Stochastic Dynamic Analysis of Cultural Heritage Towers up to Collapse

Round 1

Reviewer 1 Report

The paper presents a study about seismic performance of eight masonry towers, proposing a comparison among different solutions (analitical and numerical) and accounting for the variation of mechanical parameters.  In the end, after the performance of IDAs, authors proposed fragility curves for all towers. The paper is interesting and contains a lot of contents, which are fruit of an intensive work that deserves to be published. Nevertheless, some aspects need to be clarified before a final acceptance. Authors can see this Reviewer comments in the attached PDF file.

Comments for author File: Comments.pdf

Author Response

The paper presents a study about seismic performance of eight masonry towers, proposing a comparison among different solutions (analitical and numerical) and accounting for the variation of mechanical parameters.  In the end, after the performance of IDAs, authors proposed fragility curves for all towers. The paper is interesting and contains a lot of contents, which are fruit of an intensive work that deserves to be published. Nevertheless, some aspects need to be clarified before a final acceptance. Authors can see this Reviewer comments in the attached PDF file.

The authors deeply appreciate your constructive comments.

1. With this regard, I suggest to increase the number of works about this topic. Here some suggestions:

https://doi.org/10.1080/15583058.2020.1841366

10.1007/s10518-019-00656-7

10.1002/eqe.2927

The authors found the suggested citations relevant; they were added in the list of references of the revised manuscript.

2. Also with reference to the masonry towers authors could extend the literature review. Here a suggestions: 10.1007/s10518-016-0061-y

The suggested article was added in the list of references of the revised manuscript.

3. Honestly, I don't agree with this concept. Maybe authors would like to point out to a consolidate practice in the construction of masonry buildings that in many cases (e.g. old buildings) ignores the seismic actions.

In my opinion this Sentence needs to be revised.

The reviewer is correct that this statement is not precise and may lead to confusion. The authors meant that, even in cases where during the construction of masonry buildings some measures for seismic action resistance were taken, these were only empirical and inadequate. In this regard, the sentence is now revised to read (see lines 62-69):

Traditional masonry buildings are not generally able to show a sufficient seismic resistance due to ageing of materials and intrinsic inadequacies: poor tensile strength of masonry, high weight/strength ratio, insufficient connection with timber diaphragms and inhomogeneous nature of material. Evidence in some cases of constructions with an intention to resist seismic actions in areas of high seismicity by incorporation of timber and steel elements in the walls can be found only locally [2–7] but even in these cases not following a rational design.

4. The figure is fantastic!

Thank you for your comment.

5. Maybe authors could add a sentence in which specify that, despite the construction tecnique is the same, the mechanical parameters of towers can be extremely different, caused by several factors (type of blocks, type of mortars, history of the towers, humidity and so on)

Following the reviewer’s suggestion, this phrase was revised to read (see lines 156-160):

The inspection of masonry has shown a similar construction technique among them. It is noted, though, that despite this similar construction technique, a different response to similar loading conditions should be expected; this is due to the fact that each towers’ mechanical characteristics are largely affected by a number of factors; geometry of blocks and bonding, type of mortars, history of each tower, humidity etc., to name a few.

6. Considering the height of the buildings investigated, auhtors could mention some advances in FRS estimate, accounting for higher modes effects, e.g. - https://doi.org/10.3390/buildings11020038

The suggested article was added in the list of references of the revised article. We thank the reviewer for this suggestion.

7. Which software has been used?

The FE software Abaqus has been used which is now cited in the revised manusrcipt.

8. How did authors estimate this set of parameters?

The range of the material parameters has been based on the literature [8–14]. Reference to the respective articles is now made in the revised article.

9. Please, use the same software for making figures (e.g. Matlab as for Figure 9)

The figure has been revised accordingly.

10. Is the mesh influencing the results? Is the discretization same for all models? Observing the figure, it seems that a different size of the FE is disposed and this could provide different results among the models

A sensitivity analysis was carried out before the analysis and the size of FE’s was ensured that does not influence the results. This is now stated in the text, see lines 315-318.

