Department of Civil Engineering National Taiwan University

1. Department of Civil Engineering National Taiwan University US-Taiwan Workshop on Liquefaction Generation of Uniform Hazard Accelerogram Representing from “Dominant Earthquake” for PBSD C. H. Loh Department of Civil Engineering, National Taiwan University, Taipei, Taiwan J. F. Chai & W.Y. Jean National Center for Research on Earthquake Engineering, Taipei, Taiwan National Chiao Tung University November 3-4, 2003

2. Deep Zone (Depth > 35 km) 4 3.5 < M < 4.5 5 4.5 < M < 5.5 6 5.5 < M < 6.5 7 6.5 < M < 7.5 8 7.5 < M < 8.5 Shallow Zone (Depth < 35 km) 4 3.5 < M < 4.5 5 4.5 < M < 5.5 6 5.5 < M < 6.5 7 6.5 < M < 7.5 8 7.5 < M < 8.5 Department of Civil Engineering National Taiwan University

3. Select a Site Identify Dominant Earthquake using Concept of Hazard-consistent Magnitude & Distance Generate Site-Specific Uniform Hazard Response Spectrum Generate Phase Spectrum Using Attenuation of Group Delay Time Develop Spectrum Compatible Time History Department of Civil Engineering National Taiwan University Generation of Uniform Hazard Accelerogram Representing from “Dominant Earthquake”

4. Site A p0 Annual Probability of Exceedaance Hazard-Consistent Magnitude Department of Civil Engineering National Taiwan University Develop Hazard-Consistent Magnitude and Distance

5. Department of Civil Engineering National Taiwan University

6. Uniform Hazard Response Spectrum ․ ․ Return Period =2475 yr ․ ․ ․ ․ Period, T Spectral Acceleration, Sa ․ Annual Probability of Exceedance ․ ․ ․ Return Period =475 yr Structural Period, T Spectral Acceleration, Sa Department of Civil Engineering National Taiwan University Seismic Hazard Analysis (based on Spectral Acceleration Attenuation Form)

7. Department of Civil Engineering National Taiwan University • Generate Uniform Hazard Acceleration Response Spectrum • (for different return period) with modification of site characteristics, • Determine Hazard-consistent Magnitude & Distance from • “Dominant Earthquake” Generate Spectrum Compatible Time History ? ? Phase Spectrum

8. Department of Civil Engineering National Taiwan University Modeling of phase spectra • Wavelet analysis • Concept of group delay time • Stochastic characteristics of group delay time • Regression model of group delay time

9. A Method to Identify Wavelet Coefficients using Phase Spectrum : wavelet coefficient : analyzing wavelet Department of Civil Engineering National Taiwan University Wavelet Formulation (1) Time history of j-th component Meyer’s mother wavelet is used

10. N=217＝131072 j=0 Wavelet decomposed wave j j=16 Department of Civil Engineering National Taiwan University Average Group Delay Time and Its StandardDeviation - Using Wavelet Analysis - dt=0.01 Group Delay Time

11. t-distribution (f=3) Gauss-distribution t-distribution (f=3) Gauss-distribution Department of Civil Engineering National Taiwan University Distribution Characteristic of the Group Delay Time tgr(w) t-distribution Gauss-distribution

12. Standard deviation Average Department of Civil Engineering National Taiwan University Substitute hazard consistent magnitude & distance

13. Mean Value jtgr： Central arrival time Standard Deviation jtgr Duration Meyer Wavelet Transformation tjgr()=J()/ Fourier Transformation jtgr J() tjgr() jtgr x(t) xj(t) XJ() Department of Civil Engineering National Taiwan University AJ() Time History Analysis: Modeling of Phase Spectrum

14. Select a “Site” Determine the “Dominant Earthquake” for this site Dominant Earthquake : Hazard-consistent Magnitude Hazard-consistent Distance Liquefaction Assessment & Generation ground motion time history for PBSD Department of Civil Engineering National Taiwan University

15. Annual Probability of Exceedance 10-4 10-3 10-2 10-1 1.0 Return Period: 475 year Return Period: 2475 year Hazard Consistent Magnitude, M Hazard Consistent Distance, D Department of Civil Engineering National Taiwan University Hazard Consistent Magnitude & Distance at Nan-Tou City

16. Nan-Tou City (Radius=25km) Chelungpu Fault ⋆ Department of Civil Engineering National Taiwan University The “Dominant Earthquake” for Nan-Tou city will be induced by Chelungpu Fault

17. Department of Civil Engineering National Taiwan University For Nan-Tou city: Consider 2475 year return period The hazard-consistent magnitude : ML=7.2 The hazard-consistent distance: R=25km This is consistent with the Chi-Chi earthquake induced by Chelungpu Fault The phase spectrum obtained from the ground motion data of Chi-Chi earthquake can be used to simulate spectrum consistent ground motion.

18. Department of Civil Engineering National Taiwan University Attenuation equation for PGA, Sa(T=0.3 sec), Sa(T=1.0 sec),

19. Design acceleration response spectrum developed using and Department of Civil Engineering National Taiwan University

20. SDS = Fa SSD SD1 = Fv S1D SDS SSD SaD=SD1/T SD1 S1D T 0.2T0 T0D 1.0 T 0.2T0 T0 1.0 Department of Civil Engineering National Taiwan University Modification with Site Amplification

21. Department of Civil Engineering National Taiwan University Chi-Chi Earthquake: Spectral Acceleration at T=1.0 sec Observation Estimation

22. Department of Civil Engineering National Taiwan University Chi-Chi Earthquake: Spectral Acceleration at T=0.3 sec Observation Estimation

23. ■︰ 0.55g ■︰ 0.50g ■︰ 0.45g ■ ︰ 0.40g ■︰ 1.0g ■︰ 0.9g ■︰ 0.8g ■ ︰ 0.7g (T=1.0) (T=0.3) Department of Civil Engineering National Taiwan University Distribution of spectral acceleration (based on township unit) at design level with return period of 2475 year

24. TCU045 TCU052 TCU129 TCU202 CHY028 KAU047 Department of Civil Engineering National Taiwan University

25. Department of Civil Engineering National Taiwan University Example

26. Department of Civil Engineering National Taiwan University

27. Average and Standard Deviation of tgr R=50km R=25km R=10km R=50km R=25km R=10km Department of Civil Engineering National Taiwan University

28. Department of Civil Engineering National Taiwan University Example

29. Department of Civil Engineering National Taiwan University

30. Department of Civil Engineering National Taiwan University Original Ground Motion Spectrum-consistent Ground Motion

31. Department of Civil Engineering National Taiwan University Original Ground Motion Spectrum-consistent Ground Motion

32. Department of Civil Engineering National Taiwan University Conclusions 1. A Procedure for generating “Dominant Earthquake” ground motion was developed. 2. Regression equations are derived to model the group delay time characteristics of earthquake motions observed during the 1999 Chi-Chi earthquake, 3. The above method (including hazard-consistent magnitude and distance, uniform hazard accelerogram) can be applied to the liquefaction assessmentin engineering problem, 4. The generated uniform hazard accelerogram representing from “Dominant Earthquake” can be used for PBSD,

33. Department of Civil Engineering National Taiwan University The End Thank you for your attention