Peformance Analysis of Aseismic Base Isolation System for a Multi-story Buildind

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P e r f o r m a n c e a n a l y s is o f a s e i s m i c b a s e i so l a ti o n

s y s t e m s f o r a m u l t i s t o r y b u i ld i n g

F . G . F a n a n d G . A h m a d i

Department of Mechanical and Aeronautical Engineering Clarkson University Potsdam NY

13676 USA

N . M o s t a g h e i

Department of Civil Engineering University of Toledo Toledo Ohio 43606 USA

I . G . T a d j b a l d a s h

Department of Civil Engineering Rensselaer Polytechnic Institute Troy NY 12181 USA

A c o m p a r a t i v e s t u d y o f t h e p e r f o r m a n c e s o f s e v e r a l l e a d i n g b a s e i s o la t io n d e v i c e s i n c l u d i n g t h e

Rubber Bea r ing wi th and wi thou t l ead core , the S l id ing-Jo in t , the F rench S ys tem , and the

Res i l i en t -F r ic t ion i so la to r wi th and wi thou t uppe r s l id ing p la te fo r a m ul t i - s to ry bu i ld ing un der

se i sm ic g round acce le ra t ions i s ca r r i ed ou t . S eve ra l ea r thquake ground acce le ra t ions inc lud ing

E1 Cent ro 1940, P ac o im a Dam 1971, and M exico Ci ty 1985 ea r thquakes a re cons ide re d . The

acce le ra t ion , the base d i sp lacem ent and the s t ruc tura l de f lec t ion re sponse spec t ra fo r the s t ruc -

tu re wi th d i f fe ren t base i so la t ion sys tem s under va r ious condi t ions a re ob ta ined and d i s cus sed .

S eve ra l s ens i t iv i ty ana lyses fo r va r ia t ions in the pa ram ete r s o f the i so la to rs and /or s t ruc tu re a re

a l so ca r r i ed ou t . T he e f fec t iven es s o f va r ious base i so la to rs un de r a va r ie ty o f condi t ions a re

s t u d ie d a n d a d v a n t a g e s a n d d i s a d v a n t ag e s o f d i f f e r e n t s y s t e m s a r e d i s c u s s e d . T h e r e s u lt s s h o w

t h a t t h e a c c e l e r a t i o n t r a n s m i t t e d a n d t h e c o l u m n s t r e s s e s o f t h e s t r u c t u r e c a n b e e f f e c t i v e l y

reduc ed by us ing prope r ly de s igned base i so la t ion sys tem s . The re su l t s o f the sens i t iv ity

ana lyses show the f r i c t ion- type i so la t ion sys tem s a re l e s s s ens i t ive to the va r ia t ions in the

a m p l i t u d e a n d f r e q u e n c y c o n t e n t o f th e g r o u n d e x c i t a t io n i n c o m p a r i s o n t o t h e R u b b e r B e a r i n g

base i so la to rs. T he s tudy a l so show s tha t the peak acce le ra t ion s t ransm i t t ed by the f r i c t ion- type

i so la to rs a re no t s ign i f i can t ly a f fec ted by sm a l l va r ia t ions in f r i c t ion coe f f i c ien t . F ur the rm ore ,

va r ia t ions in m ass ra t io and dam ping of the s t ruc ture o r the i so la to r do no t s ign i f i can t ly a f fec t

the peak re sponses .

I N T R O D U C T I O N

T h e c o n v e n t i o n a l t e c h n iq u e f o r a s e i sm i c d e s i g n o f s t r u c -

tu res i s to s t reng then the s t ruc tura l m em bers in o rde r to

wi ths tand s t rong ea r thquakes . However , th i s s t reng then-

ing s t ra tegy inev i tab ly l eads to h ighe r m asses and hence

h ighe r s e i sm ic fo rces . A s t ruc ture des igned in th i s way

m a y s u r v i v e a s t r o n g e a r t h q u a k e , w h i l e t h e r e c o u l d

resu l t in to le rab le dam ages to i ts m e m b ers , a s we l l a s , to

i t s s ens i t ive in te rna l equ ipm ent . Moreover , the econo-

m i c a l c o n s i d e r a t i o n l i m i t s t h e c o n s t r u c t i o n o f a c o m -

ple te ly s a fe s t ruc tu re wi th in the bounds o f t rad i t iona l

d e s i g n m e t h o d o l o g y .

An a l t e rna t ive des ign s t ra tegy i s to i so la te the s t ruc -

t u r e f r o m t h e g r o u n d m o t i o n d u r i n g t h e e a r t h q u a k e

s t rong m ot ion . The base i so la t ion concep t has been sug-

ges ted a long t im e ago . Acc ord in g to K e l ly ~ .z , a s ea r ly

as 1909 , a Br i t i sh phys ic ian had app l ied fo r a pa ten t on

Paper accepted May 1989 Discussion closes September 1991

Computational Mechanics Publications 1991

s e p a r a ti n g a b u i l d i n g f r o m t h e g r o u n d b y a l a y e r o f t a lc

or s and . However , i t was on ly in the l a s t th ree decades

tha t th is des ign co ncep t has rece ived s e r ious a t t en t ions .

T h e b a s e i s o l at io n d e s i g n m e t h o d o l o g y a p p e a r s t o h a v e

cons ide rab le po ten t i a l in p reven t ing ea r thquak e dam ages

to s t ruc tures and the i r in te rna l equ ipm ent . A la rge

n u m b e r o f b a s e i s o l a t i o n s y s t e m s f o r v a r i o u s t y p e s o f

s t r u c t u r e h a v e b e e n s u g g e s t e d . S e v e r a l o f w h i c h h a v e

been deve loped and used to p ro tec t bu i ld ings , b r idges ,

nuc lea r pow er p lan t s , and o the r s t ruc tu res aga ins t ea r th -

quakes . Ex tens ive rev iews on h i s to r ica l deve lopm ents

a n d r e c e n t l i t e r a t u r e o n t h e s u b j e c t w e r e p r o v i d e d b y

Kel ly t .2 . The re for e , o n ly b r ie f d esc r ip t ions o f s eve ra l

l ead ing base i so la t ion sys tem s which a re cons ide red in

th i s s tudy a re p resen ted in th i s s ec t ion .

