Skip to main content
Log in

The ductility-based strength reduction factor for the mainshock–aftershock sequence-type ground motions

  • Original Research Paper
  • Published:
Bulletin of Earthquake Engineering Aims and scope Submit manuscript

Abstract

This manuscript investigates the strength reduction factor of single degree of freedom system with constant ductility performance subjected to the mainshock–aftershock sequence-type ground motions. The recorded and artificial sequence-type ground motions are used. The aftershock ground motions in sequence are scaled to have different relative intensity levels. Four hysteretic models are used to simulate the different type of structures. The effects of period, ductility factor, site condition, aftershock, hysteretic behavior and damping are studied statistically. The results indicate that the strong aftershock ground motion has more obvious influences on strength reduction factors in short period region than on those in long period region. The degrading behavior would decrease the strength reduction factor of structure with short period at a magnitude of <20 %, while it would increase that of structure with medium-long period at a maximum level of 20 %. Finally, a predictive model, incorporating the effect of aftershock, is proposed to determine the strength reduction factor in the seismic design.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

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

    Article  Google Scholar 

  • Augenti N, Parisi F (2010) Learning from construction failures due to the 2009 L’Aquila, Italy, earthquake. J Perform Constr Facil 24:536–555

    Article  Google Scholar 

  • Ceci AM, Contento A, Fanale L, Galeota D, Gattulli V, Lepidi M, Potenza F (2010) Structural performance of the historic and modern buildings of the University of L’Aquila during the seismic events of April 2009. Eng Struct 32:1899–1924

    Article  Google Scholar 

  • CEN (2003) Eurocode 8: Design of structures for earthquake resistance, part 1: general rules, seismic actions and rules for buildings. European Committee for Standardization, Brussels

    Google Scholar 

  • Chakraborti A, Gupta VK (2005) Scaling of strength reduction factors for degrading elasto-plastic oscillators. Earthq Eng Struct Dyn 34:189–206

    Article  Google Scholar 

  • Das S, Gupta VK, Srimahavishnu V (2007) Damage-based design with no repairs for multiple events and its sensitivity to seismicity model. Earthq Eng Struct Dyn 36:307–325

    Article  Google Scholar 

  • Di Sarno L (2013) Effects of multiple earthquakes on inelastic structural response. Eng Struct 54:673–681

    Article  Google Scholar 

  • Efraimiadou S, Hatzigeorgiou GD, Beskos DE (2013) Structural pounding between adjacent buildings subjected to strong ground motions. Part II: the effect of multiple earthquakes. Earthq Eng Struct Dyn 42:1529–1545

    Article  Google Scholar 

  • Elnashai AS, Jefferson T, Fiedrich F, Cleveland LJ, Gress T (2009) Impact of New Madrid seismic zone earthquakes on the central USA: Volume I. Mid-America Earthquake (MAE) Center Repeort, No. 09-03

  • Faisal A, Majid TA, Hatzigeorgiou GD (2013) Investigation of story ductility demands of inelastic concrete frames subjected to repeated earthquakes. Soil Dyn Earthq Eng 44:42–53

    Article  Google Scholar 

  • FEMA 440 (2005) Improvement of nonlinear static seismic analysis procedures. June, chapter 3

  • Fragiacomo M, Amadio C, Macorini L (2004) Seismic response of steel frames under repeated earthquake ground motions. Eng Struct 26:2021–2035

    Article  Google Scholar 

  • Gillie JL, Rodriguez-Marek A, McDaniel C (2010) Strength reduction factors for near-fault forward-directivity ground motions. Eng Struct 32:273–285

    Article  Google Scholar 

  • Goda K (2012) Nonlinear response potential of mainshock–aftershock sequences from Japanese earthquakes. Bull Seismol Soc Am 102:2139–2156

    Article  Google Scholar 

  • Goda K, Taylor CA (2012) Effects of aftershocks on peak ductility demand due to strong ground motion records from shallow crustal earthquakes. Earthq Eng Struct Dyn 41:2311–2330

    Google Scholar 

  • Han R, Li Y, van de Lindt J (2014) Seismic risk of base isolated non-ductile reinforced concrete buildings considering uncertainties and mainshock–aftershock sequences. Struct Saf 50:39–56

    Article  Google Scholar 

  • Hatzigeorgiou GD (2010a) Behavior factors for nonlinear structures subjected to multiple near-fault earthquakes. Comput Struct 88:309–321

