hett 97 software analysing thermal stresses

7/25/2019 HETT 97 Software analysing thermal stresses

1/7

M a t e r i a ls a n d S t r u c t u r e s / M a t 6 r i au x e t C o n s t r u c t i o n s

Vol. 30 Apri l 1997 pp 167-173

im u l a ti o n o f t h e r m a l s tr es s in r e i n f o r c e d c o n c r e t e a t

e a r ly a g e s w i th a s im p l if ie d m o d e l

A g n e s N a g y

Departmen t of Structural Engine ering, Lu nd Institute of Technology, Sweden

A B S T R A C T R I~ S U M I5:

T h i s p a p e r is p r i m a r i l y c o n c e r n e d w i t h s tr es se s a n d

c r a c k i n g i n r e i n f o r c e d c o n c r e t e c a u s e d b y r e s t r a i n e d

t h e r m a l d e f o r m a t i o n s d u r i n g t h e h y d r a t i o n p r o c e s s .

S i m u l a t i o n o f t h e r m a l s tr es se s a n d c r a c k o c c u r r e n c e i s

c a r r ie d o u t w i t h a s im p l i f i e d m o d e l . B y v a l id a t i o n

a g a i n s t t e s t s , i t i s s h o w n t h a t t h e s i m p l e , o n e - d i m e n -

s i o n a l m o d e l g iv e s a re a s o n a b l e e s t i m a t e o f t h e t h e r m a l

s t r e s s d e v e l o p m e n t . T h e m o d e l i s b a s e d o n a f e w i n p u t

p a r a m e t e r s l i k e t e m p e r a t u r e h i s t o r y , s t i f f n e s s d e v e l o p -

m e n t a n d t e n s il e s t r e n g th d e v e l o p m e n t . B y m e a n s o f a

p a r a m e t r i c i n v e s t i g a t i o n , t h e a g e - d e p e n d e n t s t i f f n e s s o f

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

as th e d ec i s iv e mate r ia l ch a r ac te r i s t i c s r eg ar d in g th e th e r -

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

h a s n o e f f ec t p r i o r t o c r a c k i n g b u t a c l e a r c r a c k r e d i s t ri b -

u t in g r o le in th e p o s t - c r ack in g s ta te .

C et a r t ic l e d iscu t e d es co n tra in te s e t d e l a f i s su ra t io n d u

b ~ to n a r m ~ d u e s a u x d ~ fo r m a ti o ns t h e r m i q u e s a u c o u r s d e

l ' h y d r a t a ti o n . U n e s i m u l a t i o n d e s c o n tr a in t es t h e r m i q u e s

e t d u d ~ v e lo p p em en t d es f i s su res a ~ t~ e f fec tu ~ e a u m o yen

d ' u n m o d u l e s i m p l ~ ' L A p r ~ s v a l i d a t i o n p a r d e s e s s a i s , c e

m o d u l e s i m p l e e t u n i d i m e n s i o n n e l f o u r n i t u n e e s t i m a t i o n

r a is o n na b le d u d e l o p p e m e n t d e l a c o n t r a in t e t h e r m i q u e .

C e m o d u le e s t b a s~ su r u n h o m b re l im i t~ d e p a ra m ~ t res,

d o n t l' h is to riq u e d es t em p a tu res e t l e d e lo p p em en t d e l a

r ig id i t~ e t de la r i s tance h la t raction . U ne invest iga t ion

p a ra m ~ t r iq u e a m o n t r~ q u e la r ig id it~ en fo n c t io n d e l' d g e

d u b o n e t l 'h i s to r iq u e d e tem p a tu res so n t l e s ca ra c t i s -

t iq u es q u i d e rm in en t l e n i vea u d e co n t ra in t e t h erm iq u e .

I I a ~ q a lem en t ~ t~ m o n t r~ q u e l e r en fo rcem en t n ' a a u cu n

e ff et a v a n t la f i s s u r a t i o n , m a i s q u ' i l j o u e u n r 6 l e i d e n t

d a n s l a n o u ve l l e r~ p a r ti ti o n d es i s su res a p r~ s i s su ra t io n .

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

T h e o c c u r r e n c e o f c ra c ks i n y o u n g c o n c r e t e d u r i n g

h y d r a t i o n d e p e n d s m a i n l y o n t w o g r o u p s o f fa c to rs : t h e

m a t e r i a l c h a r a c t e r i st i c s o f t h e y o u n g c o n c r e t e , a n d t h e

r e s tr a i nt c o n d i t i o n s o f th e c o n c r e t e s t r u c t u r e . M o d e l l i n g

th e r mal c r ack in g a t ea r ly ag es i s a co mp lex p r o b lem s in ce

t h e m e c h a n i c a l p r o p e r t i e s o f t h e c o n c r e t e , l i k e s t if fn e ss

an d s t r en g th , an d th e th e r mal p r o p er t ie s , l ik e th e co ef f i -

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

h y d r a t io n p r o cess . A lso , th e r es t r a in t co n d i t io n s f o r a r ea l

s t r u c t u r e a r e d i f f i c u l t t o e s t i m a t e b e c a u s e o f tl ~ e w i d e

r an g e o f p o ssib il it ie s b e tw een th e f u l ly - r es t r a in ed an d th e

f r ee cases . Sev er a l so p h is t i ca ted an a ly s i s p r o g r ams ex is t ,

w h ich tak e acc o u n t o f th ese fac to r s an d m ak e i t p o ssib le to

s i m u l a t e t h e e v o l u t i o n o f t h e r m a l l y - i n d u c e d s tr es s, e . g.

