Characterization of fiber distribution in steel fiber reinforced cementitious composites with low water-binder ratio
Jiaping Liu, Changfeng Li*, Jianzhong Liu, Zhaojin Du & Gong Cui
State Key Laboratory of High Performance Civil Engineering Materials, Jiangsu Research Institute of Building Science, Nanjing 210008, China
Received 7 January 2010, accepted 7 December 2011
Image analysis technique is introduced to characterize fiber distribution in steel fiber reinforced cementitious composites. Through cutting and polishing of specimen, image acquisition of specimen surface, extraction of fiber feature, and measurement of related fiber parameters, i.e., dispersion coefficient and orientation factor, are given to quantitatively analyze fiber distribution. Effects of specimen size, fiber volume fraction and aggregate characteristics on fiber distribution are discussed. Results show that the dispersion coefficient increases with the increase of specimen size and with the decrease of fiber volume fraction and aggregate size, but the changes are small. The orientation factor of fiber is affected by boundary effect, while the influence will get smaller and smaller with the increase of specimen size, especially for the specimen size larger than 50 mm. With the increase of fiber volume fraction, the orientation factor in each direction deviates from 0.5, and the orientation factor in y-direction decreases. Aggregate characteristics have a significant effect on fiber distribution, with the increase of aggregate size, the orientation factors in x- and y- directions increases, while that in z-direction decreases.
With the increase of aggregate content, the orientation factors in y- and z-directions increase, while that in x-direction decreases.
Keywords: Image analysis, Steel fiber, Dispersion coefficient, Orientation factor
Cracking of cementititous composites critically affects the durability of concrete structure, and fibers are commonly used to improve the material’s toughness and reduce cracking. These fibers are dispersed randomly in all directions. However, the real fiber distribution in cementitious composites is strongly influenced by various factors, such as fiber characteristics (fiber diameter, length, shape and content), matrix feature (matrix composition, rheological behavior) and placing method1. The fiber distribution has an influence on the contribution of strengthening and toughening of fibers to cementitious composites and the non-uniform fiber distribution would decrease the strengthening effect of fibers2,3. So it is necessary to evaluate the degree of fiber distribution to better understand the fiber distribution and make full use of fibers. Therefore, suitable testing methods are required to determine the parameters about fiber distribution, which will be conducive to create a link between fiber distribution and matrix properties, and provide guidelines on mix proportion design and construction technology of fiber reinforced cementitious composites.
Several methods have been used to characterize fiber distribution in fiber reinforced cementitious composites, such as X-ray transmission photograph, AC-impedance spectroscopy and image analysis technique. X-ray transmission photograph was an indirect method to evaluate fiber distribution.
Redon et al.4 detected the fibers in each direction by Fourier transform of X-ray image and obtained the fiber orientation factor. Ferrara and Meda5 used the X-ray image to identify fiber content and distribution within structural elements, to control the quality of products. But it was difficult to distinguish the grey levels corresponding to the fibers from the grey levels of the matrix.
AC-impedance spectroscopy was non-destructive method. By AC-impedance spectroscopy, fiber orientation, global segregation and local aggregation could be qualified6,7. However, it could not give real fiber distribution and could only be used to electric conductive fibers, such as steel and carbon fibers. Image analysis technique was the most common and effective method to characterize fiber distribution. After capturing images by digital camera8, fluorescence spectrum9, or SEM10, image processing and analyzing were followed to obtain
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*Corresponding author (E-mail-lichangfeng37@163.com)
the fiber distribution. Sououshian et al.11 used the number of fibers per unit cross-sectional area to evaluate fiber dispersion and orientation, considering the effect of surrounding boundaries.
Lee et al.12 introduced a mathematical method to determine the three-dimensional fiber orientation by the geometry of the elliptical cross-sectional shape on the polished surface. Based on the theory of point processing, Akkaya et al.8 proposed four kinds of functions to characterize aligned fiber distribution in cement composites.
