Abstract
Despite the various studies carried out to evaluate the effects of seismic sequences on structures, the matter of the time gap required to be considered between the mainshock and its corresponding aftershocks in dynamic analyses has never been focused on directly. This subtle but in the meantime effective subject, influences the amount of accumulated damage caused by earthquake sequences. In the present study, 244 near fault ground motion components from 122 earthquakes were applied to a wide variety of single degree of freedom systems having vibrating period of 0.05–7 seconds with linear and nonlinear behavior. Furthermore, 2 planar steel moment-resisting frames, having 3 and 12 stories, were subjected to a set of 30 ground motion components. The purpose of this investigation was to estimate the required time for the structures to cease the free vibration at the end of the mainshock. The main purpose is to generate an estimation that is function of structural system’s parameters and the strong motion duration. Excellent correlations were obtained between the rest time and the following parameters: the combination of natural period of single degree of freedom systems, as well as the strong motion duration of earthquake sequences. In consequence, a formula is proposed which estimates the optimized required rest-time of a structure based on natural vibration period, as well as the duration of strong motion. Additionally, results obtained from the dynamic analysis of the steel frames validate the rest-time values achieved by the proposed formula.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Availability of data and materials
Data and material are available.
Code availability
The developed codes are available.
References
Amadio C, Fragiacomo M, Rajgelj S (2003) The effects of repeated earthquake ground motions on the non-linear response of SDOF systems. Earthq Eng Struct Dyn 32:291–308. https://doi.org/10.1002/eqe.225
Chopra AK (2006) Dynamics of structures. Theory and applications to, 3rd edn. Prentice Hall Inc., Upper Saddle River
Clough RW, Penzien J (1995) Dynamics of structures, 3rd edn. Computers & Structures Inc, Berkeley
Deierlein G, Baker J, Chandramohan R, Foschaar J (2012) Effect of long duration ground motions on structural performance. PEER Annual Meeting
Far H (2017) Advanced computation methods for soil-structure interaction analysis of structures resting on soft soils. Int J Geotech Eng 13:352–359. https://doi.org/10.1080/19386362.2017.1354510
Gallagher PR, Reasenberg AP, Poland DC (1996) The ATC TechBrief 2, earthquake aftershocks—entering damaged buildings
Goda K (2012a) Peak ductility demand of mainshock-aftershock sequences for Japanese earthquakes. In: Proceedings of the fifteenth world conference on earthquake engineering, Lisbon, Portugal
Goda K (2012) Nonlinear response potential of Mainshock-Aftershock sequences from Japanese earthquakes. Bull Seismol Soc Am 102:2139–2156. https://doi.org/10.1785/0120110329
Goda K (2015) Record selection for aftershock incremental dynamic analysis. Earthq Eng Struct Dyn 44:1157–1162. https://doi.org/10.1002/eqe.2513
Han R, Li Y, van de Lindt J (2015) Assessment of seismic performance of buildings with incorporation of aftershocks. J Perform Constr Facil 29:04014088. https://doi.org/10.1061/(ASCE)CF.1943-5509.0000596
Hansen PC, Pereyra V, Scherer G (2013) Least squares data fitting with applications. JHU Press
Hatzigeorgiou GD (2010) Behavior factors for nonlinear structures subjected to multiple near-fault earthquakes. Comput Struct 88:309–321. https://doi.org/10.1016/j.compstruc.2009.11.006
Hatzigeorgiou GD (2010) Ductility demand spectra for multiple near- and far-fault earthquakes. Soil Dyn Earthq Eng 30:170–183. https://doi.org/10.1016/j.soildyn.2009.10.003
Hatzigeorgiou GD, Beskos DE (2009) Inelastic displacement ratios for SDOF structures subjected to repeated earthquakes. Eng Struct 31:2744–2755. https://doi.org/10.1016/j.engstruct.2009.07.002
Hatzigeorgiou GD, Liolios AA (2010) Nonlinear behaviour of RC frames under repeated strong ground motions. Soil Dyn Earthq Eng 30:1010–1025. https://doi.org/10.1016/j.soildyn.2010.04.013
Hosseini SA, Ruiz-García J, Massumi A (2019) Seismic response of RC frames under far-field mainshock and near-fault aftershock sequences. Struct Eng Mech 72:395–408. https://doi.org/10.12989/sem.2019.72.3.395
Hoveidae N, Radpour S (2020) Performance evaluation of buckling-restrained braced frames under repeated earthquakes. Bull Earthq Eng. https://doi.org/10.1007/s10518-020-00983-0
