Magazine of Concrete Research, 2009, 61, No.

5, June, 379–386
doi: 10.1680/macr.2008.00092

Development of model parameters for early-age

properties and crack-width prediction of
slag concretes
T. Aly* and J. G. Sanjayan†

RMIT University; Monash University

A study to develop the parameters of the models for predicting the deformation characteristics of normal-strength
concrete incorporating slag-blended cements at early age is presented in this paper. By comparing with the previous
experimental results, it was found that the basic shrinkage and creep factor decreased significantly owing to the
expansion of slag concrete during the first week of moist curing. When utilising the developed models for estimating
the crack width, it was found that the initial crack width of concrete subjected to restraint drying shrinkage is
reduced if the slag content level increased up to 50 and 65% in the concrete mixture. Further, slag concrete tends
to have less crack width and lower number of cracks in the long term compared with that with no slag.

Introduction
mental effects of cracks are to increase the susceptibil-
The prediction models presented in the current litera- ity of reinforcement to localised corrosion. Also,
ture for shrinkage and creep may perform well for cracking makes the member more flexible, which leads
long-term behaviour but not satisfactorily for early to an increase in deflection under service loads. Cracks
age.1,2 Further, these models may not be applicable for form when the tensile stress in concrete exceeds its
concretes containing slag-blended cements. Previous re- tensile strength.4 Limiting the crack width is important
search work by Aly and Sanjayan3 showed that slag from the aesthetic point of view. There is no widely
concrete experienced less shrinkage and cracking ten- accepted model for estimating crack width and crack
dency if moist cured for 7 days compared with ordinary spacing. Various models in the literature have been
Portland cement (OPC) concrete. The physical and proposed by different researchers.5 The current study
chemical compositions of the slag and OPC used in the presents models of predicting the initial crack width at
previous work3 are also presented in this paper as seen early age for slag concretes cured for 1 day and 7 days.
in Table 1. The current paper presents a study for
developments of early-age empirical model parameters
for shrinkage and creep factor to predict the number
Research significance
of cracks and crack width in the long term for slag
concrete. Long-term durability of concrete is one of the major
When shrinkage is restrained, cracking of concrete concerns for engineers in designing reinforced concrete
may occur. Restrained shrinkage cracks can form structures. The current designs in the literature are
through the full depth of a member, resulting in an based on empirical formulae (e.g. a certain minimum
increase of permeability of concrete. The major detri- percentage reinforcement for shrinkage crack control).
These empirical methods have served well in the ma-
jority of cases. When the physical properties of con-
* Department of Civil, Environmental and Chemical Engineering, cretes are significantly different, however, such as in
RMIT University, Melbourne, Australia the case of using slag-blended cements in concrete,
† Department of Civil Engineering, Monash University, Clayton, VIC
these empirical models may not work satisfactorily in
3800, Australia
all conditions. Thus it would be useful to develop meth-
(MACR 800092) Paper received 4 May 2008; last revised 25 October ods based on fundamental models, namely models for
2008; accepted 28 October 2008 shrinkage and tensile creep behaviour of concrete at
379

www.concrete-research.com 1751-763X (Online) 0024-9831 (Print) # 2009 Thomas Telford Ltd

Aly and Sanjayan

Table 1. Property of cementitious materials

Constituent/property: %

SiO2 Al2 O3 Fe2 O3T MgO CaO Na2 O TiO2 K2 O MnO P2 O5 SO3 LOI F SG

OPC 19.90 4.70 3.38 1.30 63.93 0.17 0.245 0.446 0.079 0.063 2.54 2.97 360 3.15
Slag 32.5 13.00 0.22 5.47 42.10 0.21 1.080 0.250 5.470 bd 4.1 0.35 435 2.92

F, fineness (m2 /kg); SG, specific gravity; bd, below detection

early age, so that the design methods are more robust The drying shrinkage data obtained from the unrest-
and cater for a wider range of concretes than the rained shrinkage tests of slag concretes cured for 7 days
current methods. This research contributes to the in previous work3 were used to find functions that
development of such models in this paper. provide the best-fit estimation of drying shrinkage with
time. The shrinkage functions that provided the best fit
were obtained by modifying the parameters provided
Development of model parameters for by Gilbert7 for the curves presented in the code.2 The
early-age properties results presented in Figures 1 to 4 show the best fit
with the data of measured shrinkage for 0, 35, 50 and
Shrinkage model 65% slag mixes respectively compared with the model
For normal and high-strength concrete, a general for predicting the drying shrinkage. It is obvious that
model is proposed6,7 for estimating the total shrinkage this model used for predicting the drying shrinkage at
(endogenous + drying) as follows early age is overestimated for mixes incorporating 50
and 65% slag replacement level; however, it is under-

sh ¼
e:sh þ
d:sh (1)
estimated for 0% and 35% slag mixes. This is attribu-
where
e:sh is the endogenous shrinkage given by ted to the fact that this model does not account for the
expansions in slag concretes when moist cured for 7
¼

