半経験的波形合成法による1976年中国唐山地震(M_s 7.8)の震央域における強震地動の推定(梗概)

lxt

!}

UDC:550.34{100)

Journal

ol

StTuctural

and

Construction

EngLneering

(Transachons

oi

AIJ)

No.

407,

January,

1990

_rg4O7e

HdyptN\ftptreXas"vaEM

･199Off

₁

_R

ESTIMATION

OF

STRONG

GROUND

MOTION

IN

EPICENTRAL

REGION

OF

THE

1976

TANGSHAN,

CHINA,

EARTHQUAKE

_(M,

_7.

₈₎

BY

SEMI-EMPIRICAL

METHOD

by

KAZUO

DAN',

TAKAHIDE

WATANABE"

and

TEIJI

TANAKA"',

Members

of

A.I.J.

1.

Introduction

The

1976

Tangshan

earthquake

of

M,

7.

8

caused

huge

damage

to

northeast

China

and

it

enhanced

the

development

of

earthquake-resistant

design

of

structures

in

China,

There

have

been

many reports on

this

earthquake

with regard

to

loss

of

life,

damage

to

_structures

and

_grounds,

the

source mechanism, seismic

activities,

crustal structures, and so

on,

However,

few

investigations

have

been

_performed

to

estimate

the

characteristics of

the

strong

_ground

motion

in

the

epicentral region

by

seismological

or earthquake-engineering approaches,

although

they

_provide

better

guidelines

for

the

earthquake-resistant

design

of structures.

Dan

et at,

(1989

a,

1989

b)'i･'2,

based

on an approximate source spectrum

for

_the

far-field

shearwave,

_proposed

a semi-empirical method

for

synthesizing

earthquake

_ground

motions using small-event records as

Green's

functions

'

They

_simulated

the

far-field

_{accelerograms}

_from

the

main shock of

the

Tangshan

earthquake

by

using

the

records of

its

second

largest

_{aftershock of}

_Ms

6,

9

in

order

to

show

the

applicability

of

their

method

to

an earthquake with a

'

magnitude _{of about}

₈

_and

to

_obtain

_the

_appropriate

_fault

_models

_for

_the

_{main shock.}

_It

_{was concluded}

_that

_the

peak

accelerations,

the

durations,

_and

the

spectial characteristics of

the

accelerograms were simulated well

by

the

semi-empirical _method

_and

_that

_the

_appropriate

fault

_{models were obtained among}

_clifferent

_source

parameters

that

were

determined

from

iow-frequency-motion

_analysis

in

_seismology.

In

this

paper,

the

accelerograms

in

the

epicentral region of

the

1976

Tangshan

earthquake

are estimated

by

using

the

records of several

small

aftershocks with rnagnitudes of about

5

which were

observed

in

the

damaged

area,

In

order

to

airive at

the

reason

for

_the

huge

damage,

the

_peak

v.alues of

the

simulated accelerograms are

compared

with

those

evaluated

by

empirical

formulas

that

were obtained

from

other

large

earthquakes.

The

durations

_and

_the

acceleration _{response spectra}

_of

_the

_{synthesized motions}

_are

_{also compared with}

_those

_for

_{some records}

observed

in

the

epicentral

_{regions of}

the

1971

San

Fernando,

California,

earthquake,

the

1979

Imperial

Valley,

California,

earthquake, _and

the

₁₉₈₅

Michoacan,

Mexico,

earthquake.

2.

The

1976

Tangshan,

China,

earthquake

A

large

earthquake of

M,

7.

8

(lat.

_39"38'N,

long.

118011'E,

_focal

depth

₁₁

km)*3

_hit

_Tangshan,

_acity

_located

_in

Hebei

Province,

northeast

China,

on

July

28,

1976.

According

to

_the

_State

_{Seismological}

_Bureau

_(SSB)'`,

_the

highest

seisrnic

intensity

on

the

Chinese

scale

was

xx

.

The

area of

intensity

over

X

was

₃₇₀

km2

which represents

58.7

%

of

Tangshan,

and

the

area of

intensity

over

or

was

_1,800

km2

which covers

the

entire

city

and

some neighboring _counties,

The

_seismic

intensity

_on

_the

Chinese

_scale

_is

_generally

_equivalent

_to

_that

_on

_the

_Modified

Mercalli

_<MM)

_{scale, although some}

_differences

_{may arise}

_between

_the

_{characteristics}

_{of structures}

_in

_China

_and

those

in

other countries

to

which

damage

is

observed

to

determine

the

seismic

intensities.

Another

large

_earthquake

Note

:

Seme

_parts

of this_paper were presented at the

Sino-Japan

Conference

on

Seisrnojogical

Re$earch

in

19S9,

Beijing,

China.

'

Ohsaki

ReseaTch

Institute,

Shimizll

Corpoiation,

_M.

Eng.

"

Ohsaki

Research

Institute,

Shimiiu

Cerporation,

Di.

Eng,

i-i

0hsak;

Research

Institute,

Shimizu

Corporatien,

Dr.

Sc.

