Abstract
Analytical expressions are proposed for predicting the rocking response of rigid free-standing building contents subjected to seismic-induced floor excitations. The study considers a wide range of rigid block geometries and seismic floor acceleration histories that were recorded during actual earthquakes in instrumented Californian buildings, so as to cover, in a fully probabilistic manner, the entire spectrum of potential pure rocking responses, i.e. from the initiation of rocking up to the block overturning. Contrary to past observations on anchored building contents (prior to any failure in their anchorage system that could alter their response and mode of failure), it is shown that the response of free-standing blocks is not influenced by the predominant period of the supporting structure. The proposed set of equations can be utilised for estimating the response statistics and consequently for undertaking an analytical seismic fragility assessment on rocking building contents.
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Data availability
The datasets generated and analysed during the current study are available from the corresponding author on reasonable request.
References
Bachmann JA, Vassiliou MF, Stojadinović B (2017) Dynamics of rocking podium structures. Earthq Eng Struct Dynam 46:2499–2517. https://doi.org/10.1002/eqe.2915
Bachmann JA, Strand M, Vassiliou MF, Broccardo M, Stojadinović B (2018) Is rocking motion predictable? Earthquake Eng Struct Dynam 47(2):535–552. https://doi.org/10.1002/eqe.2978
Bakalis K, Vamvatsikos D (2018) Seismic fragility functions via nonlinear response history analysis. J Struct Eng (ASCE) 144(10):04018181. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002141
Baker JW, Cornell CA (2006) Which spectral acceleration are you using? Earthq Spectra 22(2):293–312. https://doi.org/10.1193/1.2191540
Benjamin JR, Cornell CA (1970) Probability, statistics, and decision for civil engineers. McGraw-Hill, New York
Calvi P, Sullivan TJ (2014) Estimating floor spectra in multiple degree of freedom systems. Earthq Struct 7(1):12–38. https://doi.org/10.12989/eas.2014.7.1.017
Ceh N, Jelenic G, Bicanic N (2018) Analysis of restitution in rocking of single rigid blocks. Acta Mech 229:4623–4642. https://doi.org/10.1007/s00707-018-2246-8
CESMD (Center for engineering strong motion data). Data for latest earthquakes: Available at http://www.strongmotioncenter.org. Accessed May 2018.
D’Angela D, Magliulo G, Cosenza E (2021) Seismic damage assessment of unanchored nonstructural components taking into account the building response. Struct Saf 93:102126. https://doi.org/10.1016/j.strusafe.2021.102126
Dar A, Konstantinidis D, El-Dakhakhni WW (2016) Evaluation of ASCE 43–05 seismic design criteria for rocking objects in nuclear facilities. J Struct Eng (ASCE) 142(11):04016110. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001581
Dimitrakopoulos EG, DeJong MJ (2012) Revisiting the rocking block: closed-form solutions and similarity laws. Proc Royal Soc A Math Phys Eng Sci 468(2144):2294–2318. https://doi.org/10.1098/rspa.2012.0026
Dimitrakopoulos EG, Paraskeva TS (2015) Dimensionless fragility curves for rocking response to near-fault excitations. Earthq Eng Struct Dynam 44(12):2015–2033. https://doi.org/10.1002/eqe.2571
FEMA (2012) Seismic performance assessment of buildings, applied technology council for the federal emergency management agency, Washington, DC, report no. FEMA P-58
FEMA (2000) FEMA 356-Prestandard and commentary for the seismic rehabilitation of buildings, federal emergency management agency
Filiatrault A, Sullivan T (2014) Performance-based seismic design of nonstructural building components: the next frontier of earthquake engineering. Earthq Eng Eng Vib 13(S1):17–46. https://doi.org/10.1007/s11803-014-0238-9
Fragiadakis M, Diamantopoulos S (2020) Fragility and risk assessment of freestanding building contents. Earthq Eng Struct Dynam 49(10):1028–1048. https://doi.org/10.1002/eqe.3276
