入力波の長周期成分が非線形地盤応答に与える影響

Architectural Institute of Japan

NII-Electronic Library Service Arohiteotural エnstitute 　of 　Japan

論

【

文

1

’

●

　

’

　　　

日本建築 学 会 構 造 系 論 文 報 告 集

rg

　q49号

・

1993年 7 月

Journa且of　

S1

【

uct

．

　Consti

，

　Engng

，

　Alj

、

　NQ

．

449

_，

　

July

，

1993

POTENTIAL

　

EFFECTS

　

OF

　

LONG

　

PERIOD

COMPONENTS

　

IN

　

INCIDENT

　

MOTION

ON

　

THE

　

NONLINEAR

　

GROUND

　

RESPONSE

入

力波

の

長 周

期

成分

が

_非線

_{形 地盤}

_応答

に

_与

え

る

影響

Madan

・

B

．

　

KARKEE

＊ ，　

Yoshihiro

　

8

σ

GIM

ひ

R

月 ＊ ＊ ，　

Jun

　

TOBITA

＊ ＊＊ _and

KOf

．

SA

　

TO

＊ ＊ ＊＊

　　　　　　　

カル

キ．

．

一 ・

マ

ダ

ン

B

_，

_杉

村

義

広

，

飛

田

　

潤

，

佐

藤

耕 司

　 The

　

proportion

　of　

the

　seismic 　energy 　

in

　the　

long

　

period

　range 　

is

　

believed

　

to

　

increase

　with 　the

size



of



the



earthquake

・



Considering



that　soft　sites

　

undergo



large



_号

longation



in．

_ground



_period



at

higher

　

level

．

　of　shaking

_，

　

the

　

_presence

　of　

l

』

arge 　

long

　

_period

　cQmponents 　can 　

be

　a　

destructive

　conse

．

quence

．

　

Po

仁elltial　effects 　of　successively 　

increasing

］evels 　of　

long

　

Period

　components 　are　

investi

・

gated

．

　

Response

　of　soft　sites　

is

　seen 　

to

　

be

　subs ピantially 　

influenced

　

by

　

long

　

_period

　components

．

The

　cpnsequences 　of　

deficiencies

　

in

　short 　and 　

iong

　

_period

　components 　

is

_．

also 　

discussed

．

　

Various

nonlinear

．

　

ground

　response 　characteristics 　are　

discussed

　

in

　these　contexts

．

　KegwordS

：

long

　

Period

　comPonents

_，

　reSl）onse 　sPectra 　comPatible 　

incident

　motion

，

　nonlinear 　

₉

アound 　re

−

　　　　　　　　　S）on5e

_，

　

te

ηel　of　exCi

’

tation

_，

_Precl

ρminant 　

Period

　　　　　　　　　

長

周

期成

分

，

応答

スペ _{ク ト}ル に適 合 する地 震 動

，

非 線 形 地 盤 応 答

，

入力レベ ル

，

卓

越

　　　　　　　　　 周 期

1

．

　

lntroduction

　

The

　

ground

　response 　

to

　seismic 　excitation 　

depends

　on 　

the

　

level

　

6f

　

_excitation

　owing 　

_to

　

_the

nonlinearity 　of　soft　soil　

layers

，

　

Two

　

lines

　of　research 　are 　seen 　

to

．

　

be

　

_pursued

・

in

　understanding 　

the

nonlinearity 　

in

　

ground

　response

．

　

First

，

　and 　often 　

followed

，

　cσns三sts　of　

the

　evaluation 　of　

the

　soil

response 　considering 　material 　nonlinearity 　so　as　

to

　match

．

　

the

　observed 　earthquake 　record

．

　

This

　

line

　of

research 　

has

　

Iesulted

　

in

　

the

　

development

　of　several 　methQds 　of　nonlinear 　response 　analysis

_（

e

．

_g

．

Ohsaki

］）

，

　

Prevostz

｝

，

　

Rocha

　and 　

Sesmai

〕

，

　etc

．

．

）

，

　a　comprehensive 　

treatment

　of　which 　

is

　

gi

マ

en

　

by

　

Finn4

］

_．

Secondly ，

　

there

　

have

　

been

　several 　successful 　attempts 　

in

　recent 　

years

　at　the　

direct

　

detection

　of　soil

nonlinearity 　

during

　strong 　

grollnd

　shaking

（

e

．

_g．

　

Chang

　et　al

，

　s｝

，　

Figueras

　et　a1

．

E ｝

，

　

Tokimatsu

　et　al

．

7）

etc

_．）．

　

Such

　studies 　

have

　establisheCl 　

beyond

　

doubt

　the　significance 　of 　soil 　nonlinearity 　

during

　strong

ground

　shaking

．

　

Next

，　

the

　nature 　and 　

the

　extent 　of　

ground

　nonlinearity 　can 　

be

　significantly 　

influenced

by

　

the

　

freqllency

　and 　

_phase

　contents 　of　

the

　

incQming

　excitation

．

　

This

　aspect 　of　

the

　nonlinear 　

_ground

response 　

is

　 not 　cl ¢ arly 　 understood

．

　

To

　evaluate 　

the

　worst 　

possible

　combined 　effect

_，

　

it

　would 　

be

necessary 　

to

　

investigate

　

how

　

the

　various 　site　conditions 　respond 　

to

　variations 　

inthe

　

frequency

　and 　

phase

contents 　of　

the

　

incident

　motion

．



．

　

In

　

the

　

previous

　studys 〕_on

　nonlinear 　response 　ana 】

_ysisof

　extensive 　site 　conditions

_，

　

itwas

　seen 　

that

　

the

soft　sites　undergo 　

large

　elongation 　of　

ground

　

periQd，

　with 　

the

　

increase

　

in

　

the

　

level

　of　

incident

　excitation

　　＊

Geotop

　

Corporation

，

　

Dr

．

　

Eng

，

　艸

Prof

、

_，

DepL

．

_of

Architecture

_，



Faculty

_of

Engineerillg

_，



_TQI

】oku

　　　

Univ

．

，

Dr

，

　Eng

，

翠 零 零

Research

　

Assoc

．

，

　