(1:0  e0 1 t0 )
:

e:sh e:sh (2)
⫺160

is the final endogenous shrinkage and is
where
e:sh
taken as follows
Shrinkage strain (⫻10⫺6)

⫺120

¼ (0:6 f 9  1:0) 3 50 3 106

e:sh (3)
c

where f c9 is the characteristic compressive strength of ⫺80

concrete in MPa; and the basic drying shrinkage
sh:b is
given by ⫺40
Measured shrinkage
Model⫺best fit

¼ (1:0  0:08 f 9 ) 3


sh:b c (4)sh:b Model⫺original parameters

accounts for the quality of concrete includ-
where
sh:b
0
7·0 7·2 7·4 7·6 7·8 8·0
ing the type and quantity of aggregates, cement type Age: days
and replacement level of admixtures. It may be taken in
the range 800 3 106 to 1000 3 106 depending on Figure 1. Measured and predicted shrinkage strain for 0%
the humidity and temperature environment.2 slag mix moist cured for 7 days
The drying shrinkage at time to (in days) after the
commencement of drying may be taken as follows ⫺160

sh ¼ k 1 k 4
sh:b (5)

Shrinkage strain (⫻10⫺6)

⫺120
where k1 is calculated as follows
Æ1 tdx ⫺80
k1 ¼ (6)
tdx þ 0:15th
where th is the hypothetical thickness of the structural ⫺40 Measured shrinkage
Model⫺best fit
member (in mm); td is time (in days) since the com-
Model⫺original parameters
mencement of drying and x is a constant value equal to 0
0.8. The parameter k4 depends on environmental hu- 7·0 7·2 7·4 7·6 7·8 8·0
midity and ranges from 0.5 to 0.7; and Æ1 is calculated Age: days

as follows
Figure 2. Measured and predicted shrinkage strain for 35%
:
Æ1 ¼ 0:8 þ 1:2e0 005 th (7) slag mix moist cured for 7 days
380 Magazine of Concrete Research, 2009, 61, No. 5
 Development of model parameters for early-age properties and crack-width prediction of slag concretes
⫺240
taining 50 and 65% slag content the shrinkage rate is
⫺200 reduced. Thus, the constant value (x) needs to be mod-
Shrinkage strain (⫻10⫺6)

ified to 1.35 instead of 0.8. These modifications need

⫺160 to be considered for estimating the drying shrinkage of
⫺120
concrete made with slag-blended cements at early ages.

⫺80
Creep factor model
Measured shrinkage A model for estimating the creep factor jcc is
⫺40 Model⫺best fit proposed2 on condition that the concrete stress is less
Model⫺original parameters than 50% of the characteristic strength; and the con-
0
7·0 7·5 8·0 8·5 9·0 9·5 10·0 10·5 crete is not subjected to long periods of temperature in
Age: days excess of 258C. If so, a 25% increase in jcc is recom-
Figure 3. Measured and predicted shrinkage strain for 50% mended to the following formula
slag mix moist cured for 7 days jcc ¼ k 2 k 3 jcc:b (8)
where jcc:b is the basic creep factor and is defined as
⫺300 the ratio of final creep strain to elastic strain for a
⫺250
specimen loaded at 28 days of age under a constant
Shrinkage strain (⫻10⫺6)