In order to achieve mesh-size independence of the results, a sensitivity analysis was carried out, leading to a discretisation of each tower with approximately 2,000 elements.

11. Additional comments are necessary here. I expected to see comments about the failure modes of the belfries.

The collapse mechanisms are now commented as follows, see lines 324-327:

In Figure 9 the collapse mechanism of the final step of each tower is shown: there are three towers (a, b and f) collapsing in diagonal failure (see Figure 2), two (c and e) in belfry failure and the rest (d, g and h) in a combination of diagonal failure and belfry dislocation.

12. Also in this case I expect some comments about the comparison of the solutions.

The collapse mechanisms are now commented as follows, see lines 332-338:

The incremental dynamic analyses (IDAs) result in the capacity curves compiled from the maximum displacement vs. PGA i.e. the intensity measure (IM) of the earthquake for each step. The acceleration of the seismic vibration is transformed into spectral acceleration using the dynamic characteristics of the rocking part and the results are plotted in Figure 12. As can be observed, the IDA capacity curves present a maximum spectral capacity followed by a steep negative slope. This behaviour, with the initial amplification of the capacity, has been noticed also experimentally [59].

13. Is figure 11 presenting fragility curves for each tower analysed? In this case how can be displayed the difference in terms of mechanical parameters? In addition, why did authors use PGA as IM, when before they used Sa? Finally, it is necessary to specify what authors show in Figure 12. In particular, are they combining similar models? In this case, how did they do this operation?

Indeed Figure 14 presents the fragility curve of each tower analysed. The curves can be used for the case-study or very similar to them structures in terms of architectural and mechanical properties.

We thank the reviewer for his careful reading; he is right that the IM should be Sd which by mistake was PGA in the figure’s caption.

Figure 15 presents general fragility curves for towers with similar characteristics. The operation for Figure 15 and all the details are now explained, see lines 373-382:

The fragility curves shown in Figure 14 adhere to the studied towers or similar towers with alike characteristics. To this end, three more general sets of fragility curves are generated for towers and campaniles with characteristics within the range of studied typologies (see Figure 1 and Tables 1 and 2). A distinction is made between towers and campaniles, with the latter further divided in two categories: (i) campaniles with small openings (openings < 10% of external surface) and, (ii) campaniles with large openings (openings ≥ 10% of the external surface). The fragility curves of these three sets are presented in Figure 15: towers appear to have slight or moderate damage for lower intensities but for higher intensities they can be more vulnerable than campaniles, whose vulnerability increases with the openings’ size.

14. Comments about results of fragility curves are missing. In the end, what is the main aim of this work? What is the contribute to the existing literature? Some comments should be added.

The commenting of the fragility curves is now discussed further, see lines 390-393:

The analysis shows that towers are less vulnerable, due to their less slender geometry, than the bell-towers, whose fragility increases partly to their belfry. Moreover, the openings despite a less robust structure, due to the reduced mass, improve the vulnerability.

Author Response File: Author Response.pdf

Reviewer 2 Report

The article is very interesting. It describes the seismic susceptibility of 8 monumental medieval masonry towers. The reviewer likes the article, but has the following comments on the text:

1. In Chapter 5 Authors refer to the formula (9a) from EC6. Please explain why the K coefficient was assumed to be 0.2. The standard does not provide such values. Similarly, formula (9b) is a modification of the formula from EC6. If code formulas are modified, they must be described and explain.
2. Please describe the FEM program used.
3. The work analyzes model displacements and compares the results of the numerical model with the results of analytical calculations. Were there any measurements of the deflections of existing objects? If so, what were the sizes of real deformations?
4. The name Kouris appears many times in the bibliography (Kouris L.A.S. - 7 times, Kouris S.S. - 4 times, and Kouris E.-G. - 4 times). This may suggest that they are the authors of the article. In this case, we have too many self-citations and the reviewer asks for an appropriate correction.

Author Response

The article is very interesting. It describes the seismic susceptibility of 8 monumental medieval masonry towers. The reviewer likes the article, but has the following comments on the text:

Thank you for your positive comments. The authors really appreciate it.

