Biaxial flexural behavior of ultra-high-performance fiber-reinforced concrete with different fiber lengths and placement methods

Accepted Manuscript Biaxial flexural behavior of ultra-high-performance fiber-reinforced concrete with different fiber lengths and placement methods Doo-Yeol Yoo, Goangseup Zi, Su-Tae Kang, Young-Soo Yoon PII: DOI: Reference:

S0958-9465(15)30013-5 http://dx.doi.org/10.1016/j.cemconcomp.2015.07.011 CECO 2535

To appear in:

Cement & Concrete Composites

Received Date: Revised Date: Accepted Date:

11 February 2015 25 April 2015 28 July 2015

Please cite this article as: Yoo, D-Y., Zi, G., Kang, S-T., Yoon, Y-S., Biaxial flexural behavior of ultra-highperformance fiber-reinforced concrete with different fiber lengths and placement methods, Cement & Concrete Composites (2015), doi: http://dx.doi.org/10.1016/j.cemconcomp.2015.07.011

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Biaxial flexural behavior of ultra-high-performance fiber-reinforced concrete with different fiber lengths and placement methods Doo-Yeol Yooa, Goangseup Zib, Su-Tae Kangc, and Young-Soo Yoonb,*

Abstract This study investigates the effects of fiber length and placement method on the biaxial flexural behavior and fiber distribution characteristics of ultra-high-performance fiber-reinforced concrete (UHPFRC). A number of UHPFRC panels including three different fiber lengths were fabricated using two different placement methods, and an image analysis was performed to quantitatively evaluate the fiber distribution characteristics such as fiber orientation, fiber dispersion, and number of fibers per unit area. The biaxial flexural performances including load carrying capacity, energy absorption capacity, and cracking behavior were found to be improved with the increase in fiber length up to 19.5 mm. The biaxial flexural performances were also influenced by the placement method; the specimens with concrete placed at the center (maximum moment region) showed better flexural performances than those with concrete placed at the corner. These observations were confirmed by the image analysis results, which showed poorer fiber orientation and fewer fibers across the crack surfaces at the maximum moment region for the specimens with concrete placed in the corner, compared with their counterparts.

Keywords: ultra-high-performance fiber-reinforced concrete; biaxial flexure; fiber length; placement method; fiber distribution characteristics; image analysis –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– a Department of Civil Engineering, The University of British Columbia, 6250 Applied Science Lane, Vancouver, BC V6T 1Z4, Canada. b

School of Civil, Environmental and Architectural Engineering, Korea University, 1, 5-ga, Anam-dong, Seongbuk-gu, Seoul, 136-713, Republic of Korea.

c

Department of Civil Engineering, Daegu University, 201, Daegudae-ro, Jillyang, Gyeong-san, Gyeongbuk 712-714, Republic of Korea.

*

Corresponding author.

Tel.: +82 2 3290 3320, fax: +82 2 928 7656, E-mail address: [email protected] (Y.-S. Yoon)

1. Introduction Ultra-high-performance fiber-reinforced concrete (UHPFRC) exhibits advanced performances in terms of strength (compressive strength > 150 MPa and tensile strength > 8 MPa), energy absorption capacity, fatigue performance, and durability [1-3]. However, due to its high cost (1% by volume of steel fiber is normally more expensive than the cement matrix), the application of UHPFRC to real structures has been obstructed until today. Many researchers [3-5] have investigated the possibility of improving the tensile performance of UHPFRC without changing the steel fiber content or reducing the steel fiber content without decreasing the performance. Wille et al. [4] reported that the use of twisted steel fibers (fiber length/fiber diameter (Lf/df) = 30/0.3 mm/mm) improved both the post-cracking tensile strength and strain capacities, even though lower fiber contents were used in comparison with short smooth steel fibers (Lf/df = 13/0.2 mm/mm). Moreover, Yoo et al. [3] and Aydın and Baradan [5] experimentally verified that the uniaxial flexural performance and energy absorption capacity are improved by the use of longer fibers with higher aspect ratios, because of the increase in the effective bonding area between the fiber and the matrix. These findings indicate that the fiber content required to provide a certain performance level under tension and flexure could be reduced by using twisted fibers and by increasing the fiber length (higher aspect ratio). However, poor fiber dispersion and fiber balling normally occur when the fiber length increases [6] and may cause deterioration of the tensile performance. Thus, the evaluation of tensile and flexural performances based on the fiber length is necessary, and the critical fiber length for improving these performances needs to be determined. Because of its outstanding mechanical properties as mentioned above, UHPFRC has been popular for use in thin plate structures such as bridge decks, roofs, and thin walls [7,8]. These thin plate structures are subjected to multi-axial stress states, owing to their geometry and complex loading form [9], and exhibit flow field characteristics different from those of uniaxial structures like beams and girders. However, most studies [3,4,10-12] have focused on the uniaxial tensile and flexural responses of UHPFRC using dog-bone and bending tests, and very limited literature [13,14] is available regarding its flexural performances under biaxial flexure stress. As the performance of thin plate structures cannot be directly evaluated from the dog-bone and bending tests because of the different stress states and flow field characteristics compared with uniaxial elements, the flexural performance of UHPFRC under biaxial stress needs to be investigated. Due to the high fluidity, adequate viscosity, and self-consolidating properties of UHPFRC, the structural elements made of this material are usually fabricated by placing the concrete at a target position and letting it flow [15-17]. Therefore, the fiber distribution characteristics of UHPFRC depend on the flow direction and type, causing a variation in the tensile and flexural performances [3,17-19]. Ferrara et al. [15] and Kwon et al. [17] recently reported that the flexural performance of UHPFRC is strongly affected by the fiber orientation, and thus the casting process should be designed accordingly for proper fiber enhancement. However, most studies [4,5,12,13] on the tensile and flexural

performances of UHPFRC have not considered the flow field characteristics and fiber orientation. Thus, the flexural performance of UHPFRC needs to be explored together with the fiber distribution characteristics at crack surfaces and along the flow distance. Accordingly, in this study, to investigate the biaxial flexural performance of UHPFRC, a number of UHPFRC panels were fabricated with three different fiber lengths (Lf = 13, 16.3, and 19.5 mm) using two different placement methods, and they were tested using a novel biaxial flexure test (BFT) method recently developed by Zi et al. [20]. An image analysis was employed to quantitatively evaluate the fiber distribution characteristics (i.e., fiber orientation, fiber dispersion, and number of fibers per unit area) of the UHPFRC panels based on the fiber length, placement method and flow distance, and their effects on the biaxial flexural performances were investigated to thoroughly analyze the test results.

