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

Transcription

1 The Open Civil Engineering Journal, 2015, 9, OpenAess Study on the Effet of the Strength Grade on the Creep Behavior of Conrete Zheng Wenzhong *,1,2 and Tang Can 1 1 Shool of Civil Engineering, Harbin Institute of Tehnology, Harbin, Heilongjiang, , P.R. China 2 Key Lab of Strutures Dynami Behavior and Control of the Ministry of Eduation, Harbin Institute of Tehnology, Harbin, Heilongjiang, , P.R. China Abstrat: The internal fators whih influened the onrete reep behavior have been mostly divided by the reep model at home and abroad, but the omputing is omplex. In order to diretly use the reep model in engineering onveniently, it is neessary to onsider the effet of onrete strength grade on onrete reep. 302 reep test data with a loading age of 28 d, a lasting age of 360 d, and meet ertain environmental onditions were olleted. The strength of prism with different aspet ratio and high ratio of ylinder speimen was equivalent to the standard ube strength. The relationship between the reep ompliane and reep degree and the ube ompressive strength of onrete was fitted, and influene oeffiient of the strength grade on the reep degree and reep oeffiient were obtained. The influene oeffiient an be used to determine reep value, reep oeffiient, reep degree of onrete. In this paper, the effet of the strength grade on reep was onsidered diretly, whih involves the ube ompressive strength of onrete from 15 MPa to 180MPa. The researh results an be used in broad sope and has ertain pratial value. Keywords: Conrete, reep, strength grade, influene oeffiient. 1. INTRODUCTION Creep performane is an important index in the long term properties of onrete, and the linear ompressive reep deformation an reah 1-4 times of the short term elastiity ompressive deformation. Therefore, the reep behavior must be onsidered in the design of onrete strutures in order to provide neessary safety and omfortableness. For the important engineering strutures, reep experiment of the speimen, whih is made from the same onrete used in the strutures, is the most reliability method. However, due to the omplexity and diversity, there are not always suffiient ondition to arry out reep experiment, so the empirial formula fitted from the obtained experimental data is essential [1]. There are many reep models used at home and abroad, suh as CEB-FIP series models, ACI 209 series models, GL model, B3 model, China Aademy of Building Researh model, Zhu Bofang model and Li Chengmu model et al. [2-5]. However, there are many differene in the influene fators, formula form, appliable sope and predition auray of these models due to limitation of speifi experimental ondition and the emphasis of different researhers. The inner fators, whih are influened the reep behaviors, are differentiate arefully by the obtained models at home and abroad. The orretion fator of mixture ratio of onrete was given in CEB-FIP series models. The orretion fator of ollapsibility, sand ratio and air ontent was onsidered in ACI 209 series models. The orretion fator of water ement ratio, ement ontent, sand ratio and onrete density was onsider in B3 model. It an be onluded that the orretion fator is misellaneous, and it is neessary to promote a simplified model to onsider these fators. A large number of reep experiments of onrete were onduted by Conrete institute of China Aademy of Building Researh and sientifi researh units and institutions of higher learning in China from 1982 to 1986, and the China Aademy of Building Researh model-1986 was built up based on the experimental data. The experimental results show that the strength has great influene on the reep oeffiient of onrete, and the reep oeffiient is dereased with the inreasing of strength of onrete. Moreover, the reommendation value of the influene oeffiient of the reep oeffiient of C20 onrete, C30 onrete and C40 onrete are1.15, 1 and 0.8, respetively. The strength of onrete was onsidered as the only fator that influened the reep in the China Aademy of Building Researh model-1986, whih is different with other models. Advantage of this model is the onveniene and pratial, while the shortoming is the smaller fit range and low evaluation preision of the influene oeffiient. It is neessary to supplement more experimental data to optimize this model. The relation between the strength of onrete and the reep is developed based on the 284 data olleted from the experimental data in referenes, and the olleted data was / Bentham Open