stress of 0:4 f c9 . If no measurements exist, the basic

⫺200 creep factor may be taken in the range 2.0–5.2 based
on the characteristic strength of concrete.
⫺150
The parameter k2 describes the development of creep
⫺100 with time and depends on the section geometry (the
Measured shrinkage
hypothetical thickness of the structural member, th (in
⫺50 Model⫺best fit
Model⫺original parameters
mm)), relative humidity, and duration of loading. This
0 parameter k2 is given in the charts.2 Gilbert7 fitted the
7·0 8·0 9·0 10·0 11·0 12·0 following formula to the charts as follows
Age: days
Æ2 t x
Figure 4. Measured and predicted shrinkage strain for 65% k2 ¼ (9)
tx þ 0:15th
slag mix moist cured for 7 days
where t is the time (in days) since first loading. The
parameter Æ2 is calculated as follows
days.3,8 Previous work showed that concretes made with :
Æ2 ¼ 1:0 þ 1:12e0 008 th (10)
slag-blended cements exhibited significant expansions
under moist conditions,8 and therefore the actual The parameter k3 depends on the age at first loading
shrinkage measurements should start from one day9 to occurrence,  (in days), and is given in the charts.2 To
account for the high expansions induced during the first predict higher creep for concrete loaded at early ages
7 days. the parameter k3 can be calculated as follows
The results presented in Table 2 show that the basic k 3 ¼ 1:97 þ 0:031 for 7 (days) <  < 28 (days)

and the parameter k depend on the slag
shrinkage
sh:b 1
replacement level in the mix. It is seen that the 0 and (11)
35% slag mixes have similar basic drying shrinkage. k 3 ¼ 1:97 þ 0:031 for 28 (days) <  < 365 (days)
However, increasing the slag content in the mix by 50 (12)
and 65% OPC replacement level decreased the basic k 3 ¼ 0 9 for  > 365 (days)
: (13)
shrinkage of the mix by 60 and 48%, respectively.
Further, the rate of shrinkage evolution in the predicted To account for the environment effect, an additional
model is governed by a constant value of 0.8 (the parameter k4 is introduced7 and Equation 8 is modified
power of the parameter t dx ). However, in concrete con- as follows

Table 2. Comparison of parameters of shrinkage prediction model for best fit

Property Equation No. Parameter Predicted model For best fit with measured data

0% 35% 50% 65%

Drying shrinkage 6 x 0.8 0.57 0.69 1.35 1.35

shb 900 1225 1225 485 640

Magazine of Concrete Research, 2009, 61, No. 5 381

Aly and Sanjayan

jcc ¼ k 2 k 3 k 4 k 5 jcc:b (14) 6 to 9. It can be seen that the model2 used for predict-
ing the creep factor at very early age is underestimated
where the parameter k5 accounts for the reduced influ- for 0% slag mix more than for 35% slag mix, as shown
ence on creep as the concrete strength increases and is in Figures 6 and 7. However, the model is overesti-
given by mated for 50 and 65% slag mixes, as shown in Figures
8 and 9. This is likely attributed to the delay in creep
k 5 ¼ (2  Æ3 )  0:02(1  Æ3 ) f c9
(15) factor evolution of slag concretes. The creep factor
for 50 (MPa) f c9 < 100 (MPa) started to develop at the age at which the concrete
develops tensile stress due to restrained drying shrink-
k 5 ¼ 1:0 for f c9 < 50 (MPa) (16) age (after the initial expansion of slag concrete was
0: 7 recovered).
Æ3 ¼ (17)
k 4 Æ2
6·0

However, the model to predict creep factor for the

normal and high-strength concrete is based on constant
load creep tests of concrete in compression not in 4·0

Creep factor
tension. To find whether the creep factor under con-
Measured creep factor
stant load in compression is similar to one in tension
Model⫺best fit
(if subject to restrained conditions), the measured creep 2·0
Model⫺original parameters
factor data3 presented in Figure 5 for slag concretes
cured for 7 days were compared with the predicted
values by the creep model.2,7 The following equations 0·0
were derived to calculate the creep factor jcc (ti ) based 7·0 7·2 7·4 7·6 7·8 8·0
on a step-by-step method10 to account for the increase Age: days
in tensile stress at each recovery cycle of shrinkage as
Figure 6. Measured and predicted creep factor for 0% slag
follows
mix moist cured for 7 days
jcc ð ti Þ ¼ jcc ð t i1 Þ þ ˜jcc ð ti Þ (18)
˜
c ð ti Þ 1·5
˜jcc ð ti Þ ¼ (19)

e ð ti1 Þ

where ˜jcc (t i ) is the increase in creep factor between 1·0

Creep factor

recovery cycles at time ti ; ˜
c (ti ) is the increase in

tensile creep strain and depends on the sustained stress
level between recovery cycles;
e (ti1 ) is the instanta- 0·5
Measured creep factor
neous elastic strain at time ti1 . Model⫺best fit
The results presented in Figure 5 show the measured Model⫺original parameters
creep factors for 0, 35, 50 and 65% slag mixes cured 0·0
for 7 days.3 It is obvious that the higher the slag 7·0 7·2 7·4 7·6 7·8 8·0
Age: days
content in the mix, the lower the creep factor of con-
crete.3 The curves of best fit are summarised in Figures Figure 7. Measured and predicted creep factor for 35% slag
mix moist cured for 7 days
5·0