2. Experimental Program 2.1 Materials, mix proportion, and specimen preparation The mix proportions used in this study are given in Table 1, and the physical and chemical properties of the cementitious materials, i.e., cement and silica fume, are summarized in Table 2. Silica sand with grain size 0.2 – 0.3 mm was used as fine aggregate, and 10 μm diameter silica flour containing 98% SiO2 was included as filler. To improve the homogeneity of the concrete, coarse aggregate was excluded from the mixture. The mean particle sizes of the components, illustrated in Fig. 1, were determined based on the packing density theory and results from rheological and mechanical tests [21]. To investigate the effect of fiber length (or aspect ratio) on biaxial flexural behavior, three different fiber lengths (Lf = 13, 16.3, and 19.5 mm) were incorporated at 2% by volume, leading to three series of test specimens. The geometric and physical properties of the steel fibers used are presented in Table 3 and Fig. 2, respectively. Based on our preliminary mixing, UHPFRC mixture including 2 vol.% smooth steel fibers with a diameter of 0.2 mm and a aspect ratio higher than roughly 100 exhibited slight formation of fiber ball, which leads to insufficient fiber dispersion. Thus, the maximum length of steel fibers in this study was determined to be 19.5 mm (aspect ratio of 97.5, which is slightly lower than 100). The specimens with smooth steel fibers are denoted by the letter S followed by a number referring to the fiber length. For example, S13 indicates the specimen containing 2% (by volume) of smooth steel fibers with a fiber length of 13 mm. The mixing sequence was as follows; cement, silica fume, silica sand, and silica flour were first premixed for approximately 10 min. After that, water premixed with superplasticizer (SP) was added in the dry state and mixed for another 10 min. When the mixture exhibited adequate flowability and viscosity for uniform fiber distribution, steel fibers were dispersed and then mixed for an additional 5 min. Because UHPFRC has adequate fluidity and viscosity and shows self-consolidating characteristics, the structural elements made of this material are generally fabricated by placing the concrete at a certain

point and allowing it to flow [15]. Thus, various placement methods can be used to fabricate thin plate UHPFRC structures. In this study, to investigate the effect of placement method on the biaxial flexural behaviors and fiber distribution characteristics, two different placement methods, (1) placing concrete at the corner and (2) placing concrete at the center (maximum moment region), were adopted, as shown in Fig. 3. If the cement matrix has enough viscosity to prevent the subsidence of fibers, the fiber orientation is mostly influenced by the flow field characteristics and boundary conditions such as wall effect. In the case of radial flow, the orientation of fibers is perpendicular to the flow direction, and consequently a radial fiber orientation is obtained. This specific fiber orientation is caused by the variation in flow velocities; the velocity of flow decreases with the flow distance, and thus the fibers inclined to the radial direction are rotated by the velocity gradient (Fig. 3). All the test specimens were covered with plastic sheets immediately after concrete casting and cured at room temperature for the first 48 h, before demolding. After demolding, heat curing (90 ± 2°C) with steam was carried out for 3 days. The specimens were then removed from the heat curing room and stored in the laboratory at room temperature until testing.

2.2 Test setup and procedure 2.2.1 Flow and compression tests The flow table test was performed as per ASTM C 1437 [22] to investigate the workability of UHPFRC. Freshly mixed UHPFRC was cast in a cone-shaped steel mold, and the mold was lifted off slowly to allow the concrete to flow. Then, the flow table was dropped 25 times within 15 s, and the average flow values were measured by averaging the maximum flow diameter and perpendicular diameter for the maximum diameter. The average flow of all the mixtures was found to be approximately 230–240 mm, as summarized in Table 1. The compression test was carried out as per ASTM C 39 [23]. Nine cylinders (three cylinders each) with 100 mm diameters and 200 mm lengths were fabricated and tested. An uniaxial load was applied by using a universal testing machine (UTM) with a maximum capacity of 3000 kN. To evaluate the elastic modulus and strain capacity (strain at the peak), a compressometer with three linear voltage differential transformers (LVDTs) was installed to measure the average compressive strain, as shown in Fig. 4.

2.2.2 A novel biaxial flexure test A novel BFT was recently suggested by Zi et al. [20]. This test method is an extended version of the four-point bending test, but with a round panel, and a modified version of the ring-on-ring test (ASTM C 1499 [24]), which is mostly used for glass and ceramics. Since the BFT panels exhibited a constant bending stress at the center within the area enclosed by the loading ring, an equal probability of crack formation was obtained in all directions, displaying the stochastic nature of their strengths. The schematic view of the test setup, consisting of a support ring, loading ring, and round test panel, is

shown in Fig. 5. The diameter of the tested panels was designed to be lower than 800 mm, as recommended by ASTM C 1550 [25]. If the panels were designed in accordance with ASTM C 1550, they would be too large and heavy, making them difficult to handle during testing. Based on the findings of Higgs et al. [26] and Zi et al. [20], the concrete panel geometry hp/ap = 0.24 and fp/ap = 0.05 can ensure the equi-biaxial tensile behavior from simple plate theory. Therefore, panels with 48 mm thickness and 420 mm diameter were used, and a support ring with 200 mm radius and loading ring with 50 mm radius were adopted in this study, identical to those used in a previous study [9]. The load was applied using a UTM, with a maximum capacity of 3000 kN, through displacement control, and the rate of loading was 1 mm/min during the test. As consistent results can only be obtained when the panels have a very flat bottom face, the circular sides of the specimens were capped with high-strength gypsum of 2 mm thickness, and a soft rubber pad was placed at the interface between the support ring and the panels. Since UHPFRC panels showed very gradual decrease of post-peak load carrying capacity due to its excellent fiber bridging capacity, it is assumed that the soft rubber pad has no effect on their post-peak behavior. Because the panel is placed on top of the annular support ring with soft rubber, the settlement at the support needs to be considered carefully. For this reason, an annual steel frame was mounted onto the panel, and the mid-span deflection was measured using an LVDT attached to the steel frame, as illustrated in Fig. 6. In addition, two strain gauges were attached at the center of the bottom surface of the panel to determine the first cracking.

3. Experimental Results and Discussion 3.1 Evaluation parameters Each compression test was described by a stress-strain curve, and the elastic modulus value is obtained using Eq. (1), in accordance with ASTM C 469M [27].

Ec 

0.4  f c ' f1

 2  0.00005

(1)

where fc' is the compressive strength, f1 is the stress corresponding to a longitudinal strain of 50 με, and ε2 is the longitudinal strain produced by a stress that is 40% of fc'. The equi-biaxial flexural stress of the panels tested by BFT is given by Eq. (2), which is obtained from the linear elasticity theory [28].

f 

3P 2hp2





 a 2p  bp2 ap     1  ln  1   2 2 R b  p p   

(2)

where P is the applied load, hp is the thickness of the panel, ν is the Poisson’s ratio, and Rp, ap and bp are

the radii of the panel, support ring and loading ring, respectively. The Poisson’s ratio of UHPFRC was assumed as approximately 0.192, based on a previous study [10].

3.2 Compressive behavior The averaged uniaxial compressive stress-strain curves for UHPFRC with various fiber lengths are shown in Fig. 7, and the detailed results are summarized in Table 4. The averaged curves and results were obtained from the test results of three specimens. It was observed that the compressive strength was only marginally influenced by the fiber length. The S13 specimen showed steeper stress-strain responses than S16.3 and S19.5, and its elastic modulus was approximately 9% greater than those of the latter. All the specimens exhibited a linear compressive stress-strain curve up to failure and then failed in a brittle manner (load drops to almost zero value immediately after reaching the peak), regardless of fiber length. Linearity was determined using the ratio between the elastic modulus Ec, calculated by Eq. (1), and the secant modulus for the strain at peak load E0 [29]. As the linearity of concrete increases, a lower ratio Ec/E0 is obtained. The ratio Ec/E0 was found to be approximately 1.1 for all the test specimens regardless of fiber length. The ratio Ec/E0 is about 3.5 for low-strength concrete with fc' = 7 MPa and 1.25 for high-strength concrete with fc' = 70 MPa [29], so it is of note that higher linearity was obtained for UHPFRC than for concretes with fc' of 7 and 70 MPa.

