Influence of strength and curing age on concrete fracture energy adjusted by fractal method

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1 Influence of strength and curing age on concrete fracture energy adjusted by fractal method J.G. Han 1, P.Y. Yan 2 1 epartment of Civil Engineering, Tsinghua University, Beijng, China 2 epartment of Civil Engineering, Tsinghua University, Beijng, China BSTRCT: Using RILEM TC 162-TF standard, concrete of different strength and curing age were tested to get the load-deflection curve. Then, fracture energy was calculated according to RILEM 5-FMC standard. Meanwhile, fractal method was used to adjust the fracture area during the calculation of fracture energy. Research results show that fracture energy is influenced by concrete strength, curing age and fracture style; fracture energy increase along with the increase of concrete strength and curing age after the adjustment of fracture area. 1 INTROUCTION Fracture energy is the energy dissipated during the crack of per unit area. In fracture mechanics, several models such as Fictitious Crack Mode (FCM) and Blunt Crack Model (BCM) are used to simulate concrete structure behavior under tension force. In those models, fracture energy is used as a material parameter to evaluate the failure tendency of concrete structure. The value of fracture energy can be evaluated by experiment following different specification, such as those methods recommended by Hillerborg (1985) and Bazant (1987). Meanwhile, avid (21a) and Giaccio (1993) show that the value of fracture energy can be influenced by concrete strength, coarse aggregate type and size; and Zhao (28) and Zhang (1999) show that the value of fracture energy can be influenced by specimen dimension and span to depth ratio. In this paper, using RILEM TC 162-TF standard, concrete of different strength and curing age were tested to get the load-deflection curve. Then, fracture energy was calculated according to RILEM 5-FMC standard. Meanwhile, fractal method was used to adjust the fracture area during the calculation of fracture energy. 2 EXPERIMENT 2.1 Materials and mix proportion The materials used including P.O 42.5 ordinary Portland cement, class F fly ash, silica fume with amorphous silica content more than 9%, river sand of the fineness modulus 2.8, limestone aggregate of the diameter 5-2mm, and polycarboxylate type water reducer. The mix proportion of different strength concrete is given in table 1. The workability of fresh concrete was adjusted by the dosage of water reducer to be 16mm slump. Fresh concrete was cast to steel mold and consolidated by vibration; concrete specimens were covered with a plastic

2 sheet and cured under room temperature. fter demoulding, concrete specimens were cured under standard condition, with T=2 and RT 95%. Table 1 Concrete mix proportion Number Cement Fly ash Silica fume Water W/B Sand C ggregate C C Test procedure The dimension of concrete specimen is mm. One day before the due age, concrete specimens were cut with a diamond saw to make a central notch, with the depth 25mm. after cutting, concrete specimens were cured continually until testing. The test apparatus include a servo-controlled hydraulic machine and a linear variable differential transformer (LVT) as deflection data collector. s illustrated in figure 1, the loaddeflection curve was tested according to RILEM TC 162-TF standard, with the support span to be 5mm and the deflection speed controlled as.2mm/min. Figure 1 Illustration of the three points loading. 3 RESULT N NLYSIS The typical load-deflection curve is illustrated in figure 2, and the fracture energy is calculated according to RILEM 5-FMC standard using equation 1. G = ( W + mgδ )/ F In which, G F is fracture energy (N/m); W is the area under load-deflection curve (N m); m is the weight of concrete specimen between the supports, plus two times the weight of loading arrangement which is not attached to the machine (kg); g is the acceleration due to gravity, usually equals to 9.81 m/s 2 ; δ is the deflection at the final failure of the specimen (m); and is the area of the ament, defined as the projection of the fracture zone on a plane perpendicular to the beam axis (m 2 ). (1)