Many studies on fiber distribution by various methods have been reported, but there still lack of uniform evaluation method. In this paper, the case of steel fiber is considered, dispersion coefficient and orientation factor of fiber are introduced, and effect of specimen size, fiber volume fraction and aggregate characteristics on fiber distribution are studied.
Evaluation of Fiber Distribution
Image acquisition
In this paper, two methods to determine the areas for acquiring fiber images are used. First, the edges of specimen cross-sections were considered during image acquisition, which could be used to study the effect of boundaries on fiber distribution. Second, the edges were not included in the range of image acquisition, which could be applied to more accurately analysis the effect of fiber volume fraction, aggregate characteristics on fiber distribution. The dimension of edge, where the fiber distribution would be affected, was from zero to half of fiber length13. The fibers used were 13 mm, so the affected edge was 6.5 mm, as shown in Fig. 1.
In order to improve the quality of cross-section images, the center was divided into several areas for image acquisition, and the divided number was depending on the dimensions of center. Consider the case of cross-section with the dimensions of 100 mm×100 mm, as shown in Fig. 1, the center was divided into nine areas, and then the images were collected separately for nine times. Canon EOS 5D Mark II digital camera and EF 100 mm macro lens were used to collect images from the cross-section.
The resolution of the used digital camera was 5618 pixels × 3744 pixels, and the dimensions of each area was 29 mm × 29 mm, so the spatial resolution of the image was about 0.008 mm/pixel, which was enough for identifying the steel fiber with a diameter of 0.2 mm. During the process of image acquisition, to enhance the contrast between fiber and matrix, specimen surface was exposed to strong white light, which can make smooth steel fiber become brighter. After image acquisition, image processing and image analysis of the acquired fiber images were followed.
Image processing and data output
Image-Pro Plus was used to process the acquired images, which can clearly extract fiber features and rapidly provide related fiber parameters to quantitatively characterize fiber distribution. In order to improve the accuracy of results, for each specimen, several cross-section images, whose total fibers were more than 1500, were processed. A small part of cross-section image was intercepted to introduce the image processing, and the procedures of image processing were shown in Fig. 2.
From Figs 2(a)-(e), it can be seen that, a clear fiber image was obtained after image processing, which showed white. The main operations involved in the image processing were: (i) image enhancing, (ii) image segmentation, (iii) morphologic processing and (iv) image cleaning. First, after acquiring the image from specimen cross-section (Fig. 2a), size calibration, graying and enhancing were used for obtaining high contrast gray image (Fig. 2b). Second, the gray image was converted to binary image (Fig. 2c), but there existed many ‘noises’ in the binary image, which would affect the characterization of fiber distribution. Third, opening and closing operations in the morphologic processing were applied to remove the ‘noises’ in the image, as shown in Fig. 2d. By opening operation, some isolated small points in the image can be
Fig. 1—Cross-section of specimen for capturing images
removed, and by closing operation, the small holes in the fiber images can be filled. Last, the other
‘noises’ were removed by size detection and ‘cut’
button, and the cleaned image was shown in Fig. 2e.
After image processing, the related fiber parameters were measured and output, which would provide data for the characterization of fiber dispersion coefficient and orientation factor, such as major axis length of fiber ‘A’, minor axis length of fiber ‘B’, x-coordinate of fiber center ‘X’, y-coordinate of fiber center ‘Y’, and angle between fiber major axis and vertical direction ‘α’.
Image analysis
Dispersion coefficient
In general, there were mainly two methods to characterize the degree of fiber dispersion, one was based on the fiber number on different planes and the other was based on the fiber spacing.