E m b o r g [ 1 ], D a h l b l o m [ 2 ], H a u g a a r d

et al.

[ 3 ] , Ro e l f s t r a

et

al.

[ 4 ] . C o m p l e x e l e m e n t s i n s u c h m o d e l s , s u c h a s a g e -

d e p e n d e n t c r e e p m o d e l l i n g , m a y i n t h e a b se n c e o f c o m -

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

er rors in the analys is resu lts. Fo r th is reason , i t is desirab le

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

w h i c h a r e m o s t d ec is iv e f o r t h e d e v e l o p m e n t o f t h e r m a l

s t r es s an d w h ich a r e mo r e eas i ly o b ta in ab le in a p r ac t ica l

s i tu a t io n . A n ex am p le o f a p rac tica l ap p r o a ch w i th a s im-

p l e m a t e r i a l d e sc r i p t io n c a n b e f o u n d i n J C I [ 5] .

I n t h i s p a p e r , a s i m p l i f i e d c o n s t i t u t iv e m o d e l i s u s e d

t o p r e d i c t t h e r m a l s t r e s s e s i n y o u n g c o n c r e t e . T h e i n p u t

m a t e r i a l p a r a m e t e r s r e q u i r e d b y t h e m o d e l a r e k e p t t o a

m i n i m u m . T h e v a li d it y o f th e m o d e l i s t es t ed a g a i ns t

e x p e r i m e n t a l d a t a a va il ab le i n t h e l i t e r a t u r e . A p a r a m e t -

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

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

m eu t o f th e r m al s t r es ses a t an ea r ly age .

2 . C O N S T I T U T I V E E Q U A T I O N S

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

s t r e s s a n d r e s t r a i n t c o n d i t i o n s . C o n c r e t e a n d r e i n f o r c e -

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

b e t w e e n t h e m i s si m u l a t e d b y m e a n s o f s h e a r f o rc e s a c t-

i n g a t t h e i n t e r f a c e la y e r o f t h e t w o m a t e r ia l s . T h e i n c r e -

m en t a l s t r e s s - s t ra in r e la t io n s a r e g iv en b y :

0025-5432/97 9 RILEM 1 6 7


2/7

M a t e r i a ls a n d S tr u c t u r e s / M a t 6 r ia u x e t C o n s t r u c t io n s

V o l . 3 0 A p r il 1 9 9 7

AGc = Ec(t)[Aec - o%AT]

Ac;~ = Es[A S - o~ AT ] (1) [~.~

w he re k(s and k~ are s t ress and s t rain incr em ents ( indexes o_.

c and s for con crete and s teel , respectively), E the m aterial ~

s t iffness, 0~ the coe fficien t of therm al ex pansio n an d A T is

t he t e m pe r a t u r e i nc r e m e n t . T h e e la st ic m o du l us o f t he 0.4

conc re te E C s as sumed to be age-dep enden t . J~ f f = ]" ( t. * 5h , g ' )

(:

T h e b e h a v i o u r o f t h e i n t e r fa c e b e t w e e n s te e l a n d ~ J t f f ' 1

c onc r e t e i s de s c r i be d by t he l i nea r i nc r e m e n t a l r e la t ion : ~ I [ e f t = - - = E ( t )

AS = k(t )[Auc - Aus] (2) " I Je ff

w h e r e A S is th e b o n d f o r c e i n c r e m e n t ( M N / m ) a t t h e

in te r face , Au~ and Au~ inc re m enta l d i sp lacements in con - ~ I

crete and s teel , respect ively, and k(t ) the age dependent

bond s t i f fnes s . The cons t i tu t ive re l a t ions (1) and (2) , in

c o m b i n a t i o n w i t h s t a n d a r d k i n e m a t i c a n d e q u i l i b r i u m DO t t 10 t.O Age_ ~ o y s )

r e l a t i ons , de s c r i be t he c om bi ne d un i a x i a l be ha v i ou r o f

t h e r e i n f o r c e d c o n c r e t e . T h e s e r e l a t io n s w e r e t r a n s - 5 h 0 ur 5

f o r m e d i n t o f i n i t e e l e m e n t F E M ) r e l a t i o n s a c c o r d i n g t o F ig . 1 - C r e e p i n y o u n g c o n cr e te . E s t im a t i o n o f t h e e f fe t ive

s t a nda r d p r oc e du r e s [ 6 ] a nd i m p l e m e n t e d a s a dd i t i ona l m a t e r i a l s t i f f n e s s N e f .

s u b r o u ti n e s in t o a n F E M p r o g r a m c a l le d C A M F E M [ 7] .

e(t, t ') =J (t, t ').r~(t ') (5)

3 PROPERTIES OF THE C ONC RETE AT w h e r e J ( t, t ' ) i s t he c om pl i a nc e f unc t i on . B y d e f i n i ng a n

E A RL Y A G E S effective co m plian ce as:

A g e i ng o f t he c onc r e t e i s de s c r i be d by t he c onc e p t o f J e f f = J ( ( + 5h , t ') ( 6)

e qu i va l e n t m a t u r i t y t i m e te , de f i ne d by : a nd t a k i n g E c f = 1 /J ~f f, a c e r t a i n a m ou n t o f c r e e p i s

t i n c l u d e d i m p l i c i t ly i n t h e e f f e c ti v e m o d u l u s N e f f s e e

t r = I ~ t d t (3) F ig .1 . As the c reep deform at ions decrease for inc reas ing

0 a g e a t l o a d i n g , t h e r e d u c t i o n o f t h e E c ff v a l u e a l so

w h e r e ~ t i s a m a t u r i t y f un c t i on d e s c r i be d by t he w e l l - de cr ea se s w i t h a ge. In t h is w a y , a c ons i s te n t de f i n i t i on o f

kn ow n Arrh enius expres s ion: the E-m od ulu s for a ll ages i s obta ine d .

