非線形地盤応答のための入力波のスケーリング

【論　 　文

1

　　　日本建 築学会 構 造 系論文 報告 藁 第 440号

・

1992年10月

Journal

　o‘Struct

．

　Censtr

．

　Engng

，

　AIJ

，

　

No

．

440

，

0ct

．

，

1gg2

SCALING

　

A

　

SUITE

　

OF

　

GROUND

　

MOTIONS

　

　　

　　

　

　　

　

FOR

　

COMPATIBLE

　

LEVELS

　

　　

OF

　

NONLINEAR

　

GROUND

　

RESPONSE

・

非線形 地盤 応 答

の た

め

の

入

力波

の ス

ケ

ー

リ

ン

グ

Mddon

　

B

．

　

KARKEE

＊

_，



Yoshihiro

　

SUGIMURA

＊ ＊ and 　

Jun



7

て）

BITA

＊ ＊ ＊

　　　　　　

カ ル

キ ー

マ

ダ

ン

B

．

，

杉 村 義 広

，

飛 田

　

潤

　　Noting

　the　need 　to　consider 　

different

　

levels

　of　excitation 　

in

　seismic 　microzonation

_，

　comparative

suitability 　of　selected 　methods 　of　scaling　a　suite 　of　

ground

　motions 　

is

　

investigated

．

　

It

　

is

　seen　

that

scaling 　

by

　spectrum 　

intensity（

SI

_）

’

produces

　

bet

 er　overall 　compatibility 　

in

　

level

　of　nonlinear

’

ground

　response

．



『

　　

齟

　　

Inclusion

　of　the

．

　response 　of　

long

　

_period

　oscillators

_，

　

in

　

the

　

definition

　of　

SI

，　

improves

　the　com

−

patibility

　

in

　soft　sites

．

　

Spectru

_皿

intensity

　amplification

_（

SIA

_）

is

　a　

likely

　

indicator

　of　the　

poten

−

tial

　

for

　concentrated 　

damage

　

t6

　certain　range 　of　structures

，　at　a　site

．

　

The

　concept 　of

　

limited

　

band

spectrum 　

intensity（

LBSI

）

is

　

proposed

　to　accou

’

nt　

fQr

　the　effect 　of　

large

　nonlinear 　response 　of　sof

−

ter

　S6il　sites

．

　

Keg

皿Oids ：nonlinear 　resPonse

_，

　sPectrum 　

intensity

，

　

lemel

　of　eXtiation

_，

　madulzas 　reduction 　ratio

_，

　

dOm

_｝

　　　　　　

ing

　

facter

，

　s ）ectrum 　

intensity

　amptification

　　　　　　　　　 非 線 形 応 答

，

ス ペ ク トル強 度

，

入力レ ベ ル

，

剛 性 低 下 率

，

等 価 減 衰

，

ス ペ ク トル強 度

　　　　　　　　　 増幅 率

1

’

．

．

lntroduction

　The

　earthquake 　resistant 　approach 止at　

forms

　

the

　

basic

　

philosQphy

　of　

the

　

international

　standard 　

fof

earthquake 　resistant 　

design

’｝

is

_shown

in



Table



1．



To

_realize

this



design



_philosophy

_{realistically}

in

practice，

　

it

　

is

　necessary 　

to

　

know

　what 　

the

　

different

　

levels

　of 　excitations 　mean 　 at 　a 　

given

　site

．

Microzonation

　maps 　that　consider 　

diff

_臼rent　

levels

　of

_．

excitation ：｝

・

3 ）can　

provide

　such 　

information．

　

Recent

　 lnvestlgatlons

　

have

　

shown

ample



evidence



of　nonlinear 　

ground

response

　

during

　

moderate

．

　

to

　

strong earthquakes ‘｝

’

5｝

．



Studies



based

．

on



re

一

Table

　

l

_Earthquake

　

Resistan

し

Design

　

Approabh

・

b

・n・eanalysis 　sh・w 　

th

・

t

　

th

・n・nlinea ・

ground

　response 　adds 　another 　

dimen −

sion　

_to

　

_the

　

local

　_{site　effectsfi}）

．

　

As

　a

・

・e・ult・

high

・・

1

・v・

1

・

．

・

f

　excit ・

ti

・n ・・e　n・

1

・ng・ ・

1i

・

r

・・m ・

ltip1

…

f1

・w… nr

・

C

・n・equently

・

・ep ・ ・at・

cQnsideration 　of　

the

　

different

　

levels

　of　excitation 　

is

　necessary

．

　

It

　wQuld 　

be

　most 　appropriate 　

if

　

levels

　of

excitation 　were 　made 　

to

　correspond 　to　

frequent

_，　 mediuin _，　 and 　extreme 　

levels

（

Table

　

1）

that　may 　

be

“

expected

_．

at

’

ageneral 　

locality

・

　　　　　　 E缸

thquakes

St

【uctu  s

恥α1u  t

−

1evelMedium

−

leve

正

Ext

：eme

−

level

Or

’

　 　 sロuc  5No

　

dam

　 eRe 鹹 n 釦nじ直or旧

1No

　

colla

 

da1

爺 

1ides

No

　

damageNo

　 　 　 e

．

Re

弼 麺n

　

fbnc

ロona1

Pote血 aU 　az訂dOUSNo 　

dam

　 eNo 　 　 　 e

No

．

dam

　 e

’

G

・aduat ・

St

・

d

・・_も

D

・pt

．

・f　A_町・hitect・「・

，

　

