Doç. Dr. Halit YAZICI

http://kisi.deu.edu.tr/halit.yazici/

DIMENSIONAL STABILITY of DIMENSIONAL STABILITY of

CONCRETECONCRETE

Dokuz Eylül Üniversitesi Đnşaat Mühendisliği Bölümü

� CIE 5073

� DIMENSIONAL STABILITY OF

CONCRETE

� Three hours lecture

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.

� Figure Determination of the secant modulusin the laboratory (ASTM C 469).

� 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.

Doç. Dr. Halit YAZICI

http://kisi.deu.edu.tr/halit.yazici/

DIMENSIONAL STABILITY of DIMENSIONAL STABILITY of

CONCRETECONCRETE

Dokuz Eylül Üniversitesi Đnşaat Mühendisliği Bölümü