Aci sp-227-2005
Aci sp-227-2005
Aci sp-227-2005
Editors
N.J. Gardner
Jason Weiss American Concrete Institute®
Advancing concrete knowledge
SP-227
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The Institute is not responsible for the statements or opinions expressed in its publications.
Institute publications are not able to, nor intended to, supplant individual training,
responsibility, or judgment of the user, or the supplier, of the information presented.
The papers in this volume have been reviewed under Institute publication procedures by
individuals expert in the subject areas of the papers.
Copyright © 2005
AMERICAN CONCRETE INSTITUTE
P.O. Box 9094
Farmington Hills, Michigan 48333-9094
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Why should you be interested in the shrinkage and creep of concrete? To put this
question into perspective, the load induced elastic (immediate) strains in concrete are of
the order of 300 microstrain, depending upon stress level. The ultimate drying shrinkage
can range from 400 xI 0-6 to 900 x 10-6. The creep strain can be 25% to 70% of the
immediate strain after 24 hours and may be several multiples of the immediate strain after
several years, depending on the relative humidity. If concrete is restrained against
shrinkage it can crack.
Structural engineers are concerned with the consequences of shrinkage, creep and
cracking on the serviceability and durability of their structures. Creep increases
deflections, reduces prestress in prestressed concrete elements, and causes
redistribution of internal force resultants in redundant structures. Shrinkage can cause
warping of slabs on grade due to differential drying and increased deflections of non-
symmetrically reinforced concrete elements. Materials scientists are concerned with
understanding the basic phenomena and assessing new materials and the effects of
admixtures on the mechanical behavior of concrete.
Concrete is an age stiffening material that has little tensile strength, shrinks, and exhibits
creep in sealed conditions and additional drying creep in drying environments.
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Predicting the amount of shrinkage and deflection that may occur is not easy and is
especially complicated in concrete that contains supplementary materials, chemical
admixtures, and lightweight aggregates. Supplementary cementing materials and waste
products are being used in increasing volumes in response to environmental concerns.
Admixtures have been developed to modify the behavior of fresh and hardened concrete.
Self consolidating concrete is being used in more applications. A recent development is
the marketing of shrinkage reducing admixtures.
This volume contains papers presented during four sessions sponsored by ACI
Committee 209, Creep and Shrinkage in Concrete, and ACI Committee 231, Properties of
Concrete at Early Ages, held at the ACI Spring 2005 Convention. The subjects
addressed by the authors are diverse and cover many aspects of shrinkage and creep.
Some papers pay special attention to the development, use, and evaluation of models to
predict shrinkage, creep, and deflection, while other papers consider the behavior of
early age concretes that are restrained from shrinking, resulting in the development of
residual stresses and cracking.
Papers are presented to evaluate models for predicting shrinkage and creep, which is
especially crucial asACI Committee 209 attempts to refine the models that wiii are
presented in the ACI Manual of Concrete Practice. Several papers provide a field
assessment of creep and shrinkage in concrete structures, thereby providing an
explanation of how field data should be collected and how this data can be used to refine
predictive models. Other papers deal with an improved understanding of early-age
tensile stress development, including demonstrating the measurement of creep and
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stress development. One paper presents experimental results to quantify differential
drying and thermal deflections in slabs. This volume also recognizes that modern
concretes are now no longer a simple mixture of water, cement, and aggregate. This
volume discusses specific aspects of how the shrinkage of these modern concretes may
differ from concrete made using conventional materials. Specifically, several papers deal
with the shrinkage and curing of concrete containing supplementary cementing materials,
which is especially important as the use of these materials is rapidly rising. The
shrinkage and creep behaviour of high-strength, lightweight concrete is also evaluated
and compared to existing models. One paper assesses the cracking behavior of self-
consolidating concrete, a rapidly emerging material that is often suspected to be
sensitive to shrinkage related concerns due to the higher paste volume that may exist in
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these mixtures. It is shown that self-consolidating concretes can be made to be resistant
to cracking. Finally, this volume describes a study that is focused on the development of
an approach to describe the shrinkage and early age stress development in concrete
containing shrinkage reducing admixtures.
This volume includes significant contributions by many leading research and practicing
engineers in the field of shrinkage and creep. The descriptions of field problems and the
assessment of the accuracy of predictive models may assist practicing engineers. For
researchers, the contents of this volume should be useful in the development and
evaluation of future models and laboratory measurements. Finally, it should be noted that
many people have contributed to the successful development of these proceedings, and
the editors, and authors, thank all of the anonymous reviewers who assisted in reviewing
the papers.
Co-Editors
N.J. Gardner
Jason Weiss
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TABLE OF CONTENTS
SP-227-2: AS3600 Creep and Shrinkage Models for Normal and High Strength
Concrete .............................................................................................................................. 21
by R. I. Gilbert
SP-227-7: Shrinkage and Creep Predictions Evaluated using 10-year Monitoring of the
North Halawa Valley Viaduct ............................................................................................ 143
by I. N. Robertson and X. Li
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SP-227-12: Effect of Modulus of Elasticity on Creep Prediction of High Strength
Concrete Containing Pozzolans ...................................................................................... 261
by N. Suksawang and H. H. Nassif
SP-227-17: Modeling Early Age Tension Creep and Shrinkage of Concrete ............. 349
by M.D. D'Ambrosia and D. A. Lange
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SP-227-1
by S. J. Alexander
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1
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2 Alexander
ACI member Stuart Alexander is UK-based Group Technical Coordinator for world-wide
engineering consultancy WSP Group. This involves publishing material on the intranet-
based technical library, preparing and delivering seminars, and giving expert advice. He
is also a regular contributor to technical journals, particularly on movements in building
structures.
INTRODUCTION
Concrete contracts and shrinks. The main effects to be considered in design are
early age contraction, temperature drop and long-term drying shrinkage. Restraint arises
in a number of ways. Embedded reinforcement causes deflection of slabs and beams and
contributes to shortening of columns and walls. Casting concrete against a previous pour
or as an overlay on top of an older substrate induces tensile stresses that can cause
cracking. So do metal decking and supporting beams in steel-concrete composite
construction. Similarly, external restraint from rigid elements such as in-plane walls, piles
and pile caps, and even friction from the underlying soil, can cause cracking. Shrinkage is
also significant in concrete roads and industrial ground floors, but the paper is limited to
typical structural elements in buildings.
The paper considers how to quantify these effects, and makes recommendations
for managing them.
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Alleviation by creep
Some alleviation of sustained tensile stresses, that is those arising from early age
contractions and long-term shrinkage but only seasonal temperature, is provided by
creep. Altoubat and Lange found that early age contractions were reduced very rapidly by
as much as 50%. Interestingly, the same reduction is included in BS 8007 (2) where it is
explained as a 'restraint factor'.
The figure shows that the effect is hardly significant up to one year, although ultimately
the reduction is about one-third.
Note that these reductions apply to the tensile stress in the concrete. Thus if it is
cracked the initial stress will be the stress at which it cracked and the reduction should be
applied to that stress.
where m is the modular ratio (= £ 5 I Ec) and Pn is the ratio of reinforcement area to
concrete area.
Once again, the strain &, in the reinforcement is used to define the force, and the
stress in the concrete is calculated by the conventional formula FIA +My!I. The resulting
strain at the level of the reinforcement is equated to &cs - &,, giving the uncracked
curvature as:
where S, is the net first moment of area of the reinforcement about the neutral axis of
the concrete section (ie deducting S of any compression reinforcement), Ic is the
second moment of area of the concrete section, and lg is the second moment of area
of the gross section, ie including the reinforcement multiplied by (m-1).
This differs from the British code of practice BS 8110-2 (5) in that the second
term in parentheses is excluded and the points about calculating v at 150 days and
deducting the S of compression reinforcement are not made. More importantly, both
BS 811 0-2 and the forthcoming Eurocode EN 1992-1-1 (6) state that the cracked section
properties should be used if the section is cracked under load. This needs further
consideration.
At a crack, the concrete below the neutral axis cannot transmit shrinkage strain,
and it can be shown that the fully cracked curvature is
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(4)
where Ash= 0.7 p 113 for p' = 0 (modified for p' > 0). The curvature IS the term in
parentheses.
(5)
and plotted in Figure 5 against values of Pd = I 00 As I b d. Where a method did not lend
itself to this formula directly, values were derived from the model of a 300 mm (12 in)
thick solid slab, taking d = 0.9 h and m = I7 .5. The tension reinforcement is assumed to
be the amount required for ultimate load, ie stressed to 300 MPa [I 05 ksiJ under service
load.
It can be seen that the ACI method lies 25-30% of the way between kun and kcr
while the BS and EN cracked methods lie 75-80% of the way between kun and kcr.
although this would effectively reduce to 65-70 % when used with the incorrect
deflection coefficient O.I04 (see below). Examination of figure 4 suggests that the ACI
method is realistic, and that the UK and EN methods significantly over-estimate
shrinkage deflection.
Compression reinforcement As' has been taken as zero, but similar graphs can be
produced incorporating different values of As'. Compression reinforcement is very
effective in reducing shrinkage curvature. By ACI 435R-95, providing 0.25 % additional
compression reinforcement in a section where As,req = 0.75% reduces the curvature by
29 % while adding it to the tension reinforcement increases it by I 0 %.
The 'locked-in' tensile stress at the extreme fibre in the uncracked zone from
restrained shrinkage is
using the same Eerr as used to calculate K. This stress can be significant after some time
and appears to be overlooked in codes of practice when ascertaining whether the section
is cracked under load.
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(7)
The coefficient K for shrinkage is 0.125 for a span, 0.5 for a cantilever. If the curvature
reverses over one or both supports, the coefficient is reduced by the multiplier 1 - {J/10
where fJ is the ratio (KA + Ka) I Kc in which KA, Ka and Kc are the curvatures at left
support, right support and mid-span respectively.
Confusion arises as both BS 8110-2 and EN 1992-1-1 (but not ACI) state that
the shrinkage curvature should be added to the curvature from load. This means that the
coefficient K for a simply supported span is taken as 0.1 04, not 0.125. For a cantilever the
difference is even more marked, correctly 0.5 not 0.25. In this paper it is assumed that the
various methods are all aiming to give the actual shrinkage curvature; incorporating this
curvature into the load calculation will therefore reduce the shrinkage deflection by
around 17% in a span and by 50% in a cantilever.
supporting the approach in ACI-318 (8) of including it in the additional deflection from
creep.
Casting an insitu concrete overlay onto a precast concrete substrate or base unit
is a common way of forming a homogeneous slab. However, the differential between the
contraction of the overlay and the lesser or even zero contraction of the substrate
produces internal stresses which lead to shortening and deflection of the composite unit,
and sometimes to cracking in the overlay. The same theory can be applied when the base
unit is prestressed or when it is a steel section (see below).
Consider an overlay cast onto a base section, and firstly allow the contraction of
the overlay to take place freely, as if the interface is greased. Then apply a tensile force to
the overlay with an equal and opposite compressive force on the base so that the relative
movement at the interface is eliminated (Figure 5). The force acts at an eccentricity e to
the centroid of the overlay to equalize the curvature in the overlay with that in the base.
By defining the strain in the overlay as s,, the force F = s, A. E•. Applying the
equal and opposite force to the base produces a strain at the level of the centroid of the
overlay
&n -lj. = F [l!EtAb + z(z-e)/E.,Ib] (8)
In this, suffixes a and b refer to the overlay and the base respectively. A and I are
derived from the concrete section including the reinforcement multiplied by the modular
ratio m. Reinforced concrete is generally assumed cracked below the neutral axis,
prestressed sections uncracked throughout. z is the lever arm between the centroid of the
overlay and the centroid of the base. The duration is accounted for by using creep-
modified values of E.
(10)
whence
e = z I (1 + Et/JEJ.) (11)
overlay and the base in the time period in question (see below). In many cases &b can be
taken as zero, including all concrete (including prestressed) over about one year old.
Conversely, if the base is relatively young and the overlay thin (so that early thermal
contraction is minimal), &a and &b will rapidly converge so that lD can be taken as zero, ie
the differential contraction is not significant.
The expression for F can be clarified by writing Et/JE..Aa =me MAa = l and
MAb = r2; q is a measure of the influence of the overlay on the base and r is the radius of
gyration of the base. Then
(13)
The force F is applied as an external force to the base section (not to the
composite section), enabling any property to be calculated; most important will usually
be the curvature from which the deflection is then calculated. The tensile stresses induced
may also be significant.
The method can be used over any period of time. For instance, the effects of
early age contraction are virtually immediate, so that short-term values would be used to
give the immediate deflection. Long-term values can be used to give the long-term effect,
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For thin overlays in which cracking would be visible and undesirable, it could be
controlled with reinforcement. Where the substrate is less than about 4-6 months old and
is expected to be above 15 C for the first month, it will probably be enough to provide
Pimm· In other cases, it will be advisable to provide Pmat (p;mm and Pmat are defined below).
Some assumptions need to be clarified. The first is that because the metal
decking is bonded continuously to the concrete, it can be treated in the same way as
embedded reinforcement. And because the slab is attached to the steel beam which
forces it to contract linearly it does not matter if the decking - or the reinforcement - is
not concentric in the section. For typical slab profiles with steel decking 0.9-1.2 mm
[0.035-0.047 in] thick and light fabric reinforcement, Po ranges from 1.0 to 1.4 %, ie
higher than is normal in conventional reinforced concrete slabs. Using the typical value
of the modular ratio m of 17.5 shows that the effect of the restraint is a factor of 0.80-
0.85.
The force F is applied as an external force to the steel beam (not to the
composite section) enabling the curvature and thence the deflection to be calculated. The
curvature Kis given by MIEI, so here
(14)
The principal current UK guide is the code of practice for design of composite
beams BS 5950-3-1 (9). However, shrinkage of the concrete slab is not mentioned as a
contribution to deflection. BS 5950-3-1 will be supplanted by EN 1994-1-1 ( 10),
currently available in draft. This states that "calculation of stresses and deformations at
the serviceability limit state shall take into account the effects of [inter alia] creep and
shrinkage of concrete", and further that "the effect of curvature due to shrinkage of
concrete should be included when the ratio of span to overall depth of the beam exceeds
20 and the predicted free shrinkage strain of the concrete exceeds 400 x 1o-6"
(presumably not when below these limits).
The author has carried out calculations for typical arrangements which show that
the shrinkage deflection is significant but that there is relatively little variation between
widely different steel beams; all approach span/750. A simple rule would therefore be to
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Tension is induced in the slab in three ways. First is the internal restraint of the
reinforcement and the metal deck. Taking typical values of l'cs = 400 J.lE, Eb = 200 GPa
(29 000 ksi) and m = 17.5 gives fctt = 0. 7 MPa (1 00 psi) for p = 1.0% and 0.9 MPa
(130 psi) for p = 1.4 %.
Second is the restraint of the steel beam itself. This produces a tensile stress
(15)
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The term (? + i) I l varies from about 3 for a heavy beam to as much as 15 for
a light one. Taking typical values of &cr = 325 J.lE and Eb = 11 GPa (1670 ksi) gives
fca = 0.25-0.9 MPa (35-130 psi).
Third is the restraint of the surrounding structure. This will usually be at least
0.25 MPa (35 psi).
This suggests that the resulting tensile stress will be at least 1.2 MPa (175 psi)
and could be over 2.0 MPa (290 psi). The tensile strength of concrete under sustained
loading is probably in the range 1.5-2.1 MPa (220-300 psi) for the grades of concrete
normally used in composite construction. It is clear that the possibility of the concrete
cracking is very real and should be considered, particularly where composite slabs are to
be left exposed to view. This could be controlled by providing a reinforcement content of
Prnat· It might be thought that the metal deck would perform this function, at least at right
angles to the corrugations, but evidence from sites suggests otherwise.
EXTERNAL RESTRAINT
Controlled cracks
Before showing how this understanding can be used to determine the amount of
reinforcement to be provided, it is important to consider the criteria to be applied to
cracking in these circumstances. A crack which is not controlled has an unlimited width,
and will therefore be unsightly at best and will leak if water is present. The target should
therefore be that uncontrolled cracks are unlikely to occur. A reasonable interpretation of
this would be to limit the probability of an uncontrolled crack occurring to 5 %or 1 in 20.
This would require the upper characteristic axial tensile strength.fctm.o. 95 of concrete to be
used.
In order to maintain the 5% probability, .fctm.o.95 should be used with the mean
strength of the reinforcement. US deformed high yield steel currently has design strength
414 MPa (60 000 psi) and mean yield strength 490 MPa (71 000 psi). When EN 1992-1-1
comes into use, the design strength is expected to be 435 MPa (63 000 psi) and the mean
to be at least 550 MPa (80 000 psi).
(16)
(17)
The second term in {17) is quite small and is neglected at this point, although a
correction for it is applied later. Putting Fs;::: Fe gives:
(18)
wherefct is the direct tensile strength of the immature concrete, usually taken at the age of
three days as 1.6 MPa (230 psi) for grade 28135 (4000 psi) concrete. Hughes (11)
explains that fc 1 includes a hidden partial safety factor for materials of 1.1, and quotes a
more general value fc 1 = 0.12 ifcu)0·7 , where feu is the 28-day cube strength. With /y =
460 MPa (66 700 psi), Pimm = 1.6 I 460 = 0.35 %, the figure which has been familiar to
British engineers for some years.
Three factors need to be taken into account at this point. First is the increase in
Fe from the second term in ( 17); with the minimum percentages recommended here, this
requires a multiplier of around 1.06. The other two are the variation in tensile strength at
a given compressive strength and the variation of compressive strength. EN 1992-1-1
quotes the upper characteristic tensile strength of concrete as 30 % greater than the mean
fctm· The average concrete strength is usually taken as 8110 MPa higher than the specified
minimum, and the variation is typically 20 %. Combining these two variations by the
root-sum-of-squares rule gives a multiplier of 1.36. Multiplying this by 1.06 gives 1.44.
Combined with the US ratio of design to mean for reinforcement of 4141490 explained
above, this results in:
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Pimm = 1.22 ifct.imm I /sd) (20)
wherefct.imm = 0.12 <feu+ 10)0·7• For use with EN 1992-1-1, 1.22 is replaced by 1.14.
Values of!ct,imm and Pimm for a range of concrete strengths are shown in Table 1.
It can be seen that using either ACI or EN requires more than 0.35 % reinforcement for
all likely concrete grades.
Mature concrete
BS 8007 and ACI 350 (12) cannot be relied on for designing basements to be
watertight. They are written for reservoirs, ie concrete tanks which in service will be full
of water and usually embedded in soil, often with a covering of soil on the roof. In these
conditions, shrinkage is minimal and temperature variations small. BS 8007 assumes that
if early age contractions are controlled, subsequent movements will be insignificant, or at
least less than the reduction from creep (although this is not stated).
This results in the minimum percentages in the sixth and seventh rows of Table
1, ie 0.67% rising to 0.80% for concrete grades of 28135 and 35145 MPa (4000 and
51 00 psi) respectively. These can be compared to the minimum in ACI 350 of 0.50 % for
lengths over 12m [40ft] between joints or without joints. However, ACI 224R-Ol (14)
(clause 3.5.2) states "To control cracks to a more acceptable level, the percentage
requirement needs to exceed about 0.60 %".
In the UK, comparisons can be made with BS 811 0-1 (15), which recommends
0.45% for "sections subjected mainly to pure tension", although this has previously been
thought to apply to structural tension members like hangers, and with the design of
continuous reinforced concrete pavements, for which the Highways Agency (16)
specifies 0.60 % reinforcement in one layer at the mid-depth.
Both ACI 350 and EN 1992-1-1 make an allowance for 'non-uniform self-
equilibrating stresses' in thick slabs. Although expressed in different ways, the net effects
are very similar. They are illustrated in Figure 7; as the depth of the section increases (x-
axis) a central zone can be discounted and the reinforcement provided based on the
remaining surface zones alone. The upper lines express the same effect as a reduction
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Crack widths
Two different methods of estimating crack widths are given in UK codes. Both
are in BS 8007: bond slipping is assumed for immature concrete, while no slip is assumed
for mature concrete. These two methods are combined in a single method in EN 1992-1-
1. The important point to note is that all methods first assume that the reinforcement is in
the elastic range, ie that the cracks are controlled.
The data above are based on the assumption that the average compressive strength
will be 8/10 MPa (1200 psi) above the specified minimum with a practical scatter of
20 %. This suggests that an upper limit should be written into specifications, as it is
clear from Table 1 that the minimum reinforcement content will be underestimated if
the compressive strength is too high. This could be enforced by also placing an upper
limit on cementitious material content and discouraging too-low a w/c ratio.
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Case study
Figures 8 and 9 show the floor slab of a single level basement 215 x 70 m
(700 x 230 ft) used for car parking which has cracked extensively. The slab is 350 mm
(14 in) thick, designed as a· flat slab on pile caps at two-way centers varying between 5.5
and 6.5 m (18 and 21ft). The section (Figure 10) shows that full restraint would be a
realistic assumption. Total reinforcement is 0.38 % in the middle strips, 0.60 % in the
column strips. Concrete grade was specified as 28/35, although no actual cube test results
are available.
The structure was built in the mid-1990s, although the cracks were only
observed around 2000. They are roughly parallel, at right angles to the long dimension.
They start about 27 m (90 ft) from each end and are in groups of two to five spaced at
500 to 1100 mm (20 to 42 in), followed by a gap of 2m (7ft) or more before the next
group. They are now around 0.5 mm (0.02 in) wide, although filled with a dark grey
precipitate, having leaked extensively over the three winters from 2000-1 to 2002-3,
having been below the water table for at least part of that time.
The author believes the explanation is that with p > Pimm controlled cracks did
initially form as predicted for early age contractions but because p < Prnat they later
widened uncontrollably rather than additional new cracks forming. The absence of cracks
at each end probably shows the distance needed for full restraint to develop, perhaps
aided by the inward pressure of the soil on the perimeter walls. The absence of cracks
parallel to the long sides (and of any movement at the construction joints) could be for
the same reason -the width is not much more than twice 27 m. The slab was constructed
in longitudinal strips generally 5-6 m (16-20 ft) wide, so an alternative explanation is that
The analysis above shows that the preferred approach is to select the thickness
of concrete as only that necessary to perform structurally; in many cases the minimum of
250 rom (10 in) recommended in BS 8102 (17) will suffice. Reinforcement should then
be chosen to satisfy the criteria derived above. It might seem excessive by other current
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standards, but uncontrolled cracking still occurs far too often, and if it does all the
reinforcement that is put in has been wasted.
NOTATION
area of concrete
area of reinforcement (total in both faces)
area of compression reinforcement
width of section
c depth to neutral axis (consistent with immediate or long-term condition)
d depth to tension reinforcement
Ec; Eeff modulus of elasticity of concrete; modified for long-term effects
Es modulus of elasticity of steel reinforcement
e eccentricity (defined in Figure 6)
·F force (suffixes c, s refer to concrete, reinforcement)
fct.fctm concrete tensile strength - generally, mean value
feu concrete compressive strength, expressed as eg 28/35 MPa [4000 psi] where
28 MPa [4000 psi] is the cylinder strength and 35 MPa is the cube strength
fsd reinforcement tensile design strength
(y reinforcement yield strength
(yk characteristic reinforcement yield strength (ie 95% probable)
h overall depth of section
h. effective thickness, = b hI (2 x exposed perimeter)
lc, Ig second moment of area of concrete section, gross section
K coefficient for deflection related to bending moment diagram
k, kp coefficients
suffixes
a overlay
b base (or substrate)
cr cracked
imm immature, ie in first 3-6 days
mat mature, ie older than 28 days
prov provided
req required
sh shrinkage
un uncracked
REFERENCES
Altoubat S A and Lange D A. Creep, Shrinkage, and Cracking of Restrained
Concrete at Early Age, ACI Materials Journal, July-August 2001, pp 323-331.
3 British Standards Institution, Steel, concrete and composite bridges, Part 4 Code
of practice for design of concrete bridges (BS 5400-4), London, 1990.
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16 Highways Agency (UK), Design manual for roads and bridges, volume 7,
section 2, part 3, notes on figure 2.5.
_.,....!.._t-1"~-- - - -
0 I 2
Figure 1. Typical early thermal temperature cycle for a relatively thick section
(cycle is more rapid for thin sections)
HJC
~
!~
;,
(.?
fl:l
0.~,._ _ _ _ _ _ _ _ _ __
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~r-----+-----+---------~~
"'~
~:r-----+-~~~~------~~
Figure 7. Reduction factor (upper) and illustration of surface and internal zones (lower)
against increasing overall depth of section
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Figure 10. Section through floor construction of car park basement in Figure 8
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
by R. I. Gilbert
21
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22 Gilbert
ACI Member Ian Gilbert is Professor of Civil Engineering and Head of the School of
Civil & Environmental Engineering at the University of New South Wales, Sydney,
Australia. His research interests are in the area of serviceability and the time-dependent
behavior of reinforced and prestressed concrete structures. He is actively involved in the
development of the Australian Standard AS3600.
INTRODUCTION
With the move towards higher strength reinforcing steels, the serviceability
limit states are more often the critical design consideration and reliable models for
estimating the deformation characteristics of concrete are essential. For example, when
500 MPa steel is used in a concrete structure, instead of 400 or 450 MPa steel, a smaller
quantity of reinforcement is required in a given situation to satisfy the requirements of
adequate strength. Under in-service conditions, this results in less stiffness after
cracking, and consequently greater deflections, and higher strains in the tensile
reinforcement, and consequently wider cracks. To adequately predict deflections and
crack widths, methods of analysis that realistically account for cracking and the time-
dependent deformations caused by creep and shrinkage of the concrete are required, as
are appropriate material modeling rules.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
The tensile strength,.fc" is defined in AS3600 (2) as the maximum stress which
concrete can withstand when subjected to uniaxial tension. Direct uniaxial tensile tests
are difficult to perform and tensile strength is usually assessed through either flexural
·tests on prisms or indirect splitting tests on cylinders. In flexure, the apparent tensile
stress at the extreme tensile fiber of the critical cross-section under the peak load is
calculated assuming linear elastic behavior and taken to be the flexural tensile strength
(or modulus of rupture), .fct.r· The flexural tensile strength .fct.r is significantly higher than
fc1 due to the strain gradient and the post-peak unloading portion of the stress-strain curve
for concrete in tension. The uniaxial tensile strength, !ct. is usually in the range of 50 to
60% of the measured flexural tensile strength. The indirect tensile strength measured
from a split cylinder test.fct.sp is also higher than the uniaxial tensile strength (usually by
about 10%) due to the confining effect of the bearing plate in the standard test.
Tensile strength test data shows a relatively large scatter of results and a high
degree of variability (3). In the absence of test data, formulas are often given in codes of
practice for estimating the lower characteristic flexural tensile strengthf~.r and the lower
characteristic uniaxial tensile stress /~1 • The formulas proposed for inclusion in AS3600
(2) are f~t.r = 0.6-ifc and/~= 0.36-ifc· The mean and upper characteristic values may be
estimated by multiplying f~.r or j~1 by 1.4 and 1.8, respectively. In serviceability
calculations, mean values of tensile strength should be used in most situations rather than
characteristic values (4).
The value of the elastic modulus, Ec, increases with time as concrete gains
strength and stiffness. It is common practice to assume that Ec is constant with time and
equal to its value calculated at the time of first loading. For stress levels less than about
0.4fc, and for stresses applied over a relatively short period (say up to 5 minutes), the
numerical estimate of the elastic modulus specified in AS3600-2001 (1) for concrete
strengths up to 65 MPa was originally proposed by Pauw (5) and is given by
where pis the density of concrete (not less than 2400 kg/m 3 for normal weight concrete)
and fern is the mean compressive strength in MPa at the time of first loading. Whilst
Equation (1) has been shown to provide a good estimate of the elastic modulus for
normal strength concrete, it overestimates Ec when !em exceeds about 40 MPa and is
generally felt to be unsuitable for higher strength concretes (6), (7) and (8). Carrasquillo
et al. (6) proposed
which is claimed to be more suitable for high strength concrete (when/em is in the range
50 - 100 MPa). Plots of both Equations (I) and (2) for normal weight concrete with p =
2400 kg/m 3 are shown in Figure 1.
Acknow Iedging that Equation (1) overestimates Ec for high strength concrete,
Mendis eta!. (7) proposed the following modification:
where the modification factor 11 = 1.1 - 0.002 fc.::> 1.0. Equation (3) is also plotted in
Figure 1. However, the modification factor does not adequately cater for the inadequacies
of Equation (1) and Equation (3) also overestimates Ec for some aggregate types,
particularly for concrete strengths above 65 MPa.
An alternative approach (4) is the use of Equation ( 1) when !em :;; 40 MPa and
Equation (4) whenfem > 40 MPa.
Both equations provide similar estimates of Ec at the transition point ifcm = 40 MPa).
Equation (4) is also plotted in Figure 1 for normal weight concrete and the values of Ec
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
The value of Ec given by Equations (1) or (4) is applicable for stress levels up to
about 0.4 ..fcm for normal strength concrete and up to about 0.6 ..fcm for high strength
concrete and for stresses applied over a relatively short time period (up to about 5
minutes). In general the faster the load is applied, the larger is the value of Ec. For
stresses applied over a longer time period (say up to one day's duration), significant
increases in deformation occur due to the rapid early development of creep. Yet in a
broad sense, loads of one day's duration are usually considered to be short-term and the
effects of creep are often ignored. This may lead to significant error. If short-term
deformation is required after I day's loading, it is suggested (9) that E c given by either
Eqt1ations (1) or (4) be multiplied by 0.8.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
AS3600-200I (1) suggests that values of Ec given by Equation (I) have a range of±20
percent and this is also true for Equation (4). Typical variations in Ec with age for
concrete cured under standard conditions are shown in Table 2.
CREEP OF CONCRETE
Discussion
In addition to the environment and the characteristics of the concrete mix, creep
depends on the loading history, in particular the magnitude of the stress and the age of the
concrete when the stress is first applied. When the sustained concrete stress is less than
about 0.5 fc (and this is usually the case in concrete structures at service loads), creep is
proportional to stress and is known as linear creep. The age of the concrete when the
stress is first applied, r, has a marked influence on the magnitude of creep. Concrete.
loaded at an early age creeps more than concrete loaded at a later age.
The most accurate way of determining the final creep coefficient is by testing or
by using results obtained from measurements on similar local concretes. Testing is often
not a practical option for the structural designer. In the absence of long-term test results,
the final creep coefficient may be determined by extrapolation from relatively short-term
test results, where creep is measured over a relatively short period (say 28 days) in
specimens subjected to constant stress. Various mathematical expressions for the shape
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
of the creep coefficient versus time curve are available from which long-term values may
be predicted from the short-term measurements. The longer the period of measurement,
the more accurate are the long-term predictions. Some of the more useful expressions for
cAt, r) are presented by Gilbert (9).
If testing is not an option, analytical methods are available for predicting the
creep coefficient. These predictive methods vary in complexity (9): Some are simple and
easy to use, and provide a quick and approximate estimate of cAt, r). Such a method is
included in AS3600 (I). Others are much more complicated and attempt to account for
the many parameters that affect the magnitude and rate of development of creep.
Unfortunately, an increase in complexity does not necessarily result in an increase in
accuracy, and predictions made by some of the more well-known methods differ widely
(9). The simple approach contained in AS3600 (1) does not account for such factors as
aggregate type, cement type, cement replacement materials and more, but it does provide
AS3600 (I) defines a basic creep coefficient (/Jcc.b as the ratio of final creep strain
to elastic strain for a specimen loaded at 28 days under a constant stress of 0.4 fc· In the
absence of tests, the Standard specifies (/Jccb = 5.2, 4.2, 3.4, 2.5 and 2.0 for characteristic
strengths of fc = 20, 25, 32,40 and 50 MPa, respectively. According to AS3600 (1), the
creep coefficient at any time (/Jcc may be calculated from
(5)
provided that (/Jcc is used in conjunction with Ec at 28 days (irrespective of the age at
loading); the concrete is not subjected to prolonged periods of temperature in excess of
25'C; and the sustained stress level does not exceed 0.5 fc· Where the concrete is likely
to be subjected to prolonged period of temperature in the range 25-40'C, a 25% increase
in (/Jcc is here recommended.
The factor k2 depends on the hypothetical thickness, th, the environment and the
time after loading and is given in Figure 6.1.8.2(A) in the Standard (1). The hypothetical
thickness is defined as th = 2Aiue, where A is the cross-sectional area of the member and
Ue is that portion of the section perimeter exposed to the atmosphere plus half the total
perimeter of any voids contained within the section. The factor k3 depends on the age at
first loading and may be taken from Figure 6.1.8.2 (B) in the Standard ( 1). The Standard
also suggests that the actual creep coefficient has a range of approximately ±30% of the
value predicted.
The above procedure was calibrated from creep data for normal strength
concretes, but has been shown to underestimate the early development of creep in
structural members and to underestimate creep of concrete loaded at very early ages (4).
That is, the factors k2 and k3 need to be modified. The method also tends to underestimate
creep for 40 MPa and 50 MPa concrete.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
A modified model for predicting the creep coefficient for concrete (with
compressive strength in the range 20 - 100 MPa) was proposed by Gilbert (10) and an
updated and simplified version of that proposal is outlined here and has been accepted for
inclusion in AS3600 (2). The model agrees well with the limited creep data available for
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
The creep strain at any time t caused by a constant sustained stress 0'0 shall be
calculated from E:cc = (/Jcc 0'0 /Ec(28), where Ec{28) is the elastic modulus of the concrete at
age 28 days and (/Jcc is the creep coefficient at time t.
(6)
Although similar in form to the existing equation in AS3600 (1), Equation (6) introduces
two new k factors, revises the factors k 2 and k 3 , and modifies and extends the basic creep
coefficient ( <f'cc.b) as given in Table 3.
The factor k2 in Equation (6) describes the development of creep with time. It
depends on the hypothetical thickness, th (in mm) (as defined in the Standard) and is
given by Equation (7) (and illustrated in Figure 2):
a to.s
k2 = 08
2 (7)
t ' +0.15th
where tis the time (in days) since first loading and a2 is given in Equation (8).
(8)
The factor k3 is modified from that given in AS3600 (1) to predict higher creep
for concrete loaded at early ages and is given in Figure 3.
The factor k4 accounts for the environment and is equal to 0.7 for an arid environment,
0.65 for an interior environment, 0.60 for a temperate environment and 0.5 for a
tropical/coastal environment. The factor k 5 is given in Equation (9) and accounts for the
reduced influence on creep of the relative humidity and the specimen size as the concrete
strength increases (or more precisely, as the water-binder ratio decreases).
where (10)
The proposed predictive model gives similar results to AS3600 for normal
strength concrete and provides a ball-park estimate of the creep coefficient for high
strength concrete. However, it must be emphasized that creep of concrete is highly
variable with significant differences in the measured creep strains in seemingly identical
specimens, tested undel,' identical conditions (both in terms of load and environment). The
creep coefficient predicted by Equation (6) should be taken as an average value with a
range of ±30 percent.
To illustrate the use of the model, consider the following example. The final
design creep coefficient after 30 years under load (t = 10950 days) is required for 65 MPa
concrete, located in a temperate environment, first loaded at 28 days and with a
hypothetical thickness th = 200 mm.
1.226 X 10950°·8
Equation (7) gives: k2 = = 1.205
10950°.8 +OJ 5 X 200
(or obtain directly from Figure 2).
The final creep coefficients (/Jcc (after 30 years) predicted by the above method
for concrete first loaded at 28 days, for characteristic strengths of 25 MPa to 100 MPa,
for three hypothetical thicknesses, th = I00 mm, 200 mm and 400 mm and located in
different environments are illustrated in Table 4. The numbers shown in brackets for
concrete strengths of 25 MPa and 32 MPa are the values of (/Jcc determined using the
existing procedure in AS3600 (1 ). The proposed model and the existing model in
AS3600 are in veryclose agreement for low strength concrete.
SHRINKAGE OF CONCRETE
Discussion
Concrete shrinkage strain, Ecs. which is usually considered to be the sum of the
drying, chemical and thermal shrinkage components, continues to increase with time at a
decreasing rate. Shrinkage is assumed to approach a final value, Ecs *, as time approaches
infinity. Drying shrinkage in high strength concrete is smaller than in normal strength
concrete due to the smaller quantities of free water after hydration. However, thermal and
chemical shrinkage may be significantly higher.
For normal strength concrete (f'e :5: 50 MPa), AS3600-2001 (1) suggests that the
design shrinkage at any time after the commencement of drying may be estimated from
(II)
where lics.b is a basic shrinkage strain and, in the absence of measurements, may be taken
to be 850 X 10·6; k1 describes the development of shrinkage with time and depends on the
environment and the concrete surface area-to-volume ratio (as measured by the
hypothetical thickness, th).
AS3600 (1) states that the actual shrinkage strain may be within a range of plus
or minus 40% of the value predicted. In the writer's opinion, this range may be
optimistically narrow. The approach does not include any of the effects related to the
composition and quality of the concrete. The same value of lies is predicted irrespective of
the water-cement ratio, the aggregate type and quantity, the type of admixtures, etc. In
addition, the factor k1 tends to overestimate the effect of member size and underestimate
the rate of shrinkage development at early ages. The method should be used only as a
guide for concrete with a low water-cement ratio (<0.4) and with a well-graded, good
quality aggregate. Where a higher water-cement ratio is expected or when doubts exist
concerning the type of aggregate to be used, the value of lies predicted by AS3600-2001
( 1) should be increased by at least 50%.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
The revised model for estimating shrinkage in both normal and high strength
concrete was proposed by Gilbert (4,1 0). The model divides the total shrinkage strain, &cs,
into two components, chemical plus thermal shrinkage (termed endogenous shrinkage),
&ese. and drying shrinkage, &esd. as given in Equation (12). Endogenous shrinkage is taken
to be the sum of chemical and thermal shrinkage and is assumed to develop relatively
rapidly and to increase with concrete strength. Drying shrinkage develops more slowly
and decreases with concrete strength.
At any time /0 (in days) after placing the concrete, the endogenous shrinkage is
given by
where fc is in MPa.
where &csdb• depends on the quality of the local concrete, including the type and quantity
of aggregates, cement, cement replacement materials and admixtures. In the absence of
more reliable information, &csd.b• is specified as 800 x 1o-6 for Sydney and Brisbane, 900
X 10-6 for Melbourne and 1000 X 1o- elsewhere in Australia.
6
At any time td (in days) after the commencement of drying, the drying shrinkage
may be taken as
_
a I to.s
d
k1 - (17)
~~·8 +0.15th
where
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
a 1 = 0 • 8 + 1.2e- 0.005 th (18)
As for creep, k4 is equal to 0.7 for an arid environment, 0.65 for an interior
environment, 0.6 for a temperate inland environment and 0.5 for a tropical or near-coastal
environment.
As expressed in Equation (12), the design shrinkage at any time is therefore the
sum of the endogenous shrinkage (Equation 13) and the drying shrinkage (Equation 16).
The proposed model provides good agreement with available shrinkage measurements on
Australian concrete.
To illustrate the model, consider the following example. The design shrinkage
strain is required 1000 days after the commencement of drying for 65 MPa concrete,
located in Canberra (temperate inland environment) and with hypothetical thickness th =
200 mm. For this example, td is 1000 days and 10 is taken to be 1007 days.
1007
Equation (13): &cse = 145 X 10-6 X (l.Q- e-O.I x ) = 145 X 10"6
Equation (15): Ecsdb = (1.0 - 0.008 X 65) X 1000 X 10·6 = 480 X 10-6
1.24x1000°"8
Equation (17): k
I
=- -------
1000°· 8 + 0.15 X 200
= 1.11
6
Equation (12): E:cs = I45 X 10" + 3I9 X 10"6 = 464 X 10"6
CONCLUDING REMARKS
The Australian Standard for Concrete Structures AS3600-2001 (1) is currently being
reviewed, with the intention to expand the applicability of the Standard to cover
concrete strengths up to I 00 MPa. The revised provisions concerned with the
instantaneous and time-dependent deformation characteristics of concrete, as well as the
tensile strength, have been discussed. The models that have been recommended for
inclusion in the Standard for predicting the direct and flexural tensile strengths, the
elastic modulus, the creep coefficient and the shrinkage strain for the full range of
applicable concrete strengths (20 MPa ::;:; fc ::;; I 00 MPa) have been presented. These
models have been developed to at once provide reasonable estimates of concrete
properties and deformation characteristic and at the same time to be relatively simple to
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
NOTATION
A cross-sectional area;
Ec elastic modulus of concrete;
fc characteristic compressive strength of concrete in MPa;
fern mean compressive strength of concrete in MPa;
fcm.28 mean compressive strength of concrete at age 28 days in MPa;
fc 1 characteristic uniaxial tensile strength of concrete in MPa;
fctf characteristic flexural tensile strength of concrete in MPa;
k~. k2, k3, k4 and k 5 modification factors for creep and shrinkage;
t time (in days) since first loading;
td time (in days) since the commencement of drying;
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Ee elastic (or instantaneous) strain;
TJ modification factor;
<f>cc creep coefficient for concrete (AS3600);
<f>cc.b basic creep coefficient for concrete (AS3600);
<p(t, r) creep coefficient at time t due to a stress applied at age •;
<p*( <) the final creep coefficient due to a stress applied at age •;
p density of concrete;
0"0 constant sustained compressive stress; and
• age of concrete at first loading.
REFERENCES
4. Gilbert Rl. Creep and Shrinkage Models for High Strength Concrete - Proposals for
inclusion in AS3600. Australian Journal of Structural Engineering. Institution of
Engineers, Australia. 2002; 4(2): 95-106.
10. Gilbert Rl. Serviceability considerations and requirements for high performance
reinforced concrete slabs. International Conference on High Performance High
Strength Concrete, Curtin University of Technology, Rangan and Patnaik (Eds),
Perth, 1998: 425-439.
/~(MPa) 20 25 32 40 50 65 80 100
/em (MPa) 22.5 27.9 35.4 43.7 53.7 68.2 81.9 99.0
Ec(MPa) 24000 26700 30100 32750 34800 37400 39650 42200
J;(MPa) 20 25 32 40 50 65 80 100
J: Arid
Environment
Interior
Environment
Temperate
Inland
Tropical and
near-coastal
Environment Environment
MPa th (mm) th (mm) th (mm) th (mm)
100 200 400 100 200 400 100 200 400 100 200 400
25 4.82 3.90 3.27 4.48 3.62 3.03 4.13 3.34 2.80 3.44 2.78 2.33
(4.66) (3.88} (3.28} (4.30} (3.56) (3.00) (3.97} (3.28) (2.77} (3.37} (2.73) (2.26)
32 3.90 3.15 2.64 3.62 2.93 2.46 3.34 2.70 2.27 2.79 2.25 1.90
(3.77) (3.14) (2.66) (3.48) (2.88) (2.43) (3.21) (2.66) (2.24) (2.73) (2.21) (1.83}
40 3.21 2.60 2.18 2.98 2.41 2.02 2.75 2.23 1.87 2.30 1.86 1.56
50 2.75 2.23 1.89 2.56 2.07 1.73 2.36 1.91 1.60 1.97 1.59 1.33
65 2.07 1.75 1.53 1.95 1.66 1.46 1.84 1.57 1.38 1.61 1.38 1.23
80 1.56 1.40 1.29 1.50 1.36 1.25 1.45 1.32 1.22 1.33 1.23 1.14
100 1.15 1.14 I. II 1.15 1.14 1.11 1.15 1.14 1.11 1.15 1.14 l.ll
Note: The nwnbers shown in brackets for concrete strengths of25 MPa and 32 MPa
are the values of (II.., determined using the existing procedure in AS3600 (1).
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
- - AS3600-2001 (Eqn 1)
---·- CarrasquiUo et al (Eqn 2)
- -- - Mendis et Bl {Eqn 3)
40000 ---- • Current Proposal (Eqn 4)
~ L---~------~------~------L-----_J
0 20 40 60 80 100
Average compressive strength,/"" (MPa)
1.6
a., ...
~ = ,... +O.lSt•
1.4
1.0
0.8
0.6
0.4
0.2
0.0
10 30 100 3 10 30
Days Years
rune after loading, t
1.9
1.7
!2 1.5
i 1.3
·o"
IE 1.1
u"
0
0.9
0.7
0.5
7 365
Age of concrete at time ofloading, ' (days)
1.6
1.4
a 1 = 0.8 + 1.2e- o.oos,,
1.2
kt (td is in days)
1.0
0.8
0.6
0.4
0.2
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
0
3 10 30 100 3 10 30
Days Years
Time since commencement of drying, t.!
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Synopsis: The purpose of this study was to conduct a sensitivity study on shrinkage
prediction ofconcrete utilizing theACI 209 (1 ), GL 2000 (2), B3 (3), and CEB MC 90-99 (4)
models. The sensitivity of a prediction model is function of different parameters utilized in
the equations describing the model. The influence of changing input parameters on
shrinkage prediction was investigated. The study reveals that the change of relative
humidity will result in similar sensitivity for different shrinkage models. The autogenous
shrinkage component in the CEB MC 90-99 was found to be most sensitive to strength
change at 28 days. The GL 2000 was found most sensitive to cement type while the B3
model was found to be most sensitive to specimen size and type of curing. In general the
B3 was the most sensitive model while the ACI was the least sensitive.
41
Copyright American Concrete Institute
Provided by IHS under license with ACI Licensee=UNI OF NEW SOUTH WALES/9996758001
No reproduction or networking permitted without license from IHS Not for Resale, 08/10/2015 01:24:03 MDT
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42 AI-Manaseer and Ristanovic
Akthem Al-Manaseer, FACI, is Professor and Chair of Civil Engineering at San Jose
State University, San Jose, CA. He is a member of ACI Committees 209, Creep and
Shrinkage in Concrete, and 231, Properties of Concrete at Early Ages.
