In this article we will discuss about:- 1. Definition of Creep 2. Factors Influencing the Creep of Concrete 3. Measurement 4. Magnitude 5. Effects.
Definition of Creep:
Creep can be defined as the increase in strain under a sustained constant stress, taking into account other time dependent deformations not associated with stress viz., shrinkage, swelling and thermal deformations. Thus creep is reckoned from the initial elastic strain as given by secant modulus of elasticity at the age of loading. Although all materials undergo creep under certain conditions of loading to a greater or smaller extent, but the concrete creeps significantly at all stresses and for a long time.
The creep of concrete has been found approximately a linear function of stress upto 30 to 40% of its strength. The order of magnitude of creep of concrete is much greater than that of other crystalline materials except for metals in the final stage of yielding prior to failure.
Thus it is a very important factor in the design of concrete structures as creep is several times larger than the strain on loading. If the sustained load is removed after some time, the strain decreases immediately by an amount equal to the elastic strain. Generally this strain is smaller than the initial elastic strain due to the increase in the modulus of elasticity with age. The instantaneously recovery is followed by a gradual decrease in strain called creep recovery as shown in Fig.15.7.
The shape of the creep recovery curve is similar to that of creep curve, but the rate of recovery is very fast, and its maximum value reaches more radically. The creep recovery is always smaller than the preceding creep, so that there is a residual deformation even after a period of one day under load. Hence creep is not a completely reversible phenomenon. Creep per unit stress is known as specific creep.
Creep effects may also be seen from another point of view. If a loaded concrete specimen is restrained so that it is subjected to a constant strain, creep will show itself as a progressive decrease in stress with time. This phenomenon is called relaxation and is shown in Fig.15.8.
Factors Influencing the Creep of Concrete:
Creep has been found to be affected by the following factors:
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1. Cement Paste:
It should be noted that really it is the cement paste in concrete which undergoes creep. The role of aggregate in concrete is that of restraint. The usual normal weight aggregates are not liable to creep under the stresses existing in concrete. Thus creep is a function of the volumetric content of cement paste, but the relation is not linear.
2. Aggregate Content:
It may be noted that in the majority of the usual mixes the variation in the aggregate content is small, but on increase in the volumetric content of aggregate from 65% to 75% can decrease creep by 10%. The grading, maximum size and shape of aggregate have been observed to affect the creep. It is believed that their main influence lies on the aggregate content provided concrete is fully compacted in all cases.
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In fact there are certain physical properties of aggregate which influence the creep of concrete.
They are as follows:
(a) Modulus of Elasticity of Aggregate:
This is the most important factor, influencing the creep of concrete. Higher the modulus elasticity of aggregate, the greater the restraint offered by the aggregate to the potential creep of the cement paste i.e. lesser the creep Fig.15.9.
(b) Quality of Aggregate:
The aggregate influences the creep of concrete through the restraining effect on the magnitude of the creep. The creeping of paste under load is restrained by the aggregates which do not creep. The stronger the aggregate, more is the restraining effect resulting in lesser magnitude of creep is shown in Fig.15.10. After about 25 years, sand stone shows greatest creep while lime stone shows lowest creep.
(c) Porosity of Aggregate:
Porosity also has been found to influence the creep of concrete, but is not an independent factor to influence the creep of concrete. The porosity of aggregate plays an important role in the transfer of moisture with in the concrete, which is associated with the creep of concrete, as the transfer of moisture produces conditions of development of drying creep. Higher the porosity, lower the modulus of elasticity, hence higher the creep.
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3. Effect of Mineral Composition of Aggregate:
Though it is not possible to make a general statement about the magnitude of creep of concrete made with different types of aggregates, however it has been observed that after 20 years’ storage at a relative humidity of 50%, concrete made with sand stone aggregate showed creep more than twice that of concrete made with lime stone.
The value of creep of different rocks is shown in Table 15.2 below:
Even a greater difference between the creep strains of concrete made with different aggregates was discovered by RUSCH et al. He observed that after 18 months under load at a relative humidity of 65% the maximum creep was five times that of the minimum creep. The aggregates in the increasing order of creep are basalt, quartz, gravel, marble, granite and sand stone.
Grading, shape and the maximum size of aggregate have been found to affect the creep. The greater the maximum size of aggregate graded uniform from fine to coarse aggregate, the lesser the creep of concrete. This is true more specially for low water/cement ratio concrete.
4. Effect of Light Weight Aggregate:
The recent research has indicated that weight of aggregate has no effect on creep properties. The higher creep of concrete made with light weight aggregates is due to the lower modulus of elasticity of light weight aggregate.
As a general rule, it can be said that creep of structural quality light weight aggregate concrete is about the same as that of concrete made with normal aggregate. The elastic deformation of light weight aggregate concrete usually is larger than that of ordinary concrete. Thus the ratio of creep to elastic deformation is smaller for light weight aggregate concrete.
5. Effect of Stress:
In the direct stress tests on concrete a direct relation of proportionality between the creep and the applied load has been found to exist, but the upper limit is not certain. In terms of stress-strength ratio, an upper limit between 0.3 to 0.6 has been suggested.
