dokuz eylül Üniversitesi Đnşaat mühendisli i...
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Doç. Dr. Halit YAZICI
http://kisi.deu.edu.tr/halit.yazici/
DIMENSIONAL STABILITY of DIMENSIONAL STABILITY of
CONCRETECONCRETE
Dokuz Eylül Üniversitesi Đnşaat Mühendisliği Bölümü
REFERENCE BOOKS
� P. Kumar Mehta, Paulo J. M. Monteiro,
Concrete Microstructure, Properties, and
Materials, third edition, McGraw-Hill, 2006
� Neville, A.M., Properties of Concrete,
Longman Group Limited, Fourth Edition,
1995.
� Mindness, S., and Young, J.F., Concrete,
Prentice Hall, Inc., Englewood Cliffs, 1981.
� Concrete shows elastic as well as
inelastic strains on loading, and
shrinkage strains on drying, cooling,
carbonation etc. When restrained,
shrinkage strains result in complex stress
patterns that often lead to cracking.
� In this course the nonlinearity in the stress-
strain relation of concrete, various types of
elastic moduli and the methods of their
assessment are discussed. Explanations are
provided as why and how aggregate, cement
paste, transition zone, and testing parameters
affect the modulus of elasticity.
� The stresses resulting from drying shrinkageand viscoelastic strains in concrete are not same; however, with both phenomena theunderlying causes and the controlling factorsare generally common. Major parameters thataffect drying shrinkage and creep as well as various rheological models and the methodsof predicting creep and shrinkage aredescribed.
� Thermal shrinkage is of great importance in mass concrete. Its magnitude can be controlled by the coefficient of thermalexpansion of aggregate, the cement contentand type, and the temperature of concrete-making materials. The concepts of extensibility, tensile strain capacity and theirsignificance to concrete cracking areintroduced.
IV. COURSE OUTLINE:
� Types of Deformations and Their Significance
� Elastic Behavior
� Stress-Strain Relations
� Expressions for Stress-Strain Relations
� 2. Modulus of Elasticity of Concrete
� 2.1. Determination of Static Elastic Modulus
� 2.2. Expressions for Modulus of Elasticity
� 2.2.1. ACI Building Code Model
� 2.2.2. CEB-FIP Model Code
� 2.3. Dynamic Modulus of Elasticity
� 2.4. Poisson’s Ratio
� 2.5. Factors Affecting Modulus of Elasticity
� 2.5.1. Aggregate
� 2.5.2. Cement paste matrix
� 2.5.3. Transition zone
� 2.5.4. Testing parameters
� 3. Load Independent Volume Changes of
Concrete
� 3.1. Early Volume Changes
� 3.2. Autogenous Shrinkage
� 3.3. Swelling
� 3.4. Carbonation Shrinkage
� 4. Thermal Shrinkage
� 4.1. Factors Affecting Thermal Stress
� 4.1.1. Degree of restraint
� 4.1.2. Temperature change
� 4.2. Drying Shrinkage and Creep
� 4.2.1. Mechanism and causes
� 4.2.2. Effects of loading and humidityconditions
� 4.2.3. Reversibility
� 5. Factors Affecting Drying Shrinkage and
Creep
� 5.1. Materials and Mix Proportions
� 5.2. Time and Humidity
� 5.3. Geometry of Concrete Element
� 5.4. Additional Factors Affecting Creep
� 6. Temperature Effects in Concrete
� 6.1. Influence of Early Temperature on Strength of Concrete
� 6.2. Thermal Properties of Concrete
� 6.2.1. Thermal conductivity
� 6.2.2. Thermal diffusivity
� 6.2.3. Specific heat
� 6.2.4. Coefficient of thermalexpansion
� 7. Strength of Concrete at High Temperatures
and Resistance to Fire
� 7.1. Modulus of Elasticity at High
Temperature
� 7.2. Behavior of Concrete in Fire
� 7.3. Temperature Rise in Mass Concrete
� 8. Extensibility and Cracking
� 8.1. Cracking of Concrete
� 8.2. Extensibility and Cracking
� 8.3. Thermal Stress and Cracking
� 9. Mid term examination
� 10. Viscoelasticity
� 10.1. Rheological Models
� 10.2. Basic Rheological Models
� 12. Mathematical Expressions for Creep
� 13. Methods of Predicting Creep and
Shrinkage
� 13.1. CEB 1990 Method
� 13.2. CEB 1978 Method
� 13.3. ACI Method
� 14. Fatique and Impact Resistance
� 14.1. Fatique Behavior
� 14.2. Impact Resistance
� WEEK 15. Mid term examination
� V. GRADING� In additon to two mid term examinations, term
projects will be prepared by students. The resultinggrade will be determined as follows:
� 1. mid term examination - 15 %
� 2. mid term examination - 15 %
� Term project - 20 %
� Final examination - 50 %
� Result 100 %
TYPES of DEFORMATIONS and
THEIR SIGNIFICANCE
� Concrete shows elastic as well as inelastic
strains on loading, and shrinkage strains
on drying or cooling. When restrained,
shrinkage strains result in complex stress
patterns that often lead to cracking.
