液状化地盤における杭基礎の地震応答に関する研究 : 杭基礎模型の遠心載荷実験と解析

【

論 文

1

　　　日本 建築 学 会構 造 系 論 文 報 告 集 第

439

号

・

1992

年

9

月

Joumat

　of 　

StTuc

し

，

　

Constr

，

　

Engng

，

　

AIJ

，

　

No

．

439

，

　

Sep

．

．

lgg2

・

_PILE

　

FOUNDATION

　

R

耳

SPONSE

　

IN

　

LI

Ω

UEFIABLE

　

SOIL

　

　

　

　

　

　

　

　

　

DEPOSIT

　

DURING

　

STRONG

　

EARTH

Ω

UAKES

．

Centrifugal

　

test

　

for

　

pile

　

foundation

　

model

　

and

　

correlation

　

analysis

　　　　　　液状 化

地 盤

に

お け る

杭 基 礎

の

地

震応 答

に

関

す

る

研 究

　　　　　　　

杭 基礎模 型

の

_{遠 心載}

_荷実

_験

と

解析

　　　　　　　

、

Y

ゆ

’

MfYAMOTO

＊ ，　

KenfC

’

MIUI

〜

A

＊＊ ，　

Rouald

　

F

．．

SCOT7

’

＊ ＊＊

_and



Behnam

　

UUSUMANPt

＊ ＊ ＊

　　　　　　　　　宮 本 裕 司

1

三

浦 賢 治 ，

SCOTT

　

Ronald

　

F

_，

　

HUSHMAND

　

Behnam

　

Dynamic

　centrifugal 　

tests

　were 　

performed

　

for

　a　

pile

　

foundation

　model

．

to

　

develop

　an　understand

．

ing

　of　

_pile

　

foundation

　response 　

in

　nonlinear 　

liquefiable

　soil　and 　

to

　

_provide

　

data

　

for

　verification 　of an　earthquake 　response 　analysis 　method 　

duriqg

　strong 　earthquakes

．

　

Centrifugal

　

test

　resuits 　

indi−

cate 　

that

　

pile

　

foundation

　

response 　

in　

liquefiable

　sand 　

is

　

greatly

　affected



by

　soil　

behavior

　

due

　

to

large

　

ground

　

displacement

　and 　excess 　

pore

　water 　

pressure

　

buildup．

　

The

　numerical 　model 　which consists 　of　

beam

　elements 　and 　nonlinear 　

lateral

　

Winkler

　springs

_，

　

taking

　

into

　account 　

the

　changing effective 　stress

_，

　

is

　

discussed

　

by

　comparing 　

predicted

　resul し

s

　with 　measured 　results

．

Key

ω

ordS

：‘翩 厂tfugat 　mode 〃 85‘

，

　similaritbl 厂

_礁

pile

_ノ

’oun ‘

lation

，

　effective 　stres5

_，

　

liquefaction

　　　　　　　　　 遠

心

載 荷 模 型 実 験

，

相 似 則

，

杭 基 礎

，

有 効 応 力

，

液 状 化

1

．

　

lntroduction

　

　

Many

　

high

　rise 　

buildings

　supported 　

on

　

pile

　

foundations

　

are

　

under

　

construction

　

or

　

being

　

planned

　

in

　

t

卜

e reclaimed 　coastal 　

area

　

around

　

Tokyo

　

Bay

．

　

The

　

behavior

　

of

　

such

　

structures

　

is

　

greatly

　

affected

　

by

nonlinear 　soil

．

pile

　

foundation

　

interaction

　

during

　

strong

．

earthquakes

．

　

Particularly

　

in

　

liquefiable

　

sand

deposit

，

　

furth

．

er

　complicated 　

interaction

　

is

　

expected

　

to

　

occur

　

between

　

piles

　

and

　

the

　

surrounding

satllrated 　soil 　

because

　of　

_pore

　water 　

pressure

　

generation

　

and

　

large

　

displacements

．

　

Thus

，

　

an

　

improved

aseismic

　

design

　

method

　

is

　

req

血

ired

　

to

　

take

　

into

　

account

　

nonlinear

　

soil

−pile

　

foundation

　

interaction

．

　　

Liquefied

　

soil

　

behavior

　

during

　strong 　earthquakes 　

has

　

been

　

studied

　

experimentally

　

and

　

analytically

since

　

the

　

Niigata

　earthquake 　of　

1964．

　

Several

　

constitutive

　

models

　

with

　

excess

　

pore

　

water

　

pressure

generation．

in

　

saturated

　

soil

卜

ave

　

b6en

　

proposed

_，　

for

　

example

　

by

　

Martin．

　

et

　al

．

1）and 　

Ishihara

　

et

　

aL

　z ｝

．

Effective

　stress 　

analyses

　

are

　

employed

　

to

　

predict

　

ground

　 responses

．

　

Pile

　

foundation

　r

と

sponse

　

in

liquefiable

　

soil

　

subjected

　

to

　

stron

’

g

　

earthquakes

　

has

　also 　

been

　studied 　experi 珥 entally

．

　

Tatuoka

　

et

　

al

．

3）

_，

Mori

　

et

　

al

『 4

 

．

　

Kobayashi

　

et

　al

_，

5）_and

NPmura

_{et 　al}

_・

6）

　conducted 　

shaking

　

table

　

tests

　

to

　

study

　

pile

　Tesponse

in

　

liquefiable

　

sand

．

　

during

　

earthquakes

．

　

In

　

these

　

tests

，

　

the

　stresses 　arising 　

from

　

the

　weight 　of　soil 　were much 　

less

出an 　

those

　occurring 　

in

　

the

　

field

．

　