A c la s s o f base i so la t ion sys tem s which has been

ex tens ive ly s tud ied a t the Unive rs i ty o f Ca l i fo rn ia by

Kel ly and co-w orke rs ~ 2.3 is the Lam ina ted Rub ber

Bear ing (LRB) base i so la to rs . The sys tem has been

u s e d i n t h e f o u r s t o r y F o o t h i l l C o m m u n i t i e s L a w a n d

152 Soil Dynamics and Earthquake Engineering 1991 Volume 10 Number 3 April


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Per formance analys is o f ase i smic base i so la tion s yst ems : F . -G . Fan and G . Ahm adi

Jus t i c e B u i ld ing in Sa n B e rna rd ino C oun ty , C a l i fo rn i a

a n d a n u m b e r o f b u il d i ng s i n E u r o p e , J a p a n , a n d N e w

Ze a la nd . A L R B i so l a to r i s ma d e o f a lt e rna ting l a ye r s o f

rubbe r a nd s t e e l w i th t he rubbe r be ing vu lc a n iz e d to t he

s t e e l p l a t e s . T he L R B i s r a the r f l e x ib l e i n the ho r i z on ta l

d i r e c t ion bu t qu i t e s t i f f i n t he ve r t i c a l d i r e c tion . The

ho r i z on ta l s t i f fne ss o f t he be a r ing i s a lso de s igne d in

suc h a w a y tha t i t c a n r e s i s t t he w ind fo rc e s w i th l i t t l e

o r no de fo rma t ion . F igu re l ( a ) show s a sc he ma t i c

d i a g ra m fo r a LR B i so l a to r . The G ER B sy s t e m 4 , w h ic h

i s c om pose d o f he l i c al sp r ings a nd v i sc oda m pe rs ,

be ha ve s s imi l a r t o t he LR B sys t e m in t he ho r i z on ta l

d i r e c t ion a nd i t s me c ha n ic a l be ha v iou r ma y a l so be

re p re se n te d by F ig . l ( a ) .

The l a m ina te d rubb e r be a r ing ba se i so l a to r w i th a le a d

c o re ha s found w ide a pp l i c a tions i n N e w Ze a la nd a s w e l l

a s o the r c oun t r i e s . T h i s sy s t e m i s r e fe r re d to a s t he l ea d

c o r e L R B o r t h e N e w Z e a l a n d ( N Z ) b a s e i s o l a t i o n

sys t e m. The l e a d c o re i s u se d to r e duc e the l a t e ra l

d i sp l a c e me n t a nd to o f fe r a n a dd i t i ona l me c ha n i sm fo r

e ne rgy d i ss ipa t ion , w h i l e t he f l e x ib i l i t y a nd re s to r ing

f o r c e a r e p r o v i d e d b y t h e r u b b e r b e a r i n g . T h e p e r f o r -

m a n c e o f th e N Z i s o la t o r ( L e a d c o r e l a m i n at e d r u b b e r

be a r ing ) unde r a va r i e ty o f c ond i t i ons w e re r e po r t e d in

R e fs 2 , 3 , 5 . F igu re l (b ) d i sp l a ys t he me c ha n ic a l

b e h a v i o r o f t h e N Z b a s e i s o la t io n s y s t e m . T h e m e c h a n i-

c a l b e ha v io r o f hys t e re t i c da m pe r3 6 -8 ma y a l so be

sc he ma t i c a l ly r e p re se n te d by th i s f i gu re .

B a se i so l a t i on sys t e ms in w h ic h the on ly i so l a t i on

me c ha n i sm i s s l i d ing f r i c t i on a re Pu re -Fr i c t i on (P -F) o r

S l id ing - Jo in t ba s e i so l a ti on sys t e m s . In t h i s c l a ss o f ba se

isola t ion systems, one or severa l f r ic t ion p la tes or a layer

o f sa nd a re u se d to i so l a te t he s t ruc tu re f rom the g round .

A sc he ma t i c d i a g ra m fo r P -F ba se i so l a t i on sys t e ms i s

s h o w n i n F i g . l ( c ) . T h e r e h a s b e e n a l a r g e n u m b e r o f

the o re t i c a l w ork s on the pe r fo rma nc e o f t h is c l a ss o f

I . I . , I

( a ) L R B S y s t e m ( b ) N Z S y s t e m

( c ) P - F S y s t e m

I

Y . I

i - -

( e ) E D F S y s t e m

Fig. 1.

v - - - - 1

~ i-9

( d ) R - F B I S y s t e m

Y I

I H

( f ) S R - F S y s t e m

Schemat i c d iagrams o f i so la t ion s ys t ems

i so l a to r s unde r de t e rmin i s t i c o r s toc ha s t i c g roun d e xc i t a -

t ions 9-16. In Re fs 17 and 18, the use o f a lay er of sand

a s a s imp le P -F ba se i so l a to r fo r a bu i ld ing in B e j in ,

C h ina w a s de sc r ibe d .

R e c e n t ly , a ba se i so l a t i on sys t e m re fe r re d to a s t he

R e s i l i e n t -F r i c t i on B a se I so l a t i on sys t e m (R -FB I) w a s

p ropose d by Mos ta ghe 119-2~ . Th i s i so l a to r c ons i s t s o f

se ve ra l l a ye r s o f t e f lon c oa t e d f r i c t i on p l a t e s w i th a c e n -

t r al c o re o f rubbe r . T he rubbe r p rov ide s t he r e s to r ing

fo rc e fo r t he sy s t e m a nd he nc e c on t ro l t he r e l a t i ve

d i sp l a c e me n t w h i l e e ne rgy i s d i s s ipa t e d by the f r i c t i on

fo rc e s . A n e x te ns ive s tudy o f the r e spons e s o f a f i ve -

s to ry bu i ld ing i so l a t e d by the R -FB I sys t e m w a s p ro -

v ide d by Mo s ta ghe l a nd K hod a ve rd i a n 22. F igu re l (d )

i l lu s t r a te s t he m e c ha n ic a l be ha v io r o f t he R -FB I sy s t e m.

T h e A l e x i s i s m o n b a s e i s o l a ti o n s y s t e m d e v e l o p e d b y

I k o n o m o u 23 a l s o m a k e s u s e o f t h e c o m b i n e d a c t io n s o f

s l i d ing jo in t a nd rubb e r be a r ings . T he rub be r e l e me n t i n

the A le x i s i smon sys t e m a ppe a r s t o a c t i n be nd ing w h i l e

in t he R -FB I i so l a to r a c t s i n she a r . A l though the se

de s igns a re qu i t e d i f f e re n t , t he me c ha n ic a l be ha v io r o f

the A le x i s i smon ba se i so l a to r ma y a l so be sc he ma t i c a l ly

re p re se n te d by F ig . l (d ) .

A no the r ba se i so l a t i on sys t e m w h ic h i s u se d fo r ba se

i so l a ti on o f nuc l e a r po w e r p l a n t s i n r e g ions o f h igh

s e i s m i c i t y w a s d e v e l o p e d u n d e r t h e a u s p i c e s o f E l e c -

t r ic i te de Fran ce (ED F) 24. I t has b een used in the

de s ign o f nuc l e a r pow e r p l a n ts i n F ra nc e , a nd I r a n . The

K roe be rg nuc le a r pow e r p l a n t i n Sou th A f r i c a r e l i e s on

the ED F ba se i so l a t i on sys t e m fo r p ro t e c t ion a ga in s t

e a r thqua ke . A n E D F ba se i so l a to r un it c ons i s t s o f a

l a mina te d ( s t e e l - r e in fo rc e d ) ne op re ne pa d toppe d by a

l e a d -b ronz e p l a t e w h ic h i s i n f r i c t i ona l c on ta c t w i th a

s t e e l p l at e a nc ho re d to t he ba se r a f t o f t he s t ruc tu re .