� In this chapter, causes of nonlinearity in the
stress-strain relation of concrete are discussed,
and different types of elastic moduli and the
methods of determining them are described.
Explanations are provided as to why and how
the aggregate, the cement paste, the interfacial
transition zone, and the testing parameters
affect the modulus of elasticity.
� The stress effects resulting from the drying
shrinkage and the viscoelastic strains in
concrete are not the same; however, with both
phenomena the underlying causes and the
controlling factors have much in common.
� Important parameters that influence the
drying shrinkage and creep are discussed,
such as aggregate content, stiffness, water
content, cement content, time of exposure,
relative humidity, and size and shape of the
concrete member.
� Thermal shrinkage is of great importance in massive concrete elements. Its magnitude can be controlled by controlling the coefficient of thermal expansion of aggregate, cementcontent and type, and temperature of concrete-making materials. The concepts of extensibility, tensile strain capacity, and theirsignificance to concrete cracking are alsodiscussed.
Types of Deformations and theirSignificance
� Deformations in concrete, which often lead to
cracking, occur as a result of the material’s
response to external load and environment.
When freshly hardened concrete (whether
loaded or unloaded) is exposed to the ambient
temperature and humidity, it generally
undergoes thermal shrinkage (shrinkage strain
associated with
� cooling)∗ and drying shrinkage (shrinkagestrain associated with the moisture loss). Which one of the two shrinkage strains will be dominant under a given condition depends, among other factors, on the size of themember, characteristics of concrete-makingmaterials, and mix proportions. Generally, with massive structures (e.g., nearly 1 m ormore in thickness), the drying shrinkage is lessimportant a factor than the thermal shrinkage.
� It should be noted that concrete members arealmost always under restraint, sometimes fromsubgrade friction and end members, but usuallyfrom reinforcing steel and from differentialstrains that develop between the exterior and theinterior of concrete. When the shrinkage strain in an elastic material is fully restrained, it results in elastic tensile stress; the magnitude of theinduced stress s is determined by the product of the strain e and the elastic modulus E of thematerial (σ=ε* E).
� The elastic modulus of concrete is also dependent on
the characteristics of concrete-making materials and
mix proportions, but not necessarily to the same
degree as the shrinkage strains. The material is
expected to crack when a combination of the elastic
modulus and the shrinkage strain induces a stress level
that exceeds its tensile strength (Fig. 4-1). Given the
low tensile strength of concrete, this does happen in
practice but, fortunately, the magnitude of the stress is
not as high as predicted by the elastic model.
� Influence of shrinkage and creep on concrete cracking.� Under restraining conditions in concrete, the interplay between the elastic tensile
stresses induced by shrinkage strains and the stress relief due to the viscoelasticbehavior is at the heart of deformations and cracking in most structures.
� To understand the reason why a concrete element
may not crack at all or may crack but not soon
after exposure to the environment, we have to
consider how concrete would respond to sustained
stress or to sustained strain.The phenomenon of a
gradual increase in strain with time under a given
level of sustained stress is called creep. The
phenomenon of gradual decrease in stress with
time under a given level of sustained strain is
called stress relaxation.
� Both manifestations are typical of viscoelastic
materials. When a concrete element is restrained, the
viscoelasticity of concrete will manifest into a
progressive decrease of stress with time (Fig. 4-1,
curve b). Thus, under the restraining conditions
present in concrete, the interplay between the elastic
tensile stresses induced by shrinkage strains and the
stress relief due to viscoelastic behavior is at the
heart of deformations and cracking in most
structures.
