Earthquake Engineering and Engineering Vibration

, Volume 17, Issue 4, pp 771–785 | Cite as

Direct use of peak ground motion parameters for the estimation of inelastic displacement ratio of SDOF systems subjected to repeated far fault ground motions

  • Cengizhan DurucanEmail author
  • Muhammed Gümüş


This study is aimed at developing statistical equations to estimate the inelastic displacement ratio of singledegree- of-freedom systems subjected to far fault repeated earthquakes. In the study, peak ground motion parameters are used to define the scatter of the original data. The ratio of peak ground acceleration to peak ground velocity, and peak ground velocity of the ground motion records and structural parameters such as period of vibration and lateral strength ratio are used in the proposed equations. For the development of the equations, nonlinear time history analyses of single-degree-offreedom systems are conducted. Then, the results are used in a multivariate regression procedure. The equations are verified by comparing the estimated results with the calculated results. The average error and coefficient of variation of the proposed equations are presented. The analyses results revealed that the direct use of peak ground motion parameters for the estimation of inelastic displacement ratio significantly reduced the scatter in the original data and yielded accurate results. From the comparative results it is also observed that results obtained using equations specific to peak ground velocity or peak ground acceleration to peak ground velocity ratio are similar.


C1 peak ground velocity peak ground acceleration far fault ground motions sequential ground motions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Akkar S and Kucukdogan B (2008), “Direct Use of PGV for Estimating Peak Nonlinear Oscillator Displacements,” Earthquake Engineering &Structural Dynamics, 37(12): 1411–1433.CrossRefGoogle Scholar
  2. Akkar S and Bommer JJ (2005), “Empirical Prediction Equations for Peak Ground Velocity Derived from Strong-Motion Records from Europe and the Middle East,” Bulletin of the Seismological Society of America, 97(2): 511–530.CrossRefGoogle Scholar
  3. Akkar S and Özen Ö (2005), “Effect of Peak Ground Velocity on Deformation Demands for SDOF Systems,” Earthquake Engineering & Structural Dynamics, 34(13): 1551–1571.CrossRefGoogle Scholar
  4. American Society of Civil Engineers (2007), Seismic Rehabilitation of Existing Buildings, ASCE/SEI Standard.Google Scholar
  5. Applied Technology Council (2005), “Improvement of Nonlinear Static Seismic Analysis Procedures,” Report FEMA 440, Federal Emergency Management Agency, Washington, DC, 2005.Google Scholar
  6. Ay BÖ and Akkar S (2014), “Evaluation of a Recently Proposed Record Selection and Scaling Procedure for Low-Rise to Mid-Rise Reinforced Concrete Buildings and Its Use for Probabilistic Risk Assessment Studies,” Earthquake Engineering & Structural Dynamics, 43(6): 889–908.CrossRefGoogle Scholar
  7. Aydemir ME (2013), “Inelastic Displacement Ratios for Evaluation of Stiffness Degrading Structures with Soil Structure Interaction Built on Soft Soil Sites,” Structural Engineering and Mechanics, 45(6): 741–758.CrossRefGoogle Scholar
  8. Bates DM and Watts DG (1988), Nonlinear Regression Analysis and Its Applications, New York: Wiley.CrossRefGoogle Scholar
  9. Building Seismic Safety Council (2000), Pre-Standard and Commentary for the Seismic Rehabilitation of Buildings, FEMA-356, Federal Emergency Management Agency, Washington DC.Google Scholar
  10. Changhai Z, Duofa J, Weiping W, Cuihua L, Weidong L and Lili X (2018), “Hysteretic Energy Prediction Method for Mainshock-Aftershock Sequences,” Earthquake Engineering and Engineering Vibration, 17(2): 277–291.CrossRefGoogle Scholar
  11. Chopra AK and Chintanapakdee C (2004), “Inelastic Deformation Ratios for Design and Evaluation of Structures: Single-Degree-of-Freedom Bilinear Systems,” Journal of Structural Engineering, 130(9): 1309–1319.CrossRefGoogle Scholar
  12. Cosenza E and Manfredi G (2000), “Damage Indices and Damage Measures,” Prog. Struct. Engng Mater., 2: 50–59.CrossRefGoogle Scholar
  13. Durucan C and 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 Dynamics and Earthquake Engineering, 89: 163–170.CrossRefGoogle Scholar
  14. Durucan C and Dicleli M (2015), “Ap/Vp Specific Inelastic Displacement Ratio for Seismic Response Estimation of Structures,” Earthquake Engineering & Structural Dynamics, 44(7): 1075–1097.CrossRefGoogle Scholar
  15. Erduran E and Kunnath SK (2010), “Enhanced Displacement Coefficient Method for Degrading Multi-Degree-of-Freedom Systems,” Earthquake Spectra, 26(2): 311–326.CrossRefGoogle Scholar
