Assessment of a Full-Scale Unreinforced Stone Masonry Building Tested on a Shaking Table by Inverse Engineering

Round 1

Reviewer 1 Report

see attached file

Comments for author File: Comments.pdf

Author Response

Response to reviewer 1

We kindly thank the reviewer for her/his effort to improve our submitted manuscript. We made a considerable effort to tackle the reviewer’s comments and we believe that the clarifications and amendments in the revised version have substantially improved the original one. The revised parts of the manuscript related to the comments of the reviewer are cited in blue italics font.

Regarding the comments of the reviewer:

Comment 1

The paper does not appropriately and exhaustively convey the procedure that has been followed to derive the updated parameters. It would be beneficial to add a flowchart to explain stages of the initial and step-by-step calibration up to the final values. 

Response to comment 1

The calibration procedure is explicitly described in section 4. Each step is presented in a separate subsection (4.2 to 4.7). As per reviewer’s suggestion a flowchart of the procedure illustrating the procedure schematically is now added and a short presentation of the steps is added in section 4.1 as follows:

“The procedure is illustrated in Figure 5 and can be summarised as follows:

1. Step 1: from the laboratory testing the material properties and the frequency response functions (FRF’s) of the structure.
2. Step 2: a FE model of the structure is built based on the previously found material properties.
3. Step 3: static condensation is performed to reduce the degrees of freedom (DOF’s) of the model.
4. Step 4: the derivatives of the constitution matrices of the model (M mass, K stiffness and C damping) are estimated.
5. Step 5: using the data from steps 2 to 4 the FRF’s are estimated.
6. Step 6: FRF’s from steps 1 and 6 are compared and new material properties are estimated.
7. Step 7: the optimisation procedure returns to step 2 until the comparison shows an acceptable convergence.
8. Steps 2 to 7 are explicitly described in the following sections 4.2 to 4.7.”

Figure 5. Flowchart of the calibration procedure.

 

Comment 2

Also a table reporting all the values of the parameters (initial and updated) could be useful to cross-interpret the graphs reported in figure 8.

Response to comment 2

As per reviewer’s suggestion a table reporting all the values of the parameters (initial and updated) is now added (see section 5.3):

Table 3. Elastic (E) and shear (G) moduli in GPa for each test phase of the building’s structural members.

Member	Modulus	initial	Phase 1	Phase 2	Phase 3	Phase 4
East wall	E	2.55	1.81	1.38	0.99	0.88
	G	0.84	0.35	0.26	0.16	0.10
West wall	E	2.55	2.39	2.35	2.31	2.04
	G	0.84	0.62	0.59	0.57	0.48
OOP walls	E	2.55	2.52	2.07	1.99	1.97
Diaphragm	G	0.35	0.35	0.23	0.16	0.14

 

Moreover, the legends of Figure 9 were removed outside the plots so that they are not hiding any values:

(a)	(b)		(c)

Figure 9. Degradation of (a) elastic and (b) shear moduli (Equation 16) and (c) their ratio between subsequent phases from FE calibration.

 

Comment 3

At page 5, lines 164-168 the authors argue that since stonework is more randomly oriented, then an anisotropic model suits better the modelling of the material at the macroscale. It is opinion of this reviewer that more randomness of the orientation of the internal structure would instead be generating a more isotropic response.

Please justify with more details or revise this choice, which is a crucial one, possibly not correct in your analyses.

Response to comment 3

Masonry is a heterogeneous and anisotropic material. In the case of brickwork there is a strong directional dependence of the response due to its periodic pattern. The authors agree with the reviewer that this phenomenon is less intense in the case of stonework. Nonetheless, there has been reported in several experimental and analytical studies that orthotropy exists in stone masonry (e.g. [1–5]). Namely, the low values of the ratio of the in-plane shear to elastic modulus G/E of stonework can be justified only for an anisotropic material (e.g. [1,3]). Therefore, although in other cases an isotropic model could be valid, in the present study would not help identifying the decaying of G/E with increased cracking.

This justification is now added, see section 4.2:

“During the calibration process masonry is considered as an orthotropic material [31–35]. Orthotropy is essential to study the evolution of the shear to elastic moduli ratio G/E.”

