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Attenuation of Inelastic Spectra and Its Applications

Attenuation of Inelastic Spectra and Its Applications. Yousef Bozorgnia, Mahmoud Hachem, Kenneth Campbell. PEER GMSM Workshop, UC Berkeley October 27, 2006. Background: Selected Ground Motions. 3122 Horizontal records 64 Worldwide earthquakes Magnitude: 4.3 - 7.9

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Attenuation of Inelastic Spectra and Its Applications

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  1. Attenuation of Inelastic Spectra and Its Applications Yousef Bozorgnia, Mahmoud Hachem, Kenneth Campbell PEER GMSM Workshop, UC Berkeley October 27, 2006

  2. Background: Selected Ground Motions • 3122 Horizontal records • 64 Worldwide earthquakes • Magnitude: 4.3 - 7.9 • Distance range: 0 – 200 km

  3. Computation of inelastic spectra • Inelastic spectra were computed for 3122 horizontal records • For periods: • 0.02 to 10 sec

  4. Computation of inelastic spectra • Computed parameters: • Strength • ductility • displacement • energy,… • Inelastic spectra for: Constant ductility; Constant strength; Constant damage index • Overall: > 1,240,000 nonlinear runs

  5. Attenuation of Inelastic Spectra • Having computed: • Inelastic spectra: 3122 (records) * 5 (ductility ratios), and • Damage spectra: 3122 (records) * 5 (damage index values) • For a given value of ductility or damage index • Nonlinear regression analyses were performed to correlate inelastic response to • Magnitude • Distance to fault • Soil condition • Style of faulting • …

  6. Attenuation of Inelastic Spectra -- Model

  7. Attenuation of Inelastic Spectra:For Different Ductility Ratios

  8. Mag Saturation Attenuation of Inelastic Spectra:For Different Magnitude

  9. Attenuation of Inelastic Spectra Attenuation of Elastic Spectrum Becomes a Special Case

  10. DI1= (- e)/(mon-1) (1-1) + 1 EH/EHmon Normalized Hysteretic Energy Normalized Ductility • DI=0, if Elastic response • DI=1, if it reaches deformation capacity under monotonic lateral deformation • Other performance states fall between DI=0,1 Damage Spectra (Bozorgnia & Bertero, 2003)

  11. DI=0, Elastic spectrum Damage Spectra: An example

  12. DI=0, Elastic spectrum Attenuation of Damage Spectra

  13. Displacement Inelastic Spectra

  14. Use of Inelastic Spectra for GMSM Simple scaling using attenuation of inelastic spectra Inelastic spectrum matching

  15. Scaling of Ground Motion Scaling Law of Inelastic Spectra: Bertero, Mahin, Herrera (August 1976) • For given ductility and period, • If you want to scale “Yield strength” Cy by a factor of λ • You will have to scale time history by scale factor λ

  16. Selection and Scaling of THs: Step1 • Select: Target Performance Level • Select ductility; or Damage Index, or … • Select: period • Select: site of the structure • Mag, Style of Faulting, Rrup, Vs30, …

  17. Step2:Initial Selection of Time Series • Various options … • M,R,… bin • M,R,ductility,… bin • M,R,DI,… bin • …

  18. Example

  19. Inelastic Spectrum Matching

  20. Given Inelastic Design Spectrum (e.g., attenuation of inelastic spectra)

  21. And a Record

  22. Is it possible to modify the record to match the Inelastic Spectrum?

  23. Inelastic Spectra; Ductility=4 Answer: Yes

  24. Initial Final Ground Motions

  25. It is relatively fast …

  26. Thank You!

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