W he ne ve r t he re i s no s l i d ing in t he f r i c t i on p l a t e , t he

ED F sys t e m be ha ve s a s a LR B a nd the f le x ib i l it y o f t he

ne op re ne pa d p rov ide s i so l a t i on fo r t he s t ruc tu re . The

p re se nc e o f t he f r i c t i on p l a t e se rve s a s a n a dd i t i ona l

sa fe ty f e a tu re fo r t he sy s t e m. W he ne ve r t he g round

a c c e l e ra t ion be c ome s ve ry l a rge , s l i d ing oc c u rs w h ic h

d i ss ipa t e s e ne rgy a nd l imi t s t he a c c e l e ra t ion t r a nsmi t t e d

t o t he s u p e r s t r uc t u r e . T h e b e h a v i o r o f t h e E D F b a s e

i so l a to r i s show n sc he ma t i c a l ly i n F ig . l ( e ) .

A ba se i so l a t i on c onc e p t w h ic h c omb ine s t he de s i r a b l e

f e a tu r e s o f t he R - F B I a n d t h e E D F s y s t e m s w a s p r o -

pose d in R e f . 25 . T h i s sy s t e m w h ic h i s r e fe r re d to a s t he

S l id ing R e s i l i e n t -F r i c t i on (SR -F) ba se i so l a t i on sys t e m

is a R -FB I un i t w i th a n a dd i t i ona l uppe r f r i c t i on p l a t e .

The be ha v io r o f t he SR -F i so l a to r is show n sc he m a t i -

c a l ly i n F ig . l ( f ) . W he ne ve r t he re i s no s l i d ing in t he

uppe r f r i c t i on p l a t e , t he SR -F ba se i so l a to r be ha ve s a s a

R -FB I un it . Fo r h igh g round a c c e l e ra t ions , s l id ing in the

uppe r f r i c t i on p l a t e oc c u rs w h ic h p rov ide s a n a dd i t i ona l

me c ha n i sm fo r e ne rgy d i ss ipa t ion a nd inc re a se s t he

ove ra l l e f f e c t ive ne ss o f t he i so l a t i on sys t e m.

G e ne ra l de s ign re qu i re me n t s fo r a ba se i so l a t i on

sys t e m a nd de s ign c r i t e r i a fo r ba se - i so l a t e d bu i ld ing

w e r e d e s c r ib e d i n R e f s 2 6 - 2 8 . I n t h e s e w o r k s , c o d e -

type c r i t e r i a r e ga rd ing a l l ow a b le ba se d i sp l a c e me n t ,

pe a k t r a nsmi t t e d a c c e l e ra t ion , na tu ra l pe r iod a nd

se i smic c oe f f i c i e n t w e re sugge s t e d . G u ide l ine s r e ga rd -

ing the de s ign o f t he rubbe r be a r ing ba se i so l a t ion

sys t e m w i th o r w i thou t a l e a d c o re w e re a l so p re se n te d

i n R e f s 2 6 - 2 8 . R e c e n tl y , M o s ta g h el et al. 29 3

d e s c r i b e d t h e d e s i g n p r o c e d u r e f o r t h e R - F B I s y s t e m .

Soil Dynamics and Earthquake Engineering 1991 Volu me 10 Num ber 3 April 153


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P e r f o r m a n c e a n a l y s i s o f a s e i s m i c b a s e i s o la t io n s y s t e m s : F . - G . F a n a n d G . A h m a d i

I n s p i te o f a l a r g e n u m b e r o f s t u d ie s o n p e r f o r m a n c e s

o f d i f f e r en t b ase i so la t i o n sy s t em s , t h e ad v an t ag es an d

d i sad v an t ag es o f v a r i o u s sy s t em s a re n o t we l l u n d er -

s t o o d . On e d i f f i cu l t y h e re i s t h e d es i r ed r eq u i r em en t s

a re n u m e ro u s . Had j i an an d T sen g 3~ h av e p o in t ed o u t

e l ev en d es i r ed p e r fo rm an ce c r i t e r i a r e l a t ed t o sa fe ty an d

re l i ab i li t y o f t h e iso l a t ed s t ru c tu re . Rec en t l y , S u e t

al.25 32 h a v e c a r r i e d o u t s e v e r a l c o m p a r a t i v e s t u d i e s o f

d i f f e r en t b ase i so l a t i o n d ev i ces fo r r i g id an d sh ear b eam

s t ru c tu res . F an

e t a l .

33.34 cons idere d the p erfo rm anc es

o f v a r i o u s b ase i so l a t i o n sy s t em s fo r a m u l t i - s t o ry

b u i l d in g u n d er a h o r i zo n t a l s i n u so id a l g ro u n d m o t io n .

In t h i s wo rk , p e r fo rm an ces o f sev era l b ase i so l a t i o n

sy s t em s d esc r i b ed ea r l i e r fo r a m u l t i - s t o ry , sh ear f r am e

su b j ec t t o sev era l se i sm ic g ro u n d m o t io n s a r e s t u d i ed .

Th e eq u a t i o n s o f m o t io n fo r v a r i o u s b ase i so l a t i o n

sy s t em s a re d esc r i b ed . Th e g o v ern in g eq u a t i o n s fo r f r i c -

t i o n a l b ase i so l a t i o n d ev i ces an d t h e c r i t e r i a fo r t r an s i -

t i o n b e tween d i f f e r en t p h ases o f m o t io n a r e h ig h ly

n o n l in ea r . Co n s id e rab l e ca re i s n eed ed i n fo rm u la t i o n o f

t h e co m p u ta t i o n a l m o d e l fo r h an d l i n g t h ese r a th e r s t i f f

eq u a t i o n s . Ut i l i z in g t h e fo u r th -o rd er Ru n g e -Ku t t a

sch em e, a co m p u ta t i o n a l a l g o r i t h m fo r accu ra t e n u m er i -

ca l ev a lu a t i o n o f t h e r esp o n se o f t h e b ase i so l a t ed s t ru c -

t u re i s d ev e lo p ed . Th e p eak ab so lu t e acce l e r a t i o n o f

each f l o o r , t h e p eak b ase d i sp l acem en t , an d t h e p eak

s t ru c tu ra l d e f l ec t i o n fo r v a r i o u s b ase i so l a t i o n sy s t em s

are ev a lu a t ed an d t h e r esu l t s a r e co m p ared wi th each

o th er an d w i th t h o se o f t h e f i x ed -b ase s t ru c tu re . T h e

acce l e ra t i o n r esp o n ses b o th i n t im e an d f r eq u en cy

d o m a in s a r e ex am in ed . A se r i es o f sen s i ti v i t y s t u d i es fo r

v ar i a t i o n s i n f r i c t i o n co ef f i c i en t an d n a tu ra l p e r i o d o f th e

i so l a to r , a s we l l a s , d am p in g an d m a ss r a t i o o f th e s t ru c -

t u re a r e a l so ca r r i ed o u t . T h e e f f ec t s o f t h e v e lo c i t y -

d ep en d en ce o f f r i c t i o n co ef f i c i en t i s a l so s t u d i ed an d

d i scu ssed .

