An Open Database to Evaluate the Fundamental Frequency of Historical Masonry Towers through Empirical and Physics-Based Formulations
, Cédric Giry 1,*,†, Claire Limoge Schraen 2, Jade Lépine 3, Clarisse Choueiri 3, E. Diego Mercerat 4 and Philippe Guéguen 5Round 1
Reviewer 1 Report
The manuscript reports and collects a database of 242 masonry towers, which have been assembled from an extensive literature review. The database is properly described and discussed by comparing geometrical features of the towers. After that, the paper tries to quantify the contribution of global and local features on the evaluation of the main frequency.
The subject of this paper in worthy of consideration, and the manuscript can be considered quite well organized. The Authors have made a great job, and only few minor comments are reported with the aim to improve presentation of the paper:
- pag. 2, lines 61-62: “Two generic formulation of empirical and physics-based relations found in the literature are then proposed”. Is it not clear if the formulation are already available in literature or if the formulation are proposed by the authors.
- pag. 5, line 131. The meaning of “the effective height Heff” shoud be clearly reported (to this referee best knowledge, this term was originally introduced in Ref. [8]).
- pag. 5, lines 140-150. Description of the database can be improved. Please report the name of the tower 5.69 m height. Please check the correctness of the word “breadth” (width seems better).
- pag. 5, lines 150-152. The Giotto’s tower can be considered a remarkable Cultural buildings such as the Tower of Pisa. The Authors in this respect can consider to quote these reference (in addition to Ref. [52]):
Pieraccini M.et al.(2009).Structural testing of historical heritage site towers by microwave remote sensing. Journal of Cultural Heritage 10 (2):174–82. https://doi.org/10.1016/j.culher.2008.09.006
Spinelli P. et al. (2023). Preliminary Assessment Of The Seismic Behaviour Of Giotto’s Bell Tower In Florence, International Journal of Architectural Heritage, 17(1):23-45. https://doi.org/10.1080/15583058.2022.2145527
- pag. 8, line 228. A change of 0.31 Hz might seems quite important. It would be interesting to specify the % (considering the case where this variation has been observed). Or, in general, to connect this information with the tower.
- pag. 10, line 250. “A generic formulation of the empirical models found in the literature is proposed”. See first comment. Ref for Eq. (1) should be reported.
- pag. 10, lines 255-256. Please specify the “dedicated studies” (the ones cited in Tab. 3?)
- Fig. 10. The fig. reports the “empirical models” listed in Tab. 3. Nevertheless, in this table, for each empirical model (1 to 7) different values of the parameters are provided. It is hence not clear what are the values adopted to report the computed values of the frequencies in this figure.
- pag. 14, line 296: “”p(x)”. Why the dependence from (x), maybe (z)? Please check the Fig. 13.
- pag. 17, line 322. “volumic elements”. Maybe “3D finite elements” would be better. In general a description of the F.E. Model built with Cast3M should be explicitly reported here to help reading (number of elements, degree of freedom, type of finite elements, sensitivity analyses of the F.E. Model, etc.).
- pag. 26. Conclusion. It is suggested to shorten this section, by summarizing main results presented/obtained in the manuscript (are the Authors sure that accelerometric data is less sensitive than velocimetric measurements).
See previous section.
Author Response
Response to Reviewer 1 Comments
Point 1: pag. 2, lines 61-62: “Two generic formulation of empirical and physics-based relations found in the literature are then proposed”. Is it not clear if the formulation are already available in literature or if the formulation are proposed by the authors.
Response 1: The authors thank the reviewer for clarifying this sentence. The empirical and physics-based formulations already exist in the literature, and the Ritz-Rayleigh formulation applied to a tower is proposed by Kohan et al., 2011. The novelty of our study is to propose a generic formulation of the existing ones for more flexible use, an update of the regression coefficients, and an evaluation of the contribution of the tower’s features (Ritz-Rayleigh approach) through sensitivity analysis. Furthermore, a Python code is provided to evaluate the fundamental frequency from the different approaches. We propose to rewrite the sentence in the manuscript (see in red, page 2, line 61-63): “We update empirical and physics-based models derived from existing relations found in the literature ([186], [187], [122], [1], [74], [188], [189]) to consider the tower dynamic features.”
Point 2: pag. 5, line 131. The meaning of “the effective height Heff” shoud be clearly reported (to this referee best knowledge, this term was originally introduced in Ref. [8])
Response 2: The reviewer is absolutely right. We propose to complete the description and specify the reference (see in red, page 4, line 133-134). “the effective height Heff (defined by [8] as the difference between the absolute height of the tower and the height of its constrained portion)”.
Point 3: pag. 5, lines 140-150. Description of the database can be improved. Please report the name of the tower 5.69 m height. Please check the correctness of the word “breadth” (width seems better).
Response 3: The authors thank the reviewer for allowing us to clarify these two points. We add the name of the tower 5.69 m high (see in red, page 4, line 144-145 : "water tower in Pompei number 3 in [130]"). Width and breadth are synonyms. It's not easy to choose one over the other since both terms are used in the literature: Shakya et al., 2016 used "breadth" in their paper, whereas Bartoli et al., 2017 preferred "width". However, we follow the suggestion of the reviewer and we use the word “width” in the updated manuscript.
