Creep is defined as the gradual increase in strain with time for a constant applied stress after accounting for other time-dependent deformations not associated with stress, namely, shrinkage or swelling and thermal strain. Hence, creep is reckoned from the elastic strain at loading, which depends upon the rate of application of stress (see Section 3.2) so that the time taken to apply the load should be quoted. Also, since the secant modulus of elasticity increases with time, the elastic strain decreases so that creep should be taken as the strain in excess of the elastic strain at the time in question. However, the change in elastic strain is usually small and creep is reckoned from the elastic strain on first application of load. Like other engineering materials, concrete can suffer a time-dependent failure, which is known as creep rupture or static fatigue. Figure 3.7 represents the general strain-time history of such a material. Initially, there is a high rate of primary creep and then a steady rate of secondary creep before failure occurs after the tertiary creep stage, as characterised by the rapid development of strain. In the case of concrete, the stress needs to exceed approximately 0.6 to 0.8 of the short-term strength for creep rupture to occur in either compression or tension. Concrete is often described as a brittle material since it readily cracks under small strains, but in the case of creep rupture it can develop large strains prior to failure, providing an advantage of early warning in the case of sudden and catastrophic failure. Figure 3.8 illustrates the pattern of stress and strain for varying rate of loading and level of sustained stress leading to creep rupture; actual experimental results for compression were obtained by Rusch (1960) and for tension by Domone (1974). Very high rate of loading produces a near linear stress-strain curve with a higher strength than in the usual standard test (Fig. 3.8(a)), but decreasing the rate of loading or increasing the test duration produces non-linear curves due to creep and microcracking with a lower strength (creep rupture). The creep rupture envelope tends to a constant limit of between 0.6 and 0.8 of the usual short-term strength, depending on the type of concrete and mode of loading. With sustained stresses below approximately 0.6 of short-term strength, creep rupture is avoided and time-dependent strain due to primary and some secondary creep takes place for several years. Depending on the type of mix and other factors, creep of dry-stored concrete can be between two and nine times the elastic strain at loading, with around 70% occurring after one year under load (Brooks, 2005).
As stated earlier, the definition of creep is the increase in strain for a constant sustained stress and is determined from concrete specimens after deducting any drying shrinkage (measured on a separate specimen) and the initial elastic strain. Figure 3.9(a) shows the components of strain involved. In the case of sealed concrete, which represents mass or large-volume concrete where little or no moisture is lost, only basic creep occurs, but when the concrete is allowed to dry additional drying creep occurs even though drying shrinkage has been deducted from the measured strain; the sum of basic and drying creep is sometimes called total creep. Creep is a partly reversible phenomenon. When the load is removed, there is an immediate, almost full, elastic recovery of the initial elastic strain, followed by a gradual decrease of strain called the creep recovery (Fig. 3.9(b)). The recovery quickly reaches a maximum and is only small, e.g. 1±25% of the 30-year creep (Brooks, 2005). Consequently, creep is mostly irreversible in nature.
Like shrinkage, creep can be expressed in units of microstrain (10ÿ6), but because of the dependency on stress, specific creep (Cs) is often used with units of 10ÿ6 per MPa. Other terms are creep coefficient (@) . The creep coefficient is defined as the ratio of creep to the elastic strain on loading and for a unit stress:
The effects of creep can be realised from another viewpoint. When a concrete specimen is loaded and then prevented from deforming, then creep will manifest itself as a gradual decrease or relaxation of stress with time, as illustrated in Fig. 3.10. Relaxation is of interest in connection with loss of prestress in prestressed and post-tensioned concrete and cracking processes (see Section 3.3). Apparatus for the determination of creep of any type of concrete is recommended in ASTM C512 (1987) and for prefabricated aerated or lightweight concrete by BS EN 1355 (1997). Alternative methods are described in Neville et al. (1983) and Newman and Choo (2003). There have been many theories proposed to explain the creep of hardened cement paste and concrete, which are too numerous to include within the scope of this chapter. Most agree that creep at normal stresses is caused by the internal movement of water adsorbed or held within the C-S-H, since concrete from which all the evaporable water has been removed exhibits little or no creep unless high temperatures are involved. Movement of water to the outside environment is required for drying creep to occur. Although basic creep is associated with sealed or mass concrete, it is thought that internal movement of water occurs because all the pores do not remain full of water. The dependency of basic creep on strength is indirect evidence that empty or part-empty pores are a main factor. Creep also occurs at high temperatures when non-evaporable water is removed and this is thought to be due to movement of interlayer or zeolitic water, viscous flow or sliding between gel particles (Illston et al., 1979; Mindess and Young, 1981; Neville et al., 1983; Bazant, 1988; Brooks, 2001). The source of creep of concrete is the hydrated cement paste and not normal weight aggregate of good quality. Some light aggregates may exhibit creep. However, like shrinkage, the role of aggregate is an important factor in creep due to the restraining influence on the cement paste through its stiffness or modulus of elasticity and volume concentration. The relationship between modulus of elasticity of aggregate and relative creep of concrete is shown in Fig. 3.11. For a constant water/cement ratio, the volume of cement paste or total aggregate in concrete has a significant effect on creep (Neville and Brooks, 2002). However, in practice, concretes with similar workability normally have similar cement paste contents and so the differences in creep are not large.
For example, in normal weight concretes having aggregate/cement ratios of 9, 6 and 4.5, and corresponding water/cement ratios of 0.75, 0.55 and 0.40, the cement paste contents are 24, 27 and 29%, respectively. On the other hand, when the cement paste content is constant, an increase in water/cement ratio increases creep as shown in Fig. 3.12.