Giouvanidis AI, Dimitrakopoulos EG (2017) Seismic performance of rocking frames with flag-shaped hysteretic behavior. J Eng Mech (ASCE) 143(5):04017008. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001206
Giouvanidis AI, Dimitrakopoulos EG (2018) Rocking amplification and strong motion duration. Earthq Eng Struct Dynam 47(10):2094–2116. https://doi.org/10.1002/eqe.3058
Housner GW (1963) The behavior of inverted pendulum structures during earthquakes. Bull Seismol Soc Am 53(2):403–417
Kazantzi AK, Vamvatsikos D (2015) Intensity measure selection for vulnerability studies of building classes. Earthq Eng Struct Dynam 44(15):2677–2694. https://doi.org/10.1002/eqe.2603
Kazantzi AK, Vamvatsikos D, Miranda E (2020) Evaluation of seismic acceleration demands on building nonstructural elements. J Struct Eng (ASCE) 146(7):04020118. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002676
Kazantzi AK, Lachanas CG, Vamvatsikos D (2021) Seismic response distribution expressions for on-ground rigid rocking blocks under ordinary ground motions. Earthq Eng Struct Dynam 50(12):3311–3331. https://doi.org/10.1002/eqe.3511
Konstantinidis D, Makris N (2009) Experimental and analytical studies on the response of freestanding laboratory equipment to earthquake shaking. Earthq Eng Struct Dynam 38(6):827–848. https://doi.org/10.1002/eqe.871
Konstantinidis D, Nikfar F (2015) Seismic response of sliding equipment and contents in base-isolated buildings subjected to broadband ground motions. Earthq Eng Struct Dynam 44:865–887. https://doi.org/10.1002/eqe.2490
Lachanas CG, Vamvatsikos D (2022) Rocking incremental dynamic analysis. Earthq Eng Struct Dynam 51(3):688–703. https://doi.org/10.1002/eqe.3586
Lachanas CG, Vamvatsikos D, Vassiliou MF (2022a) The influence of the vertical component of ground motion on the probabilistic treatment of the rocking response of free-standing blocks. Earthq Eng Struct Dynam. https://doi.org/10.1002/eqe.3643
Lachanas CG, Melissianos VE, Vamvatsikos D (2022b) Spatial variability of ground motion hazard and preliminary regional damage assessment of ancient monuments. In: Vayas I, Mazzolani FM (eds) Protection of historical constructions. PROHITECH 2021. Lecture notes in civil engineering, vol 209. Springer, Cham. https://doi.org/10.1007/978-3-030-90788-4_49
Linde SA, Konstantinidis D, Tait MJ (2020) Rocking response of unanchored building contents considering horizontal and vertical excitation. J Struct Eng (ASCE) 146(9):04020175–04020181. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002735
Lopez Garcia D, Soong TT (2003) Sliding fragility of block-type non-structural components. Part 1: unrestrained components. Earthq Eng Struct Dyn 32(1):111–129. https://doi.org/10.1002/eqe.217
Luco N, Cornell CA (2007) Structure-specific scalar intensity measures for near-source and ordinary earthquake ground motions. Earthq Spectra 23(2):357–392. https://doi.org/10.1193/1.2723158
Makris N, Kampas G (2016) Size versus slenderness: two competing parameters in the seismic stability of free-standing rocking columns. Bull Seismol Soc Am 106(1):104–122. https://doi.org/10.1785/0120150138
Makris N, Konstantinidis D (2003) The rocking spectrum and the limitations of practical design methodologies. Earthq Eng Struct Dynam 32(2):265–289. https://doi.org/10.1002/eqe.223
Makris N, Roussos Y (2000) Rocking response of rigid blocks under near-source ground motions. Géotechnique 50(3):243–262. https://doi.org/10.1680/geot.2000.50.3.243
Makris N, Vassiliou MF (2013) Planar rocking response and stability analysis of an array of free-standing columns capped with a freely supported rigid beam. Earthq Eng Struct Dynam 42(3):431–449. https://doi.org/10.1002/eqe.2222
Massey FJ (1951) The Kolmogorov–Smirnov test for goodness of fit. J Am Stat Assoc 46(253):68–78
Miller LH (1956) Table of percentage points of Kolmogorov statistics. J Am Stat Assoc 51(273):111–121
National institute of standards and technology (NIST), (2018) NIST GCR 18–917–43 report: recommendations for improved seismic performance of nonstructural components. https://doi.org/10.6028/NIST.GCR.18-917-43