(Manuscript

receiyed

July

3,

1989;Paper

accepted

November

Z,

1989)

-23-NII-Electronic Library Service

4e,eoN

39.50N

i

i

Ql(Qianan)

YUrrutian)

#2.oV4Ms7.1

i

AR(Airfield)A#3oe

#1

CH

(Changli)

CM(CementMi]1)Ms7,8

Ms6.9

_{rc1:1976,JuL31,Ms5,O'4,Ms5.5'e}

#2:1976,Aug,8,Ms5,1'4,Ms4S'9'

o

50km#3:1976,Aug.15,ML4.8･S

#4:1976,Aug,31,Ms5.5'4,Ms5.6'e

{1)MS7,8,Mo2.0

×

1027dyne･cm

(2)MS7.1,Mo2.0

×

102Sdyne･cm

(3)MS6.9,Mo5,2XI025dyne･crn

(4)MS6.2,Mb4,9

×

1024dyne-em

OYNE-C"lem 1di 10N

lov

]ON

3g,oeN

6.o e.s zo 1,s e.D

117.soE

ns.oOE

118.5'E

119･O"E

_Fig.2

_Relationshlp

_between

_Ms

_and

_Mi

_{of the}

Fig.1

Locations

of the

fault

model

for

the

main shock

(straightsolid

lines),

lg76

Tangshan,

China.

earthquake

aftershocks used as

Green's

functiens

(small

circles) and observation and

its

major afteTshecks.

stations

(solid

triangles).

of

M,

7,

1

(lat.

39"50'N,

long.

118039'E,

focal

depth

10

km)'3

occurred

45

km

away

from

Tangshan

on

the

same

day

15

hours

following

the

main shock,

These

large

earthquakes

caused

tremendous

darnage

to

Tangshan,

killed

242,OOO

persens

and

injured

164,ooo

persons

seriously.

The

big

cities of

Beijing

and

Tianjin

were also severely

affected.

The

damaged

area

exceeded

30,

OOo

km2

and

the

shock

was

felt

in

over ene-third

of

China's

area.

4.

76-million-me

of

floor

area of civil

buildings

(g4

%

of

the

total)

and

6.

71-rnillion-m2

of

floor

aTea of

industrial

buitdings

(80

%

of

the

total>

collapsed or were

extensively

damaged

in

Tangshan.

Municipal

public

faciiities

were

also

seriously

damaged.

No

earthquake･resistant

design

was employed

for

these

buildings

and structures, except

that

a seismic

intensity

of

va

at maximurn was considered

in

the

design

ef a

few

industrial

facilities,

The

direct

loss

of

_property

was

estimated

to

be

8

billien

Yuan

'

RMB

In

the

region of

56

to

400

km

away

from

the

epicenter,

175

accelerograms were recorded

during

the

main shock and major aftershocks of

Ms7.1

and

6.9.

After

the

main shock occurred,

temporary

strong-motion observations of aftershocks

in

the

damaged

area

began

to

operate and

fortunately

obtained

abottt

₁₀₀

records of

_3s

aftershocks

(M,3.5-5.8)

at

five

stations.

Most

of

the

records were observed

by

RDZI-12-66-type

strong-motion accelerograph, whose reliable

frequency

range

is

from

e.5

to

35

Hz

(IEM,

lg86>*5.

Zhang

_(lg88)'fi

estimated

the

effective

_peak

acceleration

in

the

epicentral

region of

the

main shock

by

considering acompiex

inhomogeneous

source model.

He

regarded

the

rectangular

fault

of

the

main shock as an aggregate ofmany circular sub-sources,

The

aveTage

dynamic

stress

drop

of each sub-source was obtained

to

be

206

bars

from

the

Fourier

spectra

_gf

the

accelerograms recorded at

Beijing

Hotel

station.

The

effective

peak

acceleration

in

the

epicentral

region was estimated

to

be

70o-1,

500

Gal

by

considering

the

locality

of

the

average

dynamic

stress

drop

whose

level

was

300

baTs

near

the

hypocenter.

In

his

research,

however,

there

remains uncertainty on

determining

the

distribtttion

of

the

average

dynamic

stress

drop.

3.

Fault

model

tor

the

main

shock

Dan

etal,

(1989

a,

1989

b)'"t

_proposed

asemi-empirical method

based

on

an

approximate source spectrum

for

the

far-field

S

wave

_proposed

by

Brune

<1970)",

one of

the

w-square models, and sirnulated accelerograms

from

the

main shock at

two

st'ations

of

Beijing

Hotel

and

Fengcun

Bridge,

whose epicentral

distances

are

154

and

398

km,

respectively.

They

used

the

records of

the

second

largest

aftershock as

Green's

functions.

After

examination of

416

different

fault

models

that

were

determined

from

the

results of research

by

seismologists,

the

appropriate

fault

models

for

the

main shock were obtained as

follows

:

the

ruptured

fault

width

W

is

15

km,

the

seismic

moment

M,

is

1.

6-2,

1

×

102'

dyne.cm,

and

the

rupture velocity v

is

2,3-2.5kmlsec.

The

rigidity

",

the

S-wave

velocity

B,

and

the

-24-Mo

(1)

(2)e

(3)

C4)

_Ms

Tabiel

Source

_parameters

_of

the

main shock and

its

afteishecks used as

Green's

functions.

