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Creep, Shrinkage and Durability Mechanics of Concrete and
Concrete Structures Tanabe et al. (eds) 2009 Taylor & Francis
Group, London, ISBN 978-0-415-48508-1
Creep and shrinkage of self compacting concrete: Experimental
behaviorand numerical model
C. Mazzotti & C. CeccoliDISTARTStructural Engineering,
University of Bologna, Bologna, Italy
ABSTRACT: In the present paper, the results of an experimental
campaign concerning the rheologicalproperties of hardened
self-compacting concrete are presented. Four mixes of
self-compacting concrete havebeen cast, with different compressive
strength. For each mix, compressive strength and shrinkage
evolution withtime have been monitored along a period of time of
about one year. Creep tests have been performed at twodifferent
stress levels, 35% and 55% of compressive strength, and with two
different ages at loading (7 and 28days). Results have been
compared with Model Code 1990 provisions. Finally, a simplified non
linear creepmodel has been proposed which is able to properly take
into account the effect of remarkable strength increasewith time
observed in young self compacting concretes.
1 INTRODUCTION
The different methodology followed to obtain self-compacting
concrete (SCC) in different countries(Ouchi et al. 2003) and the
limited number of stud-ies concerning its long-term behaviour
(Persson 2001,2005, Poppe & De Shutter 2001, Seng & Shima
2005,Mazzotti et al. 2006) make still not clear if
currentInternational Standards apply successfully also forSCC (Klug
& Holschemaker 2003, Vidal et al. 2005,Landsberger &
F.-Gomez 2007). Moreover, it is noteven assessed if long-term
properties can be predictedwith reference to conventional
mechanical and phys-ical parameters only (like strength, w/c, . .
.) or theadoption of parameters concerning the mix design
isneeded.
In the present paper, the results of an experimen-tal campaign
concerning the rheological propertiesof hardened SCC are presented.
Four mixes of SCChave been cast, with different compressive
strengths(the main parameter adopted in European standards
toidentify concrete class), i.e. from C30/35 to C50/55.For each
mix, compressive strength and elastic mod-ulus evolution with time
have been monitored along aperiod of time of about one year (for
further details,see Mazzotti et al. 2008).
As for the creep tests, sustained stress levels (rang-ing from
35% to 70% of compressive strength at theage of loading) have been
applied to cover the rangeof application from cast-in-place to
prestressed struc-tures and to verify if conventional stress limits
forlinear viscoelasticity can still be applied to SCC ele-ments.
Two different ages at loading (7 and 28 days)have been considered.
Effect of sustained load and
aging conditions on compressive strength has beenalso
investigated.
Long-term experimental data exhibits significantdifferences with
Model Code 90 (MC90, CEB-FIP 1991) predictions. Hence, the study
confirms thatnot only a new calibration process of parameters
gov-erning creep laws is needed to cover the case of SCCbut,
probably, time evolution laws should be also mod-ified. For these
reasons, an improved version of apreviously proposed (Mazzotti et
al. 2006) non linearcreep model has been described, which is able
to prop-erly take into account the effect of remarkable
strengthincrease with time observed in young self
compactingconcretes.
2 MATERIAL PROPERTIES
In order to compare the rheological properties of SCCwith
different strengths, a series of mixes rangingfrom normal to
medium-high strength has been pre-pared. A detailed description of
mix compositionsadopted is reported in Table 1, whereas
water/cementand water/binder ratios and fresh-state properties
(flowcone, J-ring and V-Funnel tests) are reported inTables 2 and
3, respectively. SCCs have been castwith different types of cement,
same super plasti-cizer and viscosity-agent (coupled together) and
theyhave slightly different w/b ratio. Experimental testshave been
conducted on cylinders. After demolding,all specimens have been
cured at RH = 60% andT = 20C, except for mix 1 whose cylinders
havebeen stored at RH = 98% until one day prior to tests.
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Table 1. Mix composition of SCC mixes n. 14.
Component Type Unit Mix 1 Mix 2 Mix 3 Mix 4
Cement 32.5 II AL kN/m3 3.55 3.60 Cement 42.5 II AL kN/m3 4.40
Cement 52.5 I kN/m3 4.40Filler kN/m3 1.99 1.73 1.10 1.10Fine sand
04 mm kN/m3 9.68 8.63 8.26 8.26Coarse sand 812 mm kN/m3 4.70 5.50
5.20 5.20Gravel 1225 mm kN/m3 1.82 1.81 2.40 2.40Glenium Sky lt/m3
7.00 9.60 7.50 7.50H20 lt/m3 173 205 204 209
Table 2. Water/cement and water/binder ratio of mixes n.14.