3 1 8 Load / N eflection / mm Figure 2 Illustration of the load-deflection curve. Using equation 1, the fracture energy of different strength concrete at the age of 7 and 28 days are calculated and given in figure 3. In figure 3, the number on the abscissa after the dash stands for the curing age and the number before the dash stands for concrete strength grade. s can be seen in figure 3, although fracture energy increases along with the prolongation of curing age, the fracture energy does fluctuate along with the increase of strength; there is not a direct relation ship between concrete strength and fracture energy. Yan (21) and arwin (21b) s research results also testified such phenomenon, they think the character of the aggregate and fracture style have significant influence on the fracture process, thus influence the loaddeflection curve and calculated fracture energy. 25 Fracture energy /N/m C4-7 C4-28 C6-7 C6-28 C8-7 C8-28 Strength grade and curing age Figure 3 Influence of strength and curing age on fracture energy. *: C8-28 specimen manifests sudden fracture at maximum load during test. To enhance the precision of the calculated fracture energy, the influence of fracture style on the roughness of the fracture area is considered in this paper. Thus fractal method is adopted to adjust the ament area used in equation 1. First, a morphology analyzer is used to measure the area of the fracture surface, as illustrated in figure 4, and the result is presented as the area ratio of the measured fracture area and its projection area, which is given in figure 5. s can be seen in figure 5, along with the increase of strength and curing age, the area ratio tend to decrease, and for high strength concrete, the influence of strength is more significant than curing age.

4 2 15 Z axis /mm Y axis /mm 5 5 X axis /mm 1 15 Figure 4 Morphology of the fracture surface rea ratio C4-7 C4-28 C6-7 C6-28 C8-7 C8-28 Strength grade and curing age Figure 5 Influence of strength and age on area ratio. Then, fractal method is used to calculate the fractal dimension of the fracture surface. ccording to Mandelbrot (1984) s box-cutting method and Lange (1993) s calculating method, the fractal dimension can be expressed as equation 2. = log ( r) r 2 lim r log In which, is the fractal dimension; r () is the area ratio of fracture surface area and its projection; r is the length ratio used to measure the fracture surface area and its projection. Using a series of area ratio and length ratio data, a graph can be made and the slope can be calculated, thus the fractal dimension can be calculated. fter the calculation of fractal dimension, Saouma (1994) s calculating method is used to adjust the ament area in equation 1, the adjusted fracture area is expressed as equation 3. = L 2(2 ) ( ) L (2) (3)

5 In which, is the adjusted fracture area (m 2 ); L is the unit used to measure the projection of the fracture area, in this paper it is defined as 1mm; L is the unit used to measure the size of CSH gel, Saouma defined it as.4 inch. fter the adjustment of ament area and substitute the value of by in equation 1, the adjusted fracture energy is given in figure 6. It can be seen in figure 6 that the fracture energy increases along with the increase of concrete strength and curing age Fracture energy /N/m 1 5 C4-7 C4-28 C6-7 C6-28 C8-7 C8-28 Strength grade and curing age Figure 6 Influence of strength and curing age on fracture energy after adjustment of fracture area. 4 CONCLUSION Research results show that fracture energy is influenced by concrete strength and curing age. fter the adjustment of fracture area using fractal method, the influence of fracture style on fracture energy is considered, and experiment results show that fracture energy increase along with the increase of concrete strength and curing age. cknowledgment This work is supported by the National Science and Technology Supporting Plan of China under grant 28BE61B5. Reference Bazant, Z. P. and Pfeiffer P..(1987) etermination of fracture energy from size effect and brittleness number, CI Materials Journal, 84(6): avid,. Barham, S. Kozul, R. and Luan, S.(21) Fracture energy of high-strength concrete, CI Materials Journal, 98(5): Giaccio, G. Rocco, C. and Zerbino, R. (1993) Fracture energy (GF) of high-strength concretes, Materiaux et constructions, 26(161): Hillerborg,.(1985) The theoretical basis of a method to determine the fracture energy GF of concrete, RILEM Materials and Structures, 18 (16): Lange,.. Jennings, H.M. and Shah, S.P. (1993) Relationship between fracture surface roughness and fracture behavior of cement paste and mortar, Journal of merican Ceramic Society, 76(3): Mandelbrot, B. Passoja,.E. and Paullay,.J.(1984) Fractal character of fracture surfaces of metal, Nature, 38 (19): Saouma, V.E. and Barton, C.C. (1994) Fractals, Fractals, fractures, and size effects in concrete, Journal of Engineering Mechanics, 12(4): Yan,. Wu, K. R. Zhang,. and Yao, W. (21) Effect of fracture path on the fracture energy of highstrength concrete, Cement and Concrete Research, 31(11):

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