3.3 Biaxial flexural response 3.3.1 Determination of first cracking point Fig. 8 illustrates the typical initial load-deflection and stress-strain behaviors of a UHPFRC panel. Initially, the strains in the perpendicular directions showed almost identical behavior, because of the isotropic flexural tensile stress state of the panel. Around 320 με, the strains suddenly increased without a significant change in the load, in response to the occurrence of the first crack. This point coincided exactly with the point in the load-deflection curve where nonlinearity was first observed. Therefore, the first cracking point was defined as the point of limit of proportionality (LOP) in the load-deflection curve. The first cracking properties, including strength and deflection, are summarized in Table 5. The first cracking strength and corresponding deflection showed no noticeable differences according to the fiber length and placement method.

3.3.2 Load versus deflection response It is very important to obtain an accurate average load-deflection curve. Since the individual curves obtained in this study exhibited similar shape each other, the following averaging procedure was adopted for simplicity, similar to that suggested by a previous study [30]. The deflection was assumed to increase in 0.05 mm increments, and the load was calculated based on a linear interpolation of the test data (Fig. 9(a)). After applying this procedure to all the test specimens, the load data was averaged at identical

deflections (Fig. 9(b)), so that the data points were equally spaced on the deflection axis. The average load-deflection curves for all the test series are shown in Fig. 10, and the averaged values of the parameters characterizing the biaxial flexural performances of UHPFRC are summarized in Table 5. Regardless of fiber length and placement method, all the test specimens showed deflection-hardening behavior and similar load-deflection responses. For all fiber lengths, the specimens with concrete placed at the center exhibited higher load carrying capacities than their counterparts with concrete placed at the corner. For example, in the case of S13, the average peak load of the specimens with concrete placed at the center was found to be 96.2 kN, approximately 21% higher than that of the specimens with concrete placed at the corner. Similar observation was reported by Barnett et al. [31] that the placement method is clearly influence in the mechanical properties of UHPFRC panels based on ASTM C 1550 [25], and the panel placed at the center showed highest load carrying capacity compared with the panels randomly placed and placed at perimeter. In addition, the load carrying capacity and deflection capacity (deflection at the peak) increased with increasing fiber length up to 19.5 mm. For example, the S19.5 specimens showed approximately 26% and 13% higher peak loads and 153% and 67% higher deflections at the peak compared to the S13 and S16.3 specimens, respectively. Based on a previous study [3], the increases in the load carrying capacity and deflection capacity according to the fiber length were also obtained for the uniaxial flexural behaviors of UHPFRC beams, and the beams with concrete placed at the maximum moment region exhibited higher load carrying capacity than those with concrete placed at the corner.

3.3.3 Energy absorption capacity (toughness) The flexural behavior of fiber-reinforced concrete (FRC) is classified as either deflection-softening or deflection-hardening [11]. Because UHPFRC exhibited deflection-hardening behavior, the points at the first crack (LOP) and the peak (modulus of rupture (MOR)) were considered in this study to investigate the energy absorption capacity, which is represented in terms of toughness value. Besides the LOP and MOR, four other deflection points were defined as follows: – d2.5: point with net deflection equal to L/160, where L is the span – d5: point with net deflection equal to L/80 – d10: point with net deflection equal to L/40 – d15: point with net deflection equal to L/26.7 In this work, d2.5, d5, d10, and d15 indicate the points with deflections of 2.5, 5, 10, and 15 mm, respectively. ASTM C 1550 [25] recommends using the points with deflections of 5 mm (L/160), 10 mm (L/80), 20 mm (L/40), and 40 mm (L/20) for a panel with a span length of 800 mm. Thus, the authors used the above deflection points of d2.5, d5, and d10, similar to the ASTM standard. However, as the deflection

could only be measured up to 15 mm due to limitations in experimental equipment, d15 was adopted instead of the point with deflection equal to 20 mm (L/20). Fig. 11(a) shows the toughness values of the panels with concrete placed at the corner up to and including d5, whereas Fig. 11(b) illustrates the toughness values of the panels with concrete placed at the corner at the deflection points of MOR, d10, and d15 on the descending branch of the curve. The same arrangement was adopted for the panels with concrete placed at the center in Fig. 11(c) and (d). The toughness values at LOP exhibited no noticeable differences with the fiber length, regardless of the placement method. The same observation was true for all the specimens up to d2.5. On the other hand, after MOR, the toughness values for all the test specimens increased with increasing fiber length up to 19.5 mm. For example, at point d15 in the descending range of the load-deflection curve for panels with concrete placed at the center, the toughness values were found to be 1635.24 kN·mm for S19.5, 1360.78 kN·mm for S16.3, and 1205.72 kN·mm for S13. Thus, for toughness values up to d15, the S19.5 specimen exhibited the toughest response, while the S13 specimen showed the lowest toughness, and the S16.3 specimen had values in between those two. As shown in Fig. 11(b) and (d), the same trend was observed at d10 and MOR. The S16.3 specimen with concrete placed at the center showed higher toughness values at deflection points of up to d10 compared with the S19.5 specimen with concrete placed at the corner. This result indicates that although the energy absorption capacity is generally improved by increasing the fiber length, it is also affected by the placement method, which can cause different fiber orientations. Therefore, the placement method should be carefully designed to ensure proper fiber enhancement. To investigate the comparative performance of fibers, the toughness values were normalized by those of the S13 specimens, as illustrated in Fig. 12. All the test specimens showed a higher increase in the toughness ratio with increasing fiber length at the higher deflection points. This is because the slip capacity and ultimate slip of the fiber increase with the fiber length.

3.3.4 Cracking behavior All the test specimens produced multiple radial micro-cracks with deflection-hardening behavior, as shown in Fig. 13. For panels with concrete placed at the center, two different failure modes such as flexural failure mode and punching failure mode were observed, as in Fig. 13(a), whereas panels with concrete placed at the corner only failed by a flexural failure mode into three or four pieces, as shown in Fig. 13(b). All the test specimens exhibited localized cracks, which are circumambient to the casting points (center or corner), indicating that the enhancement of biaxial tensile strength by the steel fibers is higher at the casting point than that at other parts. Thus, the specimens with concrete placed at the center showed higher load carrying capacities than those with concrete placed at the corner. In addition, the number of localized cracks and their locations were randomly distributed as the BFT can take into account the stochastic nature of strength.

The cracking properties (i.e., number of cracks and crack spacing) of UHPFRC, illustrated in Fig. 14, showed large variations with fiber length and placement method. The specimens with longer fiber lengths exhibited more cracks and smaller crack spacing. In addition, the specimens with concrete placed at the center showed more cracks and smaller crack spacing for all fiber lengths compared with their counterparts.

4. Fiber Distribution Characteristics To investigate the effects of fiber length and placement method on the fiber orientation and dispersion, cross-sectional saw cuts were made, as shown in Fig. 15. For the specimens with concrete placed at the center, the fiber distribution characteristics in all radial directions are theoretically identical, so two random cutting surfaces were investigated (Fig. 15(a)). On the other hand, the fiber distribution characteristics of specimens with concrete placed at the corner are different depending on the flow distance, and therefore three cutting surfaces (0º, 45º, and 90º from the casting position) were assessed (Fig. 15(b)). Images of the cutting planes were obtained using a high-resolution camera, and the fibers were separated from other components on the cutting plane by converting the RGB images to binary images using a threshold algorithm. Four coefficients that quantitatively evaluate the fiber orientation and dispersion were calculated based on the coordinate and shape of the fibers, using the image analysis technique shown in Fig. 16 [18,32].