F

・ ・ul・

y

・

f

　

E

・

gi

・e・・

．

　　

ing

，

．

Tohoku

・

U

皿

iv

．

帥 Prof

．

，



Dept

．

_of

．

ATchitectnrb

，



FacuLty

_ofErLgineering

，

TohQku

　　

Univ

∴

Dr

．

　

Eng．

康鱒

ResearcE　Assoc

．

，

_Dept

．



_oI



Architecture

，



Faculty



of

_En

・

　　gineeling

，

　

TQhoku

　

Univ

．

，

Dr

，

　

Eng

．

東 北 大学 工 学 部 建 築 学 科 　大 学 院生

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 〉

Architectural Institute of Japan

NII-Electronic Library Service

ArchitecturalInstitute of Japan

Significant

nttmbers of

the

structttres

in

large

cities

in

Japan,

such as

Tokyo,

are

founded

in

rnedium

to

soft

_ground.

For

example, of

the

772

sites, each representing a

block

in

the

_grid

system of

47o

m

north-south

by

370

m east-west

in

the

central

_part

of

Tokyo,

738

(more

than

95

%

)

were classified`) as

medium and soft, according

to

the

_ground

classification recommended

in

the

Japanese

code

for

earthquake resistant

design

of

buildings

(Table

_5).

About

40

%

₍₃₀₄

sites) were classified as soft

In

addition, expansion of

the

congested central city area often

leads

to

water

front

developments

in

reclaimed

land,

causing

further

increase

in

the

_percentage

of soft

_ground.

Thus

the

investigation

of

medium and soft

_ground

beh4vior

with respect

to

different

levels

of excitation

is

of

_primary

concern

in

microzonation.

This

_paper

is

an attempt

to

form

a

basis

for

such

investigation.

One

of

the

_problems

in

mapping stable

local

site effect

for

microzonation

is

the

selection of

input

ground

motion

that

can adequately reflect

the

_potential

severity of

future

earthquakes,

Combined

effect

of a suite of

_ground

motions may

be

considered

for

this

_purpose.

For

such combination

to

be

rational, a

'

scaling

_procedure

is

needed

to

normalize all

the

ground

motions.

Based

on

the

inelastic

response

analysis of single

degree

of

freedom

(SDOF)

oscillators,

Hall

et al.'} _report

_that

_scaling

_by

spectrum

intensity

_(SI)

results

in

the

least

dispersion

in

spectral ordinates.

Nishikawa

et al.S) also consiclered

nonlinear

SDOF

oscillators

in

their

investigation.

They

recommend

the

use of

_peak

_ground

velocity or

SI

in

case of structures with elastic

_period

longer

than

abeut

O.3

seconds, and

the

use of

_peak

acceleration

for

structures with elastic

_period

shorter

than

about

O.

2

seconds.

This

study

follows

similar

approach,

but

is

concerned with

the

nonlinear response of various

types

of

_ground,

and

the

discrete

nonlinear model of actual soil

_profiles

is

considered

for

investigation.

It

would

be

necessary

to

consider

the

complete soil-structure

interaction

system

for

realistic study of $caling methods,

However,

this

study

is

aimed at seismic microzonation, and

the

emphasis

is

on

the

identification

of a method suitable

for

nonlinear

free

field

_ground

response,

_paTticularly

at medium and soft sites.

The

level

of excitation

experienced

by

a structure

depends

on

the

type

of

_ground

underneath.

Different

site conditions are

characterized

by

different

_patterns

of substantial variations

in

stiffness across

depth.

Thus

the

nonlinear

response of

_ground

is

by

nature

_quite

different

from

that

of structure.

As

a result,

it

seems worthwhile

_to

investigate

the

relative suitability of

different

methods of scaling a suite of

_ground

motions

for

compatibility

in

the

level

of nonlinear

_gTound

response.

Nonlinear

ground

response

basically

involves

absorption,

transmission,

and amplification of

earthquake wave energy, contained

in

different

_period

bands,

by

soil

deposits.

It

seems appropriate

to

premise

that

energy related

parameters

would

be

effective

in

sca]ing a suite of

_ground

motions.

The

investigation

is

carried out

in

two

_phases.

Initially

the

scaling

_parameter

that

results

in

the

least

overall

dispersion

in

the

level

of nonlinear response,

in

different

site conditions,

is

selected.

Subsequently,

detailed

investigation,

about

different

aspects of nonlinear respones,

is

made

in

case of

the

_parameter

selected

in

the

first

phase.

2.

Methodology

Ground

MotiDns

and

Scaling

Parameters

:

Ten

different

ground

motions,

four

from

the

Miyagiken

Oki

earthquake of

June

1978,

and six

from

other

earth-quakes

in

Japan

and

USA,

as

shown

in

Table2,

were selected.

Ground

mo-tions

from

small

to

large

sizes

based

on

total

energy content are

included,

and

there

is

wide variation

in

the

distribu-tion

of energy

in

diffeTent

_period

bands

as shown

in

Fig.

1(a).

The

ing

Fourier

spectra of

_ground

motions scaled

by

Housner's

spectrum

intensity

(SI)

are

shown

in

Fig.1(b)

for

compari-son.

Four

scaling

_{parameters:(1)}

Peak

_ground

acceleration

(PGA),

(

2

)

Peak

_greund

veloc-ity

_(PGV),

₍₃₎

Housner's

SI9'

with

damping

5

%,

and

(4)

Rate

of energy

input'O)

(P')

were

con-sidered.

