Piles Under Dynamic Loads

8/19/2019 Piles Under Dynamic Loads

1/25

Missouri University of Science and Technology

Scholars' Mine

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Piles Under Dynamic LoadsM. Novak

$e Uni"ersi# of Wesern Onario, London, Onario, Canada

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2/25

Proceedings: Second International Conference on Recent Advances

In

Geotechnical Earthquake Engineering and Soli Dynamics

March 11-1.5 1991 St. Louis Missouri Paper No. SOA14

Piles Under Dynamic Loads

M. Novak

Professor of ivil Engineering The University of Western Ontario

London Ontario Canada

SYNOPSIS The

paper

deals with some of the more recent developments in

p i l e

dynamics. It reviews

the progress in

the ana lys i s

of s ing le

pi les and p i l e groups, f ie ld as well as l abora tory exper i

ments and so i l -p i l e - s t ruc ture in te r ac t ion . The in f luence o f p i l e - so i l i n t e r face i s discussed and

extensive

references

are

given.

INTRODUCTION

Pi l es have been used

for

hundreds

of

years bu t

the

l a s t twenty

years

or

so

have

seen

a

remarkable increase in i n t e r e s t

in

p i l e dynamics.

There

are a

few reasons

for

t h i s : good s i t e s

which

do not requi re

pi les

are

ge t t ing

scarcer

and thus p i l i ng

i s

used

more

widely; new

important areas of appl icat ion have

emerged,

for

example of fshore

towers and

nuclear powerplants;

pi les have repea tedly f a i led

in earthquakes or

were damaged; and f ina l ly , dynamics

of

shal low

foundations

has reached a poin t

of sa t i s f ac tory

understanding

thus sh i f t ing

research i n t e res t s to

les s understood foundat ion types . The aim of the

s tudies i s to increase the sa fe ty

of

the pi l e s

and the s t ruc tures they support

and

to

be t t e r

understand

the

in te r ac t ion between the pi l e s and

the

s t ruc tures

under both c r i t i c a l and

opera t iona l condi t ions .

The

damage to

pi l e s may re su l t

from

a few

causes

such as v ib ra t ion ef f ec t s , l i quefac t ion ,

and

embankment movements. A comprehensive survey

of

pi l e

damage

during earthquakes in

Japan

was

presented

by

Mizuno (1987) but damage to pi l e s

also

occurred

in

the

Alaska earthquake

of

1964,

the

Mexico City

earthquake

of

1985

and the Lorna

Pr ie ta earthquake

of

1989.

Pi le

behavior

i s ,

of

course,

very

complex

and

t h i s might have lead Terzaghi and Peck (1967) to

s t a t e tha t heore t ica l

refinements in

deal ing

with pi l e problems

are

completely out o f

place

and can be

sa fe ly ignored .

For tuna te ly , not everybody got

discouraged

by

t h i s

pessimist ic

eva lua t ion and

a

number of

ana ly t ica l

and

numerical approaches

to

the

analysis

o f p i l e

dynamic behavior have been

developed.

These

approaches

provided

a

much

sounder theore t ica l

basis for

p i l e

design than

the equiva lent cant i l ever concept

or o ther

purely

empir ical methods

which

dominated

the

f i e ld for

decades. Never theless , some

d i f fe rences

between

the

var ious theore t ica l

approaches

ex i s t

and the

experiments repor ted are sometimes inconclusive;

also ,

some uncer ta in t ie s

are inev i t ab le

when

applying an

i dea l i zed theory to f i e ld condi t ions .

Thus, it may be usefu l

to

review

some of

the

433

approaches

in

order t h a t

we may

examine

t he

di f ferences

among

them and

summarize

what

can be

learned from experiments and f i e ld observa t ions .

There

are

di f f e r en t dynamic

loads

t h a t can ac t

on pi l e s : earthquake

forces ,

wave forces,

wind

forces , machine unbalances

e tc .

Here, t he

emphasis

is pr imar i ly on condi t ions relevant

to

earthquake loading. Dealt with are p roper t i es

and behavior

of

s ing le p i l e s and p i l e groups,

in te r ac t ion with

the

cap,

p i l e

experiments ,

p i l e

s t ruc ture in te r ac t ion

and a

few

other

top ics .