U h ( 1 1_ / T h e r e f e r e nc e t i m e t rc f= 5 hou r s i s c hos e n s o t ha t t he

[ ~ t e x P R - [ 2 9 3 ' 1 ') ( 4) c r e e p de f o r m a t i ons ha ve m os t l y t a ke n p l a c e a t ve r y e a r ly

a ges w he n c r e e p is at m a x i m um . T he c ho i c e o f r e f e r enc e

w he re T i s the t emp era ture in Ke lv in , U h the ac t iva t ing t ime as 5 hours i s a rb i t ra ry , bu t i t i s ev ide nt f rom F ig .2

ene rgy o f hy dra t io n in J / tool , and 1L the un iversa l gas tha t the resul ts a re no t s ensi tive to th i s choice . Th e s i re -

con s tant 8 .314 J /mol .K . u a t ions in the f igure a re m ade for a fu l ly- res t ra ined p la in

T h e E - m o d u l u s a s a n a g e - d e p e n d e n t p a r a m e t e r is c o n c r e t e p r i s m w i t h t h e c o n c r e t e m i x t u r e $ 2 7 9 p r e -

e va l ua t e d f r om c r e e p t e s ts pe r f o r m e d by E m bo r g [ 1 ]. s e n t e d i n S e c t i on 4 . T h e re su lt s s how tha t f o r t he t o ta l ly

T he to ta l t im e-d ep end en t s tra in e ( t, t ') at t ime t due to a e l as t ic ch oic e o f E~ff ( tr r f = 0) , the com press ive s t res s

loadin g a t t ime t ' _< t i s de f in ed as: beco m es som ew hat h igh er bu t the t ens i le s tresses coin -

c i de w i t h t hos e f o r t r e = 5 hours .

C onc r e t e a t a ve r y e a r l y a ge i s c ha r a c -

3 5~re~s Mea) teris ed by plastic be ha vio ur, see Kasai

e t a l

~~ ~ ~ 7 i [8], a nd this effect is in c lu de d in the c o m p li-

. . . . . . . . / ance as n o u nlo ad in g takes place at th is stage.

t . . . . . . . . . . . . . . A t th e t im e w h e n a c tu a l u n l o a d i n g tak es

. . . . place in practical s t ructures, the appro xim a-

t ~ef: 5h . t ref "0 t ion of elas tic beh avio ur is reasonable.

T h e t e n s i l e s t r e n g t h i n t h i s m o d e l i s

. . . . r el at ed to t he c om p re ss iv e s tr en g th o f c y li n -

0 % , j .~ /~. . , / . - ~.5 LO 2 5 -@ (d@)~ ders by the CE B form ula:

/ f~t = 0"3(fcyl) /3 (7)

-1 Al te r na t ive ly , the t ens i l e s t reng th as a

f unc t i on o f age c a n be m e a s u r e d d i r e c t ly by

F i g . 2 - S i m u l a t i o n s r e g a r d i n g

the ho i e

o f r e f er e n c e t i m e . t h e s p l i t t i n g t e s t .

1 6 8


3/7

N a g y

S i n c e t h e c a l c u l a ti o n m o d e l i s i m p l e m e n t e d i n a n F E M

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

e l e m e n t s w h e r e c r a c k i n g o c c u r s . T h i s r e d u c t i o n is

d e s c r i b e d w i t h t h e p o s t - c r a c k i n g b e h a v i o u r b y m e a n s o f

f r ac tu re m ech an ics co n ce p ts l ik e ten s io n so f ten in g s t i ffn ess

an d ch aracte ri st ic l en g th . Ac co rd in g to H i l le rb o rg

e t a l .

[9]:

E T - E t ) 8 )

8 ) 1 21r

L

w h e r e E T is t h e t e n s i o n s o f t e n i n g s t if fn e ss o f t h e c r a c k e d

e l e m e n t , E ( t ) t h e s ti ff ne ss o f t h e u n c r a c k e d c o n c r e t e , l ch

t h e a g e d e p e n d e n t c h a r a c t e ri s t ic l e n g t h o f t h e c o n c r e t e ,

a n d L t h e l e n g t h o f th e f i n i te e l e m e n t . T h e l e n g t h o f t h e

f i n i t e e l e m e n t s i n t h e c a l c u l a t i o n s i s c h o s e n t o b e l e s s

t h a n t w i c e t h e c h a r a c t e r i s t i c l e n g t h ; h e n c e , t h e v a l u e o f

th e s t if fn ess o f a c r ack ed e lem en t w i l l alway s b e a n eg a-

t iv e n u m b e r . T h u s , t h e m o d e l is b a s e d o n a b il i n e a r

c h a r a c t e r i s t i c c u r v e d e s c r i b e d b y t h e a g e - d e p e n d e n t

e f f e c t i v e m o d u l u s E ( t ) u p t o t h e p o i n t w h e r e t h e t e n s i l e

s t r e n g t h h a s b e e n r e a c h e d i n a n e l e m e n t a n d a c r a c k

ar ises , an d b y th e te n s io n so f te n in g s t if fn ess E r d u r in g

th e p o s t - c r ack in g s ta te .