    Article  Google Scholar 

  • Hatzigeorgiou GD (2010b) Ductility demand spectra for multiple near- and far-fault earthquakes. Soil Dyn Earthq Eng 30:170–183

    Article  Google Scholar 

  • Hatzigeorgiou GD (2010c) Ductility demands control under repeated earthquakes using appropriate force reduction factors. J Earthq Tsunami 4:231–250

    Article  Google Scholar 

  • Hatzigeorgiou GD, Beskos DE (2009) Inelastic displacement ratios for SDOF structures subjected to repeated earthquakes. Eng Struct 31:2744–2755

    Article  Google Scholar 

  • Hatzigeorgiou GD, Liolios AA (2010) Nonlinear behaviour of RC frames under repeated strong ground motions. Soil Dyn Earthq Eng 30:1010–1025

    Article  Google Scholar 

  • Iervolino I, Manfredi G, Cosenza E (2006) Ground motion duration effects on nonlinear seismic response. Earthq Eng Struct Dyn 35(1):21–38

    Article  Google Scholar 

  • International Building Code (IBC) (2006) International Code Council Inc., 4051 West Flossmoor Road, Country Club Hills

  • Jing LP, Liang HA, Li YQ, Liu CH (2011) Characteristics and factors that influenced damage to dams in the Ms 8.0 Wenchuan earthquake. Earthq Eng Eng Vib 10:349–358

    Article  Google Scholar 

  • Karakostas CZ, Athanassiadou CJ, Kappos AJ, Lekidis VA (2007) Site-dependent design spectra and strength modification factors, based on records from Greece. Soil Dyn Earthq Eng 27:1012–1027

    Article  Google Scholar 

  • Kunnath SK, Reinhorn AM, Park YJ (1990) Analytical modeling of inelastic seismic response of R/C structures. ASCE J Struct Eng 116(4):996–1017

    Article  Google Scholar 

  • Lee K, Foutch DA (2004) Performance evaluation of damaged steel frame buildings subjected to seismic loads. ASCE J Struct Eng 130:588–599

    Article  Google Scholar 

  • Levenberg K (1944) A method for the solution of certain non-linear problems in least squares. Q Appl Math 2:164–168

    Google Scholar 

  • Li Q, Ellingwood BR (2007) Performance evaluation and damage assessment of steel frame buildings under mainshock–aftershock earthquake sequences. Earthq Eng Struct Dyn 36:405–427

    Article  Google Scholar 

  • Mahin SA, Bertero VV (1975) An evaluation of some methods for predicting seismic behavior of reinforced concrete buildings. Earthquake Engineering Research Center, University of California at Berkeley, CA; Report No. UCB/EERC-75/5

  • Mahin SA, Bertero VV (1976) Nonlinear seismic response of a coupled wall system. ASCE J Struct Eng 102:1759–1780

    Google Scholar 

  • Marquardt D (1963) An algorithm for least-squares estimation of nonlinear parameters. SIAM J Appl Math 11:431–441

    Article  Google Scholar 

  • Miranda E (1993) Site-dependent strength-reduction factors. ASCE J Struct Eng 119:3503–3519

    Article  Google Scholar 

  • Miranda E, Bertero VV (1994) Evaluation of strength reduction factors for earthquake-resistant design. Earthq Spectra 10:357–379

    Article  Google Scholar 

  • Miranda E, Ruiz-García J (2002a) Influence of stiffness degradation on strength demands of structures built on soft soil sites. Eng Struct 24:1271–1281

    Article  Google Scholar 

  • Miranda E, Ruiz-García J (2002b) Evaluation of approximate methods to estimate maximum inelastic displacement demands. Earthq Eng Struct Dyn 31(3):539–560

    Article  Google Scholar 

  • Moustafa A, Takewaki I (2010) Modeling critical ground-motion sequences for inelastic structures. Adv Struct Eng 13:665–680

    Article  Google Scholar 

  • Newmark NM, Hall WJ (1969) Seismic design criteria for nuclear reactor facilities. In: Proceedings 4th World conference on earthquake engineering, Santiago, Chile, vol 4, pp 37–50

  • Palermo M, Silvestri S, Trombetti T, Landi L (2013) Force reduction factor for building structures equipped with added viscous dampers. Bull Earthq Eng 11:1661–1681

