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

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

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. Attenuation of Inelastic Spectra: For Different Magnitude Mag Saturation

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

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

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

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

13. Displacement Inelastic Spectra

14. Use of Inelastic Spectra for GMSM 1. Simple scaling using attenuation of inelastic spectra 2. 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. Step 3: Scaling of Time Histories Let C yTarge t be median prediction (attenuation) of inelastic spectra for the target data M, Rrup, Vs30, … Let C yAttn_i be median prediction (attenuation) of inelastic spectra for the selected record i M i, R rupi, V s30i, … Let initial selected record i corresponds to: M i, R rupi, V s30i, … with C yi (at target ductility μ ) Scale time history i by λ = C yTarge t / C yAttn_i The new inelastic spectral ordinate will be: C y_i_scaled = C yi * λ

19. Example

20. Inelastic Spectrum Matching

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

22. And a Record

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

24. Answer: Yes Inelastic Spectra; Ductility=4

25. Ground Motions Initial Final

26. It is relatively fast …

27. Thank You!