ACI Materials Journal/May-June 2012 379

Title no. 109-M36

ACI MATERIALS JOURNAL TECHNICAL PAPER

ACI Materials Journal, V. 109, No. 3, May-June 2012.MS No. M-2011-102.R2 received July 13, 2011, and reviewed under Institute

publication policies. Copyright © 2012, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published in the March-April 2013 ACI Materials Journal if the discussion is received by December 1, 2012.

Effect of Beam Size, Casting Method, and Support Conditions on Flexural Behavior of Ultra-High-Performance Fiber-Reinforced Concreteby Kay Wille and Gustavo J. Parra-Montesinos

The flexural behavior of fiber-reinforced concretes (FRCs) is typi-cally evaluated through standard tests of beams under either three-or four-point loading. Although these test methods are standard-ized, test results could vary significantly depending on specimen size, concrete casting method, and support devices used.

Results from a comprehensive experimental program aimed at evaluating the influence of these test parameters on material flex-ural behavior are presented. The investigation focused on ultra-high-strength (>150 MPa [22 ksi]) FRC, typically referred to as ultra-high-performance FRC (UHP-FRC). By varying specimen size, casting method, and support conditions to account for those normally used by researchers in accordance with ASTM C1609/C1609M and RILEM TC 162-TDF, equivalent bending strengths as low as 10 MPa (1.4 ksi) and as high as 29 MPa (4.2 ksi) were obtained using the same UHP-FRC mixture design. The degree of restraint developed at the supports intended to work as rollers was also evaluated through finite element analyses. The use of a shear friction coefficient of 0.4, which was found to be representative of that in the “high-friction” supports used in this study, led to an increase in bending strength of approximately 30% compared to beams with no axial restraint. The test results also indicate that a more specific recommendation on the casting method is needed when using highly workable FRC, given the variability in results between beams constructed following various casting methods.

Keywords: bending strength; fiber orientation; flexural strength; residual strength; self-consolidating; steel fibers; ultra-high-performance concrete (UHPC); ultra-high-performance fiber-reinforced concrete (UHP-FRC).

INTRODUCTIONThe flexural behavior (and indirectly, the tensile behavior)

of fiber-reinforced concrete (FRC) is typically evaluated through standard tests of beams under either three- or four-point loading (for example, ASTM C1609/C1609M-06 and RILEM TC 162-TDF [2002]). Although these standards require the use of “roller supports that are free to rotate on their axes” (ASTM C1609/C1609M-06) or that “rollers … shall be capable of rotating freely around their axes …” (RILEM TC 162-TDF), a significant frictional horizontal (longitudinal) force may develop in standard test setups due to a rotational restraint induced by surface friction between the roller and the support (Fig. 1(a) to (c); Fig. 2(a) to (c)). Unfortunately, the level of friction that can be developed in typical setups used for these standard beam tests is difficult to evaluate and, thus, its effect on measured flexural response is unknown.

The results obtained from standard bending tests are not only sensitive to the type of support device used but also to the casting method. ASTM C1609/C1609M-06 requires that the mold be filled “in one layer by using a wide shovel or scoop parallel to the length of the mold to place the layer uniformly along the length of the mold.” RILEM TC

162-TDF, on the other hand, requires the filling of the mold with a large portion in the middle and a smaller portion on each end of the mold, except when self-consolidating FRC is used, where “the mould shall be filled in a single pour and leveled off without compaction.”

For the case of highly workable or self-consolidating FRC and ultra-high-performance FRC (UHP-FRC), the orienta-tion of fibers in the flow direction makes the casting method particularly critical. The tendency of fiber alignment in the flow direction is determined by the flow velocity and the flow velocity gradient (Fig. 3), the flow properties of the concrete, as well as the specimen shape and dimensions (Grünewald 2004; Tiel et al. 2004; Ferrara et al. 2007; Staehli et al. 2008; Kim et al. 2008; Wille 2008). Fiber alignment in the direc-tion perpendicular to the crack plane improves the beam postcracking response due to an increased number of fibers crossing the crack and an enhanced pullout behavior in comparison to that of fibers with low angles of inclination with respect to the crack plane. At low angles between the fiber and the crack plane, high, localized bearing stresses develop during fiber pullout, which often lead to matrix failure and, thus, a reduction in pullout resistance (Laran-jeira et al. 2010; Robins et al. 2002).

