Journal of Advanced Concrete Technology Vol. 2, No. 2, 141-154, June 2004 / Copyright © 2004 Japan Concrete Institute
141
Invited Paper
State-of-the-Art Report on Control of Cracking in Early Age Concrete
Hirozo Mihashi1 and João Paulo de B. Leite2
Received 25 December 2003, revised 30 April 2004
Abstracts
Durability of concrete structures is seriously compromised by cracking in early age concrete, particularly in high-strength
or massive concrete structures. Since early age cracking is influenced by various highly interrelated factors that affect the
hydration process and stress/strain development, its behavior is highly complex and no rational methodologies for its
control have yet been established. On the other hand, demands for high strength and massive concrete structures in
modern cities are ever growing, regardless of the many durability problems. More comprehensive methodologies for the
control are therefore essential to ensure sustainability of such structures. This report reviews state-of-the-art research on
mechanisms that cause complex cracking phenomena and newly developed methodologies to control early age cracking.
1. Introduction
Cracking of concrete structures often seriously compromises not only structural integrity, but also durability
and long-term service life. Early age cracking of concrete
is a constant problem that arises from the fact that concrete interacts with its environment and experiences
complex physical and chemical changes. Early age
cracking has thus been subject of extensive research, yet
due to the large number of contributing factors and the
complex nature of the interacting phenomena, designers
have purely relied on empirical rules based on
well-confined and idealized assumptions for experimental conditions. In recent years, more realistic insights
have been gained through various research efforts in
related fields, as for example, on thermal cracking of
concrete, including research on thermal cracking of early
age concrete by a RILEM technical committee and on
mass concrete by a Japan Concrete Institute (JCI) research committee. On the other hand, the ever-growing
number of applications of high-strength concrete and
massive concrete structures makes essential the establishment of comprehensive methodology to prevent
cracking of early age concrete.
Basically, concrete structures often present volumetrical changes particularly due to thermal and moisture
related shrinkage. Volumetric instability is detrimental to
performance and durability of concrete structures because structural elements are usually restrained. When
the concrete is prevented from shrinking freely, tensile
1
Professor, Department of Architecture and Building
Science, School of Engineering, Tohoku University,
Japan.
E-mail: mihashi@timos.str.archi.tohoku.ac.jp
2
Lecturer, Department of Architecture and Building
Science, School of Engineering, Tohoku University,
Japan.
stresses are developed, which in combination with the
low fracture resistance of concrete, often results in
cracking. Given this, cracking control measures should
be devised based on consideration of several factors
including age-dependent material property development,
free shrinkage and shrinkage rate, creep relaxation and
degree of restraint, as well as external environmental
conditions. Free-shrinkage measurements may provide
useful information yet not sufficient to determine
whether concrete will crack in service. On the other hand,
constant refinements in restrained shrinkage testing
techniques have revealed contradicting results when
compared with existing data. Suitable evaluation and
modeling of material properties and accurate numerical
analysis techniques are necessary to be employed in
combination with refined shrinkage testing techniques
for solid understanding and effective control of early age
cracking. Under these circumstances, a noticeable trend
has been the reviewing of past research data to determine
future paths of research. For example, the Japan Society
of Civil Engineers (JSCE 2000) published a report entitled “Creep and Drying Shrinkage of Concrete II” and
nearly at the same time the JCI (2001) published the
“Report of Committee on Time-Dependent Deformation
of Concrete Structures Due to Creep and Shrinkage”.
The Architectural Institute of Japan (AIJ 2001) also
published a “State-of-the-Art Report on Mass Concrete”
as well as a revised version of “Recommendations for
Practice of Crack Control in Reinforced Concrete
Structures - Design and Construction (2002)”. The most
recent publication by the AIJ (2003) on this subject is
“Shrinkage Cracking in Reinforced Concrete Structures Mechanisms and Practice of Crack Control”. The
RILEM has set a technical committee (TC 181-EAS)
exclusively to deal with “Early Age Shrinkage and
Cracking in Cementitious Materials” and hosted recently
the International Conference on Early Age Cracking in
Cementitious Systems (Kovler & Bentur 2001). Shortly
before that, Tohoku University and JCI jointly organized
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H. Mihashi and J. P. de B. Leite / Journal of Advanced Concrete Technology Vol. 2, No. 2, 141-154, 2004
2. Mechanisms driving cracking in early
age concrete
Stress which arises in early age concrete leading cracking
is mainly associated to three types of deformation:
autogenous shrinkage, induced by water absorption
during hydration of cement particles, drying shrinkage,
induced by evaporation of water along concrete curing
and thermal shrinkage, owing to a poor dissipation of
heat evolved by cement hydration and cooling of the hot
concrete. The definition of autogenous shrinkage is still
subject of debate, owing to the ambiguous understanding
of the phenomenon. According to the JCI Committee on
Autogenous Shrinkage of Concrete (JCI 2002), “autogenous shrinkage” is defined as a “reduction in the global
volume of the cementitious material, caused by hydration
of cement during and after the setting process” (Fig. 1).
On the other hand, drying shrinkage is well accepted as
being a volume deformation induced by evaporation of
water from hardened concrete to the surrounding atmosphere. Considering the differences in shrinkage
mechanism, high-strength concretes with low water-cement ratios (w/c) are prone to significant autogenous shrinkage, while ordinary concretes with high w/c
are likely to incur in drying shrinkage. However, when
water evaporates from the surface of early age concrete
along desiccation during the hydration reaction process,
it is impossible to separate drying shrinkage from autogenous shrinkage that may simultaneously occur.
Autogenous shrinkage and drying shrinkage share
similar characteristics in that they are volume reductions
induced by decrease of relative humidity during concrete
hardening, yet they are very different in timing of stress
development, as well as in mechanisms as mentioned
before. While autogenous shrinkage may occur from few
hours after setting has started through several days until
the hydration is completed, drying shrinkage may occur
only after the surface is eventually exposed to environmental conditions, few days after setting starts, to the end
of the curing process. Other important difference is that
autogenous shrinkage is a uniform deformation with no
in-plane strain gradient unless the hydration heat distributes non-homogenously inside the section or deformation is locally restrained. On the other hand, since
drying shrinkage is induced by the loss of water inside
concrete through the member surface, resulting in
non-homogenously distribution of humidity within the
member, strain gradients are always observed within the
member sections (Fig. 2). As the surface dries and attempts to shrink, it is restrained by the core volume.