Properties Mix 1 Mix 2 Mix 3 Mix 4
w/c 0.48 0.57 0.46 0.47w/b 0.31 0.39 0.37 0.38
Table 3. Fresh properties of SCC mixes n. 14.
Test Unit Mix 1 Mix 2 Mix 3 Mix 4
Slump flow cm 79 79 78 66V-funnel s 7.6 5.2 5.0J-ring cm 75.5
77.5 62
3 STRENGTH EVOLUTION WITH TIME
Strength evolution with time of all mixes hasbeen investigated
by compressive tests on 100 200 mm( h) cylinders at different aging
times.Experimental results on strength variation with timehave then
been compared with provisions by ModelCode 90 according to the
equation:
fc(t0) = fci exp[s(1
28/t)], (1)
where t0 is the age of concrete (days), s is a param-eter
depending on type of cement (s = 0.25 in thepresent case) and fci
is the 28-day cylindrical com-pressive strength (mean value
obtained from tests, i.e.fci = fcm (28)). Comparison reported in
Figures 1a,b, for mixes 1, 2 and 3, 4, respectively, shows thatthe
MC90 formulation, originally defined for standardconcretes, is able
to reproduce quite well the strengthincrease of all mixes up to 90
days; after that time, codeprovision suggests a negligible strength
increase (5%from 3 to 6 months), whereas some mixes (1 and 3)
Figure 1. Time variation of compressive cylindricalstrength of
(a) mixes n. 1, 2, and (b) mixes n. 3, 4 comparedwith provision by
CEB MC90.
have been subject to a strength increase significantlyhigher
(about 15%). This is probably due to the poz-zolanic activity of
the filler adopted in the mix. Eventhough the number of tests is
very limited, analogousresults can be found in the literature
(Persson 2001).Strength increase of SCC after 3 months can
modifyalso creep effects, as will be explained in the follow-ing.
Moreover, as far as strength increase with time ofmix 4 is
concerned, results follow more regularly codeprovisions and after
few months of aging, strengthincrease is significantly reduced;
early attainment ofhigh strength values is a well known consequence
ofthe adoption of 52.5 type cement. Results concern-ing elastic
modulus evolution with time of the sameconcretes can be found in
Mazzotti et al. (2008).
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4 SHRINKAGE AND CREEP DEFORMATION
Delayed deformations have been investigated withtests on
cylinders with 2 different sizes ( h), i.e.,98 200 mm and 122 250
mm, respectively. Foreach mixture, four cylinders (two for each
diameter)have been used for creep tests at two different ages
atloading and five ( h) 98 200 mm for shrinkagetests. Tests have
been conducted in a climate room at20C and 60% RH.
4.1 Experimental set-up and instrumentation
After a wet curing period of 2 days, creep specimenshave been
exposed to RH = 60% and loaded at age of7 and 28 days from casting,
for one year at least, byusing a steel loading frames. Two
different diametersof cylinders have been adopted in order to
prescribe,within the same steel frame, two different stress
lev-els: about 36% and 55% of compression strength atthe loading
time fcm(t0) for all mixes. The first stresslevel can be thought to
produce creep strains withinthe framework of linear
viscoelasticity, whereas in thesecond case a non linear behaviour
is expected. Twocylinders for each stress level have been used.
Creep strains have been measured by using couplesof longitudinal
electrical strain gauges; the mean strainvalue is recorded. One
specimen for each stress levelhas been instrumented with two
additional transversestrain gauges. Specimens subject to shrinkage
testshave been instrumented analogously; autogenous anddrying
shrinkage have been measured starting fromtwo days from casting for
all mixes but mix 2, whoseshrinkage has been measured starting only
after sevendays from casting. Autogenous contribution has
beenobtained by using specimens sealed with plastic sheets.
4.2 Test results
In order to reduce experimental data scattering, themean values
of the experimental tests obtained fromtwo specimens are reported
in the following.
Mean strains caused by longitudinal total shrinkagefrom all
mixes are reported in Figure 2. Mixes 3 and 4show remarkably higher
values of total shrinkage withrespect to mixes 1 and 2; this can be
due to the highercement content. The reduced shrinkage strain
values ofmix 2 (with respect to other mixes with smaller
watercontent) can be also explained by considering that thetest
started only at 7 days from casting. Moreover, aftermore than one
year from loading, the rate of increaseis almost negligible for mix
1, while mix 2 still showsa significant rate of increase.