Another test feature that affects the flexural response of FRC beams is the fixing of the critical section by adding a notch. RILEM TC 162-TDF (2002) requires the beams to be notched, whereas ASTM C1609/C1609M-06 requires the testing of unnotched beams under four-point loading, for which the location of the critical section would be dictated by the presence of a weaker section within the middle third of the beam.

In addition to the aforementioned parameters (that is, support device, casting method, and presence of notch), specimen size may also affect flexural behavior measured through standard beam tests. Although a minimum specimen size dependent on the fiber length and maximum aggregate size is often specified, the use of beam sizes larger than the minimum required is also acceptable. The effect of specimen size could be particularly important when evaluating flex-ural behavior based on ASTM C1609/C1609M-06, given the fact that residual flexural strengths are evaluated at midspan deflection levels corresponding to fixed percent-

380 ACI Materials Journal/May-June 2012

ages of the span length. The application of larger deflec-tions to larger beams thus often translates into wider crack widths, which could lead to important differences in beam behavior. Specimen size could also affect fiber distribution and, thus, bending response, through the so-called “wall effect,” which represents the tendency of fibers to align along “obstacles” (that is, formwork in the case of ASTM C1609/C1609M-06 and RILEM TC 162-TDF tests). This “wall effect” is more pronounced in beams of smaller size.

In this research, a comprehensive experimental program was conducted to evaluate the effect of support conditions, casting method, and beam size on the flexural behavior of FRC. In addition to evaluating the influence of these parame-

ters, the effect of a notch (and thus of fixing the critical crack location) on material flexural behavior was evaluated. Given the increasing interest of researchers and practicing engi-neers in applications of UHP-FRCs, which are character-ized by very high compressive and tensile strengths and high ductility and durability, the experimental program focused on these materials rather than on regular FRCs.

RESEARCH SIGNIFICANCEThe effect of test variables such as specimen geometry,

roller support type, and casting method on the flexural behavior of FRC is currently not addressed in standards such as ASTM C1609/C1609M-06 and RILEM TC 162-TDF. Therefore, a comprehensive experimental program was conducted to generate necessary data to assess the influ-ence of these parameters on the flexural behavior of FRC. The experimental program was confined to highly workable UHP-FRCs, for which fiber alignment with concrete flow could substantially influence flexural behavior measured through three- or four-point bending tests.

MATERIALS INVESTIGATEDA highly workable, ultra-high-strength FRC made out

of materials commonly available in the U.S. was used in this investigation. The mixture proportions are provided in Table 1, while detailed information about the develop-ment of this mixture can be found elsewhere (Wille et al. 2011b). The compressive strength for this material, obtained from 50 x 50 x 100 mm (2 x 2 x 4 in.) prism-shaped speci-mens with ground-loaded surfaces and cured under normal laboratory conditions (water, 20°C [68°F]), was on the order of 200 MPa (29 ksi).

Three types of high-strength (tensile strength ft ≥2600 MPa [377 ksi]) steel fibers were used in this study (Table 2 and Fig. 4). Besides 13 mm (0.5 in.) long, 0.20 mm (0.0079 in.) diameter straight (S) fibers, which are commonly used in UHP-FRC, two types of deformed steel fibers were evalu-ated: 30 mm (1.2 in.) long, 0.38 mm (0.015 in.) diameter hooked (H) fibers and 30 mm (1.2 in.) long, 0.30 mm (0.012 in.) equivalent diameter twisted (T) fibers. Straight fibers (S) were used in volume fractions of either 1.5 or 2.5%, whereas hooked and twisted steel fibers were used in a volume fraction of 1.5%. Thus, a total of four different UHP-FRC mixtures were evaluated in the experimental program (refer to Table 3).

In all UHP-FRC mixtures, steel fibers were found to distribute uniformly during the mixing process. Fiber-volume fraction and length-to-diameter ratio are known to affect the

ACI member Kay Wille is an Assistant Professor in the Department of Civil and Envi-ronmental Engineering at the University of Connecticut, Storrs, CT. He is a member of ACI Committees 239, Ultra-High-Performance Concrete, and 544, Fiber-Reinforced Concrete. His research interests include the design, analysis, and modeling of ultra-high-performance fiber-reinforced concrete.