T h e c o e f f i c ie n t o f t h e r m a l e x p a n s i o n f o r c o n c r e t e

w a s a s s u m e d t o b e i n d e p e n d e n t o f a g e b u t w i t h d i f fe r e n t

value s 0~ce an d x c c d u r i n g e x p a n s i o n ( A T > 0 ) a n d c o n -

t r a c t i o n ( A T < 0 ) , r e s p e c t i v e l y . I m p o r t a n t c o n t r i b u t i o n s

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

L6 fq u is t [ 10 ] , By fo r s [11 ] , Em b o rg [1 ].

T h e i n t e r a c t i o n b e t w e e n c o n c r e t e a n d r e i n f o r c e m e n t

i s d e s c r i b e d w i t h t h e b o n d - s l i p t h e o r y , w h e r e s l i p i s

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

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

t h r o u g h t h e b o n d s ti ff ne s s k w h i c h i s g i v e n b y :

k = K 4 a S (9)

d

wh ere k i s th e b o n d s t if fn ess in M N /m 2 , K a mate r ia l p a r a -

m ete r d e p en d in g o n th e a n ch o rag e ch arac te r is tics an d th e

d i a m e t e r o f t h e r e i n f o r c e m e n t i n M N / m 3 , A s t h e a re a o f

r e i n f o r c e m e n t ba rs , a n d d t h e d i a m e t e r o f t h e r e i n f o r c e -

m en t b ars . Th e b o n d s t if fn ess k i s an ag e-d ep e n d e n t p ara -

m ete r an d in th e ab sen ce o f re l iab le e x p er im en ta l d a ta, th i s

3 o o o o - r { i t M P Q ) 7 I I I r I

I I I

I~ 0.5 19 .5 Z [~ ~.g 3.~ 3.5 ~ 0 4.5 5.0 5.5 611

F i g . 3 - E f f e c t i v e s t i f f n e s s e v l u t e d f r o m c r e ep t e s t s p e r f o r m e d t 2 0 ~

i s t a k e n i n t o a c c o u n t b y c o n n e c t i n g t h e p a r a m e t e r k to t h e

E - m o d u l u s d e v e l o p m e n t a s f ol lo w s :

k

k ( t ) = E ( t ) - - (1 0)

E 2 8

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

c r e t e , k t h e v a l u e o f b o n d s ti ff ne ss a c c o r d i n g t o e q u a t i o n

(9 ), E28 th e s t if fn ess o f a 2 8 -d ay o ld co n cre te . Fo r fu r th er

d e t a il s o n t h e s i m p l i f i e d m o d e l , s ee N a g y a n d

Th elan d er s so n [1 2 , 1 3 ] .

4 C A L I B R A T IO N O F T HE M O D E L

M o s t o f t h e t e s ts f o u n d i n t h e l i t e ra t u r e r e g a r d in g t h e

co n c re te s t r es s s ta te d u e to r es t r a in ed temp e ra tu re d e fo r -

m a t i o n s a r e p e r f o r m e d o n p l a in c o n c r e t e . F o r t h is r e a s o n ,

th e p r esen t m o d e l i s v a l id a ted aga ins t su ch tes t r esu l ts . T h e

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

smal l am o u n t o f r e in fo rc em en t an d b y se t t in g th e s t if fn ess

o f th e in te r f ace lay er v ery lo w . T h e r esu l ts o f th e s im u la -

t io n s were v a l id a ted ag a ins t ex p e r ime n ta l d a ta o b ta in ed b y

Em b o rg [1 , 1 4 ] . T w o ty p es o f co n cre te a re an a ly sed, o n e

b a s e d o n O P C f r o m S l i t e ( 2 7 9 ) a n d t h e o t h e r b a s e d o n

O P C f r o m D e g e r h a m n (A 3 00 ). T h e 2 7 9 a n d A 3 0 0 t yp e s

c o r r e sp o n d t o c o n c r e t e w i t h n o r m a l a n d s l o w h a r d e n i n g

rates, respectively. Ch aracter is t ics of the t w o con crete typ es

are p r esen ted in Tab le 1 .

T a b l e 1 C o n c r e t e c h a r a c t e r i s t ic s

C o n c r e t e C oe f f i c ie n t o f t he r m a l 2 8 - da y s f c c t re s t ra i n

c e m e n t W / C e x p a n s i o n [ 1 0 6 / ~ E - m o d u l u s

con t. C~ce ~cc

[ k g / m 3 ] [ GP a ] [ M P a ] [ da y s ]

2 7 9 0 . 6 1 9 . 5 7 . 5 3 6 . 0 4 6 . 2 0 . 2 3

A 3 0 0 0 . 5 4 1 1 .5 7 . 5 3 5 . 2 5 6 . 7 0 . 3 5

279 - Ordinary Por t land Cement t ype I (S l i t e , Sweden)

A 3 0 0 - O r d i n a r y P o rt la n d C em en t t yp e I I (D eg erh a m n , S w ed en )

