VOL. 11 - N° 66 - MATr:RIAUX ET CONSTRUCTIONS

REFERENCES

[56] LAMBOTTE R., MOMMENS A. - L'Evolution du jiuage 'du beron en fonction de sa composition, du taux de contrainte et de I'age, groupe de travail GT 22. Centre national de Recherches scientifiques et techniques pour l'Industrie cimentiere, Bruxelles, July 1976.

[57] PIHLAJAVAARA S. E. - A review of some of the main results of a research on the aging phenomena of concrete. Effect of moisture conditions on strength, shrinkage and creep of mature concrete. Cement and Concrete Research, Vol. 4, 1974, pp. 761-771.

[58] WITTMANN F. - Kriechverformung des Betons unter statischer und unter dynamischer Belastung. Rheo!. Acta., Vol. 10, 1971, pp. 422-428.

Part IV: Temperature effect on basic creep

Development of the model for basic creep in Part II is followed here by a prediction model for creep at various temperatures that are kept constant during creep. The model, which preserves the form of the double power law, reflects two opposing effects of temperature: the increase of creep rate due to heating, and the reduction of creep due to thermally accelerated hydration. Prediction of material parameters from mix composition is studied and extensive comparisons with test data indicate a good agreement.

INTRODUCnON

The double power law for basic creep, developed in Part II, will now be extended to model creep at various temperatures that are kept constant during creep. Unlike the preceding parts of this study, here we must not only model the composition influence but also decide on the proper form of the temperature effect because the model for variable temperature that we are going to investigate has not yet been proposed. . Realizing that the choice of reference temperature To

is subjective and largely arbitrary, we must conclude that the creep formula for any temperature (within a certain range) should have the same basic form. In particular, the form of double power law should be preserved for heated sealed concrete.

FORMULAS PROPOSED FOR TEMPERATURE EFFECf ON BASIC CREEP

Preserving its basic form, we may generalize the double power law as

J (t, t')= ;0 + Co (t, t'),

(34)

Co (t, t')= :: (t~-m+a) (t-t')IIT,

wher:e

It'

t~= 0 fJT (t")dt", (35)

(36)

Here CT, nT and fJT are functions of temperature, and t~ represents the equivalent hydration period (or

424

maturity) [5] e), which is defined as the period at reference temperature To needed to achieve the same degree of hydration as period t' at temperature T. Equation (36) results from assuming that the tempe­rature effect on hydration is governed by an activation energy, Q. In equation (36), T and To must be absolute temperatures. The constant 4 ooooK (representing Q divided by gas constant) has been derived empirically from the data fitted in the sequel.

Following a theoretical analysis by Wittmann [58], function CT was previously [4] suggested to also obey the activation energy concept. However, an in-depth analysis of test data revealed that this is true only for a limited range of temperatures, from about 35 to about 75°C. Beyond this range significant deviations occur, which may be due to phase changes and chemical changes, as well as simultan~ous operation of several processes controlled by different activation energies. Therefore, function CT has been identified empirically, although the basic, product form of equation (36) for <PT' as indicated by activation energy effects, rn~ been retained. Function CT' which is plotted in figure 2 in comparison with the activation energy dependence, has the form

cT = 1+(lOO/(T-253.2»3.s -1,

1 TT= 1+60lt~0.69 +0.78,

I (37)

(38)

where Co is a composition parameter, t~ is the age of concrete when temperature T is applied and T is. abso­lute temperature. Note that CT is defmed not only as a function of temperature but also as a function of t~.

According to the activation energy model for power­type creep functions [58], exponent nT would be a

(I) Reference numbers not listed at the end of this part are found in the preceding parts.

constant. Again, for a broader range of temperatures ( - 20 to 140°C) this is unacceptable. Nevertheless the form of equation (34), conforming to the activation energy model, may be retained and it suffices to take nT as temperature-dependent. By data fitting, the follciwing empirical function has been found:

0.25 BT = 1+(74/(T-253.2))7 +1. (39)

Equation (37) is approximately valid from about - 20°C to perhaps 120°C. Near the ends of the range the rise of CT with temperature is milder (fzg. 26 a).

Function BT indicates that exponent nT increases with temperature, i. e., the ratio of long-time to short­time creep increases as temperature is raised. This may be explained by the larger effect of the accele­ration of aging during the early creep period.

Equations (35), (37), (38) reflect the fact that the tempe­rature effect on creep is twofold ([60], [5]): (a) an increase in temperature increases the creep rate, but (b) it also accelerates hydration, i. e., aging. These effects, modeled by coefficients cT , 'T and t~, respectively, oppose each other. When a young concrete is heated well before it . is loaded, the equivalent hydration period t~ for the moment of load application may get sharply increased, causing a reduction of the creep increase due to heating. On the other hand, when an old concrete is heated, the change in t~ has little effect on subsequent creep, and so a strong increase of creep with temperature takes place. Modeling of both these opposing tendencies is essential for successful fitting of test data.