Point 4: pag. 5, lines 150-152. The Giotto’s tower can be considered a remarkable Cultural buildings such as the Tower of Pisa. The Authors in this respect can consider to quote these reference (in addition to Ref. [52]):
Pieraccini M.et al.(2009).Structural testing of historical heritage site towers by microwave remote sensing. Journal of Cultural Heritage 10 (2):174–82. https://doi.org/10.1016/j.culher.2008.09.006
Spinelli P. et al. (2023). Preliminary Assessment Of The Seismic Behaviour Of Giotto’s Bell Tower In Florence, International Journal of Architectural Heritage, 17(1):23-45. https://doi.org/10.1080/15583058.2022.2145527
Response 4: The reviewer is absolutely right. The authors apologize for forgiving this aspect and add it in red in the dedicated place (the reference is added as part of the exhaustive literature review: page 3, line 100 and page 4 line 155-156).
Point 4: pag. 8, line 228. A change of 0.31 Hz might seems quite important. It would be interesting to specify the % (considering the case where this variation has been observed). Or, in general, to connect this information with the tower.
Response 4: The authors agree with the reviewer. We now propose to express the variation in fundamental frequency as a percentage. This has made it possible to identify particular symptomatic cases. We connect now any variation over 10 % with the tower (most of them are linked to repair operations following a traumatic event). See corrections in red page 9 and 10.
Point 5: pag. 10, line 250. “A generic formulation of the empirical models found in the literature is proposed”. See first comment. Ref for Eq. (1) should be reported.
Response 5: Like point 1, we change the sentence (see in red, page 11, line 260-261): “We introduce the empirical model derived from the reference summarised in Table 2 as follows”.
Point 6: pag. 10, lines 255-256. Please specify the “dedicated studies” (the ones cited in Tab. 3?).
Response 6: Firstly, we have changed the way we present the empirical models we have calibrated. They are introduced in Table 3 from “Empirical model 1” to “Empirical model 7”. We precise the sentence (see in red, page 10, line 267): “The results of the seven regression models (labeled from Empirical model 1 to Empirical model 7 in Table 3 are shown in Fig. 10 with their associated coefficient of determination.”.
Point 7: Fig. 10. The fig. reports the “empirical models” listed in Tab. 3. Nevertheless, in this table, for each empirical model (1 to 7) different values of the parameters are provided. It is hence not clear what are the values adopted to report the computed values of the frequencies in this figure.
Response 7: The authors thank the reviewer to help us improve the description of Fig. 10. The results of the “empirical models”correspond now to the ones labeled from “Empirical model 1” to “Empirical model 7” in Table 3. We propose to clarify the caption of Fig. 10: “Evaluation of the fundamental frequency of towers from experimental natural frequency (gray dot) and empirical models (red cross) labeled from Empirical model 1 to Empirical model 7 in Table 3 as a function of the tower's height.”
Point 8: pag. 14, line 296: “”p(x)”. Why the dependence from (x), maybe (z)? Please check the Fig. 13.
Response 7: The reviewer is absolutely right. We forget to cancel x dependency in the correction process. The error is now corrected (see correction, page 14, line 300).
Point 9: pag. 17, line 322. “volumic elements”. Maybe “3D finite elements” would be better. In general a description of the F.E. Model built with Cast3M should be explicitly reported here to help reading (number of elements, degree of freedom, type of finite elements, sensitivity analyses of the F.E. Model, etc.).
Response 9: The authors have indeed clarified this term. We propose to delete the sentence: “The solution obtained with the Rayleigh-Ritz method is compared with a finite element computation with volumic elements to validate the model.” since it is redundant with the previous one. Page 17,line 324-326. We add information about the 3D FE model “The 3D FE model of the tower is composed of 104400 elements, 122500 nodes. 700 nodes are involved in the SSI, and 2368 nodes for interaction with an adjacent structure. Three degrees of freedom per node are used. Additional stiffness and displacement boundary conditions are managed by dual Lagrange multipliers”
Point 10: pag. 26. Conclusion. It is suggested to shorten this section, by summarizing main results presented/obtained in the manuscript (are the Authors sure that accelerometric data is less sensitive than velocimetric measurements).
Response 10: The authors follow the suggestion of the reviewer. We have reorganized and shortened the conclusion and deleted the conclusion about velocimetric and accelerometric measurements (linked to the type of instrument). See the new proposal in red.
Reviewer 2 Report
the proposal need to be strengthened by numerical simulations and deep comparison with other consistent formulations
Author Response
Response to Reviewer 2 Comments
Point 1: the proposal need to be strengthened by numerical simulations and deep comparison with other consistent formulations
Response 1: We're a bit puzzled by this comment. We have made numerous comparisons with other empirical models (Table 3 and 6, and Figure 10 and 12) and we have also provided a relevant numerical base study in order to test the sensitivity of some tower features (thousands of computations based on a RBD-FAST approach). Thank you to the reviewer for clarifying his comment if he so wishes, but without this we find it difficult to understand the need expressed.
Reviewer 3 Report
The authors used a large open database to evaluate the fundamental frequency of historical masonry towers via empirical and physics-based formulations. The topic is interesting and falls within the scope of the journal. The paper is informative and well organized. It can be recommended for publication. However, the authors must correct some format issues, especially the tables.
The quality of English language is ok
Author Response
Response to Reviewer 3 Comments
Point 1: The authors used a large open database to evaluate the fundamental frequency of historical masonry towers via empirical and physics-based formulations. The topic is interesting and falls within the scope of the journal. The paper is informative and well organized. It can be recommended for publication. However, the authors must correct some format issues, especially the tables.
Response 1: The authors sincerely thank the reviewer for its comments. We corrected the tables format (Table 1, 2, 4, and 7).