4.1 Evaluation of parameters for fiber distribution characteristics The fiber orientation is affected by fiber length and friction between the fiber and matrix. For simplification, if only the geometrical arrangement of fibers is considered, the fiber orientation coefficient, ηθ, can be calculated by [33]

 max

  

P cos 2 d

(3)

min

where θ is the angle between the fiber axis and tensile load direction, and P(θ) is the probability density function of fiber orientation. Eq. (3) was derived based on the assumption that no enhancement of tensile strength is achieved when the fibers are aligned perpendicular to the tensile direction and that the tensile strength is maximized when the fibers are aligned parallel to the tensile direction. Therefore, ηθ = 1 when every fiber is aligned parallel to the tensile direction and ηθ = 0 when every fiber is aligned perpendicular to the tensile direction. The degree of fiber dispersion can be quantitatively analyzed by calculating the fiber dispersion coefficient, αf, which is expressed by



 f  e x p  

2 xi  1   nf  

(4)

where nf is the total number of fibers in an image and xi is the number of fibers in the i th unit, which is a square portion allocated to the i th fiber, with the assumption that fiber dispersion is perfectly homogeneous. Thus, the value of αf differs from 1 for homogeneous dispersion to 0 for significantly biased dispersion. The number of fibers per unit area, Fn, can be calculated by dividing the total number of fibers by the area of the image as follows

Fn 

nf A

(5)

where nf is the total number of fibers in the image, and A is the image area. The packing density, Fc, can be calculated based on the ratio between the area of the object and the area of the object’s circumscribed circle, as follows

Fc 

Aob Ac

(6)

where Aob is the area of the object (= πdl/4) and Ac is the area of the object’s circumscribed circle (=πl2/4), as shown in Fig. 16. The packing density is also used to evaluate the inclined angle of the fiber, as expressed in Eq. (7).

Fc 

dl / 4 d d    cos  l 2 / 4 l d / cos 

(7)

Therefore, Fc = 1 indicates a circular object perpendicular to the cutting plane, and Fc = 0 denotes an extremely elongated object parallel to the cutting plane.

4.2 Correlation between biaxial flexural performance and fiber distribution characteristics at maximum moment region Fig. 17 shows the binary images obtained from the cutting planes within the loading ring (at maximum moment region). For the specimens with concrete placed at the center, the random cutting plane was determined by reason of that as previously mentioned, whereas for the specimens with concrete placed

at the corner, the cutting plane at 45º or 90º was determined based on the position of localized crack. As can be seen in Fig. 17, the specimens with concrete placed at the center showed better fiber orientation and more fibers in cutting plane than their counterparts. The fiber orientation and dispersion coefficients are shown in Fig. 18 and summarized in Table 6. Higher values of the number of fibers, packing density, and fiber orientation coefficient were obtained for the specimens with concrete placed at the center than their counterparts, whereas the fiber dispersion coefficient showed no noticeable difference with the placement method. Based on these results, it was inferred that the specimens with concrete placed at the center had higher load carrying capacities than their counterparts because more fibers existed at the crack surfaces within the maximum moment region (Fig. 18(b)). For the specimens with concrete placed at the corner, the fiber dispersion coefficient decreased with increasing fiber length, implying that better fiber dispersion along the flow of concrete is obtained in specimens with shorter fibers. Since the fibers in radial flow tend to align themselves perpendicular to the flow direction, as shown in Fig. 3, more fibers were perpendicularly aligned to the crack surfaces in the specimens with concrete placed at the center, leading to better biaxial flexural performances compared to their counterparts.

4.3 Fiber distribution characteristics according to fiber length, placement method, and flow distance Figs. 19−21 exhibit the binary images of the cutting planes at different locations. For the specimens with concrete placed at the center, a random cutting plane was investigated, based on the assumption that the fiber distribution characteristics are identical in all directions. On the other hand, for the specimens with concrete placed at the corner, three different binary images of cutting planes, located at 0º, 45º, and 90º from the casting position, were obtained to investigate the effects of flow distance and direction on the fiber distribution characteristics. For the specimens with concrete placed at the corner, better fiber orientation and dispersion were obtained in the cutting plane at 0º than in those at 45º and 90º. Moreover, the fiber orientation and dispersion in the cutting plane located at 0º (for the specimens with concrete placed at the corner) showed similar trends for the specimens with concrete placed at the center. The evaluated parameters for fiber orientation and dispersion are illustrated in Figs. 22−24. For the specimens with concrete placed at the center, the number of fibers detected in the cutting plane increased with increasing flow distance from the casting position. This is caused by that since the flow velocity decreases with the flow distance, the randomly oriented fibers are rotated perpendicular to the flow direction by the rotational moment from the velocity gradient. This effect becomes stronger with longer flow duration [34] and the tendency of fibers to be more aligned perpendicular to the flow direction was numerically verified by Kang and Kim [35]. Therefore, due to more fibers aligned perpendicular to the flow direction (higher values of packing density and fiber orientation coefficient) as flow distance increased, the number of detected fibers increased, whereas the number of non-detected fibers decreased, as shown in Fig. 25.

For the cutting planes at 90º in the specimens with concrete placed at the corner, more fiber tended to be aligned perpendicular to the cutting surface with increasing the distance from the center of specimen because of its radial flow characteristics, as shown in Fig. 26. In addition, the fibers near the wall showed highest fiber orientation coefficient than those in other regions due to the wall effect. Since the velocity of flow becomes zero at the wall, the fibers are aligned perpendicular to the cutting planes (90º). Therefore, the packing density and fiber orientation coefficient increased with increasing distance from the center of specimen and the highest values were obtained near the wall. Consequently, the higher number of fibers was obtained near the wall and the number increased with increasing distance for all test series. For the cutting planes at 45º in the specimens with concrete placed at the corner, there are some parts without fiber or with the fibers significantly inclined to the cutting plane in the middle (between center and corner), as shown in Figs. 19−21. This can be explained from Fig. 26 by the fact that the fibers are aligned parallel to the cutting planes in the middle, where the expected line of fiber orientation is in contact with the cutting plane. Therefore, the lowest packing density and fiber orientation coefficient were observed near the middle of the cutting plane (distance of 90 mm from the center), and thus lower number of fibers per unit area was also obtained near the middle. Lastly, for the cutting planes at 0º in the specimens with concrete placed at the corner, higher values of packing density and fiber orientation coefficient were obtained near the point of concrete casting, in contrast to the specimens with concrete at the center. This is because of the boundary effect of the wall, which causes the fibers at the point of concrete casting aligned perpendicular to the cutting plane in the specimens with concrete placed at the corner. The tensile and flexural strengths of UHPFRC are influenced by many factors such as fiber orientation, fiber geometry, fiber content, and matrix strength. In particular, the number of fibers at the crack surfaces strongly influences to the tensile and flexural strengths. In the BFT, the crack is first initiated at the weakest point in the loading ring (maximum moment region), and then the specimen fails by the localization of the crack. Based on the image analysis results (Figs. 22−24) for panels with concrete placed at the corner, the S13 specimen showed the lowest number of fibers inside the loading ring for the cutting planes at 90º from the casting position, whereas the S16.3 and S19.5 specimens exhibited the lowest number of fibers inside loading ring for the cutting planes at 45º. Thus, as can be seen in Fig. 13(b), the crack localization occurred near the angle of 90º from the casting position for the S13 specimen and near the angle of 45º from the casting position for the S16.3 and S19.5 specimens. Fig. 27 shows the probability density functions (PDFs) against flow distance for the specimens with concrete placed at the center. At all flow distances, the PDFs obtained from the image analysis were significantly different from those obtained from the assumption of two-dimensional (2-D) or threedimensional (3-D) random fiber arrangements. With increasing flow distance, a more left-skewed distribution was observed for all test specimens. This sinistral shift of the PDF with the flow distance

was more distinct when shorter fibers were used. This is caused by the fact that lower fiber length results in higher effective viscosity and lower the drag reduction efficiency [36]. Therefore, the magnitude of fiber-orienting torque increased with the increase in the gradient of flow velocity profile and the decrease in the plug-flow zone [37]. For this observation, it was concluded that shorter fibers tend to be more aligned perpendicular to the flow direction under radial flow than longer ones.

