The main properties of hardened concrete are:
- Deformation of concrete
- Modulus of elasticity
- Bond Strength
- Impact on concrete
- Dynamic loading on concrete
- Strength of concrete
Table of Contents
1) Deformation of Hardened Concrete
Concrete deforms when load is applied but this deformation does not follow any simple set rule. The deformation depends upon the magnitude of the load, the rate at which the load is applied and the elapsed time after which the observation is made. In other words, the rheological behavior of concrete i.e. the response of concrete to applied load is quite complex.
2) Modulus of Elasticity
- The modulus of elasticity is determined by subjecting a cube or cylinder specimen to uniaxial compression and measuring the deformations by means of dial gauges fixed between certain gauge lengths.
- It can also be determined by subjecting a concrete beam to bending and then using the formulae for deflection and substituting other parameters.
- The modulus of elasticity so found is called static modulus of elasticity.
Types of Modulus of Elasticity
- In the case of concrete, since no part of the stress-strain graph is straight, the modulus of elasticity is found out with reference to the tangent drawn to the curve at the origin. The modulus found from this tangent is referred as initial tangent modulus. This gives satisfactory results only at low stress value.
- Tangent can also be drawn at any other point on the stress-strain curve. The modulus of elasticity calculated with reference to this tangent is then called tangent modulus. This does not give a realistic value of modulus of elasticity for the stress level much above or below the point at which the tangent is drawn.
- A line can be drawn connecting a specified point on the stress-strain curve to the origin of the curve. If the modulus of elasticity is calculated with reference to the slope of this line, the modulus of elasticity is referred as secant modulus.
- If the modulus of elasticity is found out with reference to the chord drawn between two specified points on the stress-strain curve, then such value of the modulus of elasticity is known as chord modulus.
Relation between Modulus of Elasticity and Strength
Where, Ec = short term static modulus of elasticity in N/mm2
Dynamic Modulus of Elasticity
- 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% higher than the elastic 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.
- In the test, the concrete member is subjected to longitudinal vibration at their natural frequency.
- Where, Ed = dynamic modulus of elasticity; K = a constant; n = resonant frequency; L = length of the specimen; ρ = density of concrete
- When concrete is loaded, the structure undergoes elastic and inelastic deformations.
- Elastic deformations occur immediately after the concrete is subjected to a given load, according to Hooke’s Law.
- Inelastic deformations increase with time as the concrete experiences a sustained load.
- This inelastic deformation, also known as creep, increases at a decreasing rate during the loading period.
- During the first month of sustained loading, approximately one-fourth to one-third of the ultimate creep takes place.
- As time proceeds, usually one-half to three-fourths of the ultimate creep occurs during the first half year.
- Creep can be defined as the “time-dependent” part of the strain resulting from stress.
- It is the increase in strain under a sustained constant stress (load) after taking into account other time-dependent deformations not associated with stress like shrinkage, swelling and thermal deformation.
- Thus, creep is reckoned from the initial elastic strain as given by the secant modulus of elasticity at the age of loading.
- Creep is usually determined by measuring the change with time in the strain of specimen subjected to constant stress and stored under appropriate condition.
- It is generally assumed that the creep continues to assume a limiting value after an infinite time under load.
- It is estimated that 26% of the 20 year creep occurs in 2 weeks, 55% of 20 year creep occurs in 3 months and 76% of 20 year creep occurs in 1 year.
Factors affecting Creep
I) Influence of Aggregates
- 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.
II) 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.
III) 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 may be 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.
- 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.
- It is difficult to make concrete which does not shrink and crack. It is only a question of magnitude.
- 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.
Types of Shrinkage in Concrete
Shrinkage can be classified in the following way:
- Plastic Shrinkage
- Drying Shrinkage
- Autogeneous Shrinkage
- Carbonation Shrinkage
A) 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.
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.
B) Drying Shrinkage
Just as the hydration of cement is an ever lasting process, the drying shrinkage is also an ever lasting 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.
C) 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 autogeneous shrinkage. Autogeneous 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.
D) 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.
- 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.
- 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.
Relation btw Shrinkage and time
The typical relationship between shrinkage and time for which concrete is stored at different relative humidities is shown in Figure.
The graph shows that the magnitude of shrinkage increases with time and also with the reduction of relative humidity.
- The rate of shrinkage decreases rapidly with time. It is observed that 14 to 34 per cent of the 20 year shrinkage occurs in 2 weeks, 40 to 80 per cent of the 20 year shrinkage occurs in 3 months and 66 to 85 per cent of the 20 year shrinkage occurs in one year.
- Another important factor which influences the magnitude of shrinkage is water/cement ratio of the concrete. The richness of the concrete also has a significant influence on shrinkage.
- 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.
- Harder aggregate with higher modulus of elasticity like quartz shrinks much less than softer aggregates such as sandstone.
- Moisture Movement Concrete shrinks when allowed to dry in air at a lower relative humidity and it swells when kept at 100 per cent relative humidity or when placed in water.
- 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.