1. In Chapter 5 Authors refer to the formula (9a) from EC6. Please explain why the K coefficient was assumed to be 0.2. The standard does not provide such values. Similarly, formula (9b) is a modification of the formula from EC6. If code formulas are modified, they must be described and explain.

The reviewer is right for the application of the empirical formula of EC6. As it is stated in EC6, the K coefficient is not provided for stone units. The values adopted were suggested by Tomazevic (1999). This is now clarified in the revised text, see lines 275-277:

More specifically, the characteristic strength of masonry f_k is evaluated applying the Eurocode 6 empirical formula [48] and using the coefficients suggested by [53] for stone masonry.

1. Please describe the FEM program used.

We thank the reviewer for noticing this. Abaqus has been used for carrying out the analyses. The software has been cited.

1. The work analyzes model displacements and compares the results of the numerical model with the results of analytical calculations. Were there any measurements of the deflections of existing objects? If so, what were the sizes of real deformations?

There was no measurement of the deflection in the current project. Even if there has been a monitoring of the towers during the study period, there was no major seismic event, and the ‘elastic’ deflection wouldn’t be representative of the NL response examined here.

1. The name Kouris appears many times in the bibliography (Kouris L.A.S. - 7 times, Kouris S.S. - 4 times, and Kouris E.-G. - 4 times). This may suggest that they are the authors of the article. In this case, we have too many self-citations and the reviewer asks for an appropriate correction.

Three of these citation were possible to be removed, and now only the absolutely necessary references are included in the list of references.

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper deals with the seismic vulnerability of monumental un-reinforced masonry. It presents several methodologies, not for everyone there is a result. However is slightly difficult to follow the paper in some parts, making unclear which are the innovative aspects of the paper. Please underline the specific contribution of innovation presented in the research proposed in the paper. The paper is generally comprehendible, it contains some language and grammatical issues throughout, some of which make the key points difficult to follow. These need to be addressed to improve its readability and overall quality. In my opinion, the objectives need to be better specified. Some features of the presented procedure need to be further clarified to improve readability and overall quality.

In my opinion the document corresponds to the objectives of the Journal, if the paper is considered for publication by the publisher, it is necessary to make a major revision:

• Introduction: The state of the art is poor, because this subject is much studied. It is suggested to cite further papers dealing different approaches of modeling. Papers that make comparisons with approaches simplified global approaches like those described in the Guideline for Cultural Heritage Seismic Assessment (DPCM) could be considered also. As an example, a small list of references on the subject is given below:
• doi: 10.1080/15583050802347490
• doi: 10.1061/(ASCE)CF.1943-5509.0001022
• org/10.1061/(asce)cf.1943-5509.0001039
• org/10.1016/j.prostr.2018.11.057

At the end of the introduction, it is necessary to define more clearly the objectives of the research, and ought to put them in an international context.

• Line 114: “The tower with the smallest horizontal area (20.25 m2) .......” The campanile of Vatopaidion Monastery has an equally small horizontal section.
• Section 3: a small list of references on the subject is given below:
• org/10.3390/app11030942
• org/10.1007/s10518-020-01029-1
• org/10.7712/120119.7014.19565

• Section 4: Please cite the appropriate references :Housner, W.G., 1963. The behaviour of inverted pendulum structures during earthquake. Bulletin of the Seismological Society of America, 53(2), 403-417.
• Line 224: Further information about friction coefficient of 0.5 at the interface may be useful to increase the scientific quality of the paper: how is it obtained? Can you provide some reference to scientific or technical literature?
• Table 2: The required formatting is not applied.
• Section 6: FEM model and the results are poorly presented. More Figures and explanations are needed.

                What software was used for FEM analyzes? it is not reported in the paper.

• Line 268 and Page 12: Figure 8 should be Figure 10
• Line 273: How was the final step chosen?
• Line 273 and Page 12: Figure 9 should be Figure 11
• Line 278 and Page 13: Figure 10 should be Figure 12
• Figure 10: More explanations are needed.
• Line 295 and Page 15: Figure 11 should be Figure 13, in this figure "DS1, Ds2, DS3 and DS4" appear but it are not mentioned in the text, an explanation must be added.
• Line 295 and Page 16: Figure 12 should be Figure 14, in this figure "DS1, Ds2, DS3 and DS4" appear but it are not mentioned in the text, an explanation must be added.