Main

shock

6)

Aftersheck#1

(Jul.31)

Aftershock

#2

(Aug.

8)

Aftershock#3

(Aug.

15)

Aftershock#4

(Aug.

31)

Medium

Ms

7.85.0

5.5

5.1

4.8

4.2

4,6

5,5

5,6

Mo

1}[dyne-cm]

2.0

×

1027

1.0

×

1023

5.6

×

1023

1.4

×

1023

5.0

×

1022

6.3

×

lo21

2.5

×

lo22

-5.6

×

lo23

7.9

×

1023

Rigidity

_p

3.5

×

10il

dyneXcm2

Density

_p

2.9

_grarnlcm3

L

2)[km]

901.481,592,632.831.661.791.181.27O.59O.63O.931.012.632.832,953.18

IV3)

D4}

[km]

_[cm]

15

423

O.74

26.1

O.80

22.5

1.32

46.4

1.42'

40.0

O.83

29.3

O.89

25.2

O.59

20.7

O.63

17.9

O.29

10.4

O,32

9.0

O,47

16,5

O.50

14.2

1.32

46.4

1.42

40.0

1.48

52.0

1.59

44,9

S-wavevelocity

_P

Qualityfactor

Q

Oe

5)

[bar]

63

78

63

78

63

78

63

78

63

78

63

78

63

78

63

78

63

3.5

krnlsec

1,OOO

al5eg3ig:,`,//,5,".2'.?l5,a?'Tk,LLfo\:1:(Fig',:kV,-'.3g,2{,?':"hZelL,2',,D,i.",ctlgf,nvh,5L,T,w,:,fi,le:.tige,?8Ee.Sit?･g,o(LZ8,R,ash'

ftISutlhterrftirdeeeinfoSrfeilleCIItieanintOsfi5Illill.la6t)eAtfhteerfaDrafineeltdaalC.

::6esrgObg)r.a2m.

s･

The

latter

is

taken

after

the

stress

drop

of

the

quality

factor

Q were

3,

5

×

10ii

dynelcmZ,

3.

5

km/sec,

_and

_500,

_{respectively.}

_The

_{rupture of}

_the

_fattlt

was assumed

to

_propagate

radially

from

the

_hypocenter,

_The

_location

_of

_the

_fauit

_is

_shown

_by

_the

_{straight solid}

_lines

_in

_Figure

1,

The

fault

length

L

is

45

km

in

a

direction

of

N

61.

_00E

and another

45

km

_in

_adireetion

_of

S

_37.

_8eW.

_We

_adopt,

_in

_this

paper,

ML=

2,

O

×

102T

dyne.cm

_{and v[=2.}

₃

kmlsec

_{as one}

_of

_the

_{most appropriate}

_fault

_models

_for

_the

_{main shock.}

_In

this

case,

the

average

dislocation

D

and

the

st;ess

drop

_Aa

are evaluated

to

be

423

cm and

₆₃

bars,

We

should note

here

a rough

index

of error

for

our method

because

it

will

be

applied

_to

_the

epicentral region.

Taking

only

the

terms

of

intermediate-field

transverse

components

_generated

by

a

double-couple

force

(Aki

&

'

Richards,

1980)'S,

the

Fourier

spectrum of

the

displacement

can

be

limited

by

'

2

Mh(w)

3Mo(of

11

M6{w)

4mpa!r!

+

4rrnetrt

=12nAs2r2'

(1)

where _a

is

the

P-wave

_velocity,

Mh(w)

is

_the

Fourier

_transform

_pair

_of

_the

_{time-dependent}

_seismic

_moment

_Mi(

t),

and a

is

assumed

to

be

equal

to

Vg'B.

Since

the

Fourier

spectrum of

the

far-field

transverse

components can

be

written

by

[wM,{w)]1[4

rrl)E"'r],

the

error

for

the

approximation of

treating

the

records as

far-field

motions

can

be

limited

by

(11B)1(3

rw).

Here,

the

common vector

to

the

intermediate-field

motion and

the

far-field

rnotion

is

neglected.

4.

Estimation

of

strong

_ground

motion

in

the

epicentral

region

In

Figure

1,

the

solid

triangles

indicate

five

temporary

observation

stations,

The

seismic

intensities

on

the

Chinese

scale were reported

to

be

-

at

Tangshan

Cement

Mill

(CM,

lat.

_39e38'30"N,

long,

_118011'29"E)

_station,

X

at

Tangshan

Airfield

(AR,

lat.

39039'33"N,

long.

_118008'17"E)

_station,

_vr

_at

_Qianan

_{QI,

_lat.

_39057i21"N,

_Iong,

118043'52"E)

and

Changli

(CH,

lat.

39045'Z9"N,

long.

119005'44"E)

stations, and

VI

at

Yutian

(YU,

lat.

_39th53'02"

N,

Iong.

ll7044'54"E)

statien.

The

epicenters

of

the

aftershecks used as

Greenis

functions

are

aiso

_plotted

by

small circles.

Two

different

M,

of aftershocks

#1,

#2

and

#4

are

listed,

which are

taken

from

two

different

references

(SSB,

1982

and

Zhang

_{et al. ,}

1980)"'

'O.