� In practice, the stress-strain relations in concrete are much more complex thanindicated by Figure. First, concrete is not a truly elastic material; second, neither thestrains nor the restraints are uniformthroughout a concrete member; therefore, theresulting stress distributions tend to vary frompoint to point. Nevertheless, it is important toknow the elastic, drying shrinkage, thermalshrinkage, and viscoelastic properties of concrete and the factors affecting them.
Elastic Behavior� The elastic characteristics of a material are a
measure of its stiffness. In spite of thenonlinear behavior of concrete, an estimate of the elastic modulus (the ratio between theapplied stress and instantaneous strain withinan assumed proportional limit) is necessary fordetermining the stresses induced by strainsassociated with environmental effects. It is alsoneeded for computing the design stresses underload in simple elements, and moments anddeflections in complicated structures.
� Typical stress-strain behaviors of cement paste, aggregate, and concrete.� The properties of complex composite materials need not to be equal to the sum of
the properties of their components. Thus both hydrated cement paste andaggregates show linear elastic properties, whereas concrete does not.
Nonlinearity of the stress-strainrelationship
� From typical σ - ε curves for aggregate,
hardened cement paste, and concrete loaded
in uniaxial compression, it becomes
immediately apparent that unlike the
aggregate and the cement paste, concrete is
not an elastic material.
� Neither is the strain on instantaneous loading
of a concrete specimen found to be directly
proportional to the applied stress, nor is it
fully recovered upon unloading. The cause for
nonlinearity of the stress-strain relationship is
explained from studies on progressive
microcracking of concrete under load by
researchers
� In regard to the relationship between stress level
(expressed as percent of the ultimate load) and
microcracking in concrete, Figure shows that
concrete behavior can be divided into four
distinct stages.
� The progress of internal microcracking in concretegoes through various stages, which depend on thelevel of applied stress.
� Under normal atmospheric exposure
conditions (when a concrete element is
subjected to drying or thermal shrinkage
effects) due to the differences in their elastic
moduli differential strains are set up between
the matrix and the coarse aggregate, causing
cracks in the interfacial transition zone.
� Therefore, even before the application an
external load, microcracks already exist in the
interfacial transition zone between the matrix
mortar and coarse aggregate. The number and
width of these cracks in a concrete specimen
depend, among other factors, on the bleeding
characteristics, and the curing history of
concrete.
� Below about 30 percent of the ultimate load,
the interfacial transition zone cracks remain
stable; therefore, the σ-ε curve remains linear.
This is Stage 1 in Figure.
� Above 30 percent of the ultimate load, with
increasing stress, the interfacial transition zone
microcracks begin to increase in length, width,
and number. Thus, the σ/ε ratio increases and the
curve begins to deviate appreciably from a
straight line. However, until about 50 percent of
the ultimate stress, a stable system of
microcracks appears to exist in the interfacial
transition zone.
� This is Stage 2 and at this stage the matrix
cracking is negligible. At 50 to 60 percent of the
ultimate load, cracks begin to form in the matrix.
With further increase in stress level up to about
75 percent of the ultimate load, not only does the
crack system in the interfacial transition zone
becomes unstable but also the proliferation and
propagation of cracks in the matrix increases,
causing the σ-ε curve to bend considerably
toward the horizontal.
� This is Stage 3. At 75 to 80 percent of the
ultimate load, the rate of strain energy release
seems to reach the critical level necessary for
spontaneous crack growth under sustained stress,
and the material strains to failure.
� In short, above 75 percent of the ultimate
load, with increasing stress very high strains
are developed, indicating that the crack
system is becoming continuous due to the
rapid propagation of cracks in both the matrix
and the interfacial transition zone. This is the
final stage (Stage 4).
Types of elastic moduli
� The static modulus of elasticity for a material
under tension or compression is given by the
slope of the σ-ε curve for concrete under
uniaxial loading. Since the curve for concrete
is nonlinear, three methods for computing the
modulus are used. This has given rise to the
three types of elastic moduli, as illustrated by
Fig. 4-4:
� 1. The tangent modulus is given by the slope
of a line drawn tangent to the stress-strain
curve at any point on the curve.
� 2. The secant modulus is given by the slope of
a line drawn from the origin to a point on the
curve corresponding to a 40 percent stress of
the failure load.
� 3. The chord modulus is given by the slope of a line
drawn between two points on the stress-strain curve.