2 882 The Open Civil Engineering Journal, 2015, Volume 9 Wenzhong and Can transformed to a uniform from under different strength. Moreover, the olleted data inlude experimental reep results with the ompressive strength in the region of 15MPa~180MPa, whih has a wide appliation in the ivil engineering. 2. DATA COLLECTING The reep data was olleted with uniform loading age of 28d, load lasting time of 360d and standard environment beause the reep of onrete will be affeted by the stress level, loading age, load lasting time and the environment. The linear reep ompliane data was olleted In the region of linear reep (stress level f 0.5 ), the reep ompliane is not depended on the stress level [1-2], so the linear reep ompliane data was olleted. 284 data was Table 1. Experimental data of linear reep. olleted whih are fulfilled the requirement of loading age of 28d, load lasting time of 360d and standard environment stated before. The dimension of speimen, the strength at loading age of 28d and the orresponding reep ompliane were shown in Table 1. The reep ompliane is defined as the sum of reep strain at unit stress and the short time strain, whih is express as 1 r J = + (1) E where E is the elasti modulus, MPa; is the reep strain of onrete; is lasting stress, MPa. [6] C [15] C [27] C C C [28] C [7] C C C C C [29] C C C C C C C C C C C C C C C C C [16] C C C C [30] C C C C C C C C [17] C C [8] C C C C C C C C [31] C C [18] C C C C C C C C C [19] C C C C C C C C [9] C C C C C C C C C

3 Study on the Effet of the Strength Grade on the Creep Behavior of Conrete The Open Civil Engineering Journal, 2015, Volume Table 1. Contd... C C C C C C C [20] C [32] C [10] C C C C [21] C C C C C C C C C C C C [22] C C [11] C C C C C [33] C C C C C [23] C C C C C [12] C C C C C C C C C C C C C C [34] C C C C C C C C C C C C C C C C [13] C C C C C C C [24] C C C C C C C C C C C C C C C C C [14] C C C C C C C C C C C C C C C

4 884 The Open Civil Engineering Journal, 2015, Volume 9 Wenzhong and Can Table 1. Contd... MPa) C C C C C C C C C C C C C C C [15] C [25] C C C C C C C C C C [35] C C C C C C C C C C C C C C C C C [26] C C C C C C C C C C [36] P C C P C [27] C P C C P C C P C C P C C P C C P C C P C C P C C P C C P C C [37] P C C P C C Note: C76660 means a ylinder with radius r=76mm and height h=660mm; P means a prism with side length a=150mm and height h=550mm. For the ylinder, f 28 means the ompressive strength at loading age of 28d, and for the prism, f 28 means the ompressive strength of standard ubi. J is the reep ompliane at the load lasting time of 360d. 3. STRENGTH TRANSFORMING It is neessary to transform the ompressive strength in Table 1 to the ompressive strength of standard ubi (150mm150mm150mm), beause dimensions of speimens in the experimental reep data olleted in Table 1 are different, whih inlude different height width ratio prisms and different height diameter ratio ylinders. For the prism speimen, the f 28 in Table 1 is tested with standard

5 Study on the Effet of the Strength Grade on the Creep Behavior of Conrete The Open Civil Engineering Journal, 2015, Volume ubi speimen, and it is not need to transform. However, for the ylinder speimen, the height diameter ratio ( h (2 r ) ) was alulated first, then the funtion of transforming oeffiient and the height diameter ratio was fitted aording to the data in referene [39-43], whih is shown in Fig. (1). The ompressive strength of different height diameter ratio ylinders was transformed to the ompressive strength of the ylinders with a height diameter ratio of 1 aording to equation (2), and that will be transformed to the ompressive strength f of the ylinder with a dimension of 150mm300mm. Finally, the ompressive strength f was transformed to the ompressive strength of standard ubi f using f 0.8 f. ompressive strength of standard ubi f was established using the least square fitting method, whih is shown in equation (3). Equation (3) means the averaged value of the reep ompliane of the onrete ubi with different ompressive strength, whih is tested from the reep experiment at the loading age of 28d, loading lasting time of 360d and the standard environment. The relation between the reep ompliane and the ompressive strength has a little satter due to the unertainty of the reep testing environment, suh as the standard environment or room environment. The envelope urve with 95% onfidene of the data is shown in equation (4) and equation (5). Equation (4) and equation (5) mean the maximum and minimum value of the reep ompliane of different ompressive strength of onrete, whih is tested from the reep experiment at the loading age of 28d, loading lasting time of 360d and the standard environment, respetively. Fig. (1). Transforming oeffiient of ylinders with different height diameter ratio. h (2 r) 0.54 k = 1.71e h (2 r) 2 (2) where k is the transforming oeffiient of strength; h (2 r) is the height diameter ratio; h is the height of ylinder speimen, mm; r is the radius of ylinder speimen, mm. 4. RELATION BETWEEN COMPRESSIVE STRENGTH AND THE COMPRESSIVE CREEP Fig. (2) shows the satter figures of ( J, f ), whih was alulated from the transformed strength data of the olleted reep data in Table 1. It an be seen from Fig. (2) that the reep ompliane is dereased with the inreasing of the strength of onrete. The relation between the reep ompliane J at load lasting time of 360d and the averaged Fig. (2). Creep ompliane of onrete with different ompressive strength. (4 f ) 29 J e f = MPa 180MPa (3) (16 f ) 38 J e f = MPa 180MPa (4) ( f ) 20 J e f u,m = MPa 180MPa (5) where J is the total strain of unit stress at load lasting time of 360d, 10-6 MPa -1 ; f is ompressive strength of the standard onrete ubi, MPa. The empirial formula between the elastiity modulus of onrete and the ompressive strength of the standard onrete ubi is developed in referene [4], whih is shown in equation (6), and the elastiity modulus of onrete at different strength in Conrete struture design ode(gb ) is also alulated using equaton (6) u,m u,m Table 2. The standard and averaged value of the ompressive strength of the onrete ubi. Strength C15 C20 C25 C30 C35 C40 C45 C50 C55 C60 C65 C70 C75 C80 f u, k f u, m