Dept

，

　o ｛

．

Arci

漁 ecしure

，



Facuhy

o 「

E

囗

．

　　　gineering

，

　

Tohoku

　

Univ

．

，

Dr

，

　

Eng

，

＊ 承 ＊ ＊

Graduate

　

Stude

皿t

，

　

Dept

．

　of　

Architect

．

ure

，

　

Faculty

　of　

En

・

　　　

gineering

，

　

Tohoku

　

Univ

．

（株 ）ジ オ トップ

・

博士 （工学 ） 東 北 大 学工学 部 建築 学 科 　 教 授

・

博 士 （工 学 ） 東 北 大学 工 学 部 建 築 学科　助手

・

博士 〔工学 ｝ 東 北 大学 工 学 部 建 築 学 科　大 学 院 生

一

₆₉

一

N工 工

一

Eleotronio _Library

Architectural Institute of Japan ArchitecturalInstitute of Japan

weighted

by

the

maximum acceleration.

Consequently,

larger

amplification of

long

period

components

at

higher

level

of shaking was observed,

If

the

incident

motion already contains

large

long

period,

components,

_{progressively}

dominant

effect on soil nonlinearity can

be

expected,

In

this

connection

it

can

be

_pointed

out that

the

_proportion

of energy, radiated

in

the

forrn

of seismic waves of

long

_period,

increases

with size of

the

earthquake9"'e),

owing

to

_greateT

relative

clisplacement

of

the

two

sides of

the

fault,

and

to

greater

extent of

faulting.

Recognition

and evaluatien of

the

effect of such

increase

in

long

period

components, on

the

nonlinear

ground

response,

is

essential

for

the

assessment of

hazards

and

risks related

to

seismic microzonation.

In

this

_paper,

the

nonlinear response of

different

surficial site conditions, under

the

action of

incident

motions with successively

increasing

extent of

long

_period

componenets,

is

investigated.

The

incident

motion characteristics are represented

by

response spectra.

The

short

_period

ordinates, and

hence

the

-maximum

acceleration represented

by

shoTt

_period

asymptote, of

the

response spectra are

kept

the

same.

This

way a

clirect

comparative study of

the

effect

of

long

_period

components

is

rnade

_possible.

Attempt

is

made

to

investigate

how

the maximum surface

response acceleration at

different

site conditions

is

influenced

by

the

long

period

content

in

the

incident

motion, while the short

_period

components are

kept

the same.

Other

aspects of

the

effect of

long

_period

components are

discussed

based

on

the

respense spectra characteristics.

The

components of

the

incident

rnotion,

in

the

_period

band

likely

to

have

signifiQant

influence

on

the

nonlinear

_ground

response, are of

interest

in

this

investigation.

The

upper

limiti/in

such

band

depends

on

the

extent of

_ground

_period

elongation

during

the

nonlinear excursions

in

response.

Consequently,

the

term

long

_period

is

used

in

a rather

limited

sense

in

this

research, compared

to

what might

be

generally

understood

in

seismology.

Previous

research8)

indicates

that

the

_predominant

_period

of soft

sites can

be

as

long

as about

_s

seconds under

higher

level

of shaking,

Thus

the

_period

band

extending up

to

10

seconds

in

the

longer

_period

end was considered

to

be

sufficient

foF,

this

investigation,･

Specifically,

the

components of

the

input

rnotien

in

the

_period

range

O.

6-10.

0

seconds are assumed

to

constitute

long

_period

components.

The

reference

to

_ground

conditions,

in

terms

of stiff, medium and soft,

is

_profusely

made

in

the

discussions

that

follow.

These

terms

are rather

_qualitative

and

fuzzy

in

nature, and are not amenable

to

easy

_quantitative

determination.

Japanese

code

for

earthquake resistant

design

of

buildings

recom-mends a

_guideline

for

classification ef site conditions,

based

on

the

fundamental

_ground

_period

_T,.

In

line

with

the

Japanese

code,

fundamental

_ground

_period

is

the

basic

_guideline

here

as well.

The

reference

to

stiff site

includes

fundamental

_ground

_period

shorter

than

about

O.

2

seconds.

Similarly,

sites with

fundamental

_period

longer

than

about

O.

6

seconds are referred

to

as soft.

Those

in

between

are

considered to

be

mediurn.

2.

Methodology

Generatien

of

Response

SpectTa

Compatible

Motions

Artificial

earthquake

time

history

was

initially

_generated

to

match approxirnately

the

response spectra

denoted

as

target-1

in

Fig,

1,

considering random

_phase

content uniformly varying

from

_O

_to

2

n.

The

5

%

damping

response spectrum

target-1

is

tentatively

suggestedii]

to

be

applicable

for

base

layer

with

shear waye velocity

400-sOO

mls

(often

referred

to

as engineering

base

stratum

in

Japan)

due

to

magnitude

8

earthquake.

The

matching of

the

artificial

time

history

to

the

spectrurn

target-1

was

further

improved

by

time

domain

iterative

localized

perturbationsiZ'･i3'

in

the

acceleration

tirne

history.

The

matching of

the

time

history

to

the

respective spectra, at

the

control

_period

_points,

was checked after

the

end of each

iteration

cycle

te

achieve suitable

level

of compatibility,

The

numbei of control

_period

points

was selected

to

satisfy

the

conditioni!),

M,>

_2ie-

in

(:ll}l-'-････--･---'･･･-･･-･･'･'H"

･･---'･'H"'"-"

'

''''''''-''-'-'"'

'

''･'･･-･･-･

_a

₎

where,

M,

is

the

number of control

period

points,

_.ft

ancl

_.fts

are

the

extreme

frequencies

of

the

response

-70-Architectural Institute of Japan

NII-Electronic Library Service ArchrtecturalInstrtute ofJapan

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O.Ol

OA

1.o

10.0

Period

(Seconds)

Fig.

₁

Matching

of incident mQtiens to target spectra

by

time

domain

tteratiens.