INTRODUCTION
SENSITIVITY
[1]
s(p) = Shrinkage sensitivity due to change of any input parameter p such as:
relative humidity RH, specimen size, 28-day compressive strength fcm 28 •
pI = Initial value of input parameter p
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
The input parameters utilized for the different models are summarized in Table 1.
The limitations of input parameters, from Ref. 1-4, for each of the four models are given
in Table 2.
The study utilizes Equation (1) to derive sensitivity equations for each input
parameter listed in Table I. The sensitivity equations for each model are described next.
s(RH) = 1- Ksh
K P) ] x100% (2]
[ s'\t)
The results of the sensitivity analysis for different values of RH are shown in
Figure 2.
It can be observed from Figure 2 that the sensitivity hi-linearly increases as the
change of relative humidity increases and is most sensitive in the range of 80-100%. This
rate of increase was found to be higher when the change occurs from a higher initial
valueofRH.
1.14-·o.oo3s(v)
s(V/S) = 1-
s (2)
x100% [3]
1.14-0.003s(v)
s (1) '
It can be observed from Figure 3 that the specimen size sensitivity linearly
increases with change in specimen size. The rate of change in sensitivity is higher for
larger initial values of (V/S(l)). It can be observed from analyzing specimen size
parameter that if the V/S exceeds 315 the prediction values become very large and do not
reflect the actual behavior of concrete.
s (type of curing) = 1- ( ) (
b, +(t-tc)J
) x 100% [4]
( b( 2 )+ f-fc
As shown in Figure 4, moist and steam cured concrete has approximately same
sensitivities. It can be observed that early age concrete is more sensitive to the type of
curing. The sensitivity reduces as the duration of drying increases up to 500 days. Above
500 days the ACl model is not sensitive to type of curing.
s(fcm28 )= 1-(
fcmzs'
()J ~] xlOO%
2 [5]
r fcmzs(2)
1-1.18(H(2).)4
100
s(H)= 1- xlOO% (6]
1-1.18(H(I) )4
100
GL 2000 Model - Specimen Size - The change of the specimen size will
influence the change in predicted value of shrinkage as follows:
t-tc +0.12(V)
S (I)
s(V/S)= 1- 2
xlOO% (7]
t-tc +0.12(V)
s (2)
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
It can be observed from Figure 7 the larger the specimens the more sensitive the
model to change in specimen size. Also, a negative sensitivity means shrinkage increases
with reduced V/S ratio while a positive sensitivity indicates that shrinkage reduces with
increased V/S ratio. It can be observed that the positive sensitivity is almost constant for
all values of initial V/S ratio.
2
s (cement type) = [1- K( )] x 100% (8]
K(I)
A negative value in the table indicates that shrinkage increased with change of
cement type, while a positive value indicates that shrinkage decreased with change in
cement type. It can be observed from Table 3 that concrete with cement type II is most
sensitive. The increase in shrinkage predicted value of 53% was obtained when type II
cement was replaced with type III cement. The minimum shrinkage sensitivity of 13%
was obtained when type III cement was replaced with type I cement.
Shrinkage of the CEB MC 90-99 is the sum of the autogenous and drying
shrinkage component. The sensitivity of the autogenous shrinkage component sa, and of
the drying shrinkage component sdis presented separately as follows:
CEB 90-99 Model - Cement Type - Change in cement type will produce the
change in autogenous shrinkage prediction as follows:
As shown in Table 4 concrete with cement type III is most sensitive. The change
in shrinkage predicted value of 33% was obtained when the cement type III was changed
into cement type II in the same concrete specimen. The minimum shrinkage sensitivity of
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
l
Change in cement type will result in change of drying shrinkage prediction as
follows:
It can be observed from Figure 9 that the sensitivity increases with the increase
of fcm 28 . The maximum sensitivity was obtained when the cement type I was changed
into cement type II in the same concrete specimen for different values of fcm 28 . For the
constant value of fcm 2s equal to 120 MPa the maximum sensitivity was 27%.
s)H)= 0 [ 11]
[12]
s a = 1- xlOO% [13]
The sensitivity was plotted in Figure 13 for different values of fcm 28 varying
from 15-120 MPa.
less sensitive due to change of strength than the autogenous shrinkage predicted values
for lower strength concrete. Also it can be observed that the sensitivity almost changes
linearly as the change of fcm 28 increases. For the value of fcmZS(Z) equal to I5 MPa the
sensitivity is almost same for all initial values of strength.
The change of the drying shrinkage component due to a change of the fcmzs value
from 15-120 MPa is given in the following equation:
jJRH, _afo2(fcm2s(2)-fcm28(1)J]
sd = 1---<·_l e xlOO% {14]
[ jJRH(l)
[14]
It can be observed from Figure 17 that the sensitivity decreases with increase of
fcm 28 • Sensitivity of the B3 model due to change of compressive strength is in the range of
20-28% for all values of strength and water content equal to 120 kg/m 3• The influence of
water content on sensitivity is shown in Figure 28. It can be observed that concrete with
less water content is less sensitive to change in compressive strength. It can be noticed
that the sensitivity is almost constant for water content equal 70 kg/m 3•
B3 Model -Specimen Size - The sensitivity due to change of specimen size can
be determined from the following equation:
[18]
It can be observed from Equation 18 that the sensitivity is a function of the ratio
(V/S)( 1)
(V/S)(2)
(V/S) I
It can be observed from Figure 19 that when ( ) ( ) increases the sensitivity
VjS (2) .
increases nonlinearly. The graph show that for a 50% reduction in volume to surface area
ratio the sensitivity increases by 250%, while if the specimen is enlarged by 50% the
percentage sensitivity becomes 20%. As shown in Figure 19, the model is extremely
sensitive to reduction of specimen size.
As shown in Figure 20 the Kh coefficient change sign for the value of humidity
equal to 98.5%. This will result in a change of sign of the shrinkage value from negative
to positive. The sensitivity of B3 model is influenced by this change as shown in Figure
21.
B3 Model - Cement Type - The sensitivity due to change in type of cement can
be defined in the following equation:
at,]
s (type of cement)= 1- a (-J x 100%
[ I( I)
[20]
As shown in Table 5 the change of cement type II to type III is most sensitive.
The change in shrinkage predicted value of 29% was obtained when the cement type II
was replaced with cement type III in the same concrete specimen. The minimum
shrinkage sensitivity of 9% was obtained when the specimen with type III was changed to
cement type I in same concrete specimen.
212
s (type of curing) = [1- : )] x 100% [21]
2(1)
The values of a 2 for different types of curing and sensitivity as calculated from equation
(21) are shown in Table 6.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
B3 Model - Water Content - The change of water content can influence the
sensitivity of the model as follows:
o.ot9(w)~~;Ctcm28r · +27o]
0 28
s ( w) = 1- 28 x 100% [22]
r 0.019(w)~~; (fcm 28 )-0. +270
It can be observed from Figure 22 that specimen with higher water content is
less sensitive. Common sensitivity was observed for the change of initial water content
from any value to the value of 56 kg/m 3 . Analysis also showed that the sensitivity
changes insignificantly with the change of compressive strength.
The sensitivity of the models due to change of any input parameter can be a
function of several parameters as summarized in Table 7.
The models sensitivities were compared for input parameters having ·the following limits:
- 40%:$ H:::;;; 80% (All models are defined in this range)
- 18MPa:::;;; fcm 28 :::;;; 69MPa (All models are defined in this range)
The GL 2000 and CEB MC 90-99 model sensitivity due to change of specimen
size is also a function of duration of drying. The maximum sensitivity obtained for the
duration of drying equal to 7 days was calculated for both models and plotted together
with the sensitivities of the ACI 209 and B3 model as shown in Figure 24. It can be
observed that the B3 model is the most sensitive and the ACI 209 is the least sensitive
model. The GL 2000 and CEB MC 90-99 have the same sensitivity to change of
specimen size.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
As shown in Table 8 the most sensitive model due to change of cement type is
the GL 2000 model and the least sensitive is the B3 model.
CONCLUSIONS
Relative Humidity- In the range of 40-80% all models have similar sensitivity.
For relative humidity above 80%, the sensitivity for all models rapidly increases. For the
GL 2000 model the relative humidity of 96% is the critical humidity at the sensitivity
analysis indicating swelling of concrete and extremely high values of sensitivity. For the
CEB MC 90-99 model the critical value varied between 87.5 and 99% depending on the
concrete compressive strength. For the B3 model the critical value of humidity at which
swelling starts is 98.5%.
Specimen Size - The B3 model is evaluated as the most sensitive model due to
change of specimen size, while the ACI 209 is evaluated as the least sensitive model. The
GL 2000 and the CEB 90-99 models have the same sensitivities due to change of
specimen size.
Compression Strength - The CEB 90-99 model is the most sensitive model due
to change in the compressive strength of concrete. This conclusion is based on extremely
high vales of sensitivity that were obtained for the autogenous shrinkage component. The
GL 2000 model is the least sensitive model due to change of compressive strength. The
B3 model sensitivity is higher than the sensitivity of the GL 2000 and the drying
component of the CEB MC 90-99 model. The ACI model is not related to fcm2s parameter.
Cement Type - The GL 2000 model is more sensitive to cement types than the
B3 model and the CEB MC 90-99 model. The ACI 209 model is not sensitive to this
parameter.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Overall Comparison
Table I 0 summarizes the common parameters in aJI four models. In the table the
maximum values of sensitivities are considered for each model. Note that the comparison
was performed for the specific ranges of input parameters as described in Table 2. The
numbering in the table indicate the level of sensitivity of each model due to change of
input parameters. The highest number was assigned to the most sensitive and the lowest
number was assigned the least sensitive model.
AII models have similar sensitivity to change of relative humidity. The GL 2000
is the most sensitive to change of cement type. The autogenous shrinkage component in
the CEB 90-99 model is the most sensitive to 28 day compressive strength change. The
B3 model is most sensitive to change in specimen size and type of curing.
REFERENCES
2. Gardner, N.J., and Marty Lockman, "Design Provisions for Drying Shrinkage and
Creep of Normal-Strength Concrete," ACI Materials Journal, Vol. 98, pp. I59-
167, March-April2001.
3. Bazant, Z.P. and Baweja, S., "Creep and Shrinkage Prediction Model for Analysis
and Design of Concrete Structures," the Adam Neville symposium, SP-194,
Editor: Akthem Al-Manaseer, pp. 1-83,2000.
4. MuJler, H.S. and Hillsdorf, H.K., "CEB Bulletin d' information, No. 199,
Evaluation of the Time Dependent Behavior of Concrete, Summary report on the
Work of General Task Group 9," September 1990, pp. 290.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Input parameter p
ACI GL CEB-FIP
B3
209 2000 MC90-99
28-Day
compressive ---- X X X
strength, fcmzs
Relative
X X X X
Humidity
Specimen size X X X X
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
CEB-FIP
Input parameter p ACI209 GL2000 B3
MC90-99
fcm2s [MPa] --- 16-82 15-120 17.2-69
Relative Humidity, H
40-100 20-100 40-100 40-100
[%]
Specimen size,
volume to-surface ---- >19 --- ----
area ratio V/S [rom] ·
Water content, w
fkg/m 3l
---- --- --- 56-611
Sensitivity[%]
25 -15 -33 -53 13 35
Sensitivity[%]
-14 14 13 25 -17 -33
Sensitivity [%]
15 -10 -18 -29 9 23
Sensitivity[%]
-33 -60 25 -20 38 17
Autogenous shrinkage:
fcm28
fcm28,
s(fcm28) -- fcm28
Drying shrinkage: type w
of cement, l'cnus, and H
forH>87.5%
Sensitivity ACI209 B3
Maximum
-48 -60
sensitivity[%]
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Minimum
0 17
sensitivity [%]
CEB-FIP
ACI MC 90-99
Input parameter GL2000 B3
209 Drying Autogenous
shrinkage shrinkage
28-Day
compressive --- 2 1 4 3
strength, fcm28
Relat~v~ 140-SO% Similar sensitivity for all models
Humidity
Specimen size 1 2 2 -- 3
Type of cement --- 4 2 l 3
Type of curing I --- --- --- 2
0.2 +----L..;:....:.:.:.:.::::.=:::..._J-+--~---1
0+-------~--------~------~
40 60 H[%]
80 100
40 50 60 70 80 90 100
H(2) [%)
100
~ 0
fi)
~ -100
"' -200
:f
=
-300 --1
" -400
</.)
~~
I~ p-- - -I:- - "- - -:I- · · -
1
so v-- Strength is
double
lI
~
"'
6 -50
0
I
I
-ISO
0 2 3 4 5 6
fcm28( l )/fcm28(2)
Figure 5 Sensitivity of the GL 2000 Model Due to Change of Compressive Strength fcm 28
300
200
~ 100
I'
u; 0 I
~ -100
·;;;
~
c:
-200
<I>
(/) -300
-400
20 30 40 50 60 70 80 90 100
H(2) [%]
300
~ I V/S" 1~19mm I
/ I
0
~ -300
~ ~
-600 / ! '--I V/S(IJ~toomm I
i-
·;: /\..
:~
-900
II --J V/Sul 300mm l t-tc- · davs
a:; -1200
Vl
-1500 I
0 100 200 300 400
V/S(2) [mm]
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
/_
/'\.
- ~
'---I V/S(I>=IOOmm
-·.
I
-~
·;;; -1200 I -I VIS(!) 300mm 1 t-tc- davs
c: I
" -1500
{/) I
0 100 200 300 400
V/S(2) [mm]
30
I ----:-:-:---1-" --
l
~ 20
,.. 10
-- -- ..
--
~-
:~
----
--
0
" -10 .... --
eX -20 I
-30 I
0 50 100 150
fcm28 [MPa]
-+-I,n _.._I,m - - n . I -n.m ----· IJI.I --m.n
100
80
99
.....__
- '\
[\_
I
i
I
II PRH=0.2
87;5
i
I
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
:f 0 . l' ~~_./
- -50 ~-----===~;;;--"""""'=---\~;::::=======;~
"' -100 ___-r ~I Hin 80%
-150 +-----i-----+-~----i
40 60 80 100
H(2) [%]
160
~ 120 _,
I
~ 80 ~ RH=60% \
__.;:.. r--
; I
:~ 40
~
"' 0 - f,----
-40
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
60 70 80 90 100 110
H(2) [%]
- - - ·fcm28=30MPa--- fcm28=60MPa • • • • • ·fcm28=80MPa --fcm28=120MPa
200
i!-
·;;
l001====~~~~:1:5t;~~~==:I:=:]
0
:~ -100 11====:::::::;
"' -200
ii
-300 -+---+---1,...--+---+---1,..--+----1
0 20 ~ W W
fcm28 [MPa]
100 IW I~
Figure 14 The sensitivity of the CEB MC 90-99 Due to Change of f, 0128 for Different Type
fJRH(')
of Cements and - - - - = 1
fJRH(l)
150
100 r 1- 1 V/S(l)=l9mm 1
I
I
~
100 , - - - - - - - , - - - - - - - - , - - - - - - - - , !
f.. 80 I
-
-~ 60
!. ---28days
·Ei 40 -t----H--T--,----j l ·•· ···IOOdays
] 2~ ~------' . -~ ~ --300days
-20 +----+----1---...----;
0 100 200 300 400
V/8(2) [mm]
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
0 20 40 60 80
fcm28(2) [MPa]
kglm3
---70
••••• 200
--300
10+----+----r----r--~----;---~
10 20 30 40 50 60 70
fcm28(2) [MPa]
Figure 18 The Influence of the Water Content on the Sensitivity Due to Change of fcm2s
~
0
:§ -700
-100
-300
-500
300
100
-- r--....
"-..J
I.
I
1--......_
i
·;;;
g -900
en -1100
I
I
""" '\.
-1300 I '\.
-1500 i '\.
0 2 3 4 5
(v/S(1 ))/(v/S(2)}
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
~ 100
.l:-
~ 0
~"
-100
40 50 60 70 80 90 100
H(2) [%]
so~----~------~----~----~
~ 40~------~-----+------~---~~ ---ACI209
.£ 30 ~---r'-:-:-----ll----~~-....j ----GL2000
:~ 20 L----~~==::;:;:~:2:::L:_j________j -CEB90-99
lj ·······B3
~ 10~---~~--~~-----~---~.
o~~=--4------~----~~----~
40 50 60 70 80
H[%]
120~-------.------~-------,
~ 100+-------~==~~~~
~ ---ACI209
,e. 80 ---GL2000
:~ 60
-cEB90-99
-~ 40 -~--~1------t--~~=------~-------....j
----- 83
~ 20-1-~--~~--------~-------....j
0+-~--~-------+------~
0 100 200 300
V/S(2) [mm]
i_:JK:r-·T--Il ~--~=:=-
20 30 40 50 60
fcm28(2) [MPa]
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
by S. Staquet and B. Espion
Synopsis: This research focuses on deviations from the linear viscoelastic behavior of
concrete occuring at high stress levels (from 0.5 f' cto 0. 7 f' c), at early age loading (I to 2
days) and in case of unloading implying strain reversal.
A large series of creep tests was performed on high strength concrete specimens
undergoing creep under constant stress, followed by a period of recording of the creep
recovery after complete unloading. Some specimens were heat cured before loading. Some
nonlinear effects at very early age .have been observed. After unloading, experimental data
show that the creep recovery deviates strongly from the numerical predictions obtained
by the application of the principle of superposition but seems to conform rather well to the
recovery model proposed by Yue and Taerwe 3 •
This model was then applied, through a step-by-step approach, for the time-dependent
structural analysis of a precast composite prestressed bridge deck with 26 m span. The
application of the recovery model yielded computed strains which are in good agreement
with in situ measured strains, and in better agreement than the strains computed by the
application of the principle of superposition. This enhanced approach was then used to
optimize the phases of construction of this kind of structure. Thanks to this research, the
age at transfer of prestress could be significantly reduced.
67
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68 Staquet and Espion
ACI Member Stephanie Staquet is Post-Doctoral Researcher at the Department of Civil
Engineering at the Universite Libre de Bruxelles (ULB), Belgium. She is carrying
research on modelling of creep and shrinkage effects in prestressed and composite
structures, early age concrete behaviour and ultra high performance concretes.
ACI Member Bernard Espion is Professor of Civil Engineering at the Universite Libre de
Bruxelles (ULB), Belgium. His research interests include the analysis of time-dependent
effects of concrete on structural behaviour, nonlinear design, carrying capacity of slender
concrete columns and high performance concretes.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
RESEARCH SIGNIFICANCE
INTRODUCTION
Fig. I shows a typical cross section of these bridge decks along with the
indication of the location of the extensometers in an instrumented bridge deck. The basic
steps in the construction of these bridge decks are:
two high strength steel girders with an initial precamber are prestressed on a
prefabrication bench by downwards concentrated loads acting at 1/41h and 3/4th of the
span;
passive (rebars) and active (tendons) reinforcement is placed in the space that will be
filled by the bottom slab (depth: 0.25 m);
the tendons are stressed and the slab is concreted;
at an early age for the concrete of the slab (between 40 hours and 62 hours), a I st
stage of prestressing of the slab is obtained by releasing the concentrated loads
acting on the steel girders, immediately followed by a znd stage of prestressing
through the release of the anchorage forces at the ends of the bonded tendons;
These bridge decks have been designed up to now with a classical computation
method where the time-dependent effects are taken into account within the framework of
a pseudo-elastic analysis with a variable modulus method 1 • The modular ratios given in
1
the NBN5 are intended for selected situations only (m = 5.59 at the transfer of
prestressing; m = 9.05 for sustained loads; m = 4.97 for variable loads). It has been
shown that the strains computed by this method differ significantly from the strains
measured in situ on an instrumented bridge deck, in particular from one year after
construction2 • These composite bridge decks are rather heterogeneous from the point of
view of their viscoelastic behavior and, as a consequence, the authors felt that it would be
useful to assess more thoroughly their time-dependent behavior. In a previous part of the
2
research , they used the method that relies on the numerical step-by-step evaluation of the
hereditary integral of the principle of superposition.
The step-by-step method used in the first part of this research applies the
superposition principle of the linear theory ofviscoelasticity which assumes that concrete
creep strains depend linearly upon the sustained stress level. Hence, a partial unloading is
considered as a negative load which induces an equal but opposite creep to that which
would be caused by a positive load of the same magnitude applied at the same time.
However, it appears that after a period of compression creep, creep recovery is
significantly less than predicted by the superposition principle. In the construction phases
of this composite prestressed bridge deck, the bottom side concrete fibers undergo a
stress/strain history of significant unloading when the permanent loads are applied step-
by-step.
Among existing approaches for modelling this phenomenon, the authors focused on the
so-called two-function method for the prediction of concrete creep under decreasing
stress proposed by Yue and Taerwe 3• In this approach, the nonlinear behavior caused by
unloading is divided into two parts: a classical linear creep law J for loading and a creep
recovery law J, for unloading. The stress-dependent strain (initial + creep) is computed
from Eq.l:
n n
&a (t,t 0 ) = a 0 .J{t,t0 ) + L J(t,t;).~a(t;) + L J, (t,t0 ,t;).~a(t;)
I I
[1]
where J (t, {j) =creep function (1/MPa)
o 0 = initial compression stress value
(supposed to be a loading) applied in t 0 (MPa)
.:1o (ti) = variation of stress inti (loading or unloading) (MPa)
J, (t, to, ti) =creep recovery function (liMPa)
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
where
Experimental data have shown that creep recovery decreases with the increase of
the age at loading (to) and the duration of loading (ti - to) and that the development of
recove7 is more rapid when load is applied at an early age or for short durations of
loading . In Eq.2, it can be seen that the final value and the rate of development of the
recovery function are influenced by the loading history.
compared with the values predicted by the 1999 version of the CEB-MC90 mode1 4 for
creep and shrinkage under constant stress and by Eq.2 proposed by Yue and Taerwe 3 for
the creep recovery law. The concrete mix proportions are: 680 kg/m 3 of sand from Maas
river (0/5), 1200 kg/m3 of limestone aggregates (7/14), 400 kg/m 3 of early high strength
Portland cement (CEMI 52.5 R LA), 8 kg/m3 of water reducing admixture (Visco 4) and
132 l/m 3 of mixing water. The total volume of water, including the liquid part of the
water reducing admixture is 138 l/m 3 and the water/cement ratio is 0.345. The
recommendations 5 issued by RILEM TC I 07 to perform tests under drying (23 C, 53 %
relative humidity) and sealed (23 C) conditions have been followed. Creep specimens
have been loaded at various ages (I day, 30 hours, 36 hours, 2 days, 28 days) under
different levels of stress (50 %, 60% and 70% off cJ where j is the age of concrete at
loading) and have been completely unloaded at various ages (28 days, 55 days, 140 days,
210 days, 338 days) in order to have different durations of loading. Some of the
specimens have been heat-cured at 45 C during the day after their molding and kept in
the same environment as the bridge decks submitted to heat curing in the same
conditions. We report hereafter only some results with a level of stress equal to 50 and 60
% off cJ which is the maximum level of stress reached in these bridge decks. For a level
of stress equal to 70 % off cj, some nonlinear effects at very early age were observed and
are supposed to be linked to the evolution of the degree of hydration. The influence of
this percentage as well as the effect of the heat curing on the creep function was
previously analyzed in detail 6• The average concrete compressive strength f cJ is
Figs.2 and 3 show the total and basic creep functions measured on non-heated
specimens loaded at 28 days and unloaded at 55 days with a level of applied stress equal
to 50 % of f cj· The measurements are compared with values predicted by the CEB-
MC90 model code4 (1999) with application of the superposition principle or with the
creep recovery Jaw 3 for the unloading. In both cases, basic and total, the difference
between measurements and predicted values after unloading is significant when the
superposition principle is applied whereas the trend of the experimental values is well
reproduced with the application of the creep recovery law.
In case of heat curing before loading, the CEB-MC 90 model code 4 proposes to
use an equivalent-time to take into account the actual maturity of concrete for the
computation of the age of concrete at loading. According to the Arrhenius law, an
equivalent-time tot is first computed with Eq.4:
4000
tor= M;.exp[13.65--- - -]
273 +I';
[4]
toejf=tor·[ 91.2
2 +tor
+l]a
[5]
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
When the level of applied stress is higher than 40% of f cj. the CEB-MC90
model code 4 proposes an expression for a multiplier k which increases the creep
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
coefficient.
[6]
A bridge deck with 26m span (belonging to a viaduct situated at the entrance of
Brussels South Station) has been instrumented at the third of the span and at mid-span
values and that the application of the step-by-step method for evaluating the principle of
superposition of linear viscoelasticity leads to computed results which are in better
agreement with recorded data2 • It can now be seen that an even better agreement between
strains measured in situ and computed values is found with the step-by-step method
incorporating the recovery phenomenon.
Fig.l5 shows the evolution of the corresponding computed stresses at the bottom
level of the steel girder. At this level, the steel girder is in tension after pre-bending. But
after the transfer of prestressing, compression increases in the lower flange of the girders
due to the combined effects of creep and shrinkage of concrete. Fig.l6 yields the
evolution of the computed stress at the bottom fiber of concrete slab at mid-span: it
should be observed that no tension appears neither with the classical step-by-step method
and the method incorporating the creep recovery law nor with the simple computation
method 1 (NBN5) used for the design of these bridge decks. It has been shown2 that the
application of the principle of superposition method yields much higher values for the
long-term prestress losses than the design method using the modular ratio. However,
prestress losses are reduced in the analysis that takes into account the deviation of the
The comparison between measured and computed strain values has shown that a
very good agreement is obtained by taking into account the creep recovery law in the
modelling. Hence, this approach can be used to optimize the phases of construction of
these composite bridge decks. In Figs.l7 to 21, a conventional history was assumed to
compute the evolution of stresses in the structure. It proceeds as follows: prestressing
occurs at t' (Table 2), concreting of the webs takes place at t" (Table 2), some equipment
is installed at 130 days and the ballast is placed in two stages, at 270 days and 305 days.
Fig.17 shows the evolution of the computed stresses in the concrete slab by
application of the two-function method in three situations: firstly, the bridge is not heated
and prestressed at 2.6 days as the instrumented one (curve 1); secondly, the bridge is
supposed to have been heat cured for one day after casting according to the evolution of
temperature given in Fig.l 0. Then, two cases are considered: in the 151 one (curve 2), toetf
is used to compute the age of concrete at loading (Eq.5, Model 2) and in the 2"d one
(curve 3), to. only is considered (Eq.4, Model 1). Curves 1 and 3 seem to yield close
results. However, curve 2 representing the results of the analysis that takes into account
the type of cement (to.11) on the effect of heat curing shows that prestress losses are
reduced when the type of cement is introduced (via Eq.5) in the analysis.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Experimental creep data on laboratory heated specimens have shown previous!/
that the computation must be done with toeff instead of to 1• Hence, by considering only
heated bridge decks, the age at prestressing t' and the age t" at the casting of the second
concrete phase were changed in order to optimize the construction phases (see Table 2).
Fig.18 shows the results of different simulations by applying the step-by-step method and
Fig.l9 shows the corresponding results obtained by the analysis with the two-function
method. In Fig.19, we can see that we can still count on a residual concrete compressive
stress (under permanent loading) of 4 MPa at 10000 days (30 years) by applying heat
curing and releasing the prestressing at 20 hours (0.833day); but by comparison, the
residual concrete compressive stress in a non heated bridge deck prestressed at 2.6 days
(like the instrumented deck) is only 2. 7 MPa.
Figs.20 and 21 show the corresponding stresses in the second phase concrete at
the upper fiber of the section at mid-span by applying the step-by-step method (Fig.20)
and the two-function method (Fig.21). At this fiber, the difference between the stresses
computed by the two methods is not significant. These illustrations indicate that, due to
creep and shrinkage of concrete, the stress in the concrete at the top fiber of the cross
section reach more than 3 MPa in tension, but also that these stresses are significantly
reduced when the ballast is installed.
This research has focused on a new kind of composite prestressed bridge deck
with strong stress redistribution between steel and concrete within the cross section and
also significant prestress losses. The purpose of the present paper was to analyze in detail
the influence of some non linear effects of concrete creep in the time-dependent analysis
of such kind of highly heterogeneous structures. A laboratory investigation was set up to
study experimentally the influence of early age loading at high stress levels and the
influence of heat curing on the creep function. It was shown that, for the concrete
considered, these parameters were correctly taken into account by the full application of
the 1999 version of the CEB MC90 prediction model. Then, the phenomenon of creep
recovery after unloading was considered and was found well reproduced by the two-
function method.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
precaster.
REFERENCES
1 NBN5, Steel Bridges, draft for the part: Composite Bridges, Doc.270/43 F*,
Belgian Institute for Standards, Brussels, 1987, (in French).
2 Staquet, S., Rigot G., Detandt, H. and Espion B. "Innovative Composite Precast
Prestressed Precambered U-Shaped Concrete Deck for Belgium's High Speed Railway
Trains", PCI Journal, September-October 2004 issue.
3 Yue, L.L. and Taerwe, L., "Two-function method for the prediction of concrete
creep under decreasing stress", Materials and Structures, 26, 1993, pp.268-273.
6 Staquet, S., and Espion, B., "Effects of heat treatment on creep functions of high
performance concrete loaded at very early age", Proceedings of the IX1h Conference on
Advances in Cement and Concrete: volume changes, cracking, and durability (D.A.
Lange, K. Scrivener and J. Marchand, eds.) , Copper Mountain, CO, August 2003,
pp.4 71-480.
7 Staquet, S., Detandt, H. and Espion, B., "Field investigation of a new kind of
composite railway bridge deck", Proceedings ofthe 61h International Conference on Short
ACKNOWLEDGEMENTS
• Vibrating wire
extensometer
- Strain gage
0,00006 -t-----------_/~'+---------i f
0,00005 -t----------/--:;>P----/-------l
0,00004 +--------..¥"~,r----a-------j
0,00003 +-.•.-=~~~~~~-----+~~.~~==--9
-- ! --.--..---
0,00002 +---------------'.--------1
0,00001 +-----------------'0.--~~=j
(t-28) in days
0,0001
0,00009
.
Creep function l (1/MPa)
......
0,00006 I
0,00005 I
0,00004
0,00003
0,00002
• ~ • . .~ I
II
0,00001 ~-·- I
·-~-------- .... (i-i8jiii[d.ysl
0
0,0001 0,001 0,01 0,1 1 10 100 1000 10000 1
0,00006 t------/---::A)~-~~;.::;2::::::::::'~
.,.
/.7 '---- -·-·--·-·
0,00004 +---~.....-;±t ~-· \~--·-
W! ---
0,00002
(1·2) inda)'l!
0+----~-----~----~---~
0.0001 0,001 0,01 0,1 10 100 1000 10000
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
- -~·-
\ ....•..... -······;;;;;c.
0,0000!
(1-l)in days
0,00002 +------------------___;
(t-1) in days
Figure 6 Total creep functions of the heated specimen loaded at 1 day (under 50%)
and unloaded at 210 days
0,00008
0,00002 ~----~-----------------1
Figure 7 Basic creep functions of the heated specimen loaded at 1 day (under 50%)
and unloaded at 210 days
0,00012
·· ···· pn:dicted J, 60'A., supc:rpositi011 principleI ~"/
0,0001 //l
0,00008
o'"/ -··· .-· ·-····
0,00006
..y
0,00004 . -~
~
0,00002
(t-2) in days
Figure 8 - Total creep functions of the non-heated specimen loaded at 2 days and
unloaded at 140 days
0,00016
i•
O,OOOJS Total creep limction J (1/MPa)
experimental J
- pn:dicted J, with recovery
...... predicted J, superposition princi lc
I
I /;,
0,00014
0,00012 //i
0,0001
//
~-~·-/ ·- .... ···- ..
0,00008
0,00006
.& " ...
. ./
0,00004
0,00002
(t-1) in days
Tempen~~ur<inC
70
600
~ : ~ • J8
• )2
o NBNS
400 +---------~~----------~-----~;~~~~~
200
.YotPI:I
-200
Strain (Jimlm)
200
...
~-1--------~----~r-----~------~----~~
time in days
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
.
· · · · · · supell)Osilion principle
~
100
4b..6M
0 r ~
c c c"c<\l
-100
Sln:ss(MPa)
150
sot----------+------------------------_,
~
.....~
-50+-----------------~--~-~--.'-
• ......._"'::----t"" ...~"'-._-
.."',---""-- __-___-___ -____- ___---1
-100 +---------------------------------'-"'---=-l
time ia days
-150 +-----~~----~-----~--------------1
0,1 10 100 1000 10000
Figure 15-- Computed stresses in the steel girder at the bottom level at mid-span
Sln:Ss(MPa)
• NBNS
I
-step-by-step with recovery
-2 +----------+-1 ······ suuert><>Oiticn Drinci 1e
L
r-_-__-..-::-
....~-..--='---j
-4
-6
-8
-10
. ··J
-12
..· /
-14
-16 .l
-18 ..'1 .. ·· .. - /
-20
J ... v
-22
time in days
-24
0,1 10 100 1000 10000
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
-20
~ ';?" j-Curve I:Non-heawd,f=2.6d
I -Curve 2: Heated, tp = ld, Modell
-22
time in days
-24
0,1 10 100 1000 10000
Figure 17- Stresses computed with recovery function in the concrete at the
bottom fiber at mid-span
Stt<:ss(MPa)
Or--~~~~r--------------,
·2
;:: l ---- i
,.........--___...,.,
~ :=-=-=-=-=-=-=-:~:~:~=-=-=-=-=-=-=-=-=-=-=-=-=-~........-::::~:;~::-.
..'-: ._- :-. -:·_-:· l'i'j.---j. II
-8+-----~~~'+-----------~~~------~
-10 +-----f+-+:-;-1:
r-----..,..::::;-~7'+-s-----1
-12 +-----+.-~~.,..,:f-----~-,
~::=--------1
...
I
I
4
·1 !j ~"#' Non~heatcd. t' 2.6d i
-16 +-----+.-:
-i-!<-!;f-~--:;-~~~-'-"~;.=.----! -Heated, t' =0.833d ~ I
-18 +-------f-1,+:d ... ~--Z::.------1
~· f,cz!lii ---Heated, t' = ld
•2 ot-----w.'~'i""'F-,.---------i -·-·Hcated,t'=I.Sd .
-22t-------\lt-j
IJLH ······Heated.f:o:2d "i 1,
• ~ ~ time in days I
-24
0,1 10 100 1000 10000
Figure 18 - Stresses computed with the principle of superposition in the concrete at the
bottom fiber at mid-span
-
So-ess (M]>a)
-2
:!~
-4
-6 l 1:
I j:
-8
\ !:
-10 I j:
I·:
-12
-14
: jj ~
-16 : !i ~?;."" Non-heated. t' a 2.6d
-18
-20
-22 , ,; time in days
-24
0,1 10 100 1000 10000
Figure 19- Stresses computed with recovery function in the concrete at the
bottom fiber at mid-span
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
3,5 ./-
3 .#'V
2,5 ff
2 / .6
1,5 / //
I / //
// _//_
0,5
&/ //
s
0
-0,5
//
-I 1--1 Non-heated, f 2.6cl //
-1,5 -Heated, I'= 0.833d II
---Heated, I'= ld
-2 -·-·Heatcd,l'=l.Sd
-2,5 ····· Hcate<l I' 2d time in days
-3
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Figure 20 - Stresses computed with the principle of superposition in the concrete at the
upper fiber at mid·span
Slless(MPa)
4
3,5 Non-heated, f =2.6cl
-Heated, f = 0.833<1
.QW
2,5
3
2
---Heated, f = ld
-·-·Heated, f D I.Sd
, #
The analysis includes nonlinearity due to cracking of the concrete, as well as the time
dependent deformations of composite cross section due to creep, shrinkage and
temperature. American Concrete Institute (ACI) and American Association of State
Highway and Transportation Officials (AASHTO) approaches are considered in modeling
the time dependent material behavior. Age-adjusted effective modulus method with
relaxation procedure is used to include the creep behavior of concrete. The partial restraint
provided by the abutment-pile-soil system is modeled using discrete spring stiffuess for
translational and rotational degrees of freedom. The effects of creep and shrinkage on the
service life are illustrated and the results from the analytical model are compared with the
published field test data of a two-span continuous integral abutment bridge.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
85
Copyright American Concrete Institute
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86 Arockiasamy and Sivakumar
ACI member M. Arockiasamy, is a Professor and Director of Center for Infrastructure
and Constructed Facilities under Department of Civil Engineering at Florida Atlantic
University, Boca Raton, FL. His research interest includes concrete durability, bridges,
advanced polymer matrix composite materials, and infrastructure systems.
ACI student member M. Sivakumar, is a Design Engineer at PTE Strand Co. Inc.,
Hialeah, FL. He pursued his Ph.D., at Florida Atlantic University. His research interest
includes creep, shrinkage and thermal induced stresses in concrete structures.
INTRODUCTION
Integral abutment bridges (Figs. 1-2) are becoming popular among a number of
transportation agencies owing to the benefits, arising from elimination of expensive
joints, instailation, and reduced maintenance cost. Integral abutment bridges
accommodate superstructure movements without conventional expansion joints and
hence avoid problems associated with bridge deck joints. One of the advantages of
integral construction is better seismic resistance due to the added redundancy. The
integral bridges differ from regular rigid frame bridges in the manner of distribution of
stresses due to temperature change, prestressing, creep, shrinkage, and restraints provided
by abut~ent foundation and backfill. Although the majority of the integral abutment
bridges perform adequately, many of them operate at high stress levels (Burke, M.P. Jr.,
1990). Although the stress levels generated by secondary effects are weii understood
from the field observations and performance (Kunin, J., and Alampaili, S., 2000), these
effects are not weii quantified. Design and construction practices are based largely on
past local experience and thus empirical in nature. Because of limited knowledge on the
behavior of integral abutment bridges, no unified design guidelines are available to
foiiow. Integral abutment bridge designs rely on the experience, empirical formulae, and
simplified design assumptions based on the performance of existing bridges rather than
theoretical considerations.
When the superstructure is subjected to sustained service loads, it undergoes
nonlinear time-dependent deformations in the concrete due to creep and shrinkage in
addition to nonlinearity produced by cracking of the concrete. The stress and strain in a
reinforced or prestressed concrete structure vary over a period of time due to gradual
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
RESEARCH SIGNIFICANCE
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Under the sustained stress, crc applied at time ! 0 , the total strain, Ec at any time t
including the instantaneous and the increase in strain due to creep is
c c (t) = ; : i;: j[1 + Q1 (t, t 0 )] ( 1)
This linear relationship is true within the range of stresses under sustained loads,
and allows superposition of the strain due to changes in stresses and shrinkage. Thus, the
total strain in concrete due to instantaneous and gradually applied stress, Llcrc and
shrinkage, Esb is
l+Q'(t,to) r6o-,(t) l+Q'(t,r) () ( ) (2)
cc(t)= a"c{t0 ) ( ) + Jo ( ) dcrc r +&511 t,t 0
Ec t 0 Ec r
If the gradual stress increment is assumed to be applied at time t0 and sustained to age t, a
reduced creep coefficient can be used to calculate the creep strain. With this
simplification, the integral equation is eliminated and Eqn.(2) is modified as
l+Q1(t,t 0 ) ()I+ XQ'(t,t 0 ) ( ) (3)
&c ()
t =ere (t 0 ) ( ) +~eTc t 1 ) +csh t,t 0
Ec fo Ec \.to
where x is the concrete aging coefficient to account for the effects of aging on the
ultimate value of creep for stress increments or decrements occurring gradually after the
application of the corresponding load.
The total strain at any fiber 0 (Fig. 3) at any time t is the sum of the
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
instantaneous strain &ai• time-dependent strains due to creep, shrinkage and prestress, Llc0
and strain due to self equilibrating force due to temperature effects Ll&or and given by:
Cot = Coi + Ll&o + Ll&or (4)
and the total curvature K 1 at time t is
Kr = Ki + L1K + LIKr (5)
where ICi = instantaneous curvature
LIK = time-dependent increment in curvature due to creep
L1Kr = curvature due to self equilibrating force due to temperature effects
Instantaneous Analysis
For any applied moment, M; and axial force, N; the instantaneous strain, e0 ; and
curvature, K; are obtained from
{
& 0 ;}
K; = E,.AAI- B
I [ IB -AB]{N;}
2
M; ) -
(8)
where e0 ; = instantaneous strain at reference fiber 0
K; = the instantaneous curvature
N; = the resultant initial axial force
M; = the initial bending moment about the reference fiber 0
A= fdA= area of transformed cross section
B = JydA =first moment of transformed area about top fiber
Eref= modulus of elasticity of reference material
f
I = y 2 dA = the second moment of the transformed section about the top surface
ofthe section
The instantaneous stresses across the depth of the composite section are
acij = ECA&oi + YcjK;) (9)
asij = E, (coi + YsjKi) (10)
where CTcij = instantaneous stress at /h fiber of concrete
CTsij = instantaneous stress at /h fiber of steel
EcJ =modulus of elasticity of/h fiber of concrete
E, = modulus of elasticity of steel
YcJ =distance between the reference fiber and/h fiber of concrete
y sJ = distance between the reference fiber and /h fiber of steeI
Assuming the strain distribution to remain unchanged in any time interval, i.e.,
the total strain is assumed held constant and the creep and shrinkage components change,
then the instantaneous strain component must also change by an equal and opposite
amount. When the instantaneous strain changes, the concrete stress also changes. The
stress on the cross section is, therefore, allowed to vary freely due to relaxation.
Consequently, the internal actions change and equilibrium is not maintained. To restore
equilibrium, an axial force, LJN and moment, LJM must be applied to the section. The
change of strain due to creep and shrinkage may be considered to be artificially prevented
by restraining actions of- LJN and- LJM When LJN and LJM are applied to the section, the
restraining actions are removed and equilibrium restored. The restraining forces LJN and
LJM are calculated as follows:
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
£.1
= age adjusted effective modulus of one of the /h concrete element
Shrinkage: If the shrinkage is assumed uniform over the depth of the section and
completely unrestrained, the shrinkage induced fiber strain, which develops during the
time interval (t,t0 ) is &sh (t,t0) and curvature is zero. The restraining forces required to
prevent this uniform deformation are given by
11M shrinkage = - i
}=I
Eej (B cj &shi )
(14)
Relaxation: For a prestressed concrete section, restraining forces required to prevent the
reduced relaxation in the tendon must also be included. The restraining forces required to
prevent the tensile creep in the steel (which causes relaxation) are
"
/lN relaxation = LA
k=l
pskl10" prk
(15)
11M relaration = i
k=l
A psk /),. 0" prk Y psk (
16
)
The restraining forces are calculated as the sum of the four terms:
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
from,
11&0 } 1 [ I, (21)
{ AK = E (A I - B 2 ) - Jj
e ee e ·e
where :x(t,to) is the concrete aging coefficient, which accounts for the effect of
aging on the ultimate value of creep for stress increments or decrements occurring
gradually after the application of the initial load.
The change of concrete stress, L1acj at a point in the /" concrete element at a
depth y below the reference fiber is equal to the sum of the stress loss due to relaxation of
the age-adjusted transformed section, and the stress which results when L1N and L1M are
applied to the cross section.
I'J.acj = £.J~Jeo; + YK;)+ &shj- (!J.eo + yi'J.K )] (23)
The stress change with time in the/" layer of steel is
I'J.a sj = Esj (i'J.e 0 + Ysji'J.K) (24)
Based on the principle of superposition, the total concrete strain at any time is
assumed to be the sum of instantaneous strain due to applied load and strains due to time
effects consisting of creep, shrinkage of concrete, relaxation of prestress and temperature
effects. In addition to the time-dependent effects, if the structure is statically
indeterminate, time effects cause a gradual distribution of redundant moment, oM over
the period of application of the sustained load. Hence, each cross section will be
In stage IV, the deck slab is assumed to attain sufficient strength and the girder
and slab act together as a composite unit. The properties of composite cross-section are
considered in the analysis for this stage. Since the abutment and the deck are integrally
cast, the end supports are no longer simple supports. Now the composite system becomes
statically indeterminate. Age difference between the girder and the slab is considered in
the time-dependent analysis. The time dependent analysis is carried out assuming
composite section with distinct characteristic strengths both for girder and the slab. An
internal redistribution of forces takes place due to creep, shrinkage of concrete and
relaxation of prestressing steel of the girder, and differential creep and shrinkage of the
deck slab due to difference in age of concrete in the girder and the slab. The associated
deck shortening is accommodated by the lateral deformation of the abutment. The axial
force and bending moment in the abutment are calculated based on the lateral
deformation resulting from the creep, shrinkage of concrete. The composite girder is
assumed continuous over supports for time dependent analysis. The time-dependent
restraint forces developed are determined due to creep, shrinkage of concrete and
relaxation of prestress and continuity of the structural system. The changes of forces are
expressed in terms of the unknown strains and curvature considering the equilibrium and
compatibility conditions. The time-dependent changes in the redundant force are
calculated due to creep, shrinkage of concrete, and relaxation of prestressing steel, and
the temperature gradient in the composite section. It is assumed that most of the time-
dependent changes due to creep and shrinkage of concrete and relaxation of prestressed
steel take place prior to the application of live load and that no cracking occurs up to this
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
In stage V the live load is assumed to be applied to the member. The additional
internal forces produced due to the live load produce instantaneous changes in stress and
strain and are assumed to cause cracking, which reduces the effective area of the section.
The analysis of cracked members is carried out in two phases: i) uncracked condition in
which concrete and steel are assumed to behave elastically and exhibit compatible
deformations. Full area of the concrete cross-section is effective and the strains in
concrete and reinforcements assumed compatible; ii) fully cracked section, in which the
concrete in tension is ignored, and the cross-section is considered to be composed of the
reinforcement and concrete in compression zone.
After the application of live load, the instantaneous stresses are evaluated at
various fibers along the span. If the stress at the extreme fiber exceeds the tensile strength
of the concrete, then the section is analyzed using the properties of cracked section. The
cracked region length is identified based on the actual concrete tensile stress. In the
cracked region, the fictitious decompressive forces are computed, along with the forces
that cause cracking of the cross-section. The eccentricity at which the resultant of the
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
cracking forces act is evaluated and the positions of neutral axis computed at various
sections along the span in the cracked region.
