department of civil engineering national taiwan university

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


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


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


k

kk

kk pyYME

pyYMEpM

/))((

))(()(

0

00

k

kk

kk pyYE

pyYEp

/))((

))(()(

0

00

An

nu

al

Pro

ba

bil

ity

of

Ex

ce

ed

aa

nc

e

Hazard-Consistent Magnitude

Site A

p0

0pM

)()(),)(( 0 ikiki j

jikk PmPmpyYP

Develop Hazard-Consistent Develop Hazard-Consistent MagnitudeMagnitude and and DistanceDistance


Spectral Acceleration, Sa

An

nu

al

Pro

ba

bil

ity

of

Ex

ce

ed

an

ce

Period, T

Structural Period, T

․․

․

․․

․․

․ ․

․

Sp

ec

tra

l A

cc

ele

rati

on

, S

a

Return Period =475 yr

Return Period =2475 yr

Uniform Hazard Response Spectrum

Seismic Hazard Analysis

(based on Spectral Acceleration Attenuation Form)


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


)(

2

)(1

)(2

)(

)(1

)(

,

,j

j

RRM

RRMjj

tgr

jjtgr

M

j

N

kjkjk tatx

1

1

0

Wavelet Formulation

jka : wavelet coefficient: analyzing wavelet tjk

(1) Time history of j-th component

M

jjkjkj tatx

1

ktt jjkj 22 2

,

Meyer’s mother wavelet is used

A Method to Identify Wavelet Coefficients using Phase Spectrum


0.1 0.5 1 5 100

10

20

30

40

Gro

upe

dela

y ti

me

t gr(ω

) (s

ec)

Period(sec)

dt=0.01

TfT jj 3232 2

j=0

j

j=16

N=217 ＝ 131072

Wavelet decomposed wave

d

dtgr Group Delay Time


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

0.05

0.1

0.15

tgr

f

j=09

t-distribution (=3)

Gauss-distribution

2

12

21 xxf X

2

2

1exp

2

1

x

xf X

t-distribution

Gauss-distribution


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


jN

ij

ij

grjtgr N

t

1

jN

i

jtgri

jgrj

jtgr t

N 1

22 1

Average Standard deviation

d

dtgr

)(

2

)(1

)(2

)(

)(1

)(

,

,j

j

RRM

RRMjj

tgr

jjtgr

Substitute hazard consistent magnitude & distance

))(()( 00 pyYMEpM ))(()( 00 pyYEp

Meyer Wavelet Transformation

x(t) xj(t) XJ()J()

AJ()

tjgr()

jtgr

jtgr

Fourier Transformation

tjgr()=J()/

Mean Value jtgr ：

Central arrival time

Standard Deviation jtgr

Duration

dtttxa

fktt

tatxtx

kjkj

jjjj

kj

j j kkjkjj

*

,,

22/

,

,,

3

2

3

2;22

)()()(

Time History Analysis:Time History Analysis: Modeling of Phase Spectrum



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


Ann

ual P

roba

bili

ty o

f E

xcee

danc

e10

-4

1

0-3

1

0-2

1

0-1

1

.0

Hazard Consistent Magnitude, M Hazard Consistent Distance, D

Return Period: 475 year

Return Period: 2475 year

Hazard Consistent Magnitude & Distance

at Nan-Tou City


The “Dominant Earthquake”

for Nan-Tou city will be

induced by Chelungpu Fault

⋆

Nan-Tou City

(Radius=25km) Chelungpu Fault


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.


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

ctra

l Acc

ele

ratio

n(g

)

Sas (0.3)

Sal(1 .0 )

PG A

A ttenuation C urveD ata: M =7.0 , H=10KM

)](exp[

32

541aMa MaaRea

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),


SD1

T0 1.0

SaD=SD1/T

Period (sec) 0.2T0

SDS

0.4SDS

Des

ign

spec

trum

SaD

T0=SD1/ SDS

0.4SDS

2.5T0

Design acceleration response spectrum developedDesign acceleration response spectrum developed

usingusing DSS and 1DS

0

001

00

00

5.2;4.0

5.2;

2.0;

2.0;/34.0

TTS

TTTTS

TTTS

TTTTS

S

DS

D

DS

DS

aDDS

D

S

ST 1

0


),()(~

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


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


Chi-Chi Earthquake: Spectral Acceleration at T=0.3 sec


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



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


)(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


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


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


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


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


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 engineering national taiwan university

Documents

hazardconsistent distance

earthquake engineering

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modeling of phase spectrum

different return period

engineering problem

attenuation equation

national taiwan university