Consequently, cracking caused by drying shrinkage initiates from the surface area. Then as the core volume
dries, it undergoes shrinkage deformation, which when
subjected to restraint, induces tensile stress leading to the
development of cracks throughout the section. Note that
initial cracking due to autogenous shrinkage may already
exist. Around 5 to 10 hours after hydration starts, at the
time when the concrete microstructure starts to form,
autogenous shrinkage deformation, if free, increases as
hydration further progresses. Yet if it is restrained, significant tensile stress may arise inducing cracking.
Thermal shrinkage differs from the two former in the
Drying
(a)
Water
Water
(b)
Depth
Autogeneous
Subsidence shrinkage
Bleeding
chemical
water
shrinkage
Pore
tn
1.0
Cement
(c)
Setting
(d)
Depth
Hydration
products
0.0
Unrestrained deformations
0.0
Restrained deformations
Cracks
0.0
Stress
Hydration products
Placing
0.5
Stress
Cement
Cement
h
Stress
Water
Depth
Chemical
shrinkage
Hardening
Fig. 1 Definition of autogeneous shrinkage (JCI 2002).
hext=0.5
t1
Depth
another conference to provide a forum of exchange of
ideas particularly focused in controlling fracture mechanics of early age of concrete, the “International
Workshop on Control of Cracking in Early Age Concrete” (Mihashi & Wittmann 2002). Meanwhile, the JCI
Committee on Autogenous Shrinkage of Concrete completed its 2-year research project, begun in 2000, and
published a comprehensive report on the latest findings
(JCI 2002).
This paper gives an overview, specifically from the
mechanical aspect, of the status of current research on
cracking of early age concrete and its control, topics that
are drawing increasing attention as mentioned above.
The objective is to provide experts with awareness of
state-of-art research and advances fracture mechanics
and control of cracking of early age concrete.
Restrained deformations with crack
formation
Fig. 2 Stress distribution and crack formation in a drying
concrete element (Martinola et al. 1998 © by Aedificat reprinted with permission).
H. Mihashi and J. P. de B. Leite / Journal of Advanced Concrete Technology Vol. 2, No. 2, 141-154, 2004
fact that it is not related to moisture movements but with
fluctuations in internal and external temperatures.
Thermal shrinkage includes the effects of diurnal temperature changes (Mohamed & Hansen 1996), as well as
the response of massive concrete structures to the heat
generated during hydration (Springenschmid et al. 1985).
As cement hydrates in an exothermic reaction, a large
quantity of heat is generated. Dissipation of such heat in
large structures is relatively slow. The excessive rise of
heat accelerates the hydration process and causes the
concrete set in an expansive condition. Then as the concrete cools, shrinkage occurs, which often leads to
cracking. Recently, several works have focused on calculation of thermal stresses and their potential to induce
cracking (Springenschmid 1995).
In some cases of practice, concrete members are subjected to loading during early age, given rise to creep
strains, which are gradual increase in strain over time
under sustained loads. Creep in concrete differs from the
creep observed in other structural materials in the fact
that it occurs at room temperature. When the concrete
member is restrained, the reverse phenomenon may be
observed as stresses gradually relax. Stress relaxation not
only occurs in the instance of external loading but also in
the case of shrinkage stresses, adding further complexity
to the matter. Note that while creep and relaxation are
separated in conventional mechanics literature to properly distinguish stress and strain states, they are often
used interchangeably to describe the same phenomenon
in concrete literature, as they are viewed as same phenomenon.
Hence early age cracking mechanism is a complex
interplay among development or growth of strength,
progress of autogenous and/or drying shrinkage, creep
deformation and stress relaxation. When examining this
mechanism, it is important to consider the strain component of each causal factor separately. Thus, the total
strain at time t may be defined by equation (1) as proposed by the CEB-FIP (1991):
εT (t ) = εelastic (t ) + εcreep (t ) + εshrinkage (t ) + εthermal (t )
(1)
The sum of εelastic and εcreep represents the material’s
mechanical response to stresses, i.e. stress dependent
strains, while εshrinkage and εthermal are stress independent
volumetric changes caused by moisture movements and
thermal variations. Hence the stresses that cause cracking
of early age concrete are, in case of absence of external
loading, induced by restraint of deformations. There may
be different types of restraints at work in structural concrete. Restraining may be imposed by alien bodies acting
on the concrete material, such as reinforcing bars inside a
member; by concrete joints connecting a member to an
adjoining member with high stiffness; and even by the
core concrete of a member when non-homogenous strain
distributions are created internally according to the
temperature and humidity distributions, as explained in
the case of drying shrinkage. In practice, restraints are
nearly always, and to a considerable extent, at work in
143
concrete structures, yet hardly detaining completely the
movements of concrete members. Therefore, it is usually
difficult but essential to evaluate the effective level of
restraint, which depends on the ratio between the local
stiffness of the concrete and that of the surrounding
concrete or adjoining structural elements. According to
the parametric studies by Weiss et al. (1999), reduction in
the restraint level delays the crack initiation, suggesting
that the restraint level λ is a key factor for predicting
crack initiation in concrete. The latter study also draws
attention to the influence of the shrinkage rate on the
stress development and age of cracking. For high restraint levels, a faster shrinkage rate will result in earlier
arising of cracks. On the other hand, when the restraint
level is low, cracks develop slower as the shrinkage rate
increases. This means that high restraint levels are more
concerning in concrete with a low w/b, since the decrease
in w/b accelerates the rate and intensity of autogenous
shrinkage.
3. Material properties of early age concrete
The accuracy of stress analysis of restrained shrinkage
depends primarily on how the required mechanical
properties are described. Most mechanical properties are
rapidly changing at early age, particularly in the period
when the concrete changes from liquid to solid state. The
key mechanical properties required for analysis at early
age are modulus of elasticity, tensile strength and those
governing the viscoelastic behavior of the material. In
principle, every material property contributing to the
shrinkage behavior and early age cracking is dependent
on the progress of cement hydration or the hydration
product, and varies significantly according to concrete
age, component materials, mixture proportions and curing environment. This section focuses on recent research
findings with regard to the creep characteristics under
tensile stress causing cracking, the unavoidable rise in
hydration heat during the hydration process of
high-strength concrete that undergoes especially significant autogenous shrinkage, and the linear expansion
coefficient associated with thermal expansion accompanying the rise in hydration heat.