D i r e c t l y a f t e r p o u r i n g ( t = 0 i s d e f i n e d a s t h e p o u r -

i n g t i m e ) , t h e e n d s o f t h e s p e c i m e n a re f r e e u n t i l t i m e

t

t r e s t r a i n t

w h e n t h e s p e c i m e n is f u l ly r e s t r a i n e d

( i n t h e t e s t s , r e s t r a i n t c o u l d n o t b e a p p l i e d

b e f o r e t h e c o n c r e t e h a d d e v e l o p e d a c e r t a i n

a m o u n t o f s tr e n g th ) . T h e e v a l u a t e d m a t e r i a l

s t if fn ess as a fu n c t io n o f eq u iv a le n t ag e is sh o w n

i n F i g. 3 . T h e t e m p e r a t u r e h i s t o r i e s f o r t h e t w o

t y pe s o f c o n c r e te w e r e r e c o r d e d b y E m b o r g [1 ,

1 4] d u r i n g r e l a x a t i o n t e st s p e r f o r m e d o n c y l i n -

d r ic a l s p e c i m e n s st o r e d u n d e r w a t e r . T h e s p e c i -

m e n s w e r e h e a t e d b y t h e s u r r o u n d i n g w a t e r i n

t h e t a n k t o g i v e a h y d r a t i o n c u r v e r e p r e s e n t a -

t i v e f o r a c o n c r e t e w a l l w i t h a t h i c k n e s s o f 0 . 7

m . T h e t w o t e m p e r a t u r e c u r v e s a r e p r e s e n t e d

i n F i g. 4 . A ls o , a r a p id E - m o d u l u s d e v e l o p m e n t

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

2 7 9 a r e p r e s e n t e d i n t h e f i g u r e s u s e d l a t e r i n

t h e p a r a m e t r i c i n v e s t i g a t io n .

1 6 9


4/7

M a t e r i a l s a n d S t r u c t u r e s / M a t 6 r i a u x e t C o n s t r u c t io n s V o l . 3 0 , A p r i l 1 9 9 7

F ~ N x

/

z 3 4 6

Fig. 4 -

T e m p e r a t u r e c u r v e s

for 279 and A300.

~ ~ J l I u ~ D L u U I

[ .0 / / M o d e l

IOD /

Test

I.O 0.5 1.1] 1.5 Z.0

I res t ro i n t O.Z3 oy~

Z.5 3.0

Fig. 5 - Stress developmen t in 279 c o n c r e t e

I I , , . . ,F o i lu r

I

o i I z 3 4 5

t

re51vaint

= 0 .3 5d o y ~

Fig. 6 - Stress developme nt n A300

c o n c r e t e

1 7 0

T i m e c

7

r

T im e d a y

3.5 4 .D

Time

(do415)

7

T h e r e s u l t s o f t h e c a l i b r a t i o n a r e

shown in F igs . 5 and 6 fo r the two con-

c r e t e t y p e s . T h e m o d e l s h o w s r a t h e r

g o o d c o n f o r m i t y w i t h t h e t e st r es u lt s ,

e s p ec i a ll y d u r i n g t h e p e r i o d w h e n t h e

concre te i s compressed . The d i f f er ences

on the tensi le s ide, i e the low levels at

fai lure in the tests compared to the ten-

s i le s t r eng th , cou ld be due to the p res -

en ce o f t e r t i a ry c r eep . A n o t h e r r ea s o n

c o u l d b e t h e u n d e s i r e d e c c e n t r i c i t y i n

the tes t se t-up . T he r esu lt s o f the ca l ib ra-

t ion r eveal tha t the s impl i f ied mod el can

predict the thermal s tresses in a sat isfac-

to ry manner .

5 P A R A M E T R I C

I N V E S T I G A T I O N

To get an idea about the sensi t ivi ty of

the s imulat ion resul ts , a parametr ic inves-

t iga t ion was conduc ted . O ne o f the f ac-

t o r s s t u d i ed i n t h e i n v es t i g a t i o n i s t h e

tempera tu re var ia t ion dur ing hydra t ion .

A s imula t ion wi th increased tempera tu re

var ia t ion fo r conc re te 279 was car r ied

o u t a cco r d i n g t o F i g . 4 . A l l t h e o t h e r

i n p u t p a r am e t e r s w e r e k ep t u n ch an g ed .

T h e r e s u lt s o f t h e s i m u l a t i o n a r e p r e -

sen ted in F ig . 7 . W i th the increased tem -

p e r a tu r e , t h e m a x i m u m c o m p r e s s iv e

s t r e s s i s ab o u t t h e s am e a s f o r n o r m a l

279, but the tensile stress increases much

faster. This is in accordance with the idea

that a faster temperature increase dur ing

the init ial s tage does no t create h igh c om -

pressive s tresses s ince the concrete s t i f f -

ness has not yet dev eloped.

T h e i n f l u en ce o f st i ff u e s s d ev e l o p -

ment is s tudied by assuming a rapid s t i f f -

n e ss d e v e l o p m e n t a p p l ie d to t h e 2 7 9

co n c r e t e , s ee F i g . 3 . A r ap i d d ev e l o p -

m e n t o f E ( t ) r e s u l t s i n a s i g n i f i c a n t

increase in compress ive s t r ess , and the

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

smal ler than in the r ef erence case , see

Fig. 8.

I f bo th the tem pera tu re and the s ti ff -

ness values are increased simultaneously,

t h e c o m p r e s s i v e s t r e s s b e c o m e s m u c h

higher , but in addit ion the tensi le s tresses

increase more r ap id ly than in the r ef er -

enc e case. Th e results o f the s im ulat ion

are presented in Fig. 9.

