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Nonlinearearthquakeresponseanalysisandenergycalculationforseismicslitshearwallstructures

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丫匕1.

1 N 0 2 E A R I,

H QU A KE E N G IN E E R IN G A N I) E N G IN E E R IN G VI B R A TIO N D e c e m b e r 2 0 0 2

A rt ie le ID: 16 7 1

一

3 66 4 (2 0 0 2 )0 2一

02 2 7一

10

N o n lin ea r ea rth q u a k e r esP0 n se a n a lysis a n d en e r g y c a lc u la tio n

fo r S e ism ic slit sh e a r W a ll str u C tu r e s

Jia n g H u anj

u n 卞(蒋欢军)an d L u笼 lin 丰(吕西林)

Sta te Ke ,,

La b o ra to ry for D isa ste ,

,

R edu

。才io n in C iv il EI : g in e e rin g,

肠n心i Un i,

, ers i以 Sha n g ha i Z 0 0 0 9 2,

Ch in a

A b str a e t: B as e d 。n the e o n e ep t o f stru e tu ra l pa ssiv e e o n tro l, a n

ew 钾pe o f slit she ar w a ll,

w ith im p r o v e d 、e ism ie

Pe

rfo rma n c e w he n c o m pare d to an or d inary

so lid sh ea r w all,

W a s Pro Po sed by th eau thor s in 19 9 6

.

T he id e a h as b ee n v eri fi e d

by a se rie s o f Pse u d o 一sta tie an d dyn a m ie te sts.

ln this Paper a m ac r o nu m e ri ea l m od

e l is d eve lo Pe d fo r th e w a lle Ie m e nt an d th e

en er g y d iss iPatio n d e v ic e.

The n , n o n lin e ar ti毗 址 sto ry a n alysis 15 earr ied o u t fo r a 1 0

一sto ry slit she ar w a ll m o d el te ste d o n a

shak in g tab le.

Fu rt he

rmo r e

,

the se ism ie in Pu t e n erg y an d the in d iv id u al en e rg y d issiPa te d by the e o n 1Po n en ts

arec a le u la te d b y a

m e th o d ba sed o n N e w m a rk一

pa ssu m p tio n s fo r this she a r w all m o d e l

,

an d th e ad v an t嗯e s o f th is sh ear w a ll are fu rt her

d e m o n s tra te d by the e a le u la tio n re s u lts fr o m the v iewPo in t o f e n e rg y

.

Fin ally,

a c eo rd in g to th e se ism ie d a m a g e e rite rio n o n

theba sis o f Pla stie ac e u m u l乞Ltiv e e n erg y an d m a x im u m r es

pon se

、

the o Ptim a lana ly sis 15 c a rr ie d o u t to se le et de

sig n Pa ram e ter s fo r

th e e n e rg y d is siPa tio n d e v i仁e·

K eyw o r ds : she ar w al ] : e n e电y d iss ip a tio n ; tim e histo ry a n a ly、15 ; o p tim a la n a ly sis ; se ism ie d a m a g e er ite rio n

1 In tr o d u c tio n

R e in fo re e d e o n e re te sh e ar w al ls a re w ide ly u se d in

se is m ie re g io n s d u e to the ir hig h la tc r飞11 卜ril’

!h e ss a n d

stre n g th.

H o w ev e r, th ey als o te n d l、” 之一l【l认 c t la rg e

a m o u n ts o f seismie fo rc e s a n d e n e rg y

.

A e e o rd in g to

Pr e v io u s s e ism ie h a z ar d in ve stig a tio n s ,

the d am a g e ,

w hi eh 15 m o s tly e o n e e n tra te d a t th e b a se ,

15 g en e r ally

ve ry d iffi e u lt to r ePa ir. TOs o lve th e se Pro b le m s

,

in sPire d by the fi rs t inno v a tiv e id e a o f e a stin g v erti c al

s lits in to in fi lle d w all Pa n els in fr a m e d s tru e tu re s

Pro Po s ed by M u to in 19 6 9, a n e lle rgy dissiPa tio n sh e a r

w allw a s Pro Po s e d by th e a u th o r s (L u a n d W u ,

19 9 6 ).