Some general comments:

-The novelty of work is not highlighted. The proposed procedure (two-step analysis) should be better explained.

- Paragraphs 3 and 4 should be better linked with the results of the paper.

- There are few references in the paper. To strengthen it, I propose to broaden the base by comparing them with other papers in this area.

- Finally, another deficiency of the paper is the inadequately described and elaborated detail numerical model.

Author Response

The paper deals with the seismic vulnerability of monumental un-reinforced masonry. It presents several methodologies, not for everyone there is a result. However is slightly difficult to follow the paper in some parts, making unclear which are the innovative aspects of the paper. Please underline the specific contribution of innovation presented in the research proposed in the paper. The paper is generally comprehendible, it contains some language and grammatical issues throughout, some of which make the key points difficult to follow. These need to be addressed to improve its readability and overall quality. In my opinion, the objectives need to be better specified. Some features of the presented procedure need to be further clarified to improve readability and overall quality.

The previous version of the text was quite succinct in some parts to keep its length short. The authors made an effort to address the reviewer’s comments and revise the text throughout. Necessary explanations have been now added.

Regarding the contribution of the paper, this is now discussed in the last paragraph of the introduction as follows, see lines 70-89:

To prioritise the needs of structural strengthening for preserving architectural heritage, their vulnerability should be assessed [29] and along with risk scenarios possible losses should be evaluated. In this framework, our aim is a statistical treatment of the vulnerability generating fragility curves, as a fast tool for assessing the seismic capacity of masonry towers. To this end, we studied the towers’ population and selected a representative group of towers to estimate their average response characteristics in terms of expected damage. The basic features of the selected case-study towers are presented in section 2. Limit analyses have been carried out to define firstly the collapse mechanism. Section 3 presents the theoretical framework of limit analysis as well as the collapse mechanisms considered. Once the critical mechanism has been identified, finite element (FE) simulations and analyses are carried out to investigate the seismic performance of the cracked structure with a gradually increasing intensity up to collapse of several time-histories. In each step the maximum displacement at the top is measured. In section 5 the considered time-histories are presented and a parametric analysis for the material properties is carried out. Then, in section 6, NL explicit dynamic analyses for the case-study towers are performed and the displacement capacities are estimated. Using the properties of the collapse mode at hand, we convert these displacements into spectral quantities. Proposing a new definition of the damage thresholds for rocking structures, we generate a set of fragility curves to describe damage and out-of-plane collapse expressed in terms of spectral displacement.

In my opinion the document corresponds to the objectives of the Journal, if the paper is considered for publication by the publisher, it is necessary to make a major revision:

 Thank you for your comment.

• Introduction: The state of the art is poor, because this subject is much studied. It is suggested to cite further papers dealing different approaches of modeling. Papers that make comparisons with approaches simplified global approaches like those described in the Guideline for Cultural Heritage Seismic Assessment (DPCM) could be considered also. As an example, a small list of references on the subject is given below:
• doi: 10.1080/15583050802347490
• doi: 10.1061/(ASCE)CF.1943-5509.0001022
• org/10.1061/(asce)cf.1943-5509.0001039
• org/10.1016/j.prostr.2018.11.057

The reviewer is right to say that there has been a vast research towards the retrofit and strengthening of URM towers. The state-of-the art in the introduction of the present paper can never be complete and the reference list contains representative works, which fit closely to the specific context of the manuscript. The suggested citations are now added in the revised manuscript.

At the end of the introduction, it is necessary to define more clearly the objectives of the research, and ought to put them in an international context.

 Already done. Please refer to our first response to this reviewer’s comments.

• Line 114: “The tower with the smallest horizontal area (20.25 m2) .......” The campanile of Vatopaidion Monastery has an equally small horizontal section.

Amended.

• Section 3: a small list of references on the subject is given below:
• org/10.3390/app11030942
• org/10.1007/s10518-020-01029-1
• org/10.7712/120119.7014.19565

The suggested works were included in the list of references of the revised manuscript.