Huang W, Qian J, Fu Q (2012) Damage assessment of RC frame structures under mainshockaftershock seismic sequences. In: Proceedings of the 15th World Conference on Earthquake Engineering (15WCEE), Portugal, Lisbon
Li Q, Ellingwood BR (2007) Performance evaluation and damage assessment of steel frame buildings under main shock-aftershock earthquake sequences. Earthq Eng Struct Dyn 36:405–427. https://doi.org/10.1002/eqe.667
Massumi A, Monavari B (2013) Energy based procedure to obtain target displacement of reinforced concrete structures. Struct Eng Mech 48:681–695. https://doi.org/10.12989/sem.2013.48.5.681
Mirtaherf M, Amini M, Rad MD (2017) The effect of mainshock-aftershock on the residual displacement of buildings equipped with cylindrical frictional damper. Earthq Struct 12:515–527. https://doi.org/10.12989/eas.2017.12.5.515
Moustafa A, Takewaki I (2011) Response of nonlinear single-degree-of-freedom structures to random acceleration sequences. Eng Struct 33:1251–1258. https://doi.org/10.1016/j.engstruct.2011.01.002
Papaloizou L, Polycarpou P, Komodromos P et al (2016) Two-dimensional numerical investigation of the effects of multiple sequential earthquake excitations on ancient multidrum columns. Earthq Struct 10:495–521. https://doi.org/10.12989/eas.2016.10.3.495
Pu W, Wu M (2018) Ductility demands and residual displacements of pinching hysteretic timber structures subjected to seismic sequences. Soil Dyn Earthq Eng 114:392–403. https://doi.org/10.1016/j.soildyn.2018.07.037
Ruiz-García J, Negrete-Manriquez JC (2011) Evaluation of drift demands in existing steel frames under as-recorded far-field and near-fault mainshock-aftershock seismic sequences. Eng Struct 33:621–634. https://doi.org/10.1016/j.engstruct.2010.11.021
Samimifar M, Massumi A, Moghadam AS (2019) A new practical equivalent linear model for estimating seismic hysteretic energy demand of bilinear systems. Struct Eng Mech 70:289–301. https://doi.org/10.12989/sem.2019.70.3.289
Tabatabaiefar S, Fatahi B, Samali B (2012) Finite difference modelling of soil–structure interaction for seismic design of moment resisting building frames
Xie, Junju, Wen, Zenping, Li X (2012) Characteristics of strong motion duration from the Wenchuan Mw 7.9 earthquake. In: 15th World Conference on Earthquake Engineering. Lisboa, p 10
Xie X, Lin G, Duan YF et al (2012) Seismic damage of long span steel tower suspension bridge considering strong aftershocks. Earthq Struct 3:767–781. https://doi.org/10.12989/eas.2012.3.5.767
Zhai CH, Wen WP, Chen ZQ et al (2013) Damage spectra for the mainshock-aftershock sequence-type ground motions. Soil Dyn Earthq Eng 45:1–12. https://doi.org/10.1016/j.soildyn.2012.10.001
Zhai CH, Wen WP, Li S et al (2014) The damage investigation of inelastic SDOF structure under the mainshock-aftershock sequence-type ground motions. Soil Dyn Earthq Eng 59:30–41. https://doi.org/10.1016/j.soildyn.2014.01.003
Zhang Y, Shen J, Chen J (2020) Damage-based yield point spectra for sequence-type ground motions. Bull Earthq Eng 18:4705–4724. https://doi.org/10.1007/s10518-020-00874-4
Zhu TJ, Tso WK, Heidebrecht AC (1988) Effect of peak ground a/v ratio on structural damage. J Struct Eng 114:1019–1037. https://doi.org/10.1061/(ASCE)0733-9445(1988)114:5(1019)
(2016) Seismic provisions for structural steel buildings. American Institute of Steel Construction (AISC), Chicago
(2017) Minimum design loads and associated criteria for buildings and other structures. ASCE Standard. American Society of Civil Engineers, Reston
(2000) FEMA 356—prestandard and commentary for the seismic rehabilitation of buildings. American Society of Civil Engineers (ASCE), Washington
Funding
This research was supported by the Kharazmi University Grant. The authors would like to thank the Kharazmi University.
Author information
Authors and Affiliations
Contributions
Conceptualization: [RMP, SH, AM]; Formal Analysis: [RMP, SH]; Methodology: [RMP, SH, AM]; Validation: [AM]; Writing – original draft: [SH]; Writing – review & editing: [AM].
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Clinical Trials Registration
Not applicable.
Ethical statements
The developed method is the original effort of the authors which is not submitted or published elsewhere.
Gels and blots/image manipulation
Not applicable.
High risk content
Not applicable.
Plant reproducibility
Not applicable.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Pirooz, R.M., Habashi, S. & Massumi, A. Required time gap between mainshock and aftershock for dynamic analysis of structures. Bull Earthquake Eng 19, 2643–2670 (2021). https://doi.org/10.1007/s10518-021-01087-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10518-021-01087-z