choice of non-cohesive soils is understandable; however, it should be specified that it is not realistic, though being conservative. Indeed, if water accumulates at wall back, it means that the fine part of the material is not negligible. If so, in the non-saturated part of the backfill, we should have some cohesion.
Line 205: Equation 2 seems strange as 1/0.7 = 1.429 instead of 1.385. Please check the parameters of equation 2.
Figure 7 : change the line type as the colours do not differentiate enough in white&black print.
Table 7: The way Ux and Uy are combined to obtained Ux+Uy is not 100% clear. Is it simply a sum?
Some typos:
Line 60 VS Line 93: The format of the citation does not seem consistent. Please check the consistency.
Table 7: PGAff, PGVff, .., the subscripts FF are not clearly defined at their first occurence.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThe study deals with the seismic fragility assessment of cantilever retaining walls with cohesionless foundation soil and backfill materials. For this purpose, three different heights are evaluated considering five pre-defined initial conditions (global safety factors). The structural models for nonlinear analyses are elaborated by making use of finite element methods. Seismic response of the soil - wall system is conducted based on non-linear time history analyses. The study relies on a comprehensive work conducted through numerical analyses. Some further clarification is needed in my opinion. Please see below my comments:
- Scaling factors of input motions used for the dynamic analyses should be re-considered. The modification of the frequency content should be evaluated in order to discuss the implications in the structural response of the walls analyzed;
- A Rayleigh damping of 5% at frequencies 7.6 and 19 Hz was considered. Please clarify the value adopted or include some references;
- The dispersion in the structural response was estimated considering three limit states independently. My suggestion is to estimate the dispersion as a function of each limit state and consider these values in the fragility analysis;
- Fragility curves were computed assuming a prior LogNormal distribution. Other distributions could be also evaluated and discuss its implication in the fragility of this type of structures. The authors could also try to derive their own analytical distributions from the empirical cumulative function of the structural response;
- The parameters that define the fragility curves could be also provided in a table to be employed in further studies;
- The quality of several figures is rather low. Not sure if this is the effect of the conversion to pdf, but please fix.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsAuthors provided acceptable comments to questions in general. However, response to the comments 2 and 3 of Reviewer is not satisfactory and needs to further mentioned.
First,
As provided by the authors different approaches such as IDA can be used for plotting fragility curves. However, in IDA, some ground motions may need to be scaled to large IM values to produce collapse (this situation is also valid for the current study some earthquake are scaled more than 20 which is so high), which raises several concerns. First, it is computationally time consuming, as it requires many structural analyses to be performed with increasing IM levels, to observe a collapse. Second, and the more importantly, the large-IM results are less practically relevant, as the fragility function values at large IM levels are of less interest than values at small IM levels (Baker 2015- https://doi.org/10.1193/021113EQS025M, Baker and Cornell 2005- https://doi.org/10.1002/eqe.474).
Above comments mainly used to determine fragility functions or curves in probabilistic respect considering the different IMs which is related to seismic background of the site or structure/infrstructures topology. Accordingly, the authors’ response “fragility curves do not necessarily concern a specific level of hazard or a specific location” is not completely right, because fragility curves, finally, determined for seismic risk analysis, vulnerability or cost estimation issues.
Second,
Showing a good convergence with the mean normalized acceleration response spectrum of the original records do not necessarily mean the selected earthquake are compatible since it is stated by numerious studies (Kostinakis et al. 2015- https://doi.org/10.1016/j.engstruct.2014.10.035, Ye et al. 2011- 10.1002/tal.693, Cantagallo et al. 2012- http://dx.doi.org/10.1016/j.probengmech.2011.08.016, Ebrahimian et al. 2015- 10.1007/s10518-015-9755-9, Akkar et al. 2005- 10.1002/eqe.492 etc.) that displacement demands are well correlated with acceleration response spectra.
On the other hand, authors were right in claiming that some suggested references were not opened or related to study due to copy-paste error. Accordingly, following studies (not limited to given studies) including SDOF systems close to systems related to retaning walls need to be specified for selection/scaling of earthquakes which is one of the uncertain issue in the current study.
https://doi.org/10.1002/eqe.3173 and https://doi.org/10.12989/eas.2021.21.4.395
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsIt is sad that the main major comments were not really addressed by the authors.
Instead they provided explanations "only" to the reviewer, while the reviewer is asking to have more details inside the paper.
Comment 1: it is not clear if the water level represents a real possible increase of water level (drainage problems), or if it represents a damaged state due to other actions (seism, weathering).
Comment 3: Even if someone found that these intensity measures are independent, it could be interesting to see if the principal is conserved for your analyses. Most importantly, one could imagine to do some correlation matrices, or to compute some model reduction analysis.
In addition, the reviewer thinks that the coefficient "a" of the linear regression is not dimensionless, as it relates "ln(PGVff)" with "ln(Uy)" for instance in Figure 10. Therefore, to his opinion, the scale ("length") of the x-axis will affect the practicality.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 3
Reviewer 1 Report
Comments and Suggestions for Authors-
Reviewer 2 Report
Comments and Suggestions for AuthorsDear authors,
The last issues have been solved by the authors.
Indeed, as the plots are in log, the results are dimensionless (sorry...)
It was not expected that PGA was the best IM to predict the vulnerability of a retaining wall, but it is the results from these simulations.
All IMs are indeed correlated, and you are looking for the best one. I would be curious to see if seismic duration is more relevant than PGA (or something like seismic duration above a given acceleration threshold.
Good luck,
Best regards,