O,59.s"e

o.og8<

-O.5

eg･.e-.E

Fig.2

Fig.3

O.53-:tg o.os<

-O.5

aab8e=aE<

O,O 10,O 20,O 30.0 40,O 50.0 oo.O

Time(Soeonds) i

o

o.1 o.2 o.s 1,o 2.o s.o te.o

Period(Seconds)

(a)

ARTEQ 2compatible te spectrum target-2and

{b)

Founer

spectrum.

O,O

10.0

20,O

30.0

40,O

50,O

60.0

Xme(Seconds)

1

o

O,1

O.2

O.5

1.0

2.0

5.0

10.0

Period(Seconds)

(a)

ARTEQ

1

compatible tospectrum target-1 and

(b)

Fourler

spectTum.

'

O,5@g'g o.og<

-O,5

egsks.E-cE< Fig.4

Do lo,o x},e 3o,e 4o.o so,o 6o.o

Time<Seconds) "

o

O,1 O.2

O.5

1.0 2.0 5.0 10.0

Pedod(SeooDds)

(a)

ARTEQ3 cernpatibre tospectrum target-3 and

(b)

Fourier

spectrum.

spectrum, and

e

is

the

spectral

damping.

The

input

motion obtained

by

matching

the

response spectrum

target-1

is

denoted

as

ARTEQ1.

Response

spectra

target-2

and

target-3,

shown

in

Fig.1,

were

obtained

by

tentatively

modifying

target-1

to

include

larger

spectral response at

longer

period

_points.

The

input

motion

ARTE9

1

was next

further

modified

by

the

time

domain

iteration

scheme, mentioned

above,

to

match

the

spectra

target-2

and

target-3

respectively.

The

corresponding

input

motions

ARTEQ

2

and

ARTEQ

3

have

successively

higher

long

_period

components.

The

level

of matching

to

the

corresponding

target

spectra

is

also shown

in

Fig.

1.

The

incident

motions

ARTE9

1,

ARTE9

2

and

ARTE93,

and their

Fourier

spectra are shown

in

Figs.2,

3,

and

4

respectively,

All

the

three

target

spectra correspond

to

peak

ground

acceleration of

400

Gals

based

on

the

short

_period

asymptote of

the

response spectra, and

they

have

the

same short

penod

content

(up

te

O,6

seconds).

Minor

departures

in

the

_peak

acceleration were adjusted

for

by

acceleration

pulse

scaling method suggested

by

PreumonttZ).

This

way,

the

matching of

the

time

history,

to

the

short

_period

asymptote

in

the

target

spectra, was achieved with minimum overall change

in

the

spectral contents.

The

necessary adjustment

in

the

maximum acceleration was,

however,

only of

the

order of

less

than

about

two

_percent,

Additionally,

two

earthquake motions were censtructed

to

have

unusually small short and

long

_period

components,

This

was

done

by

defining

two

additional response spectra shown

in

Figs.

5(a)

and

6(a).

The

response spectrum

target-4

in

Fig.5

(a)

was obtained

from

target-3

by

reducing

the

period

components shorter

than

O.

2

seconds

to

a minimurn.

Similarly,

target-5

in

Fig.

6(a)

was obtained

from

target-1

by

drastically

reducing

the

components with

period

longer

than

1,O

seconds.

LONEQ3

and

SORE9

1

were obtained

by

matching

ARTE9

3

and

ARTEQ

1

to

target-4

and target-s respectively.

Architectural Institute of Japan ArchitecturalInstitute of Japan

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O,1 02

O.5

1.0

2.0

5.0

10,O

Period(Seconds)

Fig.5

(a)

Response

spectrum target-4,

(b)

Compatible

tion LONEQ3, and

(c)

Fourier spectrum.

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t.o Period(Seconds)

10.0

1,tl･ttttt ,SOREQIMaxO.408gtt.t' ･･,l･,e,ttttt

tttt

,

t.t'.tt..tt

e,o10.020.030,O40.0 Time(Seconds)50.060.0

o

O,1 O,2

_,

O.5p,ri,Sig...d2,.)O

_s,o

10,O

(a)

Response

spectium target-5,

(b)

Compatible

mo-tion SOREQ 1,and

(c)

Fourier spectrurn.

The

input

motions are shown

in

Figs.

5(b)

and

6(b),

ancl

the

corresponding

Fourier

spectra are shown

in

Figs.

5{c)

and

_6(c).

SORE9

1

and

LONEQ

3

were utilized

to

compare

the

relative

influence

of

the

short and

long

_pe;iod

components.

As

uncertainties exist

in

the

estimation of

the

period

band

in

which

the

seismic energy of a

destructive

future

earthquake would

be

dominant,

it

would

be

useful

to

understand

the

relative

importance

of short and

long

_period

components

in

nonlinear

ground

response.

Such

information

can

be

vital

in

the

seismic microzonation considering

different

levels

of

incident

excltatlon

Selection

of

Soil

Profiles

for

Investigation

The

ground

profiles

from

Sendai

and

Tokyo

were considered

for

this

investigation.

The

soil

profiles

were selected

te

include

a range of sites,

from

the

sections across

firm

ground

to

bay

areas, as shown

in

Figs.8(a)

and

9(a).

Altogether

58

soil

profiles,

20

from

sendai and

38

from

Tokyo,

were considered.

Fig.8(a)

shows

17

of

the

20

sites

from

Sendai.

Similarly,

Fig.9(a)

shows

20

of

the

38

sites

from

Tokyo.

The

numbers

directly

above

the

soil

_profiles

in

Figs.8(a)

and

9(a)

are

the

sequential site

numbers

increasing

towards

the

bay

area.

The

missing numbers

indicate

profiles

not shown.

The

shear

wave velocity

for

different

soil

types

was estimated

from

the

correlation of

initial

shear modulus

G,

with standard

_penetration

test

N-vaiues,

G,=1

200

×

N"'S(t/m2)").

The

Tokyo

sandy

gravel

layer

was used as

the

base

layer

for

soil

_profiles

from

Tokyo.

Similarly,

the

soft rock underlying

the

Sendai

area was

assumed

to

be

the

base

layer

for

soil

_profiles

from

Sendai.

Nonlinear

Response

Analysis

The

stiffness of soil

layers

during

the

inelastic

time

domain

response was

determined

by

the

hysteretic

model..