5. Conclusions In this study, the effects of fiber length and placement method on the biaxial flexural behaviors and fiber distribution characteristics of UHPFRC panels were investigated. From the above discussions, the following conclusions can be obtained:

1) All test panels exhibited deflection-hardening behavior with multiple micro-cracks. The first cracking strength and corresponding deflection showed no noticeable difference with fiber length and placement method, whereas the load carrying capacity and deflection capacity (deflection at the peak) increased with increasing fiber length up to 19.5 mm (S13 < S16.3 < S19.5). In addition, the panels with concrete placed at the center (maximum moment region) provided a higher load carrying capacity than those with concrete placed at the corner. 2) The S19.5 specimen exhibited the toughest response, whereas the S13 specimen showed the lowest toughness, and the S16.3 specimen had values in between. The S16.3 specimen placed at the center showed higher toughness at deflection points up to d10 compared to the S19.5 mm specimen placed at the corner, indicating that the energy absorption capacity is influenced by the fiber length as well as the placement method. 3) The panels with concrete placed at the center failed by two different failure modes (flexural failure and punching failure), whereas the specimens with concrete placed at the corner only failed by the flexural failure mode. The panels with concrete placed at the center and higher fiber lengths showed more cracks and smaller crack spacing than their counterparts. 4) Based on the image analysis results, the panels with concrete placed at the center had better fiber orientation and more fibers in the area of the maximum moment region than those with concrete placed at the corner. This mainly caused the specimens with concrete placed at the center to show higher load carrying capacities than their counterparts. 5) For the panels with concrete placed at the center, a more left-skewed distribution of PDF for fiber orientation was observed with increasing flow distance, and this sinistral shift was more distinct when shorter fibers were used. For the panels with concrete placed at the corner, the fiber distribution characteristics varied with the angle of the cutting plane from the casting position and the distance from the center of the specimen. Due to the boundary effect of the wall, the highest fiber orientation was obtained near the wall, regardless of the cutting plane. In addition, the crack localization was

obtained where the lowest number of fibers was observed.

ACKNOWLEDGEMENTS This research was supported by a grant from a Construction Technology Research Project 13SCIPS02 (Development of impact/blast resistant HPFRCC and evaluation technique thereof) funded by the Ministry on Land, Infrastructure, and Transport.

REFERENCES [1] Graybea1 B, Tanesi J. Durability of an ultrahigh-performance concrete. J Mater Civil Eng 2007;19(10):848–854. [2] Farhat FA, Nicolaides D, Kanellopoulos A, Karihaloo BL. High performance fibre-reinforced cementitious composite (CARDIFRC) – Performance and application to retrofitting. Eng Fract Mech 2007;74(1–2):151–167. [3] Yoo DY, Kang ST, Yoon YS. Effect of fiber length and placement method on flexural behavior, tension-softening curve, and fiber distribution characteristics of UHPFRC. Const Build Mater 2014;64:67–81. [4] Wille K, Kim DJ, Naaman AE. Strain-hardening UHP-FRC with low fiber contents. Mater Struct 2011;44(3):583–598. [5] Aydın S, Baradan B. The effect of fiber properties on high performance alkali-activated slag/silica fume mortars. Compos Part B Eng 2013;45(1):63–69. [6] Lankard DR. Prediction of the flexural strength properties of steel fibrous concrete. In: Proceedings CERL conference on fibrous concrete, Construction Engineering Research Laboratory, Champaign, 1972, pp. 101–123. [7] di Prisco M, Lamperti M, Lapolla S, Khurana RS. HPFRCC thin plates for precast roofing. Proceedings of the Second International Symposium on Ultra High Performance Concrete, Kassel, Germany, Mar., 2008, pp. 675–682. [8] Saleem MA, Mirmiran A, Xia J, Mackie K. Ultra-high-performance concrete bridge deck reinforced with high-strength steel. ACI Struct J 2011;108(5):601–609. [9] Kim J, Kim DJ, Zi G. Improvement of the biaxial flexure test method for concrete. Cem Concr Compos 2013;37:154–160. [10] Yoo DY, Kang ST, Lee JH, Yoon YS. Effect of shrinkage reducing admixture on tensile and flexural behaviors of UHPFRC considering fiber distribution characteristics. Cem Concr Res 2013;54:180–190. [11] Naaman AE, Reinhardt HW. Proposed classification of HPFRC composites based on their tensile response. Mater Struct 2006;39(5):547–555. [12] Nguyen DL, Kim DJ, Ryu GS, Koh KT. Size effect on flexural behavior of ultra-high-performance hybrid fiber-reinforced concrete. Compos Part B Eng 2013;45(1):1104–1116.

[13] Yoo DY, Kim J, Zi G, Yoon YS. Effect of shrinkage-reducing admixture on biaxial flexural behavior of ultra-high-performance fiber-reinforced concrete. Const Build Mater 2015;accepted. [14] Barnett SJ, Lataste JF, Parry T, Millard SG, Soutsos MN. Assessment of fibre orientation in ultra high performance fibre reinforced concrete and its effect on flexural strength. Mater Struct 2010;43(7):1009–1023. [15] Ferrara L, Ozyurt N, di Prisco M. High mechanical performance of fibre reinforced cementitious composites: the role of ‘‘casting-flow induced’’ fibre orientation. Mater Struct 2011;44(1):109–128. [16] Yang IH, Joh C, Kim BS. Structural behavior of ultra high performance concrete beams subjected to bending. Eng Struct 2010;32(11):3478–3487. [17] Kwon SH, Kang ST, Lee BY, Kim JK. The variation of flow-dependent tensile behavior in radial flow dominant placing of Ultra High Performance Fiber Reinforced Cementitious Composites (UHPFRCC). Const Build Mater 2012;33:109–121. [18] Wille K, Tue NV, Parra-Montesinos GJ. Fiber distribution and orientation in UHP-FRC beams and their effect on backward analysis. Mater Struct 2014;47(11):1825–1838. [19] Kang ST, Lee BY, Kim JK, Kim YY. The effect of fibre distribution characteristics on the flexural strength of steel fibre-reinforced ultra high strength concrete. Const Build Mater 2011;25(5):2450– 2457. [20] Zi G, Oh H, Park SK. A novel indirect tensile test method to measure the biaxial tensile strength of concretes and other quasibrittle materials. Cem Concr Res 2008;38(6):751–756. [21] Park JJ, Kang ST, Koh KT, Kim SW. Influence of the ingredients on the compressive strength of UHPC as a fundamental study to optimize the mixing proportion. Second International Symposium on Ultra High Performance Concrete, Kassel, Germany, 2008, pp. 105–112. [22] ASTM C 1437-07, Standard test method for flow of hydraulic cement mortar, American Society of Testing and Materials, 2007, pp. 1–2. [23] ASTM C 39/39M-12a, Standard test method for compressive strength of cylindrical concrete specimens. American Society of Testing and Materials, 2012, pp. 1–7. [24] ASTM C 1499-09, Standard test method for test method for monotonic equibiaxial flexural strength of advanced ceramics at ambient temperature, American Society of Testing and Materials, 2013, pp. 1–13. [25] ASTM C 1550-12a, Standard test method for flexural toughness of fiber-reinforced concrete (using centrally loaded round panel), American Society of Testing and Materials, 2012, pp. 1–14. [26] Higgs WAJ, Lucksanasombool P, Higgs RJED, Swain MV. Evaluating acrylic and glass-ionomer cement strength using the biaxial flexure test. Biomaterials 2001;22(12):1583–1590. [27] ASTM C 469/C 469M-14, Standard test method for static modulus of elasticity and poisson’s ratio of concrete in compression, American Society of Testing and Materials, 2014, pp. 1–5. [28] Timoshenko SP, Woinowsky-Krieger S. Theory of plates and shells. 2nd ed. New York: McGrawHill, 1959.