Assessment of fiber dispersion was performed on the basis of fiber spacing. In actual, fibers in cementitious composites did not uniformly distribute, so the degree of fiber dispersion can be evaluated by the ratio of real average spacing to theoretical average spacing of fibers. Real average fiber spacing is the average distance between each fiber center and the nearest fiber center from it. Theoretical average spacing of fibers is determined by Eqs (1) and (2), on the basis of ‘fiber spacing theory’ proposed by Romualdi in 196414, supposing fiber uniformly distributed in cementitious composites,
β=S1/S … (1)
5 / * /
S= π η d P … (2)
with β is dispersion coefficient of fibers, S1 is real average fiber spacing, calculated by center x-coordinate ‘X’ and y-coordinate ‘Y’ of fibers by image processing and analysis, S is theoretical average spacing of fibers, η is orientation factor of fibers, 0.513, d is diameter of fibers and P is volume fraction of fibers
Orientation factor
The orientation factor η is defined as the average ratio of the fiber length Pi (PX, PY or PZ) in a certain direction (x, y, or z direction) to the actual fiber length P of all fibers in cementitious composites.
According to the study of David Dupont13, the fiber three-dimensional orientation should be 0.5 by theoretical derivation, supposing fiber uniformly distribute in matrix and not affected by boundaries.
Actually, fiber orientation is commonly affected by many factors and do not uniformly distribute in any direction, which would have an effect on the performance of cementitious composites. So, it is important to characterize the real fiber distribution, to better understand the fiber reinforced cementitious composites and their performance.
Consider the case of the xy cutting plane, orientation factor of fiber was derived, supposing fiber remained straight after mixing and casting of
Fig. 2—Flow chart of image processing procedures (a) original color image, (b) enhanced gray image, (c) binary image, (d) morphologic processed image, (e) cleaned image and (f) data output
cementitious composites. The fiber cross-section image was shown in Fig. 3. From Fig. 3, it can be seen that the fiber showed elliptical in the cross-section of specimen, and the size of ellipse, the angle between fiber major axis and vertical direction will be changed with fiber orientation. Therefore, the orientation factor of fiber can be obtained by the feature of ellipse, including major axis length of fiber
‘A’, minor axis length of fiber ‘B’, and angle between fiber major axis and vertical direction ‘α’, which can be obtained by image processing. Lee et al.12 and Zak et al .15 introduced the method for determining the fiber orientation on the basis of the elliptical-shaped fiber cross-sections. Consider the case of xy cutting plane, the angle between fiber and z-direction can be determined with Eq. (3).
cosθ =B/A … (3)
So the orientation factor in z-direction can be calculated using Eq. (4),
ηz=Pz/P = P*cosθ/P=cosθ = B/A … (4) Then, the projected fiber length in xy plane can be obtained with Eq. (5), and the orientation factor in x- and y-directions can also be derived, as illustrated in Eqs (6) and (7),
Pxy = P*sinθ … (5)
ηx=Px/P=P*sinθ*sinα/P=sinθ*sinα … (6) ηy=Py/P=P*sinθ*|cosα|/P=sinθ*|cosα| … (7) Orientation factor of single fiber in three-dimensional space can be obtained by the above derivation, as the xy plane as cutting plane. For the other cutting planes, such as xz plane, yz plane, the principle and derivation of the calculation of fiber orientation factor was similar. For each specimen, orientation factor should be the average value of orientation factor of all fibers.
Experimental Processes
Raw materials and mix proportions
The cement used was P.Ⅱ52.5 ordinary Portland cement produced by Onada Corp. in Jiangsu Province, China. The sand fineness modulus was 2.5. The fibers and polycarboxylate-based superplasticizer (PCAⅣ-B) were provided by Jiangsu Bote New Materials Co., Ltd in Jiangsu Province, China. Five volume fractions of steel fiber were used including 0.6%, 1.0%, 1.4%, 1.8%, 2.2%; three ranges of coarse aggregate size were contained including 5-10 mm, 10-15 mm, 15-20 mm; three ratios of binder to aggregate were selected including 1:1.5, 1:2.0, 1:2.5.
The properties of fibers were given in Table 1. The mix proportion of mortar was shown in Table 2 and the mix proportion of concrete was shown in Table 3.