The

subject o f pi l e dynamics received a

comprehensive

t reatment

in

the

s t a t e - o f - t h e - a r t

repor t by Taj imi ( 1977) , covering developments up

to

1977, and in a

few

spec ia l volumes, i . e . De

Beer

e t

al .

(1977), O Nei l l

and

Dobry (1980),

Nogami

(1987)

and

Prakash

and

Sharma

(1990). A

number o f papers

on pi l e s were

presen ted to t h i s

conference.

These are l i s t ed together

a t the end

of

the

References.

Among

the

spec ia l

areas

of

pi l e dynamics not considered

here

are i n t egr i ty

t e s t i ng and p i l e dr iv ing . Recent data on

these

subjects can be found in

Fel len ius

(1988).

So

many

papers have

been published

on

p i l e dynamics

s ince

Taj imi s

(1977) s t a t e - o f - t h e - a r t

r epo r t

t ha t it i s

impossible

to re fe r

to

a l l

of

them in

t h i s

r epo r t

of

l imi ted

scope. The au thor

t r u s t s

tha t

the readers

wi l l understand t h i s .

SINGLE PILES

The e a r l i e s t systemat ic , t he o r e t i c a l

s tudies

of

dynamic so i l - p i l e in te r ac t ion are due to Parmelee

e t

a l . (1964),

Tajimi

(1966), Penzien (1970),

Novak (1974)

and a

few

others . Parmelee (1964)

and

Penzien (1970) employed a

non- l inear disc re te

model

and

a

s t a t i c

theory

to

descr ibe

the

dynamic

e l a s t i c s t r e s s and

displacement f ie lds .

Tajimi

(1966) used

a

l i nea r viscoe las t ic s t ra tum of t he

Kelvin-Voigt type to model the so i l and in

h i s

analysis of

the

hor izontal

response neglected

t he

ver t i ca l component of

the

so i l

motion.

Novak

(1974)

assumed l i nea r i ty and an e l a s t i c so i l

layer

composed

of

independent in f in i te s imal ly

th in hor izontal layers

extending

t o in f in i ty .

The di f fe ren t

approaches

formulated

and the data

they

yie ld

are

br ie f ly

discussed

below.


3/25


4/25


5/25

5.5

4.5

(a)

~ - - ~ 2 5 ~ - - - = 5 ~ 0 - - ~ 7 ~ 5 ~ - - ~ ~ o ~ o ~ ~ L - I ~ d ~

12

10

6

4

Floating Piles

v =

0.5

·

.-·

. - ·

.

Ep/E

5

=

1000

/

Present ( 50 Elements l

Poulos 10 Elements)

· · · · Salinera (

>

20 Elements l

X • X

Rajapakse a Shah

Ep/E

5

= 100

---

--

---

b)

z ~ - - ~ 2 5 ~ - - - - ~ 5 ~ 0 - - - - ~ 7 ~ 5 - - - - ~ ~ o ~ o ~ ~

L/d

Figure 4 Comparison

of

s t a t i c axial p i l e

s t i f f n e s s

calcu lated

by d i f f e r e n t au thors

for

homogeneous so i l :

(a)

- endbearing pi l e s , (b) -

f loa t ing

p i l e s (Present

data by

El

Sharnouby and

Novak, 1990)

J

UJ

0

>

1-

;

a.

;

30

·

.

. . .

0 33

p

·

T£5T PILE

2

2r

•

2.41N.

(6.1 em I

I • 0.000032 FT

4

27.6 cm

4

1

l;r.

•

77.9

G Z)

(a )

(b )

z

Figure 6 Schematic of p i l e separa t ion

and

so i l

modulus

reduct ion

towards ground sur face

Observat ions

of t h i s

kind

l ead to

the development

of

approaches

be t t e r

su i ted for nonhomogeneous

so i l s .

A

s ign i f ican t

improvement in the f i n i t e

element

model

was

formulated by Roesset and h i s

co-workers

(Blaney

e t a l . ,

1976;

Roesset

Angelides,

1979)

who placed

t he cons i s t en t ,

f requency

dependent boundary, derived

by

Kausel

e t

a l (1975), d i r e c t l y t o t he p i l e or out s ide the

cy l ind r i ca l

f i n i t e element zone around the pi l e .

This approach

was

then used

by

Krishnan e t a l .

(1983)

and by

Gazetas (1984)

in

t h e i r extens ive

parametr ic

s tud ies .

