Deformation of concrete results both from environmental effects, such as moisture gain or loss and heat, and from applied stress, both short- and long-term. A general view of the nature of the behaviour is given in Fig. 1, which shows the strain arising from a uniaxial compressive stress applied to concrete in a drying environment. The load or stress is applied at a time t1, and held constant until removal at time t2.

deformation of concrete
Fig. 1 The response of concrete to a compressive stress applied in a drying environment.
  • Before applying the stress, there is a net contraction in volume of the concrete, or shrinkage, associated with the drying. The dotted extension in this curve beyond time t1 would be the subsequent behaviour without stress, and the effects of the stress are therefore the differences between this curve and the solid curves.
  • Immediately on loading there is an instantaneous strain response, which for low levels of stress is approximately proportional to the stress, and hence an elastic modulus can be defined.
  • With time, the strain continues to increase at a decreasing rate. This increase, after allowing for shrinkage, represents the creep strain. Although reducing in rate with time, the creep does not tend to a limiting value.
  • On unloading, at time t2, there is an immediate (elastic) strain recovery, which is often less than the initial strain on loading. This is followed by a time-dependent creep recovery, which is less than the preceding creep, i.e. there is permanent deformation but, unlike creep, this reaches completion in due course.

Deformation of Concrete

In this article we discuss the mechanisms and factors influencing the magnitude of all the components of this behaviour, i.e. shrinkage, elastic response and creep, and also consider thermally induced strains. We will for the most part be concerned with the behaviour of HCP and concrete when mature, but some mention of age effects will be made.

Drying Shrinkage

Drying Shrinkage of Hardened Cement Paste

In past articles we described the broad divisions of water in HCP and how their removal leads to a net volumetric contraction, or drying shrinkage, of the paste. Even though shrinkage is a volumetric effect, it is normally measured in the laboratory or on structural elements by determination of length change, and it is therefore expressed as a linear strain.

A considerable complication in interpreting and comparing drying shrinkage measurements is that specimen size will affect the result. Water can only be lost from the surface and therefore the inner core of a specimen will act as a restraint against overall movement; the amount of restraint and hence the measured shrinkage will therefore vary with specimen size.

In addition, the rate of moisture loss, and hence the rate of shrinkage, will depend on the rate of transfer of water from the core to the surface. The behaviour of HCP discussed in this section is therefore based on experimental data from specimens with a relatively small cross-section. A schematic illustration of typical shrinkage behaviour is shown in Fig. 2.

Fig. 2 Schematic of strain response of cement paste or concrete to alternate cycles of drying and wetting.

Maximum shrinkage occurs on the first drying and a considerable part of this is irreversible, i.e. is not recovered on subsequent rewetting. Further drying and wetting cycles result in more or less completely reversible shrinkage; hence there is an important distinction between reversible and irreversible shrinkage. Also shown in Fig. 2 is a continuous, but relatively small, swelling of the HCP on continuous immersion in water.

The water content first increases to make up for the self-desiccation during hydration, and to keep the paste saturated. Secondly, additional water is drawn into the C-S-H structure to cause the net increase in volume. This is a characteristic of many gels, but in HCP the expansion is resisted by the skeletal structure, so the swelling is small compared to the drying shrinkage strains.

In principle, the stronger the HCP structure, the less it will respond to the forces of swelling or shrinkage. This is confirmed by the results shown in Fig. 3, in which the increasing total porosity of the paste is, in effect, causing a decrease in strength.

Fig. 3 Reversible and irreversible shrinkage of HCP after drying at 47% relative humidity (after Helmuth and Turk, 1967).

It is interesting that the reversible shrinkage appears to be independent of porosity, and the overall trend of increased shrinkage on first drying is entirely due to the irreversible shrinkage. The variations in porosity shown in Fig. 3 were obtained by testing pastes of different water:cement ratios, and in general an increased water:cement ratio will result in increasing shrinkage. Reduction in porosity also results from greater degrees of hydration of pastes with the same water:cement ratio, but the effect of the degree of hydration on shrinkage is not so simple.

The obvious effect should be that of reduced shrinkage with age of the paste if properly cured; however, the unhydrated cement grains provide some restraint to the shrinkage, and as their volume decreases with hydration, an increase in shrinkage would result.

Another argument is that a more mature paste contains more water of the type whose loss causes greater shrinkage, e.g. less capillary water, and so loss of the same amount of water from such a paste would cause more shrinkage.

It is thus difficult to predict the net effect of age on the shrinkage of any particular paste. Since shrinkage results from water loss, the relationship between the two is of interest.