And later in the same section:

“The initial ratio of shear to elastic moduli G/E is 0.33 smaller than the suggested value in many codes 0.4 [39]. The fact that the proposed ratio of G/E in codes is larger than the ac-tual one has been reported in several studies (e.g. [31,33–35]). The experimentally found ratio 0.33 would correspond to the marginal value for a Poisson ratio v = 0.5 of a homoge-neous material. This value drops as cracking appears, as shown in the next sections, and therefore, the assumption of a heterogeneous material is the only valid one.”

 

Comment 4

Also, there is some confusion generated by the inappropriate use of “smeared crack”, as all the analyses are assuming a – no doubt – linear elastic behaviour, with just a degraded value of the stiffness(es) and I would not use the term smeared crack which in literature is used for a quite well-known constitutive model for brittle materials.

Response to comment 4

The modelling approach of “smeared crack” has been extensively used for brittle materials including masonry. The basic assumption of the methodology is that masonry remains a continuum (which obviously does not happen) while its mechanical properties (stiffness and strength) are modified to consider the effect of cracking. In this context, the authors still believe that the term is suitable for the analysis and to lift any possible misunderstanding a clarification is now added (see section 4.1) as follows:

“As aforementioned the basic assumption of the FE modelling is to assume an equivalent elastic response of masonry which remains a continuum and cracking is not directly simulated but indirectly taken into account by the modified mechanical properties in accordance with the smeared crack approach.”

 

Comment 5

The authors calibrate the elastic properties of the material in different parts of the building according to their damage level, but it is evident that the damage state is in turn related to the geometric features of the portion that is being considered. Because of the nature and the direction of the strong-motion shakings (those that are meant to induce damage) it is not surprising that the north and south façade are not much affected, except for the north one (and this is due to the openings), while the west and east surely undergo more damage and, consequently, more marked decrease of the secant equivalent stiffness. And again, having more openings, the west façade is likely to be more damaged. At the same time, because of their position and constraint conditions, floors and roof are not expected to be significantly damaged, nor to play a crucial role in the dynamic response of the structure.

Response to comment 5

The damage can be easily detected by visual inspection. Therefore, the coincidence of the findings of the study with the actual situation shows the validity of the procedure and gives confidence to the results of the analysis. The following comment has now been added in section 5.3:

“On the contrary, the degradation of East wall is lower and has a sudden increase from the third to the fourth phase. This is in line with the diagonal cracks appearing in this wall at this phase (see Figures 3-4). The elastic modulus of North and South facades has a steeper increase of the degradation between the second to the third phases when the horizontal cracks are initially formed and subsequently propagated. Therefore, the analysis shows a very good coincidence with the actual damage of the structure.”

 

Comment 6

How is the “material deterioration” related to the geometric features of the structure and its dynamic response?

Response to comment 6

Please see response to the previous comment.

 

Comment 7

If anisotropy still seems for the authors the right option, how do the different stiffness parameters (in the different direction) vary? Do they evolve with comparable trends? If the proportionality is maintained during the whole process would still be the anisotropic choice be of interest then?

Response to comment 7

Please see response to comment 2, and

The ratio of the elastic moduli of masonry in the out-of-plane direction E₂ and the horizontal one E₃, as there was performed no testing, are assumed proportional to the 80% of the vertical direction E₁ based on standard values from the literature [2–5]. As damage is diagonal cracking it is valid to assume that the proportionality is maintained. In any case, any change in the proportionality of the parameters could be an interesting topic to research but not within the scope of this study.

The shear moduli G_i is assumed equal to all the three directions as this was estimated from diagonal compression tests and there was performed no testing for the out-of-plane one.

North and South walls presented a similar damage mechanism involving the gable roof and therefore, have the same parameters P₅. As the damage of North and South walls is out-of-plane the shear modulus is assumed to remain constant (i.e. G/E = 0.33).

These are now clarified in section 4.2:

“Elastic moduli of masonry in the out-of-plane direction E₂ and the horizontal one E₃, as there was performed no testing, are assumed proportional to the 80% of the vertical direction E₁ based on standard values from the literature [2–5]. The calibration parameters are presented in Table 1. North and South walls presented a similar damage mechanism involving the gable roof and therefore, have the same parameters P₅. As the damage of North and South walls is out-of-plane the shear modulus is assumed to remain constant (i.e. G/E = 0.33).”