In order to get similar fluidity, the PCA content would change with different mix proportions.
Fig. 3—Fiber cross-section image on the xy cutting plane
Table 1—Properties of steel fiber
Fiber category Fiber morphology Diameter (mm) Length (mm) Density (g·cm-3) Tensile strength (MPa)
Micro steel fiber Roundy and straight 0.2 13.0 7.8 2800
Table 2—Mix proportions of steel fiber reinforced mortar (kg/m3)
No. W/C C/S Cement Sand Water PCA Fiber
C1 0.20 1:1.5 800 1200 160 14.4 46.8
C2 0.20 1:1.5 800 1200 160 16.0 78
C3 0.20 1:1.5 800 1200 160 20.0 109.2
C4 0.20 1:1.5 800 1200 160 24.0 140.4
C5 0.20 1:1.5 800 1200 160 30.0 171.6
Specimen preparation
For the study on the effect of boundaries, six kinds of specimen size were selected including 20 mm, 30 mm, 40 mm, 50 mm, 70 mm and 100 mm and for the study on the effect of fiber volume fraction dimensions of 70 mm × 70 mm × 70 mm were applied;
for the study on the effect of aggregate characteristics dimensions of 100 mm × 100 mm × 400 mm were used. Specimens were cut and treated after seven days from casting. Take the case of specimen with dimensions of 70 mm × 70 mm × 70 mm and the y-direction as casting direction, the cut direction was shown in Fig. 4. Three kinds of cut directions were selected, such as yz plane, xy plane, and xz plane, to improve the accuracy of analysis results. After cutting, the specimen were treated by coarse grinding, fine grinding and polishing to obtain smooth surface and benefit image acquisition.
Results and Discussion
Effect of specimen size on fiber distribution
For cementitious composites, many dimensions are applied in actual engineering, and the boundaries are always present. In order to understand the degree of boundary effect, six kinds of specimen size were selected including 20 mm, 30 mm, 40 mm, 50 mm, 70 mm and 100 mm. The fiber volume fraction used was 1.0%. In theory, the orientation factor can be calculated by taking the geometrical average over the sections, considering the fiber and specimen size13. The calculation method was shown in Eq. (8), on the basis of knowing the orientation factor for the areas 1, 2 and
3 (Fig. 5), expressed as α1, α2 and α3, respectively.
The experimental and theoretical results were shown in Fig. 6.
2
1 (B Lf)(H Lf) 2 [(B L Lf) f (H L Lf) f] 3 Lf
BH
α α α
α
× − − + × − + − + ×
=
… (8) From Fig. 6a, it can be seen that the dispersion coefficient of fiber increased with the increase of specimen size, but the larger the specimen size was, the less obvious the increase of fiber dispersion coefficient. The dispersion coefficient with the specimen size of 20 mm, 30 mm, 40 mm, 50 mm, 60 mm and 70 mm was 0.336, 0.360, 0.382, 0.400, 0.410 and 0.418, respectively. With the increase of specimen size, the space of fiber distribution increased, and the degree of fiber dispersion would be improved.
So, specimen with larger dimensions is beneficial for the uniformity of fiber dispersion, at least larger than 50 mm. The dispersion coefficient of fibers has an obvious effect on their enhancement to cementitious composites, and the non-uniformity of fiber distribution will cause the decrease of the performance of fiber reinforced cementitious composites.
Table 3—Mix proportions of steel fiber reinforced concrete (kg/m3) Coarse aggregate
No. W/B B/A Cement Silica fume Fly ash Sand 5-10 mm 10-15 mm 5-20 mm Water PCA Fiber
L1 0.20 1:2.0 608 38 114 608 912 0 0 152 7.2 40
L2 0.20 1:2.0 608 38 114 456 456 0 0 152 8.0 40
L3 0.20 1:2.0 608 38 114 608 365 365 182 152 8.4 40
L4 0.20 1:1.5 720 45 135 540 810 0 0 180 7.6 40
L5 0.20 1:2.5 528 33 99 660 990 0 0 132 9.0 40
Fig. 4—Cutting direction of specimen: (a) yz direction, (b) xy direction, (c) xz direction
Fig. 5—Cross-section of specimen divided into three different orientation zones
From Fig. 6b, it can be seen that, the values obtained by the model agreed well with the experimental data, with the similar changing trend.