Parisi F, Augenti N (2013) Earthquake damages to cultural heritage constructions and simplified assessment of artworks. Eng Fail Anal 34:735–760. https://doi.org/10.1016/j.engfailanal.2013.01.005
Petrone C, Di Sarno L, Magliulo G, Cosenza E (2017) Numerical modelling and fragility assessment of typical freestanding building contents. Bull Earthq Eng 15:1609–1633. https://doi.org/10.1007/s10518-016-0034-1
Priestley MJN, Evison RJ, Carr AJ (1978) Seismic response of structures free to rock on their foundations. Bull N Z Natl Soc Earthq Eng 11(3):141–150. https://doi.org/10.5459/bnzsee.11.3.141-150
Sarma SK, Casey BJ (1990) Duration of strong motion in earthquakes. In: Proceedings of the 9th European conference on earthquake engineering. Moscow, Russia, pp.174–183
Spyrakos CC, Maniatakis CA, Taflampas IM (2017) Application of predictive models to assess failure of museum artifacts under seismic loads. J Cult Herit 23(1):11–21. https://doi.org/10.1016/j.culher.2016.10.001
Stoica M, Medina RA, McCuen RH (2007) Improved probabilistic quantification of drift demands for seismic evaluation. Struct Saf 29(2):132–145. https://doi.org/10.1016/j.strusafe.2006.03.003
Taghavi S, Miranda E (2005) Response assessment of nonstructural building elements. PEER Rep. No. 2003/05. Berkeley, CA: Univ. of California Berkeley
Vamvatsikos D, Cornell CA (2002) Incremental dynamic analysis. Earthq Eng Struct Dynam 31(3):491–514. https://doi.org/10.1002/eqe.141
Vassiliou MF (2021) Script for the seismic response of a planar rocking block, MATLAB script: available at http://hdl.handle.net/20.500.11850/521016, https://doi.org/10.3929/ethz-b-000521016 (last accessed April 2022)
Voyagaki E, Vamvatsikos D (2015) Probabilistic assessment of rocking response for simply-supported rigid blocks. SECED 2015 conference: earthquake risk and engineering towards a resilient world, Cambridge, UK
Wan X, Astroza R, Huchinson T, Conte J, Bachman R (2014) Seismic demands on acceleration-sensitive nonstructural components using recorded building response data–Case study. In: 10th U.S. national conference on earthquake engineering. Anchorage, Alaska
Yim C-S, Chopra AK, Penzien J (1980) Rocking response of rigid blocks to earthquakes. Earthq Eng Struct Dynam 8(6):563–587. https://doi.org/10.1002/eqe.4290080606
Acknowledgements
The authors would like to thank Dr. M. Vassiliou for providing the software for undertaking the numerical study on the rocking oscillators under earthquake excitations and Ms. E. Vourlakou for preparing the photorealistic image of the supporting building. We also acknowledge the constructive criticism of the two anonymous reviewers who helped improve the manuscript.
Funding
This research has been co-financed by the European Regional Development Fund of the European Union and Greek national funds through the Operational Program Competitiveness, Entrepreneurship and Innovation, under the call RESEARCH—CREATE—INNOVATE (project code: Τ1EDK-00956), project: “ARCHYTAS: Archetypal telemetry and decision support system for the protection of monumental structures”. Financial support has been also provided by the European Framework Programme for Research and Innovation (Horizon 2020) project “HYPERION–Development of a decision support system for improved resilience & sustainable reconstruction of historic areas to cope with climate change & extreme events based on novel sensors and modelling tools”, Grant Agreement number 821054.
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All authors contributed to the study conception and design. The analyses of the rocking blocks were performed by CGL. The analytical expressions were derived by AKK. The first draft of the manuscript was written by AKK and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Kazantzi, A.K., Lachanas, C.G. & Vamvatsikos, D. Seismic response distribution expressions for rocking building contents under ordinary ground motions. Bull Earthquake Eng 20, 6659–6682 (2022). https://doi.org/10.1007/s10518-022-01424-w
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DOI: https://doi.org/10.1007/s10518-022-01424-w