Thus

，

　

they

　

did

　

not

　

accurately

　

simulate

　

the

　

properties

　

of

　

soil

』

．

nonlinearity 　and 　excess 　

_pore

　

Water

　

pressure

　

generation

　

which

　

depend

　

on

　

the

　

magnitude

　

of

　

effective

stress

．

　

Recently

　

attention

　

has

　

been

　

_paid

　

to

　

centrifugal

　

model

　

testing

　

as

　

a

　useful 　

tool

　

in

　

improving

　

the

similarity

　rule 　

in

　

geotechnical

　

modeling

．

7

 

Centrifugal

　

tests

　

on

　

liquefaction

　

have

　

been

　

carfied

　

ollt

　

to

　　

庫

Senior



Research



Engineer

，



Kobori



Researc

_卜

Complex



Kajima

　　　

Corporation

　

騨

Assistant



Manager



Koboli



Research



C6mp

［ex　

Kajima

　

CQrpor

．

　　　

ation

，

　

Dr、

　

Eng．

ホ林

Prof

，

　

CalifQmia

　

Insh1ute

　of 　

Techno

］ogy

，

　

Sc

．

　

D

榊 林

Visiting



Faculty



Califomia



lnstitute

_of

Technology

，



Ph

、

D

鹿

島建

設

株

式

会社

小堀 研 究

室　

主 任 研 究 員

鹿

島建

設

株

式

会社 小

堀 研 究 室

　

次 長

・

博 士 （工 学 ）

カ リ フォ ル ニ ア 工 科 大 学

・

博士 （理学 ）

カ リフォルニ ア 工科 大 学

・

博士 （学 術 ）

Architectural Institute of Japan

NII-Electronic Library Service

ArchitecturalInstitute of Japan

represent soil

behavior

in

the

field.

Scott

et

al.

S)

_conclucted

_a

_sinusoidal

_excitation

_test

_on

_the

pile

head

ef a single

_pile

ih

a saturated

soil

deposit

to

verify

the

similarity

rule

by

comparing

the

dynamic

behaviors

of model and

_prototype.

Chang

and

Kutter"'

conducted

an earthquake

excitation

test

on

a

four-pile

_group

model

in

dry

sand

to

study

the

effect

of

nonlinear

soil

on

earthquake

response.

However,

very

few

studies

have

investigated

pile

foundation

responses

in

liquefiable

sand

deposit

during

strong

earthquakes.

Pile

foundation

response

in

a

liquefiable

soil

is

usually

analyzed

using a

two-dimensional

finite

element

methodiO)･i])･'2)

or

a

bearn-Winkler

spring

mode14)'6)'iS)']`)

incorporating

effective

stress

analyses.

Howeyer,

these

analysis

methods

lack

confirmation.

Further

experirnental

study,

therefore,

is

required

to

verify computer codes

for

calculating

the

response

of

structures

supported

on

pile

foundations

in

nonlinear

liquefiable

soil

during

strong

earthquakes.

The

object

of

this

study

is

to

develop

an

improved

understanding

of

soil-pile

foundation

interaction

effects

in

a

nonlinear

liquefiable

soil

deposit.

Dynarnic

centrifugal model

tests

were

_performed

under

a

centrifugal

acceleration

of

50

_g

on

a

model consisting ef a rigid

_pile

cap

and

a

four-pile

_group

embedded

in

dry

or

saturated

fine

sand.

Correlation

analyses

were

also

conducted

on

the

test

results

using

a

simplified

numerical

model

incorporating

an

effective

stress

analysis.

2.

Centritugal

Model

Test

2.1

Centrifuge

Equipment

and

Test

Moclet

The

centrifuge

employed

at

the

California

Institute

of

Technology

has

an approximate effective radius

of

1

m and a maximum acceleTation

of

about

175

_g.

It

is

equipped

with

a

one-degree-of-freedom

shaking

table

and

data

acquisition system.

The

soil

container

(a

laminar

box'5))

is

a

rectangular

box

made

of

1.

27

cm-thick

aluminum

layers

separated

by

_placing

roller

bearings

between

them

to

reduce

boundary

effe

¢

ts.

The

soil

container,

measured

internally,

is

35.6

cm

longx17,8crn

wide ×

25.4

cm

depth.

Dynamic

centrifugal

tests

on

a

_pile

foundatien

model

were

perfermed

at

50

_g.

Scaling

relations

in

a

centrifugal

model

test,

as

shown

in

Table

1,

require

dynamic

model

time

to

be

reduced

by

1!so,

whereas

acceleration

is

increased

by

50

times.

If

the

soil model

is

made

of

the

same material as

the

prototype,

the

stresses

in

the

model

are

the

same

as

in

the

prototype.

Thus,

the

_properties

of

soil

nonlinearity

and

liquefaction

in

the

centrifugal

test

represent

those

of

the

_prototype.

According

_te

the

sirnilarity

rule,

excess

_pore

water

_pressure

dissipation

occurs

50

tirnes

faster

than

other

dynamic

processes

in

the

model'`).

One

method

for

making

these

the

same

is

to

use

a

fluid

with

a

viscosity

so

times

that

of water.