The pos i t ive in f luenc e o f ear ly s t if f -

n e ss d ev e l o p m en t i n t h e y o u n g co n c r e t e

i s obv ious as wel l as the negat ive in f lu -

ence o f increased temp era tu re in r each-

i n g th e t e n s i l e s t r e n g t h e a r l ie r . T h e


5/7

agy

3 r s t ~ r t J ]

/

\ j

I n c r e a s e d l ~ m

/

/

/

l ~ o r m a l

T i m ~ ( {

O 0 . 5 1 . 0 I , '5 t ,O t , 5 3 0

F i g . 7 - S i m u l a t i o n w i t h

i nc re a sed te mp e r a tur e fo r

2 7 9 .

3 . 0 - 3 ~ r e s s u ~ r o )

- ~ ' [ I

1 g . . . . i _ _ / ~ _ / _ f _

F i g . 8 -

I n f l u e n c e o f r a pi d d e v e l o p m e n t o f m a t e r i a l s t if f n e ss o n

2 7 9 .

Z O - - -

I. t3 ~

0

-1.0

-Z0,

3 0 0

0 5

- 5

Z T g

N o r m a l

i / / / f

5 ZT~ I n ~ r ~ o s e _ d ~ e m p , r a p i d

Time

d ~ 9 ~ /

1 0 1 5 z 0 z 5 3 0

Fi g . 9 S i mu l a t i o n w i th inc r e ase d te mp e r a tur e a nd r a pid s t i f fne ss de v e l o pm e nt fo r

2 7 9 .

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

y o u n g c o n c r e t e t o i n c r e a se d t e m p e r a t u r e

a t e a r l y a g e s . A c o n c r e t e m i x t u r e w h i c h

g ives an ea r ly s t if fn ess d e v e lo p m en t an d a

d e l a y e d t e m p e r a t u r e d e v e l o p m e n t d u r -

i n g h y d r a t i o n w o u l d b e m o s t a d v a n t a -

g e o u s w i t h r e g a r d t o t h e r m a l c r a c k i n g .

T h e a m o u n t o f r e i n fo r c e m e n t is a n

i n p u t p a r a m e t e r o f t h e s i m p l i f ie d m o d e l

c o n n e c t e d t o t h e b o n d s t i f f n e s s a n d i t s

d e v e l o p m e n t t h r o u g h E q u a t i o n s ( 9 ) a n d

( 10 ). T h u s , a n i n v e s t ig a t i o n o f t h e r o l e o f

r e i n f o r c e m e n t m e a n s i m p l i c i t l y a n i n v e s -

t i g a ti o n o f t h e i n f l u e n c e o f b o n d s t if f-

n e ss . S i m u l a t i o n ha s b e e n p e r f o r m e d w i t h

t w o r e i n f o r c e m e n t p e r c e n t a g e s : 0 . 0 7 5 %

a n d 0 . 7 5 % , r e s p e c t i v e ly f o r a re i n f o r c e d

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

e n d s . A s s u m i n g a K v a l u e o f 2 0 0 , 0 0 0

M N / m 3 f or 2 5 - m m d i a m e t e r p la i n b ars i n

t h e a b s e n c e o f e x p e r i m e n t a l d a ta f o r

d e f o r m e d b a r s, E q u a t i o n s ( 9) a n d ( 1 0)

g i v e t h e v a l u e o f 0 .6 6 a n d 6 . 6 , r e s p e c -

t i v e l y f o r t h e r a t i o k / E 2 8 f o r c o n c r e t e

2 7 9 . K d ecreases w i th in c r eas in g d iame-

te r s ize an d fo r d e fo rm ed b ars h as s ig n i f i -

can t ly h ig h er v a lu es , s ee Gran h o lm [1 5 ] .

T h e s i m u l a t i o n s i n c l u d e t h e i n i t i a t i o n

p r o c e s s o f a c r a c k i n a ' w e a k ' s e c t i o n b y

r e d u c i n g t h e t e n s i l e s t re n g t h o f t h e c o n -

c r e te i n t h e m i d d l e o f t h e p r i s m . T h e

resu l t s in F ig . 1 0 sh o w th a t th e p r esen ce

o f r e i n f o r c e m e n t h a s a l m o s t n o e f fe c t o n

t h e s t re s s d e v e l o p m e n t i n t h e c o n c r e t e i n

c o m p a r i s o n w i t h s i m u l a t i o n s f o r t h e p l a i n

c o n c r e t e p r i s m s h o w n i n F i g . 5 . A f t e r

c r a c ki n g in t h e m i d s e c t i o n o f t h e p r i sm ,

t h e c o n c r e t e i s u n l o a d e d . I n t h e s e c o n d

case, F ig . 1 1 , th e r e i s m o re r e in fo rcem en t

i n t h e p r i s m , b u t t h e e f f e c t s p r i o r t o

c r ack in g a r e a l so n eg l ig ib le in th i s case .

T h e d i ff e re n c e s a p p e a r i n t h e p o s t - c r a c k -

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

t i a l l y u n l o a d e d , w h i c h m e a n s t h a t a s e c -

o n d c r ack wo u ld p ro b ab ly ap p ear . Th is i s

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

t r i b u t i n g r o le o f t h e r e i n f o r c e m e n t w h i c h

m a k e s t h e c ra ck s o c c u r i n g m o r e n u m e r -

o u s a n d n a r r o w e r t h a n i n t h e p l a i n c o n -

crete .

A n o t h e r f a c to r o f m a j o r i m p o r t a n c e

is th e ccur cy o f t h e i n p u t p a r a m e t e rs .

