Study on the Effect of the Strength Grade on the Creep Behavior of Concrete

The internal factors which influenced the concrete creep behavior have been mostly divided by the creep model at home and abroad, but the computing is complex. In order to directly use the creep model in engineering conveniently, it is necessary to consider the effect of concrete strength grade on concrete creep. 302 creep test data with a loading age of 28 d, a lasting age of 360 d, and meet certain environmental conditions were collected. The strength of prism with different aspect ratio and high ratio of cylinder specimen was equivalent to the standard cube strength. The relationship between the creep compliance and creep degree and the cube compressive strength of concrete was fitted, and influence coefficient of the strength grade on the creep degree and creep coefficient were obtained. The influence coefficient can be used to determine creep value, creep coefficient, creep degree of concrete. In this paper, the effect of the strength grade on creep was considered directly, which involves the cube compressive strength of concrete from 15 MPa to 180MPa. The research results can be used in broad scope and has certain practical value.


INTRODUCTION
Creep performance is an important index in the long term properties of concrete, and the linear compressive creep deformation can reach 1-4 times of the short term elasticity compressive deformation.Therefore, the creep behavior must be considered in the design of concrete structures in order to provide necessary safety and comfortableness.For the important engineering structures, creep experiment of the specimen, which is made from the same concrete used in the structures, is the most reliability method.However, due to the complexity and diversity, there are not always sufficient condition to carry out creep experiment, so the empirical formula fitted from the obtained experimental data is essential [1].
There are many creep models used at home and abroad, such as CEB-FIP series models, ACI 209 series models, GL-2000 model, B3 model, China Academy of Building Research model, Zhu Bofang model and Li Chengmu model et al. [2][3][4][5].However, there are many difference in the influence factors, formula form, applicable scope and prediction accuracy of these models due to limitation of specific experimental condition and the emphasis of different researchers.The inner factors, which are influenced the creep behaviors, are differentiate carefully by the obtained models at home and abroad.The correction factor of mixture ratio of concrete was given in CEB-FIP series models.The correction factor of collapsibility, sand ratio and air content was considered in ACI 209 series models.The correction factor of water cement ratio, cement content, sand ratio and concrete density was consider in B3 model.It can be concluded that the correction factor is miscellaneous, and it is necessary to promote a simplified model to consider these factors.
A large number of creep experiments of concrete were conducted by Concrete institute of China Academy of Building Research and scientific research units and institutions of higher learning in China from 1982 to 1986, and the China Academy of Building Research model-1986 was built up based on the experimental data.The experimental results show that the strength has great influence on the creep coefficient of concrete, and the creep coefficient is decreased with the increasing of strength of concrete.Moreover, the recommendation value of the influence coefficient of the creep coefficient of C20 concrete, C30 concrete and C40 concrete are1.15, 1 and 0.8, respectively.The strength of concrete was considered as the only factor that influenced the creep in the China Academy of Building Research model-1986, which is different with other models.Advantage of this model is the convenience and practical, while the shortcoming is the smaller fit range and low evaluation precision of the influence coefficient.It is necessary to supplement more experimental data to optimize this model.
The relation between the strength of concrete and the creep is developed based on the 284 data collected from the experimental data in references, and the collected data was transformed to a uniform from under different strength.Moreover, the collected data include experimental creep results with the compressive strength in the region of 15MPa~180MPa, which has a wide application in the civil engineering.

DATA COLLECTING
The creep data was collected with uniform loading age of 28d, load lasting time of 360d and standard environment because the creep of concrete will be affected by the stress level, loading age, load lasting time and the environment.The linear creep compliance data was collected In the region of linear creep (stress level c 0.5 f ), the creep compliance is not depended on the stress level [1][2], so the linear creep compliance data was collected.284 data was collected which are fulfilled the requirement of loading age of 28d, load lasting time of 360d and standard environment stated before.The dimension of specimen, the strength at loading age of 28d and the corresponding creep compliance were shown in Table 1.
The creep compliance is defined as the sum of creep strain at unit stress and the short time strain, which is express as where c E is the elastic modulus, MPa; c is the creep strain of concrete; is lasting stress, MPa.   1 is tested with standard cubic specimen, and it is not need to transform.However, for the cylinder specimen, the height diameter ratio ( (2 ) h r ) was calculated first, then the function of transforming coefficient and the height diameter ratio was fitted according to the data in reference [39][40][41][42][43], which is shown in Fig. (1).The compressive strength of different height diameter ratio cylinders was transformed to the compressive strength of the cylinders with a height diameter ratio of 1 according to equation ( 2), and that will be transformed to the compressive strength c f of the cylinder with a dimension of   where k is the transforming coefficient of strength; (2 )  h r is the height diameter ratio; h is the height of cylinder specimen, mm; r is the radius of cylinder specimen, mm.