T he n e w sh ear w all h a s a Pu rp o se ly b u ilt一

in v e rt ie a l

slit in w hi e h a ru bb e r b elt 15 fi lle d an d so m e h o ri z o n ta l

s te e lb a rs Pa ss th ro u g h o n so m e h e ig h t in e a e h sto ry.

A

s e rie s o f e x Pe r im e n tal a n d th e o re tie al s tu d ie s h a v e

b e e n e arr ie d o u t,

in d ie a tin g th a t the se ism ie

Pe r fo rma n e e o f th e slit w all15 im Pr o ve d

, c o m Pare d to

o rd in a ry so lid shear w alls (Lu a n d W ll ,

19 9 6 ; L u a n d

Jian g,

199 8 ; Jia n g a n d L u ,

19 99 ).

T h e fa ilu r e Pa tte rn s

o f th e sli t w al l a n d th e s o lid w al l, o b tain e d fr o m

te s tin g u n d e r la te ral eyelie lo a d s , a re difl7er e n t.

Fo r th e

so lid w all,

se v e re dama g e 15 e o n e e n tra ted o n the tw o

sid e s o f the b a s e ,

w ith e ru shin g o f the e o n e r ete a n d

b u c k lin g o f th e lo n g itu d in albar s.

A s

fara s th e slit w a ll

15 e o nc e r n e d,

th e d a m a ge fi r s t o e e u rs a t the tw o s ide s

C o rre s Po n de n ee to : L u X ilin,

R e se ar c h In stitu te o f Str u e tu r aT

E n g in e erin g a n d D isa ster R e d u e tio n ,

TOn幻1 U n iv e rsity

,

1 2 3 9 S IPin g RDa d

,

Sha n g ha i 2 0 O0 9 2,

Ch in a.

Te l: (0 2 1 )6 5 9 8 2 6 6 : Fa x : (0 2 1)6 5 9 8 2 6 6 8

E一

m ail二s t@ m a il沈o n自i

.

ed u ￡ n

十L e etu r e : 车P r o 化sso r

o f th e slit elo s e to the e n erg y d is siPa tio n d e vie e s ,

w hi e h Pr o te e ts th e m a in s

trUetu re a n d slo w s d o w n the

d a m ag e Pr o e e s s , 5 0 th e d a m a g e to th e b a s e o f th e w a ll

15 而ti g a te d.

In o th e r w o rd s,

there 15 a n a d d itio n allin e

o f d efe n se in th e slit w all u n d e r the e a rt hq u a k e lo a d s.

Fu rth e

rtno re

,

it 15 ea sy to u se the slit sh e a r w all in

e n g in e er in g Pr a c tic e.

It w a s ap Plie d s u e e e s sfu lly in

tw o ta ll b u ild in g s in Shan g h ai in 19 9 7.

Tos tu d y th is

slit sh e a r w all th o ro ugh ly

, n o n lin ear e叭hq u a k e

re sPo n s e a n alysis 15 e a rr i已d o u t in th is p aPer. F o r th e

s ak e o f e o n v e n ie n ee fo r Pra e tie a l aPPlie a tio n a n d

a e e u ra e y, a m a ero m o d el (V 自le a n o e t a l. ,

19 8 8 ),

th e

m u lti一V e rt ic al

一

lin e 一elem e n t m o d e l (MV L E M ) 15

a d oPte d.

In o r de r to e v alu at e the e n erg y d issiPa tio n e a Pa eity

o f this slit she a r w all,

th e to tal se ism ie in Pu t e n e rg y

a n d th e in d iv id u al e n e rg y d iss iPat e d by th e

e o m Po n e n ts ar e c ale u la te d,

A m e th o d b a se d o n th e

N ew m ark一

pa s s u m ptio n s i、 d e vo lo Pe d he re

.