· SUBSTRUCTURE MODELING
The bridge substructure system consists of abutment wall, wing wall, the piles
supporting the abutments, and the backfill. The system is idealized as discrete springs for
translational and rotational degrees of freedom. The piles are considered to have fixed
head with no relative movement or rotation between the piles and abutment. Equivalent
cantilever length (Greimann, L. F., et al., 1987) based on stiffuess criterion is used to
evaluate the stiffness of the pile. The substructure system is analyzed considering the
support moments from the time-dependent superstructure analysis that accounts for the
creep, shrinkage of concrete and relaxation of prestress and temperature gradient in the
composite section. These forces are then apportioned to the components of the
substructure system. Based on the parametric studies (Wilson, 1988) the piles of the
substructure system are apportioned seventy five percent of the calculated moment. This
idealization is intended to represent fixed head HP steel piles, with a length to least lateral
dimension ratio of 55, which tends to produce a fairly stiff pile foundation. The
apportionment of 75% rotational stiffness to the piles is on the conservative side, whereas
the actual stiffuess could be much lower. The behavior of the laterally loaded piles due to
the axial force and bending moments determined from the substructure modeling is
evaluated by computing the lateral deflection, bending moment, shear force and stress
along the depth.
The cross-section of the bridge deck is shown in Fig. 4. The tributary width of
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
the deck slab is considered to be the effective flange width for each girder. The idealized
cross-section consists of a precast pretensioned girder and a cast-in-situ concrete slab
(Fig. 5). Age of the precast girder at the time of transfer of prestress is assumed as 3 days
and that at the time of casting of in-situ slab as 60 days. The concrete properties of the
girder and the deck slab are given in Table 1. Each pretensioned girder is assumed to
have an initial prestressing force of 4100 kN (920 kips). The self-weight of the girder is
11.99 kN/m (0.82 kip/ft.). Diaphragms of size 300 x 1200 mm (1 'x 4') are assumed at 1/3
points of the span. Additional superimposed dead load due to the self-weight of the slab,
diaphragm, overlay, barriers etc., is determined as 23.68 kN/m (1.62 kip/ft.). The live
load combinations described in the AASHTO LR.FD ( 1998) Bridge Specifications are
used in the simulations. A bi-linear temperature gradient recommended by AASHTO-
LRFD (1998) for zone 3 is considered in the analysis.
Numerical Results
The deformations and stresses due to typical sustained loads as well as the
effects of live load are computed and presented in Tables 2 to 6. Table 2 shows the time-
dependent moments at the midspan and the supports at various stages of construction.
The numerical simulation based on the AASHTO and ACI models predicts a decrease of
36 % and 42 %, in the negative moment and an increase of 72 % and 84 % in the
midspan positive moment. The redistributions can be attributed to the restraint moments
developed due to creep and shrinkage of concrete, relaxation of prestressing force in the
prestressing tendon, as well as the statical indeterminacy of the integral abutment bridge.
The instantaneous deflections of the cracked section are computed based on the
analytical model, and ACI bilinear method (Nawy, E. G., 2000) considering the elastic
and cracked moment of inertia of the cross-section. Table 3 shows the comparison of the
instantaneous deflections on the 181 51 day at the midspan based on the present study and
the bilinear method. The values of computed deflection from the present study are higher
(26 %) than those based on the bilinear method. This can be attributed to the fact that the
present study considers the variation of cracked cross-section properties along the span
instead of average values.
A stress reversal at the bottom fiber of the composite girder is observed from the
Table 6. The fiber stress changes from compression to tension in this stage, leading to
cracking upon application of the live load.
The typical dimensions of the abutment wall, wing wall, the pile supports and
the backfill for the integral abutmnet bridge under investigation are shown in Fig. 9. The
width of the abutment wall is assumed as 16.80 m (55.1 ft.). The stiffness contributions
of the wingwalls are neglected, since they are not integral with the abutment. It is
assumed that medium dense sand having a soil modulus of 17.2 MPa (360 ksf) is used as
backfill in the abutment. The influence factors are taken as 2.45 for the pile cap and 1.85
for the abutment wall. Poisson's ratio for the backfill is assumed as 0.3.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Numerical Results
The behavior of laterally loaded piles is evaluated by computing the lateral deflection,
bending moment, shear force and stress along the depth due to the axial force and
bending moments. The results of the laterally loaded pile analysis are plotted in Fig. 11
(a) - (d). Only about 50% of the depth from the pile head is shown in the figure for
clarity. Beyond this depth the values are almost constant. The pile analysis shows the
maximum pile lateral displacement to be 0.34mm (0.014 in.) and the stresses in the pile
are within the allowable limits due to the effects of creep in concrete, resulting from the
self weight of the superstructure, shrinkage, and thermal changes in the integral abutment
bridge, the concrete deck strain are small and in the range of 283 to 294 micro strains and
those in the girders in the range of 294 to 370 micro strains (Table 5). It can be seen that
the superstructure deck system is well within the elastic limits in compression without
any cracking.
The lateral displacement, moment, shear and stresses obtained by this approach are
comparable to those of the values obtained using secondary P-6 method for laterally
loaded piles (Arockiasamy et al, 2003). The plot of the results, shows the influence of the
lateral soil reactions is concentrated along the top 3.0 m (10ft.) of the pile, which is about
10 times the equivalent diameter of the pile. Beyond this depth, lateral displacement,
shear force and moment are almost negligible and the lateral forces are insignificant.
The analytical procedure developed in the present study was used in the analysis of a
two-span integral abutment bridge located on Porter Road (PR) across State Rt. 840 in
Dickson, TN. The analytical results are compared with the field measurements reported
by Basu and Knickerbocker (2003). The two-lane PR bridge has two spans of 48.46 m
(159 ft) each as shown in Fig. 12. The initial prestressing force, Pi= 195,458 N/strand
(43,943 lb/strand). The average concrete properties of PR bridge are given in Table 7.
The superstructure of the bridge was constructed in two stages. First, the pretensioned
girders for individual spans were manufactured in a precast products factory, and then
transported to the bridge site, and deck slab is cast after the girders are erected in place.
The structure was divided into 50 segments for the analysis of forces and deformations.
Table 8 compares the results based on the analytical procedure with the measured mid-
span deflection (camber) of both interior and exterior girders (PI and PE). The agreement
between the analytical values and field measurements is good.
The analysis of laterally loaded piles shows that the pile lateral displacements are
negligible and the stress in the pile well within the allowable limits (Fig. 11 ). The
influence of the lateral soil reactions is concentrated along the top 10 ft. (3.0 m) of the
pile, which is about 10 times the equivalent diameter of the pile. Beyond this depth,
lateral displacement, shear force and moment are almost negligible and the bending
stresses are insignificant.
ACKNOWLEDGEMENT
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
REFERENCES
ACI Committee -209 (1992) report on "Prediction of Creep, Shrinkage, and Temperature
Effects in Concrete Structures", American Concrete Institute, Detroit, Ml.
Arockiasamy, M., Butrieng, N., and Sivakumar, M., (2003) "State-of-the-art of Integral
Abutment Bridges: Design and Practice", under publication in the ASCE Journal of
Bridge Engineering.
Arockiasamy, M., and Sivakumar, M., (2003), "Design Considerations for Integral
Abutment Bridges in Florida", Final Report, FDOT Contract No. BC-342, Florida
Atlantic University, Boca Raton, FL.
Basu P. K., and Knickerbocker D. J., (2003) "Discrete Numerical Modeling of Jointless
Prestressed High Performance Concrete Bridges", Proceedings of the lind Concrete
Bridge Conference, Orlando.
Burke, M. P, Jr., (1990) "Integral Bridges", Transportation Research Record, No. 1275,
pp. 53-61.
Greimann, L. F., Abendroth, R. E., Johnson, D. E., and Ebner, P. B., (1987) "Pile Design
and Tests for Integral Abutment Bridges", Final Report, IOWA DOT Project HR-273, p.
302.
Kunin, J., and Alampalli, S., (2000) "Integral Abutment Bridges: Current Practice in
Unites States and Canada" Journal ofPeiformance of Constructed Facilities, Vol. 14
No 3, pp 104-111.
Ma, Z., Huo, X., Tadros, M.K., Baishya, M., (1998)," Restraint Moments in
Precast/Prestressed Concrete Continuous Bridges, PC! Journal, Nov.-Dec., pp 40-57.
Me Donagh, M.D., and Hinkley,K. B., (2003) "Resolving Restraint Moments: Designing
for Continuity in Prestressed Concrete Girder Bridges", PC! journal, July-August, pp
104-119.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Sivakumar, M., (2004), "Creep and Shrinkage Effects on Integral Abutment Bridges",
Ph.D. Thesis, Florida Atlantic University, Boca Raton, FL.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Wilson, J. C., (1988), "Stiffuess of Non-skew Monolithic Bridge Abutments for Seismic
Analysis", Earthquake Engineering and Structural Dynamics, Vol. 16, pp. 867-883.
NOTATIONS
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
AASHTO ACI
Time
(Days) End/interior End/interior
Mid-span Mid-span
Support Support
3 - -3.29E+08 - -3.29E+08
60 - -3.29E+08 - -3.29E+08
61 - 2.14E+09 - 2.14E+09
63 -1.42E+09 7.12E+08 -1.42E+09 7.12E+08
180 -9.12E+08 1.22E+09 -8.25E+08 1.31E+09
181 -2.82E+09 2.18E+09 -2.82E+09 2.18E+09
Redistribution due
to time-dependent
-35.92 71.86 -42.04 84.07
effects from 63 to
180days%
Time Strain at Curvature Stress Stress OeflecUon Interior Moment Change Change
the at the at the at mid- support at in in
centroid top bottom span reaction abutmen interior moment
of the fibero fiber of support at
(xgird~
the the reaction abutment
10 (X 10-8) I girder girder Rc MA liRe liM
Days lmm MPa MPa mm kN kN-m kN kN-m
ACI
3 -291.80 -7.72 -5.86 -8.51 -17.74 - - - -
60 -362.64 -4.55 020 1.05 -27.20 - - - -
61
63
-8.29
-148.33
55.62
-4.58
-15.61 12.62
-4.23 -6.55
70.98
5.71
-
488
-
-1420
-
0
-
0
180 -335.68 -5.57 -o.44 2.64 3B.43 488 - 0 599
181 -349.25 81.17 -8.92 34.29
49.12
AASHTO
- - - -
3 -2.91.80 -7.72 -5.86 -8.51 -17.74 - - - -
60 -483.39 -4.3B 024 1.54 -37.75 - - - -
61 -8.29 55.67 -15.61 12.62 70.98 - - - -
63 -148.33 -4.58 -4.23 -8.55 5.71 488 -1420 0 0
180 -453.79 0.39 -1.10 3.10 79.90 488 - 0 512
181 -364.69 83.25 -7.33 34.93 50.20 - - - -
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Time Deck Deck Deck Girder lop Top Prestress Bottom Girder
opfibe reinforce bottom fiber reinforce level reinforce bottom
Days men! fiber ment ment fiber
level level level
ACI
3 - - - -234.38 -238.24 -332.58 -336.44 -340.30
60 - - - -328.78 -331.05 -366.70 -368.98 -391.25
61 -
63 -105.08 -109.66 -114.25
- - -421.87 -394.06
-114.25 -116.54
285.49
-172.55
313.30
-174.84
341.11
-177.13
180 -283.07 -288.65 -294.23 -294.23 -297.01 -365.13 -367.92 -370.70
181 -349.25 -268.08 -186.91 -186.91 -146.33 845.28 886.15 926.74
AASHTO
3 - - - -234.38 -238.24 -332.58 -336.44 -340.30
60 - - - -450.82 -453.01 -506.53 -508.72 -510.91
61 -
63 -105.08 -109.66 -114.25
- - -421.87 -394.06
-114.25 -116.54
285.49
-172.55
313.30
-174.84
341.11
-177.13
180 -457.47 -457.08 -456.69 -456.69 -456.49 -451.72 -451.53 -451.33
181 -364.69 -281.43 -198.18 -198.18 -156.55 860.50 902.43 944.06
Time Deck Deck Deck Girder top Top Prestress Bottom Girder
top reinforce bottom fiber reinforce level reinforce bottom
Days fiber men! fiber men! ment fiber
level level level
ACI
3 - - - -5.86 -47.65 -66.52 -67.29 -6.51
60 - - - 0.20 -66.21 -77.34 -77.80 1.05
61 - - - ·-15.61 -78.81 57.10 62.66 12.62
63 -2.42 -21.93 -2.63 -4.23 -23.31 -34.51 -34.97 -6.55
180 0.06 -70.97 0.35 -0.44 -69.03 -53.24 -52.59 2.64
181 -10.39 -146.52 -6.58 -11.39 -187.81 3.97 11.87 31.42
AASHTO
3 - - - -5.86 -47.65 -66.52 -67.29 -6.51
60 - - - 0.24 -90.60 -101.31 -101.74 1.54
61 - - - -15.61 -78.81 57.10 62.66 12.62
63 -2.42 -21.93 -2.63 -4.23 -23.31 -34.51 -34.97 -6.55
180 0.76 -104.61 1.25 -1.10 -100.88 -70.52 -69.27 3.10
181 -10.05 -182.83 -5.93 -12.41 -246.10 -34.23 -25.50 33.01
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Fig. 2-Typical cross-section of integral abutment
l~ 6 @ 2095 mm c/c
190
762
1372
-1.60E+09
~--AAsHTOI
E ---- ----
-+-ACI
~ -1.20E+09
z
.:
c -8.00E+08 - - - - -
~
~ ~
-4.00E+08 ---- --------
:a"'c
c
..
ID
O.OOE+OO
4.00E+OB
0 50 100 150 200
llme, Days
200,----------------------------~
i -50 r~~-~l'j;j~~----------------------j=::SHTOt
-100 L__ _ _ _ _ _ _ _ _ _ _ _ --====:::J
0 50 100 150 200
Time, Days
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
~ O.OOE+OO
01
~ 1 OOE..OS
c
& 2.00E+09
3.00E..OS
0 5000 10000 15000 20000 25000 30000 35000
Span Length, mm
1830
Approach slab
Wingwall
4267
Abutment 915
1000 1000
E
E 2000 ~2000
13000 !
Q
3000
4000 4000
(a) (b)
Shear,N Strau,Nimm"'2
·2500 ·2000 -1500 -1000 -500 500 12 16 20
o~~~~~~~~~~~~
1000 1000
E
~2000 e 20oo
'
t
g
3000
4000
13000
4000
(c) (d)
Fig. 11-Pile analysis results along the depth: variation of (a) horizontal displacement;
(b) bending moment (c) shear; (d) stress
~\ 1 . _~_K_k_~__d1-n)----~\~r·G~
\---~----------------~~~~-~-·.o_ \""" ti'LONG
ABUTMENT
IPILECAPJ:
U"tTcPita'
:::::::r~~r-==~::::=::==~~=~==~~~1;;~ ... 1.... 1
WING WALl.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
20-PILES:
NP12XU
by M. A. Chiorino
Synopsis:
The long-term service behavior of modem reinforced or prestressed concrete
structures, whose final static configuration is frequently the result of a complex
sequence of phases of loading and restraint conditions, are influenced largely by
creep. Creep substantially modifies the initial stress and strain patterns, increasing
the load induced deformations, relaxing the stresses due to imposed strains, either
artificially introduced or due to natural causes, and activating the delayed
restraints. The resulting influences on serviceability and durability are twofold,
creep acting both positively and negatively on the long-terni response of the
structure.
The paper shows that use of the four fundamental theorems of the theory of
linear viscoelasticity for aging materials, and the related fundamental functions,
offers a reliable and rational approach to estimate these effects.
Extremely compact formulations are obtained, which are particularly helpful in
the preliminary design, as well as in the control of the output of the fmal detailed
numerical investigations and safety checks, and suitable for codes and technical
guidance documents.
Particular attention is dedicated to the problem of change of static system.
107
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
INTRODUCTION
or three provisional hinges. Continuity at the crown and the abutments is then
introduced at a later stage, simultaneously or in different steps, with or without
concurrent corrections of the stresses by jacking.
The resulting influences on serviceability aoo durability are twofold, creep acting
both positively and negatively on the long-term response of the structure. On one
Besides the discrete approaches in space and time - based e.g. on f.e. analyses
incorporating in the constitutive laws the time-dependent properties of the
material and solved step-by-step by appropriate numerical procedures - compact
methods for a global evaluation of the creep induced structural effects are strongly
needed. This is the case, in particular, in the preliminary design stages, like
comparison of different design solutions and construction sequences, sensitivity
analyses, etc., as well as in the control of the output of the final detailed numerical
investigations and safety checks.
1
For example, in flat three hinged arches the important delayed creep vertical deflections,
besides negatively influencing the service behavior by an unacceptable alteration of the
longitudinal profile of the structure (e.g. a bridge), may induce a non-linear response of
the arches due to second order effects, possibly leading to loss of stability (snap-through).
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Lacidogna 1993, 1999, Chiorino 2000, Chiorino eta!. 1999, 2000, 2002].
Such solutions are based on the use of the three fundamental functions:
- the compliance function J (which is normally the output of creep prediction
models),
- the relaxation functionR,
- the redistribution function~-
This general and concise approach is very suitable for design applications
and it may be recommended for the insertion in codes and technical guidance
documents 3• Consequently it has been adopted by the CEB Model Code 1990
[CEB 1993], the CEB Manual Structural Effects of Time-dependent Behaviour oj
Concrete [Chiorino and Lacidogna 1993], and, more recently, by the CEN
European Standard Eurocode 2: Design of concrete structures, Part 2: Concrete
Bridges4 [CEN 2004].
RESEARCH SIGNIFICANCE
The present paper illustrates this general approach and presents the
corresponding solutions for all the main problems of analysis of structural effects
due to creep.
2
This general approach does not introduce any approximation in the fundamental integral
equation relating strain to the applied stress and to the viscoelastic compliance J
(Appendix I, eq. Al.l), as it is the case for the methods based on the approximate
algebrization of this equation, like e.g. the age-adjusted-effective-modulus (AAEM)
method [Bazant 1972b] (Appendix 3).
3
Through the introduction of modified functions (in particular the reduced relaxation
function R *), the same compact solutions can be extended to cover the case, which is out
of the scope of the present paper, of concrete structures with external elastic (steel)
restraints. These last fonnulations - still theoretically consistent, conceptually simple and
concise - have been presented in the specialized literature [Chiorino et al. 1986, Mola
1993, Giussani and Mola 2003]. They are very helpful in the pre-design and final checks
of cable-stayed structures, concrete arches with steel tie rod, and similar structures.
4
The AAEM method has been considered by CEN Standard as an alternative to the
general approach.
At the same time, the paper discusses the implications connected with the need
of disposing of an immediate information on the values of the basic functions J, R,
~ characterizing the resolving formulations, and the relation of this problem with
the problem of selecting an appropriate creep prediction model. In fact, the
expedience of the compact formulations presented in the paper is strictly related to
the prompt availability of the numerical values of the basic functions for the
different parameters relevant to the problem under consideration.
While the conceptual and practical aspects of this last problem are discussed in
a parallel paper [Sassone and Chiorino 2005], the present paper focuses the
attention on the large differences that are found, in the trends and long-term
values of the basic functions corresponding to each model.
TYPES OF STRUCTURES
The solutions presented in this paper, derived from the direct application of
one of the four basic theorems of the theory of linear viscoelasticity for aging
materials, apply to homogeneous concrete structures with rigid restraints.
TYPES OF PROBLEMS
One of the main reasons of these common choices in the conceptual design and
in the selection of the construction process is represented by the convenience of
initially exploiting at their best the large economical and operational advantages
offered by prefabrication and/or segmental construction techniques (Fig. 3). In
some cases the initial static configuration is the result of a specific construction
process requiring temporary hinges for the rotation of structural segments which
BASIC FUNCTIONS
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Within the field of the theory of linear viscoelasticity for aging materials
(Appendix I), time dependent properties of concrete are fully characterized either
by the creep (compliance) function J(t, 'r) or the relaxation function R(t, 'r), where:
J(t, 'r) represents the stress dependent strain per unit stress, i.e. the response at
time t to a sustained constant unit imposed stress applied at time '!;
R(t, 'r) represents the stress response at time t to a sustained constant unit
imposed strain applied at time 't
The compliance and the relaxation function are reciprocally related by the integral
equation:
I
J
I= R(t0 ,t0 ) J(t,t 0 ) + J(t, r)dR('r,t0 ) =
to
I (I)
=Ec(t0 )J(t,t0 )+ fJ(t,7:)dR(r,t 0 )
'•
Redistribution function ~(t,toh)
When the static scheme of the structure is modified at a time t 1 ~ t0+ (t 0 being the
age at application of constant sustained loads and to+ the same age immediately
after loading), the redistribution function ~ measures, at a given time t, the creep
induced part of the difference between the stress distribution corresponding to an
hypothetical application of the constant sustained loads to the structure in its final
The redistribution function c; has the character of a non dimensional factor whose
values lie in the interval (0,1) (with ~ = 0 for t = t 1 ), and is related to the
compliance and to the relaxation functions through the equivalent expressions:
t
I
J(t,t 0 )-J(t 1,t0 ) == JJ(t,r)d~(T,t0 ,t 1 ) (3)
If the change of static scheme is operated immediately after the initial elastic
deformation of the structure following the application ofloads at t =to (i.e. t1 =to +)
one obtains:
(4)
The solutions for the basic problems are given in the following in application
of the four theorems of the theory of linear viscoelasticity for aging materials5•
The solutions obtained for every type of problem may be superimposed in time on
the basis of the principle of superposition forming the basis of this theory.
Denote:
S (t) = system of the stresses (internal stresses, sectional forces, external
reactions)
5
The F' and 2nd theorem conceming, respectively, the effect of imposed loads and of
imposed deformations were restated by the author within the theory of linear
viscoelasticity for aging materials in [Chiorino et al. 1980, 1984]. The 3rd theorem
concerning the effect of a single change in the static !'Cherne was first demonstrated by
the author [ibidem and Chiorino and Lacidogna 1993]. An earlier proof within the theory
of aging was given in [Levi 1951]. The 4th theorem, concerning the effect of multiple
changes in the static ~heme, was first proved in [Chiorino and Mola 1982]. See also
[Dezi, Menditto and Tarantino 1990]. A concise proof of the 4th theorem is given in
Appendix 2.
with:
elastic solution for the system of the stresses in the associated elastic
problem for the initial value Ec(t0) of the elastic modulus at t = t0 ,
elastic solution for the system of the deformations in the associated
elastic problem for Ec (t 0).
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Denote:
S 2 (t) system of the stresses for t> t 1 in the modified structure with the final
static scheme 2, with 11.2 = n1 + .:ln1 restraints,
S ei,I elastic solution for the stresses in the original structure with initial
static scheme 1, with n1 restraints,
L1S 1 (t) == creep induced correction of the stresses of the original structure,
L1S e/,1 == correction to be applied in the associated elastic problem to the elastic
solution S e/,1 in order to respect the .:ln1 additional geometrical
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
conditions imposed by the ~n 1 (external or internal) additional
restraints of the final static scheme 2, imagined as introduced before
the loads (i.e. for loads imagined as applied to the structure in the static
scheme 2, with all the n2 restraints).
(9)
The higher is the residual creep deformation capacity of the structure after the
application of all the restraints, or of the main part of them, the higher is this
tendency. ·
Compliance function J
Derived functions R. g.
Equations (1) and (2) [or (3)] enable to obtain the derived functions R, ~ from the
reference compliance J .For realistic forms of J, eq. (1) and (3) are not integrable
analyticalll and numerical integration is mandatory. Criteria for the numerical
processing were first proposed in [Bazant 1972a].
6
For the determination of the redistribution function ~'the numerical solution of integral
eq. (3) is normally preferred to the calculation of the integral of eq. (2) requiring the
previous determination of the relaxation function R. For more information see the parallel
paper [Sassone and Chiorino 2004]
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
The criteria for establishing this interactive source of information are discussed
in detail in the parallel paper [Sassone and Chiorino 2005], which illustrates the
web site created at the Politecnico di Torino (www.polito.it/creepanalysis). As a
first step the three new prediction models (CEB MC90, GL2000 [Gardner and
Lockman 2001] and B3 [Bazant and Baweja 2000]) included by ACI Committee
209 on Creep and Shrinkage in Concrete in its new draft document [ACI 209
2004] have been incorporated in the website.
The essential idea is to build up a flexible tool with a user friendly interface to
obtain, for each basic function and for any selected set of the input parameters
referring to ambient, concrete mix and size of the structural element:
- spot-type numerical evaluations of the function under consideration for given
values of the age and time variables,
- full graphical representations of the family of curves for an extended range of
values of time and age.
The web site has a flexible architecture and will be progressively extended to
include the automatic calculation of other functions of interest for the creep
analysis of structures 9•
7
For the CEB MC90 creep prediction model [CEB 1993] an extended set of graphs of J,
R and ~ for a wide spectrum of the parameters influencing the creep properties of
concrete were published in the revised edition of CEB Manual Structural Effects of Time-
dependent Behaviour of Concrete [Chiorino and Lacidogna 1993].
8
At this respect, it must be considered that in the past years the numerical integration of
the Volterra integral equations of the type of eqs. (!)and (3) was a rather slow process,
due to the limited speed of computers; as a rough indication, when more than a hundred
time steps were used, many hours of computer time could be necessary. Today, the power
of computers has grown enough to allow a true real-time integration of these equations on
a personal computer.
9
For example. the aging coefficient X (see Appendix 3) of the age-adjusted-effective-
modulus-method, and the reduced relaxation functions R* (see note 3).
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Each function has been explored until maximum values of the age t0 at loading,
and of age t1 at modification of the static scheme, of 2 years (730 days), and up to
elapsed times t larger than a reference value of 100 years = 3.65x10 4 days. This
reference value has been selected in consideration of the fact that adequate
serviceability and durability conditions must be guaranteed for an expected
service life of the same order of magnitude for important structures, like e.g.
bridges and tunnels. However, the general trends of the curves do not change in a
significant way, and the same comment may be expressed, if both the age at
loading t0 , the age t1 at modification of the static scheme, and the final observation
time t, are limited to half of these values. Extended explorations performed for
different sets of parameters - covering a wide spectrum of possible situations of
ambient, concrete mix and size of the structural element ambient - confirm the
same general trends, showing that these differences are related to the structure and
the basic conceptual fundaments of the models.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
The criteria adopted for the extrapolation depend on the conceptual fundaments
that are at the base of each creep prediction model, and that may be partly related
to different physical interpretations of the rheological behavior of concrete. As a
general consensus on these fundaments is yet far to be reached, although it may
benefit in the future of more fundamental studies in the physics of concrete
developed by the research community (see e.g. Bazant et al. 2004, and included
references), a provisional conclusion must be drawn, and a reasonable guideline
formulated, for the needs of codes and technical guidance documents and
manuals.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
In the author's opm10n, the only possible conclusion at this stage is the
recommendation to refer, in the assessment of the serviceability of structures with
respect to creep effects, to a range of long-term values for the basic functions
characterizing the different solutions comprised between an upper and a lower
bound, in order to account for the large differences still existing between different
creep prediction models.
EXAMPLES OF APPLICATION
Three examples are considered. For the sake of simplicity, and in the principal
aim of evidencing the effectiveness of the proposed solutions in sizing the main
aspects of the structural problem under consideration, two simple structural
schemes and construction sequences have been selected. More complex sequences
of loading and restraint can be analyzed easily by the same approach.
The first two examples concern a problem of modification of the static scheme
through the introduction of additional restraints in one step (cantilever built bridge
made continuous}, or in two steps Qocking of provisional hinges in a concrete
arch). The third example concerns the application of artificial imposed
A three span cantilever built bridge is considered (Fig. 3). The delayed
connection at midspan of the central span transforms the statically determinate
scheme 1, consisting (after removal of provisional side jacks on piers and fixing
lateral ends to abutments) from two simply supported beams with central
overhangs, into the continuous beam of scheme 2 (Fig. 4).
Heterogeneities of the creep properties along the structure, with particular regard
to differences in the age of concrete, are diregarded. As the bridge is built by
segmental construction technique, this last assumption would be approximately
met in the case, which is imagined here, of a sufficiently short duration of the pre-
casting and assembling phases in comparison with the amplitudes of the time-lags
between these phases, and between the assembling phase (during which the
permanent actions of self weights and initial prestressing are applied) and the
moment of variation of the static system.
For a single change in static scheme, eq. (9) (3rd theorem) applies, with t 0
representing the average age of application of the permanent actions acting before
the introduction of the continuity restraint (self weight w, and initial prestressing 10
p approximately treated as a system of imposed constant forces), and 11 the time of
introduction of the continuity restraint (casting of the mid-span segment).
Solving equations
The development in time, and the long-term value (t = 100 years = 3.65xl04
days), of the bending moment at the median section of the central spans (where
Mmei.J,w+p = M,/·'·P) is then given by the following expressions obtained from eq.
(9) for S 2 (t) = Mm 2 (t), S ''·' = Mmeu.p, and L1S e/.J = ,1Mme/.J,w+p:
M 2/tl
1m
= M e/,J,p
~ / m
+ '!!/t
=' (•, t 0, t}
1
Mf. el,l,w+p
m (11)
(12)
10
Prestressing applied to the structure in the initial cantilever static configuration.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Numerical evaluation
Only the long term values (t = 100 years) of the creep-induced stress
redistribution are investigated here. Three different creep prediction models are
considered, namely CEB MC90, GL2000 and B3.
The following values are considered for the main parameters governing the
problem through their influence on the creep compliance function J (and
consequently also, due to eq. (3), on the redistribution function~):
t0 = 28 days (average value of the age at loading and application of prestress,
neglecting the duration of the assembly phases of the cantilevers), t1 = 90 days,
relative humidity R.H.= 80 % (h = 0.8), concrete strength fck = 40 MPa, notional
=
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
size (effective thickness 2 VIS) 2Ac /u 400 mm, with reference to the average
geometrical characteristics of the cross sections of both bridges (notations for GL
2000 and B3 models in parenthesis).
I
The long term values ~(100y,28,90) of the redistribution function are obtained
from the numerical processing of eq.(3) [Sassone and Chiorino 2005]:
CEB mode/1990: 0.49
GL2000: 0.65
B3 model: 0.87.
Therefore, the three models predict very different long-term creep induced
redistribution effects
The long term bending moments M 2 (JOOy) in the final structure, due to the
permanent actions (w+p) applied to the original structure and to the stress
redistributions induced by creep, are represented in Fig.6 for CEB MC90, GL2000
and B3 models, respectively. They are compared with the moments M et,J,w+p in
the original cantilever structure (static scheme 1), and with the moments
M 1·2·w+p= Met,J,w+p+ t1Met.J,w+p evaluated for the final static scheme 2 [i.e. for the
permanent actions (w+p) imagined applied to the structure in static scheme 2].
These results confirm that the prediction models adopted in the analysis have a
considerable influence on the amount of the estimated stress redistribution due to
creep, and underline the need to refer to a range of long-term values comprised
between an upper and a lower bound, to account for differences in the models.
We will consider the case of a concrete arch constructed with three provisional
hinges, which are locked at a later stage after decentering. Fig. 9 shows e.g. the
provisional hinges adopted in the crown and abutment sections of the Fiumarella
Viaduct in Italy (figs. 7 and 8, arch span 231 m. [Morandi 1961 ]), with details of
the reinforcement of the concrete added in second phase to obtain the continuity.
The hinges are imagined to be locked in two successive steps, first the hinges at
the abutments at time t1 > t0 +and then the hinge at the crown at time t2> t 1•
At the time t = t0 of decentering and application of the dead load the arch behaves
as a statically determinate three-hinged arch. Successive locking of the hinges by
casting additional concrete establishes continuity introducing an additional degree
of restraint for each locked section.
Creep activates these delayed internal restraints influencing the long term stress
condition of the arch, which tends to approach the stress condition of a hingeless
arch. In the case of an arch with a center line corresponding to the funicular curve
for the dead load, creep gradually reintroduces the reduction H' of the thrust 11 due
to axial shortening, and the consequent displacements of the thrust line and
parasite moments, that were eliminated by the introduction of the provisional
hinges.
As this is a case of a double change in the static scheme, eq. (10) (4'h theorem)
applies, withj= 2.
The example is dealt with in the following in a schematic form, without reference
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
to a specific case study. The evaluation of the elastic terms may be performed in
practical cases with reference to the elastic theory of arches, taking advantage of
11
With respect to the thrust H calculated for a three-hinged arch. The reduction H' of the
thrust His applied at the elastic center of the arch [Timoshenko 1965]
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
L1S e/, 1 redundant correction to be applied to S e/, 1 in order to
respect the additional geometrical constraints imposed at t
= t1 by the elimination of the hinges at the abutments;
s e/, 2 = s e/,1 +L1S e/,1 = elastic solution for the system of the stresses
Static scheme 3: Hingeless arch
L1S •1•2 redundant correction to be applied to S e/, 2 in order to
respect the additional geometrical constraints imposed at t
= t2 by the elimination of the hinge at the crown;
s •1•3 = s '1•2 +L1S e/, 2 = elastic solution for the system of the stresses.
Solving equations
The development in time, and the long term value (t = 100 years), of the system
S(t) ofthe stresses in the arch are obtained from eq. (10):
Numerical evaluations
Only the long-term values (t 100 years) of the creep-induced stress
redistribution are discussed here.
In usual situations the difference between t 1 and t2 is rather limited (of the order of
the days or of a few weeks), while the time interval between the application of the
loads at t0 and the first locking of hinges may be of the order of some weeks or a
few months, as a maximum
As far as the restraining conditions at the jacking section are concerned, it must be
noted that they depend on the arrangement of the jacks. Most frequently jacks are
placed on two lines on each side of the centroid of the arch section (Crozet, Fig.
13), or they are distributed on the perimeter of the section (Gladsville, Fig. 11).
Therefore the continuity of the arch is not interrupted and a delayed locking of the
jacking section by additional concrete does not introduce any additional restraint.
The problem to be considered in this case is simply a problem of sustained
geometrical actions (2nd theorem, constant imposed deformations) 12 •
Solving equation
Let .1 S el,t, represent the elastic stress response in the arch to the constant
deformation imposed by jacking, evaluated for the initial value Ec(t0) of the elastic
modulus at t = t0 (i.e. the initial value of the imposed stress correction).
The development in time, and the long term value (t = 100 years), of the stress
correction .1 S(t) are obtained from eq. (8)':
(15)
12
Crown section has been forced in some cases with a single line of jacks at its centroid
(Krk Bridge, [Stoidanovic and Sram] (1981), fig. 14). Therefore, the initial restraint
condition at loading in this section is equivalent to a hinge. If the jacking section is finally
locked at a later stage by additional concrete, the continuity is established in the section
with an increase of the level of restraining (change of static system). In this case two
problems coexist: a problem of sustained constant geometrical actions, and one of
modification of the static scheme. Their solutions may be sought separately on the l:asis
of the indications given in this paper, and then superimposed in time in application of the
principle of superposition.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Numerical evaluations
Only the long-term values (t 100 years) of the creep-induced stress are
discussed here.
Inspection of the diagrams of the relaxation function in Fig. 15 for the different
creep prediction models shows that the long-term creep induced attenuation of the
initial stress correction is rather drastic, in particular if jacking is applied when
concrete is still rather young.
The preceding discussion concerning the creep induced structural effects on the
stress distribution in hingeless concrete arches, subjected to one of the two
different widely used technical artifices aimed to improve the stress distribution in
service - i.e. adoption of provisional hinges or jacking - shows that the effect of
creep tends to substantially reduce the long term benefits of both techniques 13•
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
It is observed that, in spite of the fair to good ratings that - depending on the
statistical indicators adopted - have been attributed in the recent literature to all
three models in their evaluation with respect to the experimental results contained
in the data bank and concerning the compliance J, these significant differences
arise as a consequence of an extrapolation process. This extrapolation process is
essentially developed in the J domain, in order to extend the time horizon of its
prediction beyond the typical durations of the experimental investigations, whose
results are summarized in the data bank, up to significant values of elapsed times
and of the ages at loading of the order of magnitude of the service life of
important structures. The compliance values for high ages at loading are needed
for the subsidiary numerical determination of the secondary functions R and ; .
This aspect deserves proper attention in the present discussions taking place
within international associations on the proper prediction models to be considered
in practical design situations.
The paper is concluded by the presentation of two case studies concerning the
effect of creep in case of changes in the static scheme in prestressed cantilever
built bridges and in reinforced concrete arches. A third example concerns the
effect of creep on the stress corrections obtained by jacking of the arches.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
At this respect, in the author's opinion the only possible conclusion at this
stage is the recommendation to refer, in the assessment of the serviceability of
structures with respect to creep effects, to a range of long-term values for the
basic functions characterizing the different solutions comprised between an upper
and a lower bound, in order to account for the large differences still existing
between different creep prediction models.
ACKNOWLEDGEMENTS
The author is indebted to Franco Levi, professor emeritus of the Politecnico of
Turin, Honorary President of CEB and FIP and Honorary Member of ACI, for
continuous guidance and encouragement. The assistance of Dr. G. Lacidogna and
Dr. M. Sassone is gratefully acknowledged.
APPENDIX 1
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Fundamentals of linear viscoelasticity of aging materials applied to concrete
Introducing the creep (compliance) function J(t, r) and the' relaxation function
R(t, r) and summing the responses to all uniaxial stress and strain increments
introduced at times r, the following integral relations are obtained to model the
responses at time t to sustained variable imposed stresses or strains:
I I
where:
l::crr (t) = r.c(t) - l::cn(t) = stress-dependent strain,
ec (t) = total strain at time t,
l::cn(t) =stress-independent strain,
a(t) = stress at time t,
and the hereditary integrals must be considered as Stielties integrals in order to
permit discontinuous stress or strain histories a(t) and t:ccr(t) If the law of variation
ofthe imposed stress or strain is considered continuous after an initial finite step,
the ordinary Rieman definition of the integral applies and eqs.(A 1.1) and (A 1.2)
may be written in the form:
f
I
where J and R represent the uniaxial 14 creep and relaxation operators [Mandel
1958, 1974, Bazant 1975).
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
J(r+il,r)
I
=J(r,r) =Ec(r)
-- (Al.3)
1
T(t,r)=--+C(t,r) (Al.4)
Ec(r)
14
Extension of eq. (Al.l) to multiaxial stress may be easily performed [Bazant 1975] and
it can be shown that under the assumption of isotropic behaviour and constancy of the
creep Poisson's ratio v(t, 1), which is sufficiently confirmed by experimental evidence at
least for sealed specimens [see e.g. list of references in Bazant 1975], creep deformability
of concrete is fully characterised by J(t, r).
It must be noted that for structural analysis only the compliance function J(t, 'l') is
of importance (and the related functions R(t, 'l') and ~ (t,t 0,t1)). The conventional
separation adopted in eq. (A1.4) and the value of ..1 in eqs. (Al.3) and (Al.5)
have no influence on the result of the analysis, except in the definition of the
"initial" (nominally elastic) state of deformation or of stress due to a sudden
application of actions (respectively forces or imposed deformations, see e.g. eqs.
(6)' and (8)' in the text). Such a state is in effect by itself a matter of convention
depending on the procedures in the application of the actions at t = t0 on the
structure, on the initial time t0 + ..1 of observation of the effect and on the
measuring procedures 15 •
Standard numerical procedures for the solution of the integral equation (1) have
been developed [Bazant 1972a] and they have been incorporated in design
manuals [Chiorino et al., 1980, 1984, Chiorino and Lacidogna 1993, 1999],
bringing to an end a line of research, which has occupied some fifty years, aimed
15
The elastic modulus Ec2s is tenned Eci in the CEB Model Code 1990 [CEB 1993] and
Ec in the CEB Design Manual (Chiorino and Lacidogna 1993]. It is defined as the tangent
modulus of the stress-strain diagram obtained for monotonically increasing compressive
stresses <ic or strains Ec at a rate of ic:tl"' 1MPa 1sec or je, 1= 30 ·I o_.sec_,, respectively.
For current ACI model and model GL2000 refer to the specific documents.
For model B3 a reference value .:l = 10 sec= 0.00012 days has been adopted in the
examples of the basic functions (Fig. 15), and in the examples of application.
APPENDIX2
(A2.1)
APPENDIX3
Eq. (Al.l)' may be written in the following equivalent algebraic form when the
creep function is ofthe type ofeq. (Al.6):
(A3.3)
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
The approach based on the aging coefficient X [Bazant 1972b] leads to solutions
that are in some cases equivalent to the fundamental solutions of the general
approach based on theory of linear viscoelasticity for aging materials developed in
this paper (general method), e.g. in the cases of constant imposed loads (static
actions) or deformations (geometrical actions), or of a linear combination of these
problems.
For the problems of variation of static scheme this equivalence is limited to the
case, seldom encountered in practical design situations, of a single variation of
static scheme introduced at t =to+ immediately after the application of the loads 16•
In fact, from eq. (A3.2) one obtains the following relations between the basic
functions of the general method and the aging coefficient:
and therefore:
;; ( +) _ I R(t,t 0 ) _ _....!.!/>_,_(t..:...,t-"-
0 "--)-:- (A3.6)
"' t,fo,lo - - -
Ec(t 0 ) 1+ X¢(t,lo)
On the contrary, the solution based on the aging coefficient X is not valid if the
change of static scheme is operated at any time t 1 after the time t0 of application of
the loads, which is the case in most practical design situations. The only correct
solution is obtained in a very straightforward way on the basis of the 3rd theorem
using the redistribution function ~(t,t0,t1).
Similarly, the aging coefficient method is inapplicable to deal with the problem of
multiple successive changes of static system (which is also a frequent case in most
practical design situations). The only correct and simple solution is obtained
superimposing the effects of the successive changes of static scheme, as indicated
1
by the 4 h theorem. In all these cases the solutions based on the aging coefficient X
may introduce unacceptably large errors.
16
In fact, in this case we may imagine to reach the final static configuration applying the
loads on the final static scheme with all the restraints (a problem of constant imposed
loads) and introducing, immediately afterwards, a state of constant imposed deformations
to annul the geometrical constraints introduced by the additional restraints.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
REFERENCES
ACI ( 1992), Prediction of Creep, Shrinkage, and Temperature Effects in Concrete
Structures, ACI 209R-92 (under revision by ACI Committee 209), 47 pp.
ACI 209 (2004), Guide to Factors Affecting Shrinkage and Creep of Hardened
Concrete, Chapter 5 - Modelling and Calculation of Shrinkage And Creep, Draft
Document.
Bazant Z. P. and Baweja S. (2000), Creep and shrinkage prediction model for
analysis and design of concrete structures: Model B3. in: A. Al-Manaseer ed., A.
Neville Symposium: Creep and Shrinkage -Structural Design Effects, ACI Fall
Convention, 1997, ACI SP-194, pp. 1-83.
Chiorino M.A. and Mola F., (1982), Analysis of Linear Visco-Elastic Structures
Subjected to Delayed Restraints, in: F.H. Wittman ed., Fundamental Research. on
Creep and Shrinkage of Concrete, Mart. Nijhoff Publ., pp. 485-496.
Chiorino M.A. (Chairm. of Edit. Team), Napoli P., Mola F. and Koprna M.,
(1980, 1984), CEB Design Manual on Structural Effects of Time-dependent
Behaviour of Concrete, CEB Bulletin N° 142/142 bis, Georgi Publ. Co., Saint-
Saphorin, Switz., 1984, 391 pp. Final Draft April 1980, CEB Bulletin
d'Information N° 136, 268 pp. and appendixes.
Chiorino M.A., Creazza G., Mola F. and Napoli P. (1986), Analysis of Aging
Viscoelastic Structures with n-Redundant Elastic Restraints, Fourth RILEM
International Symposium on Creep and Shrinkage of Concrete: Mathematical
Modelling, Z.P. Bazant ed., Northwestern University, Evanston, 1986, pp. 623-
644.
Chiorino M.A. and Lacidogna G. (1993), Revision of the Design Aids of CEB
Design Manual on Structural Effects of Time-Dependent Behaviour of Concrete
in Accordance with the CEB/FIP Model Code 1990, CEB Bulletin d' Information
N° 215,1993, 297 pp.
Chiorino M.A. and Lacidogna G. (1999), General Unified Approach for Creep
Analysis of Concrete Structures, ACI-RILEM Workshop Creep and Shrinkage of
Chiorino M.A., Dezi L. and Tarantino A.M. (2000), Creep Analysis of Structures
with Variable Statical Scheme: a Unified Approach, in: A. Al-Manaseer ed., A.
Neville Symposium: Creep and Shrinkage - Structural Design Effects, ACI Fall
Convention, 1997, ACI SP-194, 2000, pp. 187-213.
Chiorino M.A., Lacidogna G. and Segreto A. (2002), Design Criteria for Long-
term Performance of Concrete Structures Subjected to Initial Modifications of
51
Static Scheme, in Concrete Structures in the 21st Century, Proceedings of the 1
fib Congress 2002, Osaka, October 13-19,2002, pp. 285-294.
Colonnetti G. (1914), Sui problema dell'arco elastica con o senza cerniere (On the
Problem of the Elastic Arch with or without Hinges), Atti della Reale Accademia
dei Lincei, Anno CCCXI, Vol. XXIII, 2° Sem., Roma 1914, pp.254-257. See also:
Scienza delle Costruzioni (Statics and Theory of Elasticity), Vol. 2, Einaudi,
Torino, 1955 (in Italian).
Dezi, L., Menditto, G., and Tarantino (1990), A.M., Homogeneous Structures
Subjected to Repeated Structural System Changes, J. Engrg. Mech., ASCE, Vol.