S i m u l a t io n s w i t h t h e s i m p l i f i e d m o d e l

fo r a p r ac t ica l case sh o w th a t a r e la t iv e ly

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

t o r y r a d ic a l ly c h a n g e s t h e t h e r m a l s tr es s

s t a t e . T w o t e m p e r a t u r e h i s t o r i e s a r e

u s e d i n t h e s i m u l a t i o n s , p r e s e n t e d i n

F i g. 1 2 , o n e b e i n g m e a s u r e d d u r i n g t h e

1 7 1


6/7

M a t e r i a ls a n d S t r u c t u r e s / M a t 6 r i a u x e t C o n s t r u c t io n s

V o l . 3 0 A p r il 1 9 9 7

51re55

M P o )

f L - [

F i g . I 0 - S t r e s s i n c o n c r e t e w i t h r e i n f o r c e m e n t p e r c e n t a g e 0 . 0 7 5%

a n d k / E 28 = 0 .6 6 . F - f i r s t e l e m e n t i n t h e p r i s m ; M - m i d s e c t i o n i n t h e p r i s m .

5 t r e 5 5

M P o l

: s

- I

Fig . 11 - S t r e s s in c onc re te w i th

reinforcement percentage

0.75 %

a n d k / E 28 = 6 .6 . F - f i r s t e l e m e n t i n t h e p r i s m ; M - m i d s e c t i o n i n t h e p r i s m .

Tempe.rolure (%)

G0

t,0

Z0

5imulaled

Tim e (daus)

t g 5 113 17- 1 4 1B 15 2_0

F i g . 1 2 - C o m p a r i s o n o f m e a s u r e d a n d g e n e r a t e d

temperature

3

o

-1

-Z

-3

-4

-5

M P o }

wi lh m easured

~0i~h 6im ul0 ttd

~_~emperalure

,.--I TiPtoedQ.~5

F i g . 13 - S i m u l a t i o n b a s e d o n m e a s u r e d a n d g e n e r a t e d t e m p e r a t u r e d a t a .

c o n s t r u c t i o n p ro c e s s a n d t h e o t h e r g e n e r a t e d

w i t h a 2 D p r o g r a m f o r t h e s a me c o n s t r u c -

t ion . Th e resu l ts o f s tres s s imula t ion show

t h a t w i t h t h e m e a s u r e d t e m p e r a t u r e d a t a ,

t h e c o n c r e t e w o u l d o b v i o u s ly c r a c k in c o m -

par i son to the case wi th genera ted t empera-

tu re da ta showing no t en den cy to c rack , see

Fig. 13.

The s imulated temperature in Fig. 12 dis-

p lays a some what re t a rded deve lopm ent and a

s lower cool ing process , probably due to s im-

p l i f i c a t i o n s i n t r o d u c e d i n t h e c a l c u l a t i o n s .

For a m ore de ta i led descr ip t ion o f the p rac t i -

cal case and th e tem pe ratu re calculations, see

Nag y [13] . Com par i son o f the s imula tions in

Fig. 13 shows a radical change in the s t ress

s t a t e i n t h e c o n c r e t e c o r r e s p o n d i n g t o t h e

erro r in the temp eratu re inpu t data. I t i s rea-

sonab le to be l i eve tha t even 2D model s a re

ve ry sensit ive to such an error .

6 C O N C L U S I O N S

Thermal s t res ses in concre te occur a t an

ear ly age as a consequenc e o f rest ra ined the r -

mal defo rmat ions . At th i s age , the mater i a l

characteris tics of the c onc rete are in d evelop -

me n t a n d t h e r e s t r a i n t c o n d i t i o n s i n a r e a l

s t ructure are diff icu l t to assess . In this s tudy,

an a t t empt has been m ade to p red ic t the ther -

ma l s t r e s s e s w i t h a l i n e a r o n e - d i me n s i o n a l

const i tu t ive model . According to the cal ibra-

t ion o f the m ode l to tes ts , the s imple material

descr ip t ion o f the concre te wi th a min im al se t

o f requ i red inpu t parameters has a good capa-

bi l i ty to predict thermal s t resses . The resul ts

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

cient ly accurate for thermal s t ress analysis in

p rac t i ca l app l i ca t ions where the in fo rmat ion

n e e d e d f o r a mo r e c o mp l e x a n a l y s i s i s n o t

available.

The age-dependen t mater i a l s t i f fness , i n

combina t ion wi th the t empera tu re var i a t ion ,

has been found to have the g rea tes t in f luen ce

on the th erm al ly - indu ced st resses . An ear ly

growth in s t i ffness and a delayed temperature

developm ent wo uld c l ear ly reduce the r i sk o f

therma l c rack ing in youn g concre te .

T h e r o le o f r e in f o r c e me n t ha s b e e n f o u n d

to be m inor p r io r to c rack ing bu t w i th a c l ear

crack red i s t r ibu t ion e f fec t in the pos t -c rack-

ing s ta te . Th i s e f fec t depends on the am oun t

of reinfo rcem ent , and i t i s d is t inct ly clear for a

r c i n f o r c e m e n t p e r c e n t a g e o f 0 . 7 5 c a l c u la t e d

accord ing to the c l as s i ca l theory tha t su f f i -

c i e n t t e n s i o n mu s t b e t r a n s f e r r e d f r o m t h e

s t e e l t o t h e c o n c r e t e i n o r d e r t o c r a c k t h e

c o n c r e t e w i t h o u t y i e l d i n g t h e s t e e l . T h u s ,

1 7 2


7/7

agy

th is s imple analysis proves the w el l -k now n fact that due

to the red i s t r ibu t ion ro le o f the re in fo rcem ent severa l

cracks can appear ins tead of a few wid er ones .