With reference to creep tests, specific creep func-tion C = (v/)
for all mixes, loaded at 7-day agefrom casting at low and high
stress levels (0.35 and0.55 fcm), are reported in Figures 3a, b,
respectively;
Figure 3. Specific creep of all mixes at (a) low and (b)
highstress levels for 7 days age at loading.
Table 4. Compressive strength of all concrete mixes at thetime
of loading t0.
Compressive strength (MPa)
Mix 1 Mix 2 Mix 3 Mix 4
t0 = 7 days 32.20 26.50 33.50 49.63t0 = 28 days 42.62 34.34
40.05 57.85
in Table 4, the concrete strength for each mix at thetime of
loading is reported. Shrinkage strain has beensubtracted in order
to retain creep contribution only.After about one year of loading,
mixes 1 and 4 showsimilar creep strains at both stress levels; with
moredetails, mix 4 shows an higher rate of increase for thewhole
test duration and the change in convexity ofspecific creep curve is
detected only at a later stage
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00.01 0.1 1 10 100 1000
Time (days)
Shrin
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Mix 1Mix 2Mix 3Mix 4
(1)
(2)
(3)
(4)
Figure 2. Drying shrinkage strains from all mixes.
0
50
100
150
200
250
300
0.001 0.01 0.1 1 10 100 1000Time (days)
C(M
Pa-1 )
mix 1 - 0.36 fcmmix 2 - 0.36 fcmmix 3 - 0.36 fcmmix 4 - 0.36
fcm
(1)
(2)
(3)
(4)
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fcm
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Figure 4. Specific creep of all mixes at (a) low and (b)
highstress levels for 28 days age at loading.
with respect to mix 1. Differences between slopesof curves can
be explained considering the differentstrength evolution with time
of two different mixes(see Figure 1). Mix 1, in fact, is subject to
a moreprogressive strength increase, reducing delayed creepstrains
due to the constant load application causingconcrete internal
compaction (Bazant & Kim 1979);on the contrary, mix 4 attains
very rapidly its finalcompressive strength, reducing the beneficial
effect ofconcrete compaction. From an analytical point of view,this
behaviour can be predicted by considering the ratio(t) = 0/fcm(t)
as a reducing factor of the creepcompliance. Specific creep curve
for other mixes isqualitatively similar but with higher values,
probablydue to the type of cement and the higher w/c ratio.
In Figures 4a, b, similar behaviour can be observedfor specimens
loaded at an age of 28 days. In thiscase, non linear amplification
of creep function C athigher stress levels is more pronounced with
respectto younger concrete: for mix 1, non linear amplifica-tion is
about 1.3 for specimens loaded at 7 days and1.5 for specimens
loaded at 28 days; the smaller non-linear creep behaviour at high
stress levels for youngconcretes can be considered as an effect of
concretecompaction (Mazzotti et al. 2005). Non linear
creepamplification is smaller for mix 3 because the twoloading
levels (36% and 44%) are much closer thanfor other mixes.
As for the non-linear creep behaviour, Figures 5a, bshow creep
strain at increasing time under loading vsthe applied stress level
for mix 2 and 4, respectively;moreover, in these Figures, two
extrapolation lines are
Figure 5. Creep strain vs applied stress at different timesafter
initial loading for mixes (a) n. 2 and (b) n. 4, with 7-dayage at
loading.
also reported; they have an initial linear behaviourfollowed by
a non linear creep strain increase andcorrespond to very short (0.2
days) and medium(7 months) time intervals under loading. Starting
fromstress level /fcm of about 0.35 0.40 an apprecia-ble non linear
behaviour can be observed; consideringthe young age at loading of
two concretes under test(t0 = 7 days), this result is in agreement
with thewell recognized stress limit of linear viscoelasticity
forstandard concretes. Mix 4 shows higher non-linearity,probably
due to its higher compression strength.
4.3 Comparison with internationalrecommendation (MC90)
Experimental results have been compared with MC90predicting
curves, considering T = 20C, RH = 60%and 2A/u = 50. Ability of MC90
to describe timeevolution of delayed strains for SCC with
differentstrength is investigated.