[29] Graybeal BA. Compressive behavior of ultra-high-performance fiber-reinforced concrete. ACI Mater J 2007;102(2):146–152. [30] Zhao Z, Kwon SH, Shah SP. Effect of specimen size on fracture energy and softening curve of concrete: Part I. Experiments and fracture energy. Cem Concr Res 2008;38(8):1049–1060. [31] Barnett SJ, Lataste JF, Parry T, Millard SG, Soutsos MN. Assessment of fibre orientation in ultra high performance fibre reinforced concrete and its effect on flexural strength. Mater Struct 2010;43(7): 1009–1023. [32] Lee BY, Kim JK, Kim JS, Kim YY. Quantitative evaluation technique of PVA (polyvinyl alcohol) fiber dispersion in engineered cementitious composites. Cem Concr Compos 2009;31(6):408–417. [33] Xia M, Hamada H, Maekawa Z, Flexural stiffness of injection molded glass fibre reinforced thermoplastics. Int Polym Process 1995;10(1):74–81. [34] Stähli P, Custer R, van Mier JG. On flow properties, fibre distribution, fibre orientation and flexural behaviour of FRC. Mater Struct 2008;41(1):189–196. [35] Kang ST, Kim JK. Numerical simulation of the variation of fiber orientation distribution during flow molding of Ultra High Performance Cementitious Composites (UHPCC). Cem Concr Compos 2012;34(2):208–217. [36] Zang LX, Lin JZ, Chan TL. On the modelling of motion of non-spherical particles in two-phase flow. 6th International Conference on Multiphase Flow, ICMF 2007, Leipzig, Germany, 2007. [37] Ferrara L. High performance fiber reinforced self-compacting concrete (HPFR-SCC): a “smart material” for high end engineering applications. 3rd International Workshop on Heterogeneous Architectures and Computing, Madrid, 2012, pp. 325–334.

List of Tables Table 1 Mix proportions Table 2 Chemical compositions and physical properties of cementitious materials Table 3 Properties of smooth steel fibers Table 4 Summary of compression test results Table 5 Summary of results derived from biaxial flexure test Table 6 Parameters for fiber orientation and dispersion within maximum moment region

Table 1 Mix proportions Unit weight (kg/m3) Silica Silica Water Cement fume flour 20 160.3 788.5 197.1 236.6 [Note] SP = superplasticizer W/B (%)

Silica sand 867.4

SP (%) 2.0

Flow (mm) 230–240

Table 2 Chemical compositions and physical properties of cementitious materials Composition % (mass) CaO Al2O3 SiO2 Fe2O3 MgO SO3 Specific surface (cm2/g) Density (g/cm3)

Cement 61.33 6.40 21.01 3.12 3.02 2.30 3,413 3.15

Silica fume 0.38 0.25 96.00 0.12 0.10 200,000 2.10

Table 3 Properties of smooth steel fibers Name S13 S16.3 S19.5

Diameter, df Length, Lf (mm) (mm) 0.2 13.0 0.2 16.3 0.2 19.5

Aspect ratio (Lf/df ) 65.0 81.5 97.5

Density (g/cm3) 7.8

Tensile Elastic modulus strength (MPa) (GPa) 2500.0

Table 4 Summary of compression test results Compressive strength, Strain at the peak, fc' (MPa) εu (mm/mm) S13 201.8 (2.14) 4.3×10-3 (0.00034) S16.3 204.5 (1.63) 4.9×10-3 (0.00011) S19.5 197.3 (0.89) 4.5×10-3 (0.00016) [Note] (): items in parentheses = standard deviation Name

Elastic modulus, Ec (GPa) 50.9 (0.55) 46.3 (0.17) 46.1 (0.88)

200.0

Table 5 Summary of results derived from biaxial flexure test Unit

S13

S16.3

Corner Center Corner Center Corner LOP PLOP kN 44.29 (10.19) 47.75 (2.91) 47.22 (11.14) 42.70 (3.87) 46.04 (1.98) fLOP MPa 18.32 (4.22) 19.75 (1.20) 19.53 (4.61) 17.66 (1.60) 19.04 (0.82) δLOP mm 0.20 (0.036) 0.18 (0.020) 0.19 (0.015) 0.17 (0.010) 0.21 (0.020) ToughLOP kN·mm 4.71 (1.77) 5.07 (0.45) 4.29 (1.34) 3.66 (0.71) 4.76 (0.47) MOR PMOR kN 79.37 (3.81) 96.19 (6.53) 94.36 (6.35) 101.09 (5.52) 98.70 (7.42) fMOR MPa 32.83 (1.58) 39.79 (2.70) 39.03 (2.63) 41.82 (2.28) 40.82 (3.07) δMOR mm 3.14 (0.767) 3.78 (0.023) 4.96 (0.996) 5.51 (1.670) 8.45 (1.696) ToughMOR kN·mm 216.20 (66.32) 323.00 (24.01) 409.35 (56.76) 495.32 (187.60) 743.47 (168.89) d2.5 Pd2.5 kN 77.90 (3.93) 93.23 (6.53) 90.47 (6.99) 94.85 (2.61) 88.46 (6.12) δd2.5 mm 2.5 2.5 2.5 2.5 2.5 Toughd2.5 kN·mm 164.86 (10.76) 194.75 (9.30) 187.52 (18.37) 195.05 (5.53) 178.14 (13.91) d5 Pd5 kN 74.62 (4.90) 93.50 (6.81) 93.18 (6.01) 98.79 (4.30) 95.33 (6.90) δd5 mm 5.0 5.0 5.0 5.0 5.0 Toughd5 kN·mm 360.57 (18.45) 431.66 (25.38) 418.71 (34.86) 441.78 (14.86) 409.41 (28.96) d10 Pd10 kN 57.56 (7.85) 76.82 (12.66) 85.49 (2.57) 93.89 (6.12) 96.49 (8.39) δd10 mm 10.0 10.0 10.0 10.0 10.0 Toughd10 kN·mm 698.15 (45.48) 865.35 (71.36) 874.51 (54.26) 933.68 (45.56) 894.10 (68.85) d15 Pd15 kN 39.31 (6.27) 55.48 (21.09) 69.28 (2.13) 75.81 (4.40) 87.99 (7.59) δd15 mm 15.0 15.0 15.0 15.0 15.0 Toughd15 kN·mm 941.17 (85.24) 1205.72 (138.41) 1266.86 (53.48) 1360.78 (64.84) 1364.48 (102.97) [Note] P = load, f = biaxial flexural strength, δ = mid-span deflection, Tough = toughness, (): items in parentheses = standard deviation