Th e r esu l t s sh o w th a t t h e t r an sm i t t ed acce l e r a t i o n an d

th e co lu m n s t r es ses o f th e s t ru c tu re can b e s i g n i f i can t ly

red u ced b y u s in g p ro p er ly d es ig n ed b ase i so l a t i o n

sy s t em s . Th e f r ic t i o n a l sy s t em s g en era t e h ig h f r eq u en c y

p eak s i n t h e acce l e r a t i o n r esp o n ses , h o wev er , t h ese h ig h

f r eq u en cy p eak s d o n o t l ead t o l a rg e s t ru c tu ra l d e fo rm a-

t i o n s . Th e r esu l t s o f t h e sen s i t i v i ty an a ly ses sh o w th e

f r i c t i o n - ty p e i so l a t i o n sy s t em s a re l e s s sen s i t i v e t o

v ar i a t i o n s i n th e am p l i t u d e an d f r eq u en cy co n t en t o f th e

g r o u n d e x c i t a ti o n i n c o m p a r i s o n t o t h e L R B , a n d t h e N Z

b ase i so l a to r s . Th e s t u d y a l so sh o ws t h a t t h e p eak

acce l e ra t i o n s t r an sm i t t ed b y t h e f r i c t i o n - ty p e i so l a to r s

a re n o t s i g n i f i can t l y a f f ec t ed b y sm al l v a r i a t io n s i n f ri c -

t i o n co ef f i c i en t . F u r th e rm o re , v a r i a t i o n s i n m ass r a t i o

an d d am p in g o f th e s t ru c tu re o r t h e i so l a to r o n ly s l i g h tl y

a f f ec t s t h e p eak r esp o n ses .

G O V E R N I N G E Q U A T I O N S

T h e e q u a t i o n s g o v e r n i n g t h e m o t i o n o f v a r io u s b a s e

i so l a t i o n sy s t em s an d t h e c r i t e r i a fo r m o t io n t r an s i t i o n s

o f f r i c t i o n a l sy s t em s h av e b een d esc r i b ed a t l en g th i n

R e f . 3 3 . T h e r e f o r e , o n l y a b r i e f d e s c r i p ti o n i s n e e d e d

h ere . F o r a m u l t i - s t o ry , l u m p ed -m ass , sh ear b u i l d in g

wi th d i f f e r en t b ase i so l a t i o n sy s t em s , t h e eq u a t i o n s o f

m o t io n an d t h e c r i t e r i a fo r m o t io n t r an s i t i o n s a r e su m -

m ar i zed i n t h i s sec t i o n .

L R B s y s t e m

T h e s c h e m a t i c d i a g r a m f o r t h e L a m i n a t e d R u b b e r

Bear in g b ase i so l a t io n sy s t em i s sh o wn in F ig . l ( a ) . T h e

e q u a t io n s o f m o t i o n o f a m u l t i - st o r y f r a m e w i th a L R B

sy s t em a re g iv en as ,

~' + 2g'o~0o + ~02s + ~ cti ~ = -j~g

i=l

(1)

[ m ] l e } + [ c ] l x ] + [k ] lx } = - ( ~ ' + ~ g ) [ m ] { l l

(2)

wh ere s i s t h e r e l a t i v e d i sp l acem en t b e tween t h e b ase o f

s t ru c tu re an d t h e g ro u n d , x i i s th e d i sp l acem en t o f t h e

i t h f l o o r r e l a t i v e t o t h e b ase as sh o wn in F ig . 2 , y g i s

t h e h o r i zo n t a l g ro u n d acce l e ra t i o n , an d [m ] , [ c ] , [ k ]

r ep resen t m ass , d am p in g , an d s t i f fn ess m at r i ces , r e sp e c-

t i v e ly . Th e n a tu ra l c i r cu l a r f r eq u en c y o f th e b ear in g

O:o , and i t s ef fec t ive dam ping rat io ~'o are d ef ine d as

k o

2~ ~ = M O:o = ~ (3)

w h e r e Co an d ko are t h e d am p in g an d t h e h o r i zo n t a l

s t i f fn ess o f t h e b ea r in g , r e sp ec t i v e ly . Th e m ass - r a t i o

para me ter c~i i s def ined as

mi m

li - M C~b = --~, M = mb + m~ (4)

i=l

wh ere m i is t h e m ass o f th e i t h f l o o r , m b i s th e m ass o f

t h e b ase an d M i s to t a l m ass o f th e s t ru c tu re . Here , [ 1 }

i s a co lu m n v ec to r a l l o f wh o se e l em en t s a r e u n i t y an d

a d o t o n t o p o f a l e t t e r d en o t es a t im e d er iv a t i v e . A

n a tu ra l p e r i o d

To

o f ab o u t 2 sec (% = 7r r ad / sec ) i s

c o m m o n l y s u g g e s t e d f o r t h e L R B b a s e i s o l a t i o n

sy s t em s . T h e e f f ec t i v e d am p in g r a t io o f t h e i so l a to r ~'o

v ar i es co n s id e rab ly wi th t h e s tr a in o f th e ru b b er . Acc o r -

d in g t o Ref s 3 5 an d 3 6 , i t m ay b e as h ig h as 0 .3 fo r l o w

s t r a in an d r ed u ces t o ab o u t 0 .0 5 fo r h ig h s t r a in . Here ,

an i n t e rm ed ia t e v a lu e o f 0 .0 8 fo r ~ 'o i s co n s id e red i n

a~ ,~,_~3 ~ l ~ ard FLOOR

z~~ ~ 2 n d FLOOR

Fi g . 2 . S t r u c t u r a l mo d e l o f a t h r e e - s t o r y b u i l d i n g w i t h

a b a s e i s o l a t i o n s y s t e m

154 S o i l Dy n a m i c s a n d Ea r t h q u a k e En g i n e er i n g , 1 9 9 1 , Vo l u me 1 0 , Nu mb e r 3 , Ap r i l


4/20

P e r f o r m a n c e a n a l y s i s o f a s e i s m i c b a s e i s o la t io n s y s t e m s : F . - G . F a n a n d G . A h m a d i

m o s t c a s e s . N o t e a l s o t h a t t h e m o t i o n o f t h e G E R B

s y s t e m m a y a l s o b e d e s c r i b e d b y e q u a t i o n ( 1 ).

