General comment to journal editor:
It is difficult to address the issues as the discussers did not number them. In order to make it clear what issue we are addressing, we have repeated and summarized some of the statements.
RESPONSE BELOW
---We first wish to thank the discussers for their interest in this paper and their comments which seek to further understanding regarding earthquake-induced pounding response. We are also happy that the discussers found the paper, describing the risk of greater demand in terms of increase in seismic displacement as a result of pounding, to be interesting.
The discussers’ comments fall into the following 3 categories.
(a) They introduce some related recently published studies that were not considered in the subject paper.
(b) They discuss of some of the works cited in the paper under discussion; and (c) They make some statements about contents of the subject paper
The authors believe that the introduction of recent references provided by the discussers [2-5] in (a) is useful for those with further interest in this topic. The authors are responding to comments related to items (b) and (c).
(b) The discussers state that the papers by Lin et al. [6,7] do not involve spectral analysis (as stated by the authors of the subject paper) while other papers by Lin et al. [8,9] do. The authors contest this point, but it does raise an interesting issue about the definition of “spectral analysis”. There currently does not seem to be an accepted definition within earthquake engineering but the words indicate multiple analyses of structures with different frequencies/periods. Presumably it could be ascribed to:
i) simple structures with one primary degree-of-freedom. This is accepted in the term “earthquake response spectra” (E.g. Newmark and Hall, 1982; Pal et al. 1987) and has been used in various spectral analysis studies (E.g. Rodgers et al, 2007; Rodgers et al, 2008; Rodgers et al, 2012).
ii) multidegree-of-freedom structures with the same number of degrees of freedom and same basic form, or
iii) multidegree-of-freedom structures of different types.
Furthermore, for interbuilding pounding studies, either one or both structures may be analysed with a range of frequencies/periods for spectral analysis.
In all Lin et al. references [6-7] multi-storey buildings were considered. A range of building periods, with a constant interval between the periods was used for at least one building (see Figures 7, 9, and 13 in reference 6, Figure 10 in reference 7, Figure 2 and 3 in reference 8 and Figure 4 in reference 9 of the discussion).
(i) The discussers seem to have trouble with the statement made by the authors of the subject paper that "there is a lack of a complete risk analysis that could be used to increase understanding of the risk for general cases and thus be used as a template to create guidelines". They also state that [2] and [6] proposed pounding risk estimates for general cases. In addition, they state that [4] proposes an approach for the performance-based design of the critical separation distance that can also be used for code calibration. Because of this, they assert, the statement by the authors of the subject paper is incorrect.
In response the authors of the subject paper want to emphasise the difference between “risk” and “probability”. Risk is related to the probability multiplied by the consequences. For such a risk consideration, the authors of the subject paper believe that a parameter associated most with adverse consequences should be used. In a complete risk analysis, costs as a result of direct damage, death/injury, and downtime could be considered. In general, the structural response parameter that is generally considered to relate to loss is drift/displacement, especially as it is possible to limit many acceleration-related losses by careful detailing. For this reason, it is believed that the current study, which computes directly the probability of various levels of displacement demand, is significantly closer to describing risk than previous studies. It should also be noted that while previous studies have considered the pounding probability, the pounding itself may be a poor estimator of risk since in some cases the impact decreases displacements of the critical structure.
(ii) The discussers state that the analysis procedure employed considered seismic intensities with only a fixed exceedance probability, rather than a complete hazard curve, and assumed the structural parameters as deterministic. Based on this, they conclude that the analysis procedure proposed does not represent a “complete risk analysis".
In response a number of points are made:
1) The authors chose to conduct a “scenario type” analysis, for a discrete level of shaking, rather than a full “probabilistic type” analysis (considering the hazard curve) for this design oriented paper. This is for engineering design practice, easy inclusion in design methods and codes, and easy verification around a straightforward criterion.
2) While loss estimation techniques are becoming popular, they are not appreciated by the vast majority of structural engineers who are not clear about the
assumptions that are made, the input values, and the methodology. This results in no trust in the output (MacRae et al. 2014). A study considering the hazard curve and more parameterised approaches was not conducted here because it relies on assumptions that are often difficult to verify and are less directly considered in design.
3) In the same way that performance based earthquake engineering (PBEE) is under development, rather than being fully realized (as evidenced by the large amount of ongoing research on this topic), so is the development of a “complete risk
analysis”. The authors of the subject paper never claimed to have fully achieved this and believe that the study undertaken is a major, or more complete, step in this direction than the previously available studies as stated. Furthermore, in the conclusions it is stated that more developments are required.
They then state that the main effect of inelastic building behavior when compared to the linear case is to promote in-phase motion of the two systems, as explicitly discussed in [10]. Furthermore, they argue that the statement that the inelastic building response reduces the pounding risk is not generally valid and provide an example supporting this.