With the increase of specimen size, the orientation factor in y-direction increased, while the increasing amplitude became smaller and smaller, especially for the specimen size larger than 50 mm. After the casting of specimen, the fiber orientation was restricted by boundaries, so the fiber near boundaries would change their directions and the real fiber orientation would change. The boundary effect would be weakened with the increase of specimen size.
Effect of fiber volume fraction on fiber distribution
Five kinds of volume fractions were considered including 0.6%, 1.0%, 1.4%, 1.8% and 2.2%, the dimension of specimens were 70 mm × 70 mm × 70 mm. The test results were shown in Fig. 7.
From Fig. 7a, it can be seen that, with the increase of fiber volume fraction, the dispersion coefficient of fibers decreased slightly. The dispersion coefficient was 0.443, 0.428, 0.421, 0.405, and 0.400
respectively. On one hand, with the increase of fiber volume fraction, the viscosity of fiber reinforced cementitious composites increased and the friction between particles increased, which made fiber distribution more difficult, and the dispersion coefficient of fiber decreased. On the other hand, space of fiber distribution in all directions would be smaller with fiber volume fraction increased, so the capacity of fiber distribution decreased, and the degree of fiber dispersion was affected. Orientation factor of fiber in a certain direction reflects the enhancement of fibers in that direction, which with a value of 0.5 while fibers uniformly distribute in any directions15. From Fig. 7b, it can be seen that, orientation factor of fiber deviated from 0.5 in each fiber content and each projected direction which showed that fibers in matrix were not distributed uniformly in all directions. This was due to the vibration of fiber reinforced cementitious composites after casting. Moreover, orientation factor of fiber deviated from 0.5 more with fiber volume fraction
Fig. 7—Effect of fiber volume fraction on fiber distribution (a) dispersion coefficient and (b) orientation factor
Fig. 6—Effect of specimen size on fiber distribution (a) dispersion coefficient and (b) orientation factor
increased, which was caused by mutual interference between fibers. From Fig. 7b, it can be also seen that orientation factor of fiber in y-direction was lower than that in x- and z-direction, which was caused by vibration of fiber reinforced cementitious composites and the tendency of fiber distribution in horizontal direction. With the increase of fiber volume fraction, the effect would be weakened.
According to the study by Nataraja et al.16, 17, the reinforcing index RI=wf*l/d, where, wf is the weight fraction of fiber. Effect of fiber volume fraction on fiber distribution was given in Fig. 7. Consider x-direction as the direction of tensile stress, the NRI of tensile stress (normalized reinforcing index) was calculated based on RI, considering the orientation factor and dispersion coefficient of fibers, as shown in Table 4.
From Table 4, it can be seen that, with the increase of fiber volume fraction, the OF (orientation factor) increased, which was beneficial for the increase of RI;
the DC (dispersion coefficient) decreased, which would reduce the reinforcement of fiber. The OF and DC were normalized to calculate the NRI. The normalized reinforcing index RI=wf*l/d*NOF*NDC.
Although the increase of fiber orientation factor increased the NRI, the decrease of fiber dispersion coefficient decreased the NRI. Due to the positive and negative effects, for the increase of fiber volume fraction, the difference between RI and NRI was not obvious.
Effect of aggregate on fiber distribution Effect of coarse aggregate size
Three size range of coarse aggregate was used to study the effect of aggregate size on fiber distribution including 5-10 mm, 5-15 mm and 5-20 mm; the fiber volume fraction was 0.5%. The test results were shown in Fig. 8.