S19.5 Center 43.70 (3.75) 18.07 (1.55) 0.18 (0.020) 3.92 (0.85) 122.75 (11.43) 50.77 (4.73) 8.97 (1.121) 955.91 (148.60) 105.22 (9.16) 2.5 206.05 (18.09) 114.21 (9.00) 5.0 483.43 (40.55) 120.69 (12.14) 10.0 1081.58 (93.97) 97.13 (24.43) 15.0 1635.24 (167.33)

Table 6 Parameters for fiber orientation and dispersion within maximum moment region Placement Cutting Fn Name αf Fc ηθ method plane (number/cm2) S13 corner 90º 0.391 14.71 0.602 0.415 center random 0.368 27.71 0.690 0.519 S16.3 corner 45º 0.376 24.38 0.700 0.527 center random 0.367 28.67 0.703 0.537 S19.5 corner 45º 0.375 22.97 0.693 0.521 center random 0.383 40.29 0.737 0.587 [Note] αf = fiber dispersion coefficient, Fn = number of fiber in unit area, Fc = packing density, ηθ = fiber orientation coefficient

17

List of Figures Fig. 1 Mean particle sizes of ingredients in UHPFRC Fig. 2 Image of smooth steel fibers Fig. 3 Two different placement methods for thin plate structure; (a) placing concrete at corner, (b) placing concrete at center Fig. 4 Uniaxial compression test Fig. 5 Schematic description of biaxial flexure test Fig. 6 Biaxial flexure test Fig. 7 Compressive stress-strain curves Fig. 8 Initial biaxial flexural load-deflection and stress-strain curves Fig. 9 Procedure of average of load-deflection curve (S13 with concrete placed in the corner); (a) reduction of measured data, (b) average of reduced data Fig. 10 Average load-deflection curves; (a) with concrete placed at the corner, (b) with concrete placed at the center Fig. 11 Toughness according to fiber length and placement method; (a) up to d5 (corner), (b) after MOR (corner), (c) up to d5 (center), (d) after MOR (center) Fig. 12 Toughness ratio based on S13; (a) placing concrete at the corner, (b) placing concrete at the center Fig. 13 Typical failure mode and crack patterns; (a) placing concrete at the center, (c) placing concrete at the corner Fig. 14 Cracking properties; (a) number of cracks, (b) average crack spacing Fig. 15 Identification of cross-sectional saw cuts; (a) placing concrete at the center, (b) placing concrete at the corner Fig. 16 Dimensions of inclined fiber (Left: cross-section of cutting plane, Right: side view at section A– A) [29] Fig. 17 Images of cutting plane in loading ring (Left: placing concrete at center, Right: placing concrete at corner); (a) S13 (random, 90°), (b) S16.3 (random, 45°), (c) S19.5 (random, 45°) Fig. 18 Fiber orientation and dispersion coefficients at cutting plane; (a) fiber dispersion coefficient, αf, (b) number of fiber in unit area, Fn, (c) packing density, Pc, (d) fiber orientation coefficient, ηθ Fig. 19 Binary images of cutting planes (S13); (a) placing concrete at center, (b) placing concrete at corner (0°), (c) placing concrete at corner (45°), (d) placing concrete at corner (90°)

18

Fig. 20 Binary images of cutting planes (S16.3); (a) placing concrete at center, (b) placing concrete at corner (0°), (c) placing concrete at corner (45°), (d) placing concrete at corner (90°) Fig. 21 Binary images of cutting planes (S19.5); (a) placing concrete at center, (b) placing concrete at corner (0°), (c) placing concrete at corner (45°), (d) placing concrete at corner (90°) Fig. 22 Fiber orientation and dispersion coefficients at each location (S13); (a) fiber dispersion coefficient, αf, (b) number of fiber in unit area, Fn, (c) packing density, Pc, (d) fiber orientation coefficient, ηθ Fig. 23 Fiber orientation and dispersion coefficients at each location (S16.3); (a) fiber dispersion coefficient, αf, (b) number of fiber in unit area, Fn, (c) packing density, Pc, (d) fiber orientation coefficient, ηθ Fig. 24 Fiber orientation and dispersion coefficients at each location (S19.5); (a) fiber dispersion coefficient, αf, (b) number of fiber in unit area, Fn, (c) packing density, Pc, (d) fiber orientation coefficient, ηθ Fig. 25 Schematic description of detected and non-detected fibers Fig. 26 Schematic description of fiber orientation at cutting planes Fig. 27 Probability density function (placing concrete at center); (a) S13, (b) S16.3, (c) S19.5

19

Silica flour

Sand

Cement Steel fiber

Silica fume

Cement Sand Silica flour Silica fume Steel fiber d50 =0.2–0.3mm d50 =15–25μm d50 =10μm d50=0.2–0.3μm

Fig. 1 Mean particle sizes of ingredients in UHPFRC

df = 0.2mm, Lf = 13mm df = 0.2mm, Lf = 16.3mm df = 0.2mm, Lf = 19.5mm

Fig. 2 Image of smooth steel fibers

20

F i b er

S u p p o sed fl o wd i r ect i o n

Ro t a tio n o f fi b er

F lo w v el o ci t y

Ca st i ng di re c t i on

(a) Supposed flow direction Rotation of fiber Fiber

Casting direction

Flow velocity

(b) Fig. 3 Two different placement methods for thin plate structure; (a) placing concrete at corner, (b) placing concrete at center

TEST MACHINE CROSS HEAD

LVDTs

Cylindrical specimen (φ100×200 mm)

Compressometer

TEST MACHINE FIXED SUPPORT

Fig. 4 Uniaxial compression test

P LOADING RING hp

SPECIMEN SUPPORT RING

fp

bp ap Rp Fig. 5 Schematic description of biaxial flexure test

21

TEST MACHINE CROSS HEAD

Load cell Round panel (φ 420 × 48 mm)

Loading ring (φ 100 mm)

Gypsum Support ring (φ 400 mm)

Steel frame

Rubber pads LVDT

TEST MACHINE FIXED SUPPORT

Fig. 6 Biaxial flexure test

Strain (με) 1600

1000 2000 3000 4000 5000 6000 200

S13 S16.3 S19.5

160

Load (kN)

1200

120 800 80 400

Stress (MPa)

0

40

0

0 0

0.1

0.2

0.3

0.4

0.5

0.6

Displacement (mm)

Fig. 7 Compressive stress-strain curves

Strain (με) 0

300

600

900

1200

1500

160

64 Deflection Strain_1 Strain_2

48

Limit of proportionality (LOP)

80

32

40

Stress (MPa)

Load (kN)

120

16

0

0 0

0.2

0.4

0.6

0.8

1

Deflection (mm)

Fig. 8 Initial biaxial flexural load-deflection and stress-strain curves

22

120

120 Measured data Reduced data (Spec._3)

90

Load (kN)

Load (kN)

90

Spec._1 Spec._2 Spec._3 Ave.