S ign i f i can t fu r ther progress was

made

by Kaynia

(1982a,b) and Kaynia and Kausel (1982,

1990)

who

based t he i r so lu t ion of p i l e s

in

genera l ly

layered media

on the. formulat ion of

d i sp lace

ment

f ie lds

due

to uniformly

dis t r ibu ted

forces

on cy l ind r i ca l sur faces (so ca l l ed bar r e l

load) .

(This

so lu t ion wi l l

be

discussed in

more d e t a i l

in

the

paragraph on p i l e

groups.)

Baner jee

and Sen (

1987)

presented bounda:y

element

so lu t ion

for

p i l e s embedded 1n

a

sem1-

i n f i n i t e nonhomogeneous so i l

in

which

the

so i l

modulus, E

5

, var i es l i nea r ly with

depth, z.

Baner jee

and Sen s re su l t s suggest

tha t ,

unl ike

in layered so i l s , the

f requency

var i a t ions of the

impedance

funct ions,

normal ized

by s t a t i c s t i f f

ness, are qu i t e smooth and are

af fec ted

very

little by so i l nonhomogeneity.

The ac tua l

magni

tude of the s t i f fness and damping diminishes with

E

5

(0) , however.

,

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

m m

w

w

A

few

other methods

su i tab le for l i ne a r genera l ly

layered media

use

a semi-ana ly t i ca l f i n i t e e le

ment approach.

These methods t r ea t

the wave pro

paga t ion

in the

hor izonta l di r ec t ion ana ly t ica l ly

and in the ver t i ca l di r ec t ion employ f i n i t e

e l e

ment

i dea l i za t ion including aux i l i a ry

sublayers .

The p i l e

is

modelled by

beam elements .

One of

the

advantages

of

t h i s

approach i s

t ha t

it

may

avoid the mathemat ical i l l - condi t ion ing r esu l t ing

from the

large

magnitude of

Lame s

cons tant ,

for so i l Poisson s ra t io ,

v ,

approaching 0. 5.

Solutions o f

t h i s

type were

formulated by

Tajimi

and Shimomura (1976) , Shimizu

e t a l .

(1977) ,

Waas and Hartmann (1981,

1984)

and Mizuhata and

Kusakabe

(1984).

60

FREQUENCY (CPS)

Figure 5 Comparison

of

experimental

hor izontal

response

of

s t ee l

t e s t

p i l e with theore t ica l

predict ions

(Novak

and Sheta,

1982)

2436


6/25

An approximate ana ly t ica l so lu t ion based on t he

extension

of

the Novak and

Nogami (1977) approach

was formulated for layered media by Takemiya and

Yamada (1981).

A much s impler and

very v e r sa t i l e

so lu t ion ,

p a r t i c u l a r l y well

sui ed for

high f requencies ,

was formulated

by

Novak

and

Aboul-Ella (1978a,b)

who

extended

the plane

s t r a i n approach

to include

layered

media and

incorporated t in

the

code

PILAY.

This

code

was

used l a t e r by

Novak

and

El

Sharnouby

(1983)

to generate design char t s

and

t ab l es

for parabol ic

so i l p rof i l e s , as well as

homogeneous

ones. With t h i s approach, and

assuming a parabol ic s o i l prof i l e ,

with an

al lowance

for

p i l e

separat ion in the form of

a

small

f ree length,

very sa t i s fac tory agreement

with

the

theory was obtained as ind icated by

curve c in

Fig. 5.

Roesset e t al . (1986) a l so

found

t he plane s t r a in

approach to

work very

well

for

high f requencies . For very low f requencies ,

an

adjustment

to the plane s t r a in

so i l

react ion

i s

made

for the

ver t i ca l

and hor izontal

d i r ec t ions as d iscussed

in

Novak

and

El

Sharnouby

(1983)

and implemented in the code

PILAY. The

plane s t r a in

approach

works

well

for

high

frequencies because, in a l ayer , e l a s t i c waves

tend

to

propagate

more and more hor i zon ta l ly as

the

f requency

increases ,

l i ke

in

a

wave

guide.

The sens i t iv i ty

of

t he

response to

p i l e separa

t i on

and

f ree l ength

shows

when

eva lua t ing

most

experiments . The predict ion

of the separat ion

leng th i s d i f f i cu l t and

only

empi r ica l

sugges

t ions

can

be

made

a t

t h i s

t ime.