N Z s y s te m

T h e s c h e m a t i c d i a g r a m f o r t h e m e c h a n i c a l b e h a v i o r o f

t h e N e w Z e a l a n d s y s t e m is s h o w n i n F i g . 1 b) . W h e n a

m ul t i - s to r y bu i ld ing i s i so la ted by the NZ ( or a

hys te r e t i c dam per ) base i so la t ion sys tem , the de f lec t ion

o f t h e s t r u c t u r e is g o v e r n e d b y e q u a t i o n ( 2 ) , a n d t h e

e q u a t i o n g o v e r n i n g t h e b a s e d i s p l a c e m e n t i s g i v e n a s ,

Equa t ion ( 8 ) gover ns bo th the s l id ing and nons l id ing

~ s o f m o t io n o f t h e R - FB I s y st em . T h e d e f or m a ti o n

o f s t r u c t u r e is g o v e r n e d b y e q u a t i o n ( 2) w h i c h i s c o u p l e d

wi th equa t ion ( 8 ) th r ough the ine r t i a l f o r ces . The

nons l id ing phase con t inues a s long a s

I.~g + 6o2 s + ~ Oti.~il < # g

i=l

As soon as the condi t ion ,

(10)

~ + 2~oO~o~ + O~:oS+ ~1 Q + l iX i ~ - ' ~ g (5)

i =

wh er e N i s num ber o f base i so la to r s used , and M i s to ta l

m a s s o f t h e s t r u c tu r e . T h e h y s t e r e t i c r e s t o ri n g f o r c e Q

w h i c h i s g e n e r a t e d b y t h e l e a d c o r e m a y b e a p p r o x -

i m a t e d b y W e n

S37

m o d e l a s

F

Q(s , ~) = t x - y s +

(1 -

ot )E , .Z

(6)

Y

Ig + co2 s + ~ c ~ i~ i = # g ( 1 1 )

i=

is sa t is f ied, the s l iding motion s tar ts .

T h e n a t u r a l p e r i o d o f 3 t o 4 . 5 s e c a r e s u g g e s t e d f o r th e

R - F B I b a s e i so l a ti o n s y s t e m i n R e fs 1 9 - 2 1 . I n th i s

s tudy , un les s s ta ted o the r wise ,

To

= 4 sec , # - 0 .05

and ~'o = 0.08 are used . I t is no ted th at eq uat ion s

( 8 ) - ( 1 1 ) a r e a l so a p p l ic a b l e to t h e A l e x i s is m o n s y s t e m

a s l o n g a s t h e d e f o r m a t i o n i n i ts r u b b e r e l e m e n t r e m a i n s

sm al l .

w h e r e t h e d i m e n s i o n l e s s h y s t e r e t i c d i s p l a c e m e n t Z

sat is f ies

Y Z = - 3 , 1 J I Z I Z t n -t - / 3 J I Z l ~ + 0~ (7 )

P - F s y s t e m

F i g u r e l ( c ) s h o w s t h e s c h e m a t i c d i a g r a m f o r a P u r e -

F r i c t io n b a s e i s o l a ti o n s y s t e m . T h e e q u a t i o n g o v e r n i n g

t h e d i s p l a c e m e n t o f th e P - F i s o la t o r is g i v e n a s,

I n equa t ion ( 6 ) and ( 7 ) , F r and Y r epr esen t the f o r c e

a n d t h e y i e l d d i s p l a c e m e n t o f t h e e q u i v a l e n t h y s t e r e ti c

dam per s , 13, 3 ', and 0 a r e d im ens ion les s pa r am e te r s , ~ / i s

a n i n t e g e r w h i c h c o n t r o l s t h e s m o o t h n e s s o f t ra n s i ti o n

f r om e la s t i c to p la s t i c r e sponse , tx i s the pos t to p r e -

y ie ld ing s t i f fnes s r a t io .

I n o r d e r t h a t t h e p r e d i c t i o n s o f t h i s m o d e l m a y f it t h e

exper im enta l r e su l t s , f o r ce r ta in l ead- cor e l am ina ted

r u b b e r b e a r i n g s , t h e v a l u e s o f E , . = 4 6 KN,

Y = 7 . 7 m m , o t = 0 . 157 , /3 = - 0 . 5 4 , 3 ' = 1 . 4 , 0 = 1 . 0 ,

and *1 = 1 wer e sugges ted in R ef . 7 . These va lues

t o g e t h e r w i t h t h e n a t u r a l p e r i o d To o f 2 s e c

(COo = ~ ra d/se c) , a d am pin g ra t io ~'o of 0.08 and the

m ass p e r i so la to r r a t io , M / N , of 200 tons a r e used in th i s

s tudy .

R - F B I s y s t e m

F i g u r e l ( d ) s h o w s t h e s c h e m a t i c d ia g r a m d e s c r i b i n g

t h e m e c h a n i c a l b e h a v i o r o f t h e R e s i li e n t -F r i c ti o n B a s e

I s o la t io n s y s t e m . T h e e q u a t i o n f o r t h e d i s p l a c e m e n t o f

i so la to r i s g iven a s ,

+ 2~oO~o~ + O~2oS gsgn l ( ~ ) + ~ o t i i = - g

8 )

i=

g + p.gsgn l (~) + ~ .~ o ti .~ i - g

i = l

(12)

w h e r e

sgn~

( ~ ) is de f ined by eq ua t ion ( 9 ) w i th co be ing

z e r o f o r t h e P - F s y s t e m . T h e d e f le c t i o n o f t h e b a s e

i so la ted s t r uc tur e i s gove r ned by equa t ion ( 2 ) . Wi th the

d e f i n i ti o n o f

sgn~

( ~) a s g iven by equa t ion ( 9 ) , equa t ions

( 12) and ( 2 ) gover n bo th the s l id ing and the nons l id ing

m ot ions . F or th e nons l id ing phase (, = 0 ) , equa t ion ( 12)

r educe s to g = 0 , an d the de f or m a t ion of the s tr uc tur e i s

g o v e r n e d b y e q u a t i o n ( 2 ).

The c r i t e r i a f o r m ot ion t r ans i t ions a r e iden t ica l to

those g iv en by equa t ions ( 10) and ( 11) wi th ~o m 0 .

U s u a l l y , a f r i c t i o n c o e ff i c i e n t b e t w e e n 0 . 0 5 a n d 0 . 2 a r e

used f o r the P - - F ( S l id ing- Jo in t ) base i so la t ion sys -

tem s 9-~6 . I n th i s s tud y , # = 0 . 1 i s used in m os t o f the

n u m e r i c a l e x p e r i m e n t s .

S R - F s y s t e m

The m echanica l behav ior o f the S l id ing Res i l i en t -

F r ic t ion base i so la t ion sys tem i s show n in F ig . 1 f ) . The

e q u a t i o n s o f m o t i o n o f t h e S R - F b a s e i s o l a to r a r e g i v e n

a s

2

2 ~o O~ o~ + O O oy + # j g s g n 3 ( P ) = # g s g n 2 ( ~ - y )

(13)

wh er e # and g a r e the f r ic t ion coe f f ic ien t and acce le r a -

t ion o f g r av i ty , r e spec t ive ly ; and s g n ~ ( J ) i s de f ined a s

I ~ l ~ > 0

JCs + ~2s+ ~ otiXi

sg nl (g ) = t~g ~=1 ~ = 0 (9)

- 1 ~ < 0

+ 2 ~o O ~o ~ + o~ 2 Y + # i g s g n 3 ( P ) + ~ o t i~ i = - ~ 8

i=

(14)

w h e r e t h e r e l a t iv e d i s p l a c e m e n t s y a n d s a r e d e f i n e d i n

F ig . l ( f ) , and tz and #~ r epr esen t the f r i c t ion coe f f i -

c i e n t s o f t h e u p p e r a n d t h e b o d y f r ic t i o n p l at e s , r e s p e c -

S o i l D y n a m i c s a n d E a r t h q u a k e E n g i n e e r in g , 1 9 9 1 , V o l u m e 1 0 , N u m b e r 3 , A p r i l

155


5/20

P e r f o r m a n c e a n a l y s i s o f a s e i s m i c b a s e i s o la t i o n s ys t e m s : F . - G . F a n a n d G . A h m a d i

t ive ly . With the def in i t ions

y ~ j~g ~ Oli jC

. . . . = . - 5 , = 0 (15)

gn: ~ y ) I tg

~ y < 0

The cr i te r ion for the nons l id ing phase to cont inue is the

s a me a s tha t g ive n by e qua t ion (18 ) .

