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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 - PowerPoint PPT Presentation
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Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
Generation of Uniform Hazard Accelerogram Representing Generation of Uniform Hazard Accelerogram Representing from “Dominant Earthquake” for PBSDfrom “Dominant Earthquake” for PBSD
C. H. Loh Department of Civil Engineering, National Taiwan University, Taipei, Taiwan
J. F. Chai & W.Y. JeanNational Center for Research on Earthquake Engineering, Taipei, Taiwan
US-Taiwan Workshop on LiquefactionUS-Taiwan Workshop on Liquefaction
National Chiao Tung UniversityNational Chiao Tung University
November 3-4, 2003November 3-4, 2003
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
Deep Zone (Depth > 35 km)4 3.5 < M < 4.5 5 4.5 < M < 5.56 5.5 < M < 6.5 7 6.5 < M < 7.58 7.5 < M < 8.5
Shallow Zone (Depth < 35 km)4 3.5 < M < 4.5 5 4.5 < M < 5.56 5.5 < M < 6.5 7 6.5 < M < 7.58 7.5 < M < 8.5
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
Generation of Uniform Hazard Accelerogram Representing from “Dominant Earthquake”
Identify Identify Dominant EarthquakeDominant Earthquakeusing Concept ofusing Concept of
Hazard-consistent Magnitude & Hazard-consistent Magnitude & DistanceDistance
Select a SiteSelect a Site
Generate Site-SpecificGenerate Site-SpecificUniform Hazard Response SpectrumUniform Hazard Response SpectrumGenerate Phase SpectrumGenerate Phase Spectrum
UsingUsingAttenuation of Group Delay Attenuation of Group Delay
TimeTime
Develop Spectrum Compatible Time Develop Spectrum Compatible Time HistoryHistory
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
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Hazard-Consistent Magnitude
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Develop Hazard-Consistent Develop Hazard-Consistent MagnitudeMagnitude and and DistanceDistance
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
Spectral Acceleration, Sa
An
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Period, T
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Return Period =475 yr
Return Period =2475 yr
Uniform Hazard Response Spectrum
Seismic Hazard Analysis
(based on Spectral Acceleration Attenuation Form)
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational 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”
GenerateGenerate
Spectrum Compatible Time HistorySpectrum Compatible Time History
?? ??Phase SpectrumPhase 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 EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
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M
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Meyer’s mother wavelet is used
A Method to Identify Wavelet Coefficients using Phase Spectrum
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
0.1 0.5 1 5 100
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Wavelet decomposed wave
d
dtgr Group Delay Time
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
Average Group Delay Time and Its Standard Deviation - Using Wavelet Analysis -
Distribution Characteristic of the Group Delay Time tgr()
10 20 30 40 50 600
0.05
0.1
0.15
tgr
f
j=12
t-distribution (=3)
Gauss-distribution
10 20 30 40 50 600
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t-distribution (=3)
Gauss-distribution
2
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x
xf X
t-distribution
Gauss-distribution
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
0.0625 0.125 0.25 0.5 1 2 4 8 160
10
20
30
40
50
60
70
80
90
j=-3 j=-2 j=-1 j=0 j=1 j=2 j=3 j=4
Frequency (Hz)
t gr
(sec
)
Group Delay Time : TCU052 EW
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
jN
ij
ij
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x(t) xj(t) XJ()J()
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tjgr()=J()/
Mean Value jtgr :
Central arrival time
Standard Deviation jtgr
Duration
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Time History Analysis:Time History Analysis: Modeling of Phase Spectrum
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
120 121 122Long itude (E )
2 2
2 3
2 4
2 5
La
titu
de
(N
)
75 TREIRS Stations650 Free-Field Stations
Select a “Site”Select a “Site”
Determine theDetermine the
““Dominant Dominant Earthquake”Earthquake”
for this sitefor this site
Dominant Earthquake :Dominant Earthquake :
Hazard-consistent Hazard-consistent MagnitudeMagnitude
Hazard-consistent Hazard-consistent Distance Distance
Liquefaction Assessment &Liquefaction Assessment &
Generation ground motion time Generation ground motion time history history
for PBSDfor PBSD
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
Ann
ual P
roba
bili
ty o
f E
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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 EngineeringDepartment of Civil Engineering National Taiwan UniversityNational 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 EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
For Nan-Tou city:For Nan-Tou city:
Consider 2475 year return periodConsider 2475 year return period
The hazard-consistent magnitude : The hazard-consistent magnitude : MMLL=7.2=7.2
The hazard-consistent distance: The hazard-consistent distance: R=25kmR=25km
This is consistent with the Chi-Chi earthquake
induced by Chelungpu Fault
The phase spectrum obtained from the ground motion data of The phase spectrum obtained from the ground motion data of
Chi-Chi earthquake can be used to simulate spectrum consistent Chi-Chi earthquake can be used to simulate spectrum consistent
ground motion. ground motion.