Gustavo J. Parra-Montesinos, FACI, is an Associate Professor of civil and envi-ronmental engineering at the University of Michigan, Ann Arbor, MI. He is Chair of ACI Committee 335, Composite and Hybrid Structures, and a member of ACI Commit-tees 318, Structural Concrete Building Code; 544, Fiber-Reinforced Concrete; and Joint ACI-ASCE Committee 352, Joints and Connections in Monolithic Concrete Structures. His research interests include the seismic behavior and design of reinforced concrete, fiber-reinforced concrete, and hybrid steel-concrete structures.

Fig. 1—(a) to (c) High-friction; and (d) to (e) low-friction supports.

Table 1—Mixture for UHP-FRCs

TypeUHP-FRC

proportions by weight

Portland cement Type I 1

Silica fume 0.25

Silica powder 0.25

Water 0.22

High-range water reducer 0.0054*

Steel fibers 0.15†/0.25‡

Fine Sand 1§ 0.26

Fine Sand 2|| 1.04

28-day fc′ [prism], MPa (ksi) 200 to 207 (29 to 30)

Spread value, mm (in.) 835 to 870 (32.9 to 34.3)*Solid content. †1.5% by volume. ‡2.5% by volume. §Maximum grain size of 0.2 mm (1/125 in.). ||Maximum grain size of 0.8 mm (1/32 in.).

ACI Materials Journal/May-June 2012 381

workability of FRC, with an increase in these values leading to a decrease in workability. Thus, a fiber factor cf, defined as the product of the fiber-volume fraction Vf and fiber aspect ratio lf /df (Eq. (1)), can be used as a simple parameter to esti-mate, in relative terms, the workability of an FRC mixture.

/f f f fV dc = × l

(1)

In this study, cf ranged between 1.0 and 1.6 (Table 3). An upper limit for cf of approximately 2 has been suggested for UHP-FRC by Wille et al. (2011a,c) and Naaman and Wille (2010).

EXPERIMENTAL PROGRAMThe bending behavior of the four UHP-FRC mixtures

described previously was experimentally investigated considering the following parameters:

1. Specimen size—“Medium” (102 x 102 x 406 mm [4 x 4 x 16 in.] with a 305 mm [12 in.] span) and “large” (152 x 152 x 508 mm [6 x 6 x 20 in.] with a 457 mm [18 in.] span) beams in accordance with ASTM C1609/C1609M-06.

2. Test method—Unnotched four-point (ASTM C1609/C1609M-06; Fig. 5(a)) and notched three-point (RILEM TC 162-TDF; Fig. 5(b)) bending tests on “large” beams with the aforementioned geometry. The notch was 25 mm (2 in.) high and approximately 4 mm (0.16 in.) wide.

3. Casting method—Filling the specimen first in the middle (Fig. 6(a)) or in layers (Fig. 6(b)). For layer casting, the chute along the mold was moved at three different speeds (Fig. 6(b)).

4. Type of support—High-friction (Fig. 1(b)) and low-fric-tion supports (Fig. 1(d) and (e) for “large” and “medium” beams, respectively).

Specimen preparationSilica fume and sand were first mixed for

approximately 5 minutes. Cement and glass powder were then added and thoroughly mixed for another 5 minutes. After that, and within 1 minute, water and a high-range water reducer (HRWR) were added. The concrete developed its workable consistency approximately 5 minutes after the addition of water and the HRWR. Lastly, steel fibers were added to the matrix and mixed until homogenously distrib-uted. After mixing, the UHP-FRC was placed on a 1 m (40 in.)

Fig. 2—Reaction forces in: (a) to (c) high-friction supports; and (d) to (e) low-friction supports.

Fig. 3—Effect of velocity gradient on fiber orientation (Staehli et al. 2008).

Table 2—Types of fibers used in study

Notation FormNumber of twists df, mm (in.)

lf, mm (in.) lf/df

Specified tensile

strength, MPa (ksi)

S Straight 00.20

(0.008)13

(0.51)65 2600 (377)

H Hooked 00.38

(0.015)30

(1.18)80 2900 (420)

T Twisted 6 to 80.30*

(0.012)30

(1.18)100 3100 (449)

*Manufactured out of round wire with df = 0.30 mm (0.012 in.), shaped into a prism with side dimensions a/b = 0.24 mm/0.30 mm (0.009 in./0.012 in.).