Housneris

SI

represents

a measure of energy contained

in

the

_period

band

of

O,1

to

2.5

seconds, and

the

rate of energy

mput

P',

also

_proposed

by

HousneriO),

is

a rneasure of energy

in

the

time

window of strong

shaking.

Of

the

ten

earthquakes shown

in

Table2,

SIGR786E

has

the

highest

total

energy content

_given

by

the

integral

over

the

total

duration

of

the

_ground

accelera-tion

squared.

This

_ground

motion

was assumed

to

be

the

target

motion.

All

the

other

ground

mo-tions

were scaled

by

the

four

methods

to

the

leyel

of

the

target

motlen.

The

values of

the

four

scaling

parameters

are shown

in

Table

3.

Values

in

_parentheses

are

the

re-spective scaling

factors.

The

term

TDgo%

in

Table

3

is

the

time

duration

over which

the

energy

increases

from

5

%

to

95

%

of

the

total

energy,

It

is

a measure ef

the

duration

of strong shaking.

Selection

of

Soil

Profiles

:

Fifteen

sites were selected

to

include

the

Tange of

fundamental

ground

period

Tc

encountered

in

Tokyo

area

from

the

soil

_profile

database

of

Tokyo`).

There

was

generally

seen

to

increase

for

1

200

NO'S

(tlm2)]".

Additionally,

am 4oo 2oo o-am 4co am o am 4oo 200 o am 4oo 2oo o ooo 4oo 2oo D am 4oo 2oo o 6co 4oo 2oo o am 4oo 2co o am.. 4eeg.g. ,g ooo'-CEL4ou< 2eg

(a)O.1

O,2 O,S 1.0 2.0 S,O 10,O

?eried

(Sec}

Original

Ground

Motions

Fig.1

Fourier

Spectra

Table3Scaling

leoD1200600 o1am1am6co oleco12ooam o1eno1amam o1ano1pmOmo o1am1pmOam olecot200am orieoe1eeOam oleoo1am6oo oteoo12ooam o

st

:-.

o.1 e,2 o.s 1,o 2.o s.o lo.o

Period

(Sec}

(b)

Scaled

by

Housner's

SI

of

10

Ground

Metions

Parameters

andScaling

Factors

fairly

wide variation

in

soil

types,

and

the

depth

to

base

layer

was

longer

T,.

The

shear wave velocities

for

different

soil

types

were

estimated

from

the

correlation of

initial

shear modulus

Go

with standard

_penetration

test

N-values,

G,=

soil

_profiles

from

recent soil exploration at

three

sitesi2),

Shinjuku

-31-Architectural Institute of Japan

NII-Electronic Library Service

ArchrtecturalInstrtute of Japan

Fukutoshin,

Tsukudajima,

and

Maihama,

which are in

the

order of

increasing

softness, were

included

as other

typical

cases of medium and soft

_ground.

These

are

denoted

by

S

1,

S

2,

and

S

3

in

Table

s.

Altogether

eighteen sites were considered.

Nonlinear

Modei

of

Soil

Layers

:

The

stiffness of soil

layers

during

the

inelastic

time

domain

response

is

determined

by

the

hysteretic

modeL.

For

this

study

the

strain

dependence

of

the

shear modulus and

the

equivalent

damping

factor

was

based

on

the

Masing's

type

model

developed

by

Ohsaki

et al.i3):

E=Gr,Il+a

sT.

fil---･----J-･---･･-･----･---･-･---･-････-････--･･･---･(1)

g==';'Bfl+2Ii-i+.i

sT.

e]

'

'

(2>

Where,

e:Shear strain

Table4

Constants

of

Hysteretic

Model

T:Shear stress

･

Go:Initial

shear modulus

S.:Shear

strength

g

:

Equivalent

damping

factor

Go

a,B, and

7=

s.

are constants

dependent

on

the

type

of soil.

Various

soil

types

in

the

selected soil

_profiles

were

broadly

divided

into

four

types:(1)

loam,

(2)

sand,

(3)clay,

and(4)gravel.

The

corresponding values of

the

constants a,

B,

and

₇

are shown

in

Table

4.

The

constants

for

clay and sand are as suggested

by

Ohsaki

et

al.

'3), _and

_those

for

leam

_are

selected

by

approximately matching

the

ayailable

test

resultsi`).

The

experimental

data

_points

for

loam,

which are

limited

in

stTain range of about

O.

O05

to

O.

05,

are cornpared with

the

simulated curve

in

Fig.

2.

The

constants

fer

_gravel

are arrived at

by

extrapolation

from

those

of clay and sand, using

the

concept of soil

type

factori5).

The

shear modulus

for

loam

is

assumed

to

be

normalized

by

Go

at

strain

level

of

10-6

%

obtained

by

elastic shear wave velocity, while

those

for

other soil

types

are assumed

to

be

normalized

by

G,

at the

1

₁₀

Soiitypea

_s

_Y Loam

'

,4

'

a

'

'

'

an

'

ave

'

,7

'

olo'

:

i v eE v

ge

k'E2o

,,li

'k''

ee,kee

illll･iili･lli/llit.$

.lty

, ewm,e'Y

ig･Slwt'11.'

t.