116, No.8, August, 1990, pp. 1723-1732.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Mandel J. (1958), Sur les Corps Viscoelastiques Lineaires dont les Proprietes
Dependent de l'Age (Age-dependent Linear Viscoelastic Bodies), ,Comptes
Rendues des Seances de l'Academie des Sciences, 247, 1958, Paris, pp. 175-78 (in
French).
Morandi R. (1961), L'arco peril viadotto della Fiumarella presso Catanzaro (The
arch for the Fiumarella viaduct near Catanzaro, L'Industria Italiana del Cemento,
7, 1961, pp. 341-52, (in Italian).
Stoidanovic I. and Sram S. ( 1981 ), Les ponts en arc de Krk en Yougoslavie (The
arch bridges of Krk in Yougolavia), Annales ITBTP, No. 393, April 1981, (in
French).
Sassone M. and Chiorino M. A.(2005), Design Aids for the Evaluation of Creep
Induced Structural Effects, in J. Gardner and J Weiss eds., Shrinkage and Creep of
Concrete, ACI SP-. 2005.
n rl --
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
t1 1"1 ll n n rl
~T~ -- q: tF
'
to::==== --
Fig. !-Examples of change in the static scheme.
a::::=== •
-10
~
ze -a
.....
.:.::
-
0
.....
:E
-2
6
2
7 5
Fig. 5-Bending moments in the orginal free cantilever structural configuration due to
self-weight (w), intial prestressing (p), and to their combination (w + p).
Fig. 6-Long term bending moments M 2(1 05) in the final structure. Comparisions with
moments M e1. 1·" + P (static system 1) and M ' 1• 2• "'+ P (static system 2).
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
~i·~
.
~ =~----· __. ____;
·-------l!W .... - ---··
Fig. 10-Giadsville Bridge, Sidney, Mausnell & Partners 1964: location of jacking sites.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Fig. 14-Krk Bridge, I. Stoidanovic 1981: general view during construction and
detail of jacketing section at the crown.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
¥to-•
-- ,go,....
-- l001'NI'S
Fig. 15-Examples of the diagrams of basic functions J (t, r), R (t, r), q(t, tO' t 1), for
different creep prediction models and for average values of the influencing parameters.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
From left to right CEB MC90, GL2000, and B3 models. Time in days. (for further
information refer to [Sassone and Chiorino 2005]).
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
by I. N. Robertson and X. Li
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
The long-term response of this structure is presented and compared with the initial
predictions made during the design process. Modified material properties based on short-
term shrinkage and creep tests were incorporated into the long-term prediction model to
produce significantly improved comparisons. A procedure is proposed for prediction of
upper and lower bounds for the long-term response of long-span prestressed concrete
bridges. This improved prediction model is applied to the other five units making up the
NHVV to verify its performance as a design tool.
The results of this study were then incorporated into the development of an
instrumentation system for the planned Kealakaha Bridge on the Island of Hawaii.
Application of the prediction model is demonstrated using shrinkage and creep data
determined from short-term tests performed on the concrete mixture proposed for this new
long-span box-girder bridge structure.
143
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144 Robertson and Li
ACI member Ian N. Robertson is associate professor of civil engineering at the Univer-
sity of Hawaii at Manoa. He is a member of ACI Committees 209 Shrinkage and Creep
and 352 Joints and Connections in Monolithic Concrete Structures. His research interests
are field instrumentation and monitoring of structural response to time dependent and ex-
treme events, seismic response of concrete systems, and FRP retrofit of concrete mem-
bers.
Manoa. His research interests include the prediction of long term effects on concrete
structures, and computer modeling of structural response.
INTRODUCTION
The North Halawa Valley Viaduct (NHVV) is a 1.5 km box-girder viaduct with span
lengths up to II 0 m. It is part of the new H-3 freeway on the island of Oahu in Hawaii.
The twin inbound and outbound viaducts were built by means of post-tensioned in-situ
balanced cantilever construction as described by Banchik and Khaled (I). Each viaduct
consists of three structurally independent units. Four spans of Unit 2 of the inbound via-
duct, Unit 2IB, were selected for instrumentation to provide an adequate representation of
the viaduct long-term behavior (Figure I). The instrumentation program was developed
in conjunction with T.Y. Lin International, structural engineers for the viaduct. Personnel
from the University of Hawaii (UH) and Construction Technology Laboratories (CTL) in
Skokie, lllinois, installed all instruments during construction of Unit 2IB.
The instrumentation used in this project was designed to provide long-term monitor-
ing of the structural performance of the viaduct. The measurements required to achieve
the project objectives include concrete strains, concrete and ambient temperatures, con-
crete creep and shrinkage strains, span shortening, tendon forces, span deflections, and
support rotations. In order to perform these measurements, over 200 instruments were
installed including vibrating wire strain gages, electrical resistance strain gages, thermo-
couples, extensometers, tendon load cells, base-line deflection systems, tiltmeters, and
automated datalogger recording systems.
This paper presents results from the vibrating wire strain gages, span longitudinal and
vertical deflection measurements, and tendon prestress forces. These measured results
are compared with long-term analytical predictions using SFRAME, a time-dependent
step-wise finite element analysis program written specifically for analysis of incremen-
tally constructed bridges (2). Comparisons based on the original analyses performed dur-
ing the design phase show poor correlation with the observed response. However, based
on short-term creep and shrinkage tests performed on the concrete used in the structure,
improved material parameters were developed for use in SFRAME. These updated mate-
rial parameters provide improved long-term predictions, leading to development of a de-
DESCRIPTION OF INSTRUMENTATION
Instrument Locations
Seven sections were selected for instrumentation in order to provide an adequate rep-
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
resentation of the viaduct behavior. Sections A, D, E and G are at, or close to midspan,
while B, C and Fare close to the ends of the instrumented spans as shown in Figure 1.
The primary instruments for measuring concrete strain are Vibrating Wire Strain
Gages. These gages were embedded in the concrete to measure longitudinal strain. Ten
vibrating wire strain gages were placed around the box-girder cross-section at each end
span instrumented section (B, C and F) as shown in Figure 2. Eight gages were placed
around the midspan sections (A, D, E and G) in the same locations as shown in Figure 2,
but without gages 5 and 9. For comparison with the predicted top slab strains, gages 1, 3
and 7 readings are averaged. For comparison with the predicted bottom slab strains,
gages 2, 6 and 10 readings are averaged. The predicted strains are computed at the level
of the gages using linear interpolation between top and bottom fiber predictions provided
bySFRAME.
Extensometers were installed in the four instrumented spans to monitor the overall
shortening of the box-girder. Each extensometer consists of a series of graphite rods
(6mm diameter by 6m long) spliced together to span from pier to pier inside the box
girder. The rods are coupled together and inserted into a 20mm diameter PVC pipe at-
tached to the underside of the girder top slab. One end of the rod is fixed to the top slab
A taut-wire base-line system was installed in each of the four instrumented spans to
monitor vertical deflection of the box-girders. This system consists of a high-strength pi-
ano wire strung at constant tension from one pier to the next, inside the box girder, to act
as a. reference line as shown in Figure 3. A precision digital caliper was used to measure
the distance between the base-line and steel plates attached to the underside of the top
slab. Changes in the caliper readings indicate the vertical deflection of the box girder
relative to the ends of the span. The base-line system measurements were confirmed by
comparisons with optical surveys performed by the State of Hawaii as part of the bridge
maintenance program. Figure 4 and Figure 5 show that the base-line deflections compare
well with the optical survey results for Unit 218 after 2 and 8 years of monitoring, respec-
tively. In some cases the base-line systems were able to identify apparent errors in the
optical survey readings as noted at midspan between P8 and P9, and at P9 in Figures 4
and 5. Similar errors in the optical survey results were noted at other locations, but in
general the optical survey results are assumed to provide a reasonable record of the via-
duct vertical deflections. The base-line system also produced reliable results for short-
term deflections during a load test and thermal study performed on the viaduct (4). These
vertical deflection measurements are compared with the SFRAME predictions by normal-
izing the predicted top-of-pier deflections to zero at each end of the span so as to remove
pier and foundation deformations from the predicted deflection.
The SFRAME computer program is a finite element code specifically developed for
the prediction of long-term response of segmentally constructed prestressed concrete
bridges (2). In addition to structural geometry and section properties, the input data in-
cludes a constitutive model of the concrete material. This model includes the time-
dependent variations in modulus of elasticity, shrinkage and creep. The program em-
ploys a step-wise incremental analysis of the bridge structure during and after construc-
tion. Each concrete pour, tendon stressing operation and gantry load is included as an in-
dividual step in the construction of the viaduct.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
In order to establish the creep and shrinkage response of the concrete in the NHVV,
numerous creep and shrinkage tests were performed on concrete cylinders made from the
concrete used to pour the instrumented bridge sections. These test, along with associated
strength tests, were performed at CTL in Skokie, Illinois. Creep and shrinkage tests were
initiated at 3 days, 28 days and 90 days after loading. The tests were continued for at
least one year.
Durbin and Robertson (6) compared four creep and shrinkage prediction models with
the CTL test data from this project. The prediction models considered were the current
ACI 209-92 (7), CEB-FIP Model Code 90 (5), Bazant and Baweja Simplified model B3
(8), and Gardner and Zhao (9). All of these models underestimated both the creep and
shrinkage observed in the laboratory tests.
Based on the initial 28-day data from the laboratory tests, long-term creep and shrink-
age predictions were made using an extrapolation method proposed by Bazant and
Baweja (8). This simple linearization procedure is used to correlate the predictive models
to the first 28 days of shrinkage and creep data. If the predictive model data, f/J' (t), cor-
responded exactly to the test data, rfJ(t), a plot of f/J' (t) versus r!J(t) would be a 45 o
straight line passing through the origin. In reality, these values do not correspond ex-
actly. To obtain the least deviation between the test data and the model, a least-squares
regression is calculated. The y-intercept, p 1 , and slope, p 2 , from this linear regression
are then used to modify the predicted values as follows:
¢"(t) == p 2f/J'(t )+ P1
Subsequent shrinkage and creep can then be extrapolated using these modified mod-
els. The linearization procedure produces particularly good agreement for the Gardner
and Zhao model for shrinkage, and the Bazant and Baweja model for creep (1 0). These
models were then modified for the field relative humidity and ambient temperature, and
for the average volume to surface area ratio for the box girder section, and used to predict
long-term creep and shrinkage for loading at various ages from 1 day to 3600 days. The
resulting matrix of creep and shrinkage predictions was then input as "LAB DATA" into
SFRAME for analysis of the viaduct response.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
During the design of the NHVV, TY Lin International used the CEB-90 model for
creep and shrinkage prediction, modified based on short term tests of the concrete mix-
ture proposed for the viaduct. Figure 4 shows the resulting deflections compared with the
optical survey and baseline measurements for Unit 2JB over the two-year period from
1995 to 1997. The TY Lin!CEB predicti~:m significantly underestimates the observed de-
flections, particularly in the longer spans.
In order to improve the deflection comparison for Unit 2IB, the Gardner and Zhao
model for shrinkage, and the Bazant and Baweja model for creep, modified based on
short term test data as described above, were used along with the SFRAME input vari-
ables listed in Table 1. The relative humidity of 85% was based on the average field
measurements over a two-year period. The creep and shrinkage variability was taken as
± 30% based on ranges suggested in the literature. A I 0% reduction in prestress force
was assumed based on the average forces measured in some of the span tendons, com-
pared with the specified prestress force.
After a trial and error matching procedure, this combination of parameters produced
the best agreement between predicted vertical deflections and measured deflections for
Unit 2IB for the two-year period from 1995 to 1997 as shown in Figure 4. The Gard-
ner/Bazant prediction shows far better agreement with the observed deflections. How-
ever, the use of a single set of input data is still not able to completely capture the long-
term response of this complex structure.
This same input data was later used to predict the vertical deflections for Unit 2IB for
the 8-year period from 1995 to 2003 as shown in Figure 5, as well as for the other 5 units
in the twin viaducts. Figure 6 and Figure 7 show the comparisons for Units 1 and 3 of the
inbound viaduct. Again the Gardner/Bazant prediction is a significant improvement over
the original design prediction, although variability in the material properties, prestress
force, etc. along the viaduct length results in disagreement in certain spans. Similar com-
parisons resulted for the three units making up the outbound viaduct ( 11 ).
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Figure 11 shows the average strains measured by the vibrating wire strain gages in the
top and bottom slabs of midspan section A compared with the SFRAME predictions us-
ing the Gardner/Bazant model presented earlier. Similar comparisons were obtained for
the other instrumented sections. In general, the SFRAME model tended to over-predict
the long-term strains, however the shape of the predicted strain-time relationships are
very similar to those observed in the structure.
Span Shortening
Figure 12 shows good agreement between the span shortening from Pier P 11 to P 12
as measured by the extensometer, compared with the shortening predicted by the
SFRAME Gardner/Bazant Model. The Design Envelope provides a significant margin of
error against under- or over-prediction. The lower bound prediction could be used, along
with anticipated thermal movements, to develop a conservative estimate of the expansion
joint capacity required for the viaduct.
Figure 13 shows the reduction in prestress force for one of the span tendons as meas-
ured by a load cell installed below the prestress anchor during tendon installation. The
measured tendon force is compared with the SFRAME predictions using the Gard-
ner/Bazant Model and the Design Envelope. Although the envelope appears overly con-
servative for this load cell, this was not the case for all instrumented tendons. In general,
the Design Envelope provides a safety margin against both over- or under-estimation of
the actual tendon prestress force.
will be augmented by a taut-wire baseline system similar to that used in the NHVV, but
with automated measurements using electronic displacement transducers (LVDTs). All
recorded data will be transmitted real-time to a data acquisition center at the University of
Hawaii for continuous monitoring.
Figure 15 shows the vertical deflections predicted for the Kealakaha Bridge for 50 years
after construction. Figure 16 to Figure 18 show the deflection envelopes for the 1-year,
5-year and 50-year predictions. A range of :t 30% was used for creep and shrinkage pre-
dictions since short-term test data on the bridge concrete are not yet available. The pre-
dicted midspan deflection of 114 mm after 50 years represents a deflection ratio ofL/965.
The maximum lower bound estimate of 203 mm represents an acceptable deflection ratio
ofL/542.
Span Shortening
Figure 19 shows the total predicted span shortening for all three spans, resulting in an
overall shortening of the bridge structure. This prediction can be used, along with esti-
mates of thermal contraction, to verify the capacity of the expansion joints at each abut-
ment.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Tendon Prestress Loss
Table 3 lists the predicted prestress loss for 6 tendons in the Kealakaha Stream
Bridge. These tendons represent both long and short span tendons in the end spans and
center span, and long and short cantilever tendons over one of the piers. The average
prestress loss predicted using SFRAME with the Gardner/Bazant model is 31 %. Figure
20 shows the predicted tendon prestress loss for tendon 39, a long span tendon in the cen-
ter span. At 50 years, the upper and lower bounds provide conservative estimates of the
possible maximum and minimum prestress force remaining in the tendon after all losses.
These estimates can then be used to adjust the initial prestress force if necessary, or pro-
vide open ducts for additional tendons in case they are needed in the future. If the mini-
mum prestress force predictions are adequate to ensure proper performance after 50
years, then such measures are not necessary.
1 Original SFRAME design predictions of long-term vertical deflections for the North
Halawa Valley Viaduct differ significantly from the observed deflections. This is at-
tributed to increased creep and shrinkage compared with that anticipated during the
design phase, and variability in other material and environmental properties critical to
the long-term response.
2 Creep and shrinkage predictions based on interpolation from short-term test data pro-
vided improved predictions of the viaduct vertical deflections. However, a single set
of input data could not accurately predict the deflection response for all spans in the
viaduct.
3 This improved prediction model provided reasonable estimates of longitudinal con-
crete strains, span shortening, and prestress Joss.
4 A procedure is proposed for prediction of upper and lower bound response based on
anticipated ranges of material and environmental variables. This Design Envelope is
shown to encompass virtually all observed results for vertical deflection, span short-
ening and prestress loss.
5 Application of the Design Envelope to a future structure is demonstrated using the
Kealakaha Stream Bridge to provide preliminary estimates of vertical deflection, span
shortening and prestress loss.
6 The Vibrating Wire strain gages used in this instrumentation program proved ex-
tremely reliable for long-term monitoring.
7 The base-line system used for deflection measurements was reliable and accurate,
both for short-term and long-term monitoring. This system is being adapted for use
with automated LVDT measurements for installation in the Kealakaha Stream Bridge
during a future instrumentation program.
ACKNOWLEDGEMENT
The authors wish to acknowledge the considerable assistance received during this in-
strumentation program. The input of Scott Hunter and Jose Sanchez ofT. Y. Lin Interna-
tional and Henry Russell and Tom Weinmann of Construction Technology Laboratories
was crucial to the successful implementation of the NHVV instrumentation program.
The assistance of a number of graduate students at the University of Hawaii is also
greatly appreciated. In particular, Andre Lee's tireless efforts during instrument installa-
tion, and Michael Durbin's attention to detail during data processing.
This project was supported by funds from the Hawaii State Department of Transporta-
tion and the U.S. Department of Transportation, Federal Highway Administration. This
support is gratefully acknowledged. The contents of this paper reflect the views of the
authors, who are responsible for the facts and the accuracy of the data presented herein.
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REFERENCES
1. Banchik, C. and Khaled, N., North Halawa Valley Viaduct Design and Construction.
Concrete International16(3), 1994, pp. 39-43.
2. Ketchum, M. A., Redistribution of Stresses in Segmentally Erected Prestressed Con-
crete Bridges (SFRAME), Report UCB/SESM-86/07, 1986, Univ. of California, Berke-
ley.
3. Lee, A. and Robertson, I. N., Instrumentation and Long-Term Monitoring of the North
Halawa Valley Viaduct, Research Report UHM/CE/95-08, Univ. of Hawaii, Honolulu,
HI, Sept. 1995, pp. 149.
4. Ao, Weng C. and Robertson, Ian N., Investigation of Thermal Effects and Truck
Loading on the North Halawa Valley Viaduct, Research Report UHMICE/99-05, Univ. of
Hawaii, Honolulu, HI, July 1999, pp. 217.
5. CEB-90., CEB-FIP Model Code 90, Comite Euro-Intemational du Beton. Thomas
Telford Services, 1993.
6. Durbin, M.P. and Robertson, I. N., Creep and Shrinkage of Concrete- Use and Com-
parison of Current and Proposed Predictive Models in the H3 North Halawa Valley Via-
duct Project. Research Report UHMICE/98-04. Univ. of Hawaii, Honolulu, HI, June
1998, pp. 130.
7. American Concrete Institute, Prediction of Creep, Shrinkage, and Temperature Effects
in Concrete Structures. ACI 209R-92, 1992.
8. Bazant, Z.P. and Baweja, S., Short Form of Creep and Shrinkage Prediction Model B3
for Structures of Medium Sensitivity, Materials and Structures V29, 1996, pp. 587-593.
9. Gardner, N.J. and Zhou, J.W., Shrinkage and Creep Revisited, ACI Materials Journal.
May-June, 1993, pp. 236-246.
10. Robertson, I. N., Correlation of Creep and Shrinkage Models with Field Observa-
tions. The Adam Neville Symposium: Creep and Shrinkage- Structural Design Effects,
SP 194-9, Akthem Al-Manaseer, Editor, American Concrete Institute, 2000, pp. 261-282.
I I. Li, Xianping and Robertson, Ian N ., Long-Term Performance Predictions of the
North Halawa Valley Viaduct. Research Report UHM/CEE/03-04, Univ. of Hawaii,
Honolulu, HI, June 2003, pp. 75.
12. Robertson, I. N. and Zaleski, A. B., Creep and Shrinkage Tests and Modeling for the
Kealakaha Stream Bridge. Report UHM/CE/98-02. Univ. of Hawaii, Honolulu, HI, April
1998, pp. 100.
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Tendon Tendon Force (kN) Prestress Loss
Tendon Description
No. DesiQn 50-Year kN %
1 3253 2411 842 26 End span lonQ tendon
2 3213 2442 771 24 End span short tendon
4 3378 2193 1185 35 Short cantilever tendon
19 3487 2363 1124 32 Long cantilever tendon
39 3283 2175 1108 34 Center span long tendon
54 3282 2135 1147 35 Center span short tendon
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--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
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by D. J. Carreira
Synopsis: Reinforced concrete columns under compression loads and under little or no
moment may exhibit cracking. Some cracks develop at early ages and others years later
under sustained axial loads or no significant loads at all. Flexural cracking may be
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expected from externally applied loads on columns within the tension-controlled zone in
the axial load-moment diagram. However, for columns within the compression-controlled
zone of the diagram, cracking is not normally expected to occur under allowable service
loads. Concrete shrinkage and creep, temperature variations and loading history cause all
these cracks. In this paper, the causes of these cracks are described, analyzed and
illustrated with photos of cracked columns. Design and construction recommendations to
prevent or reduce these cracks are provided.
163
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164 Carreira
ACI Fellow D. J. Carreira is a consulting civil and structural engineer and an adjunct
professor of Civil Engineering at the Illinois Institute of Technology in Chicago, IL. He
is a member and past chairman of ACI Committee 209, Creep and Shrinkage of Concrete,
of ACI Committee 301, Specifications for Concrete, Chairman of its Sub Committee A,
and ACl Committee 439, Steel Reinforcement.
INTRODUCTION
TYPES OF CRACKS
This paper considers five types of cracks in reinforced concrete columns under
compressive axial load caused by concrete creep and shrinkage, by the cement heat of
hydration, by ambient temperature changes and by unloading. These cracks develop in
addition to the expected common flexural cracks in the tension-controlled zone of
columns axial load-moment diagrams. They are classified based on their predominant
cause as follows:
1. Unloading Cracks. Through transverse cracks across the section of axially loaded
columns in compression after a significant portion of their allowable service
sustained load is removed while remaining under partial service compression axial
load.
2. Cracks in Thick Columns Under Light Loads. Shallow-to-deep transverse cracks
in thick columns under light axial compression loads compared to their allowable
maximum service axial load.
3. Cracks in Heavily Reinforced Columns. Shallow-to-through transverse cracks in
heavily reinforced concrete columns. Extreme cracking conditions occur in
composite compression members with heavy structural steel shapes.
4. Cracks from Heat of Hydration. Shallow-to-deep longitudinal cracks occur in
thick columns regardless of their longitudinal reinforcement ratio and loading
history.
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It is common to observe more than one type of crack in a column, since their causes are
common and in many situations they are not mutually exclusive.
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A discussion of the effects of shrinkage and thermal strain gradients in plain
concrete is needed to better understand how the concrete volume changes cause concrete
columns and walls to crack. These strain gradients are non-linear and vary with time.
Shrinkage strain gradients evolve slowly when compared with the thermal gradients.
Carlson (1) and Pickett (2) defined the shrinkage strain gradients in terms of the
equivalent thermal gradients by substituting the thermal constants and parameters with
those of shrinkage. Shrinkage gradients shapes are similar to thermal gradients, except
that their time scale is measured in days and years rather than in minutes and hours for
the thermal.
Let's consider simple examples of (schematic shrinkage symmetric strain)
gradients in walls. One-dimension walls are simpler compared to the two dimensions in
columns. Figure I shows a wall4 ft (1219 mm) thick (3) with a steel liner on one side,
which from the drying shrinka~e standpoint is equivalent to an 8 ft (2438 mm) wall
drying from the two opposite surfaces. Figure 2 shows shrinkage gradients in a wall 40
in (1016 mm) thick, and Figure 3 a wall 16 in (406 mm) thick. Shrinkage gradients in
these figures correspond to an environment with constant humidity and temperature.
Once the strains or thermal nonlinear gradients are known, Reference 3 provides
a procedure to consider their effects in the structural analysis of concrete members. The
Equivalent Linear Gradient (ELG) in Reference (3) models nonlinear and
nonsymmetrical strain or thermal gradients in terms of their three additive components.
They are; the axial, the curvature and the local strain or temperature components. Line I-
2 is the ELG in Figure 4 from temperature at liner surface, Tei to the outside face
temperature, Teo·
Local temperatures, T1c or shrinkage strains, E1c are the difference between the
actual nonlinear gradient and the ELG. Line 3-4 in Figure 4 is the local temperature
gradient in the vicinity of the steel liner from heat input. Local temperatures or strains
produce neither axial strain nor curvature changes on externally unrestrained members
because they depend only on the internal restraints. However, they affect the member
stiffness by the resulting cracking when local tension stresses exceed the tensile strength
of the concrete.
There is no curvature component in Figures 2 and 3 since all the gradients are
symmetric. Comparing the increment in the axial component, L1Ea from 28 days to 1.4
year in Figures 2, and to one year in Figure 3 shows larger axial shrinkage strain
components as the thickness of the wall decreases, and larger local strain components as
the section thickness increases. The size and shape function in the mathematical
prediction models of the axial shrinkage and creep strains accounts for the increment of
the axial component of the ELG.
During testing for creep, shrinkage and temperature changes, strains are
measured on the surface of the test specimen or internally as described in Reference 15.
Externally applied strain gages on the sides of the specimens measure a combination of
the axial and local strain components. Embedded axial strain gages and external strain
gages at the ends of the longitudinal axis on prismatic specimens mainly measure the
axial strain component.
CRACKING OF CONCRETE
Concrete Restraints
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Most structural design cracking analyses refer to the external restraints and
externally applied loads, and ignore the internal restraints and local stresses. ACI
Committee 207 (I 0) addresses the effects of the non-linear cooling gradients from the
cement heat of hydration in the design and construction of massive structures. Wall
thickness in nuclear power plants, (3 to 8 ft or 76 to 203 mrn) are thicker than in most
common concrete structures but by far thinner than those in dams and other massive
structures as shown in Figure 5. For nuclear containments and similar structures,
Committees ACI 349 (7), and ACI 359 (8) present design approaches for the thermal
loads on such reinforced concrete structures.
Concrete cracks when the value of the combined strains from applied loads;
internal and external restraints exceed the tensile cracking strain. Cracks widen with time
from the combined effects of concrete creep, shrinkage and the seasonal and daily
thermal actions.
Figure 5 shows temperature gradients from seasonal and daily changes (10) in a
massive wall. Since temperature seasonal changes occur during one year, relaxation from
concrete creep reduces the stresses with time. Cracks develop as concrete ages since the
modulus of elasticity increases with age while creep decreases. This explains the initial
delay in the development of cracks from seasonal temperature cycles and early
development of thermal cracking.
Concrete creep relaxes stresses from restrained thermal and shrinkage strains.
As concrete ages the relaxation effect of the creep reduces. In relatively thin members
the effect of the fast cooling from the cement heat of hydration on the development of
concrete maturity is limited. Therefore, the short duration dissipation of the heat of
hydration has a small effect on reducing the high early concrete creep. Hence, the high
early creep relaxes the early thermal and the early shrinkage induced stresses. Cracking
in thin members from external restraints occurs at later ages as concrete dries and it is
exposed to thermal cycles.
In thick members, the autogenous or self-produced curing from the cement heat
of hydration accelerates the rate of strength and modulus of elasticity development, while
reducing the early and final creep. Hence, as the member thickness increases, the
beneficial stress relaxation from early creep of the thermal and early shrinkage induced
The analysis of the interaction of the cement heat of hydration on early creep,
shrinkage, strength and modulus of elasticity is beyond the scope of this paper. These
interaction topics need further research.
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Based on the findings and suggestion from M. E. FitzGibbon in 1976, Reference
6 shows that a temperature difference of 20 °C, (36 °F) with a coefficient of thermal
expansion of 10 x 10-6/ °C, (5.5 x 10-6/ °F) results in a differential strain of 200 !!E. This
is a realistic estimate of the tensile strain at crack initiation in concrete test specimens
under short duration loads. Concrete coefficient of thermal expansion, strength, modulus
of elasticity, creep and relaxation vary with the concrete temperature and age. Therefore,
the tensile strength and the strain at cracking vary widely in technical literature even for
short duration testing at constant temperature and moisture content.
Cement content in concrete mixtures used in columns may exceed 840 lb/yd 3
(500 kg/m 3) with the cement ground very fine, (Blaine 450 to 600 m2/kg). Hence, the
nonlinear thermal gradients from heat of hydration and subsequent cooling could easily
generate temperature differentials of 40 °C (72 °F) and higher during cooling. Therefore,
the initial cracking could occur at early ages even for cross sections 20 in. (500 mrn)
thick or less. During cold weather construction, thermal shock will crack the concrete
during and after formwork removal, since the concrete with an early high elastic modulus
is still very hot.
Local shrinkage and thermal strains of 400 to 600 !!E are common at concrete
surface of thick members and they will open the initial thermal cracks. Subsequent
nonlinear cooling in winter will add to crack width.
Local strains from drying exceeding 200 J.1E occur in Figure 1 at the 4 ft (1219
mm) thick wall, after 28 days and before one year after drying. Shrinkage strains
combine with those from the cooling of the heat ofhydration and accelerate the cracking
development and widening. These cracks are common and conspicuous in nuclear
containment walls and in thick columns. They develop between one and four months
after concrete placement depending on placing temperature, the environmental conditions
and section thickness.
For the 40 in. (1016 mm) thick wall in Figure 2, cracking from shrinkage alone may
occur as early as at 28 days. The effect of cooling from the cement heat of hydration on
cracking in a 16 in. (406.4 mm) thick wall is smaller than in a 40 in. (1016 mm) thick
wall, because of the increased time lag between the thermal and shrinkage strain
gradients in the thinner wall. By the time shrinkage local strains may produce local
cracking, the stresses from the heat of hydration are relaxed by creep and cracking.
Tensile strains between 28 days and one year in Figures 2 and 3 are high enough to
produce local cracking.
Time lag between the cooling gradients and the development of significant
autogenous shrinkage and local drying shrinkage strains decreases as the column or wall
thickness increases. Usually the cement heat of hydration initiates most cracks, and
subsequently they are further widened by the drying shrinkage.
In thin members the dissipation of the heat of hydration is fast and the drying
shrinkage nonlinear gradients are very flat. Conversely, in thick members, the dissipation
of the heat of hydration is slow and the initial development of internal restraints on
nonlinear gradients is fast.
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Columns supporting silos or warehouses where heavy live loads were sustained
for a long time such that significant creep and shrinkage have occurred prior to
the live load removal. They occur in columns of old multistory warehouse
structures converted to loft apartments.
The author became first aware of these cracks during the evaluation of clinker
and cement silos scheduled for demolition in 1965 because silo walls exhibited severe
chloride corrosion after more than 40 years of seashore exposure. Surprisingly the light
crossed through the columns cracks despite that they were supporting the total design
dead load of the silos. Furthermore, no significant corrosion damage was observed on
those columns
Early in the 1970's Professor Dr. Chester P. Siess described in his class at the
University of Illinois at Champaign-Urbana, similar cracks in columns supporting grains
silos in Illinois and Indiana after seasonal unloading.
A detailed example calculation of Type 1 Cracks is shown in the Appendix. In
this example nonlinear strain gradients as well as the temperature contribution are
ignored. Several case studies, not included in this paper, show the stress in reinforcement
remains elastic after a long time under sustained load very close to the unfactored loads
corresponding to their nominal strength. This condition is typical for most column
sections tabulated in the CRSI Manual (9).
Under sustained loads, concrete creep and shrinkage strains transfer the load in
the concrete to the reinforcement. This is why it is recommended to limit the force in the
reinforcement by p ~ 4.0 % or Asfy ~ 0.4 Ac:f c· Cracking of concrete after unloading
releases tension stresses at each crack location. After removal of sustained load and
Concrete creep and shrinkage are the main causes of column tension cracking
after removal of sustained live load. Creep significantly relaxes the concrete stress from
externally applied loads and from shrinkage.
Once cracks open they don't fully close back even if the initial service load Psis
re-applied. Unrecoverable creep and shrinkage strains, local shrinkage strain near the
concrete surface and dislodged concrete fragments keep cracks open.
Reinforcement with a low yield stress, fy may yield in columns under sustained
loads for a long period of time if concrete has high creep and shrinkage.
Delay the application of the sustained superimposed loads until aging has
reduced the concrete potential creep and shrinkage.
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Cracks Type 2, 3 and 4 are caused by the internal restraints of concrete tensile
strains. These internal restraints are from the reinforcement and embedded structural
steel shapes, and from the concrete nonlinear strain gradients. Combinations of
conditions such as the dimensions and shape of the columns, reinforcement ratio, the
cement heat of hydration and thermal shock during form removal define the type of
cracking. Specific combinations of similar causes differentiate crack Type 2, 3 and 4
from each other.
Since these columns are oversized for the loads they support, their reinforcement
ratio is usually low, 0.005 < p :S 0.1. In addition, large diameter bars are used to facilitate
Type 2 cracks commonly occur in thick columns supporting bridges and are
wider in dry environments. Figure 7 shows however a typical pier supporting an exit
ramp of a viaduct in Northern Illinois. Cross section is 3'-6" by 5'-4" (1067 by 1626
mrn), is 16'-4" (4978 mm) high with 20 No. 10 (No. 32) bars, 7L-5S and p = 1%.
Concrete was placed in late November 1999. Figure 8 shows a close-up view of one of
the Type 2 crack on this pier. Maximum crack width is toward the comer and in summer,
it is 0.012 in. (0.30 mm) wide.
Similar cracks occur in prestressed and post tensioned members, but they are
difficult to detect not long after the prestressing force transfer to the concrete because of
the high compressive stress in concrete from prestressing force and high early creep (13).
In precast prestressed members similar cracks are attributed to the axial thermal
contraction of concrete after overnight steam curing while the prestressed strands restrain
concrete. Cracking increases with longer spans, larger cross section dimensions, higher
placing and curing temperatures, higher temperature differentials at end of curing, and
with the shortening of the length of exposed strands between beams. In precast
prestressed members there often are two to four cracks within the middle portion of the
beam (13).
Transverse Type 2 Cracks occur around the column perimeter and in most --`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
instances they started at the comers of the columns. They are uniform in thickness and
are spaced from two to three times the smaller dimension of the column cross-section but
usually not farther apart than 4ft. (1219 mm). After the development of transverse Type
2 Cracks, longitudinal Type 4 cracks may occur in columns thicker than 5 ft. (1524 mm).
The limited amount of reinforcement and large bar diameters cannot distribute
the local strain gradients to avoid or reduce cracking. The author recommended the use
of skin reinforcement in columns and walls for crack control since the late 1970's, but it
is not used systematically to his knowledge.
Design concrete mixture to minimize creep and shrinkage as well as the effects
of the cement heat of hydration.
ACI 3I8-02 Code Section I O.I6. 7.4 limits the reinforcement ratio to 8%
maximum in columns for economic and placement reasons. A maximum ratio of 4% is
recommended to reduce congestion from splices. Limiting the reinforcement ratio
reduces the transfer of the permanent loads stresses from the concrete to the
reinforcement. This can be analytically proven following the same procedure used to
illustrate the Type I Cracks in the Appendix.
In composite compression members, the structural steel shape and the additional
reinforcing bars carry most of the dead load and the sustained live loads, even if the
concrete is designed to resist portions of the dead and permanent loads. Steel shapes in
composite columns at the lower stories of high-rise buildings are designed to carry all the
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
dead loads and most of the gravity live loads, while the concrete is designed to resist the
short duration wind and seismic loads.
Safety factors keep the steel shapes elastic under service loads, which in
combination with the concrete creep and shrinkage relax any compressive stress in the
concrete by transferring the load to the steel. Nonlinear temperature gradients from the
cooling of temperatures from the cement heat of hydration initiates cracking early in the
concrete life and well before loads are applied to the column. Nonlinear shrinkage strain
gradients internally restrained by the steel shape and the reinforcing bars gradually
further open the initial thermal cracks.
Design concrete mixture to minimize creep and shrinkage as well as the effects
of the cement heat of hydration. See recommendations under Type 4 Cracks.
Type 4 cracks are mainly caused by the concrete internal restraint of the local
tensile stress from nonlinear temperature gradients during cooling of the cement heat of
hydration. Autogenous shrinkage first and drying shrinkage later continue to widen the
original thermal cracks.
In cold weather construction, the thermal shock from the early removal of the
forms accentuates crack development. ACI 301 Specification, Section 8.3.2.4 "Control
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
of concrete surface temperature" (15) requires cooling the temperature of the concrete
gradually so that the drop in concrete surface temperature during and at the conclusion of
the curing period does not exceed 20 °F (12.5 °C) in any 24-hr. period. Without specific
instructions, this provision is difficult to enforce.
Since heavy axial loads define design of columns in high-rise structures, high
strength concrete is used to reduce cross section dimensions. High strength concrete
mixture proportions with high content of cement generate high early heat of hydration,
high early elastic modulus and the development of related cracking.
Figure 15 shows one of the two vertical Type 4 cracks in this column with the
vertical crack at center of the photo and two cracks at the sides just above the painted
border. There is a horizontal crack 0.08 in (2 mm) wide all around the perimeter just
above the sign. There is one horizontal crack at the left of the vertical crack and one
inclined crack going up at its right side. Masked by layers of paint the crack width is
approximately 0.010 in. (0.25 mm). A closed-up view of the vertical crack is shown in
Figure 16. Crack width varies from 7/32 to 9/32 inches, (6 to 7 mm) in spite of the
numerous paint layers.
Figure 17 shows two of the four Type 4 cracks in another column of the same
basement; one is wide and inclined, while the other is vertical and thinner.
Figure 18 shows the Type 4 Cracks on a circular column with a northern exterior
exposure. No corrosion was observed despite the width of the cracks. All the columns in
this building show these cracks highlighted by the blast finish. The non-linear thermal
gradients from the cement hydration combined with the autogenous, drying shrinkage
gradients and thermal shock explain the development of these cracks.
Vertical cracks in Figures 15-17 are wider at the bottom of the column than on
the top, because of the external restraint of the older concrete at the lower floor compared
with the externally unrestrained fresh concrete at the top during construction. The heat
could dissipate faster from the unformed top surface of the column than from the formed
surfaces and from the bottom in contact with older concrete. Chapter 4 in Reference 10
discusses in detail the cracking from thermal stresses in massive concrete members from
the effects of the internal and external restraints, and how to prevent them from
happening.
To avoid or to reduce the occurrence of these cracks, the effects of the cement
heat of hydration and of the autogenous shrinkage must be reduced. The following
reduces the effects ofthe cement heat of hydration:
Reduce the cement content in the concrete mixture. Substitution of cement with
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
fly ash will reduce the heat of hydration and delay the early development of
strength and modulus of elasticity. Fly ash substitution increases creep thus
benefiting crack reduction.
hydration.
Type 5 cracks are diagonal through cracks in columns of structures with post-
tensioned floor slab systems and beams. These cracks are caused by the principal tensile
stresses from imposed lateral displacement on the externally restrained column by the
post tensioning of the slab systems and the lack of appropriate shear reinforcement in the
columns in addition to ties and spirals.
These cracks share with the other four types of cracks that they are caused by
the concrete shrinkage and creep, and by the temperature changes of the floor system.
However, an external displacement is imposed on the column by the floor system
shortening from elastic, creep, shrinkage and temperature strains. Figure 19 shows a
Type 5 Crack in a column at the ramp of a parking structure.
Reference 16 discusses in detail the effects of these cracks in the structural behavior of
the columns, and how to design and built post-tensioned slab systems to minimize the
occurrence of Type 5 Cracks.
This paper explores five crack types caused by combinations of the following
factors: concrete shrinkage and creep, cement heat of hydration, ambient temperature
changes, loading history, external and internal restraints, reinforcement ratio and concrete
section shape and dimensions.
Type I cracks are transverse through cracks all around the column perimeter.
These cracks develop after a significant portion of the column allowable sustained service
load is removed. Concrete creep and shrinkage strains transfer the load in the concrete to
the reinforcement. Also, they are expanded by column restraints, reinforcement provided
and ambient conditions, but they are primarily caused by the column load history.
Type 2, 3 and 4 cracks develop when non-linear strain gradients from shrinkage,
heat of hydration and ambient temperature cycles are internally restrained.
Type 5 cracks are diagonal deep to through cracks in columns in structures with
post-tensioned floor slab systems and beams. Columns are horizontally displaced by the
floor system shortening from the elastic, creep, shrinkage and temperature strains. They
generate principal tensile stresses and these cracks.
It is common to observe more than one type of crack in a column, since in many
conditions their causes are not mutually exclusive.
For structural analysis, non-linear strain gradients are modeled in terms of the
Equivalent Linear Gradient (ELG) three temperature or strain components. That is, the
axial, the curvature and the local components. To account for the external restraints,
temperature and shrinkage linear gradients are input in commercial programs of structural
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
The analysis of the interaction of the cement heat of hydration on early creep,
shrinkage, strength and the modulus of elasticity is beyond the scope of this paper and
needs further research.
Delay the application of the sustained superimposed loads until concrete aging
has reduced the potential creep and shrinkage effects.
REFERENCES
1. Carlson, R., W., Drying Shrinkage of Large Concrete Members," Proceeding of the
American Concrete Institute, Farmington Hills, MI, Vol. 33, 1937, pp. 327-336.
6. Neville, A. M., "Properties of Concrete," Forth Edition, John Wiley & Sons, Inc.,
New York, NY, 1996,844 pp.
8. ACI Committee 359, "Code for the Concrete Reactor Vessels and Containments,"
(ACI 359-01 ), American Concrete Institute, Farmington Hills, MI. This Code is the
section III, Div. 2 of the BPV Code of the ASME.
10. ACI Committee 207, "Effect of Restraint, Volume Change, and Reinforcement on
Cracking of Mass Concrete," (ACI 207.2R-95), R-2002, American Concrete
Institute, Farmington Hills, MI, 26 pp.
11. ACI Committee 209, "Prediction of Creep, Shrinkage and Temperature Effects in
Concrete Structures," (ACI 209R-92), American Concrete Institute, Farmington
Hills, MI, 47 pp.
14. Carreira, D. J. and Burg, R. G., "Testing for Creep and Shrinkage," (ACI SP-194-12)
The Adam Neville Symposium: Creep and Shrinkage- Structural Design Effects,
American Concrete Institute, Farmington Hills, MI, 2000, pp. 381-420.
15. ACI Committee 301, "Standard Specification for Structural Concrete," (ACI 301-
99), American Concrete Institute, Farmington Hills, MI, 1999, 49 pp.
16. Carreira, D. J. and Bastidas, C., P., "Effects of Creep, Shrinkage, and Temperature
Shortening of Post-Tensioned Concrete Slabs on Columns and Supporting Walls,"
presented at the Technical Session on "Post-Tensioned Flat-Slab Design," ACI
Spring 2002 Convention in Detroit, Michigan, April 24, 2002, (In process of
publication).
Find out if cracking occurs when an axially loaded 20" (508 mm) square short
-
column is partially unloaded after 10 months (305 days) under sustained load. Consider
the effects of loading history, and the axial strain components of creep and linear
shrinkage only. Ignoring non-linear shrinkage, temperature gradients and assuming an
Data:
Ag = 400 in 2 (258,064 mm 2)
f ci = 5.0 ksi (34.5 MPa) and Eci = 4030 ksi at loading age, t1a
fc = 6.0 ksi (41.4 MPa) after loaded for 305 days
A, = 20.32 in2 (13,109.7 mm 2 ) or 16 No. 10 (36), Grade 60 bars (414)
E, = 29,000 ksi, (199,950 MPa)
p = 5.08 % (1.0% < p < 8.0%).
Initial application of service load P, on the column occurs at time t1., with an
initial modular ratio, n. and a nominal axial strength Pn of:
E
n. = _s_ = 7.2
Eci
Pu = 1586 k (7,054 kN), from CRSI Tables (9)
Pn = 2832 k (12,597 kN), for cjl = 0.7 and a 0.8 reduction of the maximum
nominal axial load capacity based on ACI 318-02 Code Appendix C.
Calculation of Elastic Stresses in Concrete, fea and in Reinforcement f,. at Time, t1•
of tbe Initial Maximum AUowable Service Load, P, Application
Ps .
fca = = 1.91 ks1 (13.1 MPa) or 0.32 f c elastic.
Ag + (n 8 -l)A 5
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
The strain in reinforcement, &sa is the same as in the concrete from strain
compatibility condition,
f
&sa= ...E. = 0.0004736 < 0.002069,for Grade 60 (414) elastic.
Es
Figures AI and A2 show stresses and strains on the reinforcement and concrete
stress-strain diagrams at time t1••
Concrete Stresses £5305 and Strain, ec305 After 305 Days Under Total Service Load P,
and Prior to tbe Removal oftbe Live Load, PsL
Stiffuess coefficient, a; from Bruegger (4) defines the elastic portion of a load or
strain applied to symmetric reinforced section acting on the reinforcement.
1
a; 0.278.
Using the "Relaxed Stress," Rfca (4) to compute stresses in concrete and
reinforcement from the sustained load and concrete shrinkage after 305 days,
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
fc305 = fca- Rfca = 0.714 ksi (4.92 MPa) from fca = 1.91 ksi (13.17 MPa).
Figure A3 shows concrete stress history from t = t 1a to t = 305 days just prior the
removal of PsL· Stress transferred from concrete to reinforcement, Tf,. is:Tf,.
Ac Rfca
=A = 22.341 k.si (154.03 MPa).
s
Since f5305 = 36.08 ksi < fy = 60 ksi, (248.73 MPa < fy = 414 MPa), the
reinforcement is elastic and in compression under the total service P s load sustained for
305 days. Figure A4 shows reinforcement stress history from t = t1a to t = 305 days just
prior the removal of PsL· The portion of PsL on A., Fsr and the portion on the concrete,
Fc305 at t = 305 days just prior to the removal ofPsL are:
The strain increase in the concrete and in the reinforcement (axial shortening)
after 305 days under load on the average, R&c 305 from Reference 4 is,
f + Ssh305Eci
ca
R&c305 = UjU305 ( U305 . ) = 0.0007704.
l + a.iX3osU305 E As
SA
c
Hence, the strain in concrete just prior to PsL removal at 305 days, &c305 is:
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
&c305 = &ci + R&c305 = 0.0004736 + 0.0007704 = 0.0012434.