The

dependence

of

the

shear modulus, and

the

equivalent

damping

factor,

was

ba$ed

on

the

Masing's

type

model

developed

by

Ohsaki

et al.i5),

The

_soil

_types

in

_the

_{selected seil}

profiles

were

broadly

divided

into

three

types:(a)

clayey soils,

(b)

sandy soil$, and

(c)

sandy

_gravel.

The

hysteretic

moclel

_parameters

a,

fi,

and

G,IS.,

for

the

three

soil

types,

are shown

in

Table1,

The

corresponding shear stress-strain

hysteretic

_plots

for

a simple sinosoidal strain

history

with

increasing

magnitude _{are shown}

in

Fig.7

for

the

three

soil

types.

-72-Architectural Institute of Japan

NII-Electronic Library Service ArchitecturalInstitute of Japan

Sites

were assumed

to

be

horizon-tally

layered,

and

the

soil

_profiles

were modeled as a series of

lumped

masses connected

by

shear springs

and

dashpots.

The

nonlinear

t'ime

domain

response analysis was carried

out

by

step-by-step numerical

integra-tion using

the

Wilson's

0-method

de-veloped

by

Ohsakii',

The

time

step

for

the

solution of

incremental

equa-tions

was

the

smaller of

the

samplirig

interval

of

O.02

seconds

in

the

input

motion and

1120

of

the

fundamental

ground

period

T,,

Lineai

interpola-tion

was used

in･case

subdiyision

_of

the

sampling

interval

was necessary.

Viscous

damping

of

2

%

was assumed

to

represent

damping

in

soil

at

initial

conditions.

The

input

motion

.was

assumed

to

be

acti'ng at an exposed surface of

base'layer

by.considering

a

transmitting

boundary

represented

by

a

fictitious

elashpot'

eRo･8eSas18Ets2ut StrainE

(%)

?o

₎

geO8gMIO-2

g

2

x･ga.

£ gOge

e-'a

mENn

-2

"NOE)gpogees]o o 2 4 Time

(seconds)

soE coe. ,,Uoge-le8-co

-30

6 O2

-2

O2

-2

O2

STrainE(%) SpainE(%) Straine(%)

Fig,7 Hysteretic model characteTistics :

(a)

Shear

modulus

degradatien

and

damping

factors,

and

{b)

Sinoseidal

strain

history

with

increasing

amplitude togethei'with

the correspend{ng

hysteretlc

plots

for

(c)

Clay,

{d}

Sand,

and

(e)

Gravel.

Tablel

Hysteretic

Model

Pararneters.

3.

Results

of

Analysis

Predom'inant

Period

of

Surface

Mo-tion

The

fundamental

ground

period

T,

was computed

from

the

consistent mass matrix and

the

stiffness

matrix

b'ased

on

the

initial

shear modulus.

Thus

Tc

repre$ents

the

ground

period

at very

low

strain

level.

The

_predominant

_period

_T.

of

the

surface response motion was evaluated

from

transfer

function

analysis.

For

this

the.Fourier

spectra of response･motions were computed, and smoothed

by

Parzen's

lag

window.

The

smoothing

bandwidth

was varied

from

O.

2

to

1.

0

Hz

depending

on

TG,

with narrower

bandwidth

for

longer

_Tc.

The

transfer,functions

were computed as

the

ratios of smoothed

Fourier

spectra

6etween

the

_ground

surface and

the

top

of

the

base

layer,

Tp

was arrived at

ftom

the

fundamental

resonant

_peak

in

the

plot

of

the

transfer

function.

Figs.

8(b)

and

9(b)

show

the

distribution

fo

T,

due

to

three

input

motions

ARTEQ

1,

ARTEQ

2,

and

ARTEQ

3,

for

the

soil

_profiles

from

Sendai

and

Tokyo

'respectively.

_The

_clotted

_lines

show

the

distribution

of

Tc,

For

stSff sites,

_T.

and

_T,,

are

_practically

coincident.

For

softer sites,

T,

is

larger

than

T,,

In

addition,

Tp

is

seen

to

elongate

further

with

the

increase

in

'long

_period

content of

the

incident

motion.

The

elongation

in

T,

of

individual

sites

in

Figs.8(b)

and

9(b),

with

the

increase

in

long

_period

components

in

the

inciaent

motion, constitutes evidence of

the

increased

level,

of nonlinear excitation.

This

effect of

the

increased

level

of excitation with

the

increase.in

long

_period

content

is

seen

to

correlate appteciably･ with

longer

T,,

The

content of

long

period

components

in

the

incident

motion

is

thus

seen

to

contribute substantially

to

the

extent of nonlinear excitation of soft

_ground

sites.

Maximum

Surface

Response

Acceleration

Figs.

8(c)

and

9(c)

show the

influence

of

the

increased

long

_perlod

contents

ip

incident

motion, on

the

maximum surface response acceleration,

for

sites

from

Sendai

and

Tokyo

respectively.

The

three

vertical

bars

for

each site represent,

from

left

to

right,

the

maximum surface response accelerations

due

-73-E-zil(i+ctlilP) 2P 1 Sol]Typesafia.st e=ShearStrain r=ShearStress a,=InitialModulus S.n=SheflrStrengLh E=DampingFaetor

g'=soilcenstant

Sua,e#SeilConstents

e=-i-i+a[8.[P

_T)+fi C}ayeysoi]s

Sandysoils

Sandygravel

5･o10.011.0L41.61.76oo,o1100.01300.0

Architectural Institute of Japan ArchitecturalInstitute ofJapan

.:.

HIROSE Rv. o[-se(m) 5:"-.l 1.02,O "m) .e. ,//r

l,.o

NOOI-NOop(3S-15,Scr)

SENDN AHMV POST

11./. 12. 13 14 _ls /･I. T6 IT :e

,-cLAyEy solLs

ma

SANDY SOILS

pm

SANDY GRAVEL

IIIIII]

soff HocK

i' ii/ji{llS,,ll'l NAGAHAMA 19 mo f'li'

11x

g,･1

s･1 ..h8eg

2,O

o,o

O.6@8sts}

o,o

"

ues

SEIHOxu TouHeKu eis

(a)

Ground

section

from

Sendai

showing

17

of the

20

sites.EOISHIOGAMA

(b)

Predominant

period

1))

corresponding

to

incident

motions

ARILEQI,

(Dotted

lineshows

_Tb

distribution).