However,

in

these

tests,

water

was

employed

because

the

_grain

size

of

the

sand

used

Table1

Similarity

rule

in

centrifugal model

test

Table2

Physical

_properties

of

Nevada

s'and

#l20

e+-.m-+n-.- 1773

--u--Pilefoundetionmodel

F-,3,s!=-O-2S

XAH4

o.o-OJ5-AH 4･eA'H2 S,30 1.44

l

,

3.45 _s.6sOPP4OPP2

DrytSaturated

e,4e t,19sand PPI

3

l'$G7GSSGSSG4SG3SG2SGI

1.58Laminar Bex 10,710.4

-o.o

-O.7Sur3

LT2-4.e

-E.7SUrl

(Unit:

m)

AH:HefizontalAcceletomeler

SG:StrainGa-ge

PP:PorePfessureTrensducer

MDisplaceme"tTransducer

Fig.1

Centrifugal

test

model

indicated

in

_prototype

scale

-50-was

smallei

than

that

of

the

_prototype

and

the

eflect

of

the

density

and

the

viscosity

of

_pore

fluid

on

the

test

results

is,

still

not

clear.

The

excess

_pore

water

_pressure,

therefore,

dissipates

502

times

faster

in

the

model

than

it

would

in

the

_prototype

with

the

same

soil.

Fig.

1

shows

the

test

_model

and.the

_positions

of

measuring

instTuments.

The

dim'ensions

in

this

figure

are

indicated

in

_prot6type

scale.

The

_pile

foundation

model

copsisted

of

a

rigid

_pile

cap

and

a

four-pile

_group.

The

_piles

were

rigidly

attached

to

the

_pile

cap,

the

weight

of

which

wa$

85.2t6n

in

_prototype

scale.

The

_rpodel

_piles

represented

prototype

tubular-steel

_piles

of

diameter

O,

48

m,

thickness

13

mrn and

length

10.

7

m, witti

pile

spacings

ef

2.

5

qiameters,

The

bending

stiffness

of

the

_pile

was

10.

9

×

103

t･m!

in

_prototype

scale.

The

soil

used

in

the

{ests

was

Nevada

sand

#120

of

O.

1

mm mean

_grain

size.

The

_physical

_properties

of

this

sand

are

listed

in

Table

2.

In

the

dry

tests,

the

sand was

_poured

into

the

box

by

the

raining

technique

to

a

depth

of

about

22

cm

in

model

scale.

In

the

saturated

tests,

de-airea

water

was

_poured

into

the

box,

.and

the

sand

was

_poured

into

the

water

by

the

raining

technique

to

a

depth

of

about

22

cm

in

model

scale.

Then,

the

_pile

foundation

model

was

pushed

into

the

soil

at

1

_g.

The

surface

of

the

soil

was

about

1

cm

below

that

of

the

water.

In

these

tests,

the

centrifuge

was

gradu.ally

brought

up

to

sOg

and

a

steady

acceleration

of

50

_g'was

maintained

for

20

minutes

before

earthquake

excitation,

to

saturate'

the

soil

completely.

Finally,

the

soil

surface

settled

about

1.

2

cm

(O.

6

rn

in

_prototype

scale)

in

the

middle.

The

soil

depth

was

about

20.

8

cm

(10.

4

m

in

_protetype

scale)

as

shown

in

Fig.

1.

The

total

unit

weight

of

the

saturated sand was

1.98t!mS

after

conseliclation

at

50g

and

its

relative

density

was

43

%.

2.2

Instrument

and

Input

Accelerations

The

instruments

used

in

the

dry

sand

tests,

as

shown

in

Fig,

1,

were

4

accelerometers

(AH),

3

linear

variable

differential

transducers

(LT)

and

7

strain

_gauges

(SG)

for

measuring

_pile

bending

moments.

In

the

saturated

sancl

tests,

4

_pore

water

_pressure

transducers

(PP)

were added

and

only4

'strain'gauges

(SG3,

SG4,

SG5

and

SG6)

were used.

Two

tests

with

different

input

ac.celeration

levels

were

con.ducted

in

the

dry

and

saturated

sand

tests.

The

input

acceleration was similar

to

the

1940

E

1

C,entro

earthquake

recerd

NS

component,

Th6

maximum

input

acceleratiohs

for

the

dry

sancl

,tests

were about

85

gal

(T-EST-D

1)

and

203

_gal

(TEST-D

2),

and'

those

for

the

saturated

sand

tests

were

about

10o

_gal

(TEST-S1)

and

250gal

(TEST-S2),

which were measured at

the

soil container

base

(AH1).

2.3

Test

Result.s

The

test

results

shown

below

are adjusted

to

prototype

scale.

Fig.

2

shows

typical

accelerqtion'time

histories,

pile

bending

moments, excess

_pore

water

pressures'and

ground

relative

displacement

rneasured

in

TEST-S

1

and

TEST-S

2.

The

excess

pore

water

pressures

in

TEST-S

1

and

TEST-S

2'

increase

according

to

the

intensity

of

the

input

acceleration.

The

_gefierated

exce'ss

_pore

water

_pressures

indicate

the

maximum

values

at

around

13

seconds, which

thereafter

decay

monotonously.

As

discussed

above

with

refeTen'ce

_to

tbe

scaling relations,

the

dissipation

of

excess

_pore

water

_pressure

in

the

prototype

would

have

occurred

so

slowly

that

the

_peak

excess

_pore

-water

_pressure

would

have

remained

for

a much

longer

time.

For

TEST-S

1,

the

ratios

of

the

maFimum

excess

pore

water

pressure

to

the

initial

effective

stress･are

about

O.

18

at

GL-3.45

m

(PP4),

O,

15

at

GL-5.3Q

m

(PP2)

ancl

O.

08

at

GL-10.4m

_(PP

1),

which

were

considerably

short of complete soil･liquefaction.

For

TEST-S2,

these

values

are

about

1.0

at

GL-3.

45

m

(PP

4),

O.

68

at

GL-5.