Concrete and Reinforcement Stresses and Strains Just After the Removal of the
Live Load, P.L at 305 Days
Concrete instantaneous elastic modulus, Ec305 and the modular ratio n 305 at t =
305 days are:
the instantaneous force in reinforcement just after unloading at t1• = 305 days is:
F,, =A, f,u = 576.39 k (2563.80 kN) > P,o = 402 k (1,788.11 kN).
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
the tension stress in the concrete, fc 1 that was initially under compression, is now
T
fc 1 = c =-0.486ksi(-2.16MPa)intension.
Ag -As .·.
Concrete axial tensile strength, f 1 varies from - 3../f: to - 6J['; psi, (-
0.249$c to -0.498.J['; MPa). For fc = 6.0 ksi (41.4 MPa) f 1 varies from -232
psi to -465 psi (-1.60 to -3.21 MPa).
Since ftc = I -0.483 I ksi (I -3.33 I MPa) < I f 1 I, through cracks release the
tension force in concrete. After cracking, the reinforcing bars support all the dead load
P,0 in compression.
The strain in concrete just after PsL removal at 305 days, EcJoso is:
fcti 1.174ksi
Ec3050 = Eci + REc305- - - = 0.0012434- = 0.0009776.
Ec305 4415ksi
From strain compatibility, the strain remaining in the reinforcement just after PsL
removal at 305 days, e, 305 is on the average the same strain as in the concrete. Hence,
E511 = Ec3oso = 0.0009776 and the corresponding residual stress, f, 305 is:
fstl = Ecti E, = 28.366 ksi < 60 ksi (195.58 MPa < 414 MPa) -+ elastic.
Reinforcement and concrete stress and strain histories are shown in Figures A4
and A5. Figure 6 shows schematically the typical Type I cracks on axially loaded
columns observed on partially unloaded columns.
In columns with low yield strength reinforcement or fy from 33 to 40 ksi (228 to 276
MPa), with low reinforcement ratio and concrete with high creep and shrinkage, the
reinforcement may yield under loads sustained for a long period of time. Reference 5
shows that the transfer load from the concrete to the reinforcement is greater as the ratio
ofreinforcement decreases even for short-term loads.
100
200
"':I..
-~
300 .,
Vl
bO
~
]
400 Vl
500
Steel liner or axis
of symmetry
600
Wall thickness
Assumed initial
gradient
0
ea2~y
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
too T
28 days
200
1.4 years
300
11 years
400
44years
88 years 500
600
-;>I I~
10"(254mm) -+ELG
Figure 2 Transient Strain Gradients Across a Wal140 in. (1016 mm) Thick
~:-rj
200
300 "':::1.
li
·~
!l.l
400
~
88 years 500 ~
]
!l.l
600
I~!
+ELG 5" (127 mm)
I
Figure 3. Transient Strain Gradients Across a Walll6 in. (406 mm) Thick
C" F'
Transient gradient' 250
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Exposed~
"1 $0 sunac.e
~\
0.9 Temperature Range in Concrete
RATIO=
Temperature Range at Surface
0.8
0.7
R 06
A .
-l Diffusivity = 1.0 if/day (0.0039 m /day) ~ 2
T 0.5
\
I
0 0.4
\
lr Adnua1 Cycle
0.3
\.
'\
0.2
""
--
VDai1y pycle i'....
0.1
\ r- 1---
0.0 0 10 20 30 40 50
Distance From Surface, ft
Column Ele•ation
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Figure 7. Concrete Pier Supporting the Exit Ramp of a Viaduct with Type 2 Cracks
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Figure 9. Columns in Seismic Zone IV. Precast Circular Column Supporting the
Bridge and Column showing Reinforcement in a Bridge Column During
Construction in Early 2004
Figure 10. Type 3 Cracks on the Circular Column in Figure 9. Despite the Paint on the
Concrete Surface, Cracks Are Visible to the Naked Eye
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Figure 11. Typical Type 3 Cracks in a Composite Column at Second Floor with Interior
Exposure in Chicago. (Arrows Show Transverse Cracks)
Figure 12. Closed-Up View of the Type 3 Crack with Arrows 1 and 2 in Figure 11
Figure 13. Closed-Up View of Type 3 Crack with Arrows 4 and 5 in Figure 11.
Notice the Loss of Concrete at the Left-Hand Side Edge of the Column
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Figure 14. Typical Type 3 Cracks in the Composite Columns at a Second Floor with an
Exterior Exposure in Chicago
Type4Crack
Figure 15. Typical Vertical and Horizontal Type 4 Cracks in a Basement Column in a
High Rise Building. Column Diameter is 7.0 ft (2134 mm)
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Figure 16. Close-Up View of the Ve1tical Wide Crack in Figure 15 and the Thin
Horizontal and Inclined Cracks on Each Side of the Vertical Crack
Type4 Crack
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
T'<"N 4 Crock
Figure 17. Typical Type 4 Cracks in a Basement Column in a High Rise Building.
One Vertical Crack Is Inclined and Wide and the other is Thinner
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Figure 18. Circular Column with Type 4 Cracks in an Exterior Exposure. No Corrosion
Observed on Any of the Columns in this Building Despite the Cracks Width and Length
fy= 60 ksi
(414MPa)
At t1a -+ P = P s
&sa= 0.0004736
Strains
fci
f ca =6.0 ksi
(41.4 MPa)
At t1a---? P = P.
Esa = 0.0004736
Strains
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
""' = 0.0004736
f,
" Strains
L &ol05 =
&.11 =
0.001244
0.0009776
r~=6ksi
(41.4 MPa)
fc = 1.91 ksi
(13.17MPa)
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Estimating Time-Dependent
Deformations of Prestressed Elements:
Accuracy and Variability
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
195
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196 Paulsen et al.
ACI student member Michael W. Paulsen is a graduate student of Civil and
Environmental Engineering at the University of Alberta, Canada. His current research
focuses on external post-tensioning as well as predictability and variability of creep and
shrinkage of concrete.
INTRODUCTION
The first objective of this paper is to compare, for one particular case study,
differences in the time-dependent response predictions resulting from changes in the
structural analysis methodology and/or the material models used to describe concrete
behaviour. ·
The second objective of this paper is to assess the variability of the material
models used in making predictions. A straightforward statistical approach is used to
determine the 95% confidence intervals on predictions of the material properties critical
to time-dependent deformations.
Two precast, prestressed girders were instrumented and monitored for strains
and deflections for a five-month period from fabrication to erection. To describe the
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
EXPERIMENTAL WORK
Overpass Description
Figure I shows the profile of the overpass and a typical section. A total of 12
precast girders were fabricated for this bridge. The construction sequence of the overpass
is summarized as follows: 1) Erect pre-cast girders on piers (2 Spans), 2) Place deck and
diaphragms to create continuity, 3) Post-tension longitudinally, 4) Make integral
bridge/abutment connection.
The girders are 38 metres long, 1.65 metres deep and cast with a high-
performance concrete. Each is prestressed with 56 - 15.2mm low-relaxation strands
(tensile strength, fpu = 1860 MPa) and contains a combination of welded-wire mesh and
deformed bars for passive reinforcement. To avoid cracking at release, some of the
prestressing strands were debonded. Figure 2 shows a typical girder cross-section, while
Table I lists sectional and material properties for the concrete, the steel reinforcement
and the prestressed reinforcement. The section was designed to remain uncracked
throughout its service life.
Laboratory Testing
Properties of the concrete mix used in the main girders of the overpass were
determined from nominally 150 x 300 mm cylinders. The cylinders were tested to
determine compressive strength gain with time, modulus of elasticity, creep and
shrinkage properties. The concrete specimens were steam cured for 12 hours to simulate
the curing conditions the girders experience, then kept at a relative humidity of 50%
( ± 4%) and a temperature of23°C ( ± 1.7°C).
The fabrication of one girder required 18 concrete batches. Strength gain,
modulus of elasticity, creep and shrinkage tests were performed on two separate batches
while compressive strength tests were performed on every batch to determine the mean
strength of each mix. Refer to Appendix A for the results from the laboratory testing
program.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
The load-histories and measurement sampling times for the test girders are
summarized in Table 2. For each sampling time at each section, I 0 strain readings were
obtained. A curvature was estimated from the 10 readings by finding the best-fit plane
section. Figure 3 shows the measured strain distributions at station III of Girder 273-01
at time t 1•
Curvatures were calculated at each section for each measurement period. These
were numerically integrated to obtain deflections. Figure 5 shows the curvature
measurements and deflections for both girders at the time of stressing.
PART 1 - ACCURACY
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Material Model
Three models were used in this study to predict the mechanical properties of the
concrete used. They are ACI 209 (1), AASHTO (2) and CEB MC-90 (3). These three
models require similar information regarding the concrete's strength, the specimen's
shape, and the environmental conditions. The ACI 209 formulation also has additional
factors based on the composition of the concrete. In this paper, this formulation will be
tem1ed ACI 209 + Mix Factors.
In addition, two material models based on the laboratory data have also been
used. The first termed Model A uses the CEB MC-90 format, and the second, Model B,
uses the ACI 209 format. The empirical constants in these formulae were fitted to the
measured test data. These models are described in Appendix A.
Two methodologies are used to predict the sectional responses with time. Both
methods are accepted structural analysis methods, and are presented in a format so that
differences may be noted. In both cases, plane-sections theory ofuncracked elements set
At any time, the curvature is computed at a number of sections along the girder
and is numerically integrated to obtain the deflected shape. With the assumption that
creep strain varies linearly with applied stress, generally considered accurate for applied
stresses up to 0.5 fcm• superposition can be used in the analysis.
The section forces considered are the normal force N acting at the reference
point and the bending moment M, taken with respect to the reference point. For a section
under the influence of prestressing and applied normal force and moment, the section
forces are calculated as:
[I]
[2]
where Pi is the prestressing force in layer j, Yrsi is the distance to the centroid of the
prestressing force for layer j, No is the applied normal load, and Mo is the applied
sectional moment, with No and M 0 being independent of prestressing and acting through
or about the reference axis. The prestressing force is usually specified as a percentage of
the ultimate strength, fru• where the prestressing behaves in a linear elastic manner. Thus
the prestressing force can be described by: ·
[3]
where ni is the number of strands in layer j, Aps is the area of one strand, Eps is the elastic
modulus of the prestressing and Ej is the strain in the prestressing strand of layer j.
[4]
[5)
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
[6]
where A , B and I are the transformed sectional properties calculated with respect to
the concrete's elastic modulus, Ec(t). The solution to equation [6] requires iteration until
the strain compatibility defined by equations [4] and [5] is met. N is positive in tension
and M is positive when causing tension on the bottom fibre.
The first of the methods considered is the simpler, and uses the effective
modulus to calculate stress related strains. The use of this method assumes that any
stresses applied on a section are done so instantaneously. The effect of creep on the
section is considered directly proportional to the creep function J(t,t0) with free shrinkage
and prestress relaxation being effectively treated as forces on the section. The procedure
is adapted from Collins and Mitchell (4) and is summarised as follows. First the load
vector is calculated as the sum of applied loads, shrinkage effects and prestressing.
where, the first vector on the right side of the equation is the applied forces on the
section,
{N(t,( tJ})
M t ' t·I .
shnnkage
= Ec ' eff ( \. (
t, tiJGcs t, ts {Ac]
Bc
[8]
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
where the prime symbol denotes an effective sectional property and is calculated as the
transformed section property with respect to the effective modulus of the concrete,
Ec,eft(t,ti). The effective Modulus is equal to the inverse of the creep function.
Ec(t,ti)
(11]
1+ <Pi(t, tJ
where <l>i (t, ti) is the creep coefficient as defined by ACI 209.
The second method follows the procedure described by Ghali et al (5). In this
method the time-dependent effects on a section are expressed by a change in strain, tle0 ,
and curvature, tl'Jf, that occur over the time period considered. This is done by first
calculating the forces required to prevent unrestrained creep, unrestrained shrinkage and
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
strand relaxation, then applying these forces to the age-adjusted transformed section. The
restraining force is:
{ ~N(t,ti)}
~M t t·
( ' ')
= {~N(t,ti)}
(t' t·I ) ~M creep
+ {~N(t,tJ}
~ ( t ' t·I) shrinkage
+ {~N(t,ti)}
~ ( t ' t·I) relaxation
{12]
where the restraining forces for creep, shrinkage and relaxation are determined as
follows:
~N(t, ti.)}
{ ~M ( t, t,
)
shrinkage
( I~ ( lAc]
= -Ec,aa t, ti JGcs t, ti
Be
[14]
[15]
E ( ) Ec(t,tJ [16]
c,aa t, ti = 1 "'· (t t.)
+ X'I'J ' I
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
-8]{--LW(t,tJ
A
~N(t, td} [17]
-
where A, B and I are the age-adjusted transformed section properties. Thus the total
strain distribution at time t after an age at loading of ti is the sum of equations [6] and
[17].
The assumption of creep linearity with applied stress allows for the
superposition of time-dependent effects for future changes in loading or boundary
conditions. Strain distributions associated with changing conditions are calculated and
summed to give the theoretical strain distribution.
Predicted Response
Sectional response was predicted using the section properties listed in Table 1
and the specified design parameters listed in Table 3. Relaxation of the strand and
transfer lengths were calculated using the recommendations of the Canadian Prestressed
Concrete Institute (6).
PART 2 -VARIABILITY
The model code formulations used thus far are basically deterministic in nature.
While they state in global terms the levels of uncertainty (CEB MC-90: coefficient of
variation of 20% for creep function, ACI 209: inherently random parameters with
coefficients of variation of 15% to 20% at best, AASHTO: cannot expect results with
error less than ± 50%), most do not provide equations that allow for a probabilistic
analysis. Without the ability to account for the variability in concrete property
prediction, it is impossible to perform a confidence analysis on service deflections in
concrete structures.
In Appendix A two material models are presented. These have been fitted using
least-squares regression. That is, the parameters ~i and ei have been determined that
minimise the sum of the square of the residual error. If we now include the internal error
of these models, the residual errors are explained by the variation in ~i and ei. These
models are now probabilistic, and the parameters are represented by their expected value
and coefficient of variation. Appendix B shows the method used to determine model
parameter variation.
Variability Results
The effect of model code format on the long-term prediction of creep is shown
in Figure 7. The measured creep function for an age at loading of 8 days is plotted. The
formulae used to predict the creep function are strength growth with time, stiffness, and
The effect of model code fonnat on the long-tenn prediction of free shrinkage is
shown in Figure 8. The measured data is shown with the predictions from Model A and
Model B and their respective 95% confidence intervals. The first 7 days of shrinkage
were not recorded, and so the equations were adjusted to account for this.
DISCUSSION
Figure 4 shows the difference between the predictions of Method 1 and Method
2 using material model A. It is seen that the predictions are nearly coincident, with both
predictions within ±8%. This suggests, that for this problem, the added complexity of
Method 2 is not justified. Figure 4 also shows that the use of an appropriate analysis
method with a tuned material model gives high accuracy in predictions of elastic and
time-dependent deflections.
only the deflected shape, but also the curvature. This gives confidence of the model to
predict the deformations of the girder in whole. Thus, mid-span camber values give a
measure of the accuracy to which the girder deformation is being predicted.
The results of the laboratory testing program allow for a reasonable assessment
of the internal uncertainty in Model A and Model B. The one assumption is that there are
no external uncertainties involved in the process of fitting these models. However,
proper testing procedures were used minimize testing errors through repetition. Also any
external uncertainties will be the same for both models and should not be biased towards
one or the other.
Figure 7 shows the effect of model code fonnat on long-tenn predictions and
confidence for the tuned material models. The two models give similar predictions up to
3 years under load; however, Model B predicts greater creep than Model A with final
values being 117x1 0"6/MPa and 88.6xl0.6/MPa for the creep function respectively. This
figure also shows that for Model A, the 95% confidence interval is tight to the prediction,
Figure 8 shows the effect of model code format on free shrinkage predictions.
The predictions from Model A and Model B are both good, and do not differ much in the
long-term. As was the case with creep, the 95% confidence interval for Model B is wider
than for Model A.
CONCLUSIONS
From the case study on the 1301h avenue and Deerfoot Trail overpass, the following
conclusions can be drawn:
• The use of an appropriate analysis method, when used with a material model that
has been tuned to the concrete mix, yields accurate predictions of the mean
behaviour.
• The difference in predictions between analysis methods was not greater than the
uncertainty in measured results; thus, the added complexity of Method 2 is not
justified in this case.
• CEB MC-90 and ACI 209 were almost equally accurate, with predictions of mid-
span deflection growth within ±16% and ±19% respectively, while AASHTO
produce results within ±30% of measured.
• The mix composition factors in ACI 209 produced an improvement of less than
3% in predictions.
• On the basis of these laboratory tests, there appears to be more model uncertainty
associated with the ACI 209 format than with the CEB MC-90 format.
ACKNOWLDEGEMENTS
The work presented herein was part of a research program leading to a Master of
Science Degree for the first author. That effort was supported by the Natural Sciences
and Engineering Research Council of Canada, Con-Force Structures Ltd, the Cement
Association of Canada and the University of Alberta. The authors would also like to
thank Azita Azamejad of CH2M Hill for her insight into the design of the overpass.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
NOTATION
REFERENCES
5 Ghali, A., Favre, R. and Elbadry, M., Concrete Structures: Stresses and
Deformations 3rd edition, Spon Press, New York, NY, 2002.
7 Silva, W.P. and Silva, C.M., LAB Fit Curve Fitting Software V 7.2.26,
http://www.angelfire.com/rnb/labfit, date of access: 2004-05-05.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
For brevity, the equations taken from CEB MC-90 and ACI 209 have been
presented in their fitted forms. Undefined terms can be found in the Notation section.
The parameters that are fitted in Models A and B are designated Si and ei respectively.
They are summarised in Table 4 along with their code recommendations.
For the parameter of compressive strength, the mean compressive strength, fern,
was used with both models. The current ACI 209 model code uses the specified strength,
thus to allow for a comparison of predictive abilities, the following relationship between
specified strength and mean strength (from CEB MC-90, based on characteristic strength)
can be used:
The following equations are used for predicting the mean cylinder strength,
fcm(t), at some time after curing, where tis the time in days:
ModeiB: [20]
The following equations are used for predicting modulus of elasticity, Ec, as a
function of mean compressive strength:
Model A: [21]
ModeiB: [22]
The long-term property tests included creep and shrinkage tests which were
conducted in accordance with ASTM C 512. The ages at loading for creep cylinders
were 1.25, 8, 28, and 84 days, and the magnitude of the sustained load was 203 kN,
which amounts to an average uniaxial stress of 11.2 MPa. The first 6 months of test data
have been used.
Model A:
For CEB MC-90, the creep coefficient is defined as the ratio of creep strain over
the 28 day elastic strain and takes the form:
[23]
where Ecc(t,ti) is the creep strain at time t, ti is the time of loading, Ec(28) is the modulus
of elasticity at 28 days, and cri(ti) is the sustained stress initially applied at ti. The
equation given by CEB MC-90 for predicting the creep coefficient of a concrete mix is
put into the following form:
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
1
/RHo
1 - RHi [ 5.3 ][ 1 ]~4 ( t - ti )~ 5 [ 241
ti A
'
= 0.98ti + 6.8 [25]
ModeiB:
ACI 209 defines the creep coefficient as the ratio of creep strain over the initial
elastic strain. This takes the form:
[26]
where Ec(ti) is the modulus of elasticity at the age ofloading. The equation given by ACI
209 for predicting the creep coefficient of a concrete mix is put into the following form:
where t1a is the adjusted age at loading, and compensates for steam curing by equating 1
day of steam curing to 7 days of standard curing.
Model A and Model B have different definitions of the creep coefficient, which
can be related through equations [23] and [26]. An alternative description of creep
effects is the creep function, which is a description of total stress related strain. Figure 8
shows the creep function predictions of Model A and model B with the measured data for
the 8-day age at loading test. The creep function is defined as:
[28]
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Model A:
Shrinkage is typically described by the free shrinkage strain. The equation from
CEB MC-90 is put in the following form for shrinkage strain prediction (microstrain):
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
[29]
where t. is the time drying begins and 13sc is a coefficient that accounts for cement type,
and is taken as 8 for this mix.
ModeiB:
The equation from ACI 209 is put into the following form for prediction of
shrinkage strains:
Shrinkage strain predictions from Model A and Model B with measured data
appear in figure 8.
Of the equations presented in Appendix A, only the equations for creep and
shrinkage of Model B cannot be put in a linear form. These were analysed using the
software LAB Fit from Silva and Silva (7). · The remaining equations can all be analysed
using multiple linear regression techniques. The process is presented for equation [24],
the creep coefficient of Model A. The values for RH, h, and fern are all known, and the
product of those factors with s 3 will be termed S3 for simplicity. To linearise, the
natural log of the equation is taken. Thus, the equation for the log of the creep coefficient
is:
ln[<hsn (t, ti )] = ln~3] + S4 ln[ 0.1 +1ti,A + s ln[ j3H t+-tti- ti ] +en
_ ]
02 5 [31]
[32]
r 1 al bl el
{~}
1 a2 b2 e2
{y} = ~~ = = [x]{~}+ {e} [33]
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
lYn 1 an bn en
It is known that the solution of {~}which minimises the sum of the square of ~he
residual errors is obtained as follows. Let us refer to this solution as {z} :
[35]
where k is the number of degrees of freedom associated with the sum of the squares of
the residual. Then the variance of the parameters of {z} is given by:
[36]
Cov(z.I 'Z·)=crz
J
2
·z· =c··s
IJ IJ
2
[37]
n
l:ef
s2 = __::1_=.:._1- - [38)
n-k-1
Refer to Table 4 for a summary of expected values and variances of the
parameters of Model A and Model B.
Nonpn:stn:ssod
8.72 xlo' 8.25 xl06 10.7 x109 946 200 xlo'
Reinforcement
Prest=scd
3.50 xlo' 385 x!o' 65.5 xl03 110 190 x!o' 25 2 7
Steel Layer I
Prestressed
434 xiO' 260 x!03 81.2 xl03 60 190 x!o' 31 8 9
Steel Layer 2
..
"Calculated about reference axiS m Ftgure 2 **y mdicates distance 1iom centrotd of sectioo to reference axiS
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
0.2
E[Q
0.0501
Variation
6.46% 8,
Value
1
E[Q
0.284
Variation
9.93%
6:! 0.95 0.988 0.90%
Stiffiless 1;. 21500 15365 0.55% 8s 4743 3570 0.52%
t;, 11.6 7.66 3.30% a. 2.49 3.32 34.7%
creep
I;. I 1.16 4.12% a, -().094 -Q.I37 10.6%
t;, 0.3 0279 2.06% a. 0.6 0.353 13.97
8r 10 7.84 35.26
t;, 108.5 141 0.67% 8s 696 616.1 3.83%
shrinkage t;1 0.5 0.341 2.35% e, 1 0.73 3.78%
a,. 55 15.7 5.59%
1600
1200
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Figure 4 - Effect of Analysis Method on Mid-Span Deflection Prediction for
Girder 273-01 using Model A
0.0
eg -0.1 .
0 Measured Data- Girder 2~1
Measurod Data · Girder 273-ID
~ ..0.2
-;;
~ -0.3
"
10 20 30
Lengtb Along Girder (m)
(a) Curvature
a so
a
'; 40
.e
! 30
I! 20
"1!.10
~
!!!
0
.
0 Mca&unxl Da1a- Girder 273-01
Meuured Da1a- Ginier 273-ID
0 10 20 30
Length Along Girder (m)
(b) Deflected Shape
~SO
:r~)~
,
"40
~ lO
f"\" Model A
CEBMC·90/ /
AASHTO
!!! •+---~----~----~--~----~----~--~----~
0 20 40 60 60 100 120 140 160
Time Under Load (Days)
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
100 20 40 6l) eo
C~Sfrtllaiii(Mh)
(c) Ct"-"'p- I Day Age atl.oadlng (d) Creep • 8 t>ay Age at l.oadlng
MS!fl'()
ACl21l9
ACl~-tMi.lif~
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Syonpsis: The study included A3 -General Paving (2 1 MPa at 28 days), A4- General
Bridge Deck (28 MPa at 28 days), and AS- General Prestress (35 MPa at 28 days) concrete
mixtures approved by the Virginia Department of Transportation (VDOT). The study also
included a lightweight, high strength concrete mixture (LTHSC) used in the prestressed
beams of the Chickabominy River Bridge, and a high strength (HSC) concrete mixture
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
217
Copyright American Concrete Institute
Provided by IHS under license with ACI Licensee=UNI OF NEW SOUTH WALES/9996758001
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218 Mokarem et al.
D. W. Mokarem is a Research Scientist at the Virginia Transportation Research Council,
Charlottesville, VA. His PhD in Civil Engineering was awarded by the Virginia
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
ACI Fellow R. E. Weyers is the Charles E. Via Jr Professor at the Virginia Polytechnic
Institute. He is a member of ACI Committees 222 Corrosion of Metals in Concrete, 365
Service Life Prediction and 548 Polymers in Concrete. He is the current chairman of 345
Concrete Bridge Construction, Maintenance, and Repair.
INTRODUCTION
Concrete experiences volume changes throughout its service life. The total in-
service volume change is the resultant of applied loads and shrinkage. When loaded,
concrete experiences an instantaneous recoverable elastic deformation and a slow
inelastic deformation called creep. Creep of concrete is composed of two components,
basic creep or deformation under constant load without moisture loss or gain, and drying
creep. Drying creep is the time dependent deformation of a drying specimen under
constant load minus the sum of the drying shrinkage and basic creep. Deformation of
concrete in the absence of applied loads is often called shrinkage.
Neville discussed the loss of water in concrete associated with drying shrinkage.
The change in volume of the concrete is not equal to the volume of the water lost. The
loss of free water occurs first, causing little to no shrinkage. As the drying of the concrete
continues, the adsorbed water is removed. The adsorbed water is held by hydrostatic
tension in small capillaries (< 50 nm). The loss of adsorbed water produces tensile
stresses which cause the concrete to shrink. The shrinkage due to the adsorbed water loss
is significantly greater than that associated with the loss of free water (3).
The objective of this study is two fold. The first objective is to observe the
magnitude of shrinkage of typical Virginia Department of Transportation (VDOT)
concrete mixtures. The second objective is to assess the accuracy of existing unrestrained
shrinkage prediction models. The models are the ACI 209 model, the CEB 90 model
used in Europe, the Bazant B3 model, Sakata model, and the Gardner/Lockman 2000
(GIL 2000) model. For the high strength concrete mixture the ACI 209 Modified,
AASHTO-LRFD, and Tadros models were also used to predict shrinkage.
The study included A3 -General Paving (21 MPa at 28 days), A4- General
Bridge Deck (28 MPa at 28 days), and A5 - General Prestress (35 MPa at 28 days)
concrete mixtures approved by VDOT. The study also included a lightweight, high
strength concrete mixture (LTHSC) used in the fabrication of prestressed beams for the
Chickahominy River Bridge, and a high strength concrete mixture (HSC) used for the
fabrication of prestressed beams for the Pinner's Point Bridge. Some of the mixtures
included slag cement, and other mixtures included pozzolans such as fly ash and
microsilica. Chemical admixtures were an air entrainer (AEA), retarder (RA), water
reducer (WR), high range water reducer (HRWR), and corrosion inhibitor (CI). The
chemical admixtures were not a study variable, only one type and manufacturer of each
admixture was used.
METHODS
Aggregate Properties
For the A3, A4, and A5 mixtures, three types of #57 coarse aggregate,
limestone, gravel, and diabase were used. The coarse and associated fine aggregate were
obtained from various locations in the Commonwealth of Virginia. The lightweight, high
strength mixture had two coarse and two fine aggregates, a lightweight and a norrnal
weight aggregate. The lightweight aggregate was both a fine and #67 expanded slate (4).
The normal weight aggregate was a natural sand and a #67 crushed diabase. The high
strength mixture had a #67 crushed diabase stone aggregate, and a natural sand fine
aggregate (5).
The mixtures included a Type IIII portland cement and a ground granulated blast
furnace slag (GGBFS). The GGBFS was a grade 120. The pozzolans used were a class
F fly ash, and microsilica which is a relatively pure amorphous silica dioxide that is 100
times finer than portland cement.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Mixture Proportioning
The mixture proportions for all mixtures are presented in Tables 1-3. Table 1
presents the mixture proportions for the A3, A4, and A5 portland cement concrete
For the A3, A4, A5, and SCM mixtures the specimens were fabricated and then
covered with wet burlap and a 6 mil polyethylene sheet for 24 hours. After 24 hours, the
specimens were demolded and placed in lime saturated water for six days. Initial length
measurement were performed on the prism specimens before they were placed in the lime
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
saturated water. After six days, the specimens were placed in a controlled environment
of 23 oc and 50%± 4% in accordance with ASTM C157-98. Subsequent length change
measurements were conducted every seven days up to 90 days, and then at 120, 150, and
180 days.
The LTHSC and HSC mixtures employed a standard cure for two batches and
an accelerated cure for two batches. The standard cure method consists of a seven day
moist cure at 23 oc ± 1.7 °C. The accelerated cure consists of elevating the specimen
temperature to increase the rate of hydration. For this study, the standard cure batches
were used to fabricate and measure length change prisms. After the seven day moist
cure, the specimens were placed in a controlled environment of23 oc and 50%± 4%.
ASTM C157-98 requires an additional curing in lime saturated water for 27 days
after the first 24 hours after the addition of water to the concrete mixture. As stated
previously, specimens in this study were cured in lime saturated water for a period of six
days after the addition of water to the concrete mixture. The reason for the nonstandard
curing conditions is that VDOT specifications requires hydraulic cement concrete
structures to be cured for a period of 7 days (7). Thus, the shrinkage results presented are
more indicative of field concrete where drying shrinkage would begin after a seven day
curing period rather than the standard 28 day curing period. It is recognized that the
pozzolanic activity would be small after seven days of moist curing. However, as stated
l,rediction Models
Five existing shrinkage prediction models were used to compare the shrinkage
measurements obtained in this study to the predicted values of each model. The
following presents the equations for the prediction models:
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
(t- t I )
s l (t, t ) = . s 1, o . I cure)
c , ( m01st [ll
Sr1 Stl,O
1
35 + (t- t h ) Sllt;t:j
s ,o
(t- t I )
s1 0
& ·1: ( t, t ·I
Sl S1,0
) = )5+(t-t
_ • )
c
1
S1!fJ
(steam I cure) [2]
1
SJ1,0
&
s
h(t,t )
0
= -s sh 00 KhS(t) [3]
2.1 I -0 28 ) -6
&shoo = -ala2 ( 26( w ) (fe) · + 270 * 10 [4]
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
K = 1- h 3 [5]
h
[6]
6
s (/ ) = (160 + IO{J (9- f I 1450)) * 10- [8]
s em se em
3
fJ ARH = 1- (RH I 100) [1 0)
[11]
112
eshu = 1000 * K * (
4350
, J * 10-6
[12]
fcm28
[13]
fJ(h) = 1- 1.18h4
[14]
fJ(t) =( (t- tc) 1/2J * 10-6
t- tc + 97(V IS)
[15]
[18]
.
f ah = - ksk,( 35.0+t
t
r
\.5lx1 o-J
[19]
fah=-kskh( 55.0+t
t h.5lx10-
J
3 [20]
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
where:
t
e0.36(Y IS)+ t 1064 -94(VI S)]
ka= 26 [21]
t 923
45+1
6 [24]
f sh = 480* 1o- :./ah
t [26]
kld=
61-4/'a+t
[27]
khs = 2.00- 0.0143H
1064-94V IS [28]
ka=
735
[29]
kr = S/(1 +r ci) --`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Unrestrained Shrinkage
Figures 1-6 present the average percentage length change and 95 percent
confidence limits for the A3, A4, and A5 portland cement concrete mixtures. These
figures also present the predicted values for the ACI 209, B3, CEB 90, and GL2000
shrinkage prediction models. The Sakata model was not presented in the figures because
of its relative poor prediction characteristic which is present in the Prediction Model
Analysis section. The measured shrinkage values for the A3, A4, and A5 portland
cement concrete mixtures are only slightly different. Considering the variability
associated with shrinkage measurements, there is no significant difference between the
three mixtures as indicated by the 95 error bars in the figures. The coefficient of
variation (COV) for the A3, A4, and A5 mixtures were relatively high at seven days
ranging from 7.6 to 19.7 percent which is to be expected for sma11 early age
measurements. From 28 to 180 days the COV were generally less than nine percent (6).
Figure 7 presents the average percentage length change for the SCM mixtures.
The COY of the SCM were similar to the A3, A4, and A5 mixtures indicating a higher·
variability at seven days than at 28 days to 180 days (6). The mixture containing fly ash
exhibited the greatest amount of shrinkage. The mixtures containing microsilica and slag
cement were not significantly different. The AS slag cement mixture had the same
diabase aggregate types as the A4 supplemental cementitious material mixtures.
Figures 8 - 13 present the average percent length change and the 95 percent
confidence limits for the LTHSC and HSC mixtures. These figures also show the
predicted values from the shrinkage prediction models.
The percent shrinkage was calculated for each of the models at seven, 28, 56,
90, 120, 150, and 180 days after shrinkage had commenced. A residual value for each
measured unrestrained shrinkage specimen was calculated as folJows:
The measured (experimental) value was an average value for each batch at seven, 28, 56,
90, 120, 150, and 180 days. Thus, if the residual value was positive, it indicated that the
model over estimated the shrinkage. If the residual value was negative, it indicated that
the model underestimated the shrinkage. The ACI 209 model is applicable for only Type
I General and Type III High Early Strength cements. Therefore, residuals were not
calculated for the A4-Diabase/Fly ash, A4- Diabase/Slag cement, and AS-Diabase/Slag
cement mixtures for the ACI 209 model, because these cementing materials hydrate at a
slower rate than a Type I or Type III cement. They are closer to a Type II cement.
An average error percentage for the seven time periods was calculated, a smaller error
percentage over the 180 day period indicates a better fit model. Table 7 presents the
average residuals and the average error percentage for the mixtures. The residual values
are also the average for the seven time periods. For example, the residuals for the A3
mixtures are the average residuals for the A3 limestone, gravel, and diabase mixtures at
seven, 28, 56, 90, 120, 150, and 180 days.
For the A3 and A4 portland cement concrete mixtures, the CEB 90 model was
the best predictor. The model had the lowest average residuals and lowest error
percentage values. The GL 2000 model was the next best predictor closely followed by
the Bazant B3 model. The ACI 209 and Sakata models were not as accurate as the other
three prediction models. For the AS portland cement concrete mixtures the CEB 90
model was again the best predictor. The Bazant B3 model was the next best predictor
closely followed by the GL 2000 model.
Overall, for the portland cement concrete mixtures, the CEB 90 model was the
best predictor, followed by the G/L 2000 and Bazant B3 models. Whereas the ACI 209
and Sakata models were not as accurate for the portland cement concrete mixtures as the
other three models. However for the A3, A4 ,and A5 mixtures, it is extremely difficult to
conclude that there is any significant difference in prediction capabilities between the
CEB 90, GL2000, and B3 models and thus these three models should be considered
equivalents.
For the fly ash and slag cement mixtures the Bazant B3, CEB 90, and GIL 2000
models were used in shrinkage prediction analyses because these cementing materials are
closer in hydration characteristics to a Type II cement rather than a Type I. The Bazant
B3, CEB 90, and G/L 2000 models include an adjustment factor for cement types,
OveraJJ, for the error percentage analysis of the data, the models tended to
overestimate the shrinkage of the portland cement concrete mixtures and underestimate
the shrinkage of the supplemental cementitious material mixtures. One of the probable
reasons is that these models predict shrinkage largely based on the average 28-day
compressive strength of the mixture. Compressive strength does not directly account for
the pore volume and pore size distribution of the mixture, which greatly affects drying
shrinkage.
The rankings for the LTHSC and HSC mixtures are presented in Table 8. The
ran kings are based on the sum of the residuals. For the LTHSC mixtures, the ranking of
the models was inconclusive (Vincent, 2003). The ACI 209 model under predicts
initially, then over predicts after 50 days. The CEB 90 model is the best early age
predictor, then under predicts after 28 days. The Bazant model under predicts initially,
then is the best predictor after 80 days and the Gardner!Lockman model under predicts
throughout drying. However, considering the variability associated with concrete
shrinkage property, there appears to be little difference between the G/L2000, Bazant 83,
and ACI 209 models.
For the HSC mixtures, the compressive strengths exceeded the limitations of
some of the models, however, these models were sti)] used to see how they performed
outside of the limitations (5). The Gardner!Lockman model is the best predictor for the
HSC mixtures. The ACI 209 and AASHTO-LRFD models under predicted initially, then
over predicted after 50 days. The CEB 90, Bazant 83, Tadros, and ACI 209 Modified
models under predicted shrinkage throughout drying.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
CONCLUSIONS
1. The A3, A4, and AS portland cement concrete mixtures exhibited about the
same amount of drying shrinkage which is to be expected for mixtures with
small differences in cement, water, and aggregate content and relatively
similar strengths.
2. The mixtures containing fly ash exhibited greater drying shrinkage than
those containing microsilica and slag cement which may be related to the
relatively short but field realistic curing period of seven days.
3. The CEB 90 model appears to be the best predictor of drying shrinkage for
VDOT Portland cement concrete mixtures. However, considering the
variability associated with shrinkage property of Portland cement concrete
5. For the lightweight high strength concrete mixtures, the CEB 90 model
ranked higher at early ages, while the Bazant B3 model ranked higher at
later ages.
6. For the high strength concrete mixtures, the G/L 2000 model ranked higher
than the other models. However, there appears to be no significant
difference between the GIL 2000, Bazant 83, and ACI 209 models.
ACKNOWLEDGMENTS
The authors would like to thank the Virginia Transportation Research Council
for funding these projects. The opinions, findings, and conclusions expressed in this-
report are those of the author and not necessarily of the sponsoring agency.
REFERENCES
1. Holt, E. and Janssen, D., Influence of Early Age Volume Changes on Long-
Term Concrete Shrinkage, Transportation Research Board, Washington, D.C.,
1998.
2. Dilger, W.H. and Wang, C., Shrinkage and Creep of High Performance
Concrete (HPC) A Critical Review, Creep and Shrinkage - Structural Design
Effects, SP-194-11, ACI, pp. 361-379, Nov. 1997.
3. Neville, A.M., Properties of Concrete, Fourth Edition, John Wiley & Sons, Inc.,
1998.
8. Bhal, N.S. and Jain, J.P., Effect of Age at the Time of Loading on Creep of
Concrete, The IndianConcrete Journal, September 1995.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
10. Bazant, Z.P., Creep and Shrinkage Prediction Model for Analysis and Design of
Concrete Structures- Model 83, Materials and Structures, v. 28, pp. 357-365,
1995.
11. Gardner, N. J., and Lockman, M. J., Design Provisions for Drying Shrinkage
and Creep of Normal-Strength Concrete, ACI Materials Journal, V. 98, March-
April2001, pp. 159-167.
12. Sakata, K., Prediction of Concrete Creep and Shrinkage, Creep and Shrinkage of
Concrete, Proceedings of Fifth International RILEM Symposium, 1993.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
13. Huo, X.S., A1-0maishi, N., and Tadros, M.K., Creep, Shrinkage, Modulus of
Elasticity of High Performance Concrete, ACI Materials Journal, v. 98, n. 6,
November-December 2001.
160-720 260-500
w/c - 0.30-0.85 - - 0.40-0.65
HumidM%) 40-100 40-100 40-100 40-100 45-80
Cement-tvoe I orill I II or III R, SL orRS lor ill -
to or t,
<: 7 Days t,:Sto t,:S 14Days <: 2 Days -
(~oist cured}
to or t,
(~earn cured) <: l-3 Days t.~to t,~ l4Days <: 2 Days -
Model includes No, but
lightweight considers No
Yes No No
concretes? aggregate
stiffness
Bazant 83 BazantB3
ACI209 ACI209
GL2000 ACI 209 Modified
Tadros
AASHTO LRFD
CEB90
0.061--~~---~------==~=::
0.05 ~---Jit""":;;....--.....-~""$""==:;~
&
; 0.04 -I---"C71'"--=--..-= c - - - - - - - - 1
....,._Prisms
ti
i 0.03 --ACI209
-......B3
.3
. 0.02 -1-b~---------------l
Figure 1: Shrinkage Prism Data with ACI 209 and Bazant B3 Models
(A3 Portland Cement Concrete Mixtures).
0.06,----------------,
0.05
& 0.04
o._---------------1
50 100 150 2 0
-0.01 .L...--------------'
nme After Cure (Days)
Figure 2: Shrinkage Prism Data with CEB 90 and GIL 2000 Models
(A3 Portland Cement Concrete Mixtures).
0.05 j------.:;ii~::::::==~==t===•---j
&
........_.Prisms
' 0.04
I. :::+-LF-------------------1
.--ACf209
...._.a3
0,01 jJ-----------------1
Figure 3: Shrinkage Prism Data with ACI 209 and Bazant B3 Models
(A4 Portland Cement Concrete Mixtures).
.......-Prisms
....... cea so
....,._QL2000
100 150
.0.01'--------------'
Figure 4: Shrinkage Prism Data with CEB 90 and GIL 2000 Models
(A4 Portland Cement Concrete Mixtures).
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
f 005
u 0.04
0.07
0.06
_
f/
..
··~ ---
Jooa
'# 0.02
0.01
,,
/?-'
'
~-"···
Figure 5: Shrinkage Prism Data with ACI 209 and Bazant B3 Models
(A5 Portland Cement Concrete Mixtures).
0.06
...
& 0.04
.- ........
;
6 0.03 LZ"
i 0.02
//_
!l
., Q.Q1 [_
50 100 150 2!0
-0.01
Time Aller Curing (llaYII
Figure 6: Shrinkage Prism Data with CEB 90 and GIL 2000 Models
(AS Portland Cement Concrete Mixtures).
"'fi 0.0400
.c
u
--~ --
.c 0.0000
~
!1 0.0200 /
';/!. 0.0100 r ----
O.CXXXJ
0 50 100 150 200
Time after curing (Days)
uosoo
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
OO'!Oi.)
OOOC'O
0
i ~0$y"(l
1::;:. AC! ?<Bi
ti
iii 0(>400 1.-..C!W!<JJ
E'
,3
~
00~00 !=-~·-
OtQ-~
j
omoo ""'"''""~"'"""'"'""'"'"""""'"'""'""'"""'""""''"""""'""""'"""""'1
oo:.n1
() ~N 100 ~~ 2tC :.:tM 3.00 300
Tim-e After Curifti (days)
Figure 8: Shrinkage Prism Data with ACI 209 and CEB 90 Models (LTHSC).
1 t::r-:::::~
i o.oooo .... _....... ·• . . . . . " .,.
rr/i·:~.-~::
1
1
~ :: i:r./~
o.=
. . . -
r.-----....----·-----~------·--·~·-------·---"'··-·-----·
~
Time All< Curing (da)'ll
~
Figure 10: Shrinkage Prism Data with ACI 209 and ACI 209 Modified Models (HSC).
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Figure 11: Shrinkage Prism Data with CEB-MC90 and Tadros Models (HSC).
Figure 12: Shrinkage Prism Data with GL2000 and AASHTO-LRFD Models (HSC).
ooooo+---------------------------~
~~~~~
00000~----~----r-----·~----~--~
0
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
239
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
ACI member and ACI Italy Chapter President, Mario A. Chiorino is Professor oj
Structural Mechanics at the Politecnico di Torino and a member of the Turin Academy oj
Sciences. He has been associated with CEB activities since I 968 as a member of the CEB
Advisory Committee, the .Committee for the CEB-FIP Model Code 1990, various
technical committees, and as editor of the CEB Design Manual "Strnctural Effects oj
Time-dependent Behavior of Concrete
INTRODUCTION
Creep analysis of structures is normally performed on the basis of the linear theory of
viscoelasticity for aging materials. A large number of practical problems concerning the
influence of creep effects on the reliability and durability of concrete structures can be
solved exactly, and in very compact closed forms, through the four fundamental theorems
of this theory, as demonstrated by the second author in a parallel paper and in previous
works [Chiorino et a!. 1984; Chiorino and Lacidogna 1993, 1999, Chiorino 2000, 2005,
Chiorino eta!. 1997, 1999, 2002]. These compact formulations are particularly suitable
for codes and technical guidance documents CEB 1993, CEN 2003, and helpful in the
global assessment of creep induced structural effects in the preliminary design stages, as
well as in the control of the output of the ·final detailed numerical investigations and
safety checks.
The conditions to be respected are the homogeneity of the concrete structure and the
rigidity of the restraints. Under these assumptions, the compact solutions are
characterized by one of the three fUndamental jUnctions, depending on the type of
problem under consideration, i.e.:
J(t,t 0) represents the strain response at time t of the material to a constant unit
sustaine~ stress applied at different ages to at loading.
R(t, t0) represents the stress response at time t of the material to a constant unit
sustained strain applied at different ages to at loading .
.;(t,t0.t1) measures the creep induced stress redistribution following a change of static
scheme at t = t1 ;? to+ , ( with t0 + = age immediately after loading); it has the character
of a non dimensional factor whose values lie in the interval (0,1) (with .; = 0 fort= t1),
and measures at a given timet the creep induced part of the difference between the stress
distribution corresponding to an hypothetical application of the constant sustained loads
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
A fourth function, termed the aging coefficient x and related by an algebraic equation
to J and R , can be used for the compact solution of many creep analysis problems, both
exactly or with different degrees of approximations depending on the type of problem,
adopting the age-adjusted-effective-modulus (AAEM) method [Bazant I 972b; see also
Chiorino et al. 1984; Chiorino and Lacidogna 1993, 1999, Chiorino 2000, 2005, CEN
2004].
