Creep, Shrinkage & Elasticity

NATIONAL INSTITUTE OF TECHNOLOGY, DURGAPUR

CE 703: CONCRETE TECHNOLOGYAssignment I

CREEP, SHRINKAGE AND ELASTICITY

Of

Submitted by: MIAAZA HUSSAIN (10/CE/61)

Conc

Creep, shrinkage and elasticity of concrete

PRONOTI YEIN (10/CE/27)

MOULI MAHASETH (10/CE/23)

1. Creep in concrete

Introduction

Concrete creep is defined as deformation or increase in strain of structure under sustained mechanical loading. Basically, long term pressure or stress on concrete can make it change shape. This deformation usually occurs in the direction the force is being applied. Like a concrete column getting more compressed, or a beam bending.

This phenomenon of creep can be accounted on by the stress strain curves of concrete obtained for different ages of loading (see fig.1.1). Stress strain curve of concrete is always a curved line and the degree of curvature depends on many factors out of which the intensity of stress and time for which the load is acting has a significant effect. As seen in fig 1.1 the time of loading has a major effect on stress and strain relationship and hence creep is also defined as the time-dependent part of strain resulting from strain. The gradual increase in strain without any change in load/ stress is due to creep effect.

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Creep does not necessarily cause concrete to fail or break apart. Creep is factored in when concrete structures are designed.

The variation of strain with time, under constant axial compressive stress, is represented in the following figure (see Fig. 1.2).

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Fig 1.2: Variation of strain with time for concrete under compression

Fig 1.1: variation in stress and strain diagram of concrete with loading time


If the load is removed, the elastic strain is immediately recovered. However the recovered elastic strain is less than the initial elastic strain, as the elastic modulus increases with age. There is reduction of strain due to creep recovery which is less than the creep strain. There is some residual strain which cannot be recovered. (See Fig 1.3)

Section 5.2.5 of IS: 1343-1980 gives guidelines to estimate the ultimate creep strain in concrete. It is a simplified estimate where only one factor has been considered. The factor is age of loading of the prestressed concrete structure. The creep coefficient θ is provided for three values of age of loading.

Table below shows Creep coefficient θ for three values of age of loading

Age of Loading Creep Coefficient, θ7 days 2.228 days 1.61 year 1.1

It can be observed that if the structure is loaded at 7 days, the creep coefficient is 2.2. This means that the creep strain is 2.2 times the elastic

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Fig 1.3: Variation of strain with time showing the effect of unloading


strain. Thus, the total strain is more than thrice the elastic strain. Hence, it is necessary to study the effect of creep in the loss of prestress and deflection of prestressed flexural members. Even if the structure is loaded at 28 days, the creep strain is substantial. This implies higher loss of prestress and higher deflection.

Factors Affecting Creep

1. Aggregate2. Mix Proportions3. Age of concrete

1. Influence of Aggregate

Aggregate undergoes very little creep. It is really the paste which is responsible for the creep. However, the aggregate influences the creep of concrete through a restraining effect on the magnitude of creep. The paste which is creeping under load is restrained by aggregate which do not creep. The stronger the aggregate the more is the restraining effect and hence the less is the magnitude of creep. The modulus of elasticity of aggregate is one of the important factors influencing creep.

It can be easily imagined that the higher the modulus of elasticity the less is the creep. Light weight aggregate shows substantially higher creep than normal weight aggregate.

2. Influence of Mix Proportions:

The amount of paste content and its quality is one of the most important factors influencing creep. A poorer paste structure undergoes higher creep. Therefore, it can be said that creep increases with increase in water/cement ratio. In other words, it can also be said that creep is inversely proportional to the strength of concrete. Broadly speaking, all other factors which are affecting the water/cement ratio are also affecting the creep.

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3. Influence of Age:

Age at which a concrete member is loaded will have a predominant effect on the magnitude of creep. This can be easily understood from the fact that the quality of gel improves with time. Such gel creeps less, whereas a young gel under load being not so stronger creeps more. What is said above is not a very accurate statement because of the fact that the moisture content of the concrete being different at different age also influences the magnitude of creep.