In compression test of concrete specimen micro cracking takes place between the stress/strength ratios of 0.4 to 0.6. Thus as cracking starts, the creep behaviour also starts changing. Thus it can be concluded that within the range of working stresses, the proportionality between the creep and stress hold good.
Above the limit of proportionality, creep increases with the increase in stress at an increasing rate and above a certain stress/strength ratio, creep produces time failure. This stress/strength ratio exists in the region of 0.8 to 0.9 of the short term static strength.
6. Effect of Strength of Concrete on Creep:
It has observed that the strength of concrete has a considerable effect on the creep with in a wide range. Creep has been found inversely proportional to the strength of the concrete at the time of application of load.
The creep of concrete of different strengths is shown in Table 15.3 below:
The linear function between the creep and stress/strength at different relative humidity is shown in Fig. 15.11.
7. Effect of Mix Proportion:
In the majority of practical mixes of similar workability, the variation of cement is very small. For example, consider normal weight aggregate concrete having aggregate/cement ratio as 9, 6 and 4.5 and the corresponding w/c ratio as 0.75, 0.55 and 0.4, by weight the cement paste content would be 24, 27 and 29% respectively. The difference in cement paste is not much. Hence the creep of these concretes also must not differ much, but in fact this is not true as w/c ratio has most significant effect on creep.
We know that w/c ratio is the main factor which influences the porosity and strength. Thus lower the water/cement ratio, higher the strength. For constant cement paste content, decrease in water/cement ratio results in decrease of creep or higher the water/cement ratio, higher the creep. Thus with in the wide range of mixes, creep is inversely proportional to the strength of concrete at the age of application of the load.
Effect of Age at the Time of Loading:
It has been observed that for a given type of concrete, the creep decreases as the age at the time of application of load increases as the strength increases with age Fig.15.12.
Effect of Type of Cement:
The effect of type of cement on creep is not direct, but the type of cement affects the strength of concrete, hence creep is affected. On the basis of equality of the stress/strength ratio most Portland cements lead sensibly to the same creep.
Effect of Fineness of Cement:
Fineness of cement affects the strength development at early ages and thus influences the creep. It has been observed that the creep with fine-nest cement was greatest at first, but after 1000 days it became least due to the high gain of strength.
Effect of Relative Humidity of Ambient Air:
It has been observed that for a given concrete, lower the relative humidity of surrounding air, higher the creep. The effect of relative humidity of 10,070 and 50% humidity on the deformation is shown in Fig. 15.13.
Effect of Size of Specimen:
Creep has been found to decrease with the increase in the size of the specimen. This size effect is expressed in terms of the volume/surface ratio of concrete member as shown in Fig.15.14.
Effect of Temperature of Concrete:
In recent past the importance of influence of temperature on creep has assumed greater importance due to the use of concrete in nuclear pressure vessels as well as in other structures as bridges, multistory buildings etc. The time at which the temperature of concrete rises relative to the time of application of load, affects the creep-temperature relationship. If the saturated concrete is heated and loaded at the same time, the creep has been found greater than when concrete is heated during curing period prior to application of load.
The effect of these conditions in shown in Fig. 15.15.
The creep of concrete cured at high temperature is smaller due to the fact that the strength of concrete is higher when cured at high temperature than when cured at normal temperature before heating and loading.
It has been observed if un sealed concrete is subjected to high temperature at the same time or just prior to the application of load a rapid increase in creep takes place as the temperature increases to about 50°C, then a decrease takes place in creep to a temperature of about 120°C and again creep increases upto at least 400°C as shown in Fig.15.16. The initial increase in creep is due to the rapid expulsion of evaporable water. When all such water has been removed, creep is reduced greatly and becomes equal to that of pre dried concrete.
Fig. 15.17 shows the creep at Sow temperature as a proportion of creep at 20°C. At temperature below 20°C (68°F) creep decreases till the formation of ice which causes an increase in creep, but below the ice point creep decreases again.
Effect of Admixtures and Plasticizers:
Admixtures and plasticizers have been found to increase the creep of concrete, but not in all cases, hence before use their effect should be tested.
Measurement of Creep:
Usually creep is determined by measuring the change with time in the strain of a specimen of concrete subjected to a constant stress and stored under appropriate conditions. A typical testing device is shown in Fig. 15.18. The spring of the apparatus ensures that the load sensibly remains constant in spite of the contraction of the specimen with time. Under such conditions, creep continues for a long time, but the rate of creep decreases with time.
Under compressive stress the creep measurement is associated with shrinkage of concrete. To eliminate the effect of shrinkage and other autogenous volume charge, it is necessary to keep a companion specimen unloaded. While this correction qualitatively is correct, and gives usable results, but some researchers maintain that shrinkage and creep are not independent. At the same time they opine that shrinkage and creep are not additive as assumed in the test. Numerous mathematical formulae relating creep and time have been suggested. One of the most convenient relations is the hyperbolic expression suggested by Ross and Lorman.