• Section 4: Please cite the appropriate references :Housner, W.G., 1963. The behaviour of inverted pendulum structures during earthquake. Bulletin of the Seismological Society of America, 53(2), 403-417.

Cited.

• Line 224: Further information about friction coefficient of 0.5 at the interface may be useful to increase the scientific quality of the paper: how is it obtained? Can you provide some reference to scientific or technical literature?

The value proposed by EC6 is 0.4. Relevant literature has been added, see lines 258-259.

This friction coefficient is slightly higher than 0.4 proposed by EC6 e.g. [51,52].

• Table 2: The required formatting is not applied.

Amended.

• Section 6: FEM model and the results are poorly presented. More Figures and explanations are needed.

What software was used for FEM analyzes? it is not reported in the paper.

Thank you for the comment. Abaqus software in now cited in the text. A more detailed presentation of the simulation is included, see lines 308-318:

Fragility analysis requires a high numerical cost. To keep this cost to an affordable level 2D models are developed using plane elements for masonry. As already mentioned the main focus is the rocking response due to the presence of cracks. The simulation of the towers’ behaviour considers cracks as predefined interfaces following the classical Mohr-Coulomb friction law. These cracks have been defined from the limit analysis presented in section 3. Obviously, these interfaces can open, rotate and slide. The material laws assumed for masonry are purely elastic as masonry deformation with respect to the opening of cracks is very small. In order to achieve mesh-size independence of the results, a sensitivity analysis was carried out, leading to a discretisation of each tower with approximately 2,000 elements. The discretisation and the stress fields for gravitational loads for the towers are shown in Figure 10.

• Line 268 and Page 12: Figure 8 should be Figure 10

Amended.

• Line 273: How was the final step chosen?

It is the final step of the analysis, before the overturn. Revision in the text (lines 329-330):

Once the mechanism collapses the analysis stops.

• Line 273 and Page 12: Figure 9 should be Figure 11

Amended.

• Line 278 and Page 13: Figure 10 should be Figure 12

Amended.

• Figure 10: More explanations are needed.

The reviewer is right for a more detailed presentation which has been added in the text, see lines 333-341.

The incremental dynamic analyses (IDAs) are performed scaling up the recordings presented in section 5.2 with a step of 0.1g. NL explicit dynamic analyses are performed in Abaqus [47]. In Figure 9 the collapse mechanism of the final step of each tower is shown: there are three towers (a, b and f) collapsing in diagonal failure (see Figure 2), two in belfry failure (c and e) and the rest (d, g and h) in a combination of diagonal failure and belfry dislocation. Belfry construction can be from masonry pillars or solid stone columns. Pro-taton belfry’ columns (Figure 9c) overturn before the final collapse. As already stated, the collapse mechanism has been defined performing a limit analysis (see section 3).

• Line 295 and Page 15: Figure 11 should be Figure 13, in this figure "DS1, Ds2, DS3 and DS4" appear but it are not mentioned in the text, an explanation must be added.

Figures numbering is corrected. The reviewer is right for a more detailed presentation which has been added in the text together with a figure, see lines 351-361.

The damage states are defined on the capacity curves from IDAs (Figure 12). Four damage states are adopted: (i) slight damage, (ii) moderate damage, (iii) extensive damage, and (iv) collapse. The general capacity curve comprises some distinct points (Figure 11): (i) a peak value signifying the onset of rocking, (ii) an ultimate linear branch which has a slope very close to the one of the limit analysis. In accordance to the capacity curve, the damage states are defined as (Figure 13): (i) the onset of the DS1 coincides with the onset of rocking, (ii) the first point of the last linear branch of the capacity curve marks the onset of DS3, and (iii) DS3 coincides with the overturn of the structure. The moderate damage state is defined with respect to the previous (DS1) and to the next one (DS3) as their mean value [37]. To derive the capacity curve the mean and the standard deviation of each damage states should be estimated from IDAs.