For small ampli

tudes, 6 , El-Marsafawi e t a l . (1990) observed t he

fol lowing approximate r e la t ionsh ip

for

p i l e

separa t ion l ength , L

8

:

Ls

d

260 , 0.001 5 5

0.005 2)

For l a rge r displacements, a large

separat ion

length may

be

needed

(Han

and

Novak,

1988) .

More

data

on

the separat ion

e f fec t

wi l l

be

given

in

the paragraph on nonl inear response.

As

for poss ib le deviat ions

o f the theore t ica l

assumpt ions from

r ea l i t y , p i l e def ic ienc ies may

also

have a profound e f fec t . This i s shown by

Wu

e t a l . (1991)

who,

in t h e i r paper to t h i s confe

rence,

examine the in f luence of p i l e necking

using a

combinat ion

of

the

BEM and FEM

adial nonhomogeneity

While the cons idera t ion of a f ree separat ion

leng th in the

ana ly s i s

may produce

the reduct ion

in both p i l e s t i f f n e s s and damping of ten observed

in

experiments , a b e t t e r measure to

t h i s e f fec t ,

or

a complementary

one,

may be to account

for

so i l

nonhomogeneity in

the

rad ia l

di r ec t ion . A

simple

way

of

doing

t h i s

i s

to

assume

a

weak,

cyl indr ica l

boundary

zone around the p i l e (Fig.

7).

The

zone i s

homogeneous

and features

a so i l

shear modulus, G., smal le r than t ha t

of

the outer

zone

and

a

l r g e ~ mater ia l damping.

The

purpose

of such a zone is to account in a very approxi

mate

way

for

so i l

non l inear i ty

in

the region

of

the h ighest

s t re sses , p i l e

separat ion ,

s l ippage

and

o ther def i c i enc ies o f the p i l e - s o i l

inter face . Such a zone was proposed

by

Novak

and

Sheta (1980). In

t h e i r

plane

s t r a in so lu t ion ,

the mass

of

the boundary zone was neglec ted in

·. G,p , v

Figure

Cyl indr ica l boundary zone around p i l e

order to preven t wave re f l ec t ions from t he

f i c t i t i o u s inter face between the

cyl indr ica l

zone

and t he

outer reg ion . These r e f lec t ions occur

with nonzero

weak zone mass, p . and re su l t in

undes i rab le undulations in bot h s t i f f n e s s and

damping

of

the

composite medium. This i s

exemplified in Fig. 8 in which a and

are

{b)

~ ~ ~ ~ ~ ~ ~ ~ ~

0 2 3

requency

0; :

r

0

W/V;

Figure 8

Dimensionless

ver t i ca l impedances

of

composi te medium with P = and

tjr

0

= 1.0 s o i l

damping r a t i o = 0.05)

nondimensional s t i f fness

and

damping cons tan t s

of the

composite

medium r espec t ive ly . These

undulat ions can make

the

so lu t ion with

P 1

0

ac tua l ly l e s s su i tab le

for

prac t i ca l

appl icat ions

(Novak

and Han,

1990).

The di f f icu l ty

with wave

r e f lec t ions can be avoided by providing

for

a

continuous

t r ans i t ion of s t re sses from the inner

zone

to the ou ter

region. Such a

so lu t ion was

explored

by Lakshmanan and Minai (1981), Dotson

and

Veletsos

1990) and

Mizuhata and

Kusakabe

(1984).

The

l a t t e r au thors found t ha t even with

the

weak

zone, the

experimental

resonance

ampli tude measured on a

43.2

m

long

p i l e was f ive

t imes l a rge r

than the

theore t ica l value while

the

resonance frequency was predic ted

qui te wel l .

This i s cons i s ten t

with

other observat ions and

i nd ica t ive o f t he need to

account

for p i l e

separat ion .

2437

Wolf and

Weber

(1986)

conducted

a more r igorous

study

of

the

effect

of

soil tension

exclusion,


7/25

also assuming the c i rcu la r cavi ty in the

unbounded

th in

l y ~

plane s t r a in)

. They

found

t ha t so i l

separatidn hardly a f fec t s hor izontal

s t i f fness , lS,, but

reduces

damping, ch, by more

than 50

per cent

Fig.