Fig. 4 The effect of water loss on the drying
shrinkage of hardened cement paste (after Verbeck and
Helmuth, 1968).

Typical data are given in Fig. 4, which shows that there is a distinct change of slope with increased moisture losses, in this case above about 17% loss. This implies that there is more than one mechanism of shrinkage; as other tests have shown two or even three changes of slope, it is likely that in fact several mechanisms are involved. 

Mechanisms of Shrinkage and Swelling

Four principal mechanisms have been proposed for shrinkage and swelling in cement pastes, which are now summarised.

Capillary tension: Free water surfaces in the capillary and larger gel pores will be in surface tension, and when water starts to evaporate owing to a lowering of the ambient vapour pressure the free surface becomes more concave and the surface tension increases (Fig. 5).

Fig. 5 Relationship between the radius of curvature and vapour pressure of water in a capillary (after Soroka, 1979).

The relationship between the radius of curvature, r, of the meniscus and the corresponding vapour pressure, p, is given by Kelvin’s equation:

ln(p/p0) = 2T/Rθρr ………(1)

where p0 is the vapour pressure over a plane surface, T is the surface tension of the liquid, R is the gas constant, θ is the absolute temperature and ρ the density of the liquid.

The tension within the water near the meniscus can be shown to be 2T/r, and this tensile stress must be balanced by compressive stresses in the surrounding solid. Hence evaporation, which causes an increase in the tensile stress, will subject the HCP solid to increased compressive stress, which will result in a decrease in volume, i.e. shrinkage. The diameter of the meniscus cannot be smaller than the diameter of the capillary, and the pore therefore empties at the corresponding vapour pressure, p1.

Hence on exposing a cement paste to a steadily decreasing vapour pressure, the pores gradually empty according to their size, the widest first. Pastes with higher water:cement ratios and higher porosities will therefore shrink more, thus explaining the general form of Fig. 3.

As a pore empties, the imposed stresses on the surrounding solid reduce to zero and so full recovery of shrinkage would be expected on complete drying. Since this does not occur, it is generally accepted that other mechanisms become operative at low humidity, and that this mechanism only applies at a relative humidity above about 50%.

Surface tension or surface energy:  The surface of both solid and liquid materials will be in a state of tension owing to the net attractive forces of the molecules within the material. Work therefore has to be done against this force to increase the surface area, and the surface energy is defined as the work required to increase the surface by unit area.

Surface tension forces induce compressive stresses in the material of value 2T/r (see above) and in HCP solids, whose average particle size is very small, these stresses are significant. Adsorption of water molecules onto the surface of the particles reduces the surface energy, hence reducing the balancing internal compressive stresses, leading to an overall volume increase, i.e. swelling. This process is also reversible.

Fig. 6 Water forces in a gel pore in hardened
cement paste (after Bazant, 1972).

Disjoining pressure: Figure 6 shows a typical gel pore, narrowing from a wider section containing free water in contact with vapour to a much narrower space between the solid, in which all the water is under the influence of surface forces. The two layers are prevented from moving apart by an inter-particle van der Waals type bond force.

The adsorbed water forms a layer about five molecules or 1.3 nm thick on the solid surface at saturation, which is under pressure from the surface attractive forces. In regions narrower than twice this thickness, i.e. about 2.6 nm, the interlayer water will be in an area of hindered adsorption.

This results in the development of a swelling or disjoining pressure, which is balanced by tension in the inter-particle bonds. On drying, the thickness of the adsorbed water layer reduces, as does the area of hindered adsorption, hence reducing the disjoining pressure. This results in an overall shrinkage.

Movement of interlayer water: The mechanisms described above concern the free and adsorbed water. The third type of evaporable water, the interlayer water, may also have a role. Its intimate contact with the solid surfaces and the tortuosity of its path to the open air suggest that a steep hygrometric energy gradient is needed to move it, but also that such movement is likely to result in significantly higher shrinkage than the movement of an equal amount of free or adsorbed water.

It is likely that this mechanism is associated with the steeper slope of the graph in Fig. 4 at the higher values of water loss. The above discussion applies to the reversible shrinkage only, but the reversibility depends on the assumption that there is no change in structure during the humidity cycle. This is highly unlikely, at least during the first cycle, because:

  • the first cycle opens up interconnections between previously unconnected capillaries, thereby reducing the area for action of subsequent capillary tension effects
  • some new inter-particle bonds will form between surfaces that move closer together as a result of movement of adsorbed or interlayer water, resulting in a more consolidated structure and a decreased total system energy.
Table 1 Summary of suggested shrinkage mechanisms (after Soroka, 1979)

Opinion is divided on the relative importance of the above mechanisms and their relative contribution to the total shrinkage. These differences of opinion are clear from Table 20.1, which shows the mechanisms proposed by five authors and the suggested humidity levels over which they act.