6 886 The Open Civil Engineering Journal, 2015, Volume 9 Wenzhong and Can 5 E = 10 ( f ) (6) u,k where E is the elasti modulus, MPa; f u,k is Cube ompressive strength of standard values, MPa. Table 2 shows the statistial data of the standard and averaged value of the ompressive strength of the standard onrete ubi. Fitting ( f, f u,k) using least square fitting method, the relation funtion is obtained f = 0.9 f 5.1 (7) u,k Creep degree C means the reep at unit stress, and the relation between the reep degree C and the reep ompliane J is C = J 1 E (8) Substitute equation (3), equation (4), equation (5) and equation (6), equation (7) into equation (8), the relation between the reep degree C and the averaged value of the ompressive strength of the standard onrete ubi f is ((4 f ) 29) C = 320e 347 (0.9 f 5.1) + 9 (9) where C is the reep degree, whih means the reep at unit stress with load lasting time of 360d,(10-6 MPa -1 ); f is the averaged value of the ompressive strength of the standard onrete ubi. The influene oeffiient of strength on the reep degree, whih is defined as the ratio between reep degree of the onrete with different strength and the reep degree of f = 30MPa at the same load lasting time, is expressed as ((4 f ) 29) k = 2.59e 2.81 (0.9 f 5.1) (10) f u,c The reep degree of onrete with different strength at load lasting time of 360d was alulated from equation (9), and the influene oeffiient of strength on the reep degree alulated from equation (10) are shown in Table 3. It an be seen from Table 3 that the reep degree is depend on the strength, and the reep degree is dereased with the inreasing of the strength. The influene oeffiient of strength on the reep of the onrete k f, whih is defined as the ratio between reep of u,c the onrete with different strength and the reep of f =30MPa at the same stress level, is expressed as k ( f 30) k f = u, u,m f (11) u,c Table 4 shows the influene oeffiients of strength on the reep at the same stress level. It an be seen from Table 4 that the reep value has little differene when the stress level is equivalent and the ompressive strength of the ubi is at the region of 20MPa~50MPa. CONCLUSION In this paper, the effet of the strength grade on the reep behavior of onrete was studied. Some important onlusions are summarized as follow: (1) The effet of ompressive strength on the reep ompliane, the reep degree and the reep strain of onrete was obtained by the fitting of reep testing data olleted from referenes. The fitting results show that the reep ompliane and the reep degree is dereased with the inreasing of ompressive strength. (2) The reep is dereased with the inreasing of the ompressive strength of onrete at the same load lasting time. The reep of onrete is inreased first and then dereased with the inreasing of the ompressive strength, and the maximum value is at the ompressive strength of the ubi at the region of 30MPa~35MPa at the same stress level. The reep value has little differene when the stress level is equivalent and the ompressive strength of the ubi is at the region of 20MPa~50MPa. (3) The effet of ompressive strength on the ompressive reep of onrete is analyzed systematially, and it is very onvenient and pratial. The influene oeffiients of strength grade on the reep of onrete with the ompressive strength in the region of 15MPa~180MPa is developed in this paper, whih has a wide appliation in the ivil engineering. CONFLICT OF INTEREST The authors onfirm that this artile ontent has no onflit of interest. ACKNOWLEDGEMENTS This work was finanially supported by the National Natural Siene Foundation of China (Grant No ). Table 3. Creep degree and influene oeffiient of strength on the reep degree. f u, m C (10-6 MPa -1 ) k f u,c Table 4. Influene oeffiients of strength on the reep of onrete. f u, m k fu,

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