In p ra c t ic e , t he l a mina te d ne op re ne pa d i s de s igne d to

ha ve a na tu ra l pe r iod o f a bou t 0 .8 to 1 .2 s e c , a nd the

fr ic t ion coef f ic ient of the fr ic t ion p la te is abou t 0 .2 . In

the p re s e n t s tudy , un le s s s t a t e d o the rw is e the va lue s o f

T,, = 1 sec (090 = 27r rad /sec ), ~'o = 0. 08 , and # = 0. 2

a re u s e d .

a nd

+ xg + 09:o5 + ~ ~ x i

s g n 3 Y ) = I t lg i=1 19 =0 (16)

~9


6/20

Performa nce analys is of aseismic base isolation sys tems: F .-G. Fan and G. Ah ma di

nume r i c a l e va lua t ion o f r e sponse s o f t he ba se i so l a te d

mul t i - s to ry she a r f r a me w a s de ve lope d in R e f . 33 . Th i s

p rog ra m i s a da p te d fo r u se i n t he p re se n t a na ly s i s . A

t ime s t e p o f A t = 0 .0002 5 se c i s u se d du r ing the c on -

t inuous pha se s o f mo t ion a w a y f rom the t r a ns i t ions . The

a c c u ra c y o f t he r e su l t s i s ve r if i e d by c omp a r ing the

re su l t s w i th t hose ob ta ine d by f ine r t ime s t e ps fo r se ve ra l

c a se s . Fo r f r i c t i ona l sy s t e ms , t he p re c i se e va lua t ion o f

the t ime o f pha se t r a ns i t i ons a re c ruc i a l t o t he a c c u ra c y

o f r e sponse a na ly s i s . The re fo re , a suc c e ss ive t ime -s t e p -

re duc ing p ro c e du re i s u se d to a pp roa c h e a c h o f t he se

t r a ns i ti ons w i th a n a c c u ra c y o f 10 -1 m /se c 2 i n

e va lua t ing the s t i c k - s l i p c r i t e r i a a nd a n a c c u ra c y o f

10 -1 m/ s e c in e va lua t ing the z e ros o f ~ (o r ~ -3> a nd

f o r t h e E D F a n d t h e S R - F s y s t e m s ) . In th i s fa s h i o n, t h e

t ime o f t ra ns i t ion i s a c c u ra t e ly de t e rmine d , a nd ba se d on

the a pp rop r i a t e c r i t e r i a , t he e qua t ions gove rn ing the

subse que n t pha se a re spe c i f i e d .

R e spo nse s o f t he t h re e - s to ry s t ruc tu re w i th va r ious

ba se i so l a to r s sub je c t t o se ve ra l e a r thqua ke g round

a c c e l e ra t ions i nc lud ing E l C e n t ro 1940 N 0 0W , Pa c o im a

D a m 1 97 1 S 1 6 E , a n d M e x i c o C i t y 1 9 85 N 9 0 W a r e

e va lua t e d . The f i r s t 20 se c r e c o rd o f E1 C e n t ro a nd

P a c o i m a D a m e a r t h q u a k e s a n d t h e f i rs t 8 0 s e c r e c o r d o f

M e x ic o C i ty e a r thqua ke a re u se d in t h is s tudy . T he pe a k

a bso lu t e a c c e l e ra t ions fo r va r ious f l oo r s , (~8 + g +

; ) 1 . ~ ,

t h e m a x i m u m d e f l e c t i o n , X 3 l m a x a nd the ma x-

imum re l a t i ve ba se d i sp l a c e me n t ,

S lmax

fo r a r a nge o f

na tu ra l pe r io d o f 0 .1 < TI < 1 se c a re e va lua t e d a nd

d i sc usse d . Se ns i t i v i ty s tud ie s on the e f fe c t s o f va r i a t ions

o f pa ra me te r s o f t he i so l a to r s a nd the s t ruc tu re fo r E l

C e n t ro 1940 e a r thqua ke a re c a r r i e d ou t . To unde r s t a nd

the e f fe c t s o f va r i a t i on in i n t e ns i ty o f g round e xc i t a ti on ,

the ma gn i f i e d a c c e l e rog ra m o f E l C le n t ro 1940 e ar th -

qua ke i s u se d a nd the pe a k re sponse s a re e va lua t e d . The

re su l t s a re c ompa re d w i th t hose fo r t he o r ig ina l E1 C e n -

t ro e a r thqua ke re c o rd a nd d i sc usse d . U n le ss s t a t e d

o the rw i se a s t ruc tu re w i th a funda me n ta l na tu ra l pe r iod

o f 0 .3 se c a nd the pa ra m e te r s o f i so l a to r s a s l i st e d in

Ta b le 1 a re u se d in t he se ns i t i v i ty a na ly s i s .

R E S P O N S E S T O E L C E N T R O E A R T H Q U A K E

In th is se c t ion , r e sponse s o f t he ba se i so l a t e d a nd the

f ixe d -ba se th re e - s to ry f r a me sub je c t t o t he a c c e l e rog ra m

of E l C e n t ro 1940 e a r thqua ke a re s tud ie d . The ba se

i so l a t i on sys t e ms de sc r ibe d e a r l i e r a re c ons ide re d a nd

the sa mple a s w e l l a s t he pe a k re sponse s a re ob ta ine d

a nd d i sc usse d .

Sample responses

The c ha ra c t e r i s t i c s o f a c c e l e ra t ion r e sponse t ime

h i s to r i e s o f t he s t ruc tu re fo r va r ious ba se i so l a t ion

sys t e m s a nd fo r t he f i xe d -ba se one a re qu i t e d i f f e re n t . In

c e r t a in r e spe c t s , t he se c ha ra c t e r i s t i c s a re impor t a n t fo r

pe r fo rm a nc e a na ly se s o f ba se iso l a t ion sys t e m s . P r io r t o

a na lyz ing pe a k s t ruc tu ra l r e sponse s unde r d i f f e re n t c on -

d i t i ons , i t i s de s i r a b l e t o e xa mine the r e sponse t ime

h i s to r i e s i n o rde r t o i de n t i fy t he be ha v io r s o f va r ious

ba se i so l a t i on sys t e ms . In t h i s se c t ion , se ve ra l sa mp le

re sponse t ime h i s to r i e s a nd the i r Fou r i e r de c ompos i t i ons

a re p re se n te d a nd d i sc usse d . A s t ruc tu re w i th a fun -

d a m e n t a l n a tu r a l p e r i o d o f 0 . 3 s e e a n d th e r e c o m m e n d e d

va lue s o f the pa ra me te r s fo r va r ious i so l a to r s a s l is t e d in

Ta b le 1 a re u se d in t he se a na ly se s . The IM SL F a s t

Fou r i e r T ra ns fo rm rou t ine FC O S T 38 i s u se d fo r t he f r e -

que nc y a na ly s i s o f a pp rox im a te t he f i r s t 20 se c o f the

a c c e l e ra t ion r e sponse s .