3.1 Elastic modulus and strength
Around the time when a microstructure starts to form as
the result of the cross-linking and consolidation of hydration products, yielded in accordance with the progress
of the hydration reaction of cement particles, the early
age concrete starts to gain strength and stiffness, which
increase with time. Berggstrom et al. (1980) pointed out
that at the age of 3 to 4 hours, concrete has very inelastic
components even under low stress and most deformations are permanent. At the ages of 8 to 10 hours, it starts
to develop clearly defined elastic and inelastic regions,
and at the age of 14 to 18 hours, begins to show similar
characteristics to those of hardened concrete. In particular, the elastic modulus of high-strength concrete
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tends to exhibit a high elastic modulus at an early stage as
compared with normal-weight concrete, which is illustrated by the fact that the elastic modulus on the second
day is approximately 80% or more of that at age of 28
days (JCI 2002). The rate at which a high elastic modulus
is gained is higher than that of compressive strength
development. Elastic modulus is usually measured based
on the pattern of increase of strain versus stress, but according to Hagiwara et al. (2002), values of tensile elastic modulus are approximately 1.1 to 1.2 times greater
than values of compressive elastic modulus. Fukasawa et
al. (2002) demonstrated the influence of the hydration
heat into the development of strength and elastic
modulus, comparing potential estimators. In addition,
drew attention to the fact that component materials may
affect substantially the development of these mechanical
properties.
experimental data has been reported with regard to the
linear expansion coefficient of early age concrete (AIJ
2003). Among various efforts to devise better measurement techniques, Yan et al. (2000) proposed a method for
isolating the strain induced by temperature changes and
managed to measure the linear expansion coefficient by
keeping the specimen temperature within a low range
between -1 and 5 degrees centigrade to restrain the progress of the hydration reaction and control autogenous
shrinkage. Based also on other research findings, it
gradually became clear that the linear expansion coefficient is usually larger for early age concrete than hardened concrete and that it is largely time-dependent (AIJ
2003).
3.2 Tensile creep characteristics
The tensile creep and compressive creep of concrete had
long been considered equal to each other. However, because tensile creep greatly affects the development of
thermal and shrinkage cracks, an increasing amount of
research has recently focused on this issue, and as a result,
a number of enlightening experimental findings have
been reported (JCI 2001, 2002, AIJ 2003).
Iriya et al. (1998, 2002) reported that compressive
creep is more prominent than tensile creep under same
stress-strength ratio, and that the older the concrete at
time of loading, the smaller the difference between the
two creep types. According to Hagiwara et al. (2002), the
specific tensile creep (creep strain per unit stress) is approximately 75% of the specific compressive creep,
regardless of the age at which loading is applied or the
loading duration. On the other hand, Yoshitake et al.
(2000) performed creep tests under environment conditions in which the hydration reaction was restricted and
reported that specific tensile creep was considerably
larger than specific compressive creep. They pointed out
that the progress of the hydration reaction had a great
effect on tensile creep and on compressive creep, though
there was clear difference between the two development
mechanisms.
However complex the phenomena may be, it is usually
possible to identify the determining material properties
through experiments, as long as they can be broken down
into independent behaviors. Nonetheless, as mentioned
earlier, hydration is a constantly progressing reaction
accompanied by nonlinear temperature rises and thermal
expansion, as well as the concurrent changes in microstructure and autogenous shrinkage behavior. All such
processes occur simultaneous and are affected by diverse
interacting factors. Hence, it seems hardly conceivable to
solely rely on experiments to identify material
time-depending properties of the early age concrete. The
determining material properties can still be identified,
though complex and highly nonlinear may be the phenomena, if carefully performed experiments are used in
conjunction with appropriate analytical models.
In recent years, remarkable progress on analytical
models of hydration process has been achieved (Sakai &
Daimon 1998). Analytical models for simulating the
cement hydration process can broadly be classified into
three categories according to the scale at which the hydration process is described (Mihashi 1998). The first
type, categorized as a microscopic model, can simulate
point by point the random hydration of each chemical
component constituting the cement particles. The second
type, referred to as meso-model, directly simulates the
growth of cement particles as the hydration process
evolves to form a skeleton (mesoscopic) structure of the
hardened cement paste. The third type projects the influence of the hydration reaction onto the material variances of macroscopic element models without considering individual particle as explicit. This model is known
as macro-model.
Bentz et al. (1996) developed a method for directly
representing the chemical components constituting the
cement microstructure as image data and relating them to
each image element, thereby simulating the random hydration reaction occurring at each image element point
by point. Since this model allows study of the hydration
process and the subsequent formation of microstructure
3.3 Linear expansion coefficient of early age
concrete
The linear expansion coefficient of concrete as in other
solid materials is generally obtained from the temperature-strain relationship, which is derived from the
measurement of changes in length brought about by
temperature change. However, in the case of just-placed
high-strength concrete, it is extremely difficult to isolate
the temperature-strain relationship because, for example,
temperature increases in accordance with the progress of
the hydration reaction and is thus difficult to control, and
autogenous shrinkage is induced as the microstructure is
constantly changing in response to the progress of the
hydration reaction. It was not until recently that reliable
4. Numerical models for simulation and
analysis of creep and shrinkage behaviors
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in a very precise way, as well as representation of the
growth behavior of void structures, the modeling results
can also be used to simulate the strength development
process and shrinkage.