RELATION BETWEEN COMPRESSIVE STRENGTH AND THE COMPRESSIVE CREEP
where J is the total strain of unit stress at load lasting time of 360d, 10 -6 MPa -1 ; f cu,m is compressive strength of the standard concrete cubic, MPa.
The empirical formula between the elasticity modulus of concrete and the compressive strength of the standard concrete cubic is developed in reference [4], which is shown in equation (6), and the elasticity modulus of concrete at different strength in 'Concrete structure design code(GB 50010-2010)' is also calculated using equaton (6) Substitute equation ( 3), equation ( 4), equation ( 5) and equation (6), equation (7) into equation (8), the relation between the creep degree C and the averaged value of the compressive strength of the standard concrete cubic cu, m f is ) 29 cu ,m 320 347 (0.9 5.1) 9 where C is the creep degree, which means the creep at unit stress with load lasting time of 360d,(10 -6 MPa -1 ); cu, m f is the averaged value of the compressive strength of the standard concrete cubic.
The influence coefficient of strength on the creep degree, which is defined as the ratio between creep degree of the concrete with different strength and the creep degree of cu, m 30M Pa f = at the same load lasting time, is expressed as ) 29 cu, m 2.59 2.81 (0.9 5.1) 0.073 The creep degree of concrete with different strength at load lasting time of 360d was calculated from equation ( 9), and the influence coefficient of strength on the creep degree calculated from equation (10) are shown in Table 3.It can be seen from Table 3 that the creep degree is depend on the strength, and the creep degree is decreased with the increasing of the strength.

The influence coefficient of strength on the creep of the concrete
Table 4 shows the influence coefficients of strength on the creep at the same stress level.It can be seen from Table 4 that the creep value has little difference when the stress level is equivalent and the compressive strength of the cubic is at the region of 20MPa~50MPa.

CONCLUSION
In this paper, the effect of the strength grade on the creep behavior of concrete was studied.Some important conclusions are summarized as follow: (1) The effect of compressive strength on the creep compliance, the creep degree and the creep strain of concrete was obtained by the fitting of creep testing data collected from references.The fitting results show that the creep compliance and the creep degree is decreased with the increasing of compressive strength.
(2) The creep is decreased with the increasing of the compressive strength of concrete at the same load lasting time.The creep of concrete is increased first and then decreased with the increasing of the compressive strength, and the maximum value is at the compressive strength of the cubic at the region of 30MPa~35MPa at the same stress level.The creep value has little difference when the stress level is equivalent and the compressive strength of the cubic is at the region of 20MPa~50MPa.
(3) The effect of compressive strength on the compressive creep of concrete is analyzed systematically, and it is very convenient and practical.The influence coefficients of strength grade on the creep of concrete with the compressive strength in the region of 15MPa~180MPa is developed in this paper, which has a wide application in the civil engineering.
150mm 300mm.Finally, the compressive strength c f was transformed to the compressive strength of standard cubic cu, m f

Fig. ( 2 )
Fig. (2) shows the scatter figures of ( J , cu, m f ), which was calculated from the transformed strength data of the collected creep data in Table 1.It can be seen from Fig. (2) that the creep compliance is decreased with the increasing of the strength of concrete.The relation between the creep compliance J at load lasting time of 360d and the averaged

Table 1 .
Contd.... P150 550 means a prism with side length a=150mm and height h=550mm.For the cylinder, f 28 means the compressive strength at loading age of 28d, and for the prism, f 28 means the compressive strength of standard cubic.J is the creep compliance at the load lasting time of 360d.

Table 1 to
the compressive strength of standard cubic (150mm 150mm 150mm), because dimensions of specimens in the experimental creep data collected in Table 1 are different, which include different height width ratio prisms and different height diameter ratio cylinders.For the prism specimen, the f 28 in Table