Creep Behaviour of Concrete
The magnitude of the creep strains can be higher than the elastic strains on loading, and they therefore often have a highly significant influence on structural behaviour. Also, creep does not appear to tend to a limit, as shown in Fig. 1 for tests of more than 20 years duration.
This figure also shows that creep is substantially increased when the concrete is simultaneously drying, i.e. creep and shrinkage are interdependent. This leads to the definitions of creep strains shown in Fig. 2.
Free shrinkage (εsh) is defined as the shrinkage of the unloaded concrete in the drying condition, and basic creep (εbc) as the creep of a similar specimen under load but not drying, i.e. sealed so that there is no moisture movement to or from the surrounding environment. The total strain (εtot) is that measured on the concrete while simultaneously shrinking and creeping and, as shown in Fig. 2, it is found that:
εtot > εsh + εbc
The difference, i.e. εtot – (εsh + εbc), is called the drying creep (εdc). It follows that the total creep strain (εcr) is given by:
εcr = εdc + εbc
It also follows that the total creep of a specimen or structural member will be dependent on its size, since this will affect the rate and uniformity of drying.
Factors Influencing Creep
Apart from the increase in creep with simultaneous shrinkage just described, the following factors have a significant effect on creep.
- A reduced moisture content before loading, which reduces creep. In fact, completely dried concrete has very small, perhaps zero, creep.
- The level of applied stress; for any given concrete and loading conditions, the creep is found to increase approximately linearly with the applied stress up to stress:strength ratios of about 0.4–0.6 (different studies have indicated different limits). It is therefore often useful to define the specific creep as the creep strain per unit stress in this region. At higher stress levels increased creep is observed, which can ultimately result in failure.
- Increasing concrete strength, which decreases the creep.
- Increasing temperature, which increases the creep significantly for temperatures up to about 70°C. Above this, moisture migration effects lead to lower creep.
- The aggregate volume concentration, illustrated in Fig. 3, which shows that the aggregate is inert as regards creep, and hence the creep of concrete is less than that of cement paste.
Neville (1964) suggested a relationship between the creep of concrete (Cc) and that of neat cement paste (Cp) of the form:
Cc/Cp = (1 – g – u)n
where g and u are the volume fractions of aggregate and unhydrated cement, respectively, and n is a constant that depends on the modulus of elasticity and Poisson’s ratio of the aggregate and the concrete. This therefore shows that:
- the properties of the aggregate are important, and they can have a substantial effect of the magnitude of the creep
- the effect of the water:cement ratio and age of the concrete need not be considered separately, since they both affect the elastic modulus the effect of other materials that also affect the rate of gain of strength, such as admixtures and cement replacement materials, can be treated similarly.
Mechanisms of Creep
Since the creep process occurs within the cement paste, and the moisture content and movement have a significant effect on its magnitude, it is not surprising that the mechanisms proposed for creep have similarities with those proposed for shrinkage. As with shrinkage, it is likely that a combination of the mechanisms now outlined is responsible.
The applied stress causes changes in the internal stresses and strain energy within the HCP, resulting in an upset to the thermodynamic equilibrium; moisture then moves down the induced free-energy gradient, implying a movement from smaller to larger pores, which can occur at several levels:
- in capillary water as a rapid and reversible pressure drop
- in adsorbed water moving more gradually from zones of hindered adsorption – this movement should be reversible
- in interlayer water diffusing very slowly out of the gel pores. Some extra bonding may then develop between the solid layers, so this process may not be completely reversible.
In sealed concrete there are always enough voids to allow the movement of moisture, hence basic creep can occur with this mechanism. With simultaneous drying, all of the processes are much enhanced, hence explaining drying creep.
Stress concentrations arise throughout the HCP structure because of its heterogeneous nature, and consolidation to a more stable state without loss of strength occurs at these points by either viscous flow, with adjacent particles sliding past each other, or local bond breakage, closely followed by reconnection nearby after some movement. Concurrent moisture movement is assumed to disturb the molecular pattern, hence encouraging a greater structural adjustment. The mechanisms are essentially irreversible.
We have seen that HCP and concrete contain defects and cracks before loading, and propagation of these and the formation of new cracks will contribute to the creep strain, particularly at higher levels of stress. This is the most likely explanation of the non-linearity of creep strain with stress at high stress levels. In a drying concrete, the stress gradient arising from the moisture gradient is likely to enhance the cracking.
Delayed Elastic Strain
The ‘active’ creeping component of HCP or concrete, i.e. mainly water in its various forms in the capillary or gel pores, will be acting in parallel with inert material that will undergo an elastic response only. In HCP this will be solid gel particles, unhydrated cement particles and portlandite crystals, augmented in concrete by aggregate particles.
The stress in the creeping material will decline as the load is transferred to the inert material, which then deforms elastically as its stress gradually increases. The process acts in reverse on removal of the load, so that the material finally returns to its unstressed state; thus the delayed elastic strain would be fully recoverable in this model.
Prediction of Creep
As with shrinkage, it is often necessary to estimate the likely magnitude of the creep of a structural element at the design stage but, again, because of the number of factors involved, prediction of creep with a degree of certainty is problematic. Brooks and Neville (1978) have suggested that a satisfactory method is to carry out short-term (28-day) tests, and then estimate creep at a later age by extrapolation using the expressions:
basic creep ct = c28 × 0.5t0.21
total creep ct = c28 × (-6.19 + 2.15 loge t)0.38
where t = age at which creep is required (days, > 28)
c28 = measured specific creep at 28 days
ct = specific creep at t days in microstrain per MPa.
If short-term tests are not feasible, there are, as for shrinkage, a number of empirical methods of varying degrees of complexity for estimating creep, often included in design codes, e.g. Eurocode 2 (BS EN 1992) and ACI (2000).
Thanks for reading about “creep behaviour of concrete”.