 

Comment 8

What is the engineering outcome of this study and how would it be possible (if possible) to generalize these results to masonry buildings of different shapes?

Response to comment 8

The main outcome of the present study is the evolution of the G/E ratio for stone masonry on a real structure as well as the procedure itself. Full-scale experiments can not be replicated to estimate average values etc. but have a tremendous value as they imitate the real conditions much better than micro and meso-scale tests.

This is now better expressed in the Abstract:

“It is shown that the deterioration is more intense for the shear moduli of the walls rather than the elastic modulus. The ratio of the in-plane shear to the elastic modulus decreases substantially.”

In the Introduction section:

“The scope of this study is to investigate the evolution of the material properties of the structure applying a dynamic analysis of the stationary response by an iterative optimisation process.”

And in the Conclusions section:

“Shear modulus appears to decrease more than the elastic modulus of the respective walls. West wall which is uniformly damaged has a regular curve with increasing shaking intensity. East wall instead has steep drops for some phases. The shear modulus of the timber diaphragm deteriorates from phase to phase. The shear to elastic moduli ratios drop to as low values as 10% for the more damaged wall.”

 

Comment 9

Would it be possible to derive, on the basis of the proposed analyses, a damage index, possibly with reference to the initial mechanical parameters, which is not clear if they are those reported in reference [31] (is it a report, paper, conference proceeding?) or calibrated differently?

Response to comment 9

It is hard to develop a generalization of the specific trends obtained from the analysis of one building with specific materials, dimensions etc.

 

Comment 10

The authors should clarify how the initial undamaged model was calibrated as it is not clear if the constitutive parameters of the initial model were derived from a “calibration analysis” or retrieved from the experimental tests (reference [33] is mentioned in addition to [31]).

Response to comment 10

The initial values of material properties for test phase 1 were as the reviewer implies the experimentally determined. This is now better clarified in the manuscript see section 4.1:

“The initial values for the calibration procedure are those found from the material testing.”

And later these are shown in Table 3:

Table 3. Elastic (E) and shear (G) moduli in GPa for each test phase of the building’s structural members.

Member	Modulus	initial	Phase 1	Phase 2	Phase 3	Phase 4
East wall	E	2.55	1.81	1.38	0.99	0.88
	G	0.84	0.35	0.26	0.16	0.10
West wall	E	2.55	2.39	2.35	2.31	2.04
	G	0.84	0.62	0.59	0.57	0.48
OOP walls	E	2.55	2.52	2.07	1.99	1.97
Diaphragm	G	0.35	0.35	0.23	0.16	0.14

 

References

1. Croce, P.; Beconcini, M.L.; Formichi, P.; Cioni, P.; Landi, F.; Mochi, C.; De Lellis, F.; Mariotti, E.; Serra, I. Shear Modulus of Masonry Walls: A Critical Review. In Proceedings of the Procedia Structural Integrity; Elsevier B.V., January 1 2018; Vol. 11, pp. 339–346.
2. Valentin Wilding Michele Godio Katrin Beyer, B. The Ratio of Shear to Elastic Modulus of In-Plane Loaded Masonry., doi:10.1617/s11527-020-01464-1.
3. Kržan, M.; Bosiljkov, V. International Journal of Architectural Heritage Conservation, Analysis, and Restoration ISSN: (Print) ( In-Plane Seismic Behaviour of Ashlar Three-Leaf Stone Masonry Walls: Verifying Performance Limits In-Plane Seismic Behaviour of Ashlar Three-Leaf Stone Masonry Walls: Verifying Performance Limits. 2021, doi:10.1080/15583058.2021.1963504.
4. Cluni, F.; Gusella, V. Homogenization of Non-Periodic Masonry Structures. Int. J. Solids Struct. 2004, 41, 1911–1923, doi:10.1016/J.IJSOLSTR.2003.11.011.
5. Tiberti, S.; Milani, G. 3D Homogenized Limit Analysis of Non-Periodic Multi-Leaf Masonry Walls. Comput. Struct. 2020, 234, 106253, doi:10.1016/j.compstruc.2020.106253.