_M,

of aftershock

#3

is

Iisted

because

its

M,

was not [eported,

Here,

we adopt

_4,

₆

and

4.

2

as

the

upper and

lower

limits

of

_M.

of

aftershock

#3

based

on

the

relationship

between

Ms

and

ML

--

₂₅

-NII-Electronic Library Service

ERL20 o-20GFth.3D D-30GnL90 e-9DGM 2S D-25GRL H

o

-e

(a)

CM

_{Aug.

15,

distance

18.8

km,

EW

component)

Peak

Acc.

21.2

Gal

(b)AR(Jul.31,distanee29.1krn,EWcomponent)

33.1

Gal

{c)

Ql

(Aug.

31,

distance

17.7

km,

EW

component)

97,4Gal

(d)CH(Aug.31.distance36.6km,EWcemponent)

26.4Gal

(e)

YU

(Aug.

8,

distance

68.7

krn,

EW

cornponent)

8,21

Gal

GAL-SEC

l.O

o.i

10.0

L.O

'D.1

CM

-t

Ms4.6

Ms4,2

10.0

1.0

10.0

LO

o.t

I.O

o.t

Ms

5,5

Ms

_5.0

AR

Ms

5.6

QI

Ms5.5

MS

5.6

MS

5.5

CH

CSEC)

Ms5.1

Ms

4.8

yv

6

t.o

lo,o

HZ

Fig.

3

Observed

accelerograms used as

Green's

functions

and their

Fourier

amplitude spectra.

The

srnooth

lines

on

the

right aremodeled spectra

for

each

M,

obtained

by

different

researcheT$*4･ '9.

_The

_solid

lines

_are

for

_the

_effective

stress of

78

bars

and the

dotted

lines

foT

63

bars.

of

the

earthquakes

in

the

Tangshan

area.

In

order

to

determine

the

source

_parameters

for

each aftershock, we

assume

the

relationship

between

Ms

and

M6

which

is

described

by

the

form

of

log

Mh=1.5M,+a.

Using

the

data

of

the

main shock ancl

the

three

major

aftershocks, we obtain

the

relationship of

log

M,(dyne.cm)=1.

5

M,+15.

5

by

the

least

squares method.

The

data

and

the

result are shown

in

Figure

2.

We

adopt

two

effective stresses of

78

bars

and

63

bars.

The

former

is

taken

after

the

stress

drop

of

the

aftershock of

M,6.9,

which was used as

a

Green's

function

to

slmulate

the

far-field

accelerograms.

The

latter

is

taken

after

the

stress

drop

of

the

fault

model

for

the

main _shock,

Here,-the

_effective

stress a.

is

assumed

to

be

equal

to

the

stress

drop

Aa.

All

source

pararneters

for

each

afteTshock can now

be

determined,

because,

given

Ms

and

a,,

Mo

and

W

are calculated

by

log

Mo==1.5Ms+15.5

and

W=3

Mol

-Aa

,

Here,

L

and

Aa

are assumed

to

be

equal

to

2

W

(Geller,

1976)'tO

and

(2"D)1(zW)

(Kanamori

&

Anderson,

1975)'ii.

The

source

_parameters

of

the

main shock

and

its

aftershocks used as

Green's

functions

are summarized

in

Table

1.

The

acceleiograms

in

Figure

3

are chosen

for

each

station on condition

that

the

small earthquakes used

as

Green's

functions

occurred on Qr near

the

fault

_plane

of

the

main shock

and

that

the

accelerograms

have

sufficient

quality

for

the

simulation.

All

of

them

are

EW

components.

The

distances

to

the

hypocenter

of each

aftershock

and

to

the

fault

p}ane

of

the

main shock are

18.

8

and

5.

0

km

for

CM,

29.

1

and

6.

9

km

for

AR,

17.

7

and

16.

1

km

for

QI,

36.

6

and

39.

4

km

foi

CH,

and

68.

7

and

46.

8

km

for

YU.

On

the

right,

the

Fourier

amplitude

spectra

of

the

accelerograms are compared with

the

modeled

spectra

(Dan

et aL ,

1989

a)'!

for

each

Ms

and

each

a,,

The

quality

factor

of

the

medium

Q

is

assumed

to

be

1,OOO.

The

predominant

frequencies

are

from

1

to

20

Hz.

The

medeled spectra represent

the

observed ones well with

distances

from

17.

7

to

68.

7

km.

An

example

of

the

estimated accelerograms

for

each station

is

shown

in

Figure

4

with

its

shortest

distance

to

the

fault

plane

of

the

main shock.

It

is

the

largest

result among

four

cases.

For

the

baseline

correction,

the

synthesized accelerograms are

low-cut

with a cosine-type

function

from

O,

3

to

O.

6

Hz.