  16. Faisal A, Majid TA and Hatzigeorgiou GD (2013), “Investigation of Story Ductility Demands of Inelastic Concrete Frames Subjected to Repeated Earthquakes,” Soil Dynamic and Earthquake Engineering, 44: 42–53.CrossRefGoogle Scholar
  17. Fajfar P and Fischinger M (1988), “N2—a Method for Nonlinear Seismic Analysis of Regular Structures,” Proc., 9th World Conferance on Earthquake Engineering, 5: 111–116.Google Scholar
  18. Gutenberg B and Richter CF. (1944), “Frequency of Earthquakes in California,” Bull Seism Soc Am, 34: 185–188.Google Scholar
  19. Hatzigeorgiou GD and Beskos DE (2009), “Inelastic Displacement Ratios for SDOF Structures Subjected to Repeated Earthquakes,” Engineering Structures, 31(11): 2744–2755.CrossRefGoogle Scholar
  20. Hatzigeorgiou GD (2010a), “Behavior Factors for Nonlinear Structures Subjected to Multiple Near-Fault Earthquakes,” Computers and Structures, 88: 309–321.CrossRefGoogle Scholar
  21. Hatzigeorgiou GD (2010b), “Ductility Demand Spectra for Multiple Near-And Far-Fault Earthquakes,” Soil Dynamics and Earthquake Engineering, 30: 170–183.CrossRefGoogle Scholar
  22. Iervolino I, Chioccarelli E and Baltzopoulos G (2012), “Inelastic Displacement Ratio of Near-Source Pulse-Like Ground Motions,” Earthquake Engineering and Structural Dynamics, 41(15): 2351–2357.Google Scholar
  23. Joyner WB and Boore DM (1982), “Prediction of Earthquake Response Spectra,” USGS Openfile report, 82–977.Google Scholar
  24. Kabongo-Booto G, Hatzigeorgiou GD (2013), “Inelastic Displacement Ratio Spectrum for Near-Fault Ground Motions,” International Journal of Engineering and Technology, 5(6): 694–697.CrossRefGoogle Scholar
  25. Liu T and Zhang Q (2016), “Ap/Vp Specific Equivalent Viscous Damping Model for Base-Isolated Buildings Characterized by SDOF Systems,” Engineering Structures, 111: 36–47.CrossRefGoogle Scholar
  26. Miranda E (1999), “Approximate Seismic Lateral Deformation Demands in Multistory Buildings,” Journal of Structural Engineering, ASCE, 125(4): 417–425.CrossRefGoogle Scholar
  27. Miranda E (2001), “Estimation of Inelastic Deformation Demands of SDOF Systems,” Journal of Structural Engineering,” 127(9): 1005–1012.CrossRefGoogle Scholar
  28. Miranda E (1991), “Seismic Evaluation and Upgrading of Existing Structures,” PhD Thesis, University of California, Berkeley, Berkeley, Calif.Google Scholar
  29. Muria Vila D and Toro Jaramillo AM (1998) “Effects of Several Events Recorded at a Building Founded on Soft Soil,” 11th European Conference on Earthquake Engineering, Paris.Google Scholar
  30. Pacific Earthquake Engineering Research Center (PEER), Strong Ground Motion Database,, [30.01.14].
  31. Ruiz-García J and Miranda E (2003), “Inelastic Displacement Ratios for Evaluation of Existing Structures,” Earthquake Engineering &Structural Dynamics, 32(8): 1237–1258.CrossRefGoogle Scholar
  32. Ruiz-García J and Miranda E (2006), “Inelastic Displacement Ratios for Evaluation of Structures Built on Soft Soil Sites,” Earthquake Engineering & Structural Dynamics, 35(6): 679–694.CrossRefGoogle Scholar
  33. Ruiz-Garcia J (2011), “Inelastic Displacement Ratios for Seismic Assessment of Structures Subjected to Forward-Directivity Near-Fault Ground Motions,” Journal of Earthquake Engineering, 5(3): 449–468.CrossRefGoogle Scholar
  34. Ruiz-Garcia J (2012), “Mainshock-Aftershock Ground Motion Features and Their Influence in Building’s Seismic Response,” Journal of Earthquake Engineering, 16(5):719–737.CrossRefGoogle Scholar
  35. Shcherbakov R, Turcotte DL and Rundle JB (2005), “Aftershock Statistics,” Pure and Applied Geophysics, 162: 1051–1076.CrossRefGoogle Scholar
  36. Trombetti T, Silvestri S, Gasparini G, Righi M and Ceccoli C (2008), “Correlations Between the Displacement Response Spectra and the Parameters Characterizing the Magnitude of the Ground Motion,” 14. World Conference on Earthquake Engineering, Beijing, China.Google Scholar
  37. Veletsos AS and Newmark N (1960), “Effect of Inelastic Behavior on the Response of Simple Systems to Earthquake Motions,” Proceedings of the 2nd World Conference on Earthquake Engineering, 2: 895–912.Google Scholar
  38. Yaghmaei-Sabegh S (2012), “Application of Wavelet Transforms on Characterization of Inelastic Displacement Ratio Spectra for Pulse-Like Ground Motions,” Journal of Earthquake Engineering, 16(4): 561–578.CrossRefGoogle Scholar
  39. Zhai C, Wen W and Ji D (2015), “The Influences of Aftershocks on the Constant Damage Inelastic Displacement Ratio,” Soil Dynamics and Earthquake Engineering, 79: 186–189.CrossRefGoogle Scholar

Copyright information

© Institute of Engineering Mechanics, China Earthquake Administration and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil Engineering (Technology Faculty)Fırat UniversityElazığTurkey
  2. 2.Department of Civil EngineeringGazi UniversityAnkaraTurkey

Personalised recommendations