9b), a r esu l t

qui te

s imilar t o tha t

of Novak and Sheta 1980). In

addi t ion ,

i f shear i s

el iminated

and hence

s l ipp ing i s allowed in the zone

of

contact ,

s t i f fness i s also s t rongly reduced Fig. 9c). In

Fig. 9,

the

l i nea r case

a)

indicates the

analysis

with

tension

allowed.

The

s i ze

of

the

contact

area appears

to be

of 1 i

t t l e

ef fec t .

Many other authors s tudied the

in te r f ace

behavior.

Among

the more recent ones

are Mamoon

1990) and

He

1990). However, when applying

the

var ious plane

s t r a in

approaches to

the

in te r f ace ,

the

var ia t ion

with depth i s

a

problem

for

which

very l i t t l e

guidance

is avai lable .

Linear

,,,,,,,,.,,,

~

4.28

13.23

a)

Shear

Slipping

[) D

QG)

4.17

6.42

b)

2.32

2.60

c)

Figure 9

separation

v=0.48)

Effec t of

elimination

of

tension

in

zone Wolf Weber 1986; a

0

=0. 629,

Recognizing

the

separa t ion

e f fec t and allowing

for

t

in an

approximate

way, a reasonable

agreement

between the theore t ica l

re su l t s

and

experiments can be

obtained. This i s exemplif ied

in Fig. 10 comparing the t heore t i ca l and

experimental responses of a concrete p i l e 7.5 m

in length

and

0.

32 m

in dia . The

so i l

was

mul t i l ayered and

a

cyl indr ica l

weak zone was

assumed when

calcula t ing the

response using the

code

DYNA3.

In t h i s code, the weak zone i s

analyzed as massless but i t s mass i s added to

tha t

of

the

pi le

in fu l l or in par t .

Simila r

t e s t s and comparisons were repor ted by Gle

1981), Woods

1984)

and a number of others .

Nonlinear

Response

of Single

Pi les

The theor ies

discussed thus

far

are

essen t i a l ly

l inea r and thus qui te adequate

for

small

displacements.

At large displacements, pi les

behave in

a

nonl inear

fashion

because

of

so i l

nonlinear i ty

a t

high s t r a in ,

p i l e

separat ion

gapping), s l ippage and f r ic t ion .

To

incorpora te

these

factors

in to

a

continuum

theory i s

extremely d i f f i cu l t and

therefore , lumped

mass

models are most often used when nonl inear

analysis s required. Such models employed by

2438

1.1

1 .3

1 .2

1.1

1.0

....

o.

a

c..

o.

E

o.

G

:

0. 5

'

...

0. 1


8/25

,;oil res is tance-def lect ion relat ionships known as

p-y curves and t -x curves have been recommended

in the

l i t e ra ture .

For appl icat ions in offshore

s t ruc tu res the American

Petroleum

I n s t i t u t e

(1986) spec i f i es t he p-y curves

for

c lay as well

as

sand

making

a dif ference between s t a t i c

loading

and cycl ic

loading. Extensive data on

the

p-y curves

and

nonl inear p i l e response were

obtained by Yan

(1990)

using

model pi les

and the

hydraulic gradient s imi l i tude

method to

reproduce

prototype

condit ions. An

example of Yan's

resul ts

i s shown

in

Fig. 12.

Notice the

narrowing

and p ar t i a l

l inea r iza t ion of the

hysteres is

loop with

the

number of cyc les ;

t h i s

t rend

increases

with

depth.

Pile Deflection -

y

mm)

Figure 12 Example of p-y curve under cyc l i c

loading (Yan, 1990)

Cyclic

loading is

def ined as r e pe t i t i ve

loading

with very low

f requency so t ha t no s ign i f ican t

i ne r t i a

fo rces

and rad iat ion damping

ar i se .

t

provides bas ic ins ight in to the mater ia l

degradation

due to

so i l p l a s t i c i t y and mechanic

degradation due

to gapping

assoc ia ted with large

displacements .

Many s tudies were devoted to t h i s

subjec t but only a

few

may be mentioned here .

Trochanis

e t

a l . (1988)

found

theore t ica l ly a

dramatic

decrease

in

p i l e s t i f f n e s s due to

gapping.

Morrison and Reese (1988)

conducted

extensive fu l l sca l e

invest igat ion

of pi l e s and

pi l e

groups. To

t h i s

conference,

Purkayastha

and

Dey

(1991)

repor t

on t he i r experimental s tudy of

the degradation of ver t i ca l s t i f fness .