The

peak

acceleration of station

CM,

for

---

26

GRL

1]oo

o-llOO BA. 1]OO o-1!De

GRL

42e

o-4?o

snt

160

D-160em

2SO

o-2EO

fo)AR(distancetothefau1tis6.9km,EWcornponent)

1,188Gal

(c)

QI

{distance

to

the

fault

is

16.1

km

EW

component)

422

Gal

(e)

YU

Cdistance

to

the

fau1t

is

46.8

krn,

EW

component)

266Gal

tSEC) 6

Fig.4

Largest

example among

fouT

_{estimated accelerogTams}

for

each station

in

the

epiccntral region of

the

lg76

Tangshan

earthquake.

For

the

baseline

correction, thesynthcsized accelerograrns are

tow-cut

with a cosine-type

function

from

O.3

te

O,6Hz,

iwhich

the

_seismic

intensity

was reported

to

be

XI

,

is

about

1,

200

Gal

and

the

duration

of

the

strongest

part

is

about

10

seconds.

Further

characteristics will

be

discussed

in

the

next section.

5.

Discussion

(i)

Peak

acceleration

Four

different

results _{were obtained}

for

_{each station}

because

_of

two

different

M,

and

two

clifferent

a..

The

peak

accelerations aie summarized

in

Table

2.

The

mean value and

the

mean value ±one standard

deviation

range

in

Gal

is

_{[643-857-1,142]}

fer

CM,

_{[464-723-1,127]}

for

AR,

_{[279-343-423]}

for

_QI,

_{[115-137-164]}

for

CH,

ancl

[147-195-260]

for

YU.

Here,

we assume a

log-normal

probability

distribution

for

peak

accelerations which

is

described

by

P(a)=n

qaexp[-g/n-//-iP)'-].

(2)

The

two

_parameters

of

_p

and

_q

are

determined

by

P=t

te.,

ln

Ai,

(3)

q2=t

l:.

i,

{ln

At-

p)t.

(4)

Here,

A,

is

the

_synthesized

_peak

_{acceleration and n}

is

4,

The

range

in

Table

2

corresponds

to

[exp

<p-q),

exp

(p),

exp

(p+q)].

Several

theoretical

studies

have

been

_performed

concerning

the

movement of

the

ruptu,ring

fault

itself.

Brune

(1g7o)*'

formulated

the

maximum near-source acceleration as

(2

a.)1(irvA

t),

where a.

is

the

effective stress working

on

the

fault,

_p

is

the

density

of

the

medium,

fi

is

the

S-wave

velocity, and

At

is

a small

time

interyal

we

focus

upon.

The

_peak

acceleration of

the

rupturing

fault

itself

can

be

evaluated

to

be

620-1,

240

Gal,

where a.=63

bars,

_p=

2,9gramlcmS,

_P=3.5kmlsec,

and

At=O.1-O,2second.

Kanai

(1983)"2

obtained

the

relationship

between

the

seismic

intensity

on

the

MM

scale and

the

_peak

acceleration

27

-NII-Electronic Library Service

Table2

Peak

acceleration estimated

by

the semi-empiricat rnethod

{n

this study

(EW

component).

Station

Distanco

Intensity

[km]

CMARQICHYU

5,O6.916.139.446.8

XIxVIIVIIVI

Peak

acceleration

l)

[Gall

(571

753

1,067

1,177)

(404

551

1,034

1,188)

(252

320

409

422)

(103

142

149

164)

(139

156

252

266)

Range

2)

[Gal]

[643-857-1,142]

[464-723.1,127]

[279-343-

423]

[115t137-

1641

[147-195-

260}

Kanai

[GaU

1,238

818

236

236

156

3)

'

_Fukushima

_etal.

4)

[Gal]

[336-546-8851

[320-520-843]

[257-417-6T61

[159.257-417J

[138.224.3641

1)

Four

results are obtained

because

two

different

seismic moments and

two

different

effective

stresses

are

assumed

for

each aftershoek used as

Green's

function.

2)

The

range corresponds

to

the

mean and

the

mean ±ene standard

deviation

ef

the

fbur

estimated

peak

accelerations on

Lhe

assumption ofa

log-normal

probability

distribution.

3)

Estimated

values

frem

Kanai's

forrnula

described

by

equation

(5).

4)

E'stirnated

values

from

Fukushima

&

Tanaka's

formula

described

by

equation

(6).

as

Ama.=1.6

×

Ti.1-3

×

loO-LSIMM,

{s)

where

A...

is

the

peak

acceleration

in

Gai,

Tc

is

the

_predominant

_period

at

the

site

in

seconds, and

lk.is

the

seismic

intensity

Qn

the

MM

scale.

The

range of

Ama.,

Tc,

and

Il,.

is

30-330Gal,

O.2-O.9second,

and

5.75-8,

respectively.

Since

the

seismic

intensities

were reported

to

be

XI

for

CM,

X

for

AR,

vr

for

QI

and

CH,

and

V[

for

YU,

the

relationship

_provides

_1.238

Gal

for

CM

(extrapolated),

818

Gal

for

AR

(extrapolated),

236

Gal

foT

QI

and

CH,

and

l56Gal

for

YU,

with a

_predominant

_period

T.

of

O.2second,

Since

the

1940

Imperial

Valley

earthquake of

M,

7.

1,

a number of records whose

peak

accelerations are over

3qo

Gal

have

been

observed

in

the

epicentral regions of earthquakes with magnitudes of _about

7.