Effects of Creep on Concrete and Reinforced Concrete

In reinforced concrete beams, creep increases the deflection with time and maybe a critical consideration in design.

In eccentrically loaded columns, creep increases the deflection and can load to buckling.

In case of statically indeterminate structures and column and beam junctions creep may relieve the stress concentration induced by shrinkage, temperatures changes or movement of support. Creep property of concrete will be useful in all concrete structures to reduce the internal stresses due to non-uniform load or restrained shrinkage.

In mass concrete structures such as dams, on account of differential temperature conditions at the interior and surface, creep is harmful and by itself may be a cause of cracking in the interior of dams. Therefore, all precautions and steps must be taken to see that increase in temperature does not take place in the interior of mass concrete structure.

Loss of prestress due to creep of concrete in prestressed concrete structure.

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2. Shrinkage in Concrete

Introduction

Concrete is subjected to changes in volume either Autogenous or induced. Volume change is one of the most detrimental properties of concrete, which affects the long-term strength and durability. To the practical engineer, the aspect of volume change in concrete is important from the point of view that it causes unsightly cracks in concrete.

One of the most objectionable defects in concrete is the presence of cracks, particularly in floors and pavements. One of the important factors that contribute to the cracks in floors and pavements is that due to shrinkage. Shrinkage causes an increase in the tensile stress which leads to cracking and warping and external deflection before concrete is subjected to any kind of loading. It is difficult to make concrete which does not shrink and crack. It is only a question of magnitude. Concrete shrinkage is of increasing concern when focusing on maintaining durable structures

Now the question is how to reduce the shrinkage and shrinkage cracks in concrete structures. The term shrinkage is loosely used to describe the various aspects of volume changes in concrete due to loss of moisture at different stages due to different reasons.

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Fig 2.1: Cracks in a concrete slab due to shrinkage


Types of Shrinkage in Concrete

To understand this aspect more closely, shrinkage can be classified in the following way:

(I) Plastic Shrinkage(II) Drying Shrinkage (III) Autogeneous Shrinkage(IV) Carbonation Shrinkage

I. Plastic Shrinkage

Shrinkage of this type manifests itself soon after the concrete is placed in the forms while the concrete is still in the plastic state. Loss of water by evaporation from the surface of concrete or by the absorption by aggregate or subgrade is believed to be the reasons of plastic shrinkage. The loss of water results in the reduction of volume. The aggregate particles or the reinforcement comes in the way of subsidence due to which cracks may appear at the surface or internally around the aggregate or reinforcement.

In case of floors and pavements where the surface area exposed to drying is large as compared to depth, when this large surface is exposed to hot sun and drying wind, the surface of concrete dries very fast which results in plastic shrinkage. Sometimes even if the concrete is not subjected to severe drying, but poorly made with a high water-cement ratio, large quantity of water bleeds and accumulates at the surface. When this water at the surface dries out the surface concrete collapses causing cracks.

Plastic concrete is sometimes subjected to unintended vibration or yielding of formwork support which again causes plastic shrinkage cracks as the concrete at this stage has not developed enough strength. From the above it can be inferred that high water/cement ratio, badly proportioned concrete, rapid drying, greater bleeding, unintended vibration etc., are some of the reasons for plastic shrinkage. It can also be further added that richer concrete undergoes greater plastic shrinkage.

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Plastic shrinkage can be reduced mainly by preventing the rapid loss of water from surface. This can be done by covering the surface with polyethylene sheeting immediately on finishing operation; by fog spray that keeps the surface moist; or by working at night. Use of small quantity of Aluminium powder is also suggested to offset the effect of plastic shrinkage.

Similarly, expansive cement or shrinkage compensating cement also can be used for controlling the shrinkage during the setting of concrete.