..t

't

"nttm]Lw vt.= tt.t

::,･iti:kiigils'i･isl

-tte.t.v/in..tti

･:XIX:

,,2s11i

i"ski

maL.lj.

iiee.ajISs

,ll.,g

I

'

ge'I･ifif

'g"V'･g,

'

,,i/G,,i･,:

'

. '

i"}'t･

$twii･eeee//Ii:'tt,ig/･g･

ililewulliiee

i,'S/l,'S1ii'liSeiil･,

t..

itw

thvf"'

g,ii;;g}:li

'l,ill,l.iii'

ttge

ilge}

iw',''-ey:..Il-: ,,,",1･

ee"S,,

'

･

,,･',s:x\;f'

;･oegf'g･il'$:t

..=tttttv

_±

""

t/y

',

.tymt*{t

ntx'1

..t;'

AsvpLnLs!inec,EaEesn

5

Fig.2

fi4

1cr3

fi2

1ff1

le

Shear

Strain

E{%)

(a)

Shear

Modulus

Comparison

of

Simulated

Dynamic

Characteristics

of

Loam

with

Data

Points

from

Experimental

Resurts'e).

o

i,Ii

/$,i,i,lliiiss

'"

,i/\/?,

'

s

"

:i,X,l.

R

l//,ee11,,l{/gii`

r#,/?iss;rxee,es

i

iG,iiiL,ee,,kaj,,,,ma,/A

i

fi

ma'

/Tl,,,lrisiesii

'g"

11,i/g/Gi

"

lii,i

-

l,ili

£

i

･

i

･

11wa

iff4

ia3

iff2

ici

iO

Shea[

Straia

E

(%)

(b>

Equivalent

Damping

Factor

smallest strain

level

in

dynamic

tests

of

10-`

%.

The

variation with shear strain of

the

shear modulus and

the

equivalent

damping

factor,

for

the

four

types

ef soils

in

Table

4,

are shown

in

Figs.3

and

4.

Computation

of

Nonlinear

Response

:

Sites

were assuming

to

be

horizontally

layered,

and

the

soil

_profiles

were modeled as a series of

lumped

masses connected

by

shear springs and

dashpots,

The

nonlinear

time

dornain

response analysis

was carried out

by

step-by-step numerical

integration

_procedure

to

solve

the

incremental

equations of

-32-ol.'uae=gEB.rs1Eez

1

o

':ibam.:Sand':Claye:Gravel t'/TSh-.t.,

#･'"/11ili',l･,i'11f･,S"lill//1,'/li

:,:i'ill:,iS･i･:,,gii.lli,/i tSE,MblueS-th'mmM/:t

ce,s･Il･il･-iilTllli,i

･

iill･

sL,ti"g/I,g/;'s::;/

;ll,lf,･i.tt,.,"il/g,,:g･,,:;ll,

ll･it.iinmi･,･i.ll･,g,,,i/11,･iilil/ljj･

liinleglilllilgsi･ggilri

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la4

Fig.3

la3

ti2

1cr1

le

Shear

Strain

e

(%)

Strain

Dependence

of

Shear

Modulus

40AS30L:S

20itu.g

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iF,,kma.･.,,,'III･$i#,g'z,g/$l

llili,l'lleeee

ww'iltw,sc-

la';:-/ge.:xa/:es'

lxe.llsgksg:s.t'aj

iy,gllllg･igg･･

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t tt

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S,;asII.V/.

:-

.si,

,ii21:･

""

_l'.kZ

s",'-.'...te.g.ts

ifiliewl/k'k-l,//IX

41ff

Fig4

Strain

iaL3

ic2

ici

Shear

StrainE

(%)

Dependence

of

Equivalent

ie

Damping

motion.

The

_precedure

used was

Wilson's

e-method

develeped

by

Ohsakii6).

The

degradation

in

the

shearing stiffness, as well as

the

equivalent

damping

factor

as a result of

the

hysteretic

eneTgy

dissipation,

was calculated atall

the

soil

layeTs

at ea6h

time

step.

The

time

step

for

the

solution of

incremental

equations was

the

smaller of

the

digitized

time

step of

the

_ground

motion and

1120

of

Tc.

Linear

interpolation

was used

in

case subdivision of

digitized

time

step was necessary.

Viscous

damping

of

2

%

was assumed

to

represent

damping

in

soil at

initial

condition.

Nonlinear

Indicators

of

the

Level

of

Excitation

:

The

level

of strain

depenclent

quantities,

at

different

_points

in

a soil

_profile,

during

the

response

history,

can

be

regarded as

indicators

of

the

level

of excitation.

For

example,

time

window analysis of

gTound

motions

is

often carried out

to

show

the

evidence of

the

soil nonlinearity

from

reduction

in

shear

modulus and

_predominant

_period

elongation

in

time

window of stronger shaking

i'n

comparison

to

that

of

weaker shaking`).

For

the

first

_part

of

the

investigation

in

this

study,

the

maximum equivalent

darnping

factor

_n,

and

the

modulus reduction ratioAdefined as:

.

Go-Gm

A=

_G,

'""'"""'""'''''H"--H'"-"'""""-'''''''''''H'H'''''"H'""''''''''"""''''''H"(3)

where

G.

is

the

minimum shear modulus

during

response

history,

were considered as

indicators

of

the

level

of nonlinear response,

3.

Results

of

Analysis

Variation

of

_A

and

_n

Over

Depth

:

The

values of

X

and

_n

vary along

the

depth

of

the

soil

profiles.

