Round 1

Reviewer 1 Report

Comments on paper: geosciences-1268733

“Seismic Vulnerability Assessment and Simplified Empirical 2 Formulation for Predicting the Vibration Periods of Structural 3 Units in Aggregate Configuration”

General comment:

In this paper the vibration period of structural units (SUs) of 14 a typical masonry aggregate located in the historical centre of Mirandola is investigated. SUs are characterized by solid brick walls and deformable floors. The analysis results are represented in terms of risk factor, stiffness, and ductility. Secondly, the eigenvalue analysis is faithfully developed to identify the main vibration modes of the investigated SUs by proposing an empirical formulation, that allows for predicting the vibration period of structural units placed in aggregate configuration starting from the corresponding isolated ones.

The paper is well written and supported by a clear background theory. The topic is of interest aiming at evaluate the seismic vulnerability of historical site and building, typical of the region, by means of detailed computational model. The Seismic Vulnerability Assessment and the fragility assessment applied to historical aggregate buildings are of great interest, as well as the proposed Prediction of the Vibration Period.

In the opinion of this reviewer the paper is good enough for publication in Geosciences, after a minor revision to be addressed:

• Are the authors sure regarding the reference to Table C 8.5.I of NTC2018? (Pag 5/22) raw 168. Can you provide values explicitly?
• A brief comment regarding the role of damping (in structures and materials) could be of interest. It can be also provided in qualitative form, but it is of importance to underline the impact of damping in the calculation model, since it is neglected (and why it could be neglected?).
• Please provide a brief comment on the model sensitivity. Empirical values used in the calculation model are pure single values, without any uncertainty or confidence level. It would be useful to show an example in which values are expressed within a certain confidence level. This reviewer suggests to attribute at least 10% of variability and check the occurring related variability on the results.

Author Response

Reviewer 1

The authors thank the reviewer for the considerations profused for improving the manuscript presented. The new and modified parts are presented in red in the revised version of the text

-----------------------------------------------------------------------------------------------------------------------

• Are the authors sure regarding the reference to Table C 8.5.I of NTC2018? (Pag 5/22) raw 168. Can you provide values explicitly?

All the data have been appropriately revised.

• A brief comment regarding the role of damping (in structures and materials) could be of interest. It can be also provided in qualitative form, but it is of importance to underline the impact of damping in the calculation model, since it is neglected (and why it could be neglected?).

The concept of damping has been introduced in the text.

• Please provide a brief comment on the model sensitivity. Empirical values used in the calculation model are pure single values, without any uncertainty or confidence level. It would be useful to show an example in which values are expressed within a certain confidence level. This reviewer suggests to attribute at least 10% of variability and check the occurring related variability on the results.

The sensitivity analysis has been introduced appropriately in the text.

Author Response File: Author Response.pdf

Reviewer 2 Report

See the file of comments.

Comments for author File: Comments.pdf

Author Response

Reviewer 2

The authors thank the reviewer for the considerations profused for improving the manuscript presented. The new and modified parts are presented in red in the revised version of the text.

-----------------------------------------------------------------------------------------------------------------------

• Should we understand floors or ground for "floor"?

Floors are intended as structural levels. This term should be used instead of ground.

• What is the meaning of "improve" in "From the acquired results, it is observed that the behavior offered in aggregate condition considerably improves the expected seismic response of SUs, providing main engineering demand parameters (EDPs), such as maximum base shear and displacements, greater than those of the corresponding isolated SUs."? Is it "better" or "increase"?

The verb "increase" has been adopted

• A spontaneous urban process? the term "aggregate" is often used; it could be interesting to have information about the kind of link between these SUs. Is it only contact in compression? Iron rods with X elements in facades...?

“spontaneous” has been replaced with “casual”. Regarding the term "aggregate", we mean a set of interconnected buildings characterized by different structural and material properties. In the specific case, adjacent structural units share common transverse walls. In these SUs steel tie-rods are absent. In the longitudinal façades the connections among various structural units are guaranteed only by simple contact, without chaining of stones.  All these information has been briefly introduced in the text.

• LC1, limited knowledge, could you argue this parameter? It would probably merit further explanation or a study of the impact of other hypotheses on the result ...

More explanations on LC1 have been reported in the text.

• Q = 2.3? What are the arguments that allow such a choice? Why are two digits significant for this parameter?

Q=2.3 represents the global ductility parameter established for the investigated masonry type in the following paper:

Lagomarsino, S.; Giovinazzi, S. Macroseismic and mechanical models for the vulnerability and damage assessment of current buildings, Bull. Earthq. Eng., 2006, vol. 4, pp. 415–443.

which was used as a reference for the current study.

• Why, in Figure 5, use intensity to describe the hazard? Macroseismic intensity already incorporates the notion of building vulnerability; vulnerability is therefore present on the abscissa and ordinate axes ...

The analytical procedure is widely described in Lagomarsino and Giovinazzi (2006). Macroseismic intensity is generally adopted as a descriptive parameter of the seismic hazard. The damage level defined by the European macroseismic scale EMS-98, which is associated to the building vulnerability, is a variable parameter increasing with the shaking intensity.

• What is the legend for figure 6? What do the colors brown and pink correspond to? Figure 7 and associated text.

In Figure 6, pink is used to identiy the SUs of the aggregate under investigation by mechanical analyses. Brown is used to identify the buildings adjacent to the investigated pink SU. These structural parts, in fact, modify the structural behaviour of the pink SU with respect to the case when it is alone (isolated condition).