Finally, a further group of functions, called reduced relaxation functions R*, allows
application of the fundamental theorems of the linear theory of viscoelasticity for aging
materials to the analysis of heterogeneous concrete structures with elastic restraints (like
e.g. cable-stayed bridges). The 'R* functions depend on the compliance J of the concrete
part of the structure and on some characteristic parameters of the heterogeneous structure
[Chiorino et al. 1986, Mola 1993, Giussani and Mola 2003].
The compliance as a function of time t and age at loading to can be obtained from
creep prediction models suggested by technical documents of international engineering
associations, or available in the literature, on the basis of the physical parameters
(material, ambient and geometrical parameters) characterizing the concrete and the
structure, or structural element, under consideration.
The relaxation and the redistribution functions R and ~, and the reduced relaxation
functions R*, can be obtained from J through the solution of the fundamental Volterra
integral equations relating R , ~ and R* to J. The aging coefficient X is then derived as
an algebraic function of J and R. For realistic forms of the compliance, like for instance
those suggested by the principal creep models considered by civil engineering societies,
integration of the Volterra integral equations for the determinations of the derived
functions R (and thus also x), ~, and R*, cannot be obtained analytically, and numerical
integration is necessary.
Design aids to speed up the computation of both the primary function J and the
derived functions are therefore needed by researchers and designers, and are essential for
a rapid application in the design activity of the compact solutions for creep analysis
problems indicated above.
For the CEB 1990 model code creep prediction model (CEB MC90) [CEB 1993), an
extended set of charts of the primary function J, and of the derived functions R, x and ~,
for a wide range of influencing parameters, have been determined on the basis of these
numerical procedures and incorporated in the revised edition of the CEB Design Manual
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
The design tool offered to researchers and to the profession is in the format of a web
site incorporating a numerical solver, instead of traditional design charts. The numerical
solver can be included into Finite Elements codes, when dealing with structures not
exceedingly complex.
RESEARCH SIGNIFICANCE
The paper discusses the problems concerned with the development of a computer
program for the automatic computation (both numerical and graphical) of the entire set of
functions that are of interest for the creep analysis of concrete structures, on the basis of
the physical parameters characterizing the structural problem under consideration, and
with reference to the three prevailing creep prediction models (CEB MC90, B3 1 [Bazant
and Baweja2000], and GL2000 [Gardner and Lockman 2001]) published in the literature
and presently under consideration in the revision of the ACI 209 document on creep and
creep structural effects [ACI 209 2004].
To make the software available to the scientific community a web page has been
developed, from which it is possible to download the setup files and run the application
on a computer. The web page is hosted by the web site of the Politecnico di Torino and
can be reached at the web address M-ww.polito.itlcreepanalysis. The Creepanalysis
Research Group at the Politecnico di Torino will develop and upgrade the design aids as
well as the web page architecture.
As a first step the computer program allows the computation of the three functions J,
R, and ~. permitting the compact and theoretically correct solution of the majority of
practical problems concerning the evaluation of the influence of creep effects on the
reliability and durability of homogeneous concrete structures. In the future developments
of the research the architecture of the web page will be progressively extended to include
the automatic calculation of the other functions of interest for the creep analysis of
structures, like x and R*.
1
A web page has been already developed as a design tool for the quick evaluation of
J only for the B3 model. The page computes single numerical values of J at a given time t
for a given age at loading to, once the data concerning the characteristics of the concrete,
of the structural element and of the ambient have been inserted by the user [Kfistek et al.
2001].
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
The immediate availability of the basic functions allows extended comparisons of the
outputs of the different models, and an estimation of the consequent influence that the
selection of a particular model has on the assessment of structures.
The Creep Beta 1.0 program is a C++ stand-alone compiled application, that can be
installed on computers running MS Windows. The choice to develop a stand-alone
routine, complete with all the interfaces and data output features, instead of a routine
running inside a given mathematical environment, allowed the creation of an easy to use
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
tool for everybody who needs a quick print of the creep related curves.
By means of the input interface windows it is possible to input all the values required
by prediction models, as well as the initial and final time for each curve and all the
options related to calculation. The ouput consists of text files of the numerical values of
results and graphic bitmap files of the charts. Because the program is intended as a
working tool many options and settings are included.
The main window provides a graphic screen where the computed diagrams of the
different functions are drawn: all the parameters of the graphic screen can be edited by
the user, scaling, boundary and type of coordinates (linear or logarithmic). From the main
window it is possible to select what type of diagram to draw (compliance J, relaxation R
or redistribution q), the type of integration rule for the numerical solver of the integral
equation (rectangle or trapezoidal), and the number of time steps. It is possible to print
the diagrams as shown in the window.
Figures 1 to 6 present examples of the main window for both compliance and
relaxation functions, for the three creep prediction models: CEB MC90, B3 and GL2000,
for the set of parameters indicated and for selected values of the age at loading t0 • The
examples concerning the calculation of the redistribution function 4(t,t0.ti) for the three
models are presented in Figures 7 to 12, for the same set of parameters and for two
different values of the age at loading t0 , for selected values of the age t 1 at which the static
system is changed.
The following Volterra type linear integral equations hold for the determination from
the compliance J of the relaxation function R and of the redistribution function ;,
respectively [Chiorino and Lacidogna 1993, 1999, Chiorino 2005, Dezi eta!. 1990, Dezi
and Tarantino 1991]:
t
NUMERICAL SOLUTION
The classical numerical algorithm first proposed by Bazant [Bazant 1972a] was
adopted for the approximate solution of eqs. (1) and (2). The algorithm is illustrated in
Appendix I, with reference to the determination of R by eq. (1) and using the
trapezoidal rule. Considering that the term J(t 1,to) at the left side of eq. (2) is constant by
respect to time, the numerical solution of eq. (2) can be easily obtained adopting the same
algorithm, provided that t ~ to and t1 c to.
Two options are available for the approximation of the integrals with finite sums: the
trapezoidal rule and the rectangle rule. The second option allows a quicker solution and
usually leads to acceptable approximations if the number of time steps is not too small.
However, computation time is not significant even when adopting the trapezoidal rule: of
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
the order of seconds for the entire family of curves of R or ; appearing on one window.
The selection of the most convenient progressions of time steps, in terms of amplitude
of the first time interval and rate of the geometrical progression, or in terms of final time,
can be easily performed - thanks to the rapidity of the process - verifying the influence
of the refinement of the adopted subdivision of the time scale on the numerical results of
the computed function through repeated trials.
The following values are normally adequate for accuracy in the results up to third
digit for all the models:
- amplitude of the first time interval: L1 12 = tr t 1 = 0.01 day= 864 s,
- number of step per decade: m = 80,
- number of steps for I 05 days: := 550.
CREEP MODELS
The following models have been embedded in the program: CEB MC90, B3, and
GL2000. Their formulations are presented in Appendix 2, together with the input data
required by each model.
For a comparison of the predictions of the different models, equivalent conditions can
be established setting at the same values identical or equivalent parameters.
Some minor problems arise in this selection, as e.g. in the case of the parameters
related to the type of cement, due the different classification of cements in the CEB-FIP
Model Code and in American Standards. In the examples of the families of curves shown
in Figs. I to 12 the following equivalence has been adopted: normal (N) or rapid
One other minor difficulty is due to the fact that the reference concrete strength is the
characteristic strength at 28 days fck 28 (termed fck) for CEB MC90 model, and the mean
compressive strength at 28 days fcm 28 for the B3 and GL2000 models. The characteristic
strengthfck has been selected as one of the general input data in the present program. The
relationship fcm 28 = 1.1 fck28 + 5.0 (MPa), suggested by GL2000 model for an estimation
offcm28 from /ck28, has been extended also to the B3 model.
B3 and GL2000 models require the introduction of the additional parameter t c (age
when drying begins, end of moist curing, with tc"S t0 ). In the examples of the families of
curves shown in Figs. 1 to 12 a fixed value tc = 3 days has been adopted for all the
curves.
In this respect, it must be observed that model GL2000 specifies that to calculate
relaxation the correction term rJJ(tJ for the effect of drying before loading must remain
constant at the initial value throughout the relaxation period. This specification has been
extended to the calculation of the redistribution function. Therefore, when the solver
calculates for this model a curve of the relaxation function R(t,t0) or of the redistribution
function q(t,t0.fi) for a given t0 , the value of tP(tJ has been be set constant for all the
compliance curves involved in the calculation at the value calculated for t0 . On the
contrary, in B3 model the value of tc'S to is set constant for all the compliance curves
involved in the same type of calculations.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Model B3 requires the introduction of further parameters related to the concrete mix
and to curing conditions. The following values were adopted for the curves shown in the
figures:
(3)
By analogy, in the relaxation function the initial age dependent stress response due to
a unit imposed strain for L1 = t- t0 small is treated as instantaneous and elastic, i.e.:
This conventional separation is included directly in the formulations of the model for
CE8 MC90 and GL2000 models.
For GL2000 no specific indication is given on the stress duration for measuring the
initial strain and the corresponding elastic modulus EcmtO·
The immediate availability of extended sets of charts of the basic functions J, R and q,
for a wide range of material, geometrical and ambient parameters, allows easy
comparisons between the different models.
Although the reliability of creep prediction models must be evaluated with respect to
their agreement with the available experimental results (essentially concerning the
compliance J and gathered in the data bank [MOLLER 1993]), a comparison between the
predictions of the different models is not devoid of interest.
In fact, in the parallel paper [Chiorino 2005] it has been observed that, in spite of the
fair to good ratings - depending on the adopted statistical criteria and indicators -
attributed in the recent literature [ACI 2004, Al-Manaseer and Lam 2004] to all the three
models considered here, with regard to their agreement with the data bank, considerable
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
These differences concern both the shapes of the families of curves, and their long-
term values, for all the basic functions. In fact, the influence of both long elapsed times t
(e.g. for time ranges of the order of magnitude of the service life of a structure, that
largely exceed the extension of any experimental collection of data), and of almost the
entire range of ages to at loading or t1 at the moment of modification of the static scheme,
is evaluated in significantly different ways by the two groups of models. This can be
clearly observed e.g. in the set of Figures I to 3 for J, 4 to 6 for R, and of Figures 7 to 12
for q, for typical average values of the input parameters.
The reasons of these differences and their impact on design strategies, and on the
formulation of code provisions, have been discussed in the parallel paper.
The flexibility and immediateness of the program presented in this paper, allowing
extended parametric explorations, offer a valuable instrument for this kind of evaluations.
CONCLUSIONS
The general approach of creep analysis of structures based on the linear theory of
viscoelasticity and on the extended use of the four' fundamental theorems leads to very
compact and theoretically correct solutions for homogeneous structrures with rigid and
delayed restraints. The use of reduced relaxation functions allows the theoretical solution
to be extended to homogeneous structures with elastic restraints.
In this perspective the paper has presented a powerful design tool, conceived for
researchers and designers, consisting of a software application for a quick, automatic
calculation of the three basic functions (compliance function J, relaxation function Rand
redistribution function ;) characterizing these solutions, with reference to the principal
creep models presently considered by international civil engineering societies. The
computer program has been designed to be easy to use and to allow control on all the
parameters involved by the prediction models, It has a powerful graphic module for
handling and printing charts.
The three following models have been considered: CEB MC 90, B3 and GL2000. The
immediate availability of the basic functions allows extended comparisons of the outputs
of the different models, and the evaluation of the influence that the selection of a
particular model has on the assessment of structures.
To allow a large distribution of this design aid a web page has been created, from
which the software can be easily downloaded. The web page l'.rww,polito,itlcreepanalysis
is hosted by the web site of the Politecnico di Torino and will be upgraded by the
Creepanalysis Research Group with the aim of developing further automatic tools
devoted to the creep structural analysis.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
APPENDIX 1
Numerical solution of the fundamental integral equation for the determination of the
relaxation function R(t.t0 ) from the compliance function J(t.tv)_
for k>l
k-1
b.R(tk) = _
L [J(tk, ti) + J(tk, ti-l)- J(tk-I, t;)- J(tk-l, ti-l )]b.R(ti)
_,_i=::.!I_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
(AJ.3)
J(tk 'tk) + J(tk 'tk-1)
(A1.4)
In consideration of:
the particular prescribed strain history, which exhibits only an immediate
discontinuous change at time of loading to = t1 (L1Eco(tJ) = J) and remains constant
afterwards, and the corresponding stress history (relaxation function) showing a
corresponding initial instantaneous change followed by a variation (decrement) at a
decreasing rate,
- the particular shape of the creep curves described by the compliance function
J(t,to) which are characterized by significant slopes in the logarithmic time-scale for
elapsed times ranging from seconds to decades of years (rapid initial increments of the
m represents the number of steps per decade logJO (discussion in [Chiorino and
Lacidogna 1993]).
APPENDIX2
In this appendix a compact summary of the formulations and the parameters involved
in numerical calculation is given; some problems related to different definitions of
parameters are discussed at the end of each model description.
I 1 r/J(t,tO)
J( t,t 0 , = +---
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
. Ee(to) Eei
3
Eci = Eeo[(fck + f!.j)/ femot
E cO = 2.15 X 10 4
tif = 8
fcmO = 10
Ec(t)= j]E(t)Eci
5
fJE (f)= [flee (t)t·
·[ (Q/(Io)Jr(t0)]-1/r(tO)
Q(t,t 0 ) = Q1 (t 0 ) 1 +
Z(t,t 0 )
S(l)~mnh[('~:,rJ
S(t,Hanh[('',~ ' rJ 1
25 2
r sh = 0 •085t c --0.osf.cm28 -o. [2k s (VI S)]
Notes:
The value of Ecm28 is computed from the formula (*) which is considered as a part of
the model formulation.
The program calculatesfcm28 from the characteristic strength at 28 daysfck28 according
to the same formula suggested by GL2000 model.
The exponent m and n are empirical quantities assumed to be equal respectively to 0.5
and 0.1.
The value of fc. representing the age when the moist curing of concrete ends and start
the drying, must be less than t0.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
J(t,to) =-1-+_t/J_
EcmtO Ecm28
Notes:
The value offcm2B is obtained fromfck2 8 according to the formula:
fcm28 = 1.1/ck28 + 5.0
which is considered as a part of the model formulation.
The value of tc, representing the age when the moist curing of concrete ends and start
the drying, must be less than t 0
NOTATION
t = time, representing the age of concrete, in days
to = age at loading, in days
to+ = age immediately after loading, in days
t 1 ~ t0+ = age at change of static scheme, in days
lc = age when drying begins, end of moist curing, in days
J(t,to) = creep or compliance function,
R(Uo) = relaxation function
q(t,to,/1) = redistribution function
For notations specific to the CEB MC 90, 83 and GL200 creep prediction models
refer to Appendix 2
REFERENCES
ACI 209 (2004), Guide to Factors Affecting Shrinkage and Creep of Hardened Concrete,
Chapter 5- Modelling and Calculation ofShrinkage and Creep, Draft Document.
Bazant Z.P. (1972a), Numerical Detennination of Long-range Stress History .from Strain
History in Concrete, Material and Structures, Vol. 5, pp. 135-141.
Bazant Z.P. (1972b), Prediction of Concrete Creep Effects Using Age-Adjusted Effective
Modulus method, ACI Journal, Vol. 69, p. 212-217.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Bazant Z. P. and Baweja S. (2000), Creep and shrinkage prediction mode/for analysis
and design of concrete structures: Model B3. in: A. AI-Manaseer ed., A. Neville
Symposium: Creep and Shrinkage - Structural Design Effects, ACI Fall Convention,
1997, ACI SP-194, pp. 1-83.
Bazant Z. P., Cusatis G. and Cedolin L. (2004), Temperature Effect on Concrete Creep
Modeled by Microprestress-Solidification Theory, Journal of Engineering Mechanics,
ASCE, Vol. 130, No. 6,June 1, 2004,pp. 691-699.
CEB (1993), CEB-FIP Model Code 1990, CEB Bulletin d'lnformation, W 213/214,
Thomas Telford, London, 437 pp.
Chiorino M.A. (Chainn. of Edit. Team), Napoli P., Mola F. and Kopma M., (1984), CEB
Design Manual on Structural Effects of Time-dependent Behaviour of Concrete, CEB
Bulletin d'lnformation N° 142/142 bis, Georgi Publishing Co., Saint-Saphorin,
Switzerland, 391 pp.
Chiorino M.A., Creazza G., Mola F. and Napoli P. (1986), Analysis ofAging Viscoelastic
Structures with n-Redundant Elastic Restraints, Fourth RILEM International Symposium
on Creep and Shrinkage of Concrete: Mathematical Modelling, Z.P. Bazant ed.,
Northwestern University, Evanston, 1986, pp. 623-644.
Chiorino M.A. and Lacidogna G. (I 993), Revision of the Design Aids of CEB Design
Manual on Structural Effects of Time-Dependent Behaviour of Concrete in Accordance
with the CEBIFIP Model Code 1990, CEB BuUetin d' Information W 215, 297 pp.
Chiorino M.A., Dezi L. and Tarantino A.M .. ( 1997), Creep Ana~vsis of Structures with
Variable Statical Scheme: a Unified Approach, in: A. Al-Manaseer ed., A. Neville
Symposium: Creep and Shrinkage - Structural Design Effects, ACI Fall Convention,
1997, ACI SP-194, 2000, pp. 187-213.
Chiorino M.A. and Lacidogna G. (1999), General Unified Approach for Creep Analysis
of Concrete Structures, ACI-RILEM Workshop Creep and Shrinkage of Concrete, March
1"998, Revue fran~aise de genie civil, vol. 3, N° 3- 4, 1999, pp. 173-217.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Chiorino M.A., Dezi L. and Lacidogna G. (1999), Evaluation of Creep Influence on the
Modification of the Restraint Conditions in Concrete Structures, Proceedings of fib
Symposium 1999, Structural Concrete- The Bridge between People, Prague, October
1999, Vol. 2, pp.481-486.
Chiorino M.A., Lacidogna G. and Segreto A. (2002), Design Criteria for Long-tenn
PeJformance of Concrete Structures Subjected to Initial Modifications of Static Scheme,
in Concrete Structures in the 21'1 Century, Proceedings of the 1'1 fib Congress 2002,
Osaka, October 13-19, 2002, pp. 285-294.
Chiorino M.A. (2005), A Rational Approach to the Analysis of Creep Strnctural Effects,
in J. Gardner and J Weiss eds., Shrinkage and Creep of Concrete, ACI SP-. 2005.
Dezi, L., Menditto, G., and Tarantino (1990), A.M., Homogeneous Strnctures Subjected
to Repeated Structural System Changes, J. Engrg. Mech., ASCE, Vol. 116, No. 8,
August, 1990, pp. 1723-1732.
Gardner N.J. and Lockman M.J. (2001), Design Provisions for D1ying Shrinkage and
Creep ofNormal Strength Concrete, ACI Materials Journal, March-April, pp.l59- I 67.
Kiistek V., Vojtech P. and Pilhofer H-W (2001), Creep and Shrinkage Prediction on the
Web, Concrete International, January 2001, pp. 8-9.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Fig. 1- CEB MC90 model: compliance function J(t,t0 ).
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Fig. 7- CEB MC90 model: redistribution function x(t,t0 , t1) for t0 = ?days.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Fig. 10- CEB MC90 model: redistribution function x(t,t0 , t1) for t0 =28days.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Synopsis: The use ofpozzolanic material, such as fly ash and silica fume, is becoming
more popular in producing high performance/high strength concrete (HP/HSC) for various
structural applications. Many studies have addressed the mechanical properties as well
as durability ofHP/HSC, however, the effect ofpozzolans on the shrinkage and creep
behaviors are not clearly addressed. There is a need to understand and identifY how
changes in the composition and porosity of HP/HSC, and consequently the elastic
modulus, would affect its early age as well its long term performance.
The main objective of this paper is to examine the effect of using various models for
modulus of elasticity on the prediction of creep ofhigh strength concrete (HSC)
containing pozzolans. The study included an experimental program and a comparison of
available analytical models for predicting the compressive creep and modulus of elasticity
ofHSC. Results from creep tests performed on different mixes (with compressive strength
up to 90 MPa) were compared with those from prediction models available in the literature.
Three creep models, ACI 209, CEB 90, and GL 2000, were used. In addition, various values
of modulus of elasticity obtained from experimental calculation, ACI 318,ACI 363, CEB 90,
Gardner, and from an equation proposed by the authors were evaluated. Results show
that the modulus of elasticity has high impact on the accuracy of predicted creep and that
available modulus of elasticity models needs to be revised to reflect HSC containing
pozzolans.
261
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
ACI member Hani H. Nassif is an Associate Professor in the Department of Civil and
Environmental Engineering at Rutgers, The State University of New Jersey. He is a
member of ACI 343 (Concrete Bridges), ACI 435 (Deflection). He served as Secretary
and currently as an associate member of ACI 209 (Creep and Shrinkage) and Chaired
ACI 348 (Structural Safety). His research interests include Creep and Shrinkage of High
Strength Concrete and Durability of High Performance Concrete.
INTRODUCTION
properties of conventional (i.e., normal strength) concrete. Thus, there is a need to revise
and/or update these prediction models to reflect the newer and stronger materials.
The main focus of this paper is on investigating the sensitivity of each creep
prediction model when using various modulus of elasticity equations. Nine HSC mixes
containing pozzolans were made and tested in the laboratory. These mixes consisted of
three mixes with varying percentage of silica fume, three mixes with varying percentage
of fly ash (Class F), and three mixes with different combination of silica fume and fly
ash. All mixes have a 28 days compressive strength between 70 to 90 MPa. Test data on
elastic modulus from these mixes as well as from other tests have been used to form the
basis of developing an elastic modulus equation for HSC. Three creep prediction models,
ACI 209 (14) and CEB 90 (15), and GL2000 (16) are considered in this study.
RESEARCH SIGNIFICANCE
The properties of HSC containing pozzolanic material are very different from
those of normal strength concrete. Pozzolans react with the calcium hydroxide to form
cementing material that makes the concrete more dense and stronger. As a result, the
properties of HSC, specifically creep and modulus of elasticity, differ from those of
normal strength concrete. Therefore, the available creep prediction models and modulus
of elasticity equations need to be validated with new HSC experimental data. This study
investigates the effect of using various equations for modulus of elasticity on creep
prediction models ofHSC.
There are several creep prediction models but there are only two main code
models that are most commonly used in the United States and Europe, ACI 209{14) and
CEB 90 (15), respectively. There are also other available prediction models; however,
the GL2000 (16) is also considered in this study since it contains input parameters that
are available to the designer.
All three models calculate the creep coefficient, <l>(t), that Js used for
calculating the creep strain as follows:
where a is the applied stress in MPa and Ec is the average modulus of elasticity at the
day of loading in MPa. Thus, the accuracy of the prediction models when compared to
experimental data is, among other parameters, highly dependent on the modulus of
elasticity. The creep strain could also be calculated experimentally using the following:
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
where &r is the total strain (i.e., strain measured from loaded specimens), &5 is the
shrinkage strain (i.e., strain measured from unloaded specimens), and C E is the elastic
strain (i.e., instantaneous strain measured from loaded to unloaded conditions).
ACI209
The ACI 209 model is based on the creep and shrinkage models proposed by
Branson and Christianson (17). This model has been incorporated in most building codes
in the United States, as well as other countries. It is a general-purpose model and does
not set any limitation on the strength of the concrete. However, one of the requirements
of this model is that the concrete must be moist-cured for a minimum of7 days or steam-
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
cured for 1 to 3 days. The model takes the following parameters into account: 1) the
relative humidity, 2) the specimen size, 3) the type of curing method used, and 4) the age
at the end of curing duration. In addition, there are also concrete composition correction
factors that include concrete slump, fine aggregate percentage, cement content, and air
content.
CEB90
The CEB 90 model is adopted by the CEB-FIP Model Code 1990 (Euro-
International Concrete Committee and International Federation for Prestressing) and it is
based on the work by Muller and Hillsdorf (18). The model is only applicable for
concrete with a 28-day compressive strength in the range of 20 to 90 MPa. The input
parameters for this model differ from those of the ACI 209 model in compressive
strength and type of curing method. The ACI 209 model does not consider the 28-day
compressive strength whereas the CEB 90 model considers only dry curing.
GL2000
MODULUS OF ELASTICITY
1.5
Ec = (3320.jJ: + 6895) ( ~)
2320
Other equations for modulus of elasticity consist of CEB 90 (I 5), Gardner (22),
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
and Nassif et. a! (2004) (23) and are given as follows:
CEB 90:
Gardner:
Ec =3500 + 43oo.JJ:
Nassif et. al (2004) has recommended one equation that can be used for HS/HPC that
incorporates pozzolanic material as follows:
This model was developed similar to the Carrasquillo et. al (21) by obtaining the best-fit
curve of the modulus of elasticity, E c, versus the square root of the compressive
strength, .Jl: plot using various HPC data. A total of 30 HPC mixes containing silica
fume, fly ash and slag were used in developing the equation. For each of the mixes, the
modulus of elasticity at different curing ages was also considered. Fig. I shows all 168
data points as well as the 9 data points obtained from testing mixes used in this study.
Each data point represents results from tests performed on three (l02mm x 203mm)
EXPERIMENTAL INVESTIGATION
The materials used in this study were readily available resources in the State of
New Jersey. The binding materials consisted of ordinary Portland cement (OPC) Type I,
silica fume (SF), and Class F fly ash (F). All mixes contained superplasticizer and air-
entraining agent in order to ensure good workability and freeze-thaw resistance,
respectively. River sand and crushed granite were used as the fine and coarse aggregate,
respectively. The fine a~gregate (FA) had a unit weight, fineness modulus, and water
absorption of 1621 kg/m, 2.56, and 0.36 %, respectively. The coarse aggregate (CA)
had a maximum size aggrefate of 10 mm with a unit weight, specific gravity, and water
absorption were 1572 kg/m, 2.81, and 1.0 %, respectively.
All mixes were made with a constant wlb ratio of 0.27. The mix proportions
used in this study are presented in Table I. All mixes had the same amount water, FA
and CA, however, in order to acquire a range of slump between 76 and 152 mm, variable
amounts of superplasticizer were used. Three mixes had varying SF content of 5, I 0, and
15%, while the other three mixes had varying F content of 10, 20, and 30%. The last
three mixes were trinary blended concrete that contained 5% SF and 10% F, 5% SF and
20% F, and 10% SF and 20% F. The concrete was made in accordance to ASTM CI92:
Slump and air content tests were also performed on the fresh concrete in accordance to
ASTM Cl43 and ASTM Cl73, respectively. After the concrete specimens were cast,
they were sealed with plastic wrap to prevent loss of moisture.
Creep Test
For each mix, eight 152 x 305 mm cylinders were made in order to perform the
compressive creep test. Two of the eight cylinders were used to determine the
compressive strength of concrete on the testing day. Five cylinders have embedded bolts,
which were used for attaching vibrating wire strain gages (VWSGs). Out of the five
cylinders, three cylinders were loaded and the other two cylinders were kept unloaded
and used as control specimens. The creep and shrinkage strains of the loaded and
controlled specimens were measured by the VWSGs. Three external VWSG customized
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
deviated more than 2%. The VWSGs as well as the load cell were attached to the data
loggers that automatically collect strain readings every 10-minute. However, data
collection is controlled from a computer terminal and can be adjusted depending on the
test duration. The last cylinder was cut in half and placed on top and bottom of the three
loaded cylinders. The two half cylinders were used for eliminating stress concentration
on the loaded specimens that can lead to localized failure of the cylinder. The loaded
specimens as well as the two half cylinders were covered with capping compound before
loading to ensure surface flatness. The compressive creep test was performed on moist
cured specimens at 28 days with the applied load ranging between 30 to 35% of the
ultimate load.
Modulus of Elasticity
Modulus of Elasticity
Creep
percent error closest to 0 followed by Nassif et. al (2004) equation. Therefore, in the
absence of experimental results for modulus of elasticity, the equation by Nassif et. al
(2004) is recommended for calculating the modulus of elasticity for ACI 209 creep model
since it has a relatively low coefficient of variation. For CEB 90 creep model, the
modulus of elasticity equations by CEB 90 and Gardner performed the best. However, it
should be noted that these two equations do not take the concrete unit weight into
consideration and for concrete with lower unit weight, this may not be the case. Both
Nassif et al (2004) and ACI 363 modulus of elasticity equations also performed we11
when used in conjunction with the CEB 90 creep prediction model. The fact that "EXP"
does not improve the CEB 90 model shows that the model is not only dependent on
elastic modulus to predict the creep function for HSC. This is probably due to the fact
that the model was calibrated using CEB 90 modulus of elasticity rather than the actual
modulus of elasticity. As for GL 2000 creep prediction model, the "EXP" also has the
lowest mean value followed by Nassif et al. However, ACI 318 has the lowest the
standard deviation. Overall, the ACI 209 models do represents the best long-term creep
prediction model since the model has the lowest mean and standard deviation. Both ACI
209 and GL 2000 creep prediction models are more sensitive to the modulus of elasticity,
e.g. the model becomes more accurate as the modulus of elasticity improves.
ACKNOWLEDGEMENT
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
REFERENCES
6. Roy, D. M., "Fly Ash and Silica Fume Chemistry and Hydration," ACI. SP-114,
1989, pp. 117- 138.
10. Khatri, R.P., Sirivivantnanon, V., and Gross, W., "Effect of different
supplementary cementitious materials ort mechanical properties of high performance
concrete", Cement and Concrete Research, Vol. 25, No.1, 1995, pp. 209-220
11. Li, H., Wee, T.H., and Wong, S.F., "Early-age creep and shrinkage of blended
cement concrete", ACI Materials Journal, Vol. 99, No. 1, 2002, pp. 3-10
12. Maz1oom, M., Ramezanianpour, A.A., and Brooks, J.J., "Effect of silica fume
on mechanical properties of high-strength concrete", Cement & Concrete
Composites, Vol. 26, 2004, pp. 347-357
13. Jianyong, Li, and Yan, Y., "A study on creep and drying shrinkage of high
perfom1ance concrete", Cement and Concrete Research, VoL 31, 2001, pp. 1203-
1206.
14. ACI Committee 209, Prediction of creep. shrinkage and temperature effects in
concrete structures. Report No: ACI 209 R-92, American Concrete Institute,
Farmington Hills, Michigan, 1992,47 pp.
15. Comite Euro-lnternational du Beton (CEB), CEB-FIP Model Code 1990: Design
Code. London, Thomas Telford, 1993, 480 pp.
18. Muller, H.S. and Hillsdorf, H.K., CEB bulletin d' information, No. 199,
evaluation of the time dependent behavior of concrete, summary report on the work
ofgeneral task group 9. Sept. I 990, 290 pp.
19. ACJ Committee 318, Building Code Requirements for Structural Concrete, ACI
318-2002, American Concrete Institute, Farmington Hills, Michigan, 2002, 443 pp.
20. ACI Committee 363, State-of-the-Art Report on High Strength Concrete, Report
No. ACl 363R-92, American Concrete Institute, Farmington Hills, Michigan, 1992,
55 pp.
21. Carrasquillo, R. L., Nilson, A. H., and Slate, F. 0., "Properties of High Strength
Concrete Subject to Short-Term Loads", ACI Journal, Vol. 78, No. 3, May-June
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
22. Gardner, N.J., "Design provisions for shrinkage and creep of concrete", ACI
Publication, SP 194, The Adam Neville Symposium: Creep and Shrinkage -
Structural Design Effects, 2000, pp. I 01-134
23. Nassif, H., Najm, H., and Suksawang, N., "Effect of Pozzolanic Material and
Curing Methods on Elastic Modulus of High-Performance Concrete," Cement,
Concrete, and Composites, Elsevier Publishing Co. 2004 (accepted).
UNIT CONVERSION
..
-- 60000 ,--.,---.,..----,...--......----,
~ 50000
....
~ 40000
] 30000
roil
0~"'""'"'~~==~~~~~
0 80 160 240 320 400
Time (tlays}
50 ........ ,.... ,... , ..,... , .. 'J" .. ,, .. , ..., ...,.
,_ ' ACJ 209
:. 40 r
:£ '
t·
..
!30
... .
.
~ 20 [ [p}~:;;.;.;;.'-"'-~::.;..;;.;:;;.;.;;.:c..;;_"-"-"-"-::..·;,;.,;;-··\
c; · ~'~~~-- ccg%
i
<ll
I0 '
~ -+-,\CIJ6j
::-=- ~=:~~;:: ~t ,
0 "'--··~"-'-~---'--·"·--·--~---~'----'·--·'-~-'----~-----~ i
0 80 160 240 320 400
Time(Days)
so c···-----~--~-r··--·--··----,--·-------,.., ..,
";' f ACI209
~ 40 t· IS% SF, ·
....
t30 t···
,
U., 0 L
to~'... ~
~lJO :· ~(;;ttdU~t'
r.T.J .. --+- ,\Ct ll& · -:>- Nndr l!'t •'
~
() ,,._,,. __,,_ ,.,.,,... ACI363
0 100 200 300 400
Tlme(Days)
Fig. 3-Effect of modulus of elasticity on HSC containing (a) 5%, (b) 10%,
and (c) 15% SF using ACI 209 creep prediction model.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
u"... 20
=
1:!
~lO
{I)
o~·
, .-~c}.H&
····•·····ACfJ6J:
-..
~ 40
""''<:::1.3
t
.
?;, 30
~20
"= ~10
"' '~ <.::
0"·······
0 lOO 200 300 400
Time (Oay~)
Fig. 4-Effect of modulus of elasticity on HSC containing (a) 10%, (b) 20%,
and (c) 30% Fusing ACJ 209 creep prediction model.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
u.1!: 20 Lt
lto ·
"' _.._ACI:l6J
{I!;,.............,,_ _ _ _ _ _ _ __.
•
c. 40
~
.;.30
t
';:; 20
s
itO --EXP ...,,..... Gordo<~'
~ ........,....._ACJ .H$ '""'-~"" Nus~ih>t.;d
····•··•·/tCJ.l6J
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
·······<:Ui%
,...~.,.,..·V::mh~t::r
i
··i
Fig. 7-Effect of modulus of elasticity on HSC containing (a) 10%, (b) 20%
and (c) 30% F using CEB 90 creep model.
i
··~
'
l
oL
0 lOO 200 300 400
Time (l>ays)
-.-. (;ardntr
........,_......_ ~!l~si( ~t ;sf
oL.........~~~~~~~
0 100 200 300 400
Time(Days)
..
e:: 40
CEB90 (c)f
~
=-
';:30
~
U2()
5
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
GLlOOO (b)j
IO%Sf
··~·~'""' Cf B ~fl
---- t~.ardtH''t
-::-Sa"»ihl al ~
. Gl.2000
l ~
::;:40 r·l5%SF-······
l l
';;;:30 ::··'
t .
.
020:.
!§
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
- --~- (;lll:rdn('r
,g.10 ........ --ACBiti -">-i'i•S>iftUI
0
i --AW63
~-~-...-~--~-..·---··"''·""--~-~~-~--~---"'~·
j
{) 100 200 300 400
Time(D~ys)
Fig. 9-Effect of modulus of elasticity on HSC containing (a) 5%, (b) 10%
and (c) 15% SF using GL2000 creep model.
······'······ f f H- q~~
~(:!tr41.utr
-.--AOJI$ ........-;..-N"a:uifdat
--+- .~CI .\61
-~(~~_r-dn:H
-::.-,u~iJ.et af
300 400
(c~
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Fig. I 0-Effect of modulus of elasticity on HSC containing (a) 10%, (b) 20%
and (c) 30% Fusing GL2000 creep model.
-;,Jo r .
:I. '
.. '
'
.;
'-~20 ;..
&
·;:;
~
~10
--<\Cillk
"" v -.-A(I36)
0 ;,,. .............' - - - - - - - - - -
0 100 200 300 400
Thue(Days)
0 ii,_,___,____,,.,.__ _ _ _ _ _ _...
--ACIJ1>.1
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
z:
-2
2
.....,Go>
·;:
>""
.e
';
;z 0 ------~rli:llf----.--l
Q
-~o:xr
- a - A Cl 318
..,
'0 -+-ACI363
·············(~EB%
-g -1 -.:-. Gardner
-""
U ')
-::-Nassif eta!
-2
20 40 60 80 100
%Error
Fig. 13-Normal probability curve of percentage error for long term creep
(35 to 365 days) using CEB 90 creep model.
2
Go
;
·c
"'
;>
-;
e -EXP
z""
o:> 0 'f--~,:...-~r::.....;+--1- ACI 318
.."'
"=
-ACI363
----"''"--CLH 90
-c~.. {;ardner
1-1
-"'
t"'
-:.>-Nassif et al
fJl
-2
. I GL 2000 I
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
-3
-40 -20 0 20 40 60
%Error
Fig. 14-Normal probability curve of percentage error for long term creep
(35 to 365 days) using GL2000 creep model.
285
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Hardik Shah received his MSCE in Civil Engineering from Purdue University and his
BS from Nirma Institute of Technology, Gujarat University. He is currently continuing
his graduate studies at Purdue.
ACI Member Jason Weiss is an assistant professor at Purdue University. He earned his
BAE from Penn State and MS and Ph.D. from Northwestern University. He is chair of
ACI committee 123, secretary of committee 209 and 231, and a member of ACI 365,
446, and 522.
Various alternatives have been proposed to reduce the propensity for cracking including
the use of concrete with a lower water to cement ratio (w/c ), increased attention to curing ·
practices that reduce evaporation or provide external water [3], and the optimization of
the mixture proportions to increase the aggregate volume fraction [4]. Alternative
methods are also frequently sought that go beyond 'good common practice' to reduce the
potential for shrinkage cracking. For example, saturated lightweight aggregates have
been proposed as one method that can provide internal curing [5,6,7] in low water-to-
cement ratio mixtures that exhibit substantial self-desiccation shrinkage. Other
researchers have used expansive additives to counteract shrinkage [8,9). This paper
focuses on the use of an alternative approach to counteract shrinkage cracking that uses
shrinkage reducing admixtures (SRA) that are reported to change the surface tension of
the pore solution. SRA' s have been discussed in the literature for the last 10-15 years by
numerous authors [ 10,11, 12, 13, 14, 15, 16]. While several papers have demonstrated
experimental evidence to indicate the benefits of SRA, to date little information has been
presented to indicate how the effectiveness of mixtures containing SRA's could be
predicted [17].
Some attempts have been made to quantify the effects of SRA on free shrinkage. Berke
et al. proposed one series of equations to estimate the shrinkage for a series of field
concretes [14]. AI-Manaseer et al. proposed a correction to the more general Gardner-
Lockman equations to account for the addition ofSRA [18,19]. It was also proposed that
SRA could be accounted for when moisture gradients are considered by simply changing
EXPERIMENTAL APPROACH
This paper outlines the results of a research study which was intended to better document
how commercially available SRA's influence the early-age shrinkage and residual
stresses that develop when shrinkage is prevented. This paper begins with surface
tension measurements of water-SRA solutions for one commercially available SRA to
quantify how SRA's can be used to alter the surface tension of a pore solution. Length
change measurements were performed using non-contact lasers to measure the
autogenous length change of setting mortar. Free shrinkage was measured after 24 hours
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
for sealed and drying mortar. In addition to free shrinkage measurements, this paper
describes how SRA influences the rate of mechanical property development as well as
the residual strength development. These measurements are related to the surface tension
of the SRA-water solution for the purpose of predicting shrinkage based on SRA addition
rates. Restrained shrinkage tests were performed to quantify both the elastic and residual
stresses for the restrained mortars. The effect of shrinkage, mechanical property
development, elastic stress, and relaxation are discussed.
Multiple samples were prepared for the majority of tests including measurements of
surface tension, shrinkage, elastic modulus, and residual stress. Table 1 describes all the
test methods as well as the ages at which measurements were taken. For tests with
multiple measurements average values have been reported for each test age.
1
This shrinkage coefficient describes the relationship between shrinkage and the change
in relative humidity
Length change was measured in the mortar tested in this study using two different
approaches. Before the specimens reached an age of 24 hours, the deformation of the
sealed specimens (i.e., autogenous shrinkage) was measured using two non-contact lasers
as seen in Figure 2 [28]. Specimens were cast in a 25mm x 25mm x 300mm (I in x 1 in
x 12 in) steel mold. The inner surface of the mold was lined with two thin sheets of
acetate to reduce friction/bond with the mold. The small cross-sectional geometry was
used to reduce the effects of temperature on the specimen. (Note: a temperature rise of
Jess than 1°C was observed in the mortar specimens used in this study). Openings were
located in the forms at either end of the mold to provide a path for the laser light beam.
The inner surface of the openings was covered with a clear thin plastic film for the
duration of the test. It should be noted that the top of the specimens was also covered
with a plastic sheet during the test to minimize moisture loss. Further details on the laser
units and the data acquisition system can be found elsewhere [28). After 24 hours, free
shrinkage was measured using mortar prisms with a 75 mm (3 in) square cross-section
and a 250 mm (10 in) gage length. For each mixture two specimens were prepared with
two opposing sides and the ends of the prisms sealed (i.e., drying prisms), and two
additional specimens that were completely sealed with two layers of aluminum tape (i.e.,
sealed prisms). This was done to ensure that free shrinkage from the prisms can be
compared directly to the ring specimens without the need for any geometric corrections.
Drying shrinkage specimen were stored at 50% relative humidity. Free shrinkage strain
measurements have been represented using equation (2).
8 sH -
- 8exp-24 +
cl (t - to)
( )+
c3Vt-
,;-;-
td
(2)
1+ c2 t -to
where Cj, C2, and C3 are material coefficients (Table 2), t is the age of the specimen, to
corresponds to the time of initial set, td represents the age at which drying was initiated,
and ~>exp-24 is represented by equation (8) for 0.30 w/c and equation (9) for 0.50 w/c. The
first term (~>exp.24 ) corresponds to the resultant movements from the time of initial set to 24
hours as determined using the non-contact lasers, the second term corresponds to
autogenous shrinkage and the third term represents the drying shrinkage. For each set of
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Splitting tensile strength measurements were taken in accordance with ASTM C 496
using cylinders with a 100 mm (4 in.) diameter and a length of75 mm (3 in.). A 75 mm
length was utilized in order to correlate with the dimensions of the restrained rings.
Initial splitting tensile strength tests were taken when the specimens reached an age of 12
hours and continued to an age of 28 days. Testing was performed for all SRA contents
and both w/c's with two specimens at each age. The time-dependent development of
splitting tensile strength has been represented using equation (3) [29].
C4 (t-to)
() (3)
/sp t =fspao1+C4(t-to)
where C4 is a material constant that describes the rate of strength development and f spro is
the long term splitting tensile strength (Table 2). Elastic modulus measurements were
taken _on cylinders with a 100 mm (4 in.) diameter and a length of 200 mm (8 in.) in
accordance with ASTM C 597. (For further information on the fitting of mechanical
properties using this equation the reader is referred to the literature [29].) Initial dynamic
elastic modulus tests were taken when the specimens reached an age of 12 hours and
continued to an age of 28 days. Static measurements were taken at an age of seven days.
The time-dependent elastic modulus has been represented using equation (4)
Ec(t)=Eoo C4(t-to) (4)
l+C4 (t-t 0 )
where Eoo is the long-term elastic modulus (Table 2). Table 3 shows the R2 values for
equations (3) and (4) for each mixture.
The restrained ring specimen was used to assess residual stress that develops when the
concrete is prevented from shrinking freely. The rings have an outer concrete diameter of
450 mm (18 in), a height of 75 mm (3 in), and an inner concrete diameter of 300 mm (12
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
in). The mortar annulus was cast around a steel ring with a 9.5 mm (3/8 in) wall
thickness. Four strain gages were connected to the inner surface of each steel ring at
mid-height and interfaced in a half-bridge configuration with a data acquisition system.
Strain data was collected at ten minute intervals beginning approximately 30 minutes
after water came in contact with the cement during the mixing process. The specimens
were completely sealed for the first 24 hours. At an age of 24 hours aluminum tape was
used to seal the outer circumference of the ring to allow it to dry uniformly along the
radial direction from the top and bottom of the ring. The specimens were then placed in
an environment with a constant relative humidity (50%) and temperature (23°C) for the
remainder of the test. The strain in the steel was used to compute the residual stress that
develops in the mortar ring using equation 5 (for the geometry described in this paper)
CTresidual-Max == -0.0303 · Ssteez(t) (5)
An expression for the maximum incremental tensile stress can be written by considering
the ring as a 'shrink-fit problem' as described in equation (6) [29]
_ MsH(t)·Ec(t)·0.70 (6)
flae/astic-max - E~!t) 2 .42 + 2 .60
where, ~Esh (t) is the incremental free shrinkage, Ec(t) is the elastic modulus of the mortar
and Es is the elastic modulus of steel (200 GPa). The equation is given in units of MPa
and the values of the constants vary with specimen or restraint geometry [29]. This
enables the computation of the theoretical elastic stress as the sum of the incremented
stress throughout the history of the specimen. The difference between the elastic stress
determined using equation (6) and the actual stress as determined using equation (5)
provides a measure of the stress relaxation (creep and cracking) that takes place in the
specimen.
EXPERIMENTAL RESULTS
the water-SRA solutions is reduced by 54% and remains constant (Figure 3). These
measurements compare reasonably well to those previously reported for laboratory
SRA's [17,30]. The results reported in this paper for one commercially available SRA
can be represented by equation (7)
0 25
r SOLN = Ywater - 22(c SRA ) ' • if CsRA < 10 (7)
{ YsoLN=33.3 tfCsRA~lO
where CsRA is the SRA content in percentage (i.e., for I% SRA, CsRA = I). Table 4
indicates the R2 for this and other following equations.
The total shrinkage of each mixture was fit to equation (2) to obtain the coefficients as a
function of the SRA content. The fit was performed by setting C 3 to zero and determining
coefficients C 1 and C2 using the sealed specimens. After determining C 1 and C2 for the
sealed specimens, equation (2) was used to determine C 3 for the mixtures that were
allowed to dry from the top and bottom. For the 0.30 w/c mixtures, it was determined
that coefficient C2 remained essentially constant at 0.22 irrespective of the SRA content
while coefficients C 1 and C3 are represented using equations (1 0) and (11 ), respectively.