 

 

 

 

Author Response File: Author Response.pdf

Reviewer 2 Report

 

The paper examines the degradation of a masonry structure due to repeated earthquakes with increasing PGA from experimental tests. The experimental data are used to calibrate a reduced-order FE model, obtained from the first-order approximation of the governing equations, and derive the degradation of Young’s moduli.

The reviewer has the following major concerns which must be properly addressed before publication:

• The reviewer does not understand the identification algorithm. “Hankel matrix from the test data [22]. The realization of the system matrices A, B and C is carried out by the singular value decomposition [23] of the estimated Hankel matrices at instants k = 1 and 2”. How can the authors identify the dynamic equation from just two-time instants when having an entire-time history? It means that the authors are doing the procedure for all time instants and estimate the instant mode shapes and natural frequencies? However, the authors do not mention either instantaneous or stationary modal parameters. They only refer to the transfer function. The transfer function refers to the entire time history. Therefore, two aspects are dubious. The dynamic equation A is time-variant since the structure degrades. Thus estimating a single transfer function from an entire time history might be inaccurate. The authors should estimate instantaneous modal parameters. See the following reference:

 

https://link.springer.com/article/10.1007/s11803-015-0022-5

 

Additionally, how can the authors estimate the transfer function from two-time instants? Please clarify the identification procedure adequately by addressing the arisen weaknesses.

• The authors estimate a global Young’s modulus from each earthquake repetition, not instantaneous parameters, but a global one. Despite this can be questionable, not adequate discussion is given to this part. If the identification section is relatively traditional (transfer function), the authors should at least highlight the effect f repeated earthquakes on structural resilience. See the following references:

 

https://www.tandfonline.com/doi/full/10.1080/15732479.2022.2053551?casa_token=igonIDmR_IUAAAAA%3AeSw9T4nmypAKHpe-3HwczL0iJeey4MSV0wOr6uX1HxGayoyrVrcprmG5aw7ZlhOJTZueBa59xGs9eQ

 

 

 

• Is the first-order approximation adequate with such degradation of Young’s moduli? Please provide more evidence about the correctness of this assumption.
• The state-of-art on the dynamic response of URM buildings can be expanded by also considering paper comparing the operational and seismic response or papers dealing with a different identification of the structural parameters from the time histories:

https://www.tandfonline.com/doi/full/10.1080/15583058.2020.1802533?casa_token=bXVZ6SO1PU8AAAAA%3A--zy8G4veFyOabPrAvQvpm2EVumJrBzM_8KZCBxPsgIzgiDHCeGrPZIlq3pI522ZFhTh-Kc-FL7rlw

 

Author Response

Response to reviewer 2

 

We kindly thank the reviewer for her/his effort to improve our submitted manuscript. We believe that the clarifications and amendments in the revised version have substantially improved the original version.

Regarding the comments of the reviewer:

Comment 1

The reviewer does not understand the identification algorithm. “Hankel matrix from the test data [22]. The realization of the system matrices A, B and C is carried out by the singular value decomposition [23] of the estimated Hankel matrices at instants k = 1 and 2”. How can the authors identify the dynamic equation from just two-time instants when having an entire-time history? It means that the authors are doing the procedure for all time instants and estimate the instant mode shapes and natural frequencies? However, the authors do not mention either instantaneous or stationary modal parameters. They only refer to the transfer function. The transfer function refers to the entire time history. Therefore, two aspects are dubious. The dynamic equation A is time-variant since the structure degrades. Thus estimating a single transfer function from an entire time history might be inaccurate. The authors should estimate instantaneous modal parameters. See the following reference: https://link.springer.com/article/10.1007/s11803-015-0022-5

Response to comment 1

As stated in the manuscript, the estimation of the dynamic parameters is performed using the random vibration tests which follow the strong motion tests and whose signals are white noise. The response of the structure is elastic during these tests. Therefore, the identified parameters reflect the equivalent elastic properties of the cracked structural members.

The key point of the method relies on the fact that the system Markov parameters can be obtained directly from the impulse response {h(t)} forming the Hankel matrix from the random vibration test data [1]:

(1)

The realisation of the system matrices A, B and C is carried out by the singular value decomposition [2] of the Hankel and the shifted Hankel matrices for k = 1 and 2 respectively as follows:

(2)

Then, the hankel matrices are defined as [3]:

(3)

The left and right inverse of the previous matrices are:

(4)

Therefore, k is not time instance but the number of the Hankel matrix. The time instances of the random vibration test are denoted with letters p, r which form the matrix and usually are equal p = r. As random vibration test is stationary test of white noise there is no need to include the total duration. Given here that the sampling frequency is Fs = 240Hz, the Hankel matrix includes the response of 2000 instants, i.e. 8.33s.