ARTEQ2,

and

AR7EQ3

MaximumSurfacenesponseAcceleration

tttttttttttt-t-ttttttttttttt/

ttttttt-ttttttttt/t"tt/ttt-/--tttV--/tt"ttt/tt-tt/"ttt--ttttt.ttttttttt/t-ttt/tt/tt"ttttt"//tt"tttt./t/tttttttt-tttt/tt-ttttttttt./-t-t/ttttttttttt/tttttt/tt-tttttt-t

(c)

Maximum

surface acceleration corresponding

to

AR7IEel,

AR71EQ2,

and

ARTEQ3

(Dotted

line

shows the maximum acceleration

incident

at the exposed

base).

Fig.8

Ground

_pTofile

from

Sendai

and variation of T,and maxLmum suiface acce]eration.

o

-so(m)

o,oEIS

N04-N05(3504t,OO")

SHUBU

(a)

Greund

section

from

Tbkyo

showing 20 of

the

38

sites.

sJ

5.0

o,o(b)

Predominant

_period

Tl,

corresponding to

incident

motions

ARTEQI,

AR71EQg

and ARTEQ3

(Detted

line

shows

Ilr

distribution).

Aspdv<:}

O.6

o,o(c)

Maximum

surface acceleration corresponding

to

ARTEQI,

ARTEQ2,

and

ARTEQ.3

(Dotted

line

shows

the

maximurn acceleration

incident

at the exposed base).

Fig.9

Ground

proMe

from

Tokyo

and variation of

T.

and maximum surface acceleration.

-74-Architectural Institute of Japan

NII-Electronic Library Service ArchrtecturalInstrtute of Japan

to

incident

motions

ARTEQ

1,

ARTEQ2,

and

ARTE93

respectively.

The

horizontal

dottecl

lines

show

the

level

of

₄₀₀

Gals

maxirnum acceleration applied at

the

exposed

base

layer.

It

is

seen

that,

for

a

given

incident

motion,

the

maximum surface acceleration

tends

te

decrease

towards

the

bay

areas.

This

effect

is

well recognized

in

the

_previous

studies

[8,

16]

to

be

caused

by

the

mcreased nonlinearity at softer sites.

In

addition,

the

maxiinum accelerations, corresponding

to

the

_three

incident

motions

ARTE9

1,

ARTEQ2

and

ARTEQ3,

vary

to

different

degrees

within

individual

sites.

The

incident

motion

ARTEQ

3,

which

has

the

highest

long

period

content,

is

seen

to

resttlt

in

the

largest

maximum

surface acceleration

in

softer sites.

On

the contrary, the maximum acceleration at stiffer sites remain

practically

unchanged.

The

effect of

the

mcreased

long

_period

components, on

the

maximum surface acceleration,

is

more

directly

compared

in

Fig.10.

For

this

_purpose,

the

maximum

acceleration ratios

R

21

and

R

31

are

definecl

as

the

maximum surface response acceleration

due

to

incident

motions

ARTEQ2

and

ARTEQ3

respectively normalized

by

_that

due

to

the

incident

metion

ARTEQ

1.

Varia-tions

of

R21

afld

R31

with

Tc

are shown

in

Fig.

10.

It

is

seen

that

the

maximum

accelera-tions

at

_soft

sites are

highly

affectecl

by

the

content- of

long

period

components.

The

effect

in

sites with

T,

longeT

than

about

O.7

:ri;k

ag

AA

,/111la/#

'dada-''/

ss

'

$

,ec/

njiee

_,,s

"

g

,

e

$,

e,k

fi"

,11i/k/ee

O.5

O.O

O.5

1.0

I,5

Fundafnental

Ground

Period

TG

(Soconds)

'

L

FIg.10 Increase in maximum surface acceleration with

long

period

components.

to

O.

8

seconds

is

seen

to

be

_particularly

dominant.

The

effect of

leng

_period

content on

the

maximum surface acceleration

is

moderate at intermediate sites, and minimal atstiffsites.

Thus,

it

is

seen

that

the

_presence

of

large

long

_period

components, combined with

large

soil nonlinearity,

is

likely

te

cause

increase

in

the

maximum surface acceleration at soft sites.

This

effect can

be

regarded as

in

contrast

to

the

_general

expectation of

decreased

maximum acceleration

with

the

increase

in

the

level

of excitation.

Response

SpectTa

of

Surface

Response

'

Response

spectra

of

surface

response motidn, at all

the

selected sites,

due

to

the

three

input

motions

ARTEQ

1,

ARTEQ

2,

and

ARTEQ

3,

were computed

for

relative comparison of response chara ¢

teris-tics.

It

was seen

that

increase

in

the

long

_penod

content affects

the

spectral characteristics of surface motipn

depending

on

the

local

site conditions,

The

_primary

and simple effect of

the

_presence

of correspondingly

larger

spectral ordinates

in

long

_period

range

is

observed

in

all

the

sites.

The

secondary and

important

effect

is

characterized

by

larger

spectral ordinates at short

(shorter

than about

O.

1

seconcls) and

long

(longer

than

O.

6

seconds)

_period

ranges.

The

larger

spectral ordinates at short and

long

_period

ranges

is

in

contrast

to

the

relatively smaller ordinates

in

the

intermediate

_period

range of

O.

1

to

O.

6

seconds.

As

expected,

the

secondary effect was not observed

in

stiff site conclitions.

Figure

11

shows

the

suTface motion response spectra

for

three

sites

from

Sendai.

The

sites are

selected

to

represent

typical

variations with respect

to

long

period

contents

in

the

incident motion.

Fig.

11(a)

shows

the

response spectra

fer

a stiffsite

(

TG=O.

09

seconds), which

is

numbered

6

in

Fig.

s

(a),

and consists of a single

Iayer

of sandy

_gravel

over

the

soft rock

base

layer.