The

mean and standard

deviation

of

_A

for

sites

S1,

S2,

and

S3,

due

to

_ground

motions scaled

by

three

scaling methods,

.PGA,

PGV,

and

Housner's

SI,

are cornpared

in

Figs.

5,

6,

and

7.

Soil

type,

initial

shear moduli, and

the

subdivision of

the

soil

layers

are also shown.

The

relative

performance

of

the

three

scaling

_parameters,

in

_producing

compatible nonlinear response, can

be

compared

from

the

nature ofoverall

dispersion

in

A

for

S

1,

S

2,

and

S

3,

which are

in

the

increasing order of softness.

In

addition,

the

dispersion

in

differeBt

soil

layers

can

be

compared within

individual

soil

_profiles.

Compared

to

scaling

by

Housner's

SI

in

Fig.5d,

scaling

by

PGA

in

Fig.5b

is

seen

to

result

in

respectively smaller, similar, and

larger

dispersion

in

topmost,

inteTmediate

and

just

above

base

layers,

in

case of

the

relatively stiffsoil

_profils

S

1.

Scaling

by

PGV

in

Fig.

5

b

is

seen

to

results

in

the

largest

dispersion

in

all

the

soil

layers.

In

case

of soil

_profiles

S

2

and

S

3,

in

Figs.

6

and

7

respectively,

scaling

by

PGA

show

the

largest

dispersion

in

all

the

layers.

In

Fig.

6,

scaling

by

Housner's

SI

is

seen

to

result

in

the

least

dispersion

in

all

the

layers.

Scaling

by

PGV

and

Housner's

SI

show comparable

dispersion

in

case of upper

layers

of site

S3

in

Fig.7,

with

PGV

faring

better

at

deeper

layers.

The

slightly

inferior

performance

of

SI

at

deeper

layers

may

be

because

of

the

elongation of

_ground

_period,

beyond

the

_period

band

of

O.

1-2.

5

seconds considered

by

Housner9).

This

is

investigated

in

the

!atter

part

of

this

study,

from

which

the

mean

_predominant

_period

of site

S

3

is

noted

to

be

about

2.

5

seconds

-33-Architectural Institute of Japan

NII-Electronic Library ServiceSerVloe Japan of 工nstrtute Arohlteotural 1

．

O λ

O

．

O

tt

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r

’

　 　 　 ノ

　

舞

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礬

豢

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illi

： 　

ト

ぱ

　

　

　

し

匸

ー 荊

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旨

r

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ヒ

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懸

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_、

事

霎

ゐ 義

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ー

“

『

．

無

翫 瞬

舞

寒

陥

懇

驚

慰

飄

戀

…

． caltng 

by

．

ousner

’

s　

S【

〉 （

d

1

．

0

λ

0

．

0LO

λ

0

．

0

灣

盤

蟻

蒙

繋

灘

爵 鞭

鰭

灘

羈

撫

鑞

i朋 ：Lo画m

，

　S：Sand

，

　C：CI甌y

，

　G：G【a▼o

Subindices

・

A：alIu ▼ia18nd

　

D：diluvia黜

　　　　　　initial　Mod 山 s　

G

_。

0

．

Om

　

PGVby

Scaling

〉

C

（

PGAyb

Scal

血

_g

）

b

（

（

ε

ξ ユ O 自

S1

Deposit

Soil

for

入

Ratio

Reduction

S1

_（

Shinjuku

_）

　 Fig

．

5

　Modulus

・

25

．

00m　

（

a

_）

Soil

　

Deposit

LO

λ

e

．

eLO

λ

0

．

0

，

轍

鑾

鍵

韈

灘

脳

糠

麟

鍵

灘

鬣

、

驪

驪

、

嬲

覊

鑞

蠶

轗

01 　 　 　 λ 0

，

0

S

：Sand

，

　C：Clay

，

　G；Grave溷

Subindices

・

A：alluワial　and　D：diluviaI

Initial　

Mo

血 ｝us　

G

_。 　 　

IySb

calingOUS 皿er

　

s

SH

）

d

（

PGVby

Scaling

） C （

Scaling

　

by

　

PGA

S2

325goヴ 

Deposit

Soil

for

λ

Ratio

Reduction

　　　　　（

b

＞

ajima

_）

　　

Modulus

（

Tsukud

S2

　　 　EHASE 　　LAYERDeposit

一

Fig

_．

₆

総

0

，

0m

AC 鰮 DS

嘗

）

曇 診 （

［

DG

・

33

。

50m

Soi1

） a

（

Lo λ O

．

O1

．

0 λ O

．

OLO λ 0

．

0

1

懿

灘

灘

　

難

麟

編

講

撮

籍

灘

靉

墾

鏤

驫

糠

撫

醗

軈

鞴

難

蝋

講

熱

懸

鑼

蕪

D；di■凹 ▼ia匚 odu 畳us　

Go

S：SRnd

，

　C：Cla防 G：Gra▼

Svbindices

−

A：鼠llu▼ini　anI 　　　　　　且niIial　I O

。

OiTi

01dM caling



by

．

ousner

’

s　

SI

）

（

d

PGVby

Scallng

〉

C （

PGAby

Scaling

（

ε

59

自

一

_7450m

S3

Depos五

t

Soi1

for

λ

Ratio

Reduction

　 　 　

（

b

）

（

Maihama

）

Fig．

₇

Modnlus

S3

Deposit

Soil

）

a （

34

Llbrary N工 工

一

,

in

Fig,

ll.