The elastic modulus E is known to decrease with temperature beyond 50°C, the drop reaching about 20% at 100°C ([61], [62]). Like the double power law which gives proper age-dependence of elastic modulus, equation (34) seems to give approximately correct temperature dependence of the elastic modulus:

1 1 E ( ') = E ( ') =J (t' +0.1, t')

t stat t

EFFECf OF COMPOSmON ON BASIC CREEP OF HEATED CONCRETE

By fitting of test data ([59], [23], [61], [63], [64], [65], [66], [67], [68], [69], [22], [70], [71], [72]) it was verified that:

Co= ~ (~)2 (~)a 8 C C 1, (41)

where al accounts for the cement type and is the same as in equation (18) of Part II; w/ c= water-cement ratio; a/ c= aggregate-cement ratio. An increase of creep rate ~ith the water-cement ratio, as given by equation (41), IS logical to expect. The increase of Co with the aggregate­cement ratio means that the restraining effect of aggre­gate on creep is stronger at lower temperatures. Equa-

Z. P. BAZANT - l. PANULA

1.J~----------------,

1.2 .. III 1.1

• exp(4!XXl _ 4!XXl) 10 T. T

(; 5

0.251T - 253.151' Br ' 1 • 74'. IT _ 253.1517

Cr' 19.4 -1

( 100 )15

1 + T _ 253.2

60 80 100

Temperature in·C

a 120

Fig. 26. - Coefficient~ CT and BT as function of temperatu~e.

tion (41) does not involve strength, but since the strength depends on wieand al c, the effect of strength is present indirectly.

COMPARISONS WITH TEST DATA ON HEATED SEALED SPECIMENS

Fits of numerous test data shown in figures 27-34 indicate a reasonable agreement of the present model with experiments. Basic information on the test data used is given in Appendix IV ..

For some data sets important information was not reported and, therefore, has had to be assumed. e. g., for England and Ross' data it has been assumed that the heat was applied at the age of 10 days, simulta­neously with load application (i. e., no heat stabilization period before the test). Also, the initial "elastic" strains at elevated temperatures have been assumed using proportionality to the values of Marechal. For the tests of Silveira and Florentino, it has been assumed that the heat was applied three days before loading.

For Nasser and Neville's data ([68], [69]), the sand­gravel ratio was not available, and so exponent n has been assumed. The initial elastic strains have had to be assumed also (0.2x 1Q-6/psi).Papers [68] and [69] mentioned that E was not a function of temperature; therefore, the value of 1/ Eo has been found by optimiza­tion. The E-modulus was reported to increase by 22% from t' = 14 days to t' = 365 days, and the value of J (t'+O.OOl, t') has been assumed to change in pro­portion. Moreover, these data indicate, independently of curing temperature, a 22% increase of elastic modulus upon heating, which conflicts with references [61] and [62]. The deviations from test data in figures 28 and 32 must be judged in the light of the preceding remarks.

When unspecified, the unit weight of concrete has been assumed as 2,400 kglm 3

.

It is interesting to compare J (90 + 365,90) for the data of Silveira and Florentino [67], McDonald [22] and Kennedy [23]. At room temperature, the values are 0.425, 0.285, O. 285 (all in 1O-6/psi), and at elevated temperatures tested (45, 65.6 and 65. 6°C respectively), the values are 0.748,0.400 and 0.445. This is a consi­derable scatter in view of the fact that the mix parameters and test conditions were quite similar (see Appendix IV).

For temperatures beyond 95°C, the present model gives only very crude .estimates. Even though all

425

VOL 11=~jl(Jo 66 - MATI:RIAUX ET CONSTRUCTIONS

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.9

. iii Q..

....... 0.8 '" '0

C 0.7

..-.. ..... ..... 0.6

-. 0.5

0.4

0.3

0.40

0.30

0.20

Hannant, 1967

lIE. = 0,097· 10G/psi If, = 4.087 n = 0.181 m = 0.295 01 = 0.053

CT27 = 0.041 Cr53: 0.551 CT57 : 0.652 C:r75: 1.123

-10

... --.-

0 0.9

0.8

0.7

0 0.6 6'0

0

0.5

0.4 ').1 -.. ""-.I •••••

... 11 •• 0.3

r,180days

0.2

100 1000

Nishizawa and Okamura, 1970 0

lIE,,: 0.100 . 10"6/ps i 'P, : 3.234 n = 0.147 m: 0.303 0\ = 0.063

CT20= - 0.023 CT7O= 0.648 Crgo: 0.964

McDonald, 1~5 l/E',,:0.101·10 Ipsi 'f,=3.272 n =0.147 m=0.305 1)<.=0.059

CT23=-O·006 CT66= 0.668

eo

0

10

0

0

--,-

1':28 days

-.. -

.. ~~ cIJ

100

t': 90days

...-

o 600 psi . ) 22.S"C • 2400 PSI • 2400 psi

,-

Arlhanari and YU,1967

lIE. = 0.111 . 10G/psi cp, = 4.085 n = 0.167 m =0.321 0< = 0.044

CT2o :-O.032 CT40= 0.232 CT62= 0.711 CT80: 1.133

1': 15 days

• ooo£> uniaxial test

• _ •• biaxial test (",=0.2)

0 1.1

1.0

0.9

0.8

0.7

0.6

,-

0.3

0.6

0.5

0.4

1 10

England and Ross, 1962

l/E,,:0.107 '10-s/psi cp, = 3.012 CT126 = 1.861 n =0.128 CT140:1.997 m : 0.317 0( = 0.056

Cr2o:-0.032 Cr53 = 0.499 C:r77= 1.063 C:r94=1.414 Cr,,4=1.725

• 10

Johansen and Best, 1962

l/E.=0.176 '10-6/ps; f, =4.628 CT20 =-0.101 n =0.120 Cr12 =-0.266 m : 0.466 Gn-l2l =- 0.407 0< :0.036 Cn-2O):-0.412

<>

00 o

100

10 100 10 100

t- r in days

Fig. 27., - Fits of Tests of Temperature Effect on Creep by Hannant (1967) [61], Arthanari and Yu (1967) [63], Nishizawa and Okamura (1970) [64], England and Ross (1962) [65], McDonald (1975) [22] and Johansen and Best (1962) [66]. CT optimized-solid line; subscript number refers to corresponding temperature. CT with .formula -dashed line. 1/ Eo calculated from experimental E28 or optimized from basic creep data. .