Typical

_{examples of}

these

accelerograms aie

the

records observed

during

the

1966

Parkfield

earthquake of

Ms

6.

4,

the

1971

San

Fernando

earthquake of

M,6.6,

and

the

1979

Imperial

VaLley

earthquake of

M,6.9.

The

attenuation relationships of

_peak

accelerations

including

the

data

in

the

epicentral iegions mentioned above were

formulated

by

Joyner

&

Boore

{1981)'iS,

Campbelt

_(1981)'L`,

Fukushima

&

Tanaka

_(1988)'i",

and so on.

Fukushima

&

Tanaka

obtained

the

attenuation relationship of

log

Ama.

==O.41

Ms-log

[R+O.032XIO"'`i"s]-O.O034

R+1.3o,

(6)

where

Ama.

is

the

peak

horizontat

acceleration

in

Gal,

R

is

the

shortest

distance

in

km

from

the

station

to

the

fault

plane,

and

the

standard

deviation

of

the

formula

is

O,

21

in

}og-scale.

The

relationship

provides

the

mean value and

the

mean value ± one standard

deviation

range of

[336-546-885]

forCM,

[320-520-843]

forAR,

[257-417-676]

for

QI,

[159-257-417]

for

CH,

and

[138-224-364]

for

YU.

In

Japan,

on

the

other

hand,

investigations

on

the

strong'ground motion

in

epicentral region

have

been

carried out

by

many researchers.

Okamoto

(1968)'i`

suggested

that

the

upper and

lower

!imits

of

the

_peak

accelerations

in

Gal

should

be

l2M!

and

6M!

with a magnitude

M

varying

from

5.0

to

8.4.

His

results were

obtained

from

field

investigations

of

l4

diffeient

earthquakes, such as

the

behavior

of

tombstones

and

masonry

structures,

damage

analysis of

houses,

and records observed

by

accelefograph.

Omote

etal.

"978)'i'

estimated

the

_peak

accelerations

in

the

epicentrat regions of

₄

earthquakes with magnitudes of

_6.

_5-7.

_3.

They

suggested

that

the

peak

acceleration should

be

limited

by

500-600Gal

for

earthquakes with rnagnitudes

beyond

7.

Hisada

etal.

(]978)'i8,

considering

the

field

investigations,

_pteposed

9

_M'

as an averaged

_peak

acceleration at rock sites

in

the

epicentra] regions.

For

the

upper and

lower

limits

of

the

_peak

accelerations,

693

ancl

347

Gal

are obtained

from

12Me

and

6

M'.

IIere,

the

relation of

M=O.

79

_M,+1.

₄₄

_(Hayashi

&

Abe,

_1984)'tD

is

used

to

transfer

_M,

to

_M,

where

_M

is

a

magnitucle reported

from

the

Japan

Meteorological

Agency

(JMA).

The

average

_peak

acceleration at rock sites

is

evaluated

to

be

520Gal

from

9M2.

The

range of

[347-520-693]

is

two-thirds

of

the

results

for

CM

and

AR.

Conseqllently,

it

can

be

c:oncluded

that

the

pcak

acce]erations

in

the

epicentral region of

the

1976

Tangshan

earthquake were slightly

higher

than

those

for

the

same magnitude and

the

same

distances

obtained or estimated

by

-28-leo

50Ag1.ge.g

2o7gts

10tsg･gsn

2

1

e

:

P

,ZNi>il

r

,

9S.

.te.)s'.i.:.s

eeveo

ee

:::eee

e'

("e

ee

e -e

eve

ee

iX

log,,t=O.31M-e.77

spt..

LU.

×

bui

tte

Tangshan

eatthquake

3

4

5

6

7

8

Magnitu'de

Fig.5

Cornparison

ef the

_duiatien

of

ground

rnotion as a

function

of rnagnitude.

The

closed circtes and

the

breken

line

are

taken

from

Hisada

&

Ando

_(lg76>'22.

The

open ciTcles are obtained

frorn

the

accelerograms

fof

Pacoima

Dam

(PD)

of the

1971

San

Fernande

earthquake of

M,

6.

6,

Bonds

Comer

_(BC)

of the

1979

Imperial

Valley

eaithquake of

M,6.9

and

La

Union

(LU)

of

the

1985

Michoacan

earthquake of

Ms8.1.

Michoacan

earthquake of

M.

8.

1.

The

durations

of

the

those

for

the

earthquakes with

the

sarne magnitude.

(iii)

Acceleration

response spectrum

The

acceleration response spectra

for

the

estimated wave

forces

which should

be

applied

to

structures.

is

from

O.

05

to

5

seconds.

In

Figure

_6,

(a)

spectra

for

9I

and

CH.

The

three

solid

lines

for

CM,

standard

deviation.

highsecond.

other

researchers.

(ii)

Duration

of

strong

ground

motion

According

to

_Jennings

_{et aL}

(1968)'!O,

_the

_envelope

function

of acceleTograms can

be

expressed

by

E(t)=

o

ostst.

A(t-tD'1(tb-tal'

t.StStb

_A

(7>

t,S.tS

t.