From Fig. 8a, it can be seen that, with the addition of coarse aggregate, the dispersion coefficient decreased obviously, while the decrease range would not significant with the increase of coarse aggregate
size. In this paper, for studying the effect of coarse aggregate size, some fine aggregates in cementitious composites were substituted by coarse aggregates and the substituted coarse aggregates for fine aggregates were 60%. The replacement of coarse aggregates caused the decrease of mortar amount and fiber distribution space, which caused the decrease of fiber dispersion coefficient. However, with the increase of coarse aggregate size, the effect would not obvious.
From Fig. 8b, it can be seen that with the increase of size range of coarse aggregate, i.e., the increase of large size coarse aggregate, the orientation factor in x- and y-directions decreased, while the orientation factor in
Table 4—Reinforcing index
No. Vf / % wf / % OF NOF DC NDC L, mm d, mm RI NRI
1 0.6 2.08 0.509 1.018 0.443 1.000 13 0.2 1.35 1.37
2 1.0 3.47 0.532 1.064 0.428 0.966 13 0.2 2.26 2.32
3 1.4 4.85 0.542 1.084 0.421 0.950 13 0.2 3.15 3.24
4 1.8 6.24 0.548 1.096 0.405 0.914 13 0.2 4.06 4.07
5 2.2 7.63 0.554 1.108 0.400 0.903 13 0.2 4.96 4.96
Fig. 8—Effect of coarse aggregate size on fiber distribution (a) dispersion coefficient and (b) orientation factor
z-direction increased. The orientation factor in x-direction was 0.645, 0.611, 0.605 and 0.598, respectively, that in y-direction was 0.430, 0.400, 0.385 and 0.368, respectively, that in z-direction was 0.453, 0.512, 0.533, 0.547, respectively. With the increase of coarse aggregate size, the distribution space of fibers reduced, and the flow capability of fibers to the horizontal direction decreased, which caused the decrease of orientation factor in Y direction. The different phenomenon between x- and z-directions may be due to the mixing and casting method of specimen.
Effect of binder to aggregate ratio
Three ratios of binder to aggregate were used to study the effect of aggregate content on fiber distribution including 1:1.5, 1:2.0 and 1:2.5; the fiber volume fraction was 0.5%. The test results were shown in Fig. 9.
From Fig. 9a, it can be seen that, with the decrease of binder to aggregate ratio, i.e., the increase of aggregate content, the dispersion coefficient of fibers reduced, but the reduction scope was small. The dispersion coefficient was 0.411, 0.406 and 0.396, respectively. The degree of fiber dispersion may be related more to specimen mix proportions and mixing methods, which should be considered in actual project, and effective measures should be taken to improve uniformity of fiber distribution.
From Fig. 9b, it can be seen that, with the decrease of binder to aggregate ratio, the orientation factor in x-direction decreased, while that in y- and z-directions increased. With the casting and vibration of cementitious composites, different from the mortar, the flow capacity of fibers in concrete to the both sides would be restricted by coarse aggregate, which caused the decrease of orientation factor in x-direction. The more the aggregate content was, the more obvious the effect would be. Commonly, enhancement of fibers in a certain direction will be better if the fiber orientation factor is greater in this direction than that in other directions. Take the case of tensile behavior of fiber reinforced cementitious composites, the tensile strength and energy absorption capability will be improved if the orientation factor of fiber becomes larger in the tensile stress direction.
Therefore, quantitative characterization of fiber distribution had important meaning to establish the relationship between fiber distribution and properties of cementitious composites.
Conclusions
As a new research method, image analysis technique can be applied to characterize fiber distribution in fiber reinforced cementitious composites. The dispersion degree and orientation factor in 3-D of fibers can be concluded, by two- dimensional image information of fibers in the cross- section of specimen. Through cutting and polishing of specimen, image acquisition of specimen surface, extraction of fiber feature, and measurement of related fiber parameters, two parameters, dispersion coefficient and orientation factor, were given to quantitatively analyze fiber distribution.