Drying Shrinkage of Concrete

Effect of mix constituents and proportions: The drying shrinkage of concrete is less than that of neat cement paste because of the restraining influence of the aggregate which, apart from a few exceptions, is dimensionally stable under changing moisture states. The effect of aggregate content is shown in Fig. 7.

Fig. 7 Effect of aggregate content of concrete on
the shrinkage of concrete compared to that of cement
paste (after Pickett, 1956).

It is apparent that normal concretes have a shrinkage of some 5 to 20% of that of neat paste. Aggregate stiffness will also have an effect. Normal density aggregates are stiffer and therefore give more restraint than lightweight aggregates, and therefore lightweight aggregate concretes will tend to have a higher shrinkage than normal-density concretes of similar volumetric mix proportions.

The combined effect of aggregate content and stiffness is contained in the empirical equation:

 εc/ εp = (1 – g)n ……..(2)

where εc and εp are the shrinkage strains of the concrete and paste, respectively, g is the aggregate volume content, and n is a constant that depends on the aggregate stiffness, and has been found to vary between 1.2 and 1.7. The overall pattern of the effect of mix proportions on the shrinkage of concrete is shown in Fig. 8; the separate effects of increased shrinkage with increasing water content and increasing water:cement ratio can be identified.

Fig. 8 Effect of aggregate content of concrete on
the shrinkage of concrete compared to that of cement
paste (after Pickett, 1956).

The properties and composition of the cement and the incorporation of fly ash, ggbs and microsilica all have little effect on the drying shrinkage of concrete, although interpretation of the data is sometimes difficult.

Admixtures do not in themselves have a significant effect, but if their use results in changes in the mix proportions then, as shown in Fig. 8, the shrinkage will be affected.

Effect of specimen geometry: The size and shape of a concrete specimen will influence the rate of moisture loss and the degree of overall restraint provided by the central core, which will have a higher moisture content than the surface region. The rate and amount of shrinkage and the tendency for the surface zones to crack are therefore affected.

In particular, longer moisture diffusion paths lead to lower shrinkage rates. For example, a member with a large surface area to volume ratio, e.g. a T-beam, will dry and therefore shrink more rapidly than, say, a beam with a square cross-section of the same area. In all cases, however, the shrinkage process is protracted.

In a study lasting 20 years, Troxell et al. (1958) found that in tests on 300 × 150 mm diameter cylinders made from a wide range of concrete mixes and stored at relative humidities of 50 and 70%, an average of only 25% of the 20-year shrinkage occurred in the first two weeks, 60% in three months, and 80% in one year.

Non-uniform drying and shrinkage in a structural member will result in differential strains and hence shrinkage-induced stresses – tensile near the surface and compressive in the centre. The tensile stresses may be sufficient to cause cracking, which is the most serious consequence for structural behaviour and integrity.

However, as discussed above, the effects in practice occur over protracted timescales, and the stresses are relieved by creep before cracking occurs. The structural behaviour is therefore complex and difficult to analyse with any degree of rigour. 

Prediction of Shrinkage

It is clear from the above discussion that although much is known about shrinkage and the factors that influence its magnitude, it is difficult to estimate its value in a structural situation with any degree of certainty. It has been shown that it is possible to obtain reasonable estimates of long-term shrinkage from short-term tests (Neville et al., 1983), but designers often require estimates long before results from even short-term tests can be obtained.

There are a number of methods of varying degrees of complexity for this, often included in design codes, e.g. Eurocode 2 (BS EN 1992) or ACI (2000), all of which are based on the analysis and interpretation of extensive experimental data. 20.2

Autogenous Shrinkage

Continued hydration with an adequate supply of water leads to slight swelling of cement paste, as shown in Fig. 2.

Conversely, with no moisture movement to or from the cement paste, self-desiccation leads to removal of water from the capillary pores and autogenous shrinkage. Most of this shrinkage occurs when the hydration reactions are proceeding most rapidly, i.e. in the first few days after casting.

Its magnitude is normally at least an order of magnitude less than that of drying shrinkage, but it is higher and more significant in higher-strength concrete with very low water:cement ratios. It may be the only form of shrinkage occurring in the centre of a large mass of concrete, and can lead to internal cracking if the outer regions have an adequate supply of external water, e.g. from curing.