Aexp[-B{t-t.)]

t,$tStd･

when

the

seismic wave reaches

the

is

the

time

when

the

strong

part

of

the

motion

e motion

and

the

exponential

decay

of

the

motion

e of

the

strong

part,

and

Bis

the

for

the

exponential

decay.

The

_parameters

A

and

B

are

determined

by

the

least

squares

,

1989)'t],

and,

in

this

paper,

time

of

the

motion

is

defined

by

_t.=!

The

duration

ef

the

strong

_ground

by

td'ta･

compares

the

duration

as a

function

of

The

closed circles and

the

broken

line

are

isada

&

Ando

(1976)"Z2.

The

open circles

from

the

accelerograms

for

Pacoima

_Dam

1971

San

Fernando

earthquake of

Ms

6.

_6,

(BC}

of

the

₁₉₇₉

_Imperial

_Valley

.g,

and

La

Union

{LU)

of

the

₁₉₈₅

are

found

to

be

comparable

to

Here,

t.

is

the

time

statlon,

tb

starts,

t,

is

the

time

when

the

strong

_part

of

th

termlnates

starts,

A

is

the

amplitud coefficient

ta,

tb,

tc,

tnethod

_(Dan

_&

_Watanabe

the

termination

(iog

10)IB+

t..

motion

is

obtained

Figure

5

magnitude.

taken

_from

_H

are obtained

<PD)

of

the

Bonds

Corner

quake

of

Ms6

synthesized accelerograms

motions

are shown

in

Figure

6,

They

represent

_the

seismic

The

damping

factor

h

is

O.

05

and

the

range of

the

natural

_periods

shows

the

spectra

forCM,

(b)

the

spectra

ferAR

and

YU,

and

{c)

_the

AR

and

9I

are

the

mean value and

the

mean value

+

one

The

dotted

lines

for

YU

and

CH

are

the

mean values.

The

synthesized result

for

CM

shows

a value

over

2,

OOO

Gal

and

that

for

AR

shows a value over

1,

500

Gal

in

the

_period

range

between

O.

05

and

_O.

_Is

The

estimated acceleration response spectra

for

the

five

stations show ahigh

level

in

the

period

range

from

O,

Os

to

o.

15

second.

These

spectral

characteristics are

due

to

_the

_properties

of

the

aftershocks used as

Green's

functions

Since

we use

three

different

aftershocks,

this

tendency

should

be

considered common

to

_the

earthquakes

in

the

Tangshan

area.

Figures

(d),

(e)

and

(f)

compare

the

acceleration response spectra

for

CM

and

AR

with

those

for

PD,

BC

and

LU,

The

response

spectra

for

CM

and

AR

show

higher

values

than

those

for

PD

'and

BC

in

the

_period

raage

below

o.

15

second.

Hosvever,

they

are

half

of

the

response spectra

for

PD

and

BC,

and

twice

of

that

_for

_LU

_in

the

_period

range

between

O.2

and

O.8second.

Subsequently,

not only

the

large

epicentral region with

its

length

of

90

km

but

also

the

large

force

which acted on

the

_{structures with}

shoTt

natural

_periods

is

thought

to

have

caused

the

huge

damage

_in

and around

Tangshan.

This

is

because

most of

the

structures were _{made of}

brick

_whose

_natural

_periods

_{were about}

_O.

₁

_{second, and}

_because

_no

earthquake-resistant

clesign

was considered

for

them

before

this

earthquake oceurred.

-29-NII-Electronic Library Service

GgL50co

40co 3000

2Cmo

:coo

e o.esGRL4eoo3Sconm25[n20od15001ooO suo D D,OS

Fig.6

(a)'

+e

CM

-as.l

a.!

caL

GRL

4ooo l7se !DDa t250 2sea loao 2000 7sc tsoa

soo

loeo

25D

500

o o

o.s t.e zo s.o o.os o.1

o.2

o.s

1.o ?.o s.o a.es o.i o.2 a.s 1.o

2.e

s.osEc

eAL

･

GAL 4eoo 4eDo 2saD

2scx

2aoo

2mm tseo tsoo Lose 1ouo

soa

seo o o

o.s L.o za

_,s,o

a.as o.l o.2 o.s 1.o za s.o e.os o.1 o,2'

o.s

1.o

zo

s.e sEc

of

O.

05.

Figures

{a),

(b)

and

(c)

show

the

esized acceleTbgrams.

Figures

(d),

(e}

and

{D

show comparison of

the

spectra

for

CM

and

AR

Valley

earthquake of

M,6.9.

and

La

Union

(LU)

of the

1985

Michoacan

earthquake of

M,8.1,

error

ef

_peak

acceleratien

(c.

o.v.;percentage of

the

standard

deviation

to

the

mean value) of

the

log-normal

eobtained

by

exp{qt)-1

.

From

the

_peak

acceleratiohs

listed

in

Table

2,

the

c.o.v.

'

29%

for

CM,

47%

for

AR,

21%

for

9I,'18%

for

CH,

and

29%

for

YU.

pproximation

of

treating

the

records as

far-field

motions

is

limited

by

(11

fi)l

adopt

the

shortest

distance

to

the

fault

_plane

of

the

main shock as

r

and

the

_predominant

to,

the

lirnitation

of

the

approximation erroi

is

calculated

to

be

41-2,O

%

fer

CM

(here

,O

%

to

20

Hz),

30-1,5%

for

AR,

13-O.