It

can

be

seen

that

the

respective response spectra of

the

incident

motions

in

Fig.

1

are

least

modified.

This

may

be

expected

because

the stiff sites

tend

to

respond

in

tune

with

the

incident motion at

the

exposed

base.

Fig,

n(b)

shows

the

response spectra

for

site numbered

11

(

T,=O.

38

seconds)

in

Fig.

8(a),

which

is

a

thick

sandy

gravel

layer

overlain

by

a

thm

clayey

layer.

The

input

spectral characteristics

in

the

_period

range

shorter

than

about

e.

6

seconds are substantially altered compared

to

Fig.

11(a)

clue

to

the

_presence

of soft clay

layer,

However,

the

increase

in

the

long

_period

components

is

seen

to

exert only minor

-75-Architectural Institute of Japan ArchrtecturalInstrtute of Japan 2.0=.9 1,5-e･g1,osg

o,sma

o.o

2.0g=･2-1.sgas81.0<E'8"

O.5ea,,

o.o

1,59g'gge1.0gxe

o,sgen

oo

Fig.11

(a)

Site6fremSendai

_(TG=O,09

seconds).

(b)

Site11ftem

Sendai

(Tc=O,38

seconds}.

ODI

O,1

1,O

10.0

Period

_(Seconds)

(c)

Site

19

from

Sendai

(TG=O,86

seconds)

Response

spectra of suTface motion

for

thethreesites

from

Sendai

2,Ogn.8

1.5!.g

1,o<Z

O.5gca

o.o

2.0g:-8

1.sg-8

1,O<

g

,.,ca,,

o,o

1,5

.sg

1.ogS

O.5gcA,,

o.o

Fig.12

(a)

Site

9

from

Tokyo

_(TG=O.28

seconds),

(b)

Site

22

fiom

Tokyo

(TG=O.68

seconds)

O,Ol

O.1

1,O

10,O

Period

(Secends)

(c)

Site

36

from

Tokyo

_(Ta=1.02

seconds).

Respense

spectTa of surface rnotion terthe thTeesites

frorn

Tokyo.

infiuence.

Fig.

11{c)

shows

the

response spectra

for

site number

19

(

Tc=O.

86

seconds)

from

Senclai.

The

site consists of soft

deposits

in

the

bay

area, and consequently,

distinct

secondary effects can

be

noted.

It

is

seen

that

the

_presence

of

larger

long

period

components result

in

larger

spectral response

in

the

long

as well as

in

the

short

_period

ranges, with relatively small effect

in

the

intermediate

range.

Figure

12

shows

the

response

spectra

of

sites numbered

_9,

22

and

₃₆

in

the

_ground

section

from

Tokyo

in

Fig.9(a).

All

the

sites

from

Tokyo

consist of

different

combinations of clayey and sandy

layers

overlying

the

Tokyo

sandy

_gravel

layer.

As

a result,

the

long

period

components

tend

to

_play

dominant

role

in

the

nonlinear response.

Fig.12(a)

shows

the

response spectra

for

the

site with

the

shortest

T,

(O.

28

seconds) of

the

38

sites

from

Tokyo.

The

secondary effect of

increased

long

_period

components

is

noted

to

be

rather small.

Similar

to

the

characteristics observed

in

Fig.

11(c),

Figs.

12(b)

and

12(c)

show consecutively

increased

secondary effects.

Respectiye

preclominant

periods

ILp

are also shown

in

Figs.

11

and

12,

as aguide

to

the

increase

in

the

level

of excitation, owing

to

the

_pTesence

of

increased

long

period

components

in

the

mcident motion.

From

the

above

discussion

it

may

be

noted

that

the

increase

in

long

_period

components result

in

higher

level

of nonlinear shaking of soft sites, with consequent amplification of

longer

period

components.

The

larger

spectral ordinates atshort

period

range correspond

to

the

higher

maximurn surface response

acceleration noted above.

Maximum

Acceleration

at

Different

Layers

over

Depth

In

Figs.8(c),

9(c)

and

10,

the

rnaximum surface response acceleration of soft sites was seen

to

increase

with

long

_period

contents

in

the

incident

rnotion.

Fig.

13

shows

the

variation of

the

maximum

acceleration at

different

layers

over

clepth,

for

the

two

sites

from

Sendai,

nurnbered

6

and

19

in

Fig.

8

-76-Architectural Institute of Japan

NII-Electronic Library Service ArchitecturalInstitute of Japan

<a).

The

two

sites are noted

to

be

respectively

stiff ancl soft.

As

the

inctease

in

long

_period

components

in

the

incident

motion

is

seen

te

result

in

the

increased

nonlinear response of soft

sites, an attempt was made

to

inclicate

the

extent

nonlinearity

in

different

soil

layers.

For

this

purpose,

the

term

moclultis reduction ratio

[16],

clefined

as:

'

(Go"Gm)

A=

'

G,

'"'""HHMH'HH''H'H'H(2)

where

G.

is

the

minimum shear modulus

during

response

history,

was utilized,

Increase

in

the

yalue of

A

indicates

the

increase

in

the

extent of

nonlingarity, and

hence

of

the

level

of excitation.

In

addition

the

term

maximum acceleration ratio

was

defined

as

the

maXimum acceleration at any

layer

normalized

by

that

at

the

basg

layer.

Fig,13

shows variation over

depth

of

A,

the

maximum acceleration, and

the

maximum

accel-eration ratio

for

the

three

incident

motions

ARTEQ1,

ARTEQ2,

and

ARTEQ3.

In

three

incident

motions

In

contrast

-

.T

contents,

in

case of soft site

in

Fig.

13(b),

in

seen

_that

ARTE93

causes

the

largest

values

The

increase

in

content,

is

seen

to

occur

in

two

_phases

in

Fig.

13,

increases

with

the

long

explained

in

be

thought

of as

the

_product

of

the

incident

internal

base

layer.

As

a consequence,

larger

regarded as

directly

reflecied

in

the

higher

'

variation of the maximum acceleratien

from

base

sltes.

.