F igu re 3 show s the sa mple a bso lu t e a c c e l e ra t ion t ime

histor ies a t the top of s t ruc tur e , ' (~t'e + ~ +~ 3) , for

va r ious ba se i so l a t i on sys t e m s a nd f ro : t he f i xe d -ba se

(F-B) s t ruc ture . The gro und ac ce le ra t ion , .fg , i s a lso

p lo t t e d in t h i s f i gu re , I t i s no t i c e d tha t t he f i xe d -ba se

s t ruc tu re s ign i f i c a n t ly a mp l i f i e s t he g round a c c e l e ra t ion

w h i l e t he ba se i so l a t i on sys t e ms ge ne ra l ly r e duc e s t he

a c c e l e ra t ion t r a nsmi t t e d to t he s t ruc tu re . F igu re 3 (a )

show s tha t t he f i xe d -ba se d s t ruc tu re a mp l i f i e s t he

g round a c c e l e ra t ion o f E l C e n t ro 1940 e a r thqua ke to

a bou t l g . The a c c e l e ra t ion r e sponse t ime h i s to ry o f the

f ixe d -ba se d s t ruc tu re show s a na r row -ba nd osc i l l a t i on

w h ic h i s e sse n t i a l l y a r a ndom a mpl i tude s inuso ida l t ime

va r i a t i on w i th a domina n t pe r iod o f 0 .3 se c ( c o r re spon -

d ing to t he funda me n ta l na tu ral p e r iod o f the s t ruc tu re ) .

Th i s i s due to the w ide -ba nd na tu re o f g round e xc i t a t ion

a nd the l i gh t da ming o f t he s t ruc tu re . I t is .pe rhaps o f

in t e re st t o po in t o u t t ha t i n t he e a r l i e r s tudy ~ , w he r e a

s inuso ida l g round e xc i t a t i on w a s u se d , t he a c c e l e ra t ion

re sponse t ime h i s to ry a t t he t h i rd f l oo r o f s t ruc tu re a l so

Z

o

W

.J

Lid

C ~

C ~

0 .07 , t he pe a k a c c e l e ra t ion be c ome s a c ons t a n t .

Th e reason is tha t , for re la t ive ly la rger , no sl id ing in

the uppe r f r i c t i on p l a t e oc c u rs du r ing the e n t i r e du ra t ion

o f g round e xc i t a ti on . S imi l a r ly , t he pe a k a c c e l e ra t ion

re sponse fo r t he S R - F 2 sys t e m inc re ase s a s j i nc re a se s

fo r sma l l t . A s l i gh t de c re a se in the pe a k a c c e le ra t ion

in the r a nge o f 0 .09 < , < 0 .1 i s no t i c e d . Fo r

, > 0 . 1 , t h e b o d y f r ic t io n p la t es o f t h e S R - F 2 s y s t e m

st i c k to ea c h o the r , t he sy s t e m re duc e s t o a P - F un i t a nd

the pe a k a c c e l e ra t ion r e ma ins a c ons t a n t .

F igu re 10 (a) show s the e f fe c t o f va ri a t i on o f f r i c t ion

c oe f f i c i e n t on the pe a k ba se d i sp l a c e me n t r e sponse s fo r

t h e P - F , t he R - F B I a n d t h e E D F s y s te m s . It i s

obse rve d tha t t he pe a k ba se d i sp l a c e me n t r e sponse s

ge ne ra l ly de c re a se a s i nc re a se s . The e xc e p t ion i s t he

E D F s y s e m f o r w h i c h t h e p e a k d i s p l a c e m e n t r e s p o n s e

f i r s t i nc re a se s to a pe a k o f a bou t 19 c m a t / z = 0 .05 , a nd

the n de c re a se s w i th fu r the r i nc re a se i n / z . Fo r t he P -F

a n d R - F B I s y s t e m s , a 5 0 % d e c r e a s e i n t h e ir p e a k

d i sp l a c e me n t r e sponse s a re obse rve d a s ~ va r i e s f rom

0 .03 to 0 .1 . The e f fe c t s o f va r ia t i ons i n f r i c ti on c oe f f i -

c i e n t s o f t he body a nd the upp e r f r i c t i on p l a t e s on the

p e a k b a s e d i s p la c e m e n t r e s p o n s e s f o r t h e S R - F

sys t e m s a re d i sp l a ye d in F ig . 10 (b ). Th i s f i gu re

show s tha t a s i nc re a se s , t he pe a k ba se d i sp l a c e -

m e n t o f th e S R - F 1 s y s t e m f i rs t d e c re a s e s , a n d r e m a i n s

a c o n s ta n t f o r ~ > 0 . 0 7 . S i m i l ar l y , f o r t h e S R - F 2

sys t e m the pe a k ba se d i sp l a c e me n t de c re a se s w i th a n

increase in

,

up to

,

= 0 .1 a nd re ma ins a c ons t a n t fo r

la rge 1 .

The se ns i t iv i t y o f pe a k de f l e c tion r e sponse s fo r

va r ious f r i ct i ona l ba se i so l a t i on sys t e ms a re a l so s tud ie d .

Tre nds o f va r i a ti ons o f pe a k de f l e c t ions w i th c ha nge s i n

f r i c t ion c oe f f i c i e n t a re qu i t e s im i l a r t o t hose o f t he pe a k

a c c e l e ra t ion r e sponse s . A dd i t i ona l de t a i l s ma y be found

in Ref . 39 .

B a se d on the r e su l t s p re se n te d in t h i s se c t ion , i t ma y

be c onc lude d tha t a n inc re a se i n t he va lue o f f r i c t i on

c oe f f i c i e n t ( o r

~ , )

ge ne ra l ly p roduc e s h ighe r pe a k

a c c e l e ra t ion a nd pe a k de f l e c t ion , a nd low e r pe a k

d i sp l a c e me n t r e sponse s . H ow e ve r , sma l l va r i a t i ons i n

(o r , ) l e a d on ly to s l igh t c ha nge s i n t he pe a k re sponse s

o f t he s t ruc tu re .

E f f ec t s o f v e l o c i t y - d e p e n d e n t f r i c t i o n m o d e l

I t i s w e l l know n tha t t he C ou lomb l a w o f f r i c t i on i s

on ly a n a pp rox im a t ion a nd the f r i c t ion c oe f f i c i e n t be -

tw e e n su r fa c e s va ry w i th ve loc i ty , no rma l fo rc e a nd

e tc 4. The r ecent d a ta of Ref . 41 sugg ests tha t the f r ic -

t ion coeff ic ient for te f lon-stee l in te rfaces increases wi th

the sl ip ( re la t ive s l id ing) ve loc i ty and decreases wi th the

in t e r fac e p re ssu re . In t h is se c t ion , t he e f fe c t s o f ve loc i ty -

de pe nde n c e o f f r i ct i on c oe f f i c i e n t on the pe r fo rma nc e o f

t he R - F B I , t he P - F , a nd at he E D F s y s t em s a r e

s tud ied . T he N 00W c om pone n t o f E1 C e n t ro 1940 e a r th -

qua ke i s u se d a s t he g round a c c e l e ra t ion . A f r i c t i on

mode l w i th l i ne a r ve loc i ty de pe nde nc e i s c ons ide re d .