63

%

for

_QI,

5,2-O,

26

%

for

CH,

and

If

we roughly

assume

that

the

limitation

should correspond

to

2

exp

{q')-1

,

the

c.o.v.

due

to

is

obtained

to

be

half

of

the

error calculated above.

inds

of c.o.v.

Ieads

to

the

total

c.o. v. of

36-29

%

for

,

22-21

%

for

QI,

18

%･

for

CH,

and

29

%

for

YU,

It

is

concluded

that

the

deviation

of

the

tieviation

e records as

far-field

motions except

for

the

case ef

CM,

the

nearest station.

or

CM

can also

be

negligible,

however,

when we

take

10

Hz

as

a

representative

peak

points

in

Figure6(a).

picentral

region of

the

1976

Tangshan

earthquake were estimated

by

using

the

records of

es of about

5

which

had

been

observed

in

the

damaged

area,

The

fault

model

foT

the

for

the

simulation of

far-field

accelerograrns, and

the

's

functions

were

determined

from

some

theoreticaL

and

empirical

(e}

+e

t-/

QI

:1,t/'L-o

Q.L O.?

Comparison

of

the

aeceleration response spectra with

the

damping

factor

h

spectra of synth

with those

for

Paceima

Dam

(PD)

ef

the

1971

San

Fernando

eaTthquake of

M,

6.

6,

Bends

Corner

_(BC

₎

ofthe

1979

-ImpeTial

(iv)

Estimation

The

coefficient of variation

probability

distribution

can

b

is

calculated

to

be

Meanwhile,

the

error

due

to

the

a

(3

rw).

When

we

frequencies

of

1-20

Hz

as

41

%

corresponding

to

1

Hz

and

2

4.

4-O.

22

%

for

YU.

the

approximation

Consequently,

the

square root of

the

summation of

the

two

k

CM,

49-47

%

for

AR

synthesized results

due

to

the

uncertainty ef

the

source

_parameters

of

the

aftershock

predominates

over

the

due

to

the

approximation of

treating

th

The

c,o.v,

due

to

the

approximationf

frequency

from

the

6.

Conclusions

The

accelerograms

in

the

e several aftershocks with magnitud

main shock was selected among

the

most appropriate models source

_parameters

for

the

aftershocks used as

Green

relationships.

Based

on

the

resultant estimation

presented

here,

we can conclude as

follows,

O

The

peak

acceleTations

in

the

epicentral region

were

slightly

higher

values

than

those

estimated

for

the

same

magnitude and

the

sarne

distances

from

some empirical

formulas

obtained

by

other researchers.

2)

The

clurations

of

the

strong.ground motions were

comparable

to

thpse

for

the

earthquakes with

-the

same

-

30

magnitude.

_,

3)

The

large

accelerations over

1,

500

Gal

acted

on

the

structures with natural

_periods

shorter

than

o,

ls

in

the

region close

to

the

fault.

'

4)

Temporary

strong-motion observations

of

aftershocks at

the

damaged

area are very useful

for

the

estimation

of

the

strong

_ground

motion

in

the

epicentral region ef

the

main shock.

The

authoJs note

here

that

this

work was

carried

out

as a,joint research of

ORI

(Ohsaki

Research

Institute,

Shimizu

Corporation,

Japan)

and

IEM

(Institute

of

Engineering

Mechanics,

State

Seismological

Bureau,

China).

They

wish

to

express

their

appreciation

to

Dr.

Y.

Ohsaki

_(emeritus

Prof,

of

University

of

Tokyo)

and

Dr,

H.

YaTnahara

of

ORI

andProf.

J.

Xie

and

Pro

£

L.

Xie

ofIEM,

They

are alsograteful

_to

Prof,

Y.

_Yuan,

_DJ.

M.

Zhang

_and

_Mr,

_Q.

Luo

of

IEM

for

their

kind

help

in

the

study

of

the

1976

Tangshan

earthquake,

Reterences

1)

Dan,

K.

,

T.

Watanabe

and

T.

Tanaka

(1989

_a)

:

A

_{semi-empirical methed}

_to

_{synthesize earthquake}

ground

motions

based

on

approximate

far-field

shear-wave

displacement,

JouTnal

of

Structural

and

Constrttction

Engineering

{Transactions

of

AIJ),

No.396,

pp.27-36,

2)

Dan,

K.,

T.

Watanabe

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T.

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(1989b):Synthesis

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_{accelerograms of}

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_Tangshan.

_China,

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(M,

7.

8)

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3)

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'

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5)

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M,

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197G

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Tectonic

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_,H.

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_,

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Y.

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M.

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Acta

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Ie)

Geller,

R.

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Scaling

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_Bulletin

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11)

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_in

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Bulletin

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Vol.54,

No.6,

_{pp,l811-1841.}

I2)

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13)

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lg7g

Imperial

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the

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14)

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Near-source

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15)

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horizontal

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Architectural

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I6)

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'

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_:

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'