0%
2·5
4·0

2·0
Creep factor

3·0
Creep factor

1·5
2·0 65%
1·0
35% 50%
1·0 Measured creep factor
0·5
Model⫺best fit
0·0 Model⫺original parameters
7 8 9 10 11 12 0·0
Age: days 7·0 7·5 8·0 8·5 9·0 9·5 10·0
Age: days
Figure 5. Measured creep factors for OPC/slag concretes
moist cured for 7 days (% next to each line indicates % slag Figure 8. Measured and predicted creep factor for 50% slag
level)3 mix moist cured for 7 days
382 Magazine of Concrete Research, 2009, 61, No. 5
 Development of model parameters for early-age properties and crack-width prediction of slag concretes
3·0
paper. The discussion is based on the work of
2·5 Gilbert10,16 that shows when the reinforced concrete
member begins to shrink, the tensile stress in the con-
2·0 crete increases with time and the reinforcing steel bar
Creep factor

1·5
experiences a compressive stress to satisfy equilibrium.
The restraining force (N) increases gradually until the
1·0 tensile stress exceeds the tensile strength of concrete
Measured creep factor and the initial crack would occur when N ¼ Ac ft . The
0·5 Model⫺best fit width of crack immediately after cracking (initial crack
Model⫺original parameters
0·0 width) is mainly attributable to the sum of elastic con-
7·0 8·0 9·0 10·0 11·0 12·0 crete strains that are being instantly relieved upon crack
Age: days
occurrence. After the formation of the first crack the
Figure 9. Measured and predicted shrinkage strain for 65% stress distribution within the member would change as
slag mix moist cured for 7 days shown in Figure 10. In the vicinity of initial crack, the
steel caries the entire force Ncr and the stress in the
concrete is zero. In the region adjacent to the crack
As seen in Table 3 the basic creep factor jcc:b and where the distance from the crack is less than the slip
the parameter k2 depend on the slag replacement level length so (concrete bond with reinforcement), the con-
in the mix. It is shown that the higher the slag content crete and steel stresses vary in such a parabolic shape.
in the mix, the lower the basic creep factor of the mix. In the region, beyond the slip length, the stresses in
The difference in the predicted and measured creep concrete,  c1 , and steel,  s1 , remain constant. By con-
factors is attributed to the fact that this property of sidering the basic requirements of equilibrium of forces
concrete is not similar under both compression and and compatibility of deformations, Gilbert10 developed
tension.11,12 In addition, the creep strain for constant
stress is different to that under variable restrained As ⫽ area of reinforcing steel
stress.13,14 It is concluded that the model for predicting
Ac ⫽ area of concrete
the creep factor of concrete needs to be modified to
include the effects of slag-blended cements on the N(t ) N(t )
shrinkage and creep factor prediction of concrete sub-
jected to tension at early age. L
(a)

Ncr Ncr
Crack width prediction w
L
The first and final crack width and spacing for con-
(b)
crete containing slag-blended cements have not been
verified experimentally but they are predicted as shown so so
σc1 σc1
in the following sections.
Region 1 Region 2 Region 1
First crack width
15 Average concrete stress after first crack
Previous studies showed that the drying of concrete
led to cracking (age between 40 and 46 h) when there
was full restraint to the shrinkage at an age of 24 h.
However, other studies3 proved experimentally that all σs1 so
w
so σs1
concretes exhibited different cracking times when
Steel stress after first crack
exposed to drying under fully restrained condition at
7-day age. The effect of curing length 1 day and 7 days Figure 10. Crack development owing to restrained drying
on the initial crack width owing to restrained drying shinkage: 16 (a) prior to first crack; (b) immediately after first
shrinkage of reinforced member was studied in this crack