Compared to the secant modulus, instead of the
origin the line is drawn from a point representing a
longitudinal strain of 50 µm/m to the point that
corresponds to 40 percent of the ultimate load.
Shifting the base line by 50 microstrain is
recommended to correct for the slight concavity that
is often observed at the beginning of the stress-strain
curve.
� The dynamic modulus of elasticity, corresponding to a very small instantaneousstrain, is approximately given by the initialtangent modulus, which is the tangent modulusfor a line drawn at the origin. It is generally 20, 30, and 40 percent higher than the staticmodulus of elasticity for high-, medium-, andlow-strength concretes, respectively. For stressanalysis of structures subjected to earthquakeor impact loading it is more appropriate to usethe dynamic modulus of elasticity, which can be determined more accurately by a sonic test.
� The flexural modulus of elasticity may be
determined from the deflection test on a
loaded beam. For a beam simply supported at
the ends and loaded at midspan, ignoring the
shear deflection, the approximate value of the
modulus is calculated from:
� where ∆ = midspan deflection due to load P
� L = span length
� I = moment of inertia
� The flexural modulus is commonly used for
design and analysis of pavements
� ASTM C 469 describes a standard test method for
measurement of the static modulus of elasticity (the
chord modulus) and Poisson’s ratio of 150 by 300 mm
concrete cylinders loaded in longitudinal compression at
a constant loading rate within the range 0.24 ± 0.03
MPa/s. Normally, the deformations are measured by a
linear variable differential transformer. Typical σ − ε
curves, with sample computations for the secant elastic
moduli of the three concrete mixtures are shown in Fig.
4-5.
� The elastic modulus values used in concrete
design computations are usually estimated
from empirical expressions that assume direct
dependence of the elastic modulus on the
strength and density of concrete.
� As a first approximation this makes sense
because the stress-strain behavior of the three
components of concrete, namely the
aggregate, the cement paste matrix, and the
interfacial transition zone, would indeed be
determined by their individual strengths,
which in turn are related to the ultimate
strength of the concrete.
Furthermore, it may be noted that the elastic
modulus of the aggregate (which controls the
aggregate’s ability to restrain volume changes
in the matrix) is directly related to its
porosity, and the measurement of the unit
weight of concrete happens to be the easiest
way of obtaining an estimate of the aggregate
porosity.
� From the following discussion of the factors
affecting the modulus of elasticity of concrete, it will
be apparent that the computed values shown in Table
4-2, which are based on strength and density of
concrete, should be treated as approximate only.
This is because the transition-zone characteristics
and the moisture state of the specimen at the time of
testing do not have a similar effect on the strength
and elastic modulus.
Poisson’s ratio
� For a material subjected to simple axial load,
the ratio of the lateral strain to axial strain
within the elastic range is called Poisson’s
ratio. Poisson’s ratio is not generally needed
for most concrete design computations;
however, it is needed for structural analysis of
tunnels, arch dams, and other statically
indeterminate structures.
� With concrete the values of Poisson’s ratio generally
vary between 0.15 and 0.20. There appears to be no
consistent relationship between Poisson’s ratio and
concrete characteristics such as water-cement ratio,
curing age, and aggregate gradation. However,
Poisson’s ratio is generally lower in high strength
concrete, and higher for saturated concrete and for
dynamically loaded concrete.
Factors affecting modulus of elasticity
� In homogeneous materials a direct relationship
exists between density and modulus of elasticity.
In heterogeneous, multiphase materials such as
concrete, the volume fraction, the density and the
modulus of elasticity of the principal
constituents, and the characteristics of the
interfacial transition zone, determine the elastic
behavior of the composite.
� Since density is oppositely related to porosity, obviously the factors that affect the porosity of aggregate, cement paste matrix, and the interfacial transition zone would be important. For concrete, the direct relation between strength and elastic modulus arises from the fact that both are affected by the porosity of the constituent phases, although not to the same degree.
� Aggregate. Among the coarse aggregate
characteristics that affect the elastic modulus of
concrete, porosity seems to be the most important.
This is because aggregate porosity determines its
stiffness, which in turn controls the ability of
aggregate to restrain the matrix strain. Dense
aggregates have a high elastic modulus.
� In general, the larger the amount of coarse
aggregate with a high elastic modulus in a
concrete mixture, the greater would be the
modulus of elasticity of concrete. Because
with low- or medium-strength concrete, the
strength is not affected by normal variations in
the aggregate porosity, this shows that all
variables may not control the strength and the
elastic modulus in the same way.