(i) With the increase of specimen size, the decrease of fiber volume fraction and aggregate size, the dispersion coefficient increased, but the changes were small, which may be related more to specimen mix proportions and mixing methods.
(ii) The orientation factor of fiber was affected by boundary effect. The values obtained by the
Fig. 9—Effect of binder to aggregate ratio on fiber distribution (a) dispersion coefficient, (b) orientation factor
model agreed well with the experimental data, with the similar changing trend. With the increase of specimen size, the orientation factor in y-direction increased, while the increasing amplitude became smaller and smaller, especially for the specimen size larger than 50 mm.
(iii) With the increase of fiber volume fraction, the orientation factor in each direction deviated from 0.5, and the higher the fiber volume fraction was, the deviation the orientation away from 0.5 would be; the orientation factor of fiber in y- direction was lower than that in x- and z-directions.
However, with the increase of fiber volume fraction, the effect would be weakened. Due to the positive and negative effects, for the increase of fiber volume fraction, the difference between RI and NRI was not obvious.
(iv) Aggregate characteristics had a significant effect on fiber distribution, with the increase of aggregate size, the orientation factor in x- and y-directions decreased while that in z-direction increased; with the increase of aggregate content, the orientation factor in y- and z-directions increased, while that in x-direction decreased.
Acknowledgements
The study of this paper is financially supported by National Basic Research Program of China (973 Program) under (Grant No. 2010CB735801) and the National Natural Science Foundation of China (Grant No. 50908104). The research work was
performed at Jiangsu Bote New Materials Co, Ltd. in China for providing polishing facilities and image acquisition equipment. The authors would like to express their gratitude for the financial and technical support that made this project possible.
References
1 Kang S T, Lee B Y, Kim J-K & Kim Y Y, Constr Build Mater, 25 (2011) 2450.
2 Akkaya Y, Shah S P & Ghandehari M, ACI Special Publications 216: Innovations in Fiber-Reinforced Concrete for Value SP-216-1, 216 (2003) 1.
3 Bolander J E, Choi S & Duddukuri S R, Int J Fract, 154(1-2) (2008) 73.
4 Redon C, Chermant L, Chermant J-L & Coster M, Cem Concr Compos, 21(5-6)(1999)403.
5 Ferrara L & Meda A, Mater Struct, 39(4)(2006)411.
6 Woo L Y, Wansom S, Ozyurt N, Mu B, Shah S P &
Mason T O, Cem Concr Compos, 27(6)(2005)627.
7 Ozyurt N, Mason T O & Shah S P, Cem Concr Res, 36(9)(2006)1653.
8 Akkaya Y, Picka J & Shah S P, J Mater Civ Eng, 12(3) (2000) 272.
9 Kim J-K, Kim J-S, Ha G J & Kim Y Y, Cem Concr Res, 37(7)(2007)1096.
10 Shao Y, Qiu J & Shah S P, Cem Concr Res, 31(8)(2001)1153.
11 Soroushian P & Lee C-D, ACI Mater J, 87 (5)(1990) 433.
12 Lee Y H, Lee S W, Youn J R, Chung K & Kang T J, Mat Res Innovat, 6 (2)(2002) 65.
13 Dupont D & Vandewalle L, Cem Concr Compos, 27(3)(2005)391.
14 Romualdi J P & Mandel J A, ACI J Proc, 61(6) (1964) 657.
15 Zak G, Park C B & Benhabib B, J Compos Mater, 35(4) (2001) 316.
16 Nataraja M C, Dhang N & Gupta A P, Cem Concr Compos, 12(5-6)(1999)383.
17 Nataraja M C, Dhang N & Gupta A P, Cem Concr Res, 30(4)(2000)593.
18 Akkaya Y, Peled A & Shah S P, Mater Struct, 33(8)(2000)515.