As per reviewer comment the manuscript is now rephrased to clarify better the use of random vibration data and the meaning of k =1 and 2 in section 3 as follows:

“The first step of this method is to calculate the impulse response from the frequency response H(z) of the random vibration tests using the inverse Z-transform for the discrete system”.

And later:

“The realization of the system matrices A, B and C is carried out by the singular value decomposition [23] of the estimated Hankel and shifted Hankel matrices H(1) and H(2).”

The use of RV tests is also repeated at the beginning of section 4:

“Using the random vibration tests is possible to estimate the equivalent elastic properties of the building after the suffered damage (Figures 3 and 4) due to strong motion tests (sequence of tests presented in Figure 1).”

The reference has also been added to the revised manuscript.

 

Comment 2

Additionally, how can the authors estimate the transfer function from two-time instants? Please clarify the identification procedure adequately by addressing the arisen weaknesses.

Response to comment 2

Please see response to comment 1.

 

Comment 3

The authors estimate a global Young’s modulus from each earthquake repetition, not instantaneous parameters, but a global one. Despite this can be questionable, not adequate discussion is given to this part. If the identification section is relatively traditional (transfer function), the authors should at least highlight the effect f repeated earthquakes on structural resilience. See the following references:

https://www.tandfonline.com/doi/full/10.1080/15732479.2022.2053551?casa_token=igonIDmR_IUAAAAA%3AeSw9T4nmypAKHpe-3HwczL0iJeey4MSV0wOr6uX1HxGayoyrVrcprmG5aw7ZlhOJTZueBa59xGs9eQ

Response to comment 3

The equivalent elastic properties of masonry are separately estimated for each of the walls of the building. This is now better discussed in section 4.1:

“As aforementioned the basic assumption of the FE modelling is to assume an equivalent elastic response of masonry which remains a continuum and cracking is not directly simulated but indirectly taken into account by the modified mechanical properties in accordance with the smeared crack approach. The initial values for the calibration procedure are those found from the material testing.”

And later in the beginning of section 4.2:

“A linear elastic FE model is employed following the exact dimensions of the structure to study the evolution of the material properties due to cracking and damage. The model is elastic as it is calibrated with the elastic response of the stationary random vibrations. The building suffers damage which is accumulated in each test phase [28]. Therefore, the elastic properties identified from random vibration tests in each test phase reflect the secant modulus of masonry walls assuming a smeared crack equivalent elastic modulus. This approach simulates the propagation of cracks inside the body of masonry by modifying its elastic properties i.e. using 'softer' ones for a cracked wall.”

The reference has also been added to the revised manuscript.

 

Comment 4

Is the first-order approximation adequate with such degradation of Young’s moduli? Please provide more evidence about the correctness of this assumption.

Response to comment 4

SHM is widely applied using random vibration tests. The validation of the procedure is shown due to the accordance with observed damage. This is now more clearly commented in section 5.3:

“The degradation of the elastic modulus E₁ of West wall presents a regular shape due to the fact that the wall has a rather uniform distribution of cracks in all of its piers and spandrels (see Figures 3 and 4). On the contrary, the degradation of East wall is lower and has a sudden increase from the third to the fourth phase. This is in line with the diagonal cracks appearing in this wall at this phase (see Figures 3-4). The elastic modulus of North and South facades has a steeper increase of the degradation between the second to the third phases when the horizontal cracks are initially formed and subsequently propagated. Therefore, the analysis shows a very good coincidence with the actual damage of the structure.”

 

Comment 5

The state-of-art on the dynamic response of URM buildings can be expanded by also considering paper comparing the operational and seismic response or papers dealing with a different identification of the structural parameters from the time histories.

https://www.tandfonline.com/doi/full/10.1080/15583058.2020.1802533?casa_token=bXVZ6SO1PU8AAAAA%3A--zy8G4veFyOabPrAvQvpm2EVumJrBzM_8KZCBxPsgIzgiDHCeGrPZIlq3pI522ZFhTh-Kc-FL7rlw

Response to comment 5

A brief mention of SHM is now added in Introduction:

“Structural health monitoring (SHM) of masonry buildings is usually performed with ambient vibration measurements e.g. [4–7].”