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
1 10 100 1000D is tan ce (KM )
1.0E -004
1.0E -003
1.0E -002
1.0E -001
1.0E +000
1.0E +001S
pe
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l Acc
ele
ratio
n(g
)
Sas (0.3)
Sal(1 .0 )
PG A
A ttenuation C urveD ata: M =7.0 , H=10KM
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32
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f (M,R)SA(g) y
Case C1 C2 C3 C4 C5
PGA(g) 0.0036944 1.7537666 2.0564446 0.1221955 0.7831508
Sas(g) 0.0097360 1.7348416 2.0857212 0.1136533 0.8003162
Sal(g) 0.0027914 1.7730463 2.0419005 0.1154175 0.7713924
Attenuation equation for
PGA,
Sa(T=0.3 sec),
Sa(T=1.0 sec),
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
SD1
T0 1.0
SaD=SD1/T
Period (sec) 0.2T0
SDS
0.4SDS
Des
ign
spec
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SaD
T0=SD1/ SDS
0.4SDS
2.5T0
Design acceleration response spectrum developedDesign acceleration response spectrum developed
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5.2;4.0
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2.0;
2.0;/34.0
TTS
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D
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0
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
),()(~
10 RMSCCestimatedS aa
Modification with Site AmplificationModification with Site Amplification
SSD
S1D
T0.2T0 1.0T0 0.2T0 1.0T0
D
SDS
SD1
T
SaD=SD1/T
SDS = Fa SSD
SD1 = Fv S1D
120.0 120.5 121.0 121.5 122.0 122.5
Longitude,(E)
22.0
22.5
23.0
23.5
24.0
24.5
25.0
Lat
itu
de,
(N)
7.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.03
1999/9/21 EarthquakeObserved(Sal)
050100150200250300350400450500550600650700750800850900950
120.0 120.5 121.0 121.5 122.0 122.5
Longitude,(E)
22.0
22.5
23.0
23.5
24.0
24.5
25.0
Lat
itu
de,
(N)
7.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.03
1999/9/21 Earthquake
050100150200250300350400450500550600650700750800850900950
¸gRTD´ú¯¸¸ê®Æ×¥¿«á¤§µ²ªG(Sal)
EstimationEstimationObservationObservation
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
Chi-Chi Earthquake: Spectral Acceleration at T=1.0 Chi-Chi Earthquake: Spectral Acceleration at T=1.0 secsec
120.0 120.5 121.0 121.5 122.0 122.5
Longitude,(E)
22.0
22.5
23.0
23.5
24.0
24.5
25.0
Lat
itu
de,
(N)
7.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.03
1999/9/21 Earthquake
050100150200250300350400450500550600650700750800850900950
¹w´ú¼Ò¦¡¤§µ²ªG(Sas)
120.0 120.5 121.0 121.5 122.0 122.5
Longitude,(E)
22.0
22.5
23.0
23.5
24.0
24.5
25.0
Lat
itu
de,
(N)
7.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.037.03
1999/9/21 EarthquakeObserved(Sas)
050100150200250300350400450500550600650700750800850900950
EstimationEstimationObservationObservation
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
Chi-Chi Earthquake: Spectral Acceleration at T=0.3 sec
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
Distribution of spectral acceleration (based on township Distribution of spectral acceleration (based on township unit)unit) at design level with return period of 2475 yearat design level with return period of 2475 year
DSS (T=0.3)
DS1 (T=1.0)
■ ︰ 1.0g■ ︰ 0.9g■ ︰ 0.8g■ ︰ 0.7g
■ ︰ 0.55g■ ︰ 0.50g■ ︰ 0.45g■ ︰ 0.40g
120 121
23
24
25
Longtitude(o)
La
titu
de
(o )
Epicenter
0 50 100-500
0
500
Time(sec)
Acc
(gal)
Synthesize
-500
0
500
Acc
(gal)
EW component
0 50 100-500
0
500
Time(sec)
Acc
(gal)
NS component
0 50 100-500
0
500
Time(sec)
Acc
(gal)
Synthesize
-500
0
500
Acc
(gal)
EW component
0 50 100-500
0
500
Time(sec)
Acc
(gal)
NS component
0 50 100-400
0
400
Time(sec)
Acc
(gal)
Synthesize
-400
0
400
Acc
(gal)
EW component
0 50 100-400
0
400
Time(sec)
Acc
(gal)
NS component
0 50 100-300
0
300
Time(sec)
Acc
(gal)
Synthesize
-300
0
300
Acc
(gal)
EW component
0 50 100-300
0
300
Time(sec)
Acc
(gal)
NS component
0 50 100-100
0
100