Table 3. Comparison of parameters of creep factor prediction model for best fit

Property Equation No. Parameter Predicted model For best fit with measured data

0% 35% 50% 65%

Creep factor 9 x 0.8 0.25 0.80 0.80 1.25

jcc,b 3.4  30% 15.47 5.25 3.10 2.00

Magazine of Concrete Research, 2009, 61, No. 5 383

Aly and Sanjayan

the following expression for the initial crack width w did not change with time and the following parameters
by integrating the concrete strain over the length L of were estimated based on the length of the member, L,
the member as follows as 5000 mm; the cross-section area of the member is
 c1 1000 mm (width) 3 150 mm (height); reinforcement
w ¼
c L þ
sh L þ ð L  2=3so Þ (20) ratio, r, is 0.008; yield stress of steel is 400 MPa; bar
Ec
diameter is 12 mm.
The sum of the creep and shrinkage strain components The results of calculations presented in Table 4 show
is equal and opposite to the elastic strain component that all concretes cured for 7 days have relatively high-
(
c þ
sh ¼  f t =Ec ). Therefore, just before the first er crack width than those cured for 1 day. It is also seen
cracking, Equation 20 can be rewritten as follows that slag concretes have less crack width than those

 with no slag if cured for 1 day or 7 days. The crack
L 2so width of 50% slag mix was found to be similar to 65%
w ¼   f t þ  c1 1  (21)
Ec 3L slag mix cured for 1 day. However, after 7 days moist
curing, the data at failure for 65% slag mix concrete
where L is length of the member; Ec is the elastic
was not available since the restrained shrinkage test
modulus of concrete; ft is the direct tensile strength of
was ended after 4 days without failing the specimen.3
concrete at the first crack; and so, where ½so ¼ Æd b =r
Although the curing is always desirable to reduce
is the slip length.
shrinkage strain,18 it may not be favourable when deal-
Where Æ is a constant (equal to 0.08 according to
ing with restrained drying shrinkage.
Base and Murray17 and equal to 0.1 according to
Gilbert,10,16 db is the bar diameter, and r is the rein- Final crack spacing and crack width
forcement ratio As /Ac (area of steel divided by area of
After the formation of the first crack where the stress
concrete). Gilbert10,16 showed that the concrete and
is relieved, the concrete continues to shrink and the
steel stresses immediately after first cracking are
tensile stress increases with time. However, concrete
Ncr   s1 As Ncr ð1 þ C1 Þ bond with reinforcement restrains the shrinkage and a
 c1 ¼ ¼ ;
Ac Ac tensile stress builds up in the concrete over the slip
(22) length so : When the tensile stress exceeds the tensile
2so Ncr Ncr Ncr
 s1 ¼ ¼ C1 ; and  s2 ¼ strength of the concrete, a new crack develops and stress
3L  2so As As As relief occurs again. This process is repeated until the
concrete no longer shrinks and the crack pattern is estab-
where C1 ¼ 2so =(3L  2so ). If n is the modular ratio, lished. For more details, this process is well discussed
Es /Ec , the restraining force immediately after first by Gilbert.16 The derived expressions for the final aver-
cracking is as follows age crack spacing s in a fully restrained member, the
n r f t Ac final restraining force N(1), the final concrete and steel
N cr ¼ (23) stresses, and the final crack width w are as follows
C 1 þ n r ð1 þ C 1 Þ
2 s o ð 1 þ Þ
In this study, the above equations developed by s ¼ (24)
Gilbert10 were used to predict the first crack width in 3
slag concretes cured for 1 day and 7 days. The results where  is given by
of tensile stress of concrete at failure and the short- 
E

n
r  av þ
cs
term elastic modulus obtained based on the compres-  ¼
  e

E
þ f t (25)
sive strength values given in Table 4 were used to n r  av þ
cs e
predict the first crack width using Equation 21. In these
calculations, it was assumed that the member length
is the final shrinkage strain; E
is the final
where
sh e

Table 4. Predicted first crack width for OPC/slag concretes cured for 1 day and 7 days

Parameters 0% slag 35% slag 50% slag 65% slag

1 day 7 days 1 day 7 days 1 day 7 days 1 day 7 days

Cracking after drying 16.2 23.0 21.6 23.0 17.5 66.0 17.5 —
time (h) ft : MPa 1.74 2.32 1.46 1.84 0.77 1.20 0.67 —
Ec : MPa 13 077 27 172 11 198 22 684 7644 16 627 5470 —
Ncr : kN 219.8 203.9 188.3 167.3 103.3 115.0 92.2 —
c1 : MPa 1.5 1.4 1.3 1.2 0.7 0.8 0.6 —
s1 : MPa 3.7 7.7 3.2 6.3 1.8 4.3 1.6 —
s2 : MPa 183.2 194.2 156.9 159.4 86.1 109.5 76.8 —
w: mm 0.10 0.20 0.09 0.17 0.04 0.12 0.05 —