Fu rth e r Olo r e , o Ptim al a n a lysis 15 e arr ied o u t to se le c t

d e sig n Para m e ters fo r the e n erg y d iss iPa tio n d e v ic e.

2 N U m e r ie a lm o d e l

In the sli t she a r w all th e w all Pa n e l 15 rePr e s e n te d

by M V L E M in w hi eh the in fi n ite ly r ig id b e am s at th e

to P a n d b o tto m areeonn

e ete d b y so m e v er tic al tru ss

e le m e n ts Par a lleled to e a e h o ther (se e Fig.

1).

T he

e n er g y dis s iPat io n d e vie e in sta lle d in th e slit 15

m o d ele d b y tw o n o ul in ea-r sPrin g s at the to P a n d

b o tto m, e o

nne e tin g w ith th e left an d r ig h t w all

elem e n ts.

In e a eh M V LE M th e tw o o u tsid e tru s s

elem e n ts rePre se n t th e a x ial an d b e n d in g stiffne ss o f

the b o u n d ar y e o lu m n s , a n d th e in te rn al e le m e n ts

口 .

2 2 8 E A R I H Q UA KE E N G IN E E R IN G A N D E N G IN E E R IN G V IB R 八1,

IO N 饰1 1

rePI’

e s e n t th e e e n tra l w a ll Pa n e ],

w h ile th e h o riz o n ta l

sPri一19 a t th e h e ig ht o f 尹h r ePre se n ts th e s he ar s tifti 飞e s s.

T h e re la tive 一o ta tio n o f th e w a 】1 m e m b e r 15 in te n d e d to

b e a ro u n d tlle Po in t A Pla e e d o 一1 th e e e n tr o id a x is,

A

s u lta b le v alu e fo r r 15 a s s u m e d o n th e b a s is o f th e

e x Pe e te d e u r v a ru re d is tr ib u tio n alo n g th e h e ig h t.

T h e

hys te r e tie ehar a e te l·

istie s o f th is 一n o d e l e a n b e

d e s e r ib e d by th o se o f th e sh e是lr sPrin g a n d a x ia l b a l几

T his m 〔)d el a e e o u n ts fo r th e fl u e tu a tio n o f th e n e u tra l

a x is o f th e e 一() 5 5 se e tio n w he n in ela s tie be h a v io r ta k e s

Pla e e 111 th e w a ll,

w h ile th is irn Po rta n t Ph e 一lo m e n o n 15

d 15一e g a l·

d e d in th e e q u iv a le n t b e a m m o de l u tiliz e d

w id ely in e n g in e e r i一19 Pr a e tie e.

In a d d itio ll , th e

in te la e tio n b e tw e e n th e be n d in g a n d sh e a r b eh a v io r,

a n d the e fl b e t o f a x ia l fo re e o n th e be n d in g b e ha vio r

e a n b e ta k e n in to a e e o tlllt i一1 th is m o d el,

B y m e a n s 0 1一

the Prin c iPle o t’ v ir tu a l w o r k the

s tifn le s s m a trlx o f the w a ll ele 一n e llt e a n be

d e riv e d a s

门les|||、esl|||||||

,�、一

气几

一 k l,

O

O k z,

h(] 一 )

k * ,

"

艺l)J=l

“, 犷 2“2 +

乏天、, ,

‘” 2

一 k , rh

k h

k、叨

O

”

(‘一 厂) rll Z“/ ,一

艺“、, 月

”