Summarizing t he i r observat ions , Swan and Poulos

(1982)

postu late

t h a t

during

cyc l ic

l a t e r a l

loading the two forms of degradation lead

to

the

increase in pi l e def l ec t ion

and

bending s t r es ses ;

but i f t h i s degradation s t a b i l i z e s the p i l e i s

sa id

to

shakedown

to

a

s t a t e

of

permanent

s t r a ins and

res idual

s t r es ses

and

wil l r eac t

e las t i ca l ly to any

fur ther

cyc l ic loading

of

the

same in tens i ty .

When the p i l e

does

not s t ab i l i ze

in to an e l a s t i c or i ne las t i c

response,

the

p i l e

def lect ions continue

to increase and incremental

col lapse

may

re su l t .

The two

s i tua t ions

are

depicted in Fig. 13.

The shakedown phenomenon i s

favourable

from

the

Stlakodown

Incrqmczntal

Collaps.Q

Figure 13 Pi l e s t ab i l i za t ion (shakedown) and

incremental

col lapse

under cyc l i c

loading

with

constan t amplitude (Swane

&

Poulos, 1982)

poin t

o f view of the appl icab i l i ty

of

the var ious

l inea r

theor ies for dynamic response analysis .

I t

explains

why, with adequate adjustments

par t icu la r ly

for

p i l e

separa t ion

such

t heo r i es

may give

reasonable r esu l t s

as in Fig. 10,

even

in cases where overa l l s t rong

nonl inear i ty

of the

response

i s

c lea r ly manifested.

Under ver t i ca l

steady

s t a t e

vibrat ion

a

s imi la r

s tab i l i za t ion

and

par t i a l l inea r iza t ion

takes

place . Figure 14 shows

the ver t i ca l

displacement

2439

1 5

----------------------

E

E

c

E

e

0

0

1 0

0.5

Q

>

0 1 /

0

/

/

10

20

Frequency

Hz

)

•

e

•

s

14 }

Measured

o e

zs

Colcuio ed

Bockbone (]

30

Figure 14 Ver t ica l pi l e response

measured and

backcalculated for t h ree l eve l s

of

exc i ta t ion

in tens i ty (Han & Novak,

1988)

ampli tudes

measured

on

a

3.38

m

long t e s t

p i l e

with

increasing intens i ty

of

harmonic exc i ta t ion .

As

the

exc i t a t ion forces grow, t he resonance

frequencies

are

markedly reduced, i nd ica t ing

s t rong

nonl inear i ty .

To the response curves ,

backbone curves,

n ,

can be

const ructed

and from

them the

p i l e

res tor ing fo rce-d isp lacement

relat ionships are estab l i shed

(Fig.

15).

t

appears t ha t

each

response curve

has

i t s own

backbone curve

and

corresponding s t i f f n es s


9/25


10/25

-80

a)

and

(b)

Clay

Figure 18 Force-displacement r e l a t ionsh ip

for

incrementally

increas ing

hor izontal load

(Kishida

e t a l . , 1985)

PHe

Elemeo \

I

SoH

Reaction•

~

t Pile Tip X

Reactions

a

)

Figure 19 Pi l e model for ver t i ca l v ib ra t ion

al lowing

for

s l ip ,

nonl inear i ty

and i n f in i ty of

the outer zone (Mitwally Novak,

1988)

in terms

of the

s tandard geo techn ical parameters.

PILE

GROUPS

Pi l es a re usua l ly used in groups and i f they are

not

very widely spaced

they i n t e rac t

with each

other

generat ing phenomena known as p i l e - so i l

p i l e in te r ac t ion o r group e f fec t s . These ef f ec t s

have

a t t r ac ted much

i n t e res t

in

recent years .

A

number of

papers

on the subject have appeared, a

few

exhaustive Ph.D.

dis se r ta t ions

were wri t t en

e.g.

Kaynia, 1982a; Ostadan,

1983,

Mamoon, 1990,

Hassin i , 1990) and many

contr ibu t ions

have been

made

to the world conferences on

earthquake

engineering

and

are

being presen ted to

t h i s

conference.