Breugel (1992) developed a meso-model for numerical analysis that directly represents the cement particles,
considering the random distribution of particles of various sizes. Among the group of cement particles whose
arrangements depend on the w/c and particle size distributions, Breugel isolated a unit space around a larger
cement particle, which is the core of the hydration reaction. He considered that a hydration product is formed
and expanded within the unit space, which then takes in
smaller particles along with their hydration products,
creates hydration clusters and consolidates them. The
cross-linked particles represent the level of consolidation
inside the cement paste, which has close correlation with
the stress transfer mechanism, such as the development
of strength and elastic moduli. Lokhorst & Breugel
(1997) expanded this model to represent the change in
the cement paste composition during the hydration
process (Fig. 3) and managed to describe the behavior of
early age creep. Later, Navi et al. (2002) further developed Breugel’s hydration model into a three-dimensional
system to discuss void structures and stiffness changes,
as well as the development of thermal stress and the
potential risk of crack initiation in a manner that more
closely reflects reality.
Several rheological models can be cited as examples
of macro-models, in which material properties influencing the creep behavior are associated to elastic
(spring) and viscous (dashpot) elements placed together
in a series and/or parallel coupling. In most cases, such
models give a phenomenological description of the response of the concrete based on empirical analyses, but
say nothing about the actual mechanism of creep. The
age-dependent aspects of basic creep is mathematically
handled by considering the material parameters involved
in the creep model as empirical functions of the age. On
the other hand, the experimental data on creep characteristics is substantially controversial and such predictive
models may introduce substantial inaccuracies. Pioneering theories to model creep taking into account micromechanics of the solidifying process, associated to the
1-r
r
q
p
α + ∆α
σ
Burgers
1-p-q
α
cement hydration reaction, were independently proposed
by Bažant (1977) and Kawasumi et al. (1982). Hence, it
was obvious that the age-dependency of overall macroscopic creep was attributable to changes in the microstructure composition. Bažant & Prasannan (1989) succeeded later in simplifying the mathematical treatment of
age effects on creep by considering the progress of hydration reaction not as a process of change in the material
properties of hydration products themselves, but as a
production/accumulation process of individual layer
materials with age-independent characteristics. The basic
hypothesis illustrated by this model is that the volume
fractions of the volume dv(t) solidified at various times
are all subjected to a same strain εv(t). The most significant advantage in this solidification theory is that
load-bearing matter are age-independent. Adopting the
concept of a unit element represented by the so-called
Zener model, in which an elastic spring and the Voigt
(Kelvin) model are connected in series, Mabrouk et al.
(2002) proposed a parallel spring-dashpot model, where
the number of unit elements is increased in accordance
with the progress of hydration. The parameters of this
dashpot were determined based on a pore structure that
was presumed using the hydration reaction model by
Maekawa et al. (1999).
On the other hand, using Burger’s model, in which the
Maxwell and Voigt models are connected in series, Nakamura et al. (2002) simulated the rapid change in material properties in accordance with the progress of the
early-age hydration reaction, on the assumption that each
parameter of the spring and dashpot elements changes
with age. One of the special characteristics of this model
is that it allows adjusting each model component’s function to the actual creep behavior of early age concrete
(Fig. 4). In specific terms, Maxwell’s spring element and
Maxwell’s dashpot element bear the reversible instant
elastic deformation and irreversible delayed elastic deformation, respectively. The reversible delayed elastic
deformation is born by the Voigt model, in which the
spring and dashpot elements are connected in series.
Thus, it is possible to quantify each model parameter by
performing inverse-analysis on experimental results
(Hagihara et al. 2002).
Recent advances in restrained shrinkage testing has
Unhydrated cement
Cement gel
Air + water
Fig. 3 Meso-level modeling of cement hydration (Lokhorst and Breugel 1997 © by Elsevier - reprinted with permission).
Maxwell
εc
εd
α: constant
Voigt
εv
t
ε
εd
EV(t)
EM(t) ηM(t)
εv
η V(t)
Elastic Creep strain
strain
t0
εc
t1
t
Fig. 4 Schematic representation of Burgers model (Nakamura et al. 2002).
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H. Mihashi and J. P. de B. Leite / Journal of Advanced Concrete Technology Vol. 2, No. 2, 141-154, 2004
made more fashionable to experimentally determine the
effects on early age cracking behavior. Little work has
been performed to theoretically predict the age at first
cracking. Consideration is given here to some works as
examples of different approaches. Gilbert (1992) used a
strength-based approach along with the effect of continuous reinforcement to investigate the behavior of
concrete containing steel reinforcement. Strength of
materials approach has been widely used, but it has clear
limitations since it cannot account for energy absorbing
mechanisms such as fiber reinforcement. Several studies
have been conducted to investigate shrinkage-cracking
behavior using finite element modeling (Thelanderson et
al. 1989, Wittman et al. 2002) to simulate the behavior of
slabs and rings. Gryzbowski & Shah (1989) proposed a
model based on damage mechanics and found a favorably comparison between the experiments behavior and
the simulations. However, this approach relies on substantial information on material parameters and the implementation of the model is somehow cumbersome.
Weiss et al. (1998, 1999) carried out a series of simulations of ring-type and slab-type specimens undergoing
restrained shrinkage to evaluate the potential of cracking.
A fracture mechanics approach was used to predict failure and the residual stresses were estimated using the
following equation:
⎡ 1
φ(t , t ') ⎤
dε T (t , t ') = dσ (t ') ⎢
+
⎥ + dε shrinkage (t ')
E
(
t
')
E28d ⎦
⎣
(2)
where dεT(t,t’) is the total differential strain at an age t,
E(t’) is the elastic modulus and dσ(t’) is the acting stress
at the time of loading t’, E28d is the elastic modulus at 28
days, ø(t, t’) is the creep coefficient, and dεshrinkage(t’) is
the sum of autogenous shrinkage, drying shrinkage and
thermal shrinkage at t’, assuming absence of restraint.
Thereafter, assuming an effective restraint level λ,
Equation (2) can be rearranged as follows.
⎡ 1
φ(t , t ') ⎤
d σ(t ') ⎢
+
⎥ = λ ⋅ d ε shrinkage (t ')
E
(
t
')
E28d ⎦
⎣
(3)
with
λ = ⎡⎣dε T (t , t ') − dε shrinkage (t ') ⎤⎦ / dε shrinkage (t ') (0≤λ≤1)
concrete is extremely complex, it can be simulated by
numerical analysis when its mechanism is described by a
consistent analytical model and pertinent constitutive
equations are established. Thus, simulating shrinkage
behavior through numerical analysis is extremely important in that it can shed light on what factors have a
more immediate impact on the development of shrinkage
cracking and make it easier to develop fundamental crack
control measures, providing that the analytical model
properly represents the actual mechanism and that the
material property values used in the analysis more or less
represent reality. A flowchart outlining requirements for
analysis of shrinkage-crack behavior of early age concrete is presented in Fig. 5. Noted that temperature effects are not included in the flowchart, and hence when
analyzing concrete members in which the rise in hydration heat cannot be neglected, such as high-strength
concrete members, the changes in temperature distributions and their effects must be introduced onto the material property under consideration (AIJ 2003).