In Figure 6a, total shrinkage (drying+autogenous)has been
compared with provisions by MC90 formixes 1 and 4, exhibiting the
highest and the smallestshrinkage values during long-term tests. A
remarkableunderestimation of strain prediction has been observedin
both cases (sh = 60 200%). The long-termrate of increase of curves
is also poorly described byMC90: it is overestimated for mix 1 and
underes-timated for mix 4. Finally, creep strains have beenalso
compared with MC90 predictions. Coefficient = (Cexp CMC90)/Cexp
after 300 days of loading for
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(4)
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(t0)/fc(t0)
Cre
ep s
trai
n (
)
(a)
(b)
t = 0.2 dayst = 1 dayst = 5 dayst = 15 dayst = 53 dayst = 228
days
t = 3 dayst = 7 dayst = 15 dayst = 55 dayst = 233 days
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MC90 model Mix 14- MC90 model Mix 4
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7 days28 days
mix 1mix 2
mix 3mix 4
0.600.55
0.00
0.10
0.20
0.30
0.40
0.50
0.600.58
0.470.44
0.32 0.32
0.27
(b)
Figure 6. Comparison with MC90 provisions (a) longi-tudinal
drying shrinkage of mixes 1 and 4 and (b) specificcreep
amplification factor for all mixes.
0
15
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90
105
Refer
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Dryin
g shri
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Autog
enou
s shri
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Creep
,7dd,0
.36fcm
Creep
,7dd,0
.55fcm
Creep
,28dd
,0.36
fcm
Creep
,28dd
,0.55
fcm
Mix 1Mix 4
Figure 7. Strength variation due to aging and load
condi-tions.
all mixes has been reported in Figure 6b. A
systematicunderestimation of creep strains (about 3060%)givenby the
code provisionwith respect to experimental datacan be observed both
at 7- and 28-day age at loading.
4.4 Effect of aging and sustained load on strength
At the end of creep and shrinkage tests, the strengthof all
specimens under failure loading from mixes 1and 4 has been obtained
in order to evaluate the effectof sustained loading and of
different aging condi-tions (drying or sealed specimens) on the
compressive
strength of different SCCs. Figure 7 shows the com-parison
between compression strengths of specimenssubject to different
loading and aging conditions,expressed as a percentage of results
obtained understandard wet curing (T = 20, RH = 98%), afterabout
400 days from casting.
5 A SIMPLIFIED NON-LINEAR MODEL
The experimental results showed that in a number ofcases
concrete strength increase continues also afterseveral months (see
Figs. 1a, b); this is particularlytrue if reactive o partially
reactive filler has been used.Moreover, creep strain strongly
depends on appliedstress level /fcm(t), so that an appreciable
variationwith timeof concrete strength can substantiallymodifycreep
strain rate.
Furthermore, instantaneous stress-strain behaviourobserved
during the loading phases of creep testsshowed an appreciable non
linear behaviour also whenthe medium stress level is considered
(0.30 to 0.40of fcm).
In order to take into account all these experimentalfindings and
to describe the delayed behaviour alsofor medium-high stress
levels, a simplified non lin-ear creep model has been developed.
The analyticalformulation is based on the standardMC90 creep
com-pliance law, extended in the non linear range followingthe non
linear creep amplification function proposedby Bazant &
Prasannan (1989):
C(t, t0) = (t, t0)Ec,28
F[(t)]. (2)
Furthermore, the creep coefficient has been alsomodified in
order to take the mix-design parametersinto account, so obtaining
the following expression:
(t, t0) = RH (fcm) (t0) mix (t t0). (3)The first two functions
in Eq. (3) are the same
appearing in the MC90, while the other functionshave been
modified or introduced according to thefollowing expressions:
(t0) = 10, 1 + (t0) , (4)
c(t t0) =[
(t t0)H + (t t0)
]1c/p, (5)
with fcm mean compressive strength, t0 age at load-ing and H
function of relative humidity (the readeris addressed to MC90 for
further details). Coeffi-cients and 1 must be calibrated while c/p
is the
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cement/powder ratio. The new term mix is defined asa function of
mix parameters:
mix = Km[( c
G
)2 (c
p
)3]4, (6)
where c/G is the ratio between cement and aggregates(sand,
gravel, . . .) and Km, 2, 3, 4 are the param-eters to be
calibrated. Finally, the non linear creepamplification function can