� Rock core tests have shown that the elastic
modulus of natural aggregates of low porosity
such as granite, trap rock, and basalt is in the
range 70 to 140 GPa while with sandstones,
limestones, and gravels of the porous
� Rock core tests have shown that the elastic
modulus of natural aggregates of low porosity
such as granite, trap rock, and basalt is in the
range 70 to 140 GPa, while with sandstones,
limestones, and gravels of the porous
� variety it varies from 21 to 49 GPa. Lightweight aggregates are highly porous; depending on the porosity, the elastic modulus of a lightweight aggregate may be as low as 7 GPa or as high as 28 GPa. Generally, the elastic modulus of lightweight-aggregate concrete ranges from 14 to 21 GPa, which is between 50 and 75 percent of the modulus for normal-weight concrete of the same strength.
� Other properties of aggregate also influence
the modulus of elasticity of concrete. For
example, aggregate size, shape, surface
texture, grading, and mineralogical
composition can influence the microcracking
in the interfacial transition zone and thus
affect the shape of the stress-strain curve.
� Cement paste matrix. The elastic modulus of the
cement paste matrix is determined by its porosity.
The factors controlling the porosity of the cement
paste matrix, such as water-cement ratio, air content,
mineral admixtures, and degree of cement hydration,
are listed in Fig. 3-12. Values in the range 7 to 28
GPa as the elastic moduli of hydrated portland
cement pastes of varying porosity have been reported.
It should be noted that these values are similar to the
elastic moduli of lightweight aggregates.
� Transition zone. In general, capillary voids, microcracks, and oriented calcium hydroxide crystals are relatively more common in the interfacial transition zone than in the bulk matrix; therefore, they play an important part in determining the stress-strain relations in concrete. The factors controlling the porosity of the interfacial transition zone are listed in Fig. 3-12.
� It has been reported that the strength and elastic
modulus of concrete are not influenced to the
same degree by curing age. With different
concrete mixtures of varying strength, it was
found that at later ages (i.e., 3 months to 1
year) the elastic modulus increased at a higher
rate than the compressive strength (Fig. 4-6).
� It is possible that the beneficial effect of
improvement in the density of the interfacial
transition zone, as a result of slow chemical
interaction between the alkaline cement paste
and aggregate, is more pronounced for the
stressstrain relationship than for the
compressive strength of concrete.
� Testing parameters. It is observed that regardless
of mix proportions or curing age, concrete
specimens that are tested in wet conditions show
about 15 percent higher elastic modulus than the
corresponding specimens tested in a dry condition.
Interestingly, the compressive strength of the
specimen behaves in the opposite manner; that is, the
strength is higher by about 15 percent when the
specimens are tested in dry condition.
� It seems that drying of concrete produces a different effect on the cement paste matrix than on the interfacial transition zone; while the former gains in strength owing to an increase in the van der Waalsforce of attraction in the hydration products, the latter loses strength due to microcracking. The compressive strength of the concrete increases when the matrix is strength-determining; however, the elastic modulus is reduced because increases in the transition-zone microcracking greatly affects
� the stress-strain behavior. There is yet another explanation for the phenomenon. In a saturated cement paste the adsorbed water in the C-S-H is load-bearing, therefore its presence contributes to the elastic modulus; on the other hand, the disjoining pressure in the C-S-H (see Chap. 2) tends to reduce the van der Waals force of attraction, thus lowering the strength.
� The advent and degree of nonlinearity in the
stress-strain curve obviously would depend on
the rate of application of load. At a given stress
level the rate of crack propagation, and hence
the modulus of elasticity, is dependent on the
rate at which load is applied. Under
instantaneous loading, only a little strain can
occur prior to failure, and the elastic modulus is
very high.
� In the time range normally required to test the
specimens (2 to 5 min), the strain is increased
by 15 to 20 percent, hence the elastic modulus
decreases correspondingly. For very slow
loading rates, the elastic and the creep strains
would be superimposed, thus lowering the
elastic modulus further.
� The upward tendency of the E – f’c curves from different-strength concretemixtures tested at regular intervals up to 1 year shows that, at later ages, theelastic modulus increases at a faster rate than the compressive strength.
� Figure 4-7 presents a summary showing all
the factors discussed above, which affect the
modulus of elasticity of concrete.