In analyzing the behavior of cracking induced by
autogenous or drying shrinkage, it is necessary to calculate the stress at appropriate time intervals while
judging whether the calculated stress satisfies the crack
initiation or transmission conditions. However, to calculate such shrinkage stresses it is necessary primarily to
quantitatively define the driving forces, which cause
them. Hence as mentioned before, such stresses are resulting from the inhibition of free shrinkage deformation
under certain restraining conditions working on the
concrete member. On the other hand, shrinkage is induced by moisture gradients resulting by water movements towards the surface. Therefore, to calculate such
stresses is necessary accurate knowledge of the moisture
content acting at different times or the rate of moisture
diffusion and moisture distribution along the concrete
element.
Wittmann et al. (2002) performed finite element
analyses on drying shrinkage cracking of ring-restrained
(4)
Equation (3) above though relatively simples, casts
perfectly the complexity of problems involved in
shrinkage cracking of early-age concrete.
5. Analysis of shrinkage-cracking behavior
of early age concrete
Analytical models are essential to characterize the iteration between tensile creep and shrinkage, since a technique for direct experimental measurement is not yet
available. Though the deformation behavior of early age
Setting initial conditions
Modeling of hydration reaction
and microstructure. Clarification
of boundary (restraint) conditions.
Calculation of water content
distributions inside the member
section (Water movement analysis
including self-desiccation)
Non-linear water diffusion
theory of porous media.
Quantification of the
relationship between water
content and diffusion coefficient.
Calculation of unrestrained
shrinkage strain distributions
inside the member section
Quantification of the relationship
between the shrinkage strain and
water content
Calculation of restrained
shrinkage and stress
distributions
Tensile creep characteristics
and elastic modulus of early
age concrete
Crack analysis
Crack initiation-propagation
conditions / tensile softening
Fig. 5 Flowchart of numerical analysis of shrinkage cracking.
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Steel ring
508 mm
Radial drying
1.0
Crack opening (mm)
Diffusion coeff.(cm2/d)
11 mm
Mortar
0.8
0.6
0.4
0.2
0
0.5
D=α0 •exp(b.h)
D=α0/2•exp(b.h)
D=α0/4•exp(b.h)
0.6
0.7
1.0
0.8
0.6
0.4
=α
0
20
0
(b
)
.h
0
D=
0.2
0.9 1.0
0.8
D
xp
•e
ex
/ 2•
α0
α
D=
p(
b .h
/4 •
0
ex
)
p(b
80
60
40
.h)
100
Humidity (-)
Drying time (d)
Fig. 7 Water diffusion and crack propagation (Wittmann
et al. 2002).
46 mm
α ( h) =
d ε ∞ ( h)
dh
Figure 8 then shows that the drier the concrete, the
larger the shrinkage strain. It also demonstrates, by referring to a maximum amplitude α0, that the peak value
of the shrinkage strain coefficient α(h) exert substantial
influence on shrinkage-cracking behavior. Finally, α(h)
was set alternatively to two amplitude levels (α0 and α0/2)
while the elastic modulus E was also varied at three different values (15, 25 and 35 GPa). It was reported that as
the elastic modulus increased, easier the cracking occurred and also greater was the rate in which the crack
width increased. This tendency even was more pronounced when α(h) was set to the lower amplitude α0/2.
Furthermore, it was found that changing the crack resistance performance (tensile softening curve and fracture
energy GF) delayed the development of visible cracking
and restricted the tendency of the crack width to increase.
In addition, it was demonstrated that for α(h) = α0/2, the
development of visible cracking can be relatively controlled by increasing the GF value (Fig. 9). An important
conclusion was drawn from the series of analyses using
the fracture mechanics models, which showed that the
tensile strength of concrete affected the development of
microcracking cracking but had little impact on the
subsequent increase in crack width, i.e. the development
and growth of macrocracking cracking. An important
finding derived from this analytical work is that retaining
α=α0/2
1.5
1.0
0.5
0
0.4
0.6
0.8
0.6
0
2.0
0.8
0.4
α=
α
2.5
/2
α=α 0
0.2
1.0
0
Humidity (-)
α=α0/4
0
20
40
60
80
Drying time (d)
100
Fig. 8 Shrinkage coefficient and crack propagation
(Wittmann et al. 2002).
5
4
3
(5)
α=α0
Crack opening (mm)
specimens (Fig. 6) to study the effect of material properties on the shrinkage behavior. First analyses to investigate the influence of the moisture diffusivity on the
cracking development/growth showed that the diffusion
coefficient of concrete plays an important role in the
crack formation. Figure 7 shows that the faster is the rate
of water evaporation from the concrete, earlier the crack
initiates and larger becomes the crack width. Subsequently, the influence of the moisture-dependent coefficient of shrinkage α(h), given as a first derivative of the
final curve with respect to the humidity potential h, was
investigated with respect to the risk of cracking.
3.0
G 11 =350 N/m
2
G10=97.5 N/m
1
0
0
0.1
0.2
0.3
0.4
0.5
Crack opening (mm)
Fig. 6 Specimen of the ring-restrained shrinkage cracking
(Wittmann et al. 2002).
Coeff. shrinkage (10 -3)
200 mm
Crack opening (mm)
0.8
0.6
:α
G 11
=α 0
G 10:α=α0/2
0.4
0.2
G11:α=α0/2
0
0
20
40
60
80
100
Drying time (d)
Fig. 9 Strain softening and crack propagation (Wittmann
et al. 2002).
the rapid rate of water evaporation and associated
shrinkage strain is the most efficient course for controlling shrinkage. This may be more effectively obtained if
crack resistance performance is kept as high as possible
and stiffness as low as possible.
