Mainshock-Integrated Aftershock Vulnerability Assessment of Bridge Structures
Round 1
Reviewer 1 Report
Minor editing errors appear in the manuscript.
Description of figure 1 is unnecessarily duplicated (above and below the figure).
Figure 2 shows the sections of the bridge rather than views.
The model shown in the manuscript has been tested for one type of construction only. The described model has not been verified experimentally. Conclusions are based only on theoretical assumptions (numerical analysis).
The manuscript could be significantly improved if at least model tests were performed. The best verification of the proposed model would be to compare the numerical simulations with the monitoring results on the real bridge structure.
Author Response
Review 1
Thanks much Reivewer 1 for his/her constructive suggesitons. We have addressed the comments; and in the meantime, all changes are tracked in the resubmitted version (with color fonts).
- Minor editing errors appear in the manuscript. Description of figure 1 is unnecessarily duplicated (above and below the figure). Figure 2 shows the sections of the bridge rather than views.
Response:
We deleted the description (Line 16 to 27 in the original manuscript) for Figure 1 in the revised manuscript.
Figure. 2 shows the geometric model of bridge and nonlinear springs are used to simulate the soil around the pile foundation.
2. The model shown in the manuscript has been tested for one type of construction only. The described model has not been verified experimentally. Conclusions are based only on theoretical assumptions (numerical analysis).
Response: Thanks so much. To address this, we added the following in the discussion Section in the revised manuscript.
“… It is noted that the proposed modeling framework embraces sufficient flexibility, which adaptably incorporates any mainshock by parametric quadratic polynomials). Nonetheless, for future research, it is suggested that the proposed fragility model be applied for different types of real bridges or civil structures to check the applicability and validity of the model. ”
(Section Discussion, Line: 404-406)
3. The manuscript could be significantly improved if at least model tests were performed. The best verification of the proposed model would be to compare the numerical simulations with the monitoring results on the real bridge structure.
Response: Thanks much for this suggestion. It is meaningful to verify the model with the monitoring data from real bridge structure; however, such data to this date is rare (or does not exist) that include mainshock and aftershock sequences and structural responses due to them. One more possible way is to conduct lab based experiments, e.g., shake-table testing, in which multiple mainshock-aftershock sequences with variabilityies are included and structural responses including damage are recorded. For this issue, the following was added in the revised manuscript.
“… If possible, shake-table testing may be conducted in which mainshock-aftershock sequences with variable intensities are included, and different degrees of damage can be recorded. With these data, the proposed method can be further adjusted and validated. ”
(Section Discussion, Line: 404-407)
Reviewer 2 Report
In this work, the fragility functions for collapse of a pile supported bridge structures under mainshock – aftershocks sequences is proposed. The proposed method can use this model for other damage states. The probability of collapse in this work has an initial value, which increases with the mainshock intensity and have great correlation with the properties of the structure. Displacement ductility is used to judge the damage states. In the proposed method called mainshock-integrated aftershock fragility function model fits the fragility curves well in this circumstance by adding a parameter γm, which is a function of mainshock. The numerical simulations show that mainshock – aftershocks sequences have great influence on the probability of collapse of the bridges.
The paper addresses a topic posing numerical challenges and having practical significance. It is methodologically correct. The paper is suitable for publication.
However, some comments of authors to the questions below should be addressed
In the numerical example what are the estimated values of polynomial constants p1 to p9 ?
The nonlinear dynamic analysis was performed for tow earthquake excitations sequences (one mainshock and one aftershock) or more earthquake excitations sequences (one mainshock and two or three aftershocks)?
The literature review in introduction is thorough and it is very well written, however some additional references listing below regarding the behavior of structures under earthquake sequences, developed method for fragilities curve and some control scheme to avoid collapse for earthquake sequences that can be applied in breidges could be added in the introduction.
- Foteini Konstandakopoulou, Maria Konstantinidou, Nikos Pnevmatikos, George D Hatzigeorgiou, (2020), Safety and Performance of Offshore Platforms Subjected to Repeated Earthquakes, Infrastructures 5 (4), 38.
- Nikos Pnevmatikos, George Thomos, (2014), Stochastic structural control under earthquake excitations, Structural Control and Health Monitoring 21 (4), 620-633.
Author Response
In this work, the fragility functions for collapse of a pile supported bridge structures under mainshock – aftershocks sequences is proposed. The proposed method can use this model for other damage states. The probability of collapse in this work has an initial value, which increases with the mainshock intensity and have great correlation with the properties of the structure. Displacement ductility is used to judge the damage states. In the proposed method called mainshock-integrated aftershock fragility function model fits the fragility curves well in this circumstance by adding a parameter γm, which is a function of mainshock. The numerical simulations show that mainshock – aftershocks sequences have great influence on the probability of collapse of the bridges.
The paper addresses a topic posing numerical challenges and having practical significance. It is methodologically correct. The paper is suitable for publication. However, some comments of authors to the questions below should be addressed.
Response: Thanks so much for your time. We have thoroughly addressed your comments; in the meantime, we attached a revised version with color fonts that track all the changes.
- In the numerical example what are the estimated values of polynomial constants p1 to p9 ?
Response: p1 to p9, are the polynomial constants of μm , σm, and γm.
“where p1, p2, …, and p9 are the polynomial constants estimated by the least-squares method for the computation of μm , σm, and γm at different mainshock intensities.” (Section 3.1, Line: 196-197). Further to make it clear, in Fig. 7, we updated the caption to inform that each figure (Fig 7a-c) numerically fits the data and estimate the values of p1, p2, …, and p9.
2. The nonlinear dynamic analysis was performed for two earthquake excitations sequences (one mainshock and one aftershock) or more earthquake excitations sequences (one mainshock and two or three aftershocks)?
Response: In reality, many aftershocks can follow after a mainshock. To clarify this, the following was added in the revised manuscript in the discussion section.
“It was worth mentioning that many aftershocks may follow a mainshock in reality. It is possible that more than one aftershocks are considered; however, this would further complicate the potential scaling relation between the mainshock and its aftershocks. For simplicity, the primary aftershock (that is the largest in its magnitude) was used with the mainshock to form the seismic sequences.” (Section Discussion, Line: 414-415)
3. The literature review in introduction is thorough and it is very well written, however some additional references listing below regarding the behavior of structures under earthquake sequences, developed method for fragilities curve and some control scheme to avoid collapse for earthquake sequences that can be applied in breidges could be added in the introduction.
[1] Foteini Konstandakopoulou, Maria Konstantinidou, Nikos Pnevmatikos, George D Hatzigeorgiou, (2020), Safety and Performance of Offshore Platforms Subjected to Repeated Earthquakes, Infrastructures 5 (4), 38.
[2] Nikos Pnevmatikos, George Thomos, (2014), Stochastic structural control under earthquake excitations, Structural Control and Health Monitoring 21 (4), 620-633.
Response: Thanks much for the suggesiton. In the revised manuscript, the two refs. were added as following:
“Konstandakopoulou et al. studied the behavior of offshore platforms under seismic sequences and pointed out that M-A sequences cause to noteworthy cumulative damage to platforms [10].”
(Section Introduction, Line: 42-44)
“Due to that the basic characteristic of a structure may be changed when they suffered from earthquake sequences or other hazards in their lifetime, Pnevmatikos and Thomos proposed a stochastic structural control method for structures under earthquake excitations [25].”
(Section Introduction, Line: 81-83)