The

differences

at

the

base

layer

of stiffsite,

three

mptions

incident

at

the

exposed

base,

In

contrast

,

can

be

noted

in

Fig.13(b),

This

behavior

can

maximum acceleration ratio.

In

case of stiffsite

'

that

corresponding

to

ARTEQ

1

is

largest,

such

three

incident

motions approach similar values.

Fig.13(b).

T.hat

is,

the

higher

maximum sites, constituting a

two-level

effect on

the

Figure

14(a)

Fig.

13(b)

clue

to

the

incident

motion

ARTEQ

1.

ARTE93,

Distinct

reduction

in

short

_period

comparison

to

that

at

C

can

be

recognized

in

fairly

thick

soft clay

layer

between

points

B

and

SS:Sgnd;CC:Clar; SG

±

Sandrernvel btittaiShenr ModulllsG} ga.mmEg se-T,!4m

3Tts2:th/LVb

LAEyASERE InitinlShenr MedtrlusGe

Modutus MaxiMUM Mmxllnum Reduetion RstiDa) Acctlerst+ofiie) AceelerattonRnt:o

O,O 1:O O:.1 OS O" OA LO LG

･',.

'//

/mum/

./

1,.

･･1''1.･/l

li'iuanyE,i

･.j･

(n)VariAtionor1.mniimumEcceterstion,nnd'msxEmum

nc:elcrEtiDnrstlo forsite No.6trom Sendai

Modulus Maxlmdm Mnxsmtm

'

Reduct[on Ratitia) Aeceleretionie) AcctltcationRntio

o,o l.e o;1o"

'/ttts'''

'

/rmd

/thrmt

,

/mom

'

'

'

_t

/t

t..

ttt/t

'

･1,''

.t

'

i')･?,

,

O,S O.4 lt/ / //

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1,O1,6 J.i'L

O)VsriAtio]or1,maximum acoeteration, mnd maximum acctLemtion rEtio torslteNo.19ttomSertda[

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t

'

Fig.13

Soil

pr6Me, Modulus reduction raLio

A,

maxlmum

acceleration, and maximum acceteratlon ratio at

different

laye[s

for

stiff and soft sites

(numbered

6

and 19 respectively) from

Sendai.

case of stiffsite

in

Fig.

13(a),

_A

is

seen

to

be

the

same

for

the

there

is

considerable

increase

in

A,

with

the

increase

in

long

_period

di

¢ating

the

increase

in

the

extent of nonlinearity.

It

is

of

A

in･all

the

･lay6rs

acress

the

_prefile.

',

the

maximum surface acceleratien at soft sites, with

the

increase

in

the

long

_period

Initially,

the

maximum acceleration at

the

base

Iayer

period

content of

the

motion

incident

at

the

exposed

base.

This

effect can

be

terms

of

the

transfer

function

from

expgsed

base

to

base

layer.

The

base

layer

motion can

motion and

the

transfer

function

from

exposed

base

to

long

period

contents

in

the

incident

motion cart

be

maximum acceleration at

the

base

layer.

Secondly,

the

to

the

surface

is

distinctly

different

for

stiff and soft

between

maximum

_{qccelerations}

corresponding

to

the

decrea$e

and

becorne,

practically

nonexisting at

the

surface.

the

differences

tend

to

widen

_,and

become

more

pronounced

at upper

layets

of soft sites, as

be

more clearly understood

from

the

variation of

the

rati6 corresponding

to

ARTEQ

3

is

smallest, and

that

the

maximum surface acceleration

due

to

all

the

The

tenclency

is

reversed

in

cqse of

the

soft site

in

acceleration at

the

base

layer

are

further

amplified

by

soft

maximum surface response acceleration.

shows

the

inotions

at

the

top of

three

layers

denoted

as

A,

B,

and

C

in

the soil

_profile

in

Fig.

14(b)

shows

the

corresponding･ rnotions

due

te

content

in

response ac¢eleration

time

history

at

B

ln

both

Figs.

14(a)

and

14(b),

because

of

the

_presence

of

the

C

in

Fig.

1'3(b).

The

presence

of

larger

long

_period

components

in

ARTEQ

3

is

seen

to

result

in

the

response

dominated

by

lofig

_period

components at

_point

Architectural Institute of Japan ArchitecturalInstitute of Japan

O.5=.sve

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o,o

lo.o

2o.o

3o.o

4o.e so,o 6o.o

11me

(Sec)

{a)

Response to incident motien ARTEQL

'

Fig.14

Response

rnotions at three

tayers

denoted

A,

B,

arrd

C

in

and

ARTEQ3.

10

Midd!eof tayer@ betiddle of laycT@

i inpuLARreel io nput:AR7EQI s

i

i

o

---

･----

O o---

1...,.,la`:Y,,M,i

-s

'i.;l.6',6.thO.alM

-1

_I

-lo

,

-10

-.ol -.cos o zaas aol

-1

ns O o.s 1 4s o o.s

O,O 10.0

_20,O

_30.0

_40,O

_50.0

_60.0

fime

(Sec)

{b)

Response to incidentmotioll

ARIIEQ3.

Fig.13

(b)

due

to

Incident

Motions

ARTEQ

1

ggg

2

g,e,

s

_.1

10 5 o'f-le le 1.5

2to

e.s ,.L

Si,O

O,5 O.O O,5 1.0 1.5 l"indamenulGroundPeriodTG{SeDopdis}

-]e

A:TokyoSines o:sorulalsim Stax.AoelentionHatoHSI o6Aza"A e,oFig.16

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-o.OS

O orcoS O.an

-1

.0j

O os 1

-05

O O,5

StrninEfperoent) StralnElpervenO StrnineiptrcenO

Fig.

15

Effect

of the

increase

inthe

long

_periodcomponents

on the shea[ stre$s-strain

hysteretic

behavier

at

layeTs

A,

B

and

C

of

Fig.

13,

B

in

Fig.

14(b>.

The

increased

extent of

the

nonlinear excitation of

the

soil

layers,

with

the

increase

in

the

long

_period

contents, can

be

transparently

understood

from

the

comparison of shear stress-strain

hysteretic

behavior

of

the

layers

A,

B,

and

C

in

Fig.