These insights provide many useful pointers regarding
the technology of controlling shrinkage cracking in early
age concrete (JCI 2002, AIJ 2003), as well as laid theoretical and analytical basis to support recently developed
experimental research and optimize newly developed
techniques. For example, shrinkage reducing agent
and/or expansive additive can help restricting the growth
of shrinkage strain and by adding wet lightweight aggregates to high-strength concrete the rate of water
evaporation can be restricted (Schwesinger & Sickert
2002). Also, the inclusion of fibers in concrete can enhance crack resistance performance and assist to control
growth and expansion of cracking (Paillère et al. 1989).
148
H. Mihashi and J. P. de B. Leite / Journal of Advanced Concrete Technology Vol. 2, No. 2, 141-154, 2004
Analytical methods are therefore essential to achieve
optimum reduction of shrinkage rate by selecting mix
parameters and contents/proportions, including types of
cement, aggregates and admixtures, as well as to estimate
effects of member size changes on shrinkage-cracking
development and use of crack-inducing joints on the
reduction of the restraint degree.
6. Recent developments on early age
shrinkage crack testing
Generally speaking, tests on early age concrete can be
categorized into the following four types according to the
purpose of testing (AIJ 2003): 1) tests to obtain physical
property values; 2) tests to understand a behavior under
the actual conditions of the structure/members tested; 3)
tests to draw a relative comparison between characteristics and performance; and 4) tests for quality control and
inspection. Hence, the test method that should be adopted
when trying to control shrinkage cracking of early age
concrete depends on the aim of the test. For the shrinkage
cracking of concrete, the test method that is most widely
used in Japan is the Test Method for Drying Shrinkage
Cracking in Restrained Concrete, which has recently
been designated as JIS-A-1151 according to the Japanese
Industrial Standard (AIJ 2002). For the measurement of
stress induced by volume changes as a result of autogenous shrinkage, a parameter required for the prediction
of crack initiation in high-strength concrete, a revised
test method, the Draft of Stress Test Method for Autogenous Shrinkage in Concrete (JCI 2002). These two
methods are both uniaxial restraint type. The first method
uses steel forms to give an external restraint to the concrete specimen (“form type”). On the other hand, the
second method uses deformed bars embedded at the
center of a concrete specimen to provide an internal restraint (“rebar type”). In the first method (form type),
what is actually being measured is the average tensile
stress working on the member section, because restraint
stress is measured with a strain gauge attached to the
parallel side of the restraint device. On the other hand, in
the second method (rebar type), there is a difference
between strain near the rebar at the center, to which a
strain gauge is attached, and strain at the edge of the
specimen. Therefore, a strain gradient is obviously created inside the section. Thus, evaluating the measured
restraint stress based on rebar strain, as the average tensile stress working on the concrete would produce a
major error (Nakamura et al. 2002). In either case, these
testing methods are designed to draw a relative comparison of the crack resistance performance of concrete
but not to obtain physical property values. As described
before, the physical properties of a specimen undergo
great changes with age in accordance with drying and
hydration progress, and there are creep and relaxation
deformations occurring at the same time. Thus, the restraint level changes over time and it is not possible to
accurately evaluate restraint stress and shrinkage stress.
The “Cracking Frame Method”, originally developed
in Germany in the 1960s for thermal stress measurements,
has been employed as method for controlling early age
concrete cracking, particularly thermal cracking. In this
apparatus, though stiff longitudinal bars at the side of the
restraining frame separate the crossheads, the degree of
restraint was still much lower than 100% restraint. The
restraining force is measured by strain gauges attached to
the frame. Also in Germany, Springenschmid et al.
(1985) improved the frame to provide 100% restraint, for
thermal crack control purposes. The new frame, as described in Fig. 10, has been named as “Temperature-Stress Testing Machine” (TSTM). In the new frame
an actuator was attached to an adjustable crosshead to
control the distance between gauge marks at the center of
specimens having the same section to keep the distance
constant (Springenschmid et al. 1994). The length
measurements were performed using deformation
transducers on carbon fiber bars at both sides. Elsewhere,
other researchers have devised testing apparatus based on
the frame with movable crossheads, specifically for early
age concrete. Paillère et al. (1976, 1989) developed alternative solution to control the restraint level, by gripping the ends of the specimen inside of a restraint frame,
with one movable end attached to a air pressure device.
The cracking-test bench was laid horizontally for pouring
the concrete and set vertically after the mould has been
removed. Twin specimens were used, yet one of them
was restrained and the other free to shrink. The idea
behind this test setup was that the stress induced due to
restrained deformation is recorded, while the strain in the
other specimen undergoing free shrinkage is also measured. Hence, creep data can also be obtained when free
shrinkage strain of a specimen having the same mixture
proportions is recorded at the same time. A possible
8
6a
4
5
6b
2
9
7
3
1
6a
6b
7
Specimen: section 150x150, length 1500 mm
Adjustable cross-head
3 Fixed cross-head
4 Stepping motor: accuracy of advancement 1µm
5 Load cell
6 a Measurement of cross-head movement
6 b Length measurement with carbon fiber bars
7 Formwork with heating/cooling system
8 PC for controlling and recording
9 Cryostat for heating/cooling of the formwork
1
2
Fig. 10 Outline of TSTM apparatus (Springenschmid et
al. 1994).
H. Mihashi and J. P. de B. Leite / Journal of Advanced Concrete Technology Vol. 2, No. 2, 141-154, 2004
Total strain
Shrinkage+strain
Elastic strain
εthreshold
Time
(a) Total deformation of the specimen
Stress
Theoretical stress under
permanent full restraint
φσ i
φσ 1
Incremental loading
(b) Applied stress
Time
Fig. 11 Principle of the discretized restrained shrinkage
test (Bissonnette et al. 2001. Reprinted with permission of
The American Ceramic Society, www.ceramics.org. Copyright
2004. All rights reserved).
Degree of restraint: 1.0
Stress (N/mm2)
drawback in this test setup is the fact the test is carried at
vertical position, which induces rupture in the upper part
due to the influence of the self-weight of the specimen.