30

m

(PP

2)

and

O.

47

at

GL-10.

4

m

(PP1),

so

that

the

upper

layer

of

the

soil almost reached

complete

seil

liquefaction.

The

_generated

excess

_pofe

water

_pressure

(PP3)

in

the

middle

of

the

_pile

_group

is

almost

the

same

as

PP4

in

the

'

surrounding

soil

at

ne'arly

the

same

depth,

It

can

be

seen

that

the

upper

soil

between

the

_piles

reached

soil

liquefaction

as

did

the

surrounding

soil.

From

the

comparison

of

time

histories

of

PP

3

and

PP

4

for

TEST-S

1,

it

seems

_probable

that

the

high-frequency

fluctuations

observed

in

PP

2

and

PP

4

were

due

to

compression

waves

generated

in

the

saturated sand

by

the

vertical vibration

of

the

s6il container.

For

TEST-S

2,

the

fluctuations

may

have

been

caused

by

the

dilatancy

of

the

soil

during

large

strain.

The

acceleration

response at

GL-O.

75

m

(AH

3)

for

TEST-S

2

is

amplified

in

the

loweF

frequency

content

compared

with

that

for

TEST-S

1,

The

horizontal

relatiye

displacement

at

GL-O.

'75

m

(LT

3)

-51-Architectural Institute of Japan

NII-Electronic Library Service

ArchitecturalInstitute ofJapan

Fig.2

Fig3

300.

-300

20o.-Gal

-200.

100.

-100.

5

-5.10

-10O.1

o.0.1

o.

AH3:ADc.atGL-O.75m

em

50D.

-seo.

300

-300.

300s

-300.

10.

-10

2e.

-20.0.5

oO.5

oO,5

o.

AH3'

Accat

GL-O

o.oi.tkp,em,ww/,liLitLELtilfo'SS,e,3"IW,ll';lllil[!

e'P'L',,.$S".'...-.e

2

tr

tdspatGLo7sm

_iO

FICM

UT3ReviatiVediSPatGL`075M

3osec

-2

EST-Sl)

-10.)

(TEST-S2)

Measured

accelerations,

_pile

bending

moment$,

excess

_pore

water

_pressures

and

_ground

relative

displacernent

tirne

histories

in

TEST-S

1

and

TEST-S2

Ge:

Gal

Gal

1500 200 200

l

O

on D,5 1,D S,OHIIO D.1

O.5

1.e 5.0_HzlO

o.1

D.S l.O 5.e

_HllO

(Dry

sand)

ca Ga[t5o

Gal

100 200D

i

i

O,1 o,s l.o 5･O

HzlO O.1 as l.o s,oHllo

O･1

O.5 1S

5,O

HzlO

(Saturated

sand)

Acceleration

response spectra at

GL-4,

₈

m,

GL-O.

₇₅

m

and

the

_pile

cap

in

TEST-D

_1,

D

₂

and

TEST-S

1,

S2

for

TEST-S

2

is

also much

larger

than

that

'for

TEST-S

1.

For

TEST-S

2,

it

can

be

seen

that

a

large

arnplitude

with a

low

frequency

'is

eccurred

in

the

acceleration

and

the

displacement

response

at

GL-o.

7s

m

according

to

the

excess

_pore

water

_pressure

buildup,

The

acceleration

at

the

_pile

cap

(AH

4)

for

TEST-S

1

indicate

a

sirnilar

time

history

to

that

at

GL-O.

75

m

(AH

3).

The

acceleration

at

the

_pile

cap

foT

TEST-S

2,

however,

is

significantly

amplified

in

the

low

frequency

content

compared

with

that

-52-at

GL-O.

7s

m.

Fig.

3

shows

the

acceleration

response

spectra

at

GL-4.

8

m,

GL-O.

75

m

and

the

_pile

cap

for

the

dry

and

saturated

sand

tests.

The

_predominant

frequency

for

the

low

inputs

of

TEST-D

₁

and

TEST-S

1

can･

be

seen

at

about

2,

3

Hz

in

the

spectra

of

the

_ground

and

the

_pile

cap.

For

TEST-D

2

and

TEST-S2,

the

spectra

at

GL-4.8m

(AH2)

in

the

middle

level

of

the

_ground

show

almost

the

same

,response

characteristics,

but

the

spectra

at

GL-O.

75

m

(AH

3)

are

significantly

different

in

the

low

frequency

range,

The

_predominant

frequency

at

the

_pile

cap

(AH

4)

also

differs

between

TEST-D

2

and

TEST-S

2.

'The

_predominant

frequency

at

the

_pile

c'4p can

be

seen at about

1.6

Hz

and

2.3

Hz

for

TEST-D2

and

this

shifts

to

about

1.0Hz

for

TEST-S2,

Fig,4

shows

the'

ratios

of

the

smoothed

F6urier

spectra

at

the

_pile

cap

(AH4)

to

those

at

the

base

(AH1)

in

the

saturated

sand

tests.

It

is

clearly

confirmed

that

the

resonance

frequency

of

th6

soil-pile

foundation

system

is

_.about

1.8Hz

for

TEST-S

1

hnd

11

o

Hz

for

TEST-S

2,

Fig.

5

shows

the

ratios

of

the

maximum response

accglerations

to

those

of

the

input

mgtion.

It

can

be

seen

that

the

acqelerations

for

TEST-D'1

and

TEST-S1

are

amplified

in

_.the

_ground

and at

the

_pile

cap,

but

that

the

amplification

ratios

for

TEST-D2

and

TEST-S2

are

much

smaller

than

thos'e

for

TEST-D1

and

TEST-S

1.