It

is

an

indication

that

scaling

by

SI

with a

_period

band

extended

in

the

long

period

region

will

irnprove

the

compatibility

in

the

nonlinear response of soft

deposits.

Scaling

by

P'

indicated

larger

overall

dispersion,

even compared

to

that

by

PGA,

and

is

not shown

here

for

comparison.

As

mentioned earlier,

P'

is

arneasure of

the

energy

in

a

time

window and

does

not

reflect

the

di$tribution

of energy

in

different

peried

bands.

Disregard

of energy

distribution

in

different

period

bapds,

which

is

quite

diverse

in

Fig.

1(a),

is

possibly

the

reasons

for

its

_poor

_performance.

p

taratonofAand

m

forvanoussites

A

concise comparison of

the

relative

_performance

of three scaling

parameters,

for

all

the

sites

considered

in

this

study,

is

made

in

Figs.

8,

9,

and

10.

For

this

puTpose,

the

layer

of maximum

_n

due

to

the

targed

_ground

motion was

identified

in

all

the

soil

_profiles,

Then

X

and

_n

values at

the

identified

layers

due

to

scaled

ground

motions,

including

that

due

to

the

target

motion, were combined

to

_give

mean and

Standard

deviation.

Figs.8,

9,

and

10

show

the

_plots

of mean and standard

deviation

of

A,

with respect

to

Tc

values of

different

sites,

for

the

three

scaling methods.

The

maximum and minimum

values are also shown.

Sites

with

T.

shorter

than

O.

2

seconds, show

least

dispersion

for

scaling

by

PGA

(Fig.8),

and

those

with

TG

in

the

range

O.2-O.75secends

show

least

dispersion

for

scaling

by

Housner's

SI

_(Fig.10).

Similar

to

the

ebservation made above

in

case of

Fig.7,

close comparison of

sites

with

T,

longer

than

O.

75

seconds

in

Figs.

9

and

10

shows

that

scaling

by

PGV

results

in

slightly

100

gege:

80.sg 7o].tS

6o

E'

so

40

30

o.1

e.2

o.s

1.o

2.o

Fundamental

Ground

Period

Tc

(Sec)

Fig.8

Variation

of

A

for

Scaling

by

PGA

100 90A*vK 80=sV 70=veM

6ot=Te

50:oo

30

o.1

O.2

O.5 1.0 2.0 Fundamental Ground Period TG

(See}

Fig.10

Variation

of

A

for

Scaling

by

Housner's

SI

l],"/[liX,l,S,3,,fr･:i::}･lii,ii}ll//-fi,Il,18Iiii'l;ii/ta:.taj//tps,i"g'i'/L.i,g,/g.i･t

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r,i.l,l:E{e,ssltt"/ttttt

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:6

80

g/7o

i'=60

o.1

o.2

e.s

1.o

2.o

Fundamenta1

Ground Period TG

CSec)

Fig.9

Variation

of

A

for

Scaling

by

PGV

To9v.9tsptEtu.EEve:pt

6

4

2

o

ScelingbyHousner'sSI"'/4･g/l;l}slgr,/l'r,#'c･s

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i･l･ts

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ilill

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ili

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i

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Fig.11

o.1

o2

o.s

1.o 2.e

Fundamental

Ground Period TG

(Sec}

Period

Elongation

of

Ground

for

Scaling

by

Housner's

SI

-35-Architectural Institute of Japan

NII-Electronic Library Service

ArchitecturalInstitute of Japan

smaller

dispersion.

The

three

Ta

ranges of

less

than

O.2seconds,

O.

2-O.

75

seconds, and

_greater

than

O.

75

seconds, correspond

to

the

hard,

medium and soft

_ground

classifications recommended

in

the

Japanese

code

for

earthquake resistant

design

of

buildings.

Again,

the

significant elengation of

_ground

period

with

increased

nonlinearityG)

is

a

_possible

reason

for

relatively

larger

dispersion

for

scaling

by

Housner's

SI

in

case of soft sites.

The

variations of

_v

and

_X

follow

sirnilar

_patterns.

Overall

comparison of

Figs.8,

9

and

10

shows

that

Housner's

SI

is

a reasonable choice.

In

addition,

the

SI

defined

in

a

_period

band,

adequately extended

to

include

long

_period

components,

is

likely

_to

improve

its

performance

as a suitable scaling

_parameter

in

case of soft

_greund.

Thtts,

of

the

four

parameters,

with

different

characteristics

in

relation

to

energy, selected

for

relative comparison,

SI

is

selected

for

further

investigation

that

follows.

Predominant

Period

of

Surface

Response

Motion

:

The

predominant

periods

of

the

surface response motion

for

all

the

eighteen soil

_profiles,

and

for

all

the

ten

input

_gTound

motions scaled

by

Housner's

SI

were

found

out

frorn

the

tTansfer

function

analysis.

Fourier

spectra were computed using

the

acceleration

time

histories.

The

spectra were

_then

smoothed

using

the

Parzen

lag

window.

The

smoothing

bandwidth

for

the

lag

window was varied

from

o.2

to

O.

5

Hz

depending

on

T,,

with narrower

bandwidth

for

longer

Tc.

The

transfer

functigns

were computed as

the

ratios of

the

smoothed

Fourier

spectra

between

the

_ground

surface and

the

top

of

the

base

layer.

The

predominant

period

was arrived at

from

the

fundamental

resonant

_peak

in

the

transfer

function.

