Department of Civil Engineering National Taiwan University National Taiwan University 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 US-Taiwan Workshop on Liquefaction National Chiao Tung University November 3-4, 2003

Department of Civil Engineering National Taiwan University National Taiwan University Deep Zone (Depth > 35 km) < M < < M < < M < < M < < M < 8.5 Shallow Zone (Depth < 35 km) < M < < M < < M < < M < < M < 8.5

Department of Civil Engineering National Taiwan University National Taiwan University Generation of Uniform Hazard Accelerogram Representing from “Dominant Earthquake” Identify Dominant Earthquake using Concept of Hazard-consistent Magnitude & Distance Select a Site 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 National Taiwan University Annual Probability of Exceedaance Hazard-Consistent Magnitude Site A p0p0 Develop Hazard-Consistent Magnitude and Distance

Department of Civil Engineering National Taiwan University National Taiwan University

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

Department of Civil Engineering National Taiwan University National Taiwan University 1.Generate Uniform Hazard Acceleration Response Spectrum (for different return period) with modification of site characteristics, 2.Determine Hazard-consistent Magnitude & Distance from “Dominant Earthquake” Generate Spectrum Compatible Time History ?? Phase Spectrum

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

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

dt=0.01 j=0 j j=16 N=2 17 ＝ Wavelet decomposed wave Group Delay Time Department of Civil Engineering National Taiwan University National Taiwan University Average Group Delay Time and Its Standard Deviation - Using Wavelet Analysis -

Distribution Characteristic of the Group Delay Time t gr (  ) t-distribution (  =3) Gauss-distribution t-distribution (  =3) Gauss-distribution t-distribution Gauss-distribution Department of Civil Engineering National Taiwan University National Taiwan University

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

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

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

Department of Civil Engineering National Taiwan University National Taiwan University Annual Probability of Exceedance Hazard Consistent Magnitude, M Hazard Consistent Distance, D Return Period: 475 year Return Period: 2475 year Hazard Consistent Magnitude & Distance at Nan-Tou City

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

Department of Civil Engineering National Taiwan University National Taiwan University For Nan-Tou city: Consider 2475 year return period The hazard-consistent magnitude : M L =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.

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

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

Department of Civil Engineering National Taiwan University National Taiwan University Modification with Site Amplification SSDSSD S1DS1D T 0.2T 0 1.0T0T0 0.2T 0 1.0T0DT0D S DS S D1 T S aD =S D1 /T S DS = F a S S D S D1 = F v S 1 D

EstimationObservation Department of Civil Engineering National Taiwan University National Taiwan University Chi-Chi Earthquake: Spectral Acceleration at T=1.0 sec

EstimationObservation Department of Civil Engineering National Taiwan University National Taiwan University Chi-Chi Earthquake: Spectral Acceleration at T=0.3 sec

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

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

Department of Civil Engineering National Taiwan University National Taiwan University Example

Department of Civil Engineering National Taiwan University National Taiwan University

Department of Civil Engineering National Taiwan University National Taiwan University R=50km R=25km R=10km R=50km R=25km R=10km Average and Standard Deviation of t gr

Department of Civil Engineering National Taiwan University National Taiwan University Example

Department of Civil Engineering National Taiwan University National Taiwan University

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

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

Department of Civil Engineering National Taiwan University 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) in can be applied to the liquefaction assessment in engineering problem, engineering problem, 4. The generated uniform hazard accelerogram representing from “Dominant Earthquake” can be used for PBSD, from “Dominant Earthquake” can be used for PBSD,

The End Department of Civil Engineering National Taiwan University National Taiwan University