乏洞

一 k , ,

/, ( l一 r )民S ym m e tr y

( , 一 : ) 2 h Z k , ,+

艺k

, , ,

w he l·

e k z,

15 th e s he a r l·

i g id i ty o f th e h o r i z o n ta l s pr illg,

k, , ,

th e a x i a ] r ig id ity o f the n , th v e r一ie a l t一u s s e le m e n t,

h th e h e ig h t o f tlle w a ll e le m e n t,

l, , ,

th e h o r iz o n za l

山5 ta n e e be tw e e n th e l, , th v e rtie a l tru s s e ! e m e n t a n d the

e e n t ro ld a x is,

a n d z, th e to ta l n u 一刀 b e r o f the v e rt ie a l

‘,‘

L,

泛S e ,呀m

e n ‘·

冲e “‘Sp ,aC e n l e ,1‘」rn a‘, ‘x万

orre s p O

t( ) [ 11 C 是ID o v e s[ I ll ll e s s m u t l飞 x 15 洲 i , 仁, , 口 , u , , F

w h e r e u , , 、, , ,

O,

15 th e h o r iz o n ta l d i s p la e e m e n l,

v e rt ie a l d i sPla e e rn e n t, a n d ro ra t io n a r th e i th 一lo d e o n

the e e n tr o记 a x is,

r e sPe e tiv e ly,

th e r ig h t thr e e t e rm s ar e

the d i sPla e e m e n ts o f th e jth n o d e.

I n Pa s t ap Plie a tio n

o f th is 一1: o d e l,

th e Pa r a m e te r r d e fi n in g the Po si ti o n o !、

the re la t iv e ro ta ti n g e e n te r 15 a m b ig u o u s.

TOa e e o u n t

Ib r th e Ih e ts th a t 一h e r e a r e h a r d ly a一ly Po i一l ts o f

e o lltra fl e x u re in rh e sa n l e sto ry b e e a u se th e b e n d in g

1llo rn e n t e h a n g e s s lo w ly a lo n g th e h e i g h t o f s h e ar w a ll,

i飞e an b e d e ri v e d th a t r e q u a ls 0 5 o n th e b a s i s o f th e

:一ss u m Prio n o ,一

e v e n e u l·v a tu r e d i stri b u ti o n (Jia n g a n d

L u,

199 8 ).

T lle e rr o r e a n b e d e e re a s e d by i一le r e a si n g o f

th e n u l刀b e l o f w a 」1 e le m e n ts i n th e e a !e u la ti o n.

5 im ila r ly,

111 the lig h t o f th e Pr i n e iPle o f v irtu a l w o rk.

th e s t if’t’ne s s m a t r i x o f th e e n e rg y d i s s iPa ti o n d e v ic e 15

d e 一iv e d a s fo l! o w s

(2 )

OJ布,Jnz山O1,,..

w h e re k‘, 15 the

d is s iPa tio 一1 d e v i e e,

s e e t io n o f th e w a ll

S hC a l’

:一n d l

e le m e n t

r ig id ity o f

少e

’

1ll e

le n g th

th e

o f thC

d isPI

sti flh

往C e m e fl t

e l飞e rg y

C f 0 SS

n la tf lX

clo r l’

e印 O n d i n g ,

分; ,

日, ‘, 产,

日,

士

to th e a b o v e C S S m a ty lX 15

3 C o n st itu ti v e m (一d e ls

3.

1 Sh e a r fo r e e一s h e a r d e fo r m a t io n hyst e r e t ie

m o d e l

I n Pa st aPPlie a ti o n o f M V L E M,

the i rlt e l·

a e tio n

b e tw e e n s h e al* a n d fl e x u r e w a s n e g le e t e d,

a n d th e

b e n d i n g d e fo rm a tio 一1 a n d sh e a r d e fb rm a tio 一1 w e r e

e a le u la te d s e Pa r a t e ly.

I n o rd e r to o v e rc o m e th is

sh o rte o m i n g,

th e w 之111Pa一le l 15 s im Plifi e d a s a m e n 飞b ra n e

N o Z Jl: 111 9 H u a :lj

L . n e t “l一 N o : 1 11【le a : e a r th q u a k e re 印o n se a n alysis fo r se i、m ie s lit she ar w allst r u etu r e s 2 2 9

ele m e n t in th e e a le u la tio n o f sh e a r de fo rm a tio n,

th en

th e e q u a tio n s a re e sta b lish e d a e e o r din g to th e

e q u ilib r iu m e o n d itio n s o f fo re e s , e o m Pa tib ility o f

de fo rllla tio n,

a n d th e e o n s titu tiv e Iaw s fo r e o n e re te

u n d e r Pla n e stre s s e o n d itio n s.