Linear Behavior o f

Pi l e Groups

Under s t a t i c

loads, pi l e in te r ac t ion increases

group set t lement ,

r ed is t r ibu tes

t he

loads

on

ind iv idua l pi l e s and

reduces

bear ing capac i ty ,

unless t h i s reduction

i s

coun teracted

by

densi f icat ion

of

the so i l with in the

group

due

to

p i l e dr iv ing .

The

f i r s t

suggest ion

of

t h i s

kind

of e f fec t s probably can be a t t r ibu ted to

Sooysmith

(1896). The

i nves t iga t ion

of

s t a t i c

group

ef f ec t s was

put

on

a

r a t iona l

bas i s ,

re ly ing

on

continuum mechanics, by

Poulos

(1968,

1971,

1979)

and Butter f ie ld

and

Banerjee (1971).

Extensive data

on s t a t i c

group e f fec t s

are

avai lab le in

Poulos

and Davis

(1980),

But te r f ie ld

and Douglas (1981),

El

Sharnouby and Novak (1985,

1986,

1990)

and elsewhere. The s t a t i c data

are

usefu l

even

to

those

in te r es ted in

dynamics

because a t low f requencies , and par t i cu la r ly

below t he fundamental frequency

of

a s t ra tum

(Fig. 2), the dynamic

s t i f f n e s s

i s usual ly qui te

c lose to the s t a t i c s t i f f n e s s .

Dynamic

invest igat ions

of p i l e groups

are

more

recent . The

techniques

employed

are

ex tensions

of the

approaches

used for s ing le p i l e s and most

of them are l imi ted to l i nea r in te r ac t ion with no

al lowance for gapping. The

methods

r e ly

on t he

ava i l ab i l i ty

of

Green 's

funct ions

with

which

t he

load t r ans fe r

from the pi l e sur face to

so i l

can

be

calcu lated .

These loading condi t ions ,

represent ing

one

of

the

basic d i f ferences between

var ious approaches,

range

from poin t

loads

to

l ine loads ,

r ing

loads,

disk

loads

and

f ina l ly to

cy l ind r i ca l

barrel) loads; for

the

p i l e

base,

disk loads are the ru le .

Applying

t h i s loading

to individual segments in to which t he pi l e i s

d i sc re t i zed ,

the

so i l dynamic displacement f i e ld

i s estab l i shed ,

yie ld ing

the

so i l dynamic

f l e x i b i l i t y matr ix ;

inver t ing the l a t t e r ,

so i l

s t i f fness

matrix

i s obtained.

In

t h i s

process ,

the presence of the pi l e

cavi t i e s

outs ide

the

loaded segment i s

usua l ly

ignored,

which

impl ies

t ha t wave sca t te r ing among the pi l e s i s not

accounted for ,

and the so i l

displacements

are

calcu lated

e i the r for t he pi l e axes or as

averages of

the

c i rcumferent ia l va lues . A

typ ical

model for t h i s

ana lys i s i s

shown in Fig.

20.

Then

the

so i l

s t i f f n e s s matrix i s

combined

with

the

pi l e s t ruc tura l s t i f f n e s s and the

s o i l

pi l e system can be analyzed for any type of

exc i t a t ion .

Differen t

au thors

proposed

various

ref inements or

s imp l i f i ca t ions

to

t h i s

procedure.

The

f i r s t

theore t ica l ana lys i s of p i l e - so i l - p i l e

i n t e rac t ion was conducted by Wolf and von Arx

(1978) who employed an

axisymmetr ic

f i n i t e

element formulat ion to es tab l i sh the dynamic

displacement f i e ld due

to r ing

loads . Waas

and

Hartmann (

1981,

1984)

formulated

an

e f f i c i e n t

semi-ana ly t i ca l

method

which

uses

r ing

loads

and

i s well su i t ed for layered media,

proper ly

accounting

for the far

f ie ld ; the

layers

ought

to

be

th in .

Kaynia

(1982a,b, 1988)

and

Kaynia

and

Kausel (1982,

1990)

fu r ther

improved

the

accuracy

by

combining the cyl indr ica l loads, ac tua l ly a

boundary element

formulat ion,

with t he cons i s t en t

s t i f f n e s s matrix of layered

media

to account for

the f a r f i e ld . A

very s imi l a r

approach

i s

employed in

the

paper to t h i s conference

by

Kobori e t

a l . (1991) who use

the

cyl indr ica l

244


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Piles Under Dynamic Loads

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Transcript of Piles Under Dynamic Loads