The reference is now added to the revised manuscript.

 

References

1. Lenzen, A.; Waller, H. Damage Detection by System Identification. An Application of the Generalized Singular Value Decomposition. Arch. Appl. Mech. 1996, 66, 555–568, doi:10.1007/BF00808144.
2. Golub, G.H.; Reinsch, C. Singular Value Decomposition and Least Squares Solutions. Numer. Math. 1970, 14, 403–420, doi:10.1007/BF02163027.
3. Juang, J.-N.; Pappa, R.S. Effects of Noise on ERA-Identified Modal Parameters. J. Guid. Control. Dyn. 1986, 9, 294–303.
4. Aloisio, A.; Antonacci, E.; Fragiacomo, M.; Alaggio, R. The Recorded Seismic Response of the Santa Maria Di Collemaggio Basilica to Low-Intensity Earthquakes. Int. J. Archit. Herit. 2021, 15, 229–247, doi:10.1080/15583058.2020.1802533.
5. Lorenzoni, F.; Casarin, F.; Caldon, M.; Islami, K.; Modena, C. Uncertainty Quantification in Structural Health Monitoring: Applications on Cultural Heritage Buildings. Mech. Syst. Signal Process. 2016, 66–67, doi:10.1016/j.ymssp.2015.04.032.
6. Kouris, L.A.S.L.; Penna, A.; Magenes, G. Damage detection of an unreinforced stone masonry two storeys building based on damping estimate. In Brick and Block Masonry; CRC Press, 2016; pp. 2425–2432 ISBN 978-1-138-02999-6.
7. Chrysostomou, C.Z.; Kyriakides, N.; Kappos, A.J.; Kouris, L.; Georgiou, E.; Millis, M. Seismic Retrofitting and Health Monitoring of School Buildings of Cyprus. Open Constr. Build. Technol. J. 2013, 7, 208–220, doi:10.2174/1874836801307010208.

 

Author Response File: Author Response.pdf

Reviewer 3 Report

The topic of the paper is the calibration of the numerical model based on the results of the tests carried out on the experimental model.

The authors chose the parameters of the structure, which they calibrated with regard to the measurements of their eigen frequency of vibration in each loading stage.

This topic is very actual and interesting for engineering practice and scientists. The paper is well structured, and the authors have clearly emphasized assumptions and conclusions of the study. The paper is supplemented by quality graphics.

According to the reviewer, this paper is of high quality and contains a lot of material and results that are useful in further analysis of similar problems.

However, I have one question for authors. If they could additionally explain Figure 8 in the results of degradation of mechanical parameters. As expected, the western wall experienced the greatest degradation. However, it is to be expected that the southern wall will remain a relatively rigid zone and that the center of rigidity of the building will change and move towards it, while the northern wall will degrade more. Is it possible to show the forms of vibration in certain stages of the measurement?

Author Response

Response to reviewer 3

We thank the reviewer for his efforts to improve the submitted manuscript as well as for his kind words.

Regarding the comments of the reviewer:

Comment 1

However, I have one question for authors. If they could additionally explain Figure 8 in the results of degradation of mechanical parameters. As expected, the western wall experienced the greatest degradation. However, it is to be expected that the southern wall will remain a relatively rigid zone and that the center of rigidity of the building will change and move towards it, while the northern wall will degrade more. Is it possible to show the forms of vibration in certain stages of the measurement?

Response to comment 1

The walls perpendicular to the excitation were assumed to sustain similar levels of cracking in the parametric analysis. This assumption is based on the observed damage where in North and South walls the out-of-plane gable wall mechanism is activated (see Figure 4). Therefore, a single cracking parameter was introduced for both. Due to the assumption of one single parameter for both walls (parameter P5 in Table 1) the centre of rigidity will not vary in the analytical model although in reality small changes can appear. This is now stated in section 4.2 as follows:

“North and South walls presented a similar damage mechanism involving the gable roof and therefore, have the same parameters P₅.”