Carbonation Shrinkage

Carbonation shrinkage differs from drying shrinkage in that its cause is chemical and it does not result from loss of water from the HCP or concrete. Carbon dioxide, when combined with water as carbonic acid, reacts with many of the components of the HCP, and even the very dilute carbonic acid resulting from the low concentrations of carbon dioxide in the atmosphere can have significant effects. The most important reaction is that with the portlandite (calcium hydroxide):

CO2 + Ca(OH)2 → CaCO3 + H2O ……..(3)

Thus water is released and there is an increase in weight of the paste. There is an accompanying shrinkage, and the paste also increases in strength and decreases in permeability.

The most likely mechanism to explain this behaviour is that the calcium hydroxide is dissolved from more highly stressed regions, resulting in shrinkage, and the calcium carbonate crystallises out in the pores, thus reducing the permeability and increasing the strength.

The rate and amount of carbonation depend in part on the relative humidity of the surrounding air and within the concrete. If the pores are saturated, then the carbonic acid will not penetrate the concrete, and no carbonation will occur; if the concrete is dry, then no carbonic acid is available.

Fig. 9 The effect of surrounding relative humidity
on drying and carbonation shrinkage of mortar (after
Verbeck, 1958).

Maximum carbonation shrinkage occurs at a humidity of about 50% and it can be of the same order of magnitude as drying shrinkage (Fig. 9). The porosity of the concrete is also an important controlling factor. With average-strength concrete, provided it is well compacted and cured, the carbonation front will only penetrate a few centimetres in many years, and with high-strength concrete even less.

However, much greater penetration can occur with poor quality concrete or in regions of poor compaction, and this can lead to substantial problems if the concrete is reinforced.

Thermal Expansion

In common with most other materials, cement paste and concrete expand on heating. Knowledge of the coefficient of thermal expansion is needed in two main situations: firstly to calculate stresses due to thermal gradients arising from heat of hydration effects or continuously varying diurnal temperatures, and secondly to calculate overall dimensional changes in structures such as bridge decks due to variations in ambient temperature.

The measurement of thermal expansions on laboratory specimens is relatively straightforward, provided sufficient time is allowed for thermal equilibrium to be reached (at most a few hours).

However, the in-situ behaviour is complicated by differential movement from non-uniform temperature changes in large members resulting in time-dependent thermal stresses; as with shrinkage, it is therefore difficult to extrapolate movement in structural elements from that on laboratory specimens. 

Thermal Expansion of Hardened Cement Paste

The coefficient of thermal expansion of HCP varies between about 10 and 20 × 10-6 per °C, depending mainly on the moisture content. Figure 10 shows typical behaviour, with the coefficient reaching a maximum at about 70% relative humidity. The value at 100% relative humidity, i.e. about 10 × 10-6 per °C, probably represents the ‘true’ inherent value for the paste itself.

Fig. 10 The effect of dryness on the thermal
expansion coefficient of hardened cement paste and
concrete (after Meyers, 1950).

The behaviour does, however, show some time dependence, with the initial expansion on an increase in temperature showing some reduction over a few hours if the temperature is held constant.

Explanations for this behaviour have all involved the role of water, and relate to the disturbance of the equilibrium between the water vapour, the free water, the freely adsorbed water, the water in areas of hindered adsorption and the forces between the layers of gel solids.

Any disturbances will have a greater effect at intermediate humidities, when there is a substantial amount of water present with space in which to move. On an increase in temperature, the surface tension of the capillary water will decrease and hence its internal tension and the corresponding compression in the solid phases will decrease, causing extra swelling, as observed.

However, changes in internal energy with increased or decreased temperature will stimulate internal flow of water, causing the time-dependent volume change in the opposite sense to the initial thermal movement mentioned above. 

Thermal Expansion of Concrete 

The thermal expansion coefficients of the most common types of rock used for concrete aggregates vary between about 6 and 10 × 10-6 per °C, i.e. lower than either the ‘true’ or ‘apparent’ values for cement paste. The thermal expansion coefficient of concrete is therefore lower than that of cement paste, as shown in Fig. 10.

Furthermore, since the aggregate occupies 70 – 80% of the total concrete volume, there is a considerable reduction of the effects of humidity that are observed in the paste alone, to the extent that a constant coefficient of thermal expansion over all humidities is a reasonable approximation.

The value depends on the concrete mix proportions, chiefly the cement paste content, and the aggregate type; for normal mixes the latter tends to dominate. The curves for quartz and limestone aggregate concrete shown in Fig. 10 represent the two extremes of values for most normal aggregate concrete.

Such values apply over a temperature range of about 0 to 60°C. At higher temperatures, the differential stresses set up by the different thermal expansion coefficients of the paste and aggregate can lead to internal microcracking and hence nonlinear behaviour.

Thanks for reading about “deformation of concrete”.

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