• Line 295 and Page 16: Figure 12 should be Figure 14, in this figure "DS1, Ds2, DS3 and DS4" appear but it are not mentioned in the text, an explanation must be added.

 The reviewer is right to ask for more details. The method is clarified now with a new table and text, see lines 374-383, as follows:

The fragility curves shown in Figure 14 adhere to the studied towers or similar towers with alike characteristics. To this end, three more general sets of fragility curves are generated for towers and campaniles with characteristics within the range of studied typologies (see Figure 1 and Tables 1 and 2). A distinction is made between towers and campaniles, with the latter further divided in two categories: (i) campaniles with small openings (openings < 10% of external surface) and, (ii) campaniles with large openings (openings ≥ 10% of the external surface). The fragility curves of these three sets are presented in Figure 15: towers appear to have slight or moderate damage for lower intensities but for higher intensities they can be more vulnerable than campaniles, whose vulnerability increases with the openings’ size.

Some general comments:

-The novelty of work is not highlighted. The proposed procedure (two-step analysis) should be better explained.

The novelty of the work is now better presented and summarised in the abstract, the introduction and the conclusions (see also response to comment 1).

- Paragraphs 3 and 4 should be better linked with the results of the paper.

The results from the analysis of paragraphs 3 and 4 are now better linked.

- There are few references in the paper. To strengthen it, I propose to broaden the base by comparing them with other papers in this area.

The literature has been furthered and comparisons have been made.

- Finally, another deficiency of the paper is the inadequately described and elaborated detail numerical model.

The numerical model is now better presented, see response to comment above.

Author Response File: Author Response.pdf

Reviewer 4 Report

The paper studies the seismic vulnerability of 8 monumental un-reinforced masonry towers. First limit analysis is conducted to estimate the collapse mechanism and the location of critical cracks. Then nonlinear dynamic analyses are carried out. The topic is interesting however the paper presents many drawbacks. It is not clear if the authors study planar models or 3D models. If they analyze 2D models they should clear state the boundary conditions with the rest of the structure. The FE models are not clear. The authors do not refer the software with which they  performed the analysis. The authors do not refer the degrees of freedom of the model as some equation are valid under specific conditions (e.g.: equation 2).  Several symbols are not defined. There are many comments in the attached PDF file

Comments for author File: Comments.pdf

Author Response

The paper studies the seismic vulnerability of 8 monumental un-reinforced masonry towers. First limit analysis is conducted to estimate the collapse mechanism and the location of critical cracks. Then nonlinear dynamic analyses are carried out. The topic is interesting however the paper presents many drawbacks. It is not clear if the authors study planar models or 3D models. If they analyze 2D models they should clear state the boundary conditions with the rest of the structure. The FE models are not clear. The authors do not refer the software with which they  performed the analysis. The authors do not refer the degrees of freedom of the model as some equation are valid under specific conditions (e.g.: equation 2).  Several symbols are not defined. There are many comments in the attached PDF file.

Thank you for your in-depth review. The text has been in its previous version quite succinct to keep its length short. The authors made an effort to address this reviewer’s  comments and revise the text throughout. Several explanations and details are now added.

Specific responses to your major points are listed below:

Iberon or Iveron (legend of Figure 1h)

Actually, the name is reported by both writings but the more frequent is the latter which is now followed throughout the text.

where is the multiplier k in Eq. (1)?

It is lambda. Amended.

moment arrow should be made visible.

Amended.

- 2D or 3D analysis? If 2D provide plane element type.

                                  If 2D no torsional effects due to asymmetry are taken into account.

- Boundary conditions at the base of each model. No SSI are taken into account (deep foundation important for slender structures).

- Define material in terms of fb, fm and provide a relation to the outcomes of the variability material study (according to paragraph 5.1).

Even though the material is considered to be elastic the Elastic modulus is crucial.

- Is  material common for all the models?

- State clearly that the positive values of stresses correspond to compression and not tension.

