Abstract
In this study, the inelastic displacement ratio (IDR) for far-field earthquake ground motions is statistically evaluated by the modified energy damage indices, known as hysteresis energy to input energy ratio, to estimate the target displacement in performance-based design theory with an energy approach. The suggested damage model can consider the effect of the frequency content, earthquake amplitude, and ground motion duration by accounting for whole energy aspects, including kinematic energy, damping energy, hysteresis energy, and input energy, without complex parameters in its structure. The IDR is statistically determined in six damage levels, four hysteresis models, and 30 periods of vibration by performing 216,000 dynamic analyses on 300 far-field ground motions. Moreover, the effect of the period, magnitude, source-to-site distance, and soil classes are investigated. Hence, a simplified mathematical equation is proposed based on the \({C}_{DI}-T-DI\) function to estimate the target displacement in different damage levels for performance-based design. Finally, the proposed method and formula are verified by target inelastic displacements gained from dynamic time history analysis. Statistical results showed that the coefficient of variation (COV) is not too high, and the influence of record-to-record characteristics on the IDR ratio is negligible. Additionally, the proposed equation could estimate the inelastic target displacement in different damage levels and periods of vibration appropriately.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aktaş YD, Türer A (2016) Seismic performance evaluation of traditional timber Hımış frames: capacity spectrum method-based assessment. Bull Earthq Eng 14:3175–3194. https://doi.org/10.1007/s10518-016-9943-2
Amirchoupani P, Abdollahzadeh G, Hamidi H (2020) Spectral acceleration matching procedure with respect to normalization approach. Bull Earthq Eng 18:5165–5191. https://doi.org/10.1007/s10518-020-00897-x
Amirchoupani P, Abdollahzadeh G, Hamidi H (2021) Improvement of energy damage index bounds for circular reinforced concrete bridge piers under dynamic analysis. Struct Concr 22:3315–3335. https://doi.org/10.1002/suco.202000762
ASCE/SEI 7-10 (2010) Minimum design loads for buildings and other structures. American Society of civil engineers, Reston, Virginia, USA.
ASCE/SEI 7-16 (2016) Minimum design loads and associated criteria for buildings and other structures. American society of civil engineers, Reston, Virginia, USA
ASCE/SEI 7-22 (2022) Minimum design loads and associated criteria for buildings and other structures. american society of civil engineers, Reston, Virginia, USA
ASCE/SEI, 41-17 (2017) Seismic evaluation and retrofit of existing buildings. American Society of Civil Engineers, Reston, Virginia, USA.
ATC 40 (1996) Seismic evaluation and retrofit of concrete buildings. Applied Technology Council, Redwood City, California. https://doi.org/10.1193/1.1586093
Baez JI, Miranda E (2000) Amplification factors to estimate inelastic displacement demands for the design of structures in the near field. In: Proceedings of 12th world conference on earthquake engineering
Baker JW (2011) Conditional mean spectrum: tool for ground-motion selection. J Struct Eng 137:322–331. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000215
Baker JW, Lee C (2018) An improved algorithm for selecting ground motions to match a conditional spectrum. J Earthq Eng 22:708–723. https://doi.org/10.1080/13632469.2016.1264334
Casarotti C, Pinho R (2007) An adaptive capacity spectrum method for assessment of bridges subjected to earthquake action. Bull Earthq Eng 5:377–390. https://doi.org/10.1007/s10518-007-9031-8
Chopra AK, Chintanapakdee C (2004) Inelastic deformation ratios for design and evaluation of structures: single-degree-of-freedom bilinear systems. J Struct Eng 130:1309–1319. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:9(1309)
Cosenza E, Manfredi G (2000) Damage indices and damage measures. Prog Struct Mat Eng 2:50–59. https://doi.org/10.1002/(SICI)1528-2716(200001/03)2:1%3C50::AID-PSE7%3E3.0.CO;2-S
Durucan C, Dicleli M (2015) AP/VP specific inelastic displacement ratio for seismic response estimation of structures. Earthq Eng Struct Dyn 44:1075–1097. https://doi.org/10.1002/eqe.2500
Durucan C, Durucan AR (2016) Ap/Vp specific inelastic displacement ratio for the seismic response estimation of SDOF structures subjected to sequential near fault pulse type ground motion records. Soil Dyn Earthq Eng 89:163–170. https://doi.org/10.1016/j.soildyn.2016.08.009
FEMA 273 (1997) NEHRP Guidelines for the seismic rehabilitation of buildings: FEMA 273, Washington, DC, USA
FEMA 356 (2000) Prestandard and commentary for the seismic rehabilitation of buildings. Federal emergency management agency, Washington, DC, USA.
FEMA-440 (2005) Improvement of nonlinear static seismic analysis procedures. Federal emergency management agency, Washington DC, USA.
Hachem MM, Mahin SA, Moehle JP (2003) Performance of circular reinforced concrete bridge columns under bidirectional earthquake loading. PEER Report
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
Hernández-Montes E, Aschheim MA, Gil-Martín LM (2015) Energy components in nonlinear dynamic response of SDOF systems. Nonlinear Dyn 82:933–945. https://doi.org/10.1007/s11071-015-2208-9
Jafarian Y, Kermani E, Baziar MH (2010) Empirical predictive model for the vmax/amax ratio of strong ground motions using genetic programming. Comput Geosci 36:1523–1531. https://doi.org/10.1016/j.cageo.2010.07.002
Joyner WB, Boore DM (1981) Peak horizontal acceleration and velocity from strong-motion records including records from the 1979 Imperial Valley, California, earthquake. Bull Seismol Soc Am 71:2011–2038
Kermani E, Jafarian Y, Baziar MH (2009) New predictive models for the vmax/amax ratio of strong ground motions using genetic programming. Int J Civil Eng 236–247.