The

range of

disp6rsion

in

the

_predominant

_period

is

shown

in

Fig.11.

As

noted earlier,

the

_predominant

_period

is

a measure of

the

level

of nonlinear excitation.

Smaller

dispersions

in

_predominant

_period

due

to

different

scaled

_ground

motions

indicate

the

suitability of

the

scaling methed.

The

coefficient of variation

(COV)

of

the

_predominant

_period

in

Fig.

₁₁

was

found

to

lie

in

fairly

low

range of

9

to

26

%,

with an average of

17%,

indicating

that

the

different

_ground

motions

scaled

by

Housner's

SI

result

in

fairly

compatible

leyels

of nonlinear response.

The

doted

curve

in

,Fig.11

$hows

the

one-to-one relation

between

_T6

and

_predominant

_period.

Oyerall,

$ignificant

elongation

in

the

_ground

_period

due

to

nonlinearity can

be

noted

for

sites of

Tc

longer

than

about

O.

2

seconds

(ie,

medium and soft sites), with

_particularly

large

elongation

for

sites of

T,

longer

than

about

O.

35

seconds.

The

comparatively

laTger

dispersion

in

_A

for

scaling

by

Housner's

SI,

in

case of soft sites, noted

in

Figs.7

and

10,

may

be

attributed

to

the

large

elongation

in

_ground

_period

seen

in

Fig.11.

If

the

response of

long

_period

oscillators

is

suitably

ineluded

in

its

definition,

SI

is

likely

_to

serve as a

better

scaling

_parameter

in

case of soft sites.

An

attempt was made

to

investigate

this

possibility.

Fig.

12

shows

dispersion

in

A

for

_ground

motions scaled

by

PGA

for

hard

sites and

by

SI

defines

in

different

period

bands

in case of medium and soft sites.

Scaling

is

done

by

PGA

in

case

of

the

two

soil

_profiles

in

_group

₁

(see

Table

5),

and

by

Housner's

SI

in

case of nine soil

profiles

in

grounps

2

and

3.

SI

defined

in

_peroid

bands

extepded

in

the

long

_period

region are used

for

sites with

TG

longer

than

O.55

seconds.

SI

in

_period

band

O.1-4.0seconds

is

used

in

case of

four

soil

_profiles

in

groups4

and

s,

and

the

SI

in

_period

band

O.

1-6.0

seconds

is

used

in

case of

thTe'e

soft sites

in

_group

6

<Table

5).

Compared

to

Fig.

10,

the

dispersion

in

A

in

case of softer

sites

is

distinctly

decreased

in

Fig.

_12,

as a result of

the

extension of

_period

band

in

the

long

_period

region.

The

period

of a

_given

site also

becomes

longer

as

the

nonlinearity

increases

with

level

of excitationfi)1

However,

the

effect

is

similar

to

that

observed

in

a range

-36-AgevK=o=v=voec--==BE 100

90

eo

70

oo

50

40 30

o.1

o.2

o.s

1.o

2.e

Fundamenta

Ground

Period

TG

(Sec)

Fig.

12

Variatien

of

A

for

Scaling

by

SI

Defined

in

Different

Period

Bands

(by

PGA

in

of

hard

to

soft sites,

because

a

_given

the

level

of excitation

increases.

Spectrum

Intensity

of

Surface

Response

site can

be

considered to

behave

as -more soft" as

Motion

:

,

To

further

investigate,the

suitability of

SI,

in

scaling a suite of

ground

motibns,

,for

compatibility

in

the'

level

of nonlinear response,

the

SI

of surface response motions were computed

for

all

the

eighteen

sites.

The

mean and standard

deviation

of

the

Housner's

SI

of surface respbnse are

tabulated

in

Table

s.

The

Housner's

SI

of surface respon'se motions,

due

to

the

taTged

_ground

motion

input,

are also shown.

The

Housner's

SI

of surface response motion

is

simply referred

to

as

the

surface

SI.

The

_grouping

of

sites, suggested

for

microzonation of

TokyoZ),

and

that

recommended

'in

the

Japanese

Code

for

earthquake resistant

design

of

buildings,

are

also

indicated.

'Table

5

shows

that

there

is

agreement

+

between

the

SI

of surface response rnotion

due

to

the

target

ground

mot.ion

input,

and

the

ayerage

SI

of

'

surface response motions

due

to

all

the

input

motions.

The

COV

of

the

Housner's

SI

of surface response

motions

is

less

than

2o

%

for

all

the

sites.

This

is

an

indication

that

the

level

of surface response

due

to

target

input

motion

is,

on

the

average,

comparable

to

the

level

_pf

surface response

due

to

scaled

input

t

t

motions,

'

'

Table5

shows

that

Housner's

SI

of

surface response

is,

on

the

average,

greater

than

or neafly equal

to

that

of

input

motions

(195.0cm),

except

for

sites with

Tc

longer

than

1.oseconds.

Significant

elongation of

_ground

_period

noted

in

Fig.

11

is

_possibly

the

reason

for

the

reduction

in

Housner's

SI

in

ca$e of

soft sites.

･

To

investigate

this

effect,

the

term spectrum

intensity

amplification

(SIA)

was

defined

as

the

ratio of

the

surface response

SI

to

the

input

SI.

SIA

represents

the

ratio of energy

in

surface

motion

to

that

in

the

input

motion,

in

a

pre-defined

period

band.

period'band,

and may serve

'as

a suitable

band

recommended

by

Housner"),

soft

'

which

is

rather unusual.