be defined as:
F[(t)] = 1 + 2 s (t, t0)5
1 , (7)
where 1 and 2 and 5 are additional parameters tobe obtained from
a least square minimization proce-dure starting from experimental
data; moreover, thestress function s(t, t0) is the actual
stress/strength ratio,being:
s (t, t0) = (t0)fcm (t)
, (8)
in the case of constant applied load. In Eq. (7), numer-ator and
denominator indicate the effect of sustainedload and the effect of
a damage level due to instan-taneous loading. If 1 < 1, Eq. (7)
shows that, forlow load levels, F[(t)] may be smaller than
one.Creep strain obtained from Eq. (2) is then smallerthan
predicted by linear theory excluding the effect ofconcrete
compaction. The law fcm(t) representing theevolution with time of
compression strength, reportedin Figure 1, has been defined by
modifying MC90proposal according to expression:
fcm(t) = f c,28 exp{s[1 (28/t)n]}, (9)
where parameters s and n have been specifically cali-brated for
each SCC concrete mix by using experimen-tal results previously
described (see Fig. 1). Accordingto the available data, parameters
s and n range from0.2 and 0.6, and 0.280.35, respectively. The
adoptionof function s(t, t0) allows for variable rate of increaseof
mechanical properties be taken into account, par-ticularly
important for concretes loaded at early ages.Finally, the non
linear behaviour during the load appli-cation has been introduced
in Eq. (7) according to theconventional scalar damage index = 1
E/E0,where E is the secant stiffness at the end of loadingand E0 is
the initial tangent stiffness. Usually dam-age index is about
0.100.15 or 0.220.35 for low(0.35 fcm(t)) or medium (0.55 fcm(t))
applied stresslevels, respectively.
From best fitting of experimental results obtainedat different
sustained stress levels and with specimens
Table 5. Values of the parameters of the proposed non
linearcreep model obtained from best fitting of experimental
data.
1 2 Km 1 2 3 4 5
0.05 0.90 1.80 13 2.2 1.28 0.55 1.28 2.10
0
20
40
60
80
100
120
140
160
180
200
0.000 1 0.00 1 0.0 1 0.1 1 10 100 1000
Time (days)
C (
MP
a-1 )
(a)Experimental- 0.55 fcm
Experimental- 0.36 fcm
NL model - 0.55 fcm
NL model - 0.36 fcm
0
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150
200
250
300
350
0 50 100 150 200 250 300 350
C (MPa ) Model predictions-1
C (M
Pa-1
) E
xper
imen
tal d
ata
(b)
Figure 8. (a) Comparison between experimental specificcreep and
predictions by the proposed non linear model fordifferent stress
levels (0.36 and 0.55 fcm); (b) experimental vsnumerical specific
creep coefficient at different time underloading for all considered
specimens.
from all the different batches (mixes 1 to 4) the valuesreported
in Table 5 are obtained.
Hence, being 1 < 1, for low to medium stresslevels Eqs. (6,
7) predict concrete compaction.
Figure 8a shows the comparison between specificcreep function
obtained from experimental results atmedium and medium-high stress
levels (0.36 and 0.55of f c mix 2 specimens) and numerical
predictionfrom Eq. (2); good agreement can be observed both interms
of qualitative behavior and quantitative values.Not only creep
values, but also the slope of curves after400 days of loading are
well predicted. Hence, the nonlinear model is expected to be able
to correctly predictcreep strain also for longer times. Finally, in
Figure 8b,creep strain experimental values of all
consideredspecimens after different times under constant loading(1,
10, 100 and at the end of test) are plotted versus thecorresponding
numerical predictions given by Eq. (2).
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Very good prediction capability can be observed bothat medium
and medium-high stress level.
ACKNOWLEDGEMENTS
The authors would like to thank SAPABA and BASFfor providing
materials for tests. The financial sup-ports of (italian) MIUR
(PRIN 2006 Grant: Structuralapplication of self compacting
concrete) is gratefullyacknowledged.
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2009 Taylor & Francis Group, London, UK
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Chapter 88: Creep and shrinkage of self compacting concrete:
Experimental behavior and numerical model1 INTRODUCTION2 MATERIAL
PROPERTIES3 STRENGTH EVOLUTION WITH TIME4 SHRINKAGE AND CREEP
DEFORMATION4.1 Experimental set-up and instrumentation4.2 Test
results4.3 Comparison with international recommendation (MC90)4.4
Effect of aging and sustained load on strength
5 A SIMPLIFIED NON-LINEAR MODELACKNOWLEDGEMENTSREFERENCES