This different behaviour, and therefore the different colors used, is reflected in Figure 7, where grey identifies the capacity curves of the buildings in isolated condition, i.e. without the structural interactions with the contiguous Sus, while red is used for capacity curves of buildings in aggregate condition, in which the interaction among contiguous buildings is considered, as described in the text.

• On one hand, when we speak of a shearing force at the base of a group or an isolated structure, it is normal that this force is greater in the case of a group (greater mass set in motion, therefore higher seismic force if the stiffness evolves in proportion to the mass). Are we talking about overall effort or effort per cell?

The global shear force is related to the aggregate system composed by the reference SU plus the SUs close to it.

• On the other hand, when torsion is taken into account, for an isolated cell, for a group of cells? How is the stiffness of horizontal diaphragms taken into account in the 3Muri software? "The phenomenon of torsion" is mentioned in the text, but there is no indication of what is actually taken into account, and if so, under the effect of which assumptions.

Torsion is considered by the program both for isolated and aggregate Sus. In the specific case, floors are not rigid (stiffness is automatically calculated by the software based on a system of equivalent diagonals taking into account the floor configuration) and, under this condition, the centers of mass and stiffness are relocated at each step of the pushover. The torsion effect is taken into account considering the variation of ultimate displacements in the capacity curves of SUs. In fact, when torsion phenomena are significantly large, they are responsible of premature rupture of several wall panels, which lead towards a minor ductility.

• Ditto for Figure 8. The line of the bisector would better illustrate the point made in the text on the EDPagg / EDPiso comparison. This is all the more useful as the ranges of the abscissa and ordinate evolution are not identical!

The bisector has been added

• The comparison between 375,000 daN / cm and 93,333 seems particular. 375,000 seems to be a maximum and 93,000 the iso stiffness corresponding to this point; shouldn't we look at the maxima in iso and aggregate? This would amount to comparing 375,000 and ≈ 190,000; it does not change the meaning of the conclusion, but it changes the ratio 1 to 2 and not 1 to 4! (the “2” of 402% is illusory precision!).

It has been revised

• These comparisons would be more relevant if one had precise information on the taking into account of the effects of torsion and on the eigen modes associated, or not, with deformations in plane of the horizontal diaphragms (§ between the figures 8 and 9)

The remark of the reviewer is appropriate. The torsion effects could be understood much more in detail is ambient vibration tests are performed, so to correlate the achieved results with numerical ones. Nevertheless, due the lack of this experimental investigation in this study, the prediction of torsional phenomena and their effect on the structure cannot be properly validated.

• Just before Figure 9, the paragraph reports results obtained by extrapolation; what is included in the term "extrapolation?" Figure 10 gives information on isolated and aggregated behaviours, but how are ultimate displacements defined? this PDE is not indicated in table 1 of the characteristics. The first paragraph under figure 10 refers to the bibliography [4]; it is not very clear, it is a shame, because it is at the heart of the reflection carried out thereafter. A little more explanation of the assumptions used to arrive at these results would be very.

The term extrapolation is used since the three SUs studied in detail by 3Muri have been extrapoled from the considered portions (pink and brown SUs) of the whole building aggregate. This has been better explained in the text. In Figure 10 ultimate displacement values are conditioned by the crisis attained by masonry piers by either shear (drift=0.4%) or compression-bending behaviour (drift=0.6%), which has been evaluated by the 3Muri program results. The drift values have not been inserted in table 1, but they can be found in Section 3.2. In the first paragraph under figure 10 the bibliography [4] has been deleted and an explanation of the obtained results has been done.

• This is justified by the fact that the position of SU 1 (constrained on 1 side only) makes it more susceptible to damage“ is not clear! What are the detailing in terms of “constrained”? Only compressive contact? iron bar in tension? how many? ... Torsion could be a cause to the more important damage ...

The SU 1 is constrained on 1 side only, since there is only one structural unit on its right side, which limit its displacements though compressive contact (no steel tie-rods, as already told above). On the contrary, on its left side, SU 1 is free to move in direction X. In this case, the longitdinal walls are not affected by the beneficial confinement effect provided by the adjacent units, so they are subjected to torsion causing an aggravation of the damage.

Figure 11 is interesting. It would deserve to have a more developed title, in particular by indicating what graph a and graph b represent; the explanation can only be found by looking precisely at the legend of the axis of the graph (as a subscript) ... This figure deserves further analysis. By looking at the result point clouds, we see that the results obtained on the aggregates are less "high" than those of the isolated cells; there are fewer oversized cells. This is less true for minimums; therefore, reaching a ruin is not postponed to higher PAGs! On the other hand, it is not the same cells which are found at the limit of resistance. For example, cell 14 has the minimum security in X, whereas it was slightly greater than 1 in an isolated configuration. In Y, cell 2 ends up with the minimal result, while cell 4 in isolated configuration was minimal. Without going back to the need to know the assumptions made to obtain these results, these transfers of the role of fuse constitute an interesting result which deserves to be analysed and reported.

The title of figure 11 has been improved. Safety index is the ratio between capacity acceleration and demand one. Values greater than one (design threshold) indicate satisfied seismic checks. Considering that the results obtained on the aggregates are less "high" than those of the isolated cells, this means that isolated SUs performs well seismically than aggregate ones. These results reflect the outcomes of 3Muri analysis program investigations. Moreover, further analysi

Author Response File: Author Response.pdf