60

60

30

30

0

0 0

3

6

9

12

0

15

3

6

9

12

15

Deflection (mm)

Deflection (mm)

(a) (b) Fig. 9 Procedure of average of load-deflection curve (S13 with concrete placed in the corner); (a) reduction of measured data, (b) average of reduced data

Normalized deflection (δ/L)

Normalized deflection (δ/L) 0.03

90

36

60

24

30

12

0

Load (kN)

Load (kN)

48

3

6

9

12

0.03

0.0375 60

120

48

90

36

60

24 S13 S16.3 S19.5

30

12

0

0 0

0.0075 0.015 0.0225

150

60

S13 S16.3 S19.5

120

0

0.0375

0 0

15

Biaxial felxural stress (MPa)

0.0075 0.015 0.0225

Biaxial felxural stress (MPa)

0 150

3

6

9

12

15

Deflection (mm)

Deflection (mm)

(a) (b) Fig. 10 Average load-deflection curves; (a) with concrete placed at the corner, (b) with concrete placed at the center

23

LOP

600

d2.5

MOR

d5

(a)

d10

d15

2000

(b) 1500

400

200 500

6000

02000

(c)

(d) 1500

400

Toughness (kNmm)

Toughness (kNmm)

1000

1000 200 500

0

0 13

16.3

19.5

13

16.3

19.5

Fiber length (mm)

2

d2.5

d5

d10

(a)

d15

2

(b)

1.5

1.5

1

1

0.5

0.5

0

0 13

16.3

19.5

13

16.3

19.5

Toughness ratio (based on S13)

Toughness ratio (based on S13)

Fig. 11 Toughness according to fiber length and placement method; (a) up to d5 (corner), (b) after MOR (corner), (c) up to d5 (center), (d) after MOR (center)

Fiber length (mm)

Fig. 12 Toughness ratio based on S13; (a) placing concrete at the corner, (b) placing concrete at the center

24

(a)

(b) Fig. 13 Typical failure mode and crack patterns; (a) placing concrete at the center, (c) placing concrete at the corner

250

40

Ave. cracking spacing (mm)

Number of cracks

Center Corner

200 150

100 50 0

Center

Corner

30

20

10

0 0

6

12

18

24

30

0

Fiber length (mm)

6

12

18

Fiber length (mm)

(a) (b) Fig. 14 Cracking properties; (a) number of cracks, (b) average crack spacing

25

24

30

Loading ring

Loading ring

Cutting surfaces

90°

Cutting surfaces 0°

45°

Casting position

(a) (b) Fig. 15 Identification of cross-sectional saw cuts; (a) placing concrete at the center, (b) placing concrete at the corner

A

d

A

d

θ Fiber

l

Matrix

l

(a) (b) Fig. 16 Dimensions of inclined fiber (Left: cross-section of cutting plane, Right: side view at section A– A) [29]

26

Random

90°

Random

(a)

45° (b)

Random

45° (c) Fig. 17 Images of cutting plane in loading ring (Left: placing concrete at center, Right: placing concrete at corner); (a) S13 (random, 90°), (b) S16.3 (random, 45°), (c) S19.5 (random, 45°)

27

0.45

50

Center

Corner

Center

Corner

Fn (Number/cm2 )

40

αf

0.4

0.35

30

20 10

0.3

0

13

16.3

19.5

13

Fiber length (mm)

19.5

Fiber length (mm)

(a)

(b)

0.95

0.7

Center

Corner

Center

0.85

Corner

0.6

ηθ

Fc

16.3

0.75

0.65

0.5

0.4

0.55

0.3 13

16.3

19.5

13

Fiber length (mm)

16.3

19.5

Fiber length (mm)

(c) (d) Fig. 18 Fiber orientation and dispersion coefficients at cutting plane; (a) fiber dispersion coefficient, αf, (b) number of fiber in unit area, Fn, (c) packing density, Pc, (d) fiber orientation coefficient, ηθ

28

Center

Corner

(a)

(b)

(c)

(d) Fig. 19 Binary images of cutting planes (S13); (a) placing concrete at center, (b) placing concrete at corner (0°), (c) placing concrete at corner (45°), (d) placing concrete at corner (90°)

29

Center

Corner

(a)

(b)

(c)

(d) Fig. 20 Binary images of cutting planes (S16.3); (a) placing concrete at center, (b) placing concrete at corner (0°), (c) placing concrete at corner (45°), (d) placing concrete at corner (90°)

30

Center

Corner

(a)

(b)

(c)

(d) Fig. 21 Binary images of cutting planes (S19.5); (a) placing concrete at center, (b) placing concrete at corner (0°), (c) placing concrete at corner (45°), (d) placing concrete at corner (90°)

31

50

0.45

αf

0.4

0.35

S13_center S13_corner (0°) S13_corner (45°) S13_corner (90°)

Fn (number/cm2 )

(a)

Loading ring

0.3

(b) 40 30 20 10

0

70

140

210

0

70

0.95

210

0.75

(d)

(c) 0.85

0.65

0.75

0.55

ηθ

Fc

140

Distance (mm)

Distance (mm)

0.45

0.65

0.35

0.55 0

70

140

0

210

70

140

210

Distance (mm)

Distance (mm)

Fig. 22 Fiber orientation and dispersion coefficients at each location (S13); (a) fiber dispersion coefficient, αf, (b) number of fiber in unit area, Fn, (c) packing density, Pc, (d) fiber orientation coefficient, ηθ

0.45

50

(b)

Loading ring

αf

0.4

0.35

S16.3_center S16.3_corner (0°) S16.3_corner (45°) S16.3_corner (90°)

Fn (number/cm2 )

(a)

0.3

40 30 20 10

0

70

140

210

0

70

0.95

210

0.75

(c)

(d)

0.85

0.65

0.75

0.55

ηθ

Fc

140

Distance (mm)

Distance (mm)

0.45

0.65

0.35

0.55 0

70

140

Distance (mm)

210

0

70

140

210

Distance (mm)

Fig. 23 Fiber orientation and dispersion coefficients at each location (S16.3); (a) fiber dispersion coefficient, αf, (b) number of fiber in unit area, Fn, (c) packing density, Pc, (d) fiber orientation coefficient, ηθ

32

0.45

50

(b)

Loading ring

αf

0.4

0.35

S19.5_center S19.5_corner (0°) S19.5_corner (45°) S19.5_corner (90°)

Fn (number/cm2 )

(a)

0.3

40 30 20 10

0

70

140

210

0

70

210

0.75

0.95

(c)

(d)

0.85

0.65

0.75

0.55

ηθ

Fc

140

Distance (mm)

Distance (mm)

0.45

0.65

0.35

0.55 0

70

140

210

Distance (mm)

0

70

140

210

Distance (mm)

Fig. 24 Fiber orientation and dispersion coefficients at each location (S19.5); (a) fiber dispersion coefficient, αf, (b) number of fiber in unit area, Fn, (c) packing density, Pc, (d) fiber orientation coefficient, ηθ

Crack surface Detected fibers

Nondetected fiber

Side view

Front view

Fig. 25 Schematic description of detected and non-detected fibers

33

Fibers

Wall effect

90°

0°

Fig. 26 Schematic description of fiber orientation at cutting planes

3

3 d=25mm d=90mm d=170mm 2-D random 3-D random

1.8

2.4

Probability, P(θ)

Probability, P(θ)

2.4

d=25mm d=90mm d=170mm 2-D random 3-D random

1.2

1.8

1.2 0.6

0.6

0

0 0

22.5

45

67.5

90

0

22.5

45

67.5

90

Orientation (degree)

Orientation (degree)

(a)

(b)

3 d=25mm d=90mm d=170mm 2-D random 3-D random

Probability, P(θ)

2.4 1.8 1.2

0.6 0 0

22.5

45

67.5

90

Orientation (degree)

(c) Fig. 27 Probability density function (placing concrete at center); (a) S13, (b) S16.3, (c) S19.5

34