426

specimens considered here were sealed, moisture may have moved out of concrete and collected under a bulged jacket. Also, rapid redistribution of moisture within the heated specimen may have had considerable effect on creep. In particular, the present model does not describe the decrease in creep rate (i. e., in CT )

Z. P. BAZANT - L. PANULA

that is sometimes observed upon passing 100°C; see the curves near 100°C in figure 28 for Nasser and Neville's data, and the reversed order of temperatures for the curves near 100°C in figure 27 for England and Ross's data.

0.50,--------------------------;0-, Do Silveira and Florentino, 1968

1IE,=0.150·10"/psi

0.40

0.30

0.20

0.7

VI a "' ....... 0.6 '0

C

0.5 ::... ... : -,

0.4

York, Perry, Kennedy, 1910 . -.

l/E,= 0.087 . 10 Ipsi 'f, = 3.410 n = 0.~53 m =0.303 0'-.= 0.059

...:-. CT2~ = o.li ~ _ Cn • = 0.003 Cras = 0.~7 CT66 = 0.667

o 600psi.J 24'C • 2400 psi

o 600 psi J 65 6'C • 2400 psi .

" " ./

/ ./

./ ./

./

./ ./

./ ./

./

/

/ /

/

o

/ /

/ 0 / 0

/

1', 90 days

r-----------~-------------~~--~/------,~ Nasser and 1'I!~iIIe, 1965 / 8 0 l/E,= 0.085 '10 Ipsi / If, =4.308 / n = 0.140 / m=0.302 / 0< = 0.042 ./

Cn = 0.0 / - CT7I =1.122 /

CT21 =-0.043 / ~ - -CT7I = 1.700 ./~'

o o

o o

o

./ ./

./ .--O ••• /'

o

./ ./

./

"

./ ./

./

./ ,,' /' 00 .,. /'

/' 0 00 ., •• /'/'

o ..... 6/XI •• ..... . .....

•• 0· :;.--/ t'd4days

100

100

t - t'

0.7

0.6

0.9

cp, =2.987 CT20 =O.O, f=28,90.365days n =0.122 . Cr4~=0.903, 1'=28days

0.8 m = 0.326 - Cr~~ =0.957. t'=90days '" = 0.050 Cr.5 = 0.875, 1'= 365days

CT2o =-0.026, f= 28days Cr20 =-0.030. t':90days

0.7 Cr20 =-0.036, 1'= 365days

0.6

--Cr~~=0.445, t'=28days Cr4,=0.509, t'=90days Cr45.0.620. 1'=3Ei5days

• •••

10

Nasser and Neville, 1967

l/E,= 0.085 '16"1 psi 'P, =4.308 CT21 =O.O./ n = 0.140 CT46=1.023 m = 0.302 - CT7,=2.112 d. = 0.042 ..... G,-g.,=2.496

CT2I = -0.CMj8" CT." = 1.023

-CT1I = 2.712 C_=4.263

Zielinski and Sadowski, 1973

/' /

<> <>

100

0.5 IlEa =0.110 'IO-I/psi

<>

<>

o

100

<P, = 2.989 Cr20 = 0.0

m =0.123 =0.326

= 0.055

CrGO =0.542

CT20 =-0.029

Cr60 = 0.601

0.4 a

0.3

20·C

o ----.. ___ -.--.-r •• 0.2 • • t' = 123 days

10 100

In days

Fig. 28. - Fits of Tests of Temperature Effect on Creep by York, Kennedy and Perry (1970) [23], Da Silveira and Florentino (1968) [67], Nasser and Neville (1965) [68], Nasser and Neville (1967) [69], Seki and Kawasumi (1970) [70] and Sielinski and Sadowski (1973) [71]. CT optimized - solid line, CT with formula - dashed line. 1/ Eo optimized from basic creep data.

427

VOL. 11 - N° 66 - MAT!:RIAUX ET CONSTRUCTIONS

1.2 Browne. 1967

1.0

0.8

Vl .!2- 0.6

<0 '0

~ 0.4

1.0

0.8

t',7days lIE,' 0.124 .10-61ps; 'f,,3.511 n ,0.156 m ,0.307 0< ,0.060

a a o

0.2 '---'------,110---IOOL---.:...J .LO~---:'IO:----l00L----:"-J L~---:':IO---:'IOO~-'::..J '~~~--::IO:----:'lOO:-----' '=~----:::----:":---'KXX)LJ .

t-t' in days

Fig. 29. - Fits of Tests of Temperature Effect on Creep by Browne (1967) [59]. CT optimized-solid line in figure i-J. CT with formula­solid line in figure a-e. 1/ Eo optimized from basic creep data. Experimental datas are smoothed mean values.