- The property of swelling when placed in wet condition, and shrinking when placed in drying condition is referred as moisture movement in concrete.
In numerous structural applications, such as bridge decks and pavements, concrete members are subjected to repeated applications of load at a level below the ultimate strength of the concrete. Like most materials, concrete exhibits fatigue behaviour, that is, when subjected to cyclic loading of a given level but below its short-term static strength, it will eventually fail. Fatigue strength is the greatest stress that can be sustained for a given number of stress cycles without failure.
The maximum and minimum values of repeated value in a cycle of loading may be of the same sign or of opposite sign.
- The fatigue strength of concrete is usually determined in 1 million cycles or more.
- As the strength of concrete increases with age, the fatigue strength increases proportionally so that for a given number of cycles, fatigue failure occurs at the same proportion of the ultimate strength.
- The above figure shows that there is a change in the shape of the stress-strain curves under an increasing and decreasing load as the load cycle increases.
- Initially, the loading curve is concave towards the strain axis, then straight, and eventually concave toward the stress axis.
- The extent of this latter concavity is reflected by an increase in the elastic strain and, hence, by a decrease in the secant modulus of elasticity, a feature which is an indication of how near the concrete is to failure by fatigue.
6) Impact Strength
- Impact strength is based on ability of specimen to withstand repeated blows and absorb energy.
- There is not unique relation between impact strength and static compressive strength.
- For instance, the number of blows which the concrete can withstand before reaching the no-rebound condition indicates a definite state of damage.
- In impact test, no redistribution of stress is possible during the very short period of deformation.
The impact strength of concrete increases with its static compressive strength at progressively increasing rate which is shown in figure below:
7) Strength of Concrete
That factors which effects concrete strength are Effect of Porosity, Water-Cement Ratio and Aggregate Size
I) Effect Of Porosity
The hydrated cement paste contains several types of pores which have an important influence on its properties:
- Gel pores (interlayer space in C-S-H)
- Capillary pores
- Air voids
Gel pores are very small (about 2 nm in diameter) and the volume of gel water is about 28% of the cement gel. The pore size is too small to have an adverse effect on the strength and permeability of the hydrated cement paste. ‘Gel Water’ can be held by hydrogen bonding, and its removal under certain conditions may contribute to drying shrinkage and creep.
Capillary pores represent the space not filled by the solid components of the hydrated cement paste. Capillary pores are much larger than gel pores (diameter about 1 mm). For fully hydrated cement with no excess water above that required for hydration, capillary pores is about 18.5% of the original volume of dry cement. These pores can be empty or full of water, depending on the amount of water in the mix.
When cement is partly hydrated, the cement paste contains an interconnected system of capillary pores. The effect of this is a lower strength and, through increased permeability, a higher vulnerability to freezing and thawing and to chemical attacks.
These problems are avoided if the degree of hydration is sufficiently high for the capillary pore system to become segmented through partial blocking by newly developed cement gel.
Air voids are generally spherical. A small amount of air usually gets trapped in cement paste during concrete mixing. There are two types of air voids: (i) Entrapped air voids (may be as large as 3 mm) and (ii) Entrained air voids (usually range from 50 to 200 μm). Both these voids in hydrated cement paste are much bigger than capillary voids and are capable of adversely affecting the concrete.
Ii) Effect Of Water-cement Ratio
In civil engineering practice, the strength of concrete at a given age and specified curing temperature primarily depends on two factors:
- W/C ratio
- Degree of Compaction
From the above figure, compressive strength is at peak, when water to cement ratio is low. Beginning of the curve depends on the available means of compaction (that is either done with vibrators or manually hand compaction). If large size aggregates is used with low w/c ratio and high content of cement, then it exhibits retrogression of the concrete strength.
A conclusion can be made that if there is a low w/c ratio in a fresh mix than after hardening, w/c will not be able to lead to higher strength of concrete due to development of tensile stresses due to shrinkage and creep.
Duff Abram’s Principle
When concrete is fully compacted, its strength is taken to be inversely proportion to the w/c ratio.
Where, fc = characteristic concrete cylinder (15 x 30)cm strength at 28 days after proper curing (at 25°C ± 2°C)
K1 and K2 are empirical constants.
w/c = water cement ratio
Iii) Effect Of Aggregate Size
The larger maximum size aggregates gives lower surface area for developments of gel bonds which is responsible for the lower strength of the concrete. Secondly bigger aggregate size causes a more heterogeneity in the concrete which will prevent the uniform distribution of load when stressed.
When large size aggregate is used, due to internal bleeding, the transition zone will become much weaker due to the development of micro cracks which results in lower compressive strength.
8) Bond Strength
Instead of relating the strength to w/c ratio, the strength can be more correctly related to the solid products of hydration of cement to the space available for formation of this product. The gel/space ratio is defined as the ratio of the volume of the hydrated cement paste to the sum of volumes of the hydrated cement and of the capillary pores.
Relationship between strength of concrete and gel/ space ratio according to Powers:
Where, x is the gel/space ratio and 240 represents the intrinsic strength of the gel in MPa for the type of cement and specimen used.