Cl =-0.89(YsoLN)-43.8 (10)
C3 =-0.62(rsoLN )-7.2 (11)
A similar observation was found for the 0.50 w/c mixtures with a C 2 value of 0.07 and
shrinkage coefficients C 1 and C3 which are represented using equations (12) and (13),
respectively.
C1 = -0.21(rsoLN )-14. 7 (12)
C 3 ::::- 1.23(ySOLN) + 22.5 (I 3)
Figure 6 depicts several estimated shrinkage curves as a function of time along with
experimentally determined points (for clarity only three mixtures were shown). The
model correlates well with the experimentally determined shrinkage values. Shrinkage
has also been plotted as a function of SRA content and various times (Figure 7) and again
a good agreement was observed between the model and experimental results.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
One approach that can be used to assess the effectiveness of the SRA is to compare the
ratio of the residual stress in the specimens containing SRA to the plain mortar (0% SRA)
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
as shown in Figure 9. Figure 9 depicts the relative residual stress until the age of
cracking of the 0% SRA ring (7.9 days). The 0.5% SRA ring maintains a relative
residual stress of 0.8 to 1 throughout nearly the entire time, suggesting a minimal effect
of SRA at such low dosages. Higher SRA contents ( 1% to 7.5%) all show significant
decreases in the relative rate of residual stress development. The 2.5%, 5% and 7.5%
SRA rings also show an overall reduction in the magnitude of residual stresses that
develop.
The rate of stress development in a restrained ring depends upon several mechanisms
including stiffness, shrinkage and relaxation. Elastic stresses (i.e., the theoretical stress
that develops if relaxation does not occur) is a function of the product of the elastic
modulus and the shrinkage of the mortar (Eq. 6). As previously mentioned shrinkage
decreases linearly with decreasing surface tension and a similar trend has been observed
for the strength development coefficient (C 4 ) for the 0.30 w/c (equation 14) and 0.50 w/c
(equation 15) mixture, respectively
C4 = 0.14(rsoLN )-1.76 (14)
C4 = o.o3{rsoLN )+ 1.04 (15)
where YsoLN is the surface tension of the water-SRA solution. The elastic stress can be
estimated simply by inserting the expressions for shrinkage (equation 2) and the
expressions for elastic modulus development (equation 4) into the equation for stress
development (equation 6). Results of this computation can be seen in Figure 1Oa and
Figure 11 a for the two different mixtures. The elastic stress is decreased by the presence
of SRA due to the reduction in shrinkage as well as the slight reduction and retardation in
stiffness development.
A relaxation coefficient was defined as the ratio of the residual stress to the elastic stress.
It can be seen that the relaxation decreased as the dose of SRA increased (Figures lOb
and 11 b). This can be attributed to two factors. First, the addition of SRA has been
observed to reduce the creep coefficient by approximately 20% [23,24]. Second, the
elastic stress level is relatively low and as a result it would be anticipated that any
inelastic deformations that may be attributed to non-linear creep or microcracking would
be low. The residual stress was found to increase with age and to decrease linearly with
the surface tension ofthe solution (Fig JOe and lie).
This paper has demonstrated the effect of SRA on the shrinkage, early-age mechanical
properties, and residual stress of mortar. It has been shown that:
• SRA reduces the surface tension of water by up to 54%. Dosage rates of up to
10% result in a rapid reduction in the surface tension, beyond this concentration
level the addition of SRA does not alter the surface tension.
• SRA reduces the autogenous and drying shrinkage of mortar. It has been
observed that the reduction in shrinkage is linearly proportional to the change in
surface tension of the water-SRA solution. In addition, mixtures with higher
concentrations of SRA demonstrated expansion at early ages.
• SRA increases the time of setting and delays the development of material
properties, but little effect is seen on the ultimate strength or stiffness properties.
• SRA influenced the residual stress development. The addition of sufficient
levels of SRA decreased the rate of residual stress development while higher
levels of SRA reduced the overall magnitude of the residual stress as well.
• Comparing the elastic stress and residual stress indicates that more relaxation
occurs in the mixtures with lower concentrations of SRA.
NOTATION
REFERENCES
1. Shah, S. P., and Weiss, W. J., "High Strength Concrete: Strength, Permeability, and
Cracking," Proc. PCI/FHWA Int. Symp. on HPC, Orlando, Florida, 2000, pp. 331-
340
2. Weiss, W. J., Yang, W., and Shah, S. P., "Factors Influencing Durability and Early-
Age Cracking in High-Strength Concrete Structures," ACI SP-189-22 High
Performance Concrete: Research to Practice, Jan. 2000, pp. 387-410
3. Lepage, S., Dallaire, E., and Aitcin, P.-C., "Control of the Development of
Autogenous Shrinkage - Part I: Small Concrete Specimens," Int. Symp. on High-
Performance and Reactive Powder Concretes ed. Aitcin, P.C. and Delagrave, Y., ·
Sherbrooke, Canada, 1998, pp. 347-364
4. Mindess, S., and Young, J. F., Concrete, Prentice-Hall, Englewood Cliffs, N.J., 1981,
pp.671
5. Weber, S. and Reinhardt, H. W., "A New Generation of High Performance Concrete:
Concrete with Autogenous Curing," ACBM, Vol. 6, 1997, pp. 59-68
6. · van Brugel, K., Outwerk, K., and de Vries, H., "Effect of Mixture Composition and
Size Effect on Shrinkage of High Strength Concrete", Proc. of Int. RILEM
Workshop on Shrinkage of Concrete, Paris, France, 2000
7. Lura, P., Bentz, D.P., Lange, D. A., Kovler, K. and Bentur, A., "Pumice Aggregates
for Internal Water Curing," Cone. Sci. and Engineering: A Tribute to Arnon Bentur
Int. RILEM Symp., 2004, pp. 137-151
8. Enyi, C., and Huizhen, L., "Role of Expansive Admixtures in High-Performance
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Concrete," High Performance Concrete SP143-33, Proc. ACI Int. Conf. in Singapore
ed. Malhotra, V.M., 1994, pp. 575-578
9. Hori, A., Morioka, M., Sakai, E., and Daimon, M., "Influence of Expansive
Additives on Autogenous Shrinkage," Autoshrink'98, Proc. of the Int. Workshop on
Autogenous Shrinkage of Concrete, ed. E. Tazawa, Hiroshima, Japan, June 13-14,
1998,pp. 177-184.
10. Shoya, M., and Sugita M., "Application of Special Admixture to Reduce Shrinkage
Cracking of Air Dried Concrete," Hachinohe Institute of Technology, Hachinohe,
Japan, 1989,pp.l-11
11. Shah, S. P., Karaguler, M.E., and Sarigaphuti, M., "Effects of Shrinkage Reducing
Admixture on Restrained Shrinkage Cracking of Concrete," ACI Materials Journal,
Vol. 89, No.3, 1992, pp. 88-90
12. Ogaawa, A., Sakata, K., and Tanaka, S., "A Study on Reducing Shrinkage of Highly
Flowable Concrete," Advances in Cone. Tech., 2nd Canment Symp., 1995, pp. 56-72
13. Balogh, A., "New Admixture Combats Concrete Shrinkage", Concrete
Constructions, July 1996
14. Berke, N.S., Dallaire, M.C., Hicks, M.C., and Kerkar, A., "New Developments in
Shrinkage-Reducing Admixtures," ACI SP-173 Superplasticizers and Other
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
19. Gardner, N.J., and Lockman, M.J., "Design Provisions for Drying Shrinkage and
Creep ofNormal-Strength Concrete," ACI Materials Journal, Vol. 98,2001, pp. 159-
167.
20. Schie~l, A., Weiss, W. J., Shane, J. D., Berke, N. S., Mason, T.O., and Shah, S. P.,
"Assessing the Moisture Profile of Drying Concrete Using Impedance
Spectroscopy," Cone. Science and Engineering, Vol. 2, 2000, pp. 106-116
21. Attiogbe, E.K., Weiss, W. J., and See, H. T., "A Look At The Rate of Stress Versus
Time of Cracking Relationship Observed In The Restrained Ring Test," Proc. Int.
RILEM Syp., Evanston, IL., 2004, Electronic Proceedings
22. Shah, S. P., Weiss, W.J., and Yang, W., "Shrinkage Cracking-Can It Be Prevented?"
Concrete International, Vol. 20, No.4, 1998, pp. 51-55
23. Brooks, J. J., and Jiang, X., "The Influence of Chemical Admixtures on Restrained
Drying Shrinkage of Concrete", ACI SP-173 Superplasticizers and Other Chemical
Admixtures in Concrete, Proc. 5th CANMET/ACI Int. Conf., Rome, Italy, 1997, pp.
249-265
24. D'Ambrosia, M.D., Altoubat, S., Park, C., and Lange, D.A., "Early-Age Tensile
Creep and Shrinakge of Concrete with Shrinkage Reducing Admixtures," Creep,
Shrinkage, and Durability Mechanics of Concrete and Other Quasi-Brittle Materials,
eds. Ulm, F.J., Bazant, Z.P., and Wittman, F.H., Cambridge, MA, Aug. 22-24, 2001,
pp. 645-651
25. Hossain, A., Pease, B., and Weiss, W.J., "Quantifying Early-Age Stress
Development and Cracking in Low w/c Concrete Using the Restrained Ring Test
with Acoustic Emission," Trans. Res. Record, Cone. Materials and Construction
1834, pp 24-33,2003.
26. Adamson, A. W., "Physical Chemistry of Surfaces", 5th Edition, John Wiley and
Sons, Inc., 1990, pp. 777
27. Weast, R.C., Astle, M.J., and Beyer, W.H., "CRC Handbook of Chemistry and
Physics 64th ed.," CRC Press, Inc., Boca Raton, FL, 1983, pp. F-33
28. Pease B.J., Hossain, A.B., and Weiss, W.J., "Quantifying Volume Change, Stress
Development, and Cracking Due to Self-Desiccation," ACI SP-220 Autogenous
Deformation of Concrete, March 2004, pp. 23-39
29. Hossain, A.B., and Weiss, W.J., "Assessing Residual Stress Development and Stress
Relaxation in Restrained Concrete Ring Specimens," J. Cern. Con. Comp. Vol. 26
(5) July 2004, pp. 531-540
30. Ai, H., and Young, J.F., "Mechanisms of Shrinkage Reduction Using a Chemical
Admixture," Proc. of the 1Oth Int. Congress Chern. of Cern., ed. Justnes, H.,
Gothenburg, Sweden, Vol. 3, 1997
i
0.00 -101.76 -48.80 8.91 5.24 29.46
0.50 -96.38 -45.40 5.83 5.30 29.75
1.00 -97.67 -40.13 5.16 5.48 29.19
0.22
2.50 -84.11 -36.44 4.28 5.40 29.55
5.00
7.50
-75.30
-69.80 ! -27.81
-27.99
4.32
3.61
5.66
5.88
29.83
29.15
0.50w/c
SRA Content (%) c, ~ c3 c4 fsp• (MPa) E. (GPa)
i
0.00 -31.33 -63.11 3.21 3.76 26.41
0.50 -24.43 -51.11 3.28 3.39 23.90
1.00 -25.15 -42.40 2.46 3.44 23.90
0.07
2.50 -23.49 -26.04 2.35 3.30 24.51
5.00
7.50
-22.40
-24.60 ! ·22.50
-23.59
2.25
2.18
3.34
3.24
24.79
24.35
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
• Average Measurement
--Fitted Equation
0 20 40 60 80 100
SRA Concentration (%)
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
8
300 e
:I
0
] =.a
CD
c 0 E
! i=
Cll
c
4
i
-300 II)
2 -e-- 0.5 w/c- Initial Set
- 0.5 w/c- Final Set
-8-- 0.3 w/c -Initial Set
- 0.3 w/c- Final Set
0
0 4 8 12 16 20 24 0 2 4 6 8
Time (Hours) SRA Content (%)
Figure 4- Effect of SRA on (a) first 24 hours movement and (b) the time of setting for
the 0.30 w/c and 0.50 w/c mortars
200
100
! 0
"
!-100 0.3W/C
---O%SRA
---0.5%SRA
-200 ---.e.--1%SRA
-+-2.5,.SRA
-+-S%SRA
->I<- 7.5% SRA
-300
8 12 16 20 24
Time (Hours)
(a)
200
100
'll"
.:; 0
"
!-100 0.5W/C
---O%SRA
--0.5%SRA
-200 -..-1%SRA
--2.5%SRA
-+-5%SRA
-300
->I<- 7.5% SRA
0 12 16 20 24
Tlma (Houra)
(b)
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Figure 5 - Movements after time of initial set for (a) 0.3 w/c and (b) 0.5 w/c mortars
-,~..
t ·----
=-=~~:~
----- 7.5% SRA
:
•
~~~~RA
7.5'• SRA
-600 •
·-- --.__ __
-·---
-BOO
•
-1000
12 16 20 24 2B
Time (Days)
(a)
:~:~-~-}~---------:------------.-----------
]:
-200
----.__
j -400
-600
O.Sw/c
Model FilS Experimental Data
-BOO - - 0% SRA • 0% SRA
- - 2.5% SRA + 2.5% SRA
_ ----- 7.5% SRA • 7.5% SRA
1000
12 16 20 24 2B
Time(Days)
(b)
Figure 6 - Total free shrinkage with varying SRA content for (a) 0.30 w/c and
(b) 0.50 w/c mortars
200
• •
-200
];
c -400
--3Day • 30ay
-----70ay • 70oy
_1000 +--.-----.--...---~_:-:..:_;·-~2~8Oay~....!·!!_~2B~O!!ayL...j...
4
SRA Content (%)
(a)
-200
~
c -400
e0
-600 0.5wfc
Model Fits Exper1mantal Data
-800
--1Day e
1Day
- - 3Day .... 30ay
----- 70ay + 7Day
-1ooo+-~---,-----.--r-__:-:_:,:--::....!2B!!..!D'"'"I---!•!!-~2B~o~av+
0 4
SRA Content (%)
(b)
Figure 7 - Total free shrinkage at varying time for (a) 0.30 w/c and (b) 0.50 w/c mortars
i.
-
2
--+-S%SRA
-lft-7.5% SRA
i1
"'
-1+---~--,---~--.---~--~--~--T
•
Tlme(Daya)
(o)
=
!1
-1 +---~---.----~--.---~--~-~-+
4
Tlme(Daya)
(b)
Figure 8 -Residual stress development for (a) 0.30 w/c (rapid decrease in
stress indicates cracking of 0% SRA ring) and (b) 0.5 w/c mortars
1.2
~ 1
..'i
~
R 0.8
...
•&
0.6
0.4
__ .. _
0.3W/C
t
ll
&
0.2 __ ......
---0.5%SR.A
-1%SRA
-+-2.5%SAA
.............. 7.5%SAA
•
nme(Days)
(•)
1.2
{ 1
£
I'i
0.8
0.6
I 0.4
i 0.2
4
nme (Days)
(b)
Figure 9- Relative residual stress development for (a) 0.30 w/c and (b) 0.50 w/c mortars
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
--:~:~"::·::·:.- ~
1~--\~-------
.!! 2
;
i1l 0
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
30 40 50 60 70 80
Surface Tension, r ...... (dynelcm)
(a)
0.3 w/c Model Als Experimental Data
108 •
.-::.,!-..,__
-
-----
-3Day.
7 Day •
3Day
7 Day
'ii
i 0.6
-..-:-._.,_~-;-----
j 0.4 ..... _'lt.::t-~-~
i 02
~ 04---~-,,-~---.--,---.-~---.--~--+
30 40 50 oo ro w
Surface Tension, Ysouo (dyne/em)
(b)
0.3 w/c Model Fla Experimental Data
--10ay. 10ay
- -30ay. 3Day
-~~:;.:~~-·-~--!~ .. -----------------·
• ._!... .. - - - - - - -
...... -- -~
-~--------
·•4---r--.--~--.-~---.--~-.,--r--1-
30 40 50 00 70 80
Surface Tension, YsOL.N (dyne/an)
(c)
Figure 10- Effect of surface tension on (a) elastic stress, (b) ratio between residual and
elastic stress and (c) residual stress for 0.30 w/c mortar specimens
.------·- .. -.-.- - -
--,Day • 1 Doy -----------·
--3Day. 3Doy. ----
-----7Day • 7~-----
• 0.5wlc_~~T~Da1a
• 7[)ay
•
---------.-----•---;-----------------'
•
~ ro ~ ro ~
Surface Tension, y_,. (dyne/em)
(b)
_ 4 0.5 w/c Wadel F11a Experimenllll Dllla
.. --!Day • !Day ,
!:. 3
----- ----·----·f
- - 3 Day •
7 Day •
3 Doy
7 ~... ---------
--------
1
111
2 •
*----
_ _ _ .. - . . . ---- - -
..J
Jll
I 0 _..... • .....
_, +-..---.--.---..--...---.--.--..----..---+
30 ~ so ~ ro ~
Sclutfon Surfa~ Tenaian (dyne/em)
(c)
Figure 11 -Effect of surface tension on (a) elastic stress, (b) ratio between residual and
elastic stress and (c) residual stress for 0.50 w/c mortar specimens
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Synopsis: With the increasing use of self-consolidating concrete (SCC) in the concrete
construction industry, its performance in restrained structural elements is of interest in
order to assess the resistance to restrained shrinkage cracking. A new standard test
method, ASTM C 1581, which uses an instrumented ring, is employed to assess the
cracking potential of various sec mixtures under restrained shrinkage on the basis of
either the time to cracking or the rate of stress development in the material. The
performance of the sec mixtures is compared to that of conventional concrete mixtures to
assess the effect of fluidity level on resistance to restrained shrinkage cracking. In
addition, the SCC mixtures are evaluated for the effects of sand-to-aggregate ratio (S/A),
paste content, aggregate shape, and use of a shrinkage-reducing admixture (SRA) on
cracking potential. The results show that the cracking resistance of SCC is similar to that
of conventional concrete, indicating that the higher fluidity of sec is not detrimental to
performance under restrained shrinkage. The cracking potential of the sec mixtures is
found to be influenced by the mixture composition.
303
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Research in 1995.
INTRODUCTION
In this paper, a standard instrumented ring test method, ASTM C 1581, was used to
quantify the restrained shrinkage behavior of several conventional concrete and SCC
mixtures. The instrumented ring test method involves the measurement of the strain
developed in a steel ring as the concrete shrinks (7-10). The strains are monitored from
the time of casting, when the concrete is plastic, to the time when the concrete specimen
cracks. The measured strain is an indication of the level of stress developed in the
concrete. The rate at which the stress develops in the concrete, as well as the time after
initiation of drying when the test specimen cracks, can be used to classify the cracking
potential of the concrete (1 0).
RESEARCH SIGNIFICANCE
The use of SCC in precast concrete applications has increased rapidly in recent
years, with cast-in-place applications growing. With many concrete elements restrained
by adjacent structural elements, the ability of a concrete element produced with sec to
resist shrinkage cracking is of interest. In addition, SCC mixtures can be produced with a
broad range of mixture proportions and, hence, understanding how S/A, paste content,
EXPERIMENTAL PROCEDURE
The test program involved the evaluation of two conventional concrete mixtures
(Mixes 1 and 8) and twelve SCC mixtures (Mixes 2-7 and 9-14) under restrained
shrinkage using the ASTM C 1581 instrumented ring test method. All mixtures were
non-air entrained. The test specimens were cured in the molds for 24 hours and then
demolded. In line with the test procedure outlined in ASTM C 1581, the ring specimens
were sealed at the top surface and dried from the outer circumference in a temperature
and humidity controlled room at 23 ± 2°C (73 ± 3°F) and 50 ± 4 percent relative
humidity. The test specimen, shown in Fig. I, is monitored for strain development in the
steel ring from the time after casting. The concrete mixtures were produced with a Type
1111 cement at three cement contents, and at water-to-cement ratios (w/c) of 0.39 for
Mixes 1-6 and 8-14 and 0.35 for Mix 7. Two types of 13-mm (0.5-in.) maximum size
coarse aggregate, one crushed (angular) and one rounded, were used at three levels of
S/A to study the effect of aggregate shape on cracking potential. A high-range water-
reducing (HRWR) admixture was used to achieve the 175 ± 25-mm (7 ± l-in.) slump of
the conventional concrete mixtures, and a HRWR admixture and a VMA were used to
achieve the 660 ± 25-mm (26 ± l-in.) slump flow of the sec mixtures at a visual
stability index rating (4) of I or lower. The VMA was utilized to produce stable SCC
mixtures at normal levels of S/A (0.43 and 0.48). A commercially available SRA (II)
was used in Mixes 3 and 6 to determine its effect on the cracking potential of the SCC
mixtures. The mixture proportions and the· plastic properties of the concrete are
presented in Tables I and 2 for all mixtures.
TEST RESULTS
Typical data for the strains developed in the steel rings, starting from the time after
casting the test specimens up to the time of cracking, and for the free drying shrinkage
are presented in Fig. 2 and 3, respectively. As shown in Fig. 2, the sudden decrease in
compressive strain in the steel ring indicates the point of cracking for each specimen.
The net time-to-cracking of each specimen is determined to the nearest 0.25 day as the
difference between the age when a sudden decrease in strain occurred and the age drying
was initiated. For each mixture, the net time-to-cracking is the average value for the
three specimens, with values ranging from 7.25 to 22.50 days for all mixtures. The
compressive strength and modulus of elasticity values at seven days after initiation of
The time-to-cracking and stress rate at cracking are presented in Table 4 for each
mixture. These results are used to compare the performance of SCC relative to
conventional concrete and to show the effect of SCC composition on the cracking
potential of the sec mixtures.
DISCUSSION OF RESULTS
The test results for the two conventional concrete mixtures (Mixes I and 8) and the
two SCC mixtures (Mixes 2 and 9) provide the basis for determining the effect of fluidity
level on cracking potential. In this context, the fluidity of a mixture is quantified in terms
of slump or slump flow, with the sec mixtures having a higher fluidity than the
conventional concrete mixtures. The drying shrinkage, time-to-cracking and stress rate
data for these four mixtures are presented in Table 5. As seen in the table and in Fig. 4,
Mixes I and 2 cracked at approximately the same time; likewise for Mixes 8 and 9. ·
Therefore, the cracking resistance of sec is similar to that of conventional concrete,
indicating that the higher fluidity of sec mixtures is not detrimental to performance
under restrained shrinkage.
Sand-to-aggregate ratio fS/A) --Nine SCC mixtures were produced at three levels of
S/A (0.43, 0.48 and 0.54) to determine its effect on cracking potential. Table 6 presents
the drying shrinkage, time-to-cracking and stress rate data for these nine mixtures. A
comparison of the time-to-cracking results for Mixes 2, 4 and 5, Mixes 9, 10 and 11, and
Mixes 12, 13 and 14 shows the beneficial effect of lowering the S/A. This observation is
also illustrated in Fig. 5, which shows that Mix 12 (S/A = 0.43) took much longer to
crack than Mixes 13 and 14 (S/A = 0.48 and 0.54, respectively). The longer time-to-
cracking for the mixture with the lowest S/A could be explained by a lower rate of stress
buildup in the mixture, as shown by the stress rate data in Table 6. Hence, lowering the
S/A is effective in enhancing the cracking resistance of SCC under restrained shrinkage.
It has been shown that SCC mixtures with a lower S/A have a lower drying
shrinkage (5). However, for the SCC mixtures reported in Table 6, the paste contents are
the same for each group of mixtures, resulting in shrinkage values that are practically the
same in each group.
CONCLUSIONS
3. Okamura, H., and Ozawa, K., "Mix Design for Self-Compacting Concrete,"
Concrete Library oftheJSCE, No. 25, June 1995, pp. 107-120.
6. Nasvik, J., "The ABCs of SCC," Concrete Construction, V. 48, No. 3, March 2003,
pp. 40-47.
8. Hossain A. B., Pease B. and Weiss J., "Quantifying Early-Age Stress Development
and Cracking in Low w/c Concrete Using the Restrained Ring Test with Acoustic
Emission," Proceedings of the 82"d Annual Meeting of the Transportation Research
Board, 2003.
10. See, H. T., Attiogbe, E. K. and Miltenberger, M. A., "Potential for Restrained
Shrinkage Cracking of Concrete and Mortar," Proceedings of the ASTM Symposium
on Early-Age Cracking of Concrete, Dec. 2003.
II. Nmai, C. K., Tomita, R., Hondo, F., and Buffenbarger, J., "Shrinkage-Reducing
Admixtures," Concrete International, V. 20, No. 4, April 1998, pp. 31-37.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Paste content,% 35 35 35 35 35 35 37
Sand-to-aggregate ratio 0.43 0.43 0.43 0.48 0.54 0.54 0.43
HRWR, mU100 kg 4.0 6.5 6.3 6.1 6.7 6.5 5.6
VMA, mUIOO kg 2.6 2.6 1.3
SRA, mL/100 kg 7.6 7.6
Slump, mm 165
Slump flow, mm 686 686 686 660 686 686
VSI 1 1 1 1 I 0.5
Air content, % L9 2.1 1.1 1.4 1.3 1.9 1.6
Notes: I kglm = 1.685 lb/yd3
1 mUkg = 1.54 ozlcwt
1 mm = 0.04 in.
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--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
..
:5 -5
j -25
.
.5
.
l:
"'
~
-45
-65
""'
~
-85
-105
-llS
0 8 1l 16 20
Time After Casting (days)
Fig. 2 - Steel ring strains and time of cracking for selected concrete mixtures.
_.Mb:4
~ ·100
~ -200
! ----.--- -:
' ''
I I t I
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IS ---~-----,-----~------~-----~-----------------
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~
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----L------~------~------~------~-------
I
b 0
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s
-30
i"' -50
j -70
0 4 8 12 16 20 24 28
Time Mter Casting (days)
30~----~----~------~----~----~-----.
10 _I_-------~-------
. '
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.. ..
1.a
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'
-10
.
- - - - - · - - - - - - - - -l- - - - - - - - _;- - - - - - -
'
~ -30
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a..
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-50 -~--------
~0~----~--------------~------------------~
0 4 8 u 16 20 24
Time After Casting (days)
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0 4 8 ll 16 20
Time After Casting (days)
=
..
;;
-20 '
i
._,
.s -40 - ~-------
~
.=
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ii!
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-80
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Time After Casting (days)
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Synopsis: Creep and shrinkage data for two high strength lightweight aggregate
concretes were collected over a two-year period. The concretes, with unit weight of 1922
kg/m 3 ( 120 pet), were developed using expanded slate as coarse aggregate. Strengths of
55.2 MPa (8,000-psi) and 69.0 MPa ( 10,000-psi) were obtained at 56 days. Creep specimens
were loaded to 40 or 60 percent of the initial compressive strength at 16 or 24 hours after
casting. Based on this preliminary study, AASHTO-LRFD creep estimates of high
strength, lightweight aggregate concrete were within 20% accuracy for ages later than one
month. ACI-209 estimated creep of the 55.2 MPa lightweight concrete and shrinkage of
the 69.0 MPa concrete within 20% accuracy, but greatly underestimated shrinkage of the
55.2 MPa mix. When compared with normal weight, high strength concrete of similar
strength and similar cement paste content from previous research, the 69.0 MPa
lightweight mix experienced lower total strain after two years.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
317
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318 Lopez et al.
ACI member Mauricio Lopez is an Assistant Professor in the School of Civil
Engineering at the Pontificia Universidad Catolica de Chile. He received his MSc that
University in 1999, and he is currently a PhD candidate at the School of Civil and
Environmental Engineering at the Georgia Institute of Technology, Atlanta, GA. His
research interests include lightweight concrete, high performance concrete, long-term
properties and durability of materials.
ACI member Kimberly E. Kurtis is an Assistant Professor in the School of Civil and
Environmental Engineering at the Georgia Institute of Technology, Atlanta, GA. She
received her PhD from the University of California at Berkeley in 1998. She is a member
of ACI Committees 236, Material Science of Concrete, E 802, Teaching Methods and
Educational Materials, and 201 Durability of Concrete. Her research interests include
microstructure and durability of cement-based materials.
ACI member Brandon S. Bucbberg, E.l.T., is an engineer with Simpson, Gumpertz, &
Heger located in Boston, Massachusetts. He is a graduate of the Georgia Institute of
Technology receiving his BSCE in 2000 and his MSCE in 2002. His interests include
high strength/high performance concrete structure systems, materials, and forensic
investigation.
INTRODUCTION
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RESEARCH SIGNIFICANCE
Currently, the design standards do not specifically consider HPLC. Hoff (12)
concluded that the use of HPLC will not expand unless designers have confidence on its
expected properties. High-strength and high-performance lightweight concrete is a
relatively new material, and its long-term performance, especially creep, has not been
extensively investigated yet. This might be one barrier to the use of HPLC as Hoff
alluded. The objective of this research was to investigate the time-dependent behavior of
high performance, lightweight concrete for its potential use in precast prestressed bridge
girders.
According to Findley, Lai and Onaran (13), creep was first systematically
observed by Vitae in 1834, but Andrade in 1910 was the first to propose a creep law.
Since Andrade, several more models have been developed. Some models are general
mechanistic models, which include constants for different materials and properties, while
other models are more empirical for specific materials. The most used models for creep
in concrete fall in the second category - empirical models.
On the other hand, drying shrinkage of concrete was identified during the first
creep studies when a higher creep rate and strain in concrete were measured under drying
conditions. Since then, several investigators have proposed models in order to describe
and predict shrinkage.
Among the variety of methods proposed for creep and shrinkage in concrete
(14-30) two are considered herein. These are the methods proposed by the American
Concrete Institute Committee 209 (14) and by the American Association of State
Highway and Transportation Officials (15). These are not models specifically developed
for lightweight concrete. However, creep and shrinkage prediction equations proposed by
the ACI-209 were based on research performed with both normal weight concrete (NWC)
and SLC. So, they are entirely applicable to normal weight, "sand-lightweight", and "all-
lightweight" concrete. Since the AASHTO-LRFD method is an updated version of the
ACI-209 method, its equations are also applicable to SLC.
HPLCMixes
The high performance lightweight concrete (HPLC) mixes used Type III
portland cement, Class F fly ash, silica fume, 12.7 mm (1/2-inch) expanded slate as
coarse aggregate, natural sand, and high range water reducing admixture. The 56-day
design strengths were 55.2 MPa (8,000-psi) and 69.0 MPa (10,000-psi) with a unit weight
below 1922 kg/m 3 (120 pet). The mixture proportions are presented in Table 1.
Lightweight aggregate was kept above saturated surface dry condition (SSD) before
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
the diameter of the cylinders was smaller than the recommended in ASTM because
bearing capacity of the creep frames was not enough for applying the required stress
levels to 152.4 mm (6-inch) x 304.8 mm (12'-inch) cylinders. The other three deviations
were the age of loading (24 hours instead of 2 days or greater), the use of an accelerated
curing regime, and the stress-to-strength ratio (up to 60% instead of 40%). The later
changes were adopted in order to match the actual conditions of the HPLC prestressed
girders which were loaded to 60% of the initial strength and at very early ages. The
accelerated curing used insulated boxes for 24 hours in order to maintain the heat
generated during the hydration as occurs within an AASHTO Type IV girder as
demonstrated in previous research (31 ).
SHORT-TERM PROPERTIES
Plastic Properties
Slump and air content (ASTM C173: volumetric method) were measured in
laboratory and field batches. From the workability results, the 55.2 MPa (8,000-psi)
HPLC slump was 165.1 mm ± 38.1 mm (6.5-inch ± 1.5-inch). The 69.0 MPa (10,000-
psi) mix had a slump of 101.6 mm ± 12.7 mm (4.0-inch ± 0. 5-inch). The air content, on
the other hand, averaged 4.25% for the 55.2 MPa mix and 3.8% for the 69.0 MPa.
3
Plastic unit weight of HPLC varied from 1826 kg/m 3 (114 lb/ft3) to 1954 kglm
3 3
(122 lb/ft ) with most of the values close to 1922 kg/m (120 lb!ft\ The 55.2 MPa mix
averaged a dry unit weight of 1874 kg/m 3 (I 17 lb/ft3) while the 69.0 MPa HPLC
averaged a dry unit weight of 1906 kglm 3 (119 lb/rt3). These values represent 75% to
80% ofthe weight of a typical normal weight HPC.
Modulus ofEiasticity
Modulus of elasticity was measured using 152.4 mm (6-inch) x 304.8 mm (12-
inch) cylinders made from each mix according to ASTM C469. Specimens with
accelerated curing were tested at 16 hours, 24 hours, and 56 days while the ASTM-cured
specimens were tested at 56 days. The average 56-day elastic modulus, for both curing
regimens, is shown in Table 2.
At the age of 56 days, ASTM-cured specimens exhibited higher modulus of
elasticity than the accelerated-cured specimens. The difference between the two curing
methods ranged from 1% to 9 %.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Figure 4 compares the measured creep coefficient versus time and predicted
values using ACI-209 and AASHTO-LRFD models. Figure 4a shows results for 55.2
MPa HPLC and Figure 4b for 69.0 MPa HPLC. When comparing model performance
from Figure 4a, it can be concluded that ACI-209 model had the best overall
performance, closely followed by AASHTO-LRFD model.
Figure 4a shows that even though the ACI-209 model underestimated creep for
time under load less than 10 days and overestimated creep for times greater than I 00
days, this model showed the best overall agreement with the experimental data, of the
two models considered here. The AASHTO-LRFD model followed the same tendency as
ACI-209 at early ages, but continued underestimating creep at all ages. For 69.0 MPa
(1 0,000-psi) HPLC, AASHTO-LRFD model was in good agreement with experimental
data for any time under load between 1 and 600 days. The ACI-209 model tended to
overestimate creep coefficient for times under load greater than 30 days.
Table 6 presents the sum of squared error (SSE) and coefficient of determination
(R2) between experimental data and creep models for the 55.2 MPa (8,000-psi) and 69.0
MPa HPLC. This statistical comparison supports the conclusion obtained from
examination of the data in Figure 4 which indicated that the best model for estimating
creep of HPLC was the AASHTO-LRFD model. The largest R2 (0.895 and 0.927, for
55.2 MPa and 69.0 MPa HPLC, respectively) was obtained with the AASHTO-LRFD
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
CONCLUSIONS
of initial strength. Fifty and ninety percent of the 620-day creep was reached after
approximately 16 and 250 days of loading, regardless the strength ofHPLC (55.2 MPa or
69.0 MPa).
The experimental creep coefficient was compared with two empirical models
provided by AASTHO-LRFD and ACI-209. Overall, the AASHTO-LRFD model most
accurately estimated creep of the HPLC. It is proposed that one reason for the improved
accuracy may be the incorporation of the maturity of concrete, instead of age of concrete,
in the AASHTO-LRDF model.
Shrinkage after 620 days of drying at 50% relative humidity was approximately
820 !lEfor the 55.2 MPa HPLC mix and 610 !lEfor the 69.0 MPa HPLC mix. Fifty and
ninety percent of the 620-day shrinkage was reached after approximately 30 and 260 days
of drying for both the 55.2 MPa and 69.0 MPa HPLC. The AASHTO-LRFD model
again gave the best overall shrinkage estimate of the 55.2 MPa HPLC. On the other
hand, for the 69.0 MPa HPLC mix, ACI-209 model gave the best overall performance.
In addition, the performance of HPLC was compared to that of a similar normal
weight HPC. The 69.0 MPa HPLC had a total strain after 620 days under load of about
75% of that of an HPC of the same grade and similar cement paste content. The better
smaller creep and shrinkage strains of the HPLC was noticeable after one day under load.
While these preliminary results show lower long-term deformation for HPLC, as
compared to HPC, it is emphasize that these results are preliminary and are limited to
only these concrete mixes. The creep and shrinkage of HPC mixes may vary widely
depending on the aggregates, supplementary cementitious materials, and admixtures.
ACKNOWLEDGEMENTS
REFERENCES
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
PCI Convention & Exhibition, the 3rd PCI/FHW A International Symposium on
High Perfonnance Concrete, and the National Bridge Conference., Orlando, Florida,
Precast I Prestressed Concrete Institute.
33. Lopez, M., Kahn, L.F., Kurtis, K.E., and Lai, J.S. (2003) "Creep, Shrinkage, and
Prestress Losses of High-Perfonnance Lightweight Concrete", Research Report
No.03-9, Office of Materials and Research, Georgia Department of Transportation.
Atlanta, GA, pp. 310.
34. Lopez, M., Kahn, L.F., and Kurtis, K.E. (2004) "Creep and Shrinkage of High
Performance Lightweight Concrete", ACI Material Journal, V. 101 No. 5: pp. 391-
399.
35. Slapkus, A., and Kahn, L.F. (2002) "Evaluation of Georgia's High Perfonnance
Concrete Bridge", Research Report No.03-3, Office of Materials and Research
Georgia Department of Transportation. Atlanta, GA, pp. 382.
36. Goodspeed, C. H., Vanikar, S., and Cook, Raymond A. (1996) "High-Perfonnance
Concrete Definition for Highway Structures", Concrete International, V. 18 No.2: p.
62-67.
37. ASTM C 1074 (1998) "Standard Practice for Estimating Concrete Strength by the
Maturity Method", American Society for Testing and Materials, West
Conshohocken, PA.
38. Neville, A.M., Dilger, W.H., and Brooks, J.J. (1983) "Creep of Plain and Reinforced
Concrete", Construction Press, London and New York.
39. Holm, T. A., and Bremner, T. W. (1994) "High Strength Lightweight Aggregate
Concrete", High Perfonnance Concrete: Properties and Applications (Ed, Shah, S. P.
and Ahmad, S. H.), McGraw-Hill, New York, NY, pp. 341-74.
LIST OF SYMBOLS
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
HPLC: high-performance lightweight concrete
NWC: normal weight concrete
55.2MPa 69.0MPa
(8,000 psi) (10,000 psi)
design design strength
strength mix mix
Mix
Cure Regime 8L SF IOL !OF
56-day E Accelerated 27.7 26.6 29.0 27.7
Cure (4020) (3863) (4210) (4015)
ASTM 30.2 27.0 29.9 28.0
(4387) (3917) (4330) (4060)
SS.2MPa 69.0MPa
(8,000-psi) (10,000-psi)
HPLC HPLC
Factors Shrinkage Shrinkage
Rei P- Rei P-
MSE value MSE value
Time under drying 0.472 0.000 1.028 0.000
Laboratory/Field -
0.002 0.675 O.o28 0.007
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
~ 70 10,000 ];
9,000 ~
8,000 !i
7,000 .iil
-~ 40 - - 55.2 MPa (8,000-psi) Accelerated Cure 6,000 -~
Figure 1. Compressive strength vs. time of 55.2 MPa (8,000-psi) and 69.0 MPa
( 10,000-psi) HPLC mixes for accelerated and ASTM curing methods.
1.8
I
1.6
I
I I'
1.4
l!.2 t==
as5.2 MPa (8,000-psi) HPLC II
0.4
I
I
0.2 I.
0.0 ''
O.DI 0.10 1.00 10.0 100 1000
Time under Load (days)
Figure 2. Average creep coefficient of 55.2 MPa (8,000-psi) and 69.0 MPa (10,000-psi)
HPLC in logarithmic time scale.
J j<
r-- I l1
700 I '
Ill
200 ,,
II I • I
I'
II
II
100 "
I•
I
0
0.01 0.1 10 100 1000
Time under Drvin11: (days)
Figure 3. Average shrinkage of field and laboratory mixes for 55.2 MPa (8,000-psi) and
69.0 MPa (10,000-psi) HPLC in logarithmic time scale.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
2.5 ACI-20
a 55.2MP•(8,000-psi)
ii i=
r- PL~ UTed
~ 20
"0
~1.5
~
u 1.0 AASHTO
~
0.5
0.0 '
0.01 0.1 10 100 1000 10000
Time under Load (days)
b 3.0
2.5 -
a 69 MPa(lO,OOO-psi) ACI-20
d
-~ 2.0
IS
= 'IPT.r'
8
uQ, 1.5
!!
u 1.0 ..ASHTO
I.Rl
0.5
0.0
O.QI 0.1 10 100 1000 10000
Time under Load (days)
Figure 4. Comparison between measured creep coefficient and estimated from ACI-209
andAASHTO-LRFD models: (a) 55.2 MPa (8,000-psi) HPLC,
(b) 69.0 MPa (10,000-psi) HPLC.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
20 v I
IIIII"
10u
.
0.1 I 10 100 1000 10000
Time under Drying (days)
u 1111
Jill
1111
60 u AASHTO
LRFD ACI-2 09
u~II69MPa(l0,000-psi)
HPLC measured
u
20 v
10v II
..-
0.1 l 10 100 1000 10000
Time under Drying (days)
Figure 5. Comparison between measured shrinkage and estimated from ACI-209 and
AASHTO-LRFD models: (a) 55.2 MPa (8,000-psi) HPLC,
(b) 69.0 MPa (10,000-psi) HPLC.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
·~ 3000
"'2500
a
l2ooo
1500
1000
500
0
0.01 0.1 10 100 1000
Time under Load and Drying (days)
Figure 6. Comparison total strain of HPLC and HPC mixes in logarithmic time scale
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Synopsis: This paper illustrates how stress relaxation can be used to obtain valuable
information regarding the behavior of concrete at early ages. Five concrete mixtures were
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
337
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338 Pigeon et al.
M. Pigeon, FACI, is Rector at Laval University, Quebec, Canada. He previously held an
NSERC Industrial Chair on Shotcrete and Concrete Repairs at the Department of civil
Engineering. His field of expertise includes concrete durability, repair and maintenance
of concrete structures, and early-age behavior of cement-based materials.
INTRODUCTION
Various systems have been developed in recent years to study the behavior of concrete
under restrained shrinkage at early ages (I), (II). In certain cases, these systems are used
to study the stress build up due to drying shrinkage (4), (7), (12), and in others the stress
build up due to autogenous shrinkage (1), (2), (3), (5), (6), (8), (9), (10), (II), (13). In
concretes with low water to binder ratios (i.e. lower than approximately 0.40),
autogenous shrinkage is considered as one of the main causes of early age cracking, and
many reports have been published on this topic (14), (15), (16).
The stress build up due to restrained shrinkage can be considered as being influenced by
two principal mechanisms: shrinkage (which is the basic cause of the stress build up), and
relaxation (which reduces the intensity of the stresses generated). Generally in these
systems, a companion specimen is cast to allow the determination of the free shrinkage.
Based on the hypothesis that the principle of superposition of stresses and strains apply,
various parameters can thus be calculated, especially those relating to the creep
deformation of the specimen under restrained shrinkage. Although these calculations are
not rigorously valid since part of the free shrinkage itself is due to viscous deformations
(17), they can provide interesting indications concerning the parameters that influence the
results obtained.
Five mixtures were prepared for this series of experiments, at a constant water to binder
ratio of 0.35. This value of 0.35 was selected as being representative of those of
cementitious systems for which self desiccation is known to have significant effects and
induce a significant amount of autogenous shrinkage (18). The same ordinary Portland
cement was used for all mixtures. Mixture OC (ordinary concrete) is the reference
mixture. In mixture SFC (silica fume concrete), 8 % of the cement by weight was
replaced by silica fume. In mixture FAC (fly ash concrete), 25 % of the cement was
replaced by fly ash. In mixture SC (slag concrete), 25 % of the cement was replaced by
slag. Mixture VAC (viscosity admixture concrete) is similar to mixture OC, but a
viscosity modifying admixture was added to it. All mixtures were prepared at a constant
30 % paste content (to better isolate the paste effect) and with the same fine and coarse
(siliceous) aggregates. The coarse and fine aggregates were saturated at the time they
were incorporated into the mixtures. The maximum size of the coarse aggregate was
fixed at I 0 mm, i.e. one fifth of the smallest dimension of the mould in the restrained
shrinkage test equipment. The characteristics of the cement, of the fly ash, and of the slag
are presented in Table 1. Table 2 presents the composition and basic properties of each
investigated concrete mixture. The amount of binder in the mixtures corresponds
relatively well to that found in typical concretes with such a water to binder ratio. With
the exception of the viscosity modifying admixture, the only admixture that was used was
a sulphonate-based superplasticizer. The dosage was selected in order to obtain an
adequate slump for a sufficient period of time after the first contact between cement and
water, to allow proper placement operations in the test devices.
For each mixture, in addition to the two specimens required for the measurements under
free and restrained autogenous shrinkage, 9 cylinders of I OOx200 rom were cast to
determine the strength in tension (by splitting) and in compression after 7 days, and in
compression at 28 days. The cylinders used for the 7-day tests were kept sealed until
testing, while those used for the 28-day tests were cured in standard conditions.
The equipment used for the early age restrained shrinkage tests is a somewhat improved
version of that described in detail in a previous publication (5) (these improvements are
linked particularly to the deformation measurement system and to the computer program
that controls the system). It consists of two devices: the first one is used to determine the
free autogenous shrinkage from time t = 0, and the second one, which is equipped with a
movable head, is used to determine the increase in load due to autogenous shrinkage, also
from time t = 0 (Figure 1). In both set ups, the specimen is cast directly into the mould
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
The use of two parallel specimens, one under free shrinkage and the other under
restrained shrinkage, allows the calculation of certain parameters which are helpful to
study the influence of different variables (such as mixture composition) on the viscous
phenomena involved. From the stress and strain data generated in the restrained
shrinkage set up, it is possible to calculate the modulus of elasticity as a function of time
(in fact, the value of the elastic chord modulus can be obtained each time an additional
force is applied to bring the specimen back to its original position). This in tum allows
the calculation of the theoretical stress due to shrinkage, i.e. the stress that would result
from restrained shrinkage if the concrete had no relaxation capacity. Considering the
actual stress generated in the restrained shrinkage set up, the intensity of relaxation can
thus be evaluated.