Author Response File: Author Response.pdf

Reviewer 4 Report

A two-storey unreinforced stone masonry prototype was subjected to one-dimensional shaking tests. Each wall differs from the other ones having different openings. As was expected the developed damage in each wall depend on the robustness of each one as well as the direction of the excitation. Then, in a finite element model, the authors using a very complex process transformed the mechanical characteristics of each wall to coincide with the grade of damage observed. For comparison, they should kept the same properties for the four walls and applied the same process.  

In fig. 1 the PGA 0.629g is not seen as the maximum value of the vertical axis is 0.5g

The dimensions of the prototype are omitted. The location of accelerometers in elevation is not mentioned as well as the north in Fig. 2

In the paper, there are a lot of equations without an explanation of their symbols e.g equations 1, 2, 5, 7 etc.  

No explanation for choosing both the out-of-plane and the vertical Elastic moduli equal to  80% of the in-plane one is given as well as why the same G was used. Why the G only for the north and south walls depends on E1 ?

An answer is requested why they modeled the walls with solid elements with 3 DOFs neglecting the rotations instead of 5- or 6- DOFs shell elements.

The parameters of Table 2 must be explained even they are self-explanatory.

The process of paragraph 4.4 has a lot of factors not explained.

In the conclusions, the authors should mention how the results of such a complex process may be used and applied in real structures.

Author Response

Response to reviewer 4

We kindly thank the reviewer for his effort to improve our submitted manuscript. We believe that the clarifications and amendments in the revised version have substantially improved the original version. The revised parts of the manuscript related to the comments of the reviewer are cited in blue italics font.

Regarding the comments of the reviewer:

Comment 1

For comparison, they should kept the same properties for the four walls and applied the same process. 

Response to comment 1

The observed damage varies significantly among the walls of the structure. The calibration process is very demanding and a comparison with the same mechanical properties for all the walls would most probably result in an endless iterative loop without convergence.

 

Comment 2

In fig. 1 the PGA 0.629g is not seen as the maximum value of the vertical axis is 0.5g

Response to comment 2

Fig. 1 is now revised to better visualize the ground motion.

Figure 1. Sequence of 5 seismic inputs (strong motion SM and random vibration RV) of the scaled 1979 Montenegro earthquake.

 

Comment 3

The dimensions of the prototype are omitted. The location of accelerometers in elevation is not mentioned as well as the north in Fig. 2

Response to comment 3

Accelerometers were placed only at the floor and roof levels. Details regarding the test set-up and procedure have been published in the cited report, see section 2:

“The details of the experiment can be found in [1].”

Accelerometers were placed only at the level of the floor and the roof. For the sake of the completeness the dimensions are now added in Fig. 2 and 3.

Comment 4

In the paper, there are a lot of equations without an explanation of their symbols e.g equations 1, 2, 5, 7 etc. 

Response to comment 4

We carefully revised the manuscript and any symbol, superscript or subscript in the equations is now clarified.

 

Comment 5

No explanation for choosing both the out-of-plane and the vertical Elastic moduli equal to  80% of the in-plane one is given as well as why the same G was used. Why the G only for the north and south walls depends on E1 ?

Response to comment 5

The ratio of the elastic moduli of masonry in the out-of-plane direction E₂ and the horizontal one E₃, as there was performed no testing, are assumed proportional to the 80% of the vertical direction E₁ based on standard values from the literature [2–5].

The shear moduli G_i is assumed equal to all the three directions as this was estimated from diagonal compression tests and there was performed no testing for the out-of-plane one.

North and South walls presented a similar damage mechanism involving the gable roof and therefore, have the same parameters P₅. As the damage of North and South walls is out-of-plane the shear modulus is assumed to remain constant (i.e. G/E = 0.33).

These are now clarified in section 4.2:

“Elastic moduli of masonry in the out-of-plane direction E₂ and the horizontal one E₃, as there was performed no testing, are assumed proportional to the 80% of the vertical direction E₁ based on standard values from the literature [2–5]. The calibration parameters are presented in Table 1. North and South walls presented a similar damage mechanism involving the gable roof and therefore, have the same parameters P₅. As the damage of North and South walls is out-of-plane the shear modulus is assumed to remain constant (i.e. G/E = 0.33).”

 

Comment 6

An answer is requested why they modeled the walls with solid elements with 3 DOFs neglecting the rotations instead of 5- or 6- DOFs shell elements.

