Doç. Dr. Halit YAZICI

Transcription

1 Dokuz Eylül Üniversitesi Đnşaat Mühendisliği Bölümü DIMENSIONAL STABILITY of CONCRETE Doç. Dr. Halit YAZICI

2 CIE 5073 DIMENSIONAL STABILITY OF CONCRETE Three hours lecture

3 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, Mindness, S., and Young, J.F., Concrete, Prentice Hall, Inc., Englewood Cliffs, 1981.

4 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.

5 In this course the nonlinearity in the stressstrain 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.

6 The stresses resulting from drying shrinkage and viscoelastic strains in concrete are not same; however, with both phenomena the underlying causes and the controlling factors are generally common. Major parameters that affect drying shrinkage and creep as well as various rheological models and the methods of predicting creep and shrinkage are described.

7 Thermal shrinkage is of great importance in mass concrete. Its magnitude can be controlled by the coefficient of thermal expansion of aggregate, the cement content and type, and the temperature of concretemaking materials. The concepts of extensibility, tensile strain capacity and their significance to concrete cracking are introduced.

8 IV. COURSE OUTLINE: Types of Deformations and Their Significance Elastic Behavior Stress-Strain Relations Expressions for Stress-Strain Relations

9 2. Modulus of Elasticity of Concrete 2.1. Determination of Static Elastic Modulus 2.2. Expressions for Modulus of Elasticity ACI Building Code Model CEB-FIP Model Code 2.3. Dynamic Modulus of Elasticity 2.4. Poisson s Ratio 2.5. Factors Affecting Modulus of Elasticity Aggregate Cement paste matrix Transition zone Testing parameters

10 3. Load Independent Volume Changes of Concrete 3.1. Early Volume Changes 3.2. Autogenous Shrinkage 3.3. Swelling 3.4. Carbonation Shrinkage

11 4. Thermal Shrinkage 4.1. Factors Affecting Thermal Stress Degree of restraint Temperature change 4.2. Drying Shrinkage and Creep Mechanism and causes Effects of loading and humidity conditions Reversibility

12 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

13 6. Temperature Effects in Concrete 6.1. Influence of Early Temperature on Strength of Concrete 6.2. Thermal Properties of Concrete Thermal conductivity Thermal diffusivity Specific heat Coefficient of thermal expansion

14 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

15 8. Extensibility and Cracking 8.1. Cracking of Concrete 8.2. Extensibility and Cracking 8.3. Thermal Stress and Cracking

16 9. Mid term examination 10. Viscoelasticity Rheological Models Basic Rheological Models

17 12. Mathematical Expressions for Creep 13. Methods of Predicting Creep and Shrinkage CEB 1990 Method CEB 1978 Method ACI Method

18 14. Fatique and Impact Resistance Fatique Behavior Impact Resistance WEEK 15. Mid term examination

19 V. GRADING In additon to two mid term examinations, term projects will be prepared by students. The resulting grade will be determined as follows: 1. mid term examination - 15 % 2. mid term examination - 15 % Term project - 20 % Final examination - 50 % Result 100 %

20 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.

21 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.

22 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.

23 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.

24 Thermal shrinkage is of great importance in massive concrete elements. Its magnitude can be controlled by controlling the coefficient of thermal expansion of aggregate, cement content and type, and temperature of concretemaking materials. The concepts of extensibility, tensile strain capacity, and their significance to concrete cracking are also discussed.

25 Types of Deformations and their Significance 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

26 cooling) and drying shrinkage (shrinkage strain 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 the member, characteristics of concrete-making materials, and mix proportions. Generally, with massive structures (e.g., nearly 1 m or more in thickness), the drying shrinkage is less important a factor than the thermal shrinkage.

27 It should be noted that concrete members are almost always under restraint, sometimes from subgrade friction and end members, but usually from reinforcing steel and from differential strains that develop between the exterior and the interior of concrete. When the shrinkage strain in an elastic material is fully restrained, it results in elastic tensile stress; the magnitude of the induced stress s is determined by the product of the strain e and the elastic modulus E of the material (σ=ε* E).

28 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.

29 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 viscoelastic behavior is at the heart of deformations and cracking in most structures.

30 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.

31 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.

32 In practice, the stress-strain relations in concrete are much more complex than indicated by Figure. First, concrete is not a truly elastic material; second, neither the strains nor the restraints are uniform throughout a concrete member; therefore, the resulting stress distributions tend to vary from point to point. Nevertheless, it is important to know the elastic, drying shrinkage, thermal shrinkage, and viscoelastic properties of concrete and the factors affecting them.

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34 Elastic Behavior The elastic characteristics of a material are a measure of its stiffness. In spite of the nonlinear behavior of concrete, an estimate of the elastic modulus (the ratio between the applied stress and instantaneous strain within an assumed proportional limit) is necessary for determining the stresses induced by strains associated with environmental effects. It is also needed for computing the design stresses under load in simple elements, and moments and deflections in complicated structures.

35 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 and aggregates show linear elastic properties, whereas concrete does not.

36 Nonlinearity of the stress-strain relationship 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.

37 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

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39 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.

40 The progress of internal microcracking in concrete goes through various stages, which depend on the level of applied stress.

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42 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.

43 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.

44 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.

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46 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.

47 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.

48 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.

49 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).

50 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:

51 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.

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53 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.

54 The dynamic modulus of elasticity, corresponding to a very small instantaneous strain, is approximately given by the initial tangent modulus, which is the tangent modulus for a line drawn at the origin. It is generally 20, 30, and 40 percent higher than the static modulus of elasticity for high-, medium-, and low-strength concretes, respectively. For stress analysis of structures subjected to earthquake or impact loading it is more appropriate to use the dynamic modulus of elasticity, which can be determined more accurately by a sonic test.

55 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:

56 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

57 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.

58 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.

59 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.

60 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.

61 Figure Determination of the secant modulus in the laboratory (ASTM C 469).

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65 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.

66 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.

67 With concrete the values of Poisson s ratio generally vary between 0.15 and 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.

68 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.

69 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.

70 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.

71 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.

72 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

73 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

74 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.

75 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.

76 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 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.

77 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

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79 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).

80 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.

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82 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.

83 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 Waals force 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

84 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.

85 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.

86 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.

87 The upward tendency of the E f c curves from different-strength concrete mixtures tested at regular intervals up to 1 year shows that, at later ages, the elastic modulus increases at a faster rate than the compressive strength.

88 Figure 4-7 presents a summary showing all the factors discussed above, which affect the modulus of elasticity of concrete.

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90 Dokuz Eylül Üniversitesi Đnşaat Mühendisliği Bölümü DIMENSIONAL STABILITY of CONCRETE Doç. Dr. Halit YAZICI