The Ross expression for specific creep C after time V under load is as follows-
C = [t/(a +bt)] …(i)
where a and b are constants. If a graph is plotted between t and t/c, Taking t on x axis and t/c on y-axis, a straight line is obtained as shown in Fig. 15.19. The value of b is given by the slope and the intercept of t/c on y-axis gives the value of ‘a’. Thus the values of constants a and b can be determined easily from the curve. Creep strain per unit stress is called specific creep.
The straight line should be so drawn that it passes through the points at later ages also. There may be some deviation from straight line during the early period after the application of load.
From the above relation (i), when the t is infinite, the ultimate creep at infinite time will be 1/b, and when t = a/b, c will be 1/2.b i.e., it will be one half of the ultimate creep, obtained at time t = a/b.
If a loaded concrete member is kept in atmosphere and subjected to shrinkage, the deformation in the member will be developed from three different causes, namely elastic deformation, dry shrinkage and creep deformation. The time dependent deformation in concrete subjected to sustained load. In order to calculate the magnitude of creep in a member subjected to drying a companion specimen is always placed at the same temperature and relative humidity condition and the drying shrinkage of the un-loaded specimen is determined.
To find out the magnitude, of the creep the value of the drying shrinkage is subtracted from the total deformation of the loaded member. Knowing the instantaneous elastic deformation, the creep deformation can be calculated. For the sake of simplicity, it is assumed that shrinkage of concrete does not affect the creep in addition to load. In fact it should be remembered that in addition to the load, the shrinkage also has some influence on the magnitude of creep and creep on shrinkage.
Hydration under Sustained Load:
Under sustained load the cement paste undergoes creep deformation continuously. If a concrete member is subjected to a drying condition, it will also undergo continuous shrinkage process. The migration of liquid from the gel pores due to creep may develop shrinkage to some extent. Thus it can be said that, the creep, the shrinkage and slip deformation cause deformation and fine or micro cracks at the discontinuities. Along with this phenomenon the process of hydration also goes on side by side producing more gel, which heals up the fine cracks produced by creep and shrinkage.
This healing up of fine creaks by the delayed hydration process is also responsible for increasing the irrecoverable components of the deformation. Thus in actual practice, concrete structures are subjected to loading and drying and at the same time to some extent the delayed hydration also takes place. Under such complex situation the structure undergoes creep, drying shrinkage and also experiences micro cracks. Due to the progressive hydration the micro cracks formed due to any reason are healed up. This process is known as hydration under sustained load.
Magnitude of Creep:
Generally it is assumed that creep tends to a limiting value after an infinite time under load.
But later studies have shown that the increase in creep beyond twenty 20 years under load is small and as a guide following values may be assumed:
1. From 18 to 35% (an average value of 26%) of the 20 year creep occurs in 2 weeks. Some authors have suggested 25% instead of 26%.
2. From 40 to 70% (an average value of 55%) of the 20 years creep occurs in 3 months. Some authors have suggested 50% instead of 55%.
3. From 64 to 83% (an average value 76%) of the 20 years creep occurs in 1 year. Some authors have suggested 75% instead 76%.
If creep after 1 year under load is taken as unity, then the average value of creep at later ages may be assumed as follows:
1.14 times after 2 years
1.20 times after 5 years
1.26 times after 10 years
1.33 times after 20 years
1.36 times after 30 years
These values show that ultimate creep is 1.36 times the one year creep. For calculation purposes, often it is assumed that ultimate creep is 4/3 times of 1 year creep. This estimated value is correct with in ± 15% for concretes loaded at early ages.
Effects of Creep:
The creep of concrete increases the deflection of reinforced beams and in some cases it may be a critical consideration in design, the deflection due to creep increases with time.
In reinforced concrete columns creep property of concrete has been found useful. Under load elastic deformation takes place immediately. Concrete creeps and deforms. It cannot deform independent of steel reinforcement. There will be gradual transfer of stress from concrete to reinforcement. The creep results in a gradual transfer of load from concrete to reinforcement. Once the steel yields, any increase in load is taken by the concrete, so that the full strength of both steel and concrete is developed before the failure takes place. However in eccentrically loaded columns the creep increases the deformation, leading to buckling.
In case of statically indeterminate structures, column and beam junctions, creep may relieve the stress concentration induced by shrinkage, temperature changes or movements of support. In all concrete structures, creep reduces internal stresses due to non-uniform or restrained shrinkage, so that there is a reduction in cracking. Thus creep is useful for concrete structures.
In case of mass concrete structures such as dams, creep is harmful and by itself may be a cause of cracking when the interior restrained concrete undergoes a cycle of temperature change due to the development of heat of hydration and subsequent cooling. Another example of adverse effects of creep is of tall buildings, in which case the differential creep between inner and outer columns may cause movements and cracking of partitions. Thus all precautions must be taken to reduce the differential movements.
Loss of pre-stress due to creep of concrete of pre-stressed concrete structures (beams), is well known and suitable provisions should be made to prevent the loss of pre stress in the design itself.