B y e q u a tin g th e v e rtie a l

s tra in o f m e m br a n e ele m e n t w ith th a t o f the v e r tie a l

tr u ss e le m e n t lo e a te d a t the e e n tro id o f the w all

ele xn e n t,

th e e o m Pa tib ility o f d efo rm a tio n b e tw e e n

th e se tw o ele m e n ts a re ta ke n in to a e c o u n t.

T h e she a r

fo re e v e rs u s sh e a r d efo r m a tlo n s ke le to n e u rv e 15

o bta in e d by ite ra tio n Pro e e d u re.

T he d e ta ile d m e th o d

e a n be fo u n d e lsew h e r e (Jia n g a n d L u ,

19 9 8).

T he re

a re tw o c har a e te ris tic Po in ts : e ra e k in g Po in t a n d

yie ld in g Po in t.

T he e ra ek in g Po in t c o r re sPo n d s to th e

sta te tha t the m a x i一n u m Prin e iPa l te n s ile s tre s s r e a eh e s

the e ra e ki n g stre ss o f e o n e re te.

T h e yie ld in g Po in t

e o rr e sPo n d s to th e s ta te th a t th e h o r iz o n tal she a r

re in fo re e m e n t yie ld s if she a r fa ilu re h aPPe n s Prio r to

fl e x u ra l fa ilu re , o th e rw ise,

to th e s ta te th a t th e ve rt ie a l

fl e x u ra l r e in fo re e m e n t a t th e c e n tro id o f th e v e rtic a !

te n sile re in fo rc e m e n t yie ld s.

Tos im Plify th e

e ale u la tio n ,

the s ke le to n e u r v e 15 ide a liz e d in trilin e a r

fo r m, a n d the Po s t

一

yield in g s tiffne ss 15 ta ke n a s o n e

Pe re e n t o f th e e la s tie s tiffne ss

.

T h e sh e a r hys te r e tie

m o d el a d o Pted 15 a s sho w n in F ig Z (G u n ey a n d M u ra t,

198 9 ).

A de ta iled de s e riPtio n o f th is m o d e l e a n b e

fo u n d else w he re (Jia n g a n d Lu ,

19 9 9 ).

T h e m a in law s

a re s u m m a riz e d a s fo llo w s :

3.

2 H ys te re tic m o d e lfo r a x ia l b a rs

D u e to th e in s u ffi c ie n ey o f e x Pe r im e n ta l d a ta fo r

a x ia l b a rs u n d e r e ye lie lo ad s ,

th e e ale u la tin g m o d el

b a se d o n th e m a te rial e o n s titu tiv e law s 15 a d o Pte d h e re,

w hieh ta k e s th e a e tio n o f e o n e re te a n d re in fo r e e m e n t

in to a e e o u n t re sPe e tiv e ly.

T h e in te ra e tio n effe

e ts

b e tw e e n th e c ra e ke d e o n ere te a n d th e ste e l

r e in fo re e m e n t a r e e o n s id e red in te rm s o f a v e ra g e

S tfa lfl.

3.

2.

1 Th e stre ss 一stra in e urv e

tbre o n ere te u n d e r e ye lie

10 a d s

T h e str e s s 一s tr a in e u rv e 15 sh o w n in Fig.

3 (W u a n d

L u ,

19 9 6 ).

T h e te n s ile s tiffen in g 15 a e e o u n te d fo r in

this m o d el,

th e b o n d a n d sliP b e tw e e n e o n c re te a n d

re in fo rc e m e n t 15 refl e e te d in te rm s o f a v e r a g e s tre s s

a n d a v e ra g e s tra in.

For th e e o n ere te in th e b o u n da ry

e o lu m n s ,

th e str e ss 一s tra in e u rv e fo r e o n fi n e d e o n e r e te

(S c o tt e r a l.