    Article  Google Scholar 

  • Qu H, Zhang J, Zhao JX (2011) Strength reduction factors for seismic analyses of buildings exposed to near-fault ground motions. Earthq Eng Eng Vib 10:195–209

    Article  Google Scholar 

  • Rahnama M, Krawinkler H (1993) Effects of soft soil and hysteresis model on seismic demands. John A. Blume Earthquake Engineering Center, chapter 3, pp 36–37

  • Riddell R, Newmark NM (1979a) Statistical Analysis of the response of nonlinear systems subjected to earthquakes. Structural Research Series No. 468, Department of Civil Engineering, University of Illinois

  • Riddell R, Newmark NM (1979b) Force-deformation models for nonlinear analyses. ASCE J Struct Div 105:2773–2778

    Google Scholar 

  • Riddell R, Garcia JE, Garces E (2002) Inelastic deformation response of SDOF systems subjected to earthquakes. Earthq Eng Struct Dyn 31:515–538

    Article  Google Scholar 

  • Ruiz-García J (2012) Mainshock–aftershock ground motion features and their influence in building’s seismic response. J Earthq Eng 16:719–737

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Ruiz-García J, Terán-Gilmore A, Díaz G (2012) Response of essential facilities under narrow-band mainshock–aftershock seismic sequences. In: Proceedings of the 15th World conference on earthquake engineering, Lisboa, Portugal. Paper 5382

  • Ruiz-García J, Marín MV, Terán-Gilmore A (2014) Effect of seismic sequences in reinforced concrete frame buildings located in soft-soil sites. Soil Dyn Earthq Eng 63:56–68

    Article  Google Scholar 

  • Sunasaka Y, Kiremidjian AS, Toki K (2002) Strength demand spectra with uniform damage level in lifetime of structure. ASCE J Struct Eng 48A:523–530

    Google Scholar 

  • Tong G, Zhao Y (2007) Seismic force modification factors for modified-Clough hysteretic model. Eng Struct 29(11):3053–3070

    Article  Google Scholar 

  • Valles RE, Reinhorn AM, Kunnath SK, Madan A (1996) IDARC2D, version 4.0: a computer program for the inelastic damage analysis of buildings. National Center for Earthquake Engineering Research, State University of New York, Buffalo

    Google Scholar 

  • Veletsos AS, Newmark M (1960) Effect of inelastic behavior on the response of simple systems to earthquake motions. In: Proceedings of the 2nd World conference on earthquake engineering, Tokyo, Japan, pp 895–912

  • Wen WP, Zhai CH, Li S, Chang Z, Xie LL (2014) Constant damage inelastic displacement ratios for the near-fault pulse-like ground motions. Eng Struct 59:599–607

    Article  Google Scholar 

  • Zhai CH, Wen WP, Chen Z, Li S, Xie LL (2013a) Damage spectra for the mainshock–aftershock sequence-type ground motions. Soil Dyn Earthq Eng 45:1–12

    Article  Google Scholar 

  • Zhai CH, Wen WP, Zhu TT, Li S, Xie LL (2013b) Inelastic displacement ratios for design of structures with constant damage performance. Eng Struct 52:53–63

    Article  Google Scholar 

  • Zhai CH, Wen WP, Li S, Chen Z, Chang Z, Xie LL (2014) The damage investigation of inelastic SDOF structure under the mainshock–aftershock sequence-type ground motions. Soil Dyn Earthq Eng 59:30–41

    Article  Google Scholar 

  • Zhang S, Wang G, Sa W (2013) Damage evaluation of concrete gravity dams under mainshock–aftershock seismic sequences. Soil Dyn Earthq Eng 50:16–27

    Article  Google Scholar 

Download references

Acknowledgments

This investigation is supported by the National Natural Science Foundation of China (Nos. 51322801,51238012 and 91215301), the Program for International Science and Technology Cooperation Projects of China (No. 2012DFA70810), the Program for New Century Excellent Talents in University of Ministry of Education of China (No. NCET-11-08), as well as the National Science and Technology Major Project (2013zx06002001-09). These supports are greatly appreciated. The authors are grateful to the anonymous reviewers for their constructive comments and suggestions.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chang-Hai Zhai.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhai, CH., Wen, WP., Li, S. et al. The ductility-based strength reduction factor for the mainshock–aftershock sequence-type ground motions. Bull Earthquake Eng 13, 2893–2914 (2015). https://doi.org/10.1007/s10518-015-9744-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10518-015-9744-z

Keywords

Navigation