Time(sec)
Acc
(gal)
Synthesize
-100
0
100
Acc
(gal)
EW component
0 50 100-100
0
100
Time(sec)
Acc
(gal)
NS component
0 50 100-400
0
400
Time(sec)
Acc
(gal)
Synthesize
-400
0
400
Acc
(gal)
EW component
0 50 100-400
0
400
Time(sec)
Acc
(gal)
NS component
TCU052 TCU045
TCU129
KAU047
CHY028
TCU202
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
0 20 40 60-0.1
0
0.1
xj(t)
j=-3
0 0.5 1 1.5 20
0.5
1
1.5
Xj(f)
0 20 40 60-0.5
0
0.5
j=-2
0 0.5 1 1.5 20
0.5
1
1.5
0 20 40 60-0.5
0
0.5
j=-1
0 0.5 1 1.5 20
0.5
1
1.5
0 20 40 60-1
0
1
Time (sec)
j=0
0 0.5 1 1.5 20
0.5
1
1.5
Frequency (Hz)
0 20 40 60-0.5
0
0.5
xj(t)
j=1
0 1 2 3 4 50
0.5
1
Xj(f)
0 20 40 60-0.5
0
0.5
j=2
0 1 2 3 4 50
0.5
1
0 20 40 60-0.2
0
0.2
j=3
0 5 10 150
0.1
0.2
0 20 40 60-0.1
0
0.1
Time (sec)
j=4
0 5 10 15 200
0.05
0.1
Frequency (Hz)
ExampleExample
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
)(1)(
1
)( j
Rjj
tgr
)(
2)(
2
)( j
Rjj
tgr
)(
1
j )(
1
j )(
2
j )(
2
j
j= -3 26.57 0.131 9.31 0.177
j= -2 18.91 0.196 3.22 0.357
j= -1 7.86 0.411 3.73 0.349
j=0 1.92 0.730 0.70 0.729
j=1 3.34 0.588 4.01 0.289
j=2 6.28 0.432 6.49 0.167
j=3 3.97 0.546 9.94 0.068
j=4 3.64 0.559 2.07 0.448
)(
2
)(1
)(2
)(
)(1
)(
,
,j
j
RRM
RRMjj
tgr
jjtgr
120 121 122Longitude (E )
2 2
2 3
2 4
2 5
La
titu
de
(N
)
75 TREIRS Stations650 Free-Field Stations
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
0.05 0.1 0.5 1 5 100
100
200
Period(sec)
Sra
nd
ard
de
via
tion
[σtg
r](s
ec)
△ 200km △ 100km △ 50km
0
100
200
68101214
Ave
rag
e [μ
tgr]
(se
c)
△ 200km △ 100km △ 50km
Scale factor j
R=50kmR=25kmR=10km
R=50kmR=25kmR=10km
Average and Standard Deviation of tgr
)(
2
)(1
)(2
)(
)(1
)(
,
,j
j
RRM
RRMjj
tgr
jjtgr
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
40 60 80 12020
30
40
60
80100
j=-3
t g
r (sec)
R (km)40 60 80 120
20
30
40
60
80100
j=-2
R (km)40 60 80 120
20
30
40
60
80100
j=-1
R (km)40 60 80 120
20
30
40
60
80100
j=0
R (km)
40 60 80 12020
30
40
60
80100
j=1
t g
r (sec)
R (km)40 60 80 120
20
30
40
60
80100
j=2
R (km)40 60 80 120
20
30
40
60
80100
j=3
R (km)40 60 80 120
20
30
40
60
80100
j=4
R (km)
40 60 80 12046
10
20304060
100
j=-3
t g
r (sec)
R (km)40 60 80 120
46
10
20304060
j=-2
R (km)40 60 80 120
46
10
20304060
j=-1
R (km)40 60 80 120
46
10
20304060
j=0
R (km)
40 60 80 12046
10
20304060
j=1
t g
r (sec)
R (km)40 60 80 120
46
10
20304060
j=2
R (km)40 60 80 120
46
10
20304060
j=3
R (km)40 60 80 120
46
10
20304060
j=4
R (km)
Example
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
0.0 0.5 1.0 1 .5 2.0 2 .5
T (sec )
0.0
0.5
1.0
1.5
Sa(
g)
D e s ign (S 1 )
O rig in a l E Q (T yp e1 )
C a m p atia b le E Q
0 5 10 15 20 25 30 35 40 45 50 55 60Tim e(sec)
-500
-250
0
25 0
50 0
Gro
und
Mot
ion
(g) Type1
O rig inal EQ
0 5 10 15 20 25 30 35 40 45 50 55 60
T im e(sec)
-500
-250
0
250
500
Gro
und
Mot
ion
(g) Type1
C am patiable EQ
Original Ground Motion
Spectrum-consistent Ground Motion
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
0 .0 0.5 1 .0 1 .5 2.0 2 .5
T(sec)
0 .0
0 .5
1.0
1 .5
Sa(
g)
D e sign(S 1)
O rig ina l E Q (Type3)
C a m patiab le E Q
0 5 10 15 20 25 30 35 40 45 50 55 60
T im e(sec)
-500
-250
0
250
500
Gro
und
Mot
ion
(g)
Type3
O rigina l E Q
0 5 1 0 1 5 2 0 2 5 3 0 3 5 40 4 5 50 5 5 60
Tim e(sec)
-5 00
-2 50
0
2 50
5 00
Gro
und
Mot
ion
(g) Type3
Cam patiab le E Q
Original Ground Motion
Spectrum-consistent Ground Motion
Department of Civil EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University
ConclusionsConclusions1. A Procedure for generating “Dominant Earthquake” grou
nd
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 assessment in in
engineering problem,engineering problem,
4. The generated uniform hazard accelerogram representing 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 EngineeringDepartment of Civil Engineering National Taiwan UniversityNational Taiwan University