Response to comment 6

The connection of the timber floor and roof to the URM walls can be better modelled when the walls are simulated with solid elements. This is now stated in section 4.2:

“Shell elements with rotational DOF’s could be used alternatively but they can simulate the connections with timber less accurately.”

 

Comment 7

The parameters of Table 2 must be explained even they are self-explanatory.

Response to comment 7

Amended.

 

Comment 8

The process of paragraph 4.4 has a lot of factors not explained.

Response to comment 8

Amended.

Comment 9

In the conclusions, the authors should mention how the results of such a complex process may be used and applied in real structures.

Response to comment 9

The main outcome of the present study is the evolution of the G/E ratio for stone masonry on a real structure as well as the procedure itself. Full-scale experiments can not be replicated to estimate average values etc. but have a tremendous value as they imitate the real conditions much better than micro and meso-scale tests.

This is now better expressed in the Abstract:

“It is shown that the deterioration is more intense for the shear moduli of the walls rather than the elastic modulus. The ratio of the in-plane shear to the elastic modulus decreases substantially.”

In the Introduction section:

“The scope of this study is to investigate the evolution of the material properties of the structure applying a dynamic analysis of the stationary response by an iterative optimisation process.”

And in the Conclusions section:

“Shear modulus appears to decrease more than the elastic modulus of the respective walls. West wall which is uniformly damaged has a regular curve with increasing shaking intensity. East wall instead has steep drops for some phases. The shear modulus of the timber diaphragm deteriorates from phase to phase. The shear to elastic moduli ratios drop to as low values as 10% for the more damaged wall.”

 

References

1. Magenes, Guido; Penna, A.; Rota, Maria; Galasco, Alessandro; Senaldi, I. Verifica Numerico-Sperimentale Delle Indicazioni Relative Ad Edifici Esistenti in Muratura Presenti Nell’Ordinanza PCM 3274 Del 20/03/2003 e s.m.I.; Pavia, 2010;
2. Kouris, L.A.S.; Bournas, D.A.; Akintayo, O.T.; Konstantinidis, A.A.; Aifantis, E.C. A Gradient Elastic Homogenisation Model for Brick Masonry. Eng. Struct. 2020, 208, 110311, doi:10.1016/j.engstruct.2020.110311.
3. Di Nino, S.; Zulli, D. Homogenization of Ancient Masonry Buildings: A Case Study. Appl. Sci. 2020, 10, 6687, doi:10.3390/app10196687.
4. Cluni, F.; Gusella, V. Homogenization of Non-Periodic Masonry Structures. Int. J. Solids Struct. 2004, 41, 1911–1923, doi:10.1016/J.IJSOLSTR.2003.11.011.
5. Valentin Wilding Michele Godio Katrin Beyer, B. The Ratio of Shear to Elastic Modulus of In-Plane Loaded Masonry., doi:10.1617/s11527-020-01464-1.

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Most of my comments and concerns have been clarified by the Authors. 

As a side comment, this Reviewer thinks that the number of self citation in the manuscript is very high.

This said, the manuscript can be published in its present form.

 

Author Response

Self-citations were included in the previous version to address the reviewers’ comments. In this version, those were limited to the very necessary ones. Thus, previous self-citations numbered [20,29,34,42,43] are now excluded.

Reviewer 2 Report

The authors adequately addressed all the reviewer concerns. The paper can be recommended for publication.

Author Response

We thank the reviewer.

Reviewer 4 Report

1)      The authors must add the north direction  in fig. 2

2)     When describing the response of each wall they should add, maybe in parentheses,  if the wall under consideration is parallel or transverse  to the seismic excitation

Author Response

Comment 1

The authors must add the north direction  in fig. 2

 

Response to comment 1

Figure 2 is now revised to include north direction and renumbered as 1. Moreover, Figure 3 is now revised as the dimensions were included in the revised Figure 1.

 

Comment 2

When describing the response of each wall they should add, maybe in parentheses,  if the wall under consideration is parallel or transverse  to the seismic excitation.

Response to comment 2

Fig. 2 is now revised to include the direction of the seismic excitation. Moreover, a hint of the location of each wall with respect to the load (parallel or transverse) is now added in sections 2 and 5.3.