,

19 8 2 ) 15 a d o Pte d he re , a n d its hys te re tie

la w s are a s s u m e d to b e th e s am e a s fo r u n c o 月fi n e d

C o ll CfC te.

F一9.

3 T he str es s一 stra in e u l、e fo r eo llc re te u n d e r ey e lie lo a d s

F 19.

2 S he ar tb r ee 一 she a r d e fo 一m

a t一o n hyster e tie m o d e l

(l) T h e e u rv e u n lo a d s alo n g th e b a ek b o n e e u rv e if

e 一a e k in g h a s n o t h aPPe n e d in bo th o f th e tw o

d ire e tio n s.

It u n lo a d s in the d ir e e tio n to th e a d ve r se

e r a e k i一飞9 Po in t if the e ra e k in g lo a d 15 e x e e e d e d w h ile

th e yie ld in g lo a d ha s n o t be e n s u rPa s s e d.

If th e

yieldin g lo a d 15 e x e e e d ed,

the u n lo a d in g se g m e n t 15

d iv id e d in to tw o Pa rts,

w h e re the c r a e k in g lo a d 15 th e

de m a re a tio n

(2 )T he re lo a d in g s e g m e n t 15 d iv id e d in to tw o Pa rts

to re fl e e t the Pin eh Phe n o xn e n o n aft e r the yield in g lo a d

15 e x e e e d e d,

w he re th e e r a e k in g lo a d 15 also th e

d e m a re a tio n.

T h e s tiffne s s o f th e fi rs t Pa rt 15 sm a lle r ,

w h e re the e ffe e t o f th e a x ia l lo a d 15 ta k e n in to a e e o u n t.

3.

2 2 T he s tre ss 一stra in e u rv e s fo r re ill lb rc em e n t u n de r

c ye lie lo a d s

A b ili n e a r a v e ra g e stre ss 一s tra in m o d e l (se e Fig 4 )

15 u se d h e re ,

w he re th e s tiffen in g e

ffec t d u e to e o xle re te

a n d th e yield in g h a rde n in g a re e o n s id e r e d.

3.

3 H yste r e tie m o d e lfo r e n e r g y d is siPa tio n d e v ic e

T h e c h a r a c te ris tic Po in ts in th e sk ele to 一1 c L一v e e a l-

b e o b ta in e d o n th e b a s is o f th e th e o ry fo r Pile s

e m b ed d e d in e o h e s iv e 5 0 11 a n d th e sh e a r一fr ie tio n

th e o ry.

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(Lu a n d Jia n g,

19 9 8 ).

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th e sk ele to n e u r v e 15 s im Plifi e d in tr ilin e a r fo 一m.

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th e

hys te re tie m o d el 15 e s ta b lis he d by m e a n s o f re g re ss io n

(se e Fig s ).

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L u,

19 9 9 ): th e u n lo a d in g stiffne s s d e g r a d e s a e e o rd in g

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(t) 15

th e e fl e rg y d is siPa te d b y tlle w a ll e le n le n ts.

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a e e c le ra tio n ; N 15 一he to ta l n u 一n b e r o f th e P之trtie le s.

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ha s b e e n w ide ly l℃ e o g 王ziz e d.

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hys te re tie e n erg y sh o u ld b e ta k e n

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s tr u e tu re w ith th e h e ig h口w idth ra tio o f 5.

6 w a s te s te d.

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T h e o v e ra ll d im e n s io n s a n d d e ta ils o f in te r一s to ry

re in fo re e ln e n ts a re sh o w n in Fig.

6.

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m ild ste el w ire s w e re u s e d in the e o n str u e tlo n o f th e

m o d e l.

T h e m o d e lw a s e a st v e rtie a lly s to ry by sto ry

T h e d e s ig n a n d e o n s tru e tio n o f the m o d e l m e t th e

re q u ire m e n ts o f sim ilitu de th e o ry.

T h e a e e ele ra tio n

re e o rd o f E I C e n tro N一

S (194 0 ) w a s u se d a s th e in Pu t

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