APPENDIX IV

Basic Information on Test Data Used Hannant's Tests of Temperature Effect on Creep (1967)

[61). - Cylinders 4 l x 12 inch (105 x 305 mm), cured for 24 hours in molds under wet rags, then 5 months under water at 20°C, and then one month sealed in copper. Heating rates about 10°C/hr. For temperature stabilization all specimens were heated for 24 hours .before loading. Stress 2,000 psi (13.8 N/mm2). Water-cement-sand-gravel ratio 0.47 : 1 : 1.845 : 2.655. Sulphate resisting Portland cement with Plastocrete plasticizer. Coarse aggregate limestone max. size 3/8 inch (10 mm). 28-day cube strength 9,350 psi (64.5 N/mm2).

Nishizawa and Okamura's Tests of Temperature Effect on Creep (1970) [64). - Specimens 15 x 15 x 55 cm, sealed in copper, prestressed to compressive stress 120 kg/cm2 (11.8 N/mm2) at the age of 28 days. After 7 days of loading at 20°C, specimens exposed to temperature of 70 or 90°C. Water-cement-ratio 0.40, cement content 377 kg/m3, sand percentage 36.5%. (In calculations water-cement-sand­gravel ratio 0.40 : 1 : 1. 85 : 3.22 was used.) Max. size of coarse aggregate = 25 mm, normal cement. Cylinder strength 459 kg/cm2 (45 N/mm2).

McDonald's Tests of Temperature Effect on Creep (1975) [22]. --Cylinders 6 x 16 inch (152 x 406 mm) demolded after 24 hours, coated with epoxy and returned to fog room. After 24 hours another coat of epoxy, and sealed in copper. At age of 83 days, specimens recoated with epoxy, sealed in neoprene, and placed to environment of test tempe­rature, loaded at age of 90 days. Water-cement-sand-gravel ratio 0.425 : 1 : 2.03 : 2.62. Type II portland cement (404 kg/m3). Limestone aggregate, max. size 3/4 inch (19 mm). 28-day average cyl. strength 6,300 psi (43.4 N/mm2). .

Arthanari and Yu's Tests of Temperature Effect on Creep (1967) [63]. - Slabs 12 x 12 x 4 inch (305 x 305 x 102 mm), cured under wet hessian for 7 days. For tests under mass­concrete conditions sealed by epoxy resin and two coats of

428

plastic emulsion paint. Loaded at age of 15 days, stress 1,000 psi (6.9 N/mm2). Heating began I day before loading. Water-cement-sand-gravel ratio 0.564 : I : 1.125 : 2.625. Thames river gravel of size 3/16-3/8 inch (4.76-9.5 mm), ordinary portland cement. 28-day average cube strength 6,000 psi (41.4 N/mm').

England and Ross' Tests of Temperature Effect on Creep (1962) [65]. - Cylinders 4.5xl2inch (1l4x305mm), demolded at age of I day, placed under water for additional 3 days, after which stored at 17°C and 90% R.H. until tested at age of 10 days in a sealed state. The seal was a polyester resin, with fibre glass reinforcement. Water­cement-sand-gravel ratio 0.45: 1 : 2 : 4. Compressive strength of 4 inch (102 mm) cubes at age of 14 days = 5,500 psi (37.9 N/mml). Elastic modulus 5 x 106 Ib/in2

(34,480 N/mm2). Johansen and Best's Tests of Temperature Effect on Creep

(1962) [66]. - Cylinders 10 x 30 cm and 15 x 30 cm cast in steel molds and remolded at age of 1 day, then stored at 100% reI. humidity and 20°e. At age of 42 days, specimens were sealed and moved to test environment. At the end of 3 days stabilization period specimens were loaded at their respective temperatures to 30% of their ultimate strength in compression as measured at 20°C. Water-cement-sand­gravel ratio 0.7 : 1 : 3.5 : 3.5. Normal portland cement. Max. size of aggregate 3/8 inch (9.5 mm). Average compres­sive strength 179 kp/cm' (17.6 N/mm2) at the age of 42 days on cylinders 15 x 30 cm.

York, Kennedy and Perry's Tests for Temperature Effect on Creep (1970)[23]. - Cylinders 6 x 16inch(152x406mm), removed from molds 24 hours after casting. Then epoxy coat applied and specimens stored in fog room. Next, 48 hours after casting, specimens sealed in copper and placed in test environment at 73. 4°F (23°C). At age of 83 days specimens sealed in neoprene jacket, and exposed to test temperature. Loaded at age of 90 days. Water­cement-sand-gravel ratio 0.425 : 1 : 2.03 : 2.62. Cement type II (404 kg/ m3). Limestone aggregate, max. size 3/4 inch (19 rom); 28-day cyl. strength 6,560 psi (45.2 N/mm2).

t3 \0

IJ)

C-"-

CD . 0

C

----J

Komendont, Polivka, Pirtz, 1976

0.71- 1/ Eo • 0.103 . 10-6 1 psi

<p. • 3.293

n ·0.151 0.61- m - 0.303

a • 0.066

05 ~ Cu •• 0.0 Cu.' -0.004

-CT4 • '0.01 --- CT4•• 0.162

0.4 L CU •• 0.468 Cn • '0.512

0.3

0.2~

0.7 Ko

II E 0 • 0.103 ·10-6 /psi

<P. • 3.293 0.6

• 0.151

m • O. 303

05 a • 0.066

CT23 • 0.0 Cu •• -0.004

0.4 --CT4• '0.211 - - - C T43 • 0.186

Cu •• 0.938 Cu •• 0.587

0.3

0.2

~~r.~ I

Komendant, Polivka, Pirtz,

0.6 t- IIEo '0.103·10 I psi

<p. ·3.293

051-• 0.151

m '0.303

a • 0.066 0.41- CT.' '0.0, C TO" -0.005

--CT43 '0.411 - - - C T4" 0.2 17

0.31- Cu. '1.132

0.2t-~-~

03

0.2

0.1

0.7

0.6

0.5

0.4

0.3

0.2

0.1

r / 1

06

0.5

0.4

0.3

0.2

(mix A)