Bloom & Bentur (1994) modified the test setup, in ways
that allow the test was carried out in the horizontal position. The adjustable end was monitored by displacement
gauge and periodically recovered by applied tensile load
manually. Kovler (1994) developed a system with a
closed-loop computer control, in order to improve accuracy of the measurements. As the shrinkage grows to a
given strain level, the specimen is pulled by force so that
the strain returns to zero (Fig. 11a). At each step when
this is repeated, the stress needed for the forceful deformation is recorded and then plotted onto a time-stress
correlation chart to obtain the history of shrinkage stress
(Fig. 11b). Test methods as such, resetting strains to zero
in stepwise manner, are sometimes referred to as “discretized restrained shrinkage” (DRS) testing (Bissonnette et al. 2001). Owing to such advances, valuable
experimental data on the influence of component materials, mixture proportions and degrees of restraint on
shrinkage stress have been made available. Figure 11
shows the basic concept of shrinkage strain control
adopted for these testing methods.
Figure 12 shows example of results of autogenous
shrinkage testing on early age concrete using such type
of 100% strain control technique. The tendency of
shrinkage stress to increase is shown to be affected at
considerable extent by the restraint level. In the case of
conventional creep testing methods, creep strain is reported to reduce in accordance with the decrease in w/c.
However, the DRS test has been reported to yield quite
different results. In the DRS testing on early age concrete,
it is the mechanism of relaxation, rather than that of creep,
that is at work. It has nonetheless been pointed out by
some researchers that it is necessary to study the creep
149
Degree of restraint: 0.5
Degree of restraint: 0.2
Ordinary portland cement
Age (day)
Fig. 12 Changes in shrinkage stress according to restraint revels (Mizobuchi et al. 2002).
characteristics of early age concrete without being held
captive by knowledge about concrete that has completed
the hydration process, which has been accumulated
through a vast amount of past research (Bissonnette et al.
2001).
7. Criteria of shrinkage-crack initiation
Once shrinkage stress induced by the restraining effect of
drying or autogenous shrinkage deformation has been
predicted, appropriate criteria are necessary to judge
whether the shrinkage stress will lead to crack initiation.
Figure 5 outlines general requirements for criterion of
crack initiation, yet no generally accepted criterion is
currently available. Such a possibility is now within sight,
however, due to advances in accuracy of evaluation
techniques for physical properties, such as the development of TSTM and DRS testing, as well as analytical
techniques for the behavior of highly non-linear shrinkage deformations. Two recently proposed alternative
approaches for crack initiation criteria are worthy to be
mentioned.
Breugel & Lokhorst (2001) performed both shrinkage
crack and direct tensile testing using the TSTM and reported that the tensile stress at time of crack initiation
was approximately 75% of the splitting tensile strength,
regardless of the differences between the two cement
types used (four different mixture proportions) and also
regardless of the degree of hydration of each concrete.
They also reported that the uniaxial tensile strength of the
rectangular column specimen employed in the tests was
approximately 88% of the splitting tensile strength.
Based on these results, and assuming both tensile
strength and stress of a sample of shrinking specimens
described by normal distributions, the variation coefficient V, which is the ratio of standard deviation σ to average value µ, is assumed to be 10% and 8% of the
shrinkage stress and splitting tensile strength, respectively. Assuming R - S = Z, where R is the splitting tensile strength and S is the shrinkage stress, the probability
of failure (cracking), Pf is given as follows.
Pf {Z < 0} = Pf {−β}
where β is the safety performance index given by
(6)
150
(7)
Hence, assuming maintenance of a reliability limit of
5% and imposing safety coefficient γ, defined as ratio
between characteristic values of strength Rchar and stress
Schar, often a standard procedure in engineering problems,
the following equation is obtained:
γ=
Rchar µR − 1.64σ R (1 − 1.64VR ) µ R
=
=
⋅
µS + 1.64σ S (1 + 1.64VS ) µS
Schar
(8)
Therefore, safety coefficient γ of early age concrete
under tensile stress is given by
γ=
f char
σ char
=
(
0.75 f ctmspl 1 − 1.64V f
σ (1 + 1.64Vσ )
)
1.6
1.4
Coefficient of
variation V
V(σ)=10 %
V(f ctm, spl)=8 %
σ<η•fctm, spl
γ (-)
µz
µ − µS
= R
σz
σ R2 + σ S2
Safety factor (-)
β=
H. Mihashi and J. P. de B. Leite / Journal of Advanced Concrete Technology Vol. 2, No. 2, 141-154, 2004
1.2
1.0
0.8
0.6
10-1 10-2 10-3 10-4 10-5
Probability of fracture Pf (-)
0.3
0.4
0.5
0.6
0.7
0.8
Allowable stress
/strength ratio η (-)
Fig. 13 Design graph for the allowable stress/ strength
ratio, safety factor and probability of fracture (Breugel et
al. 2002).
(9)
where fctmspl is the average value of the splitting tensile
strength and the value of 0.75fctmspl is assumed as strength
criterion conforming above mentioned empirical observations that the average stress at the time of shrinkage-crack initiation is 75% of the splitting tensile
strength. The term σ represents the average value of
shrinkage stress. Thus the allowable stress ratio η, which
corresponds to the safety coefficient γ, is given as follows.
σ
f ctmspl
=
0.75 (1 − 1.64Vf )
(1 + 1.64Vσ ) γ
(10)
The diagrams in Fig. 13 represent the relationships
between the safety coefficient γ, failure probability Pf
and allowable stress ratio η. Such diagrams allow the
determination of permissible stress ratio η corresponding
to crack initiation probability Pf associated to the design
requirement for the structure performance. Permissible η
values may also be compared against the values of each
part and member obtained through numerical analysis of
shrinkage stress. If the value estimated in the analysis is
greater than the permissible η value, the probability of
crack initiation is higher than the pre-determined value
and thus changes are necessary to reduce the risk of inducing shrinkage stress.
Alternatively,
using
the
aforementioned
ring-restrained specimen (Fig. 6), Martinolla (2001)
performed a parametric study and proved that crack initiation criteria could be represented by three-dimensional
functions, the parameters being the shrinkage strain coefficient α(h), fracture energy GF and elastic modulus E
(Fig. 14). Thus, performing tests in advance to obtain
these three material properties of the concrete to be used
makes it possible to evaluate the possibility of crack
initiation. When the concrete is found to be in the crack
initiation range, the material design need pertinent
changes to make the material fall into non-cracking range
(Fig. 15).