13,

corresponding

to

the

incident

motions

ARTEQ

1

and

ARTEQ

3

as

shown

in

Fig,

15.

It

is

clear

that

the

presence

of

long

_period

components result

in

substantial

increase

in

the

level

of strain.

Effect

of

Deficient

Short

and

Long

Period

Components

O.5 1.0 1.5

IinndhmmuGrvundPdiodTb(Seoonds)

Effect

of

deficient

cornponents in

(a)

shert _period, and

(b)

long

period, on themaximurn accelera-tion.

The

input

motiQns

LONEQ

3

and

SOREQ

1,

shown

in

Figs.

5

and

6

respectively, were utilized

to

further

investigate

the

cornparative roles of

the

short and

long

_period

cornponents

in

the

incident

excitation, on

the

nonlinear

_ground

response.

Fig.

16(a)

shows

the

effect of

incident

motion,

deficient

in

short

_period

components, on

the

maximum

-78-Architectural Institute of Japan

NII-Electronic Library Service ArchitecturalInstitute of Japan

surface response acceleration.',The effect

is

:epresented

by

defining

the

ratio

RL3

as

the

maximum surface acceleration corresponding

to

LONEQ3

norrnalized

by

that

cerresponding

to

ARTE9

3.

It

is

seen

in

Fig.16(a)

that

RL3

remains nearly equal

to

unity

for

_practically

the whole range of sites

considered

in

this

investigation,

indicating

that

the

maximum acceleration amplification'is affected

little

by

components with

_period

shorter

than

o.

2

Seconds.

Similarly,

RS

1

is

the

ratio'of

the

maximum surface acceleration

due

to

incident

motion

SOREQ1

to

that

due

to

incident

motion

ARTE9

1.

Variation

of

RS

1

in

Fig.

16(b)

shows

distinct

tendency

of

decrease

in

the

maximum acceleration

amplification at soft sites when

the

long

_period

components

(longer

than

1.

0

seconds) are reduced,

it

remaining

_practically

unchanged at stiff sites,

The

response sp6ctra of surface motion

due

to

･incident

motions

LONEQ

3

and

SORE9

1

are also shown

in

Figs.

₁₁

and

_12.

The

incident

motions

LONEQ3

and'

ARTEQ3

have

similar

long

_period

components,

and

the

corresponding response spectra can

be

compared

to

identify

effect of

the

deficient

short

period

components.

From

the

comparison of

the

response spectra of

three

sites

frorn

Sendai

in

Fig.

11,

it

is

seen

that

the

deficiency

in

short

_period

(shorter

than

O.

2

seconds)

is

apparent

in

case of

the

stiff

site

in

(a),

as

indicated

by

correspondingly

Iower

spectral amplitude

in

the

range

less

_than

_O,2

seconds.

However,

as the nonlinearity

becomes

dominant

in

the

response of softer sites

in

11(b)

and

'

(c),

,the

effect of

the

deficiency

in

short

period

ceases

to

be'of

significance.

Similar

behaviot

can

be

'

noted

in

case of

the

three

sites

from

Tokyo

in

Fig.

12.

The

effect of

the

reduced short

_period

Co'Inponents

is

seen

to

_perSist

only

in

Fig.12(a),

being

_practically

absent

in

(b)

and,

(c).

Overall,

there

is

a

systematic

tendency

towards

dorninance

of

the

long

_period

components

in

the

spectral characteristics,of

the

response spectra of soft sites,

indicated

by

_practically

idehtical

response spectra

for

incident

motions

ARTEQ

3,

andLONEQ

3.

Contrary

to

the

insignificahce

of

the

short

period

components

in

the

nonlinear _{response of soft sites,}

there

is

_{a clear} and

_persistent

_effect of

the

deficiency

in

the

long

_peri.od

components

in

the

incident

motion,

_.The

seconda'ry effect noted

in

the

foregoing

discussions

is

seen

to

be

of no

_practical

consequence, even

in

case of very soft site

in

Fig.

12(c)

when

the

incident

motion

(SOREQ

1)

has

drastically

reduced

long

_period

components.

It

indicates

.that

the

incident

rnotion

dominant

only

in

short

period

components

would

not

be

Iikely

to

cause severe excitation of soft sites,

and shows

the

need

to

_give

adequate consideratibn

to

long

period

components while

d6fining

the

incident

motion'

for

seismic

'mictozgnation.

_.

'

'

'

4.

Conclusions

,

The

presence

of

larger

long

_period

components

in

the

inciclent

excitation can

influence

the

nonlinear

ground

response

in

aifferent

ways and

to

different

extent,

depehding

on

the

local

site conditions,

Based

on

this

investigation,

the

following

_potential

consequences of

the

long

_period

content can

be

noted.

1.

Soft

_ground

sites undergo

increased

level

of nonlinea[ excitation, with consequent substantial

elongation

in

_ground

_period,

as

the

long

_period

components

in

the

incident.motion

increases.

This

is

a

clear evidence

that

the

_presence

or absence of

the

long

_period

components can

be

detrimental

to

the

level

of shaking at soft･ sites.

Level

of excitation at stiffer site

is

affected

less

by

long

_period

contents,

2.

The

maximum surface re$pOnse･acceleration at soft

_ground

sites

increase

with

the

increase

in

the

long

_period

components

in

the

incident

excitation, as a result of

the

increased

nonlinear response and

consequent amplification of

long

period

compepents.

In

centrast,

the

maximum surface acceleration at stiff sites remain

_practically

unaffectecl.

3.

The

spectral characteristics of

the

surface motion at stiffsites are affected

little

6y

the

long

_period

cemponents, except

for

the

_{prirnary'effect}

of

the

appearance of correspondingly

larger

spectral ordinates.

In

contrast, response spectra at soft sites

indicate

substantial secondary effects.

The

secondary effects are marked

by

larger

spectral ordinates at

Ionger

_pefiods

as

the

long

_period

conte'nts

in

the

incident

motion

increase.

In

addition,

there

is

larger

spectral

response at short

_period

corresponding'

to

the

higher

maximum acceleration neted above.

Larger

extent of soil nonlinearity, and

hence

of

the