Komendant, Polivka, Pirtz, liE" .0.103 ·IO-s/psi

•

<P. ·3.235

·0.147

m • 0.305

a • 0.065

C T25 -0.0 C T23 C T4 • -0.086 ---C T43

CT7. -0.424 CT71

• ~'-- o 0 00

Komendant, Polivka, Pirtz, 1976

II E" - 0.103· 10-s Ipsi

<PI • 3.235

- 0.147

m • 0.305

a • 0.065

C u , -0.0

-- CT4 • - 0.278

o •

C T71 - 0.760

o o o

~=-.---

Cn , • -0.004

- -- C T4 •• 0.175

CUI -0.554

Komendant, Polivka, Pirtz, IIEo ·0.103·10-6/psi

1976

<PI -3.235

n - 0.147

m -0.305

a - 0.065

Cu •• 0.0

--C T43 '0.515

C TTI • 1.004

o 0 0

•

CT •• ' -0.005

- - - cu , - 0.205

t'=28 days (mixB)

(mix B)

0.1' II II!! 111111 III,,!! Il"'" I '\I"! !:~'O.I~I "!III OJ "II'!! 1 II 'It I '!lIIlI ,,"II' 'It'IIL

10 100 1000 0.001 a.oJ 100 0.1 10 0.01 0.1

t - t I in days Fig. 30. - Fits of Tests of Temperature· Effect on Creep by Komendant, Polivka and Pirtz (1976) [72]. CT optimized - solid line, CT witw formula - dashed line.

1/ Eo optimized from basic creep data.

N

" IJI :to N :to Z -t

:­

" :to Z C

~

VOL. 11 - N° 66 - MAT~RIAUX ET CONSTRUCTIONS

Vl Q..

...... <D

'0

C

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

0.8

0.7

0.5

0.4

0.3

Hannan!, 1967 11 Eo 'O.OBO . 1O-6/psi

<f, ,1 •. 087 Cr27' 0.041 n ,0.181 Cr53,O.SSl m,0.295 --Cr57'0.6S2 0( ,c.053 CT75 ".123

11 ...-// .......

--........ .-. ---.-:: ...

-- --= .... - •• ~ . -. ... -

0.9

0.8

0.7

0.6

0.5

Arthanari and Yu, 1967 1/Eo,0.10S·10-6/psi

'J\,4.085 CT2d'-0.032 n ,0.167 Cr40' O. 232 m '0.321 CT62'0.711 0( , 0.044 Grecf 1.133

CT20 , 0.0 CT40,0.226

- CT62 ,0.S98

Creo' 0.858

0.4 ./

0.3 t·,15days

0006 uniaxial test • ••• biaxial test

0.2 • 1",180 days

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.40

0.30

0.20

10 100

Nishi zawa and Okamura, 1970

l/Eo' 0.110· 10-&/psi 'P, ,3.234 n '0.147 m ,0.303 0( , 0.063

CT20 ,0.0 - CT70 , 0.368

CT90 ,0.919

CT20 '-0.023 - - CT70 ' 0.648

Cr90 ,0.964

McDonald,1975 -6

1/Eo,0.086·10 /psi

10

<f\ = 3.272 CT22.B ,0.0 n = 0.147 - Cr65.6 ,0.431 m = 0.305 0<. , 0.059

10

---...-

1000 0.2 LL......L..L...l....J...l.lJ

1-_l...........L....L.1-LLL1

1:!-0 _-,.J._l.........L.....L..L.J...J

...-

,al:

/ /

P

0

./ -

En91and and Ross, 1962 o

/ ~

1.1 lIEo ' 0.105.10 6 /psi

/,

/ /

/

1.0

0.9

o 0.8 o

0.7

./ 0.6

0.5

~ ,3.012 CT20, -0.032 n ,0.128 Cr53 '0.499 m '0.317 CT77=1.063 0\ =0.056 --CN4 ".414

CT20' 0.0 CT114' 1.725 CT53 '0.698 CT126,1.861 Cm ,1.254 CT140, 1.997

CT94' 1.525 CTl\4,1.864 CT126,1.760 Cn4o= 1.977

./

0 /"

/' ./

./ ~./ ~

1', 28 days /" ....-

100

0.3

0.7

0.6

10

Johansen and Best, 1962 liE, = O. 225 . 1O-6/psi

'A ,4.628 CT20=0.0 n =0.120 CT12 =-0.305 m =0.466 -Crc_12)=-0.312

\"=45 days

ex =0.036 CT(-20)=-0.314 ....- ~

. ,c, /./"<:f>

100

1.1..8

••• co oo

1'·90daY5

'1.(l~ --0,\"2 __ .......