Th e scope o f thi s paper i s to invest iga te and m odel

ther m al ly - in duc ed s tresses and the fac to rs in f lu enc ing

this process in conc rete at early ages. T he invest igat ion is

focused on the ear ly age E-mo dulus amo ng several fac-

tors influe nc ing the stress level. How eve r this discussion

c a n n o t b e c o n c l u d e d w i t h o u t r e ma r k i n g th e i mp o r t a n c e

of o ther fac to rs l ike the coef f i c i en t o f thermal expans ion

of the con cre te o r the res t ra in t cond i t ions o f the s t ruc-

ture regarding thermal s t ress development .

CKNOWLEDGEMENTS

This w ork was f inanc ia l ly suppor ted by E l fo rsk AB -

t h e S w e d i s h P o w e r G e n e r a t i o n - R e s e a r c h a n d

D e v e l o p m e n t Co .

REFERENCES

[1] E mborg , M . , 'T he rm a l S t re sses in Concre te S t ruc tu res a t E a rly

A g e ' , D o c t o r a l T h e s i s 1 9 8 9 : 7 3 D , D i v i s i o n o f S tr u c t u r a l

En gine ering , Lule~ University of Technology, 1989.

[2] Dah lblom, O. , 'Hac on-S -A P rogram fo r S imula tion o f S tre ss in

H a r d e n i n g C o n c r e t e ' , R e p o r t f r o m V a t te n f al l H y d r o P o w e r

Generation, 1992.

[3] Haugaard, M., Berrig , A. and Fredriksen, J . , 'Curing technology:

A 2 - d i m e n s i o n a l s i m u l a t i o n p r o g r a m ' , i n ' P r o c e e d i n g s o f t h e

Nord ic C oncre te Resea rch M ee t ing ' , Go thenb urg , 1993 .

[4] Roelfstra , P .E. , S alet , T .A .M . and Kuiks, J .E . , 'D efin it ion and

application of s tress-analysis-based temperature difference l imits

t o p r e v e n t e a r l y - a g e c r a c k i n g i n c o n c r e t e s t r u c t u r e s ' , i n

'P roceed ings o f the In t . Symp. RIL E M 119 T CE Avo idance o f

The rm al Cracking at Early Ages ' (E&FN Spon, 19 95).

[ 5] J a p a n e s e C o n c r e t e I n s t i t u te C o m m i t t e e o n T h e r m a l S t re s s o f

M a s s i v e C o n c r e t e S t r u c t u r e s, ' A P r o p o s a l o f a M e t h o d o f

Ca lcu la t ing Crac k W id th Du e to T h erm al S t resses' , ( Japanese

Concrete Insti tute , Sept. 1992).

[ 6 ] O t t o s e n , N . a n d P e t e r s s o n , H . , ' I n t r o d u c t i o n t o t h e F i n i t e

E l e m e n t M e t h o d ' ( U n i v e r s i t y o f L u n d , P r e n t i c e H a l l

International Ltd, 1992).

[ 7] D a h l b l o m , O . a n d P e t e rs o n , A . , ' C a m f e m - C o m p u t e r A i d e d

M o d e l l i n g B a s e d o n t h e F i n i t e E l e m e n t M e t h o d ' , R e p o r t

T V SM -3001 , L und Ins t i tu te o f T echno logy , 1982 .

[8] Kasai , Y.

et al.

'T ens i le p rope r t ie s o f ea r ly -age conc re te (T he

plastic and elastic s tra in and the extensibil i ty) ' , in 'Proceedings o f

t h e 1 97 4 S y m p o s i a o n M e c h a n i c a l B e h a v i o u r o f M a t e r i a l ' ,

Kyo to , Augus t 21 -24 1974 , 433-441 .

[9] Hillerborg, A. , M ode er, M. and Peterson, P -E. , 'Analysis of crack

f o r m a t i o n a n d c r a c k g r o w t h i n c o n c r e t e b y m e a n s o f fr a c tu r e

mechanics and f inite e lements ' , Cement and Concrete Research 6

(1976) 773-782.

[10 ] L 6fqu ist , B . , 'T e mpe ra tu re f fek te r i h~rdnande be to ng ' T ekn iska

meddelanden fr~n Kungliga Vattenfallsstyrelse ( in Swedish), Serie

B, Nr 22 , Ju ly 1946 .

[11] Byfors, J . , 'P lain Concrete a t Early Ages ' , CBI Research 3:80,

1980.

[12] Nag y, A. and Thelandersson, S . , 'Mode ll ing Therm al Effects in

You ng Concre te ' , Nord ic C oncre te Resea rch , March 1992 .

[ 1 3] N a g y , A . , ' C r a c k i n g i n C o n c r e t e S t r u c t u r e s D u e t o E a r l y

T h e r m a l D e f o r m a t i o n s ' , R e p o r t T V B K - 1 0 0 9 , D e p a r t m e n t o f

Structural Engineering, L und Insti tute o f Tech nolog y, Sweden,

1994.

[ 14 ] E m b o r g , M . , J o h a n s so n , H . , ' R e l a x a t i o n T e s t s o n Y o u n g

C o n c r e t e ' ( i n S w e di sh ) , D i v i s i o n o f S t r u c t u r a l E n g i n e e r i n g ,

Lule5 University of Tech nolo gy, 1988:01T, 1988.

[15 ] Granho lm, H . , 'Crack ing in Re in fo rced Co ncre te ' ( in Swed ish ) ,

Chahners Technical University , Gothenburg, 1958.

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hett 97 software analysing thermal stresses

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