The

pile

bending

moments at

GL+O.

2

m

(SG

6)

and

GL-2.

₂

m

(SG

3)

for

TEST-S

1,

as shown

in

Fig,

2,

indicate

a

similar waveform

to

the

acceleration

at

the

_pile

cap.

The

bending

moment

at

SG3

for

TEST-S

2,

howev'er,

has

a

large

amplitude

with

a

low

frequency

and

a

different

_phase

from

that

of

SG6.

Fig:6

_shows

the

distributions

of

the

maxirnum

_pile

bending

moment,

It

can

be

seen

that

the

distribution

for

TEST-S

1

is

similar

to

that

for

TEST-D

1.

The

distribution

for

TEST-D

2

indicates

that

the

large

bending

moment

occurs

at

a

deeper

_positien

of

the

_pile

compared with

that

for

TEST-D

1.

For

TEST-S

2,

the

maximum

bending

moments

in

the

liquefied

soil

are･rnuch

larger

than

those

for

TEST-D2,

and

a

significant

difference

can

be

seen

between

the

maximum

values

near

the

_ground

'

surface

(SG5,

SG6)

and

in

the

ground

{SG3).

The

2e,o

Fig.4

Fig.5

o

o,o 1.e

2,O

3,O

4,O

_Hz

5,O

Ratios

of

the

smoothed

Fourier

spectra at

the

_pile

cap

to

those

at

the

base

in

TEST-S1,

S2

_<by

five

times

Hanning

window}

AH4Pilecap

Retieafresponseecc.teinputaec. o 1,o 2.e

.3,o

4.o

AHSGLO.75m

AH2GL-4.em

AHI

Ratios

of maximum response acceleration

to

input

acceleratien

in

TEST-Sl,

S2

TEST-Dl,

D2

and

maximum

bending

moment

at

SG6

occvrs at

10.

24

seconds

before

reaching soil

liquefaction,

while

that

at

SG3

occurs

at

18.

04

seconds after reaching soil

liquefaction,

3.

Correlation

Anatyses'

3.,1

Analysis

Method

C6rrelation

analyses

for

the

centrifugal

test

results

were

conducted

using

a

bea'm-Winkler

spring

modelLT)

Fig.6

o,o

SG7[GL+O.Hm]

SG6 CGL.O,2)

SGS

[GL-O.5)

SG4 CGL-1.4] SG3 tGL-za SG2 tGL-3,1) SGICGL.4.s) Mex.bendingmoment :105Kg.cm lo.e 20.0

Maximum

the

_pile

in

S2

bending'

moment

distributions

of

TEST-D1,

D2

and

TEST-S1,

-53-Architectural Institute of Japan

NII-Electronic Library Service

ArchitecturalInstitute of Japan

as

shown

in

Fig.7.

Pile

foundation

was

idealized

by

a

one-stick

model with

lumped

masses

and

bending-shear

elements.

The

lumped

masses were

connected

to

the

free

field

_ground

through

nonlinear

lateral

Winkler

springs

modified

at

each

step

in

accordance with

the

_generation

and

dissipation

of

excess

pore

water

_pressures.

In

this

analytical model,

additive

masses

of

the

soil

were

not

adopted

for

simplicity,

The

rotational spring,

mainly

related

to

the

axial

stiffness

of

the

_piles

and

the

soil

resistance

at

the

_pile

tips,

was also

incorporated

at

the

_pile

head,

In

this

analysis

_procedure,

the

nonlinear

effective

stress method,

the

computer

program

DESRA

proposed

by

Finn

et

al.

iS',

_was

_utilized

for

_the

free

_ground

response.

The

obtained

displacement

and

excess

_pore

water

_pressure

time

histories

at

each

depth

were

applied

to

the

corresponding

lumped

masses

_of

the

pile

foundation

system

as

an

earthquake

input

Integratiops

in

the

time

domain

were carried out using

Newmark'sB

method

(a=O.

5,

B=O.

25).

The

centrifugal

tests

for

the

saturated

sand

indicate

that

the

excess

_pore

water

_pressure

_generated

in

the

middle of

the

_pile

_group(PP

3)

is

almost

the

same as

that

generated

in

the

surrounding

soil(PP

4).

It

seems

to

suggest

that

shear

modulus

of

the

soil

around

the

_piles

is

degraded

as

that

of

the

free

_ground

during

earthquake.

Initial

interaction

spring

values,

therefore,

are

evaluated

using

the

degraded

shear

modulus

obtained

from

the

nonlinear

free

_ground

response without

changing

the

effective

st[ess.

Then,

the

degradations

of

lateral

Winkler

springs

take

account

of

the

relationship

of

lateral

load-displacement

of

the

_pile

and

the

changing effective stress

in

the

free

_ground.

Fig.

8

shows

the

numerical model

of

the

seil-pile

foundation

system

and

the

initial

interaction

springs

employed

in

the

correlation

analyses.

Analysis

of

the

free

_ground

The

computer

_program

DESRA

is

based

on

the

shear stress-strain

relationship

of

the

Hardin-Drnevich

model with.

the

Masing

rule

expressed

as

T=

Gorl(1+Go71

Tmex)

''-''-'-''''-''-'''"-'''''''''H-''H'''""'''"'''''''"''''"'"'''''H"''''''""''

(

1

)

in

which T=shear stress, Tha.==shear strength,

_r==shear

strain and

G,=:initial

shear modulus.

The

initial

shear modulus

G,

and shear strength T.ax are modified

progressively

for

the

changing vertical

effective

stress

of saturated sand subjected

to

an earthquake.

