On the Modeling and Analysis of Brittle Failure in Existing R/C Structures Due to Seismic Loads

Reviewer’s Detailed Comments

Authors’ Reply

1.            Two words, “Modelling” and “Modeling: are mixed in the title and text. I think it is better to unify the words.

The word “Modelling” has been changed to “Modeling” throughout the text.

2.            In section 2, the authors defied the substandard RC buildings by specifying the dimensions of columns (e.g. 250mm to 500mm) or other structural members to suggest the scope of application for the developed modeling method. However, the cross-section of the full-scale specimen was 250mm x 750mm, which was somewhat larger than the dimension of the column specified in section 2. Please respond whether the full-scale specimen can represent the substandard RC buildings. Additionally, are all columns the same cross-section?

As discussed in Section 1, typical column section sizes of substandard R/C buildings range between 250 mm and 500 mm. However, the characterization of an existing R/C building as substandard is based not only on the size of the column cross section, but on a number of parameters, such as type of longitudinal reinforcement and stirrups (smooth or ribbed), concrete and steel grade, the combination of dissimilar beam and column cross section dimensions comprising the structural skeleton (strong beam – weak column combination, as in the case of the SPEAR building), unfavorable column arrangement producing torsional effects, etc. To this end, column of section sizes different than those described in Section 1 of the article can still belong to the structural system of substandard R/C buildings.

The SPEAR building was designed and constructed as representative sample of substandard buildings that were built in Southern Europe between 1954 and 1995 and according to the design practice and materials used in the same region in the early 70’s. As described in section 3.1 (lines 308-311), all columns of the SPEAR building had a 250 mm x 250 mm cross section dimension, except of column C2, whose section dimensions were 250 mm x 750 mm, simulating unfavorable column arrangement that causes torsional effect.

3.            Figure 6, please add the unit.

The units of the plan dimension in Fig. 6 were added to the caption.

4.            Line 453-465, the authors stated that “the overestimation of flexural stiffness leads to very low estimates of displacements”. In reviewer’s opinion, as the authors mentioned in Line 458-460, it is important to determine the upper bound and lower bound of seismic demand according to the presence or absence of the zero length elements, and to make a decision about the retrofit schemes based on the boundaries. Moreover, the term “overestimation” generally has a negative connotation, and scientific evidence or basis is needed to determine how much seismic demand should be evaluated to be overestimation than it actually is.

The discussion regarding the comparison between the analyses and the test results was modified according to the Reviewer's comment and the sentence containing the term “overestimation” has been rephrased.

5.            Table 5. For the s10 case, please check the results between FE Model-All Mechanism and FE Model-Flexure only since the results of the two FE models were identical. And, for the s11 and s12 cases, why are the peak drifts in y-axis for the FE models so different from those of the specimen? In other words, is it evidence that the developed modeling does not implement well the failure mechanism occurring on the y-axis in the specimen? Please respond on this issue.

The results corresponding to the s10 case FE Model-Flexure were corrected.

The deviation in the convergence of the estimated responses of both FE building models with the responses recorded at the SPEAR building in the Y direction is mainly due to the degree of accuracy requested in simulating the flexural response of the columns through fiber discretization. A finer discretization of the core of the columns than the one used in the two FE building models (see Figure 2), combined with the use of more advanced stress-strain relationships available in the OpenSees library for simulating the inelastic response of steel and concrete materials, would most probably result in better convergence between the analytically and experimentally obtained responses. However, such a fine tuning of the flexural behavior of the FE building models would not have affected the degree of influence that the simulated brittle mechanisms of response along the column lines of the SPEAR building have in the overall seismic response of the FE building models.

6.            Conclusions. Structural classification is required for the substandard RC buildings covered in this study. Although the target buildings can be classified by construction year, the developed modeling is focused on the RC moment frame rather than RC shear wall system. In other words, the modeling method is not sufficient to cover all substandard RC buildings (e.g., how to modeling and analysis the RC shear wall system?).

True statement. A clarification pointing out that the proposed methodology refers to sub–standard R/C moment-resisting frames was added in the beginning of the Conclusions, in addition to the pre-existing clarification in Line 679 which states that guidelines for modeling all brittle localized strength mechanisms apply to frame members.

Reviewer’s Detailed Comments

Authors’ Reply

reinforced concrete (R/C)

This abbreviation is now explained in the Abstract and Applications paragraph.

I suggest to enlarge this part, by characterizing the references to be more informative.  In addition, I suggest to describe the possibility to account for brittle failures in post processing, as by checking the shear stress on modelled ductile models (some examples are provided for buildings pre-1980 in https://doi.org/10.1007/s10518-020-01033-5; https://doi.org/10.1007/s10518-019-00774-2).

These references were added as no. 28 & 29 and integrated in the article.

The description is clear, but the figure is not really clear. In addition, why did you add a central element in the zone where the stress is low?

Figure 1 simply illustrates the possible location of the different types of zero-length elements along a column line used in simulating different types of strength mechanisms. Specifically, the central element in the zone where the stress is low simulates the shear behavior of column web, which in R/C columns usually develops in the form of diagonal cracks of 30 to 45 degree inclination with respect to the column axis, and at mid-length of the clear column height.

How did you obtain this M-Theta law? Is it the result of a specific experimental campaign??

In most commercial FE programs, the response of zero-length elements is usually defined in terms of M-Theta laws. To this end, column shear strengths that are calculated according to the expressions of the RSA system, as presented in the Appendix, were converted in M-Theta format. This was done by considering previous experimental evidence on the response of substandard R/C columns subjected to lateral loading. For more information, please see “FIB Bulletin 24: Seismic Assessment and Retrofit of Reinforced Concrete Buildings, State-of-the Art Report prepared by Task Group 7.1, 771 Federation of Structural Concrete (FIB), Lausanne, Switzerland, 2003”. In addition, it is commonly accepted that column rotation at the state of yielding of their longitudinal reinforcement is in the range of 0.5%.

The numerical application is clear but some questions need to be answered:

1. what about numerical convergence of the system?

2. what about the time of analysis?

3. Could you express the results in terms of percentage differences between the experimental test and the numerical simulations? This can help the reader to better display the obtained results with the proposed approach.

The degree of numerical convergence and the required analysis time are completely dependent on the tolerance set by the user regarding the response of the different types of non-linear elements in the FE model. Generally speaking, no significant difference was observed in terms of convergence rate and time requirements by either simulating the brittle mechanisms of failure in FE building models according to the proposed methodology, or by simulating only the flexural response of the same buildings.

Comments regarding the degree of numerical convergence and the required analysis time as well as a more detailed discussion of the comparison between the experimentally and analytically obtained results were added in Section 3.3.