Fig. 14 Risk of crack formation as a function of fracture
energy, coefficient of shrinkage and Young's modulus
(Wittmann et al. 2002).
Mean coeffi. of shrinkage α (‰, 1/h)
η=
2.8
2.4
Cracking
2.0
A1
1.6
1.2
Pa
5G
1
E = 25G Pa
E=
A3 = 35GPa
E
No cracking
0.4
1.0
0.8
0.4
0.2
0
0
1.2
0.6
A2
0.8
1.4
100
200
300
400
500
0
Fracture energy (N/m)
Fig. 15 Crack control by materials design (Martinola
2001).
H. Mihashi and J. P. de B. Leite / Journal of Advanced Concrete Technology Vol. 2, No. 2, 141-154, 2004
8. Smart materials for preventing shrinkage
cracking
Smart materials have been thoroughly developed in this
decade in various fields including civil engineering. In a
quite loose definition, smart materials are equipped with
functions such as sensing (detecting presence of matter
or problem), processing (judging which and/or when an
action should be taken) and actuating (putting planned
operations into action). According to such concepts,
some concrete composites have been designed for
self-controlling shrinkage problems and prevent cracking
in early age concrete. An example of “smart” concrete
was developed by Mihashi et al. (2002) for controlling
the hydration heat, in order to prevent problems of
thermal cracking (Fig. 16). Paraffin microcapsule containing a hydration retarder agent was mixed in the concrete composition. Once the temperature of concrete
rises up to a certain value, which is specified by using
types of paraffin with different melting temperatures, the
microcapsules melt releasing the hydration retarder agent.
Hence, the temperature of concrete may be controlled
under the specified value and thermal stress may be neglected. The new material proved to be efficient in controlling the temperature under a certain level suitable for
the steady hydration and to mitigate the rapid increase
and decrease of temperature in concrete. Note that the
outcome is quite different from techniques in which
hydration retarder products are directly introduced in the
mixture. In the latter though the hydration heat is reduced,
depending on the size of the element, thermal gradients
may still arise from the core to the surface. The results
obtained in the experiments using former controlling
technology large specimens prove that it can be applicable to practical uses in concrete technology. It was suggested also that if microcapsules made with different
1
Concrete
Hydration Retarder Agent (HRA)
Capsule
Capsule detects
hydration heat
(Sensing)
2
Capsule melts at a
designed temperature
(Processing)
3
Capsule releases the HRA
to delay hydration process
(Actuating)
Fig. 16 Schematic description of the smart concrete
mechanism.
151
types of paraffin are blended, the melting temperatures
may be varied to further moderate the increasing and
decreasing rates of temperature. A study on the effects of
using a cocktail of microcapsules with different melting
temperatures is currently under development.
Dhir et al. (1994) investigated the development of
another new material also obtained through chemical
intervention in the hydration process, which shows
promising capabilities to control drying shrinkage. The
concept involves tailoring the concrete composite by
adding water-soluble chemicals during mixing to reduce
water evaporation as the concrete is exposed to
air-drying. In this way, the “self-curing” concrete would
dispense any externally applied curing. The researchers
tested six different chemicals, five of which were synthetic water-soluble polymers and one was a natural
chemical and showed that some chemicals have a positive self-curing effect. The research was conducted on
ordinary concrete; however, the concept may warrant
further study to determine its applicability to HPC. Dhir
et al. (1996) performed additional research on the influence of microstructure on the physical properties of
self-curing concrete. Standard compressive tests as well
as initial surface absorption tests (ISAT) were carried out
on concrete specimens of the new material, whose results
suggested the chemicals produce some alterations in the
microstructure. Results revealed that the new material
shows significant improvement in surface quality and
compressive strength when compared with air-stored
concrete. Although further investigation is required on
the feasibility of formulating self-curing concrete, particularly as it relates to high-performance concrete, these
studies appear to offer encouraging results.
Another material tailoring technique that showed
promising results to control autogenous shrinkage consists of the introduction of soaked lightweight aggregate
to enhance the curing of high-strength concrete. Some
research in Germany focused on the replacement of a
portion of normal weight aggregate by lightweight aggregate to provide a supply of water within the concrete
to sustain the curing process (Weber & Reinhardt 1996).
This technique has proven to be effective in offsetting
some of the effects of self-desiccation in low water-cement ratio concrete. The concept is relatively simple - to store water for curing inside the concrete by using
lightweight aggregate with high moisture content. This
research investigated the trade off between the benefits
of additional moist curing versus the potential strength
loss from using lightweight aggregate. The insensitivity
of the high-strength concrete with lightweight aggregate
to the type of curing was a significant benefit when
compared with the concrete with normal weight aggregate. This can be attributed to the availability of internal
moisture from the lightweight aggregate for the continuation of curing, which was independent of the external curing method. Within the lightweight aggregate
concrete, curing can continue even after the surface becomes impervious, thus reducing the need for additional
152
H. Mihashi and J. P. de B. Leite / Journal of Advanced Concrete Technology Vol. 2, No. 2, 141-154, 2004
moist curing. Similar research was developed by
Schwesinger & Sickert (2002) using a lightweight aggregate (Liapor 9.5) consisting of expanded clay with a
spherical geometry and a pore volume of approximately
55 %. The spherical shape and the relatively dense outer
shell of the lightweight aggregate make reliable its use
for the production of High-Performance Concrete. Thus,
the internal moisture conditions were able to reduce or
eliminate autogenous shrinkage.
9. Concluding remarks
As many complex and interacting factors affect shrinkage cracking of early age concrete, experiments used to
yield contradicting results. Consequently, developing a
crack control measure used not to be seen as feasible task.
However, remarkable advances in research have gradually shed light on the dominant factors involved in these
phenomena. It is now then possible to, at certain extent,
properly evaluate the physical properties that determine
the phenomena in question and predict shrinkage behavior by performing numerical analysis using the
physical properties obtained. Further advances in research, as well as broad application and deployment of
the findings to actual design and construction are in our
doorstep.
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