The explanations are now introduced in the text, see lines 308-318:

Fragility analysis requires a high numerical cost. To keep this cost to an affordable level 2D models are developed using plane elements for masonry. As already mentioned the main focus is the rocking response due to the presence of cracks. The simulation of the towers’ behaviour considers cracks as predefined interfaces following the classical Mohr-Coulomb friction law. These cracks have been defined from the limit analysis presented in section 3. Obviously, these interfaces can open, rotate and slide. The material laws assumed for masonry are purely elastic as masonry deformation with respect to the opening of cracks is very small. In order to achieve mesh-size independence of the results, a sensitivity analysis was carried out, leading to a discretisation of each tower with approximately 2,000 elements. The discretisation and the stress fields for gravitational loads for the towers are shown in Figure 10.

And later, lines 333-341:

The incremental dynamic analyses (IDAs) are performed scaling up the recordings presented in section 5.2 with a step of 0.1g. NL explicit dynamic analyses are performed in Abaqus [47]. In Figure 9 the collapse mechanism of the final step of each tower is shown: there are three towers (a, b and f) collapsing in diagonal failure (see Figure 2), two in belfry failure (c and e) and the rest (d, g and h) in a combination of diagonal failure and belfry dislocation. Belfry construction can be from masonry pillars or solid stone columns. Pro-taton belfry’ columns (Figure 9c) overturn before the final collapse. As already stated, the collapse mechanism has been defined performing a limit analysis (see section 3).

Figure 9: legend of stresses should be more clear. - stress legend should be readable for all sub-figures

- collapse mechanism corresponds to which earthquake event? what is this? larger letters

Figure’s 11 collapse mechanisms apply to all the earthquakes as it has been determined through the limit analysis. Figure 11 is now better visualised.

Conclusions should be derived from Fig. 10.

Figure 10 is now better commented.

define damping ratio

Damping ratio is 5% stated in the manuscript (see lines .

Describe the method used in the present paper.

No general comments are excepted.

The reviewer is right to ask for more details. The method is clarified now with a new figure and as follows, see lines 351-361:

The damage states are defined on the capacity curves from IDAs (Figure 12). Four damage states are adopted: (i) slight damage, (ii) moderate damage, (iii) extensive damage, and (iv) collapse. The general capacity curve comprises some distinct points (Figure 11): (i) a peak value signifying the onset of rocking, (ii) an ultimate linear branch which has a slope very close to the one of the limit analysis. In accordance to the capacity curve, the damage states are defined as (Figure 13): (i) the onset of the DS1 coincides with the onset of rocking, (ii) the first point of the last linear branch of the capacity curve marks the onset of DS3, and (iii) DS3 coincides with the overturn of the structure. The moderate damage state is defined with respect to the previous (DS1) and to the next one (DS3) as their mean value [37]. To derive the capacity curve the mean and the standard deviation of each damage states should be estimated from IDAs.

(a), (b), (c) should be indicated.

Furthermore, a sketch of each case study should be provided .

A detailed explanation is now given together with a caption (a,b,c), see lines 374-383:

The fragility curves shown in Figure 14 adhere to the studied towers or similar towers with alike characteristics. To this end, three more general sets of fragility curves are generated for towers and campaniles with characteristics within the range of studied typologies (see Figure 1 and Tables 1 and 2). A distinction is made between towers and campaniles, with the latter further divided in two categories: (i) campaniles with small openings (openings < 10% of external surface) and, (ii) campaniles with large openings (openings ≥ 10% of the external surface). The fragility curves of these three sets are presented in Figure 15: towers appear to have slight or moderate damage for lower intensities but for higher intensities they can be more vulnerable than campaniles, whose vulnerability increases with the openings’ size.

Which exactly are the conclusions?

The main conclusions regard the procedure followed in the analysis, the definition of the damage state and the fragility curves. The paragraph has been revised to better present them, more specifically see lines 410-425:

The capacity curves of the towers with cracks are only meaningful in terms of spectral acceleration and displacement. The capacity curve comprises some distinct features: (a) an initial peak denoting the onset of rocking and, (b) a final descending line leading to overturn very close to the line of the limit analysis. Damage states are defined in terms of these features: the onset of rocking is assumed to coincide with the threshold of slight damage, while the two extremes of the final line denote the extensive and complete damage states. Following this procedure, the mean values of the damage state thresholds have been derived for each tower and each earthquake excitation, as well as their standard deviations. Further to this analysis, three main tower types are considered: (i) towers, (ii) campaniles with few openings, and (iii) campaniles with large openings. The mean value and the standard deviations were evaluated.