So,

b4nds

:

O.

1-1.

0

s,

1.

0-2.

5

s,

2:

5-4.

0

s

bands'were

consi

of

long

_period

components.

Fig.13

Fig,

13s

shorter

than

about

O.

35

seconds.

period

band,

in

comparison

to

that

in

this

studiy,

SIA

becomes

greater

than

one

gFound

tend

to

exhibit

high

increased

level

of excitation,

it

period

band

as

the

level

of excitation

'

It

is

seen

in

the

SIA

in

_period

band

of O. IL2. 5secopds

seen

to

be

smaller

than

nnity even when a

it

is

necessary to consider

SIA

in

nonlinear response of soft sites.

Table5

Spectrum

Intensity

bf

Surface

Response

Motion

JapaneseHeusner'stMean soi]ToSellCededuetetargetHeusner'sSlStandard Ne.(sec)Group2)GroupingmotieninputofsurfaceDeyiatienc,o.v.

(ern)resnse(em)

'

Har

'

'

'

'

2O.14

199.53 208.4211.43e.os

'

'

'

'

'

4O.23

207.4S

212.698.39e.ou

5e.26

208.01

2oo.5816.26O,08

6O.292

209.03 197.7516.23O,08

7{Sl)O.31

240.tl 262.93･22.02O,08

8O,33

Medium27S.IS 260.4031.68O.12

'

'

'

tt

'

10O.5D.3

229.86

206L6231.22O,15

11(S2)O.53

301.SO

243.3237.69e,15

'4

'

'

'

'

13e.67

747.78 21S.8033.05O,15 4'

_'

_'

_'

_'

151.oo

_147.77

_{161.5928.66O.!8}

'

Seft

'

'

'

'

17{S3)1.436

139.1･4 139,2718.glO.14

lg1.68

90.78 S9.529,66O.il

It

can

be

a suitable

indicator

of

the

local

hazard

at a site,

to

structures

in

the

parameter

for

microzonation.

However,

based

on

the

_period

sites

in

Table

5

are

likely

to

be

iden'tified

as

less

hazarclous,

attempt was made

to

compare

SI

in

narrower

_period

bands.

Four

_period

and

4.0-6.0s,

were

tentativelY

considered,

The

later

two

dered

to

aecount

for

the

_ground

period

elongation

in

Fig.

_11,

indicating

amplification

shows

the

vaTiation of

SIA

with

7::.

hows

that

SIA

remains

fairly

unchanged

in

the

different

_period

bands,

in

base

of sites with

T,

Fer

sites with

T,

longer

than

O.35

secondsl

SIA

increases

in

longer

shorter

_period

band.

For

the

site with

longest

Tc

considered

in

only

in

the

longest

period

band

in

Fig.13,c.

Thus

softer

er

SIA

at

longer

_period

band.

Noting

that

the

_ground

becomes

sqfter with

can

be

expected

that,a

given

ground

will exhibit

higher

SIA

at

longer

mcreases.

Fig.

13

that

mean

SIA

for

site

S

3

,is

well above unity

in

Figs.

13

c and

13

d.

In

contrast,

in

noted

to

be

smaller

than

unity

in

Table

5.

The

SIA

was

wider

period

band

of

O.

1

--6.

0

seconds was considered.

Thus,

narrower

bands,

so as

to

adequately reveal

the

_potential

hazard

due

to

It

seems

logical

to

introduce

the

concept.of

Limited

Band

Spectrum,

-37-Architectural Institute of Japan

NII-Electronic Library Service

ArchrtecturalInstrtute ofJapan

Intensity

_(LBSI)

to

represent

SIA

in

different

_period

bands.

The

four

_period

bands

considered

here

are

tentative.

The

actual

bands

could

be

based

on

the

study of

the

natural

_periods

of

different

types

of

structures at a

locality,

so

that

the

hazard

to

a

_group

of structures

in

a

_period

band

is

_properly

reflected.

The

band,

however,

cannot

be

so narrow as

to

be

close

to

a single

_period

_point

itself,

and suitable

balance

between

two

extermes

is

needed.

It

may also

be

noted

that

the

resonant

_peaks

of

transfer

function

for

softer sites are

flatter6),

rather

than

sharp, and

include

a

fairly

wide range of

_periods.

As

a

result,

it

seems more

logical

to

think

in

terms

of

_period

band

instead

of a single

_point.

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Fundarnental Ground Peried

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Spectrum

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4,

Conclusions

Of

the

four

scaling

_parameters,

with varying

degrees

and

type

of energy representation,

Housner's

SI

is

seen

to

_produce

the

most compatible nonlinear respnose of medium sites

(TG

range

o.2

to

O,

75

seconds).

Housner's

SI

and

PGV

_produce

comparable compatibirity, with

PGV

faring

slightly

better,

in

case of soft sites

(

Tc

longer

than

O,

75

seconds).

Scaling

a suite of

_ground

motions

by

SI,

defined

in

a

_period

band

adequatery extended

to

account

for

the

ground

period

elongation of soft sites,

improves

the

compatibility

in

nonlinear response of soft sites.

PGA

seems

to

be

appropriate

for

hard

sites of

_Tc

less

than

about

_O,

₂₀

seconds, where

the

effect of nonlinearity

is

small.

The

rate

of

energy

input,

which

is

a measure of energy content

in

the

time

window of strong shaking, with complete