II. Drying Shrinkage

Just as the hydration of cement is an everlasting process, the drying shrinkage is also an everlasting process when concrete is subjected to drying conditions. The drying shrinkage of concrete is analogous to the mechanism of drying of timber specimen. The loss of free water contained in hardened concrete, does not result in any appreciable dimension change. It is the loss of water held in gel pores that causes the change in the volume. Under drying conditions, the gel water is lost progressively over a long time, as long as the concrete is kept in drying conditions. Cement paste shrinks more than mortar and mortar shrinks more than concrete. Concrete made with smaller size aggregate shrinks more than concrete made with bigger size aggregate. The magnitude of drying shrinkage is also a function of the fineness of gel. The finer the gel the more is the shrinkage.

Just as drying shrinkage is an ever continuing process, swelling, when continuously placed in water is also an ever continuing process. If a concrete sample subjected to drying condition, at some stage, is subjected to wetting condition, it starts swelling. It is interesting to note that all the initial drying shrinkage is not recovered even after prolonged storage in water which shows that the phenomenon of drying shrinkage is not a fully reversible one.

Just as the drying shrinkage is due to loss of adsorbed water around gel particles, swelling is due to the adsorption of water by the cement gel. The water molecules act against the cohesive force and tend to force the gel particles further apart as a result of which swelling takes place. In addition, the ingress of water decreases the surface tension of the gel.

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Note: The property of swelling when placed in wet condition, and shrinking when placed in drying condition is referred as moisture movement in concrete.

III. Autogenous Shrinkage

In a conservative system i.e. where no moisture movement to or from the paste is permitted, when temperature is constant some shrinkage may occur. The shrinkage of such a conservative system is known as autogenous shrinkage. Autogenous shrinkage is of minor importance and is not applicable in practice to many situations except that of mass of concrete in the interior of a concrete dam.

IV. Carbonation Shrinkage

Carbon dioxide present in the atmosphere reacts in the presence of water with hydrated cement.

Calcium hydroxide [Ca(OH)2] gets converted to calcium carbonate and also some other cement compounds are decomposed. Such a complete decomposition of calcium compound in hydrated cement is chemically possible even at the low pressure of carbon dioxide in normal atmosphere. Carbonation penetrates beyond the exposed surface of concrete very slowly.

The rate of penetration of carbon dioxide depends also on the moisture content of the concrete and the relative humidity of the ambient medium. Carbonation is accompanied by an increase in weight of the concrete and by shrinkage.

Carbonation shrinkage is probably caused by the dissolution of crystals of calcium hydroxide and deposition of calcium carbonate in its place. As the new product is less in volume than the product replaced, shrinkage takes place.

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Carbonation of concrete also results in increased strength and reduced permeability, possibly because water released by carbonation promotes the process of hydration and also calcium carbonate reduces the voids within the cement paste. As the magnitude of carbonation shrinkage is very small when compared to long term drying shrinkage, this aspect is not of much significance.

Factors Affecting Shrinkage

Shrinkage is affected by:

I. Water-cement ratio: the shrinkage increases with increase in water cement ratio as shown in fig. 2.3. The richness of the concrete also has a significant influence on shrinkage.

II. Cement content: the shrinkage increases with increase in cement content as shown in fig: 2.3 but is inter related to water-cement ratio because of the necessity to maintain workability. It is not much affected by the cement content if the water content per unit volume is constant.

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Fig 2.2: Different types of shrinkage damage to a structure


III. Ambient Humidity: One of the most important factors that affect shrinkage is the drying condition or in other words, the relative humidity of the atmosphere at which the concrete specimen is kept. If the concrete is placed in 100 per cent relative humidity for any length of time, there will not be any shrinkage; instead there will be a slight swelling. The typical relationship between shrinkage and time for which concrete is stored at different relative humidity is shown in Fig. 2.4 The graph shows that the magnitude of shrinkage increases

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Fig 2.3: Effect of water cement-ratio and cement content on drying shrinkage


with the reduction of relative humidity. But immersion of concrete in water causes the reverse, i.e. expansion.