Using the mean and the standard deviation, a set of vulnerability curves expressed in terms of spectral displacement are proposed, which can be used for cultural heritage structures with the characteristics of the three groups. By using these curves, fast and meaningful conclusions can be deducted regarding the risk management of masonry towers.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

All the comments and suggestions have been satisfactorily fixed by authors. The paper is ready to be published.

Author Response

We thank the reviewer for his comment.

Reviewer 3 Report

The manuscript has been sufficiently improved.

Author Response

We thank the reviewer for his comment.

Reviewer 4 Report

The authors replied to the reviewers’ comments and the paper has modified. However, there are still some drawbacks in the paper. The manuscript can be accepted if the following points are corrected/ answered:

1. Line 176 and equation 1: k and λ must be corrected.
2. In figure 2 some lines are not shown properly.
3. Legend of figure 5 is not readable.
4. Please make comments on figure 6.
5. The authors should explain if the openings have been taken into account as they are different for each side of the towers.
6. Line 164: are correct the units of the weight?

Author Response

Response to the reviewer’s comments

The authors replied to the reviewers’ comments and the paper has modified. However, there are still some drawbacks in the paper. The manuscript can be accepted if the following points are corrected/ answered:

We thank deeply the reviewer for his insightful comments catching several details. Below point-by-point answers are provided.

1. Line 176 and equation 1: k and λ must be corrected.

Corrected (we apologise for not already be so).

1. In figure 2 some lines are not shown properly.

We have tried to adjust the figure including the SDOF systems as suggested by the reviewer the previous time. The response to that comment unfortunately was not included in the responses of the previous revised manuscript. However, the result was confusing as the reviewer can see below:

A new figure could be added showing the SDOF for each case separately, but this was not deemed necessary.

Moreover, the angles beta and theta shown by the reviewer were the same as in the drawing of Figure 3.

Regarding the present comment, we were not sure which lines are implied by the reviewer. To this end, we rotated the arrow of Fig. 2b so as to make it clearer.

The revised figure is:

1. Legend of figure 5 is not readable.

Improved:

1. Please make comments on figure 6.

The difference in the response of the analytical and the numerical model is due to two factors: (i) the numerical model considers an elastic body, and (ii) the coefficient of restitution estimated by Housner overestimates the energy loss due to bouncing [1–3]. This now commented in the document, see lines, 266-269:

The difference in the response of the analytical and the numerical model is due to two factors: (i) the numerical model considers an elastic body, and (ii) the coefficient of restitu-tion estimated by Housner [46] overestimates the energy loss due to bouncing [50–52].

1. The authors should explain if the openings have been taken into account as they are different for each side of the towers.

The façade with the most critical mechanism has been simulated or the one with the higher percentage of openings. This is now stated in the manuscript, see lines 311-313:

The façade with the most critical mechanism has been simulated (Figure 10b,f) or, the one with the higher percentage of openings (Figure 10a,c,d,e,g,h).

1. Line 164: are correct the units of the weight?

Thank you for your comment. The units have been corrected.

References

1. Čeh, N.; Jelenić, G.; Bićanić, N. Analysis of restitution in rocking of single rigid blocks. Acta Mech. 2018, 229, 4623–4642, doi:10.1007/s00707-018-2246-8.
2. Kalliontzis, D.; Sritharan, S.; Schultz, A. Improved Coefficient of Restitution Estimation for Free Rocking Members. J. Struct. Eng. 2016, 142, 06016002, doi:10.1061/(asce)st.1943-541x.0001598.
3. Chatzis, M.N.; Espinosa, M.G.; Smyth, A.W. Examining the Energy Loss in the Inverted Pendulum Model for Rocking Bodies. J. Eng. Mech. 2017, 143, 04017013, doi:10.1061/(asce)em.1943-7889.0001205.

Author Response File: Author Response.pdf