That i s , i t i s i s assumed tha t the dynamic fr ic t ion coeff i -

c ient i s g iven as

= o + ~lz l (23)

in which o is the s ta t ic f r ic t ion coeff ic ien t , ~ i s the s l ip

ve loc i ty be tw e e n su r fa c e s i n c on ta c t , a nd ~ i s a

pa ra m e te r w h ic h i s t he r a te o f va r i a ti on o f /~ w i th t he

s l id ing ve loc i ty . E qua t ion (23 ) w i th a r a nge o f va lue s o f

be tw e e n 0 to 0 .5 s /m i s u se d fo r a na lyz ing the se n -

s i t i v i t y o f pe r fo rma nc e s o f f r i c t i ona l ba se i so l a t i on

sys t e ms to ve loc i ty -de pe nde nc e o f f r i c t i on c oe f f i c i e n t .

The va lue s o f f r i c t i on c oe f f i c i e n t a s l is t e d in Ta b le 1 are

use d fo r / z o in t he a na ly s i s .

F igu re 11 show s the pe a k a c c e l e ra t ion r e sponse s a t t he

top of s t ruc ture and the peak sl ip ve loc i ty versus ~. I t i s

obse rv e d tha t t he a c c e l e ra t ions a nd the s l id ing ve loc i t i e s

are not sensi t ive to the var ia t ions in ~. The except ion is

the pe a k s l i d ing ve loc i ty o f t he ED F sys t e m w h ic h

show s a 50% de c re a se a s ~ inc re a se s fo rm z e ro to

0 .5 s /m .

The va r i a t i on o f ma x imum ba se d i sp l a c e me n t w i th

a re show n in F ig . 12 . The pe a k s l i p d i sp l a c e me n t ,

( s -Y ) lma x , fo r t he E D F sys t e m i s a l so show n in th i s

f igu re . I t i s obse rve d tha t bo th the t o t a l ba se d i sp l a c e -

men t , s Im~x, and the s l ip d isplac eme nt o f the ED F

system are not sensi t ive to the var ia t ions in ~. The

r e s ul ts f o r t h e R - F B I a n d t h e P - F s y s t e m s s h o w

gra dua l r e duc t ion in t he pe a k ba se d i sp l a c e me n t

re sponse s a s ~ inc re a ses . Se ns i t i v it i e s o f pe a k de f l e c t ion

re sponse s o f f r i c t iona l ba se i so l a t i on sys t e ms to ve loc i ty

de pe nde nc e o f f r i c t i on c oe f f i c i e n t a re a l so s tud ie d . The

re su l ts (w h ic h a re no t s how n he re due to spa c e l im i ta t i on

bu t ma y be found in R e f . 39 ) show tha t t he va r i a t i ons o f

do not have a s ignif icant e ffec t on the peak def lec t ion

re sponse s .

1

v

Z

o

t i

.d

h i

r O

n

1 0 - [

Peak Accel l ro tion

. . . . . . Peak Sl id ing Veloc i ty

P-F

......... .Epr ~-re

i i I i i i

0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5

see/m)

F ig . 1 1. E f f e c t s o f v e lo c i t y - d e p e n d e n t f r i c t io n c o e f f i -

c i e n t o n p e a k a c c e l e r a t io n a n d p e a k s l i d i n g v e l o c it y

r e s p o n s e s

E

G

t~J

>

0

Z

Y

1 .8 sec ,

t h e a c c e le r a t io n r e s p o n s e sp e c t r u m f o r t h e S R - F s y s t em

c o i n c id e s w i th t h at f o r th e R - F B I s y s t e m an d t a k e s a n

a l m o s t c o n s t an t v a l u e o f a b o u t 0 . 2 5 g . T h e p e a k a c c e le r a -

t ions fo r t he ED F s ys t e m a re ide n t i c a l t o t hos e fo r t he

L R B s y s t e m f o r

To

> 1 .5 sec . In th is range the pea k

a c c e l e r a t i o n f o r t h e L R B / E D F a n d t h e N Z s y s t e m s

de c re a s e ra p id ly w i th a n inc re a s e in

To.

F i g u r e 1 4 s h o w s t h e p e a k b a s e d i s p l a c e m e n t s f o r

va r ious ba s e i s o l a t ion s ys t e ms ve r s us

To.

I t i s obs e rve d ,

fo r

To

< 1 .5 sec ,

the

pe a k ba s e d i s p l a c e me n t r e s pons e s

a re l e s s t han 10 c m fo r a l l ba s e i s o l a tion s ys t e m s c on -

s ide re d . A s

To

i nc re a s e s , t he pe a k ba s e d i s p l a c e me n t

f o r t he L R B / E D F s y s t e m i n c re a s e s s h a rp l y , a n d r e a c h e s

a m a x i m u m o f a b o u t 2 5 c m a t To = 2 .5 s e c . The pe a k

b a s e d i sp l ac e m e n ts f o r t h e R - F B I a n d th e S R - F

s ys t e ms c o inc ide fo r To > 2 s e c a nd inc re a s e on ly

s l ight ly wi th

To.

The va r i a t ions o f t he pe a k de f l e c t ions o f t he s t ruc tu re

w i th

To

fo r d i f fe re n t ba s e i s o l a t ion s ys t e ms a re s how n

in Fig . 15 . I t i s not iced tha t the peak def lec t ions for the

L R B , t h e N Z , a n d t h e R - F B I s y s t e m s a r e q u i te l ar g e

fo r

To

< 1 .5 s e c , w h i l e t ha t fo r t he ED F s ys t e m i s

a b o u t 0 . 5 t o 1 c m . T h e S R - F b a s e i so l a ti o n s y s te m i s

the on ly s ys t e m w h ic h a ppe a rs t o be in s e ns i t i ve to a

l a rge va r i a t ion in

To.

I t i s a l s o o b s e r v e d t h a t t h e S R - F

s ys t e m l e a ds to the low e s t s t ruc tu ra l de f l e c t ions fo r

To < 1 .5 s e c . Fo r To > 2 s e c , t he pe a k de f l e c t ion

r e sp o n s es fo r t h e R - F B I a n d t h e S R - F s y s te m s

be c ome ide n t i c a l a nd re ma in a pp rox ima te ly a c ons t a n t

' 0 . 3 0

E

0 . 2 5

Z

hl

m

0 . 2 0

b J

0

n 0 . 1 5

u 3

~ o ~ o

. . < . ' . : i .

- . .

J ~ o . . . .

Peformance Analysis of Aseismic Base Isolation System for a Multi-story Buildind

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