~$)-~'1. ./" P-S·@..!I S - __ _ - -f$ A __ - _--r~

0.4 ~~.-- -20

0.5

o 600 psi ] • 2400 psi 22.8'C

• 2400 psi

100

t-t' in days

6.- ---- _ _ CT20 =-0.101 Crt-12) =-0.407 Cr'2 = -0.266 c,.~) =-0.412

Fig. 31. - Fits of Tests of Temperature Effect on Creep by Hannant (1967) [61], Arthanari and Yu (1967) [63], Nishizawa and Okamul (1970) [64}, England and Ross (1962) [65], McDonald (1975) [22] and Johansen and Best (1962) [66]. CT and 1/ Eo botb calculated wi! formula.

430

~ ... '0

.EO ~

:... .... ~ -,

Z. P. BAZANT - L. PANULA

0.50,--------------------,.-------,.--, a

0.40

0.30

0.20

0.1

0.7

0.6

York. Perry, Kennedy. 1910

1/E.=0.100·10-6/psi ", =3.410

a a

n =0.153 m =0.303 fA =0.05J

CT.M= 0.003 ~=0.661

o 600 pSi. ] 24"C • 24oops.

o 600 psi ] 65 6'C • 2400 psi .

II a

Nasser and Neville. 1965

1/E •• 0.096·1lf/psi <A .4.308 Ii = 0.140 m = 0.302 0( = 0.042 Cn , =- O. 043 Crll =1.1

10

0.7

Seki and Kawasumi, 1970 liE. - 0.102 10-' / psi

.p, - 3.354

n - 0.11I1

0.6 m -0.305

a -0.063

CT20 - -0.0211(" -28days' 0.5 CT40-0.184 (,'-29day.'

C170 -0.713 (,'- 29 days,

CT20 - -0.029 (" -96 days' 0.4 er..-0.211 (t'-IOOday.'

CTTO"O.831(,'-105doy.' 0' 60 ~ 1

~

10

100

A> 0 ~. c1>. • 0.3 (I 0 \_?-86O"",.,...,' ""'..-....

10

• 0

a a

a •

a • • a ••

.-' .... • c#' • • 000 00

0

0

1', 90 days

100

100

0.9

0.8

0.7

0.6

0.4

0.3

00 Silveira and Florentino, 1968

1IE. = 0.111·11J'6 /psi If, = 2.981 n = 0.122 m = 0.326 0\ = 0.050

CT20 = - 0.026, t' = 28 days CT20 = - 0.030, I' = 90 days CT20 = -0.036, 1'= 365days CT4, = 0.445,. t' = 28 days CT45 = 0.509, I' = 90 days CT45 = 0.620. t' = 365 days

0.2 • •

• 1 10

Nasser and Neville, 1961

lIE.= 0.096 '10'6/psi 0.7 '1\ =4.308

n =0.140 m =0.302

0.6 0(.0.042 c,.21 = -0.068 c,.41\ .1.023

0.5 CT71 = 2.712 C"",=4 .

0.4

0.3

0.2

Zielinski and Sadowski,

0.5 I I Eo =0.108 '10-' Ipsi

= 2.989

1973

o

cp, n =0.123 CT20 = '0.029

m =0.326 CT60 = 0.601 0.4 a =0.055

o

0.2 • • 10

t - t' in .days

o o

100

•

o

o

t' = 123 days

100

o

o

a

Fig. 32. - Fits of Tests of Temperature Effect on Creep by York. Kennedy and Perry (1970) [23]. Da Silveira and Florentino (1968) [67]. Nasser and Neville (1965) [68]. Nasser and Neville (1967) [69]. Seki and Kawasumi (1970) [70]. Zielinski and Sadowski (1973) [71]. CT and 1/ Eo both calculated with formula.

431

VOL. 11 - N° 66 - MATI:RIAUX ET CONSTRUCTIONS

'Vi Q.

ID .......

'0

c

1.2 Browne. 1967

t'= 7days lIEo= 0.102· 10-6/psi

1.0 ~=3.511 n =0.156 m =0307

0.8 0( = 0.060

0.6 o

o

0.2

1.0

0.8

0.6

0.4

10 100

t'= 180 days CT20= -0.027 CT40= 0.199 CTfI5= 0.673 CT93.5" 1.203

0

10

1000

0

100

t' = 28 doys 'CT2Q = -0.022 CTo4()= 0.159 CTf15 = 0.536 C193.5= 0.958

10

0

0

0

1000

100 1000

1'= 400 days CT2o=-0.031 CT40= O. 223

0

0 o c • • •

1'= 60 days CT2Q = - 0.024 CT40 =0.172 CTf15 =0.582 Gm3.5 = 1.040

10

~().~ c c

c c

100 1000

c c

t- t' in days

Fig. 33. - Fits of Tests of Temperature Effect on Creep by Browne (1967) [59]. CT and 1/ Eo both calculated with formula. Experimental datas are smoothed mean values.

Da Silveira and Florentino's Tests of Temperature Effect on Creep (1968) [67). - Prisms 20 x 20 x 60 cm, in copper jackets. Heat is assumed to be applied 3 days before loading. Water-cement-sand-gravel ratio 0.5: 1 : 2.35 : 3.84. Granite aggregate, modified portland cement, similar to ASTM type II. Cement content 314.6 kg/m" 8-day cube strength 297 kp/ cm2 (29. 1 N/ mm2).