In response, the authors thank the discussers for picking up this point about the reason for the decreased inelastic response. It is an obvious oversight by the authors. It is well known that inelastic response of structures is seldom less than the elastic response and is on average similar or greater than that of elastically responding structures, depending on the period. The yielding is likely to reduce the relative motion between the structures, rather than reducing the motion of individual structures as the discussers have described. Also, while the authors described the observations from their study alone, they believe that the case study by the discussers showing that inelastic response may not always reduce the response, has value. (iii) The discussers dispute the statement that the analysis methodology presented for peak displacements is readily transferrable and generalizable to accelerations.
In response the authors acknowledge that there are rapid changes in velocity, and hence accelerations at impact. However, the forces likely to be critical for structural design are related to the displacements which can be obtained via the accelerations computed using the method described.
Moreover, the full original quote stated “The analysis presented for peak displacements, Sd, is readily transferrable and generalizable to accelerations, Sa, or any similar acceleration metric of interest”. The statement was primarily about the method of analysis more than the specific results.
In closing, the authors wish to thank the discussers for their comments and opinions. They are pleased that their work, presented in a simple and verifiable format for design and considering displacements as the demand parameter, has caught their attention. They also welcome any further open discussion as an opportunity to improve understanding of published works and to receive feedback on opinions.
New references cited:
MacRae G. A., Chanchi J., and Yeow T., “What Structure is Best?”, Australian Structural Engineering Conference (ASEC), 9 July to Friday 11 July 2014, Auckland, PN:177. Newmark, N. M., and Hall, W. J. 1982. “Earthquake Spectra and Design,” Engineering
Monographs on Earthquake Criteria, Structural Design, and Strong Motion Records, Vol 3, Earthquake Engineering Research Institute, Oakland, CA.
Pal S., Dasaka S.S., Jain A.K., “Inelastic Response Spectra”, Computers & Structures, 25(3), 1987, pp 335–344.
Rodgers, GW, Chase, JG, Roland, T and MacRae, GA (2012). “Spectral analysis for a semi-active-passive net-zero base-shear design concept,” Earthquake Engineering & Structural Dynamics (EESD), Vol 41(8), pp. 1207–1216, ISSN: 0098-8847. DOI: 10.1002/eqe.1177 Rodgers, GW, Mander, JB, Chase, JG, Leach, NC, and Denmead, CS (2008). “Spectral
Analysis and Design Approach for High Force-to-Volume Extrusion Damper-based Structural Energy Dissipation,” Earthquake Engineering & Structural Dynamics (EESD), Vol 37(2), pp. 207-223, ISSN: 0098-8847.
References used by discussers:
[1] Chase JG, Boyer F, Rodgers GW, Labrosse G, MacRae GA. Probabilistic risk analysis of structural impact in seismic events for linear and nonlinear systems. EarthquakeEngineering and Structural Dynamics 2014; doi: 10.1002/eqe.2414.
[2] Tubaldi E, Barbato M, Ghazizadeh S. A probabilistic performance-based risk assessment approach for seismic pounding with efficient application to linear systems. Structural
Safety 2012; 36-37: 601-626.
[3] Tubaldi E, Freddi F, Barbato M. Probabilistic seismic demand analysis for pounding risk assessment. Proceedings of 11th International Conference on structural safety and
reliability (ICOSSAR2013), New York, USA, 16-20 June 2013.
[4] Barbato M, Tubaldi E. A probabilistic performance-based approach for mitigating the seismic pounding risk between adjacent buildings. Earthquake Engineering and Structural Dynamics 2013; 42(8): 1203-1219.
[5] Bradley BA. A comparison of intensity-based demand distributions and the seismic demand hazard for seismic performance assessment. Earthquake Engineering and Structural Dynamics 2013; 42(15): 2235–2253.
[6] Lin J-H, Weng C-C. Probability analysis of seismic pounding of adjacent buildings. Earthquake Engineering and Structural Dynamics 2001; 30(10): 1539-1557.
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[7] Lin J-H, Weng CC. A study on seismic pounding probability of buildings in Taipei metropolitan area. Chinese Institute of Engineers 2002; 25(2):123–135.
[8] Lin J-H. Separation distance to avoid seismic pounding of adjacent buildings. Earthquake Engineering and Structural Dynamics 1997; 26(3): 395-403.
[9] Lin J-H, Weng CC. Spectral analysis on pounding probability of adjacent buildings. Engineering Structures 2001; 23 (7): 768-778.
[10] Kasai K, Jagiasi RA, Jeng V. Inelastic vibration phase theory for seismic pounding. Journal of Structural Engineering 1996; 122(10): 1136-1146.