Table 3—Different types of UHP-FRC investigated in this study

Notation

Steel fibers

Type/notationin Table 2

Fraction Vf,vol.-%

Fiber factor cf Geometry

UHP-FRC-H1.5 H 1.5 1.2 Hooked

UHP-FRC-T1.5 T 1.5 1.5 Twisted

UHP-FRC-S1.5 S 1.5 1.0 Straight

UHP-FRC-S2.5 S 2.5 1.6 Straight

Fig. 4—Steel fibers used in this research. (Note: 1 mm = 0.0394 in.)

382 ACI Materials Journal/May-June 2012

long chute with an inclination of approximately 30 degrees. This helped the concrete release part of the air entrapped during the mixing process; however, it also contributed to the alignment of fibers. After filling the beams to full capacity, the specimens were covered with plastic sheets and stored at room temperature. Twenty-four hours after casting, the spec-imens were taken out of their molds and stored in a water tank at approximately 20°C (68°F) for an additional 25 days. All specimens were tested at 28 days.

InstrumentationAn infrared-based tracking system, capable of continu-

ously measuring the position in space of selected points (markers) on the beam surface, was used in all test speci-mens for deflection/deformation monitoring. The marker layouts for the various beam types tested are shown in Fig. 5.

EXPERIMENTAL RESULTS AND DISCUSSIONThe behavior of the test specimens was evaluated based

on the relationship between the equivalent bending stress sfl and midspan deflection. The equivalent bending stress was calculated as follows

2

6fl

M MS b h

×s = =

× (2)

where M is the applied moment; and b and h are, respec-tively, the beam cross-sectional width and height, excluding the notch height, if applicable. The maximum value of sfl is referred to as the equivalent bending strength. It should be noted that the equivalent bending stresses are calculated assuming linear elastic behavior and, thus, the peak value cannot be taken as a measure of the tensile strength of the UHP-FRC materials tested. Three specimens were tested for each series and the equivalent bending stress-versus-deflec-tion responses were averaged for reporting purposes. It should be mentioned, however, that the response of each individual specimen in a series was within 10% of the mean response.

Thus, the use of three specimens per series was found to be adequate for the evaluation of bending performance.

Effect of specimen sizeThe results from six series of UHP-FRC unnotched

beams tested with “low-friction” supports and reinforced with a 1.5% volume fraction of either hooked fibers (UHP-FRC-H1.5), twisted fibers (UHP-FRC-T1.5), or straight fibers (UHP-FRC-S1.5) were analyzed to investigate the influence of specimen size on bending behavior (Table 4). The test setup is shown in Fig. 5(a) and (c) for “large” and “medium” beam specimens, respectively. In these series, the same casting method was used, which consisted of filling the mold by letting the concrete flow first in the middle of the beam (Fig. 6(a)).

The equivalent bending stress-versus-midspan deflection response for the six series of beams is shown in Fig. 7. It should be noted that midspan deflections were normalized by the span length, as specified in ASTM C1609/C1609M-06. As can be seen in Fig. 7, the behavior of medium and large beams was nearly identical for all three test series, the medium beams showing a slightly higher equivalent bending strength (+6%). It is possible that this slightly greater strength could have been caused by a higher fiber “wall effect” (and thus fiber alignment) in the smaller beams (Kameswara Rao 1979; Soroushian and Lee 1990; Kooiman 2000; AFGC-SETRA 2002; Dupont 2003; Grünewald 2004; Markovic 2006). It should be mentioned that the size-depen-dent correction for tensile strength in AFGC-SETRA (2002) results in a strength decrease of 9% as the specimen height is increased from h = 100 mm (4 in.) to h = 150 mm (6 in.) (that is, from “medium” to “large” beams).

Effect of test method (three-point notched beams versus four-point unnotched beams)

The results from the tests of six series of “large” beams, all supported with “low-friction” devices, were used to evaluate differences in flexural behavior between unnotched beams tested under four-point loading (ASTM C1609/C1609M-06)

Fig. 5—Setups used for testing of beams with low-friction supports.

Fig. 6—Middle and layer casting and corresponding flow direction.