Nasser and Neville's Tests of Temperature Effect on Creep (1965) [68]. - Cylinders 3 x 9 ~inch (76 x 235 mm), sealed in polypropylene jackets, stored from 24 hours onwards in a water bath at the desired temperature and loaded at age of 14 days. Water-cement ratio 0.6 and aggregate-cement ratio 7.15. Max. size of aggregate 3!4 inch (19 mm). Aggregate was a mixture of dolomite and hornblende. Cement type III (320 kg/m3). Strength 5,660 psi (39 N!mm') at 14 days measured on cylinders 3 x 9 i inch (76 x 235 mm). Stress! strength ratio 0.35.

Nasser and Neville's Tests of Temperature Effect on Creep (1967) [69]. - Cylinders 3 x 9 tinch (76 x 235 mm), stored in water at 70°F (21°C) up to 1 week prior to appli­cation of load. Concrete 1: 7.15 mix; water-cement ratio of 0.6. Max. size of dolomite and hornblende aggregate was 3/4 inch (19 mm), cement type III (320 kg/m3). Speci­mens loaded at age of 1 year and remained under water while loaded. Mean strength at the time of load application (determined on specimens of same size) = 7,250 psi (50 N/mm').

Browne's Tests of Temperature Effect on Creep (1967) [59]. - Cylinders 6 x 12 inch (152 x 305 mm), sealed at casting in 1/16 inch (1.6 mm) polypropylene jackets, cured at room temperature. Heat applied 1 day before loading. Water-cement-sand-gravel ratio 0.42: I : 1.45 : 2.95. Ordinary portland cement, crushed foraminiferal limestone, max. size 1.5 inch (38 mm). Average 6 inch (15.2 cm) cube strength = 7,250 psi (50 N/mm2).

432

Zielinski and Sadowski's Tests of Temperature Effect on Creep (1973) [71]. - Cylinders 160 x 480 mm within the first 70 days stored in atmosphere 100% relative humidity and temperature 20-23°C, then sealed with rubber coat. Specimens were heated at the age of 120 days and loaded three days later. Water-cement-aggregate ratio 0.456 : 1 : 4.154. Sand! cement-gravel/ cement ratio assumed to be 1.9: 2.254. Cement ordinary Portland Cement type I, 450 kg/m3, aggregate crushed basalt and river sand, max. size 20 mm. 120 day compressive cylinder (160 x 160 mm) strength 430 kg/cm2.

Seki and Kawasumi's Tests of Temperature Effect 01

Creep (1970) [70]. - Cylinders 150 x 600 mm were cas. into 0.2 mm copper jackets. Specimens loaded at room temperature (20°C) at the age of 28 and 96 days. The tempe­rature 40°C was applied at the age of 28 and 97 days and loaded at the age of 29 and 100 days. The temperature 70°C was applied at the age of 27 and 104 days and specimens loaded when they were 29 and 105 days old. Water-cement­sand-aggregate ratio 0.4: I: 1.761: 3.834. Normal Portland cement 343 kg!m', fine aggregate Fuji-Gawa river sand, coarse aggregate from the river Ara-Kawa. 28-day cylinder strength 445 kp/cm'.

Komendant, Polivka and Pirtz's Tests of Temperature Effect on Creep (1976) [72]. - Cylinders 6 x 16 inch (152 x 406 mm) sealed with butyl rubber against moisture loss and cured at 73°F (23°C) until five days prior to the age of loading. The specimens were then heated to test temperatures II 0 and 160°F (43 and 71°C) at a rate of 24°F / day (13. 3°C/ day) and remained for the duration of the creep test. Specimens were loaded at the age of 28, 90 and 270 days. Cement, Medusa type II. Mix A: water­cement-sand-gravel ratio 0.381: 1 : 1.734: 2.605; 28-uay cylinder strength 6,590 psi (45.4 N/mm2). Cement 706 Ibs/cy (419 kg/m'). Max size of aggregate 1.5 inch.

-l:>. w w

(/)

a. "-

'" , 0

C

<-

J

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.7

0.6

0.5

0.4

0.3

0.2

0.61-

0.51-

04r

Komendanl, Polivka, Pirlz, 1976

IlEa -0.101 ·1O-s/p.i

<#0, - 3.293

- 0.151

m - 0.303

a - 0.066

CU> - 0.00

Cn> - 0.162

Cn, -0.512

o a •

Komendonl, Pol ivka, Pirlz, 1976

I lEo ·0.101·10'6 /psi

<#0, ·3.293

·0.151

m ·0.303

a C n> • 0.00

C 70. ·0.186

C TTI ·0.587

Komendanl, Polivka, Pirlz, 1976

II Eo ·0.101·10'6 /psi

<#0, ·3.293

·0.151

m ·0.303

a ·0.066

Cn •• 0.00 a,[ <,. •• am Cn, ·0.685

0.2 0 0

8 !5

0.1 10

0.71- Komendanl, Polivka, Pirlz, 1976

I I Eo -0.101 ·10-6 /p.i

0.61- <1>, - 3.235

n - 0.147

m - 0.305 0.51- a ·0.065

Cu. ·0.00

04~ C T 4! ·0.153

CTTI ·0.483

a't I' = 28 days (mix A) 10.2 • ! .-.!-~--=-O a

0

""==bd. 0

0

.p09 0.7

0 Komendanl, Polivka, Pirlz, 1976

0 IlEa ·0.101·10-' Ip.i (1

/ a·r <#0, (1

·3.235

·0.147

0.5 m - 0.305

a ·0.065

0.41- C Ta • 0.00

C T4! -0.175

C TTl ·0.554

°T 0.2 a 0 0

• • 0 r-0.1

a

0 rf'l~ Komendanl, Polivka, Pirlz, 1976

0 a.~ a I I Eo .0.101·1O-'/psi 0

0 <#0, ·3.235

0.5 - 0.147

m - 0.305

041- a ·0.065

Cu •• 0.00

031-C 70. ·0.205

C TT , ·0.646

021 a

(7i,X,~,)"I ·0

0.1 100 1000

t - t' In days

I' =28days (mix8)

o 09

o

(mix B)

Fig, 34, -. Fits of Tests of Temperature Effect on Creep by Komendant, Polivka and Pirtz (1976) [72], CT and 1/ Eo both calculated with formula.