IV. Aggregate: Aggregate plays an important role in the shrinkage properties of concrete. The quantum of an aggregate, its size, and its modulus of elasticity influence the magnitude of drying shrinkage. The aggregate which exhibit moisture movement themselves and have low elastic modulus causes large shrinkage. Harder aggregate with higher modulus of elasticity like quartz shrinks much less than softer aggregates such as sandstone. Concrete using sandstone may shrink twice as much as one using limestone. An increase in maximum size decreases the shrinkage. The grading and shape has little effect on shrinkage. The effect of type of aggregate on the shrinkage is shown in fig: 2.5

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Fig 2.4: Variation in Shrinkage with decreasing relative humidity of surrounding air


V. Size and shape of specimen: both the rate and ultimate magnitude of shrinkage decreases with surface/volume ratio of the specimen

VI. Type of cement: The rapid hardening cement shrinks somewhat more than the others

VII. Admixtures: The shrinkage increases with the addition of calcium chloride and reduces with lime replacement

VIII. Effect of time: Shrinkage takes place over long periods. However, large fraction of the ultimate shrinkage (which is mainly the drying shrinkage) takes place at early times and the small fraction of the ultimate shrinkage (which is mainly the carbonation shrinkage) takes place over long periods.

Percent of 20-year shrinkage

Occurs in

14-34 2 weeks40-80 3 months66-85 1year

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Fig 2.5: Effect of type of aggregate on drying shrinkage of concrete


IX. Other factors: The steam curing has effect on shrinkage unless applied at high pressure.

3. Elasticity of concreteElastic Strains: These are the instantaneous deformations that occur when an external stress is first applied.

Elastic strain in concrete, as defined above, depends on the externally applied stress and the modulus of elasticity of concrete:

Elastic strain = externally applied stress/Modulus of elasticity of concrete

Modulus of Elasticity of Concrete

Modulus of elasticity is the property of concrete where the material is treated as elastic Concrete is not a truly elastic material, as evident from the nonlinear stress-strain curve for concrete, shown in the following Fig.:

Typical Stress-Strain Plot of Concrete

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Fig 3.1: Stress- strain curve for concrete


(1) At stress below 30% of ultimate strength, the transition zone cracks remain stable. The stress-strain plot remains linear.

(2) At stress between 30% and 50% of ultimate strength, the transition zone micro cracks begin to increase in length, width and numbers. The stress-strain plot becomes non-linear.

(3) At 50 to 60% of the ultimate stress, cracks begin to form in the matrix. With further increase to about 75% of the ultimate stress, the cracks in the transition become unstable, and crack propagation in the matrix will increase. The stress-strain curve bends towards the horizontal.

(4) At 75 to 80% of the ultimate stress, the stress reaches a critical stress level for spontaneous crack growth under a sustained stress. Cracks propagate rapidly in both the matrix and the transition zone. Failure occurs when the cracks join together and become continuous.

Note: Modulus of elasticity for concrete determined from an experimental stress-strain relation curve, is generally termed as static modulus of elasticity (Ec) whereas the modulus of elasticity determined through the longitudinal vibration test is termed as dynamic modulus of elasticity (Ed)

if we consider the stress strain curve of the first cycle, the modulus of elasticity could be defined as initial tangent modulus, secant modulus, tangent modulus or chord modulus as shown in fig: below

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Fig 3.2: Different Modulus of elasticity


1. The “initial tangent modulus”: It is given by the slope of a line drawn tangent to the stress-strain curve at the origin2. The “tangent modulus”: It is given by the slope of a line drawn tangent to the stress-strain curve at any point on the curve3. The “secant modulus”: It is given by the slope of a line drawn from the origin to a point on the curve corresponding to a 40% stress of the failure stress4. The “chord modulus”: It is given by the slope of a line drawn between two points on the stress-strain curve

Determination of modulus of elasticity of concrete

I. The modulus of elasticity of concrete can also be determined by subjecting a cube or cylinder specimen to uniaxial compression and measuring the deformations by means of dial gauge fixed between certain gauge lengths. Dial gauge reading divided by gauge length will give the strain and load applied divided by the area of cross section will give the stress.