Since creep is related to the water/cement ratio it can be expected to be related to strength. Indeed, it has been found that over a wide range of mixes made with similar materials, creep is approximately inversely proportional to the strength of the concrete at the age of application of load. Moreover, for stresses less than approximately 0.6 of the short-term strength, creep is proportional to the applied stress, so that combining the dual influences leads to the stress/ strength ratio rule, namely, that creep is approximately proportional to the stress/ strength ratio (Neville et al., 1983). Consequently, since the strength increases with age, creep can be expected to decrease as the age at loading increases (Fig. 3.13).
Experimental work on saturated concrete specimens exposed to the atmosphere at different relative humidities shows that the drier the atmosphere the higher the creep. Figure 3.14 demonstrates that trend, the 100% curve approximating to that of basic creep so that the additional creep for 75 and 50%relative humidities is drying creep. If the concrete is allowed to dry out prior to application of load then creep is much less. However, it is ill-advised to allow concrete to dry out prematurely in order to reduce creep because of the risk of inadequate curing and cracking due to restrained or differential drying shrinkage (see Section 3.3.6). Creep of concrete is affected by size of member in a similar manner to drying shrinkage (see Fig. 3.6). Expressing size as the volume/exposed surface area ratio (V/S) or effective thickness ( 2V=S), which represents the average drying path length, total creep decreases as the volume/surface ratio or size increases (Fig. 3.15). Of course, it is the drying creep component that is influenced since basic creep is unaffected by size. This can be seen when the size of the member is large (mass concrete) when no moisture transfer to the environment takes place and basic creep occurs. It is also apparent from Fig. 3.15 that the influence of shape of concrete member is a secondary factor in creep and can be neglected. The influence of temperature on creep is complex and not fully understood, as it depends upon the time when the temperature of the concrete rises relative to the time of application of load (Neville et al., 1983). Figure 3.16 demonstrates different experimental results for concrete stored at elevated temperature in water (basic creep). Compared with normal-temperature creep, heating just prior to loading accelerates creep, and heating just after loading produces an additional component termed transitional thermal creep. In the case of drying concrete (total creep), elevated temperature causes increases in creep in a similar manner, but when the evaporable water has been removed (between approximately 80 and 120 ëC) there is a decrease in creep before increasing again (Neville et al., 1983). At very high temperatures, such as in fire, very high creep occurs, termed transient thermal strain (Khoury et al., 1985). The type of cement will affect creep if the strength changes at the time of application of load. When the stress/strength ratio at the age of loading is the same, most Portland cements lead to approximately the same creep, but the strength development under load is a factor, e.g. creep will be lower for a greater strength development (Neville and Brooks, 2002). The latter influence is apparent when certain mineral admixtures, such as fly ash and ground granulated blast-furnace slag, are used as partial replacements for Portland cement. The resulting slower pozzolanic reaction often leads to a later strength development than in the case of Portland cement. Figure 3.17 shows the general trends for fly ash, blast-furnace slag, silica fume and meta- kaolin, which are mainly based on the analysis of results of previously published data (Brooks, 2000). That analysis accounted for any changes in aggregate content and water/cementitious materials ratio on creep by considering the relative stress/strength ratio so that the effect of just the mineral admixture could be assessed. Although there is a large variation, it can be seen that fly ash and slag can lead to significant reductions in creep. In the case of the finer mineral admixtures: silica fume and metakaolin, there are larger reductions in creep for replacement levels of up to 15%, but then for silica fume creep increases as the replacement level increases. Generally, the addition of chemical admixtures, plasticisers and super- plasticisers, to make flowing concrete causes a 20% reduction in creep at a constant stress/strength ratio, although the effects do vary widely (Brooks, 2000). When the same admixtures are used as workability aids or water reducers, creep will be less due to the lower water content. As well as reducing shrinkage (see Section 3.3), the use of a shrinkage-reducing admixture appears to reduce drying creep, although experimental verification is limited. For design purposes, estimation of elastic deformation, creep and drying shrinkage are considered together in Codes of Practice. From only a knowledge of strength, mix composition and physical conditions, BS 8110: Part 2 (1985) gives creep and shrinkage after 6 months and 30 years, depending upon the relative humidity and size of member. ACI 209 (1992) and CEB-FIP (1999) methods express creep and shrinkage as functions of time and allow for all the main influencing factors that have been discussed earlier. Alternative models are available by Bazant and Baweja (1995) and Gardner and Lockman (2001). Creep and drying shrinkage estimates by all methods are not particularly accurate (+- (30% at best) mainly because they fail to account for the type of aggregate (Brooks, 2005). For more accurate estimates and for high performance concretes containing several admixtures, short-term tests are recommended. The test duration should be of at least 28 days using small laboratory specimens made from the actual concrete mix and then measured creep and shrinkage-time data extrapolated to obtain long-term values, which are then adjusted according to the required member size and the average relative humidity of the storage conditions (Brooks and Al-Quarra, 1999). All methods of prediction give an estimate of the creep function (equation 3.6) and drying shrinkage, the total strain, t; to, at age t when determined from age to being given by:
The importance of creep in structural concrete lies mainly in the fact that, in the long term, it can be several times the elastic deformation when first loaded.
Consequently, the designer has to assess creep in order to comply with the serviceability requirement of deflection in particular. There are other effects of creep, most of which are detrimental, such as loss of prestress in prestressed concrete and differential movements in tall buildings, but creep can be beneficial when relieving stress induced by restraint of deformations.