It is also possible to calculate the creep deformation in the restrained shrinkage specimen
by subtracting (at any given point in time) the cumulative sum of the strains in the
restrained shrinkage specimen from the free shrinkage in the companion specimen. This
can be explained as follows. If concrete had no creep or relaxation capacity, the stresses
in the restrained specimen would be purely elastic and the cumulative sum of the strains
would be equal to free shrinkage (assuming that shrinkage deformations and elastic
deformations do not influence one another, i.e. that the principle of superposition of
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
stresses and strains applies). However, the cumulative sum of the strains is not equal to
free shrinkage because the specimen that is restrained is under load and undergoes a
creep type deformation in addition to the shrinkage deformation.
TEST RESULTS
The results obtained for the five mixtures tested are presented in Figures 2 to 6. In each
figure, the following data is presented for a given mixture: the free autogenous shrinkage
versus time, the stress generated in the restrained specimen versus time, the modulus of
elasticity versus time, and the theoretical elastic stress versus time. The first two values
(shrinkage and stress) are direct experimental measurements, whereas the two others are
calculated values. The theoretical elastic stress was calculated as follows, using the
modulus of elasticity (E(tn)) values obtained from the curve fit of the computed data
plotted on the figures:
To illustrate how the restrained shrinkage system is operated, Figure 7 shows the
deformations and stress measured in the restrained shrinkage set up for mixture SC.
The values of the tensile strength at 7 days (sealed conditions) and the compressive
strengths at 7 days (sealed conditions) and 28 days (standard conditions) are given in
Table 2.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
The free shrinkage strains after 20 and 120 hours, which represent the intensity of the
stress generating mechanism, is also given in Table 3. As can be seen, the theoretical
stress after 120 hours is strongly related to the shrinkage value, since the variation of the
modulus of elasticity with time is quite similar for all five mixtures (see Figures 2 to 6).
However, on the contrary, the effective stress generated after 120 hours is not directly
related to the shrinkage value. As a matter of fact, the highest value of the stress
generated in the group of five mixtures corresponds approximately to the median
shrinkage value.
Relaxation, as creep, can be considered dependant on the average stress level to which
the specimen is subjected. It is thus interesting to analyze the test results taking this more
directly into consideration. Table 4 was prepared for this purpose. It shows, for each
mixture, the average stress level between 20 hours and 120 hours, together with the
relative relaxation, i.e. the difference between the increase in the theoretical stress and the
increase in the stress generated between 20 hours and 120 hours, divided by the average
stress during the same period. The relative relaxation can be simply viewed as the
absolute relaxation (in MPa) divided by the average stress during the same period.
Globally, the results in Table 4 are in good agreement with those in Table 3. The relative
relaxation is high when the relaxation ratio is low, and it is low when the relaxation ratio
is high. The global observations made on the basis of the relaxation ratios between 20
hours and 120 hours can thus be considered valid.
It is not possible, with the information presently available, to determine, for the five
mixtures tested, the mechanisms which are the main cause of the observed variation of
the relaxation capacities. Creep in tension has been linked to interfacial phenomena (19).
It could thus perhaps be hypothesized that there is a link between the use of mineral
additives and the relaxation capacity of a mixture, due to the influence of such additives
on interfacial phenomena.
CONCLUSION
The results presented in this paper indicate that the stress due to early age restrained
autogenous shrinkage is quite variable, in good part due to the variation in the relaxation
capacity of the mixtures. Both the relaxation ratio, defined as the stress generated divided
by the theoretical stress, and the relative relaxation, defined as the absolute value of stress
relaxation (the difference between the theoretical stress and the stress generated) divided
by the average applied stress, can be used to illustrate and analyze the variation of the
relaxation phenomena as a function of the type of mixture tested.
ACKNOWLEDGMENTS
This project was funded by Lafarge, by the Natural Sciences and Engineering Research
Council of Canada (NSERC) and by the Fonds pour Ia Formation de Chercheurs et
/'Aide ala Recherche (FCAR) of the government of the province of Quebec.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
2. Paim:re AM, Buil M, Serrano JJ. Effect of fiber addition on the autogenous
shrinkage of silica fume concrete. ACI Mater J 1989; 86(2): 139-144.
7. Altoubat SA, Lange DA. Creep, Shrinkage, and Cracking of Early Age Concrete.
ACI Mater J, 2000; 98(4):323-331.
10. Ohno Y, Nakagawa T. Research of test method for autogenous shrinkage stress in
concrete. In: Autogeneous Shrinkage of Concrete. London, U.K.: E & FN Spon,
1998. p. 351-358.
11. Japan Concrete Institute. JCI Research Report of Autogenous Shrinkage, 1996. p.
199-201.
I4. MacDonald DB, Krauss PD, Rogal1a E. Early-age transverse deck cracking 1995,
Concr Int; 17(5):49-51.
15. Burrows RW. The visible and invisible cracking of concrete, Monograph N° II,
American Concrete Institute, 1998. 71 p.
17. Hua C, Acker P, Ehrlacher A. Analyses and models of the autogenous shrinkage of
hardening cement paste - Part I: Modelling at macroscopic scale. Cern Concr Res
1995; 25(10):1457-1468.
18. Charron, J.-P., Zuber, B., Marchand, J., Bissonnette B, Pigeon M. Influence of
temperature on the early-age behavior of concrete. Proceedings of the International
RILEM Symposium ,Evanston, USA, 24 March 2004, Edited by K. Kovler, J.
Marchand, S. Mindess and J. Weiss (RILEM Publications), 263 pp.
I9. Bissonnette B, Pigeon M. Tensile creep at early ages of ordinary, silica fume and
fiber reinforced concrete. Cern Concr Res 1995; 25(5):1075-1085.
Binder
Content
CSAType 10
Silica fume Fly ash Slag
Cement
Chemical(%)
Si<h 20.33 92.66 36.07
Ah03 4.10 0.56 10.16
Fe203 2.87 1.51 0.74
CaO 61.86 0.70 35.60
MgO 2.74 0.63 12.71
803 3.12 0.25 3.50
Alkalis 1.09 1.21 0.83
LOI 2.77 3.16 0.00
Mineralogical(%)
c3s 57
c2s 15
C3A 6
CJ" 9
PSD (% passing)
75 llffi 99.1 100
45J.lm 90.7 96.9
10 lliD 35.2 40.4
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Concrete mixtures
oc SFC FAC sc VAC
Constituents
Type 10 cement (kg/m 3) 447 407 317 292 446
Additive s.fume fly ash slag VA 1
(addition rate by weight of binder) (8%) (25 %) (35 %}
(kg/m3) 35.4 lOS 157 0.178
Water (kglmJ) 156 155 148 157 156
10-mm crushed granite (kglm3) 800 797 797 797 798
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
t=20hto 120h
Concrete mixture ID .1.tsJ,frto Gexp. avg. . .1.crel.lh.- acr••p.
(10"6) (MPa) CJ'exp. avg.
oc 72 0.40 3.83
SFC 107 0.70 4.26
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l1.5
~
~ 1.0
"'
~,.;,;,;;;;;;;;;;;;;;;;;;;.L.......J--..J
0
0 24 48 72 !Ill 120 144 24 48 72 96 120 144
Time elapsed since cas11ng (h) Time elapsed since casting (h)
Fig. 2-DRS test results for concrete mixture OC: a) Shrinkage strains and Young's
modulus; b) Shrinkage-induced stress
Fig. 3-DRS test results for concrete mixture SFC: a) Shrinkage strains and Young's
modulus; b) Shrinkage-induced stress
50 1.5
400
w;;
-10
30"
~
..
_1.0
0..
~ ~20 ~
£
~
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Iii 0.5
"' -30 .,
Gi
1oe
~~~~~~~~0
0 24 48 72 96 120 144 24 48 72 96 120 144
Time eJapsed since casting (h) Time elapsed since casting (h)
Fig. 4-DRS test results for concrete mixture FAC: a) Shrinkage strains and Young's
modulus; b) Shrinkage-induced stress
40 0 3.0
5
300. ...
"-
[ ~2.0
20 ~ !
., "'
Gi
1.0
10.!.
24 48 72 96 24 48 72 96 120 144
Time elapsed since casting (h) Time elapsed since casting (h)
Fig. 5-DRS test results for concrete mixture SC: a) Shrinkage strains and Young's
modulus; b) Shrinkage-induced stress
24 48 72 96 120 144
Time elapsed since casting (h) Time elapsed since casting (h)
Fig. 6--DRS test results for concrete mixture VAC: a) Shrinkage strains and Young's
modulus; b) Shrinkage-induced stress
2.5
0
2
'b
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Synopsis: Creep and shrinkage of concrete were studied under constant load and
restrained conditions during the first week after casting. Concrete behavior was
characterized by a uniaxial test that measures shrinkage deformation and restrained
shrinkage stress. The extent of stress relaxation by tensile creep was determined using
superposition analysis. The experimental measurements were compared with current
creep and shrinkage models to assess their validity for early age prediction. The ACI 209
equation for creep is currently not applicable to early age, but modifications are proposed
that fit a database of early age behavior. The B3 model has been previously modified to
accommodate early age creep, and this modification was employed in the current study.
Test results for normal concrete with different w/c ratios are discussed.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`--- 349
Copyright American Concrete Institute
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350 D'Ambrosia and Lange
ACI member Matthew D. D'Ambrosia is a PhD candidate at the University of Illinois at
Urbana-Champaign. His research interests include early age creep and shrinkage of
concrete, early age stress and cracking, high performance concrete, shrinkage reducing
admixtures, and self-consolidating concrete.
INTRODUCTION
The volumetric instability of concrete at early age is a cause for cracking in numerous
concrete pavements and structures. Recent use of high performance concrete materials
increases the risk of cracking at early age. Volumetric deformation is attributed to drying
shrinkage, autogenous shrinkage, and thermal dilation. These changes are critical in
young concrete when it is most vulnerable to cracking. Drying shrinkage and tensile
creep are especially important if concrete is restrained. Tensile stress will develop due to
restrained shrinkage and may cause cracking. Tensile creep is beneficial as a stress
relaxation mechanism, relieving part of the tensile stress that develops due to shrinkage.
Autogenous shrinkage may be significant at early age in low w/c ratio materials, thus
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
The accurate prediction of early age cracking in concrete is essential for evaluating the
durability of concrete structures. Cracking reduces durability by providing a path for
water and aggressive ions to penetrate the material and induce corrosion of reinforcing
steel. To predict cracking, it is necessary to understand how early age volume changes,
such as drying shrinkage, induce stress and how creep mechanisms act to relax part of the
stress. Models have been developed that evaluate the creep and shrinkage behavior of
concrete. Current models include ACI 209 and RILEM Draft Recommendation B3 [7,
8]. The experimental data used to construct and validate these models was primarily
based on compressive creep results from constant load tests on mature concrete.
However, to predict early age cracking in concrete, we should consider tensile creep of
early age concrete under restrained conditions. In the following paragraphs, we examine
the usefulness of the ACI and B3 models for evaluating early age tensile creep at variable
stress levels.
shrinkage and deformation under restrained conditions or under constant load [6]. The
materials tested in this study were concretes with w/c ratio of 0.40, 0.44, and 0.50 with
the same aggregate type and cement source. The mixture proportions are shown in Table
1. The 0.40 and 0.44 mixtures were used to study restrained drying conditions and a w/c
of 0.50 was used to study creep under constant stress. For each test, two companion
specimens were cast in a temperature and humidity controlled environmental chamber.
The conditions during testing were 23°C (±0.5° C) and SO% (±S %) relative humidity.
The dimensions of each specimen are given in Figure I. The steel end grips, which
transmit the applied load, remained in place for the duration of the test. Steel form work
was removed from the sides of the specimen at 23 hours. To avoid early load application
from evaporative cooling associated with formwork removal, the specimens equilibrated
to room conditions for one hour before a restraining force was initiated. Evaporative
cooling may cause significant deformation during early age testing, which can then lead
to misinterpretation of test data [6, 9]. A sealed barrier of self-adhesive aluminum foil
was used to impose a condition of symmetric drying from only two sides. A rounded
transition in specimen geometry minimizes stress concentrations and interactions
between the specimen and the end grip [10]. To minimize friction between the specimen
and the table surface, a 3mm (1/8") thick Teflon™ sheet was used. Deformation was
measured using an extensometer consisting of a linear variable differential transformer
(L VDT) and a steel rod positioned on the top of the concrete specimen for a total gage
length of 622.3 mm (24.5 in). Steel brackets with bolts anchored into the concrete
specimen supported the measurement assembly. The test measurements began at 24 hrs
for this study, but previous work has included successful measurements as early as I0
hours [6]. A 20 kN (5 kip) load cell in line with a 90 kN (20 kip) servo-hydraulic
actuator controlled the load applied to the specimen.
The unrestrained specimen, shown in Figure 2, was used to measure free shrinkage. The
second specimen, shown in Figure 3, was connected to the actuator and tested in a
computer controlled closed-loop configuration. Two different load scenarios were used
in this study. First, a constant load test was performed with a stress/strength ratio of 0.4
based on the 1 day indirect tensile strength measured using the split tensile method
according to ASTM C496. The second test simulated a restrained load condition
whereby the specimen was allowed to undergo shrinkage within a very small threshold
strain value. A restraining force was then applied to compensate for this deformation
once the threshold value was reached. The load was applied at a constant rate until the
specimen returned to its original length. A threshold value of 0.005mm (8 f.u;) was
determined experimentally to be the minimum effective value within the limitations of
the measuring equipment.
Strain measured from the unrestrained specimen was compared to the restrained or
constant load specimen to ascertain creep deformation. Typical test data is displayed in
Figure 4. The difference in deformation between the unrestrained specimen and the
cumulative strain in the restrained specimen is attributed to creep. The total tensile creep
where Ec is the total creep strain, Er is the cumulative restrained deformation and ~:, is
unrestrained shrinkage. Creep compliance, also referred to as specific creep or creep per
unit stress, can then be calculated from the experimental measurements according to
The ACI 209 and B3 models were developed to predict drying shrinkage and
compressive creep in mature concrete. The prediction of tensile creep at early age due to
restrained drying and autogenous shrinkage requires careful reexamination of these
equations. The amount of available experimental data from early tensile creep and
shrinkage is increasing, and this allows for modification of these models to account for
early age behavior.
where &e is the elastic strain, &c is the creep strain, &, is the shrinkage strain and aLiT is the
thermal dilation. Elastic deformation and creep are dependent on the stress, cr, therefore
the elastic and creep strain are written in terms of a compliance function J, given as
This relationship assumes that creep is linearly dependent on stress, which has been
validated at stress levels up to 40% of the ultimate strength. for mature concrete in
compression [11]. However, this may not be the case in early age concrete subjected to
tensile stress, hence the need for improvement of the current prediction models. Tensile
creep may include microcracking, which contributes to nonlinear behavior. Generally
microcracking is thought to occur only at high levels of applied stress, but it has been
shown that due to the presence of a drying gradient, microcracking can occur at the
surface even in unrestrained shrinkage specimens [12,13].
The ACI model recommended by committee 209 is based on the model developed by
Branson et a/. [14]. It uses empirical creep correction factors for curing, relative
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
J t t' = -1 - ( 1+ (t-t')'~' v
(,) E(t') d+(t-t')'l' " '
J
where E(t') is Young's modulus of elasticity at the loading time t', and d and 1f1 are
constants.
The shrinkage strain &5 (t,t0) is modified by correction factors for relative humidity,
duration of drying, slump, cement content, aggregate, and air content and is given by the
equation
( t t 0 )a
&
s
(t t ) =
'o fc+(t-tJa <'
where ! 0 is the time at which drying begins, fc and a are constants, and c,,' is the ultimate
shrinkage. Recommendations are given for each constant, based on standard test
conditions. Recommended equations for each parameter account for deviations from
standard conditions.
The B3 model developed by Bazant et al. [8] is based in part on the solidification theory
for concrete creep [ 15]. Total strain is calculated according to
where J(t,t') is the compliance function, tis the age of concrete, and t' is the age at
loading. J(t,t ') can be subdivided further into
where q 1 is the instantaneous compliance, Co(t,t') is the basic creep component, and
CJ..t,t') is the drying creep component. Co(t,t') and CJ..t,t) are given by
q1 through q5 are constant parameters, <sh is the shrinkage half-time, and H(t) represents
the average relative humidity of a cross section as a function of time. A detailed
explanation of the model and it's parameters is given in reference [8).
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
[Note: The new coefficient was called q 5 in the original reference but has been renamed
q6 here to avoid confusion with the drying creep parameter q5]. 0stergaard demonstrated
the improvement of fit in his study, where he considered wet-cured samples and altered
only the basic creep component of the prediction model to produce successful results.
The ACl equations were applied to a concrete mixture with a w/c of 0.50. A comparison
between creep strain measurements from a constant load test and the ACI model
prediction is shown in Figure 5 using two different values for Vu, the ultimate creep
coefficient. The lower curve reflects the ACI recommended constants modified for test
conditions, and the other uses an ultimate creep coefficient Vu of 13.5, which is beyond
the recommended range of the parameter. The prediction fits the experimental data quite
well - demonstrating that even early age creep can be modeled with the ACI equation -
but only after the vu parameter has been modified beyond a realistic range. This finding
confirms the limitation on the ACI model of a loading age of 7 days, which is reasonable
for structural loads. For earlier loading ages from deformation due to drying and
autogenous shrinkage or temperature change, modifications of some kind are necessary to
apply this prediction.
The following modifications are suggested, in the form of additional creep and shrinkage
correction factors for early age. For creep, the equation has the form
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
where tis time, t' is the loading time, and sis the setting time, in days. The parameter r
was obtained from fitting experimental data and was determined to be 1.4 for normal
concrete. The parameter depends on the rate of early strength gain and should be reduced
for high early strength concrete. The values of this correction factor equation are shown
over time and for different loading ages in Figure 6. It can be observed that the function
approaches one as the loading time exceeds 7 days, thereby reducing the model to its
original form.
where t is time, 10 is the length of curing, and s is the setting time, all given in days. The
parameter z was obtained from fitting experimental data and was determined to be 5.6 for
normal concrete. The parameter depends on the diffusion rate, which is dependent on the
degree of hydration and should probably be reduced for high early strength or steam
cured concrete. This equation approaches one as the curing time exceeds 7 days,
reducing the model to its original form, as shown in Figure 7.
The shrinkage constant fc in the original ACI model needs to be reduced for early age
concrete. The recommended values according to ACI are 35 for normal concrete and 55
for steam cured concrete, suggesting that the parameter is dependent on degree of
hydration or rate of strength gain. For early age, this parameter should be adjusted to
account for young concrete. In this study, a value of 25 was used for normal strength
concrete at early age.
The modified B3 (MB3) and modified ACI (MACI) models were used to predict creep
and shrinkage for concrete mixtures with 0.40, 0.44 and 0.50 wlc ratios under restrained
drying conditions. The elastic modulus for this material was approximated using the ACI
equation [7]. The model predictions for shrinkage at early age closely fit the
experimental data after the proposed modifications are made, as shown in Figure 8
through Figure 10. No modifications were needed for the original B3 model to account
for early age drying or autogenous shrinkage in this study. However, it is reasonable to
be cautious about applicability of the model to materials with lower w/c ratio beyond the
range of the study. Lower wlc ratio materials with high autogenous shrinkage were not
considered in the current study. The model predicted shrinkage decreases in proportion
to the w/c ratio, as it is known that the drying rate decreases with diffusion rate for
smaller pores. Autogenous shrinkage at early age will increase for lower w/c ratios in the
first few days. Figure 11 shows the effect of autogenous shrinkage at early age as w/c
decreases. It can be seen that the early shrinkage of the 0.25 wlc material is 5 times
greater than the 0.50 material in the first hours of drying. The timing of early age
shrinkage measurements is important because after one week the low wlc ratio materials
are no longer shrinking rapidly. The current model does not account for cases where
autogenous shrinkage dominates behavior.
The model predictions of tensile creep agree with experimental data, as shown in Figure
12 through Figure 14. The original models without modifications are also shown for
comparison. The MB3 model incorporates equations from [8] and early age parameter
values used by 0stergaard et a/. No additional terms were used to account for drying
creep at early age. After several days of drying, the restrained stress will exceed 40% of
the material strength, causing microcracking damage to occur. After 4-6 days, the creep
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
is not equivalent to the elastic modulus, since the stress increments are not equal for each
step and concrete at early age is not a well-behaved linear elastic solid. However, the
comparison does reveal both the influence of aging (i.e. increase in stiffness) and
softening (i.e. microcracking).
CONCLUSIONS
The study considered constant load and incremental restrained load cases for
measurement and modeling of early age tensile creep and shrinkage of concrete. An
experimental program measured early age tensile creep and shrinkage and the results
were used to develop suggestions for improving existing models. The experimental
results were compared to the ACI 209 and B3 prediction models. The following
conclusions were drawn:
• Suggested changes to the ACI 209 model enable the prediction of early age
creep and shrinkage. The changes are in the form of correction factors that can
be employed in the same manner as other factors that are already in the model.
• The B3 model predicted early age shrinkage with reasonable accuracy without
any changes in its original formulation. However, to account for autogenous
shrinkage, lower w/c ratios should be investigated at early age.
• The B3 model, modified by 0stergaard for basic creep, was successfully used
for early age tensile creep under both constant load and restrained drying
conditions. No further modifications were made to account for drying creep at
early age.
The authors would like to thank the Illinois Department of Transportation for their
generous support of this work as part of Project IHR-R29 of the Illinois Cooperative
Highway Research Program.
REFERENCES
Pailh~re,
A. M., Buil, M., Serrano, J. J., "Effect of Fiber Addition on the Autogenous
Shrinkage of Silica Fume Concrete," ACI Mat. J., V. 86, No.2, 139-144, 1989
Bloom, R. and Bentur, A., "Free and Restrained Shrinkage of Normal and High Strength
Concretes," ACI Mat. J, V. 92, No.2, 211-217, 1995
Kovler, K., "Testing System for Determining the Mechanical Behavior of Early Age
Concrete under Restrained and Free Uniaxial Shrinkage," Materials and Structures, V.
27,324-330, 1994
Pigeon, M., Toma, G., Delagrave, A, Bissonnette, B., Marchand, J., and Prince, J. C.,
"Equipment for the Analysis of the Behaviour of Concrete Undere Restrained Shrinkage
at Early Ages," Mag. Con. Res., V. 52, No.4, Aug., 297-302,2000
K. Kovler, "Shock of evaporative cooling of concrete in hot dry climates", ACI Concrete
International, V. 10,65-69, 1995
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Grasley, Z.C., Lange, D.A., D'Ambrosia, M.D. "Drying Stresses and Internal Relative
Humidity in Concrete," Materials Science of Concrete VII, ed. Jan Skalny, submitted
October (2003).
Branson, D.E. Deformations of Concrete Structures, McGraw Hill, New York, 1977
0stergaard, L., Lange, D A., Altoubat, S A., Stang, H., "Tensile basic creep of early-age
concrete under constant load," Cement & Concrete Research, V. 31, No. 12, 1895-1899,
2001
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38.4" (1.0 m}
3.5"(90mm}
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Figure 6. Creep correction factor values versus time for different loading
times at early age
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- "'I \\
' :r .·,~~"[,~'t"i±c::'i,~~!
0 · ··• .. ,, ... ; ... ,.,.. ,.... _. ...... ~....... .,. ...... .,.. .,.. ..,, .... ,_.,,,,,,"<''''''': .... j
0 10 15
Time(OB)'II)
Figure 7. Shrinkage correction factor values for different curing times at early age
1-2®1··
f 250 i · :.: ~=e.4e
i :300f.J
'
=~:=
···--">
--350 ~- ··-·· . ·················:~ .
.i
-400 ~..._...., ...,.......;. .. ,...,....,...,..+··············,••·i•••••••!'''''''''''; ., ..••••., •. ,,,,-i:···~··~·-..-··.,-·•.; •• ._. ...,.•• ~··•v••f••..,.··•···•·••••··'
0 1 2 3 4 5 6 8
Age(days)
Figure 8. Shrinkage measurements compared with ACI and B3 models for w/c =0.40
l ·• . ·
e .j , "'%,..
Figure 9. Shrinkage measurements compared with ACI and B3 models for w/c =0.44
-~ I--··:·x:~~:r:~·~=r·-·---·----~---·---·-
1 \ ', X
f100t .
'·; ~1:
,~~,'X
'
~
....
~ -1so; >:.:x:;:~ ·
~ ~ "'--!'~
e -:1.00 i ' ;',:..·,~-
~ j . ...~.... . .
f -250 i '. . ''-
:e j r--·~x. . .dA~o_·Kl·--:...._. · ~ ..~"" ·
"'.JOI)r.,····1 - -··....... -"·"·---~-----------""'1··.::.:~:-.
~ ~ ,..... .. ACI~ j
·350 i••• l. . :.:.:.~.".:"'. . .! .... '········· .......... .
-- -·~·····. --.
.
...COO -1·-·:•··: , .....,...,... j ...••..,.. ..,•.., .•.~ ·········.-··.···+· ···•···•···r·-t···•··•r······ ... -•.;. ...,.,._ .. .,. ...,... .j. •••, .................~
0 2 3 4 5 6 8
Age (days)
Figure 10. Shrinkage measurements compared with ACI and B3 models for w/c =0.50
I
\ ·lOOt------r··--
'l! ·!
l! -1so ·i .. c· ::;:;:;i~;o:25
l ll
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
.-wJc=0.32 •..
'
·200 1· -i -o-wfc=0.40 .
J I -~~t:::~~
·250 ..............;..._.,.,..t.............;_..•.~.,•...:.....-.-·;-~·-···~~----..···•·-··~~-
1.0 1.5 2.0 2..5 3.0 3.5 4.0 4.5 5.0
~{days)
l ' • w!C~~.49
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
0.7-f· -83"""""
0.1 j
ooL
'
' .... : .
., .••, .. ._ ..._. .., •. , ........, •• .,. ..., .. .,. ...... .,. •• ,_. •• ._. •• ,_. •• ._. ••
. 1
~··••••v••v•·..-···
0 2 6 7 8
Figure 12. Modified ACI and B3 model prediction for tensile specific creep, w/c =0.40
<'
oe H
i ~ l
t 0.5 _j -~
c j
~Q.4i
u 1
iJi 03 'j
"' 0.2.~
0.1 j'
0 2 l 4 5 6 7
Age(days)
Figure 13. Modified ACI and B3 model prediction for tensile specific creep, w/c =0.44
X l
Figure 14. Modified ACI and B3 model prediction for tensile specific creep, w/c = 0.50
400 T ••••·····••••••••••••••·• .•
l
3501
-=l
!
:: 2001
;
~ l ~ r=;:~-;-~_l;f ~-\~
1Sil"'" 1j
l:r
~ ---~~ti.3711U
0
1
. . . . . :l~~.~~~l
0 20 40 00 80 100 120
Stlilln (lO"miM) --`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
! 7
"b
~ 6
~
i 5
~ ~
I 3
2
4 5 II
Agc{dnys)
Figure 16. Stress-strain ratio over time under restrained drying conditions
j ~~AQ~- --ro •
l ~ "--~-~-~~-------·'
~
Figure 17. Modified ACI and B3 model prediction for early age tensile creep strain
under fully restrained conditions, w/c =0.40
.1
180
160
i. 140
E
~120
~ 100
Ill 80
!oo
40
20
2 6 7
Figure 18. Modified ACI and B3 model prediction for early age tensile creep strain
under fully restrained conditions, w/c = 0.44
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
I 140t---'~ifled~CI
E ~ '
___ T __ _
'
80 t--- ---:
' '
, , t' .· , . . , I
20 t------ t-- -~'-~' /.--- --- ->---- --:----- -<------ ~ ----- -l
0~'~~~·~~~~-+~~~~~·~~+·~~+-~~1
0 2 3 4 5 6 7
Age (days)
Figure 19. Modified ACI and B3 model prediction for early age· tensile creep strain
under fully restrained conditions, w/c = 0.50
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Synopsis: Temperature effects are the predominant cause for volume change in concrete
pavements. This paper describes an experimental investigation of thermal volume change
conducted to improve the understanding of joint movement in concrete pavement. Four
slab strips containing embedded strain gauges and thermocouples were monitored in a
controlled environment under four heating rates. Each strip was monitored for translation,
rotation, and warping height. Key findings of the experiment include the internal strain
distribution and non-linear thermal gradients produced by asymmetrical heating. The
laboratory data are compared with long-term data from an instrumented parking lot
pavement. Analysis of the data provides insight into the prediction of thermal movements
and determination of thermal stress development in pavements.
367
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368 Miltenberger et al.
BIOGRAPHICAL SKETCH:
ACI member Matthew A. Miltenberger, is a Business Development Manager
with Vector Corrosion Technologies, Inc. He holds an MS in structural engineering, and
a BBA in construction management. He is a member of ACI Committees 222, Corrosion
of Metals in Concrete; 355, Anchorage to Concrete; and 365 Service Life Prediction.
Matt was a co-recipient of ACI's Wason Medal for Most Meritorious Paper in 2000.
ACI member Emmanuel K. Attiogbe, is the Director of Technical Services at
Master Builders, Inc., Cleveland, Ohio. He received his PhD in Civil Engineering from
the University of Kansas specializing in structural engineering and concrete materials.
He is a member of ACI Committees 231, Properties of Concrete at Early Ages; 236,
Material Science of Concrete; the T AC Technology Transfer Committee, and the
Concrete Research Council. He was awarded ACI's Wason Medal for Materials Research
in 1995.
Anthony R. Stoddard is a Systems Development Technician at Master
Builders, Inc., Cleveland, Ohio. He is certified as ACI Laboratory Technician Level 1
with over I 5 years experience in electronics and instrumentation.
RESEARCH SIGNIFICANCE
Volumetric changes of concrete slabs on grade in response to environmental
changes have been recognized for decades, but are still not well understood. (1-4)
Numerous investigations into drying shrinkage induced curling of slabs on grade and
thermal warping of pavements have been performed, but a procedure for pavement
design that links structural analysis and environmental behavior is Jacking. (5-12) This
study describes the behaviors and presents a theoretical framework for unraveling the
complex nature of pavement response to the environment.
CONCEPTUAL BASIS
Curling of slabs on grade and warping of pavements are similar phenomena in
as much as the concrete reacts to the environment by changing shape. Curling is the
positive curvature that results from drying shrinkage at the top surface of a slab on grade
or pavement, causing slab edges to lift. Thermal warping can be characterized as the
positive curvature caused by rapid cooling of the pavement surface, or as the negative
curvature caused by heating of a pavement surface from solar radiation. In both curling
and warping, the concrete reacts to the environment by changing shape. This shape
change is the concrete's response to the non-linear strain profile produced by the
environment.
For curling, the non-linear strain profile is caused by moisture loss from the
concrete to the environment. Moisture loss from a slab is a process whereby the water
vapor pressure inside the concrete equilibrates with the water vapor pressure of the
ambient environment. At the interface between the air and concrete, this equilibration
occurs rapidly, but as the drying front progresses inward the equilibrium moisture content
is controlled by the rate of vapor permeation. This results in a transient moisture profile
that begins as a very sharp moisture profile and progressively becomes more gradual over
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
(E -E )
E
f
= ft
hn
fb yn + E
fb
(1)
(E -&)
E = I b y+E (2)
n h b
C'-
2·&ft ·(1-n)+&jb ·(n 2 +5n)
"b- (6)
(n+l)·(n+2)
where:
b Slab element design width
Ec Elastic modulus of the concrete
Fx Force in the horizontal direction
EXPERIMENTAL PROCEDURE
The experimental procedure used to evaluate thermal warping involved casting
electrical resistance cables, thermocouples and vibrating wire strain gauges, (VWSGs),
into four concrete beams 260-mm wide x 184-mm deep x 2.36-m long, as shown in Figs.
5 and 6. One beam contained no reinforcement, and the other three contained one
continuous No.3 (-10-mm diameter) reinforcing bar located at 47, 92, or 143 mm from
the top surface. Mixture proportions are provided in Table 1.
Fig 5 shows that the beams were inverted when cast so that the electrical
resistance cable could be carefully located at the top surface of the beam. A 7.62 m (25
ft) length of 65.6 watt/m (20 watt/ft) cable, fitted with a grounded plug, was cast into
each beam. Six thermocouples and five VWSGs, were also placed in each beam.
Horizontally, the thermocouples were located 125 mm (5 in.) from each end along the
center line of the beam; the strain gauges were centered approximately 1.18 m (46.5 in.)
from each end. Vertically, the thermocouples were located at mid-height and
approximately 5 mm from the top and bottom surface; the VWSGs were located 30, 62,
92, 122, and 154 mm from the top surface. Each VWSG was individually calibrated and
contained .a thermistor for temperature measurement. The combination of thermocouples
and VWSG thermisters produced seven temperature measurements through the depth of
each beam producing a complete temperature profile.
In addition to the beams, eight 102-mm diameter x 203-mm high concrete
cylinders and four 75 x 75 x 286 mm length change prisms were cast for determination of
compressive strength in accordance with ASTM C 39, modulus of elasticity in
accordance with ASTM C 469, and the coefficient of thermal expansion in accordance
with CRD C-39. Test results are provided in Table 2.
The beams were maintained in a moist condition using wet burlap and plastic
unless placed in the test apparatus. The concrete was at least I4-days old prior to testing.
The test apparatus is shown in Figs. 7 to 9. The test apparatus consisted of a pan
with a cooling coil connected to a heat exchanger; roller supports with one "fixed end"
and one "free end"; a bridge for mounting five micron-resolution digital deflection
gauges for vertical displacement measurements; and two laser displacement gauges with
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
± lmm range for horizontal displacement measurements of the top and bottom of the
beam. The "fixed end" of the apparatus had a 25-mm diameter rod located at mid-height
of the beam to force horizontal movement to occur at the "free end". The entire
apparatus was rigidly attached to the laboratory concrete floor using grouted screw inserts
and leveling bolts. Once leveled, the apparatus was grouted in place using a precision
non-shrink grout to provide a stable base and heat sink. The floor and base of the pan
were oiled prior to installation to facilitate subsequent removal and cleaning.
The testing sequence consisted of an overnight initialization period at room
temperature, a five to six-hour heating period followed by an overnight cooling period,
and subsequent heating and overnight cooling cycles. The temperature of the water in
contact with the bottom of the beam was maintained at 20 ± 1 "C by the heat exchanger at
all times. Vertical and horizontal displacements were recorded manually, while the
thermocouples and VWSGs were recorded digitally. A five-minute time increment was
4. The translational strain in Table 3 was calculated as the mean horizontal movement
recorded by the non-contact transducers divided by the beam length, 2362 mm. The data
in the column labeled "Mean Temperature Change" were calculated as the change in the
mean ofthe top and bottom surface temperatures. The data in the column labeled
"Middle Temperature Change" were calculated as the change in the middle thermocouple
measurements. The free strains were calculated by multiplying the temperature change
by the coefficient ofthermal expansion from Table 2.
The equivalent rotational stress and strain at the top surface were calculated
from deflection measurements using Eq. 7 and Eq. 8, respectively. Eq. 7 was derived
from basic mechanics principles (14) assuming a uniformly loaded beam and a
rectangular cross section. The measured rotational strain was calculated as the difference
between the laser measurements and the height of incidence on the specimen, using a
gage length of 1181 mm. One-halfoftbe slab element length was used as the gage
length because the test apparatus allows rotation ~n both ends of the specimen, but the
laser only measured the rotational displacements on one side.
()" = 384·6·h·E
2
c (7)
I 80·L
384 ·6 ·h
& =---,.--
2
(8)
1 80·L
where:
a, Top surface stress
c, Top surface strain
8 Mid-span deflection
L Length of the slab element, (2363 mm)
"fixed end" and friction at the roller supports. In hindsight, it would have been better to
design the apparatus with two "free-ends", using four lasers to measure horizontal
displacements.
The cross-sectional area ratio of reinforcement to concrete was less than 1% in
this experiment. This quantity of steel reinforcement did not produce clear performance
differences, so all the beams were treated in a similar manner.
It is well documented ( 15, 16) that the coefficient of thermal expansion varies
with moisture content. The beams in this experiment were maintained in a moist
condition until placing on the test apparatus, and then were exposed to an ambient
environment of 20 'C and 40% relative humidity on the top and sides, and were in
contact with a water bath on the bottom. Also, the top surface was heated during the
testing program that accelerates the rate of drying. Differential drying of the top surface
induces curling, as illustrated in Fig. 10 by the progressive increase of negative strain
(contraction) at the top surface and positive strain (expansion) at the bottom surface.
Creep may also play a role in the progression of strain at constant temperature in Fig. I 0,
but is not incorporated in the data of Table 3 and Table 4 because all gauges were tared
prior to each heating event.
The relationships represented in Fig. 12 to Fig 14 indicate:
1. The free deflection and rotational strain of concrete exposed to a thermal
gradient can be estimated by multiplication of the difference between the
top and bottom temperature and the coefficient of thermal expansion.
2. The translational strain of concrete exposed to a thermal gradient can be
estimated by multiplication of the temperature change at the centroid and
the coefficient of thermal expansion. Similar behavior has been
documented in instrumented pavement sections. (17)
In addition to these two relatively obvious relationships, the data from this
experiment clearly indicates that geometric distortion caused by one-sided drying or
heating at the surface of slabs will produce movement in the opposite direction at the
base. This behavior is illustrated in Fig. 10 by the sharp change in the bottom surface
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
CONCLUDING REMARKS
• The movement of concrete pavement in response to the environment is
very complex. Thermal warping, curling, and sliding of panels across
the ground occur simultaneously.
• Light reinforcement does not appear to produce a discemable
difference in thermal movement.
• Thermal translation can be estimated by the product of change in
temperature at mid-height in the slab and the coefficient of thermal
expansion.
• Thermal rotation can be estimated from the difference between the top
surface and bottom surface temperature.
• When restraint from adjacent slabs or structures is present, thermal
expansion can produce forces sufficient to slide slabs across the
ground, permanently widening the joints.
• If grit enters joints, daily thermal cycles can continue to shove the slabs
apart. Most of this behavior occurred in the first year.
REFERENCES
1. Thomlinson, J., "Temperature Variations and Consequent Stress Produced by Daily
and Seasonal Temperature Cycles in Concrete Slabs", Concrete and Constructional
Engineering, Vol. XXXV, No.6, June 1940, pp. 298-307.
2. Thomlinson, J., "Temperature Variations and Consequent Stress Produced by Daily
and Seasonal Temperature Cycles in Concrete Slabs", Concrete and Constructional
Engineering, Vol. XXXV, No.7, July 1940, pp. 352-360.
3. Burke, M.P., "Reducing Bridge Damage Caused by Pavement Forces, Part 1: Some
Examples", Concrete International V 26, No. 1, Jan. 2004, pp 53-57.
4. Burke, M. P., "Reducing Bridge Damage Caused by Pavement Forces, Part 2: The
Phenomenon", Concrete International V 26, No.2, Feb. 2004, pp 83-89.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
(#57 Limestone)
3
Fine Aggregate 515 kglm3 (1133 lbs/yd )
200
160
~ 160
e 14o
im 120
100
e
,g 80
1: 60
..
.!iP 40
:z: 20
0
·50 0 50 100 150 200 250
Free Strain, IL&
Fig. l - Hypothetical free strain profiles for a pavement exposed to solar radiation.
A) morning, B) mid-day, C) afternoon, D) evening.
-------~--------
! : &f :
~~~~~~~~: J~),~~~ ~~~~~~~r=~=~~~-St~~~~-
_______ _ ----X-------~- -NetStraln
:on : ;
--------- ------.--------;--------,--------
1
_________________ J ________ J ________ o j I _______ _
I o I
' '
-------~--------~--------~--------
'
'I '0 'I
-------~--------~--------~--------
' o I
Fig. 2- Net strain, e., resulting from free strain profile A, ef' from Fig. 1, showing
rotation and regions of residual compression (-), and tension (+)"stress.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
60 -----------------~-----~-----
'
.c ' '
Cl
40 ' '
-------.-----
"ii '
::t 20
0
-125 -100 -75 -50 -25 0 25 50
Strain, 111:
Fig. 3 - Residual strain profil~ resulting from free strain profile A in Fig. 1.
&tb
Fig. 4 - Schematic of free, er and net, e", strain profiles with nomenclature
used in Eq. 1 through Eq. 4.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Fig. 8 - Photograph showing roller on "fixed end" of test frame and water bath
-TopS..r.•«>
··--·SQ!tornSti~.:e
150
-tOO ! , ....... ,., ..... , .. ··· '"" · ,...... ,... ~---·······--....... ,,. ............-,.......__.,,""'"''"'""·-··
0 eo 60 100 120 14() 160
Tim&,hr
Fig. 10- Response of control beam to curling and the 821, 219,
and 484 W/m2 heating cycles, respectively
1.0-r--------------------,
09 -------------------------------------------------
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
nme, hr.
Fig. 11 - Deflection of control beam during the 821 W/m 2 heating cycle
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
{: 0--~= ~;//~/
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
! 90
...............·····
30 60 90 120 150 180 210
Measured Translation Strain, ps
0 ~ ~ 60 60 ~ ~ ~
---------or- ---~----------------------------
0"
2: --~-~--~-->""- ---------------------------------------
20 4D eo so 100 120 140
Measured Rotational Strain, pa
3.5
1:
§ 30
"
': 2.5
I
-~----------------------~------------------
; 1
_________ Heating __ .:_ Cooling. ______ -----
~ 2.0
1:
1 1.s
lii
1.0 ------------~---- ---------- _1 __ _
I
0.5 ------------------------------~-----------
0.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
Time, hr
Fig. 15- Mean power term (line) and range of values determined
from temperature profiles.
r--------------------------------------.~
140 - - - - - - -- - -- - --- - -- -- -- - - - - - ---- - - - - - - -- - - - - - - --
120 "
! u
r:."'lOO ... I!
I.. so
.!!
~60
3S
..i!
!l
30~
~
., 40 --
"'
20 "
20
10 ll 14
Fig. 16 - Mean joint opening strain for a 200-mm thick parking lot pavement in
Cleveland, OH showing daily fluctuations
I~
! 100
l
~ -~
-100
·150 -1----------~----------~----------------+ 15
0 10 12 14
Fig. 17 - VWSG data for gauges located near sawn joints in a 200-mm thick pavement in
Cleveland, OH, showing daily fluctuations.
..
u
,. f
··~~-----~-----·~~------L·~-----:t _____ ~-
•• ,. '
20 l
(oo
· ·. . ~ ·.:: r ~: ~: 10 lI
--~·.:-.--- -:~·~- ------~~- . -.-/------- ~ 1-- -f.!~---
•, \I ~ =.~ !-' '•, ...... • \
---- -: . ·~~- ------7S•~ ~·-•-- -------"" -:--""""-"""" "
E-~-~-T:..:empentll~::.::;::.n:.__~~-~-~~-~-~--t-•o
~ oo m ~ ~ ~ ~ m m ~ * -
Time from CasliDg, Days
Fig. 18- Mean joint opening strain for a 200-mm thick parking lot pavement in
Cleveland, OH, showing seasonal effects.
~ ~ m ~ ~ ~ ~ m m ~ m -
Time from Casting, Days
Fig. 19 - VWSG data for gauges located near sawn joints in a 200-mm thick parking lot
pavement in Cleveland, OH showing seasonal effects.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Length
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Area
square inch square centimeter (cm 2) 6.451
Volume (capacity)
ounce cubic centimeter (cm 3) 29.57
gallon 3 0.003785
cubic meter (m ):1:
cubic inch cubic centimeter (cm 3) 16.4
cubic foot cubic meter (m 3) 0.02832
cubic yard cubic meter (m 3):1: 0.7646
Force
kilogram-force newton (N) 9.807
kip-force newton (N) 4448
pound-force newton (N) 4.448
Pressure or stress
(force per area)
kilogram-force/square meter pascal (Pa) 9.807
kip-force/square inch (ksi) megapascal (MPa) 6.895
newton/square meter (N/m 2 ) pascal (Pa) I.OOOE
pound-force/square foot pascal (Pa) 47.88
pound-force/square inch (psi) kilopascal (kPa) 6.895
Temperature§
deg Fahrenheit (F) deg Celsius (C) fc =(If - 32)/1.8
deg Celsius (C) deg Fahrenheit (F) tF = 1.8tc + 32
* This selected list gives practical conversion factors of units found in concrete technology. The reference
source for information on SI units and more exact conversion factors is "Standard for Metric Practice" ASTM E
380. Symbols of metric units are given in parentheses.
t E indicates that the factor given is exact.
:j: One liter(cubic decimeter) equals 0.001 m 3 or 1000 cm 3.
§ These equations convert one temperature reading to another and include the necessary scale corrections. To
convert a difference in temperature from Fahrenheit to Celsius degrees, divide by 1.8 only, i.e., a change from 70
to 88 F represents a change of 18 For 1811.8 = 10 C.
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
Index
A creep recovery, 67
aging, 107 curling, 367
Alexander, S.D. B., 195
Alexander, S. 1., I D
Al-Manaseer, A., 41 D'Ambrosia, M.D., 349
Arockiasamy, M., 85 deflection, 1
Attiogbe, E. K., 303, 367 deformational characteristics, 21
autogenous shrinkage, 285, 337 delayed restraints, 107
design, I
B design aids, 239
Barcelo, L., 337
Bissonnette, B., 337 E
Boily, D., 337 early age, 67, 337, 349
bridge, 67 early age contractions, 1
bridge monitoring, 143 elastic modulus, 21
Buchberg, B., 317 Espion, B., 67
c F
camber prediction, 195 fly ash, 217, 261
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
v
viscoelasticity, l 07
w
warping, 367
web site, 239
Weiss, J ., 285
Weyers, R. E., 217
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---
--`,```,,``,,,`,,,``````,,,,```,-`-`,,`,,`,`,,`---