ACI Materials Journal/May-June 2012 383

and notched beams tested under three-point loading (RILEM TC 162-TDF). In the unnotched beams under four-point loading, the critical crack develops at the weakest section within the middle third of the span. Cracking in notched beams under three-point loading, on the other hand, is forced to initiate at the notched section, where the reduction in the cross-sectional area (and not a weaker composite) makes this section substantially weaker than the adjacent sections. There-fore, the equivalent flexural strength of FRC evaluated through testing of notched beams should, in general, be greater than that obtained through testing of unnotched beams.

All beams, whether notched or unnotched, showed multiple cracking. However, only a single crack widened significantly, which controlled beam behavior at large deflec-tions (Fig. 8(a) to (f)). As shown in Fig. 8(g) to (i), notched beams exhibited higher flexural strengths than unnotched beams, as expected. The difference in peak flexural strength ranged between approximately 25 and 60%.

Effect of casting methodThe effect of casting method was evaluated by comparing

the results from the tests of nine series of “medium” unnotched beams supported by low-friction devices. Seven beam series were cast following a layer-casting procedure

(Fig. 6(b)), as specified in ASTM C1609/C1609M-06, whereas the UHP-FRC in the other two series was first cast in the middle of the beam (RILEM TC 162-TDF; Fig. 6(a)).

To evaluate the effect of casting speed when following a layer-casting method, three different chute speeds (Table 4 and Fig. 6(b)) were applied. The chute speed was defined as follows: “slow” speed (0.13 m/s [5 in./s]), which allowed the chute to travel along the beam length in approximately 3 seconds; and “medium” speed (0.25 m/s [10 in./s]) and “high” speed (0.5 m/s [20 in./s]), which corresponded to less than 2 and 1 seconds per beam length, respectively. The observed flowing behavior of layer-cast UHP-FRC is illustrated in Fig. 6(b). It should be noted that a slow movement of the chute caused a snake-like pattern, leading to areas where fibers tended to orient vertically. This snake-like pattern can be avoided by increasing the speed of the chute (shown as “fast” in Fig. 6(b)). Increased speeds led to a thin layer casting with a preferred fiber alignment along the beam axis. In this case, the chute speed should be limited such as to avoid a break in flow. It should be kept in mind that RILEM TC 162-TDF and ASTM C1609/C1609M-06 require beams to be rotated 90 degrees along their longitudinal axis prior to testing; thus, vertical faces during casting become horizontal faces during testing.

Fig. 7—Bending behavior of “medium” and “large” beams for three different UHP-FRCs.

Table 4—Average equivalent bending strengths, MPa (ksi)

Notation PreparationSupport(friction)

Large beam Medium beam Medium beam

Middle casting

Layer casting

Slow Medium Fast

UHP-FRC-H1.5Notched Low 20.1 (2.9) [3.5] — — — —

Unnotched Low 16.3 (2.4) [4.7] 17.4 (2.5) [2.3] — — —

UHP-FRC-T1.5Notched Low 26.2 (3.8) [3.2] — — — —

Unnotched Low 16.4 (2.4) [4.3] 17.3 (2.5) [3.3] — 25.0 (3.6) [0.8] 32.0 (4.6) [1.8]

UHP-FRC-S1.5

Notched Low 20.0 (2.9) [7.7] — — — —

Unnotched Low 14.8 (2.1) [3.8] 15.8 (2.3) [2.3] 10.0 (1.4) [6.5] 15.0 (2.2) [4.4] 21.8 (3.2) [4.7]

Unnotched High — — 15.8 (2.3) [4.8] 20.5 (3.0) [9.8] 29.0 (4.2) [2.9]

UHP-FRC-S2.5Unnotched Low — — — 22.1 (3.2) [3.9] 28.0 (4.1) [1.8]

Unnotched High — — — 34.0 (4.9) [2.1] 39.2 (5.7) [1.3]

Notes: “—” is no tests performed; values in brackets are maximum deviation, %, from the mean value.

384 ACI Materials Journal/May-June 2012

For the UHP-FRC specimens constructed following a middle casting procedure, the flow in the middle of the spec-imens followed a funnel-like shape during casting. The high workability of the UHP-FRC mixtures led fibers to align following the concrete flow (that is, fiber alignment along the funnel). The required 90-degree rotation of the beams along their longitudinal axis prior