1000

!" :u m

e z -I

:-

~ Z C

~

VOL. 11 - N° 66 - MAT~RIAUX ET CONSTRUCTIONS

REFERENCES

~[59] BROWNE R. D. - Properties of concrete in reactor vessels. Proceedings, Conference on Prestressed Con­crete Pressure Vessels, Institution of Civil Engineers, London, England, group C, paper 13, 1967, pp. 11-31.

[60] BAzANT Z. P., Wu S. T. - Thermoviscoelasticity of aging concrete. Journal of the Engineering Mechanics Division, ASCE, Vol. 100, No. EM3, Proc. Paper 10621, June, 1974, pp. 575-597.

[61] HANNANT D. J. - Strain behaviour of concrete up to 95°C under compressive stresses. Group C, paper 17. Conference on Prestressed Concrete Pressure Vessels, Institution of Civil Engineers, London 1967, pp. 57-71.

[62] MARECHAL J. C. - Variations in the modulus of elasticity and Poisson's ratio with temperature. Paper SP34-27. Concrete for nuclear reactors, Vol. I, ACI Special Publication SP-34. American Concrete Institute, Detroit, Michigan, 1972, pp. 495-503.

[63] ARTHANARI S., Yu C. W. - Creep of concrete under uniaxial and biaxial stresses at elevated temperatures. Magazine of Concrete Research, Vol. 19, No. 60, September 1967, pp. 149-155.

[64] NISHIZAWA N., OKAMURA H. - Strength and inelastic properties of concrete at elevated temperature. Paper SP34-22. Concrete for nuclear reactors, Vol. I, ACI Special Publication SP-34 American Concrete Institute, Detroit, Michigan 1972, pp. 407-421. .

[65] ENGLAND G. L., Ross A. D. - Reinforced concrete under thermal gradients. Magazine of Concrete Research, Vol. 14, No. 40, March 1962, pp. 5-12.

Un modele de preVISion pratique des deformations du beton en fonction du temps. III. Fluage en sechage. -1£ modele pratique de determination du jluage et du retraitexpose dans les parties I et II de ce menwire est . a present applique au jluage en ambiance seche et a temperature constante. £augmentation du jluage due au sechage est reMe au retrait. On donne les formules pour determiner les parametres des materiaux a partir de la resistance du beton et de la composition du'melange, et on les verifie par des comparaisons nombreuses avec les resultats d'essai pub lies.

IV. Influence de la temperature sur Ie flUage de base. -Le developpement d'un modele pour Ie (luage de base

434

[66] JOHANSEN R, BEST C. H. - Creep of concrete with and without ice in the system. Bulletin RILEM, No. 16, September 1962, pp. 47-57.

[67] DA SILVEIRA A., FLORENTINoC. A. - Influence of temperature on the creep of mass concrete. Paper SP25-7. Temperature and concrete. ACI Publication SP-25. American Concrete In&titute, Detroit, Michigan, 1971, pp. 173-189.

[68] NASSER K. W., NEVILLE A. M. - Creep of concrete at elevated temperatures, Journal of the American Concrete Institute, Vol. 62, December 1965, pp. 1567-1579.

[69] NASSER K. W., 'NEVILLE A. M. - Creep of old conc"rete at normal and elevated temperatures, Journal of the American Concrete Institute, Vol. 64, February 1967, pp. 97-103.

[70] SEKI S., KAWASUMI M. - Creep of concrete at elevated tempera!ures. Paper SP34-32. Concrete for nuclear reactors, Vol. I, AC I Special, Publication SP-34, American Concrete Institute, Detroit', Michigan, 1972, pp. 591-638.

[71] ZIELINSKI J. L., SADOWSKI A. - The influence of moisture content on the creep of concrete at elevated temperatures, 2nd International Conference on Struc­tural Mechanics. in Reactor Technology, 1973, paper H6/3, pp. 1-8.

[72] KOMENDANT G. J., POLIVKA M., PIRTZ' D. - Study of concrete' properties for prestressed concrete reactor vessels, Final report-part II, Creep and strength cha­racteristics of concrete at elevated temperatures, Report No. UC SESM 76-3, Structures and Materials Research, Department of Civil Engineering, Report to General Atomic Company, San Diego, California Berkeley, California, April 1976.

qui est ['objet de la deuxieme partie de ce memo ire est suivi ici par un modele de determination du jluage a differentes temperatures maintenues constantes durant Ie phenomene. Ce modele qui preserve la loi de double puissance traduit deux efJets contraires de la tempera­ture : ['augmentation de la vitesse du jluage due a la chaleur et la diminution du jluage due a ['acceleration de l'hydratation par la chaleur. L'erude comprend la determination des parametres des materiaux a partir de la composition du melange et de nombreuses compa­raisons avec les resultats d'essai indiquent une bonne concordance.

To be continued by Parts Vand VI.