Strain =Dial gauge reading/gauge length = dl/L

Stress = Load/Cross sectional area= P/A

A series of readings are taken and the stress-strain relationship is established.

II. Deflection: E can be determined from testing of beam also.

For central point load, Max. Deflection, δ = WL3/48EIxx

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Factors affecting modulus of elasticity

Elasticity of concrete is effected by:

I. Cement and aggregate factors : Since concrete is a composite material, consisting of cement paste and aggregate, its modulus of elasticity depends on the moduli of elasticity and the volume fractions of cement paste and aggregate, as follows:

Ec = [{(1-Va)Ep + (1+Va) Ea} / {(1+Va)Ep + (1-Va) Ea}]Ep

Where, Ec = modulus of elasticity of concrete

Ep = modulus of elasticity of cement paste

Ea = modulus of elasticity of aggregate

Va = volume fraction of aggregate = 1-Vp

Vp = volume fraction of cement paste = 1-Va

• Ep depends on the porosity of cement paste and the porosity of cement paste depends on the gel/space ratio (Ep is approximately proportional to the cube of the gel/space ratio) and gel/space ratio finally depends on the w/c ratio (gel/space ratio is inversely proportional to w/c ratio)

Note: The reason behind relating Ep with compressive strength of concrete lies in the fact that the compressive strength is also affected in the same way as, Ep.

• Ea for lightweight aggregates is found to be much lower than that for the normal weight aggregate. This is why the elastic modulus of lightweight concrete is less than that of the normal-weight aggregate (Ec, light weight concrete = 0.4 to 0.8 Ec, normal weight concrete)

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II. Moisture condition factor: The moisture condition of the specimen is a factor: a wet specimen has a modulus of elasticity higher than by 3 to 4 GPa than a dry one.Note: The effect of moisture condition of specimen is reverse in case of the compressive strength.

III. Condition of curing: Another factor affecting the modulus of elasticity of concrete is the manner in which the test cylinders were cured. In general, concrete specimens that were cured in moist conditions resulted in a modulus value higher than those cured in dry conditions. This is due to the fact that in dry conditions concrete is more likely to have drying shrinkage. Drying shrinkage causes small cracks. These small cracks thus will cause the concrete to have a reduced modulus of elasticity.

IV. Age of concrete: As age increases, E increases

V. Mix proportion (C + A + W): All ingredients will have its own effect. For a given mix, the effect of one variable should be considered keeping all other variables constant.

VI. Strength of concrete: As strength increases, E increases as shown in Table below

Table: Variation of modulus of elasticity (GPa) with compressive strength (MPa) for concrete

Compressive strengthfck (MPa)

Modulus of elasticityE (GPa)

20 22.430 27.440 31.650 35.460 38.7

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VII. Rate of loading: As the rate of loading increases, E also increases as the creep effect is less

VIII. Size and shape of specimen : Cube vs. cylinder, small vs. large

IX. Effect of transition zone: The void spaces and the micro cracks in the transition zone play a major role in affecting the stress-strain behavior of concrete. • The transition zone characteristics affect the elastic modulus more than it affects the compressive strength of concrete. • Silica fume, metakaolin, RHA in concrete has significant effect on E

References:

[1] Concrete Technology by MS Shetty[2] Concrete Technology (Theory and Practice), 4th Edition by ML Ghambir[3] VTU EDUSAT Programme 16 Lecture Notes on Elasticity, Shrinkage and Creep by Dr. M. C. Natarara[4] Concrete Technology by Neville[5] Advanced Concrete Technology 2: Concrete Properties, edited by John Newman, B S Cho[6] www.aboutcivil.org

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Fig 3.3: Variation of modulus of elasticity with compressive strength


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Creep, Shrinkage & Elasticity

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