Mahboubi S, Shiravand MR (2019a) Seismic evaluation of bridge bearings based on damage index. Bull Earthq Eng 17:4269–4297. https://doi.org/10.1007/s10518-019-00614-3
Mahboubi S, Shiravand MR (2019b) Proposed input energy-based damage index for RC bridge piers. J Bridg Eng 24:04018103. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001326
MathWorks I (1994) MATLAB: high-performance numeric computation and visualization software: MATLAB notebook suite user’s guide. MathWorks, Incorporated.
Mazzoni S, McKenna F, Scott MH, Fenves GL (2006) OpenSEES command language manual. Pac Earthq Eng Res PEER Center 264:137–158
Miranda E (1991) Seismic evaluation and upgrading of existing structures. University of California at Berkeley, CA, USA
Miranda E (1993) Evaluation of site-dependent inelastic seismic design spectra. J Struct Eng 119:1319–1338. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:5(1319)
Miranda E (2000) Inelastic displacement ratios for structures on firm sites. J Struct Eng 126:1150–1159. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:10(1150)
Miranda E (2001) Estimation of inelastic deformation demands of SDOF systems. J Struct Eng 127:1005–1012. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:9(1005)
Miranda E, Bertero VV (1991) Evaluation of structural response factors using ground motions recorded during the Loma Prieta earthquake. CSMIP-1991
Nassar AA, Krawinkler H (1991) Seismic demands for SDOF and MDOF systems. Stanford University, CA, USA
Negro P (1997) Experimental assessment of the global cyclic damage of framed R/C structures. J Earthq Eng 1:543–562. https://doi.org/10.1080/13632469708962377
Park YJ, Ang AHS (1985) Mechanistic seismic damage model for reinforced concrete. J Struct Eng 111:722–739. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:4(722)
Rahnama M, Krawinkler H (1993) Effect of soft soils and hysteresis models on seismic design spectra. John A. Blume earthquake engineering research centre report No. 108, Department of Civil Engineering.
Reyes JC, González C, Kalkan E (2018) Improved ASCE/SEI 7–10 ground-motion scaling procedure for nonlinear analysis of buildings. J Earthq Eng 25:597–620. https://doi.org/10.1080/13632469.2018.1526140
Riddell R, Garcia JE, Garces E (2002) Inelastic deformation response of SDOF systems subjected to earthquakes. Earthq Eng Struct Dyn 31:515–538. https://doi.org/10.1002/eqe.142
Ruiz-García J (2011) Inelastic displacement ratios for seismic assessment of structures subjected to forward-directivity near-fault ground motions. J Earthq Eng 3:449–468. https://doi.org/10.1080/13632469.2010.498560
Ruiz-García J, Miranda E (2003) Inelastic displacement ratios for evaluation of existing structures. Earthq Eng Struct Dyn 32:1237–1258. https://doi.org/10.1002/eqe.271
Ruiz-García J, Miranda E (2004) Inelastic displacement ratios for design of structures on soft soils sites. J Struct Eng 130:2051–2061. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:12(2051)
Ruiz-García J, Miranda E (2006) Inelastic displacement ratios for evaluation of structures built on soft soil sites. Eng Struct Dyn 35:679–694. https://doi.org/10.1002/eqe.552
Ruiz-García J, Miranda E (2007) Probabilistic estimation of maximum inelastic displacement demands for performance-based design. Eng Struct Dyn 36:1235–1254. https://doi.org/10.1002/eqe.680
Ruiz-García J (2010) Evaluation of coefficient method for seismic assessment of existing buildings built on soft soil sites. In: Improving the seismic performance of existing buildings and other structures. pp 465–476
Seneviratna G (1997) Evaluation of inelastic MDOF effects for seismic design. Stanford University, CA, USA
Shimazaki K, Sozen MA (1984) Seismic drift of reinforced concrete structures. Hazama-Gumi Ltd., Tokyo, Japan (in Japanese)
Stone WC, Taylor AW (1992) A predictive model for hysteretic failure parameters. In: Proceedings of the 10th world conference on earthquake engineering, Madrid, Spain. pp 2575–2580
Veletsos A, Newmark NM (1960) Effect of inelastic behavior on the response of simple systems to earthquake motions. In: Proceedings of the 2nd world conference on earthquake engineering
Veletsos AS, Newmark NM, Chelapati CV (1965) Deformation spectra for elastic and elastoplastic systems subjected to ground shock and earthquake motions. In: Proceedings of the 3rd world conference on earthquake engineering
Wen WP, Zhai CH, Li S et al (2014) Constant damage inelastic displacement ratios for the near-fault pulse-like ground motions. Eng Struct 59:599–607. https://doi.org/10.1016/j.engstruct.2013.11.011
Zhai CH, Wen WP, Chen ZQ et al (2013a) 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, Zhu TT et al (2013b) Inelastic displacement ratios for design of structures with constant damage performance. Eng Struct 52:53–63. https://doi.org/10.1016/j.engstruct.2013.02.008
Zhai CH, Wen WP, Li S, Xie LL (2012) The influences of seismic sequence on the inelastic SDOF systems. In: 15th world conference on earthquake engineering. Lisbon, Portugal
Zhou Y, Song G, Tan P (2019) Hysteretic energy demand for self-centering SDOF systems. Soil Dynam Earthq Eng 125:105703. https://doi.org/10.1016/j.soildyn.2019.105703
Funding
The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors have not disclosed any competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Amirchoupani, P., Abdollahzadeh, G. & Hamidi, H. Development of inelastic displacement ratio using constant energy-based damage index for performance-based design. Bull Earthquake Eng 21, 3461–3491 (2023). https://doi.org/10.1007/s10518-023-01652-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10518-023-01652-8