Physical

congtants employed

in

correlation

analyses

fer

the

saturated

sand

are

shown

in

Table

3.

The

initial

shear

modulus

_G,

is

estimated

from

Go=AI(2J7-e)21(1+e)I(ain,)ii2･･-･---･--･-･----･--･--･---･-･-･-･･-･-･･･････---･-･--･･(2)

in

which

e==void

ratio

and

a'.,=initial mean effective stress'9'.

The

coefficient

A,

obtained

by

resonant

column

test,

is

modified so as

to

correspond

to

the

resonance

frequency

of

the

free

_ground

in

the

low

input

test.

The

shear

strength

Tth..

is

obtained

from

the

Mohr-Coulomb

yield

condition.

Fig.

9

shows

the

variations

in

initial

shear

modulus

of

the

soil witlt

depth.

In

this

figure,

the

degraded

shear modulus

for

evaluating

initial

interaction

springs

are

also

indicated,

These

values

are

obtained

from

the

secant

Fr

M-J8super

ng.

Fig.7

Lumped

masses and

bending-shear

elements

model with

lateral

Winkle[

springs

for

pile

foundation

system

-54-Freeground GL Om

-O,6

.1.8

-3.o

.4.2.

-5.o

･6.0

-7.e

.B.2

-9.3

.le,4

12 KsKfi T KKso Pi:e ka TEST-PlTEST-D2vasr-slTEST-S2

ig16A83.125.161,62

ts12,S6.5610,73,35

ts20.410.Sle.35.82

ig26.914.72S.3S.35

ig30,917,330.4iO,4

Kse3S.O20.035.612.6

ig42.324.7".916.5

Kse51.330,656,621.6

ts63.538,772,128,9

kio85.753.4101.040.B

KR{xlOG2.531.172,49o,es

Fig.8

hs-O･05

::-.D/i,2,1811:g/,22,[,D2,l

CUnit:ten･cm}

Numerical

model and

initial

interaction

Table3Physical

soil constants

for

correlation analyses

lnternal

iriction

anglel

Q'

35e

Void

ratio:e

_O,69

Density:

_M(tim3}

1,98

Permeabiiity:

k(cmXsec}

_5.2xlO'a

Coeff.

ofearth

_pressure

at

re$t:

Ko

_O.45

th

8

= "

g

.o

Numberotcycres

Fig.ID

Liquefaction

resistance curve

by

analysis

and

cyclic

simp}e

shear

tests

of undrained

saturated

sand

modulus

of

the

backbone

curve

of

each

layer

using

Eq.(1)

at

the

effective

shear

strain

(O.65-rmax),

which

are

evaluated

'frem

the

non-linear

fre,e

_ground

response without changing

the'

effective stress.

The

excess

_pore

water

_pressure

_generation

Au])

is

defined

by

'･

AU=ErA

svd'''''''H'''HH

-r'""""'H'

(

3

)

where

'

..,,.""--.･･･.H.,."･･-･i･a--･･･-･-･･･-･･----･-･･･(4)

-.,."",..,..."L,.".,..."".-･･-･････(5.)

sand

at

an effective

stress

u',

Ae.d=volumetric,

Ci,

C2,

C3,

C"

K2,

m

4nd

n

are estimated

loading

and

unloading

tests,

These

,=O.114,

C,=1,2,

C,=O.17,

C,=L36,

the

liquefaction

resiFtance

curve

calculated

GLOm

-2,e

-4.eiaom

-ae

-8.0

-ID.e

IPL/-1lbll11-:::-: l -; :

-l

i

'

-.h

t t 1

-1

'1

1-Initialshearrnedulus

/

L 1TEST-Sl

L-l/

Ll

'..-,

Ln'

:l

,l

'ITEsT.sL2-I

tl/

Li,

, F

//

'

of

Parameters

one-dimensional

parameters

are alse modified

to

simulate

liquefaction

resistances

obtained

by

the

cyclic simple

shear

test

lue.s

employed

in

the

correlation

analyses

are

C

shows

in

comparison

with

the

cyclic

simple

shear

test

results

of

undrained

saturated

o

looo

2ooo

3ooo

3soe

''･

ShearmoduTusG

_CVm2}

Fig.9

Variations

of

shear

'modulus

with

depth

for

-TEST-SI

S2

･

'

'

AEvd=Ci(?'-CzEvd)+CseZdl(?'+C,evd)''''':

Er=(a')'-"lmK2(aaP-M-･-･･'---･--･-･-･-･---･

in

which

E.=one-d'imensional

rebound modulus strain

increment

under simple

shear

condition.

according

to

cyclic simple

shear

tests

and

r,esults.

The

va

K2=O.OOI

(tlm2),

m=O.1

and

n=O.19,

Fig.10

using

these

paramgters,

sand.Evaluation

of'

the'interaction

springs

The

nonlinear

lateral

load-displacement

relationship

of

a

_pile

is

also

based

on

the

Hardin-Drnevich

model with

the

Masing

rule as

shown

in

Fig.

11.

Ipitial'

lateral

Winkler

spring$

K.o

at each

depth

are

evaluated

by

the

inversion

of

soil

flexibilities

by

ring

loads

at

the

nodes

as

shown

in

Fig.12.

The

positioh

of

the

node

corresponds

te

that

_gf

the

lumped

masF

of

the

_pile.

The

soil

di$placementE

can

be

expressed

_qs

･

･

'

lul=[dw]lpl'"-'"''''''--'-''-'-,--''''''"v'''''-'i''''''''''''HH'''H'''''r''''''''`'''"''"''H"H--''(6)

where

lui

and

lpl

_are

_the

vectors

of

lateral

displacement

and

load

at

_.the

nodes,

and

[dw]

is

the

flexibility

'

matrix

of

the

soil.