384 Magazine of Concrete Research, 2009, 61, No. 5

 Development of model parameters for early-age properties and crack-width prediction of slag concretes

effective modulus of the concrete to include the effect The 65% slag mix was found to have similar crack
of creep in the long term and is given by E
e ¼ width but lower number of cracks compared with 0%
Ec =(1 þ 
); 
is the final creep factor; n
is the slag mix. In general, it is found that concretes contain-
effective modular ratio (Es =E
e ); and  av is the average ing slag-blended cements have less crack width and
stress in the uncracked concrete and is assumed to be lower number of cracks in the long term.
( c1 þ f t )=2.
n
As 
E

N (1) ¼   av þ
cs e (26)
C2 Conclusions
where C2 is given by C2 ¼ 2so =(3s  2so ); The prediction models presented in the current litera-
ture for shrinkage and creep may perform well for

¼ N (1)
¼ 2 so
 s2 ;  s1 
; long-term behaviour but were found unsatisfactory for
As 3 s  2 so s2 early-age concrete containing various amounts of slag-
(27)

blended cements. This study showed that when slag-

¼ N (1)   s1 As
 c1
Ac blended cements are used in concrete, these predictive
" # models need to be modified to account for the expan-



 c1 2

sion of slag concrete when moist cured for 7 days. The
w ¼ 
s 

so þ
sh s (28)
Ee 3 followings conclusions have been drawn based on the
materials used in this study.
In this study, the final shrinkage and creep factor of (a) Increasing slag content in the mix within the range
slag concretes moist cured for 7 days were predicted 50–65% replacement level decreased the basic
after 1000 days by using the predictive shrinkage and shrinkage by an average of 54%.
creep factor models that developed at early age in the (b) The higher the slag content used in mix, the lower
sections on the shrinkage model and creep factor the basic creep factor.
model. The predicted final shrinkage and creep factor (c) The predicted basic creep factor in concrete con-
for each mix were used based on the correction for taining no slag cement is very low. This is likely
hypothetical thickness (th ¼ 130.5) for predicting the attributed to the fact that creep of concrete in
final crack spacing and width.16 The calculations sum- tension is higher than in compression.
marised in Table 5 are based on the assumption that the (d) By using the expressions developed by Gilbert
tensile strength and elastic modulus ( ft ¼ 2.8 MPa, model10,16 for predicting the crack width it was
Ec ¼ 39 000 MPa) are constant for all mixes. It is well found that the initial crack width of 50 and 65%
known that these parameters are proportional to the slag concretes mixes is lower than that of 0% slag
square root of the concrete compressive strength gain at early age. The crack width in 35% slag mix is
(ACT 209R-92). Previous work showed that concretes relatively high.
containing different slag contents exhibited almost (e) Concretes containing slag-blended cements have
similar magnitude of compressive strength after 28 days less crack width and lower number of cracks in the
of age.15 long term compared with that with no slag content.
It is seen that 50% slag mix has the lowest crack
width and number of cracks compared with all mixes.
A study by Li et al.19 using the ring test type showed
Acknowledgements
that the onset of first cracking took longer time, and
the ultimate crack width was lower for 50% slag mix The authors gratefully acknowledge the financial
when compared with 0% slag mix. Results from this support provided by the Independent Cement and Lime
study for 50% slag mix are consistent with the findings Pty Ltd (ICL) (Industry Partner) and the Australian
of Li et al.,19 although the technique used to test the Research Council (Linkage Project Grant No.
restrained shrinkage cracking behaviour is different. LP0349121) for this research project.

Table 5. Effect of slag content on final cracking spacing and crack width of concrete moist cured for 7 days

Mix Shrinkage Creep factor (r ¼ 0:007; d b ¼ 20 mm; f t ¼ 2:8 MPa; Ec ¼ 39 000 MPa)

sh (3106 ) j
cc (3106 ) N(1): kN s: mm c1 : MPa s2 : MPa s1 : MPa m: L/s w: mm

0% slag 610 5.06 360 1328 2.8 342.6 57.4 4 0.32

35% slag 714 7.14 361 1360 2.8 344.0 56.0 4 0.29
50% slag 354 3.46 396 3278 2.8 376.8 23.2 2 0.17
60% slag 452 2.91 369 1564 2.8 351.3 48.7 3 0.32

Magazine of Concrete Research, 2009, 61, No. 5 385

Aly and Sanjayan

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port 209R-92. Illinois at Urbana-Champaign, 2000.
2. Standards Australia. AS3600. Concrete Structures. Stan- 13. D’Ambrosia M. D. Early Age Tensile Creep and Shrinkage of
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curing. Materials and Structures Journal, 2008, 41, No. 4, 633– ment and modelling of concrete tensile creep and shrinkage at
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