The

soil

displacements

iul

caused

by

lateral

ring

loads

ipl

in

a

layered

stratumM}

are

'

caLculated at

O.

25

Hz,

which almost

corrgsponds

to

the

_.static

condition.

The

soil

flexibility

at

the

i-th

node

is

obtained

from

the

superposition

of

soil

displacements

at

the

i-th

node

by

ring

loads

at

all

nodes.

'

Then,

the

lateral

VVinkler

spring

at

the

i-th

node

is

approximately

obtained

from

the

'inversioh

ol

the

soil

flexibility

expressed

･as

.'

'

'

Kk=[Zd.]'i･--･････････-･-･-･･-･--･･･-･･･････i･･---･-･-･･････････････--･--････････--･:･･････---(7)'

where･Kg,'

is

jthe

initial

lateral

Winkler･spring

at

the

i-th

node.

As

described

before,

initial

lateral

Winkler

springs were evalgated

using

the

degraded

shear

modulus

as

shown

in

Fig.g.

The

initial

ultimate

lateral

soil

reFistance

Pfi..,

at

the

i-th

node.

is

assumed

by

BromsZi)

to

be

thiee

Architectural Institute of Japan

NII-Electronic Library Service

ArchitecturalInstitute ofJapan

P

=

Ks

Pma

timestep

Fjg.11

Nonlinear

relationship

tirnes

the

Rankine

_passive

Pixaxe=3

alKpdl

where

aS

is

the

initial

is

_pile

diameter

and

Pile

group

effect

is

resistances using

the

aH==K#/(NKE)---････-･-･･-t･--･･-････-･･-････--･･･-･･･-･･-･---･----････i･･i･･-･･･-･･･-･･-･-･･･-･･-･ where

N,

K#

and

Kit

are

the

number

of

_piles,

N-piles

and

the

same

TEST-S

1

and

O.

56

for

TEST-S

2

by

the

three-degraded

shear rnodulus resistance

P:,,.o

taking

K&==aHIVKst

Pftaxo=aHNPmaxo

where aHN

is

the

equivalent

number

of

_piles.

domain

are

modified

Ks=Kk(a'lal)'1!

Pmax==Pfuxo(a'laa)

where

o'

is

the

effective

The

rotational spring

is

evaluated

modulus of

the

soil.

The

viscous

damp

the

lateral

Winkler

sprmgs

system.

The

viscous

hysteresis

damping

at

each

damping

censtants

employed

3.2

Results

of

analysis

Fig.

13

shows

the

_predicted

acce

compared

with

those

measured

accelerations.

spectra

for

TEST-D

1

foundation

system

is

mod

for

TEST-D

2

also

correspond

foundation

in

the

nonlinear

soil

cap

indicates

a

slightly

discrepancy

may

be

due

to

an underestimated

hysteresis

damping

for

th

-56-lateral

load-displaceJllent

Fjg.12

by

of

Winkler

spTing

'

pressure

expressed

as

H.H-..,.,.,..,.,...,.""...HH.H"""...""-.-････-･･-･----･--･･････････-･･--･･(8)

effectivestress,

K},=(1+sin

diC)f(1-sin

di'),

O'

is

theinternal

fTiction

angle,

d

l

is

_pile

length

equivalent

to

the

i-th

node.

incorporated

for

the

initial

lateral

Winkler

springs

and

the

ultimate

lateral

soil

pile

group

efficiency

a,

defined

by

(9)

'

the

value

of

horizontal

static

impedance

at

the

_pile

head

for

value

for

a

single

_pile,

respectively.

The

value of

a"

is

obtained

as

O.

57

for

dimensional

thin

layered

element

method22)･2S)

using

the

,

The

equivalent

lateral

Winkler

spring

K&

and

the

ultimate

lateral

soil

account

of

the

_pile

_group

effect

are

defined

by

l

..

.".,..,....

.HH.,.",.".,."...---.""-.----････････---･-

･----

----

-

_CIO)

The

values

of

K.

and

P...

at each

ti,me

step

in

the

time

according

to

the

chang

in

the

effective

stress

defined

by

l

-t---Jii---t----t---JJ---l----

-

---

--

----J---l--t--+---

---

---(11)

stress

at

each

time

step

and

aa

is

the

initial

effectiye

stress.

under

a

_pinned

conditien

at

the

_pile

head

using

the

degraded

shear

ing

ernployed

is

1

_per

cent

for

_pile

foundation

and

5

_per

cent

for

'

at

the

first

mode

by

the

eigenvalue

analysis

of

the

soil-pile

foundation

damping

for

the

rotational

spring

is

estimated

by

averaging

the

equivalent

depth,

which

are

obtained

from

the

nonlinear

free

_ground

response.

The

in

correlation

analyses

are

also

shown

in

Fig.8.

Ieration

time

histories

at

GL-O,

75

m

(AH

3)

and

the

_pile

cap

(AH

4)

for

TEST-D1,

D2.

Fig.14

shows

response

spectra

for

the

predicted

and

It

can

be

seen

that

the

preclicted

acceleration

time

histories

and response

are

in

_good

agreement

with

the

measured

results,

showing

that

the

soil-pile

eled

appropriately

for

the

low

acceleration

input.

The

_predicted

accelerations

to

the

measured

results,

and

the

response

characteristics

of

the

pile

are

represented

well.

However,

the

_predicted

acceleration at

the

_pile

larger

maximum

amplitude

compaTed with

the

measured

result.

This

e

lateral

Winkler

spring

and

the

JPF.;.."t

-tl---t-"i1-1dllnodLt

:Ring

load

i .

p,

{u}=[diij{P}

i

l

Kso'=[?d,,]'i

i

i

l

Kso:tnitiaE-aterai

vfinklerspring inodei

i1:1

H,:

Displecement

i

ull

.iliL..:/

...J"'i""

ring

load

in

layered

stratum

'

rotational

spring

during

a

large

displacement

of

the

_pile,

Fig.

15

shows

the

_predicted

acceleration

time

histories

at

GL-O.

75

m

(AH

3)

and

the

_pile

cap

(AH

4)

compared with

those

foT

TEST-S

1,

S

2.

Fig.

16

shows

response

spectra

for

the

_pledicted

and

measured

accelerations.

For

TEST-S

1,

_the

_predicted

acceleration

response

spectrum

at

GL-4.

8

m

is

sgmewhat

smaller

than

the

measured results

because

the

generation

of

excess

_pore

water

_pressures,

as

shown

in

Fig,

17,

are

overestimated.

The

_predicted

responses

at

GL-O.75

m

and

the

_pile

cap,

however,

show

good

agreement

_with

the

measured results.

It

can

be

seen

that

the

_generation

of

excess

_pore

water

pressure

is

too

small

to

affect

the

response at

the

pile

cap.

The

_predicted

relative

displacement

of

the

ground

also

agree

well with

the

measuTed result

as

shown

in

Fig.18.

For

TEST-S2,

the

_predicted

acceleration

responses

agree

well with

the

measured results,

although

the

maximum'vhlues

are slightly underestimated.

It

is

found

_that

_the

shift

in

_predominant

freqliency

ef

the

soil-pile

foundation

system

by

4aeGal AH4:puecap

'

ANALYSIS

_3ooGal

TANEg+YSIS

.400200

-200

l

1iewre

---TEST

AkV+wtVeMeeNbV-"M;J

_:osec

4oo

.400

Gal300

-300

ec

･

AH3･GLO75m

ec

Fig

13

(TEST-D2)

Comparisons

of

_predicted'

histories

at･GL-O.

75

m and

TEST-Dl,

D2

sec

acceleration

tl'me

the

_pile

cap with

･soe

Gal200

-2oe

Galgse

.450

･

Gai250

-2se

(TEST-Sl)

ec ec ec

Fig.15

CTEST-S2)

Comparisons

of

_predicted

acceleration

time

histories

at

GL-O.

75

m

and

the

_pile

cap with

TEST-Sl,

S2

'

Fig.14

GalIS Ga]15

CompaTisons

of

predicted

TEST-Dl,

D2

Gab2oo Gal2soO

(TEST-Dl}

･

O,1 acceleration Gat25 Gal25oo

e.5 1.D S.OH,ID O.1

(TEST-D2)

response spectra at'GL-4.8m,

O.5 i,O 5,O_HIIO

GL-O,

75

m and

the

_pile

cap with

Architectural Institute of Japan

NII-Electronic Library Service

ArchitecturalInstitute ofJapan

Fig.16

O,2

-O,2e.2

.O,2O.5

-o.sO.5

15Gal Gallse

Comparisons

TEST-S

1

'

dns100

en o.s l.o

(TEST-Sl)

Galloe _Hl of

_predicted

acceleTation

S2

s.o to Hl

{TEST-S2)

Tesponse

spectra

at

ec ec ".5Fig.17 ec

Fig.19

ec

Comparisons

of

_predicted

excess

_pore

water

pressure

time

histories

at

GL-3.45m

and

GL-s.3m

.ith

TEST-S1,

S2

WinklersprjngatGL+O.6m

i-4.0

WlnklerspringetGL-3,Orn

4.0ytcm)

Calculated

relationship analysis

nonlinear

lateral

loa

of

Winkler

springsd-displacement

in

TEST-S2

1,5

.1,S1.0

-IM10.0

-le.o

s.o

Ga!200

DA Gal2oo O.5 t.O 5D le Hl

o] O.5 1.0 S.O_H.ID

GL-4.8m,

GL-O.75m

and

the

_pile

cap

with

ec ec ec

.,,,1:-1

-ew"GL･;;rt;nv}.)trt.

(TEs.i.L;;;･;

'

"''"

'

""'

'''"'''!6',,,

Fig.18

Comparisons

of

_predicted

_ground

relative

displacement

time

historie's

at

GL-O.75m

and

GL-4.8m

with

TEST-S1,

S2

soil

liquefaction

is

represented

well

by

the

prop-osed

model.

This

is

evidenced

by

comparing

the

predicted

and measured

acceleration

response

spectra

at

the

_pile

cap.

The

_geneTation

and

dissipation

processes

of

excess

_pore

water

press-ures,

as

shown

in

Fig.

17,

and

the

relative

ground

displacements,

as sh6wn

in

Fig,18,

also

agree

'

well

with

the

measured

results,

Fig.

19

indicates

the

calculated

lateral

load-displacement

rela-tionships

of

the

_piLe

at

GL'O.

6

m and

GL-3.

0

m

for

TEST"S

2.

It

is

clear

that

the

lateral

Winkler

spring$

are

degraded

by

the

increase

of

the

pile

displacement

and

the

excess

_pore

water

pressure

buildup,

and

that

the

degradations

are

much

larger

at

GL-O.6m

than

at

GL-3.0m

due

to

a

large

_pile

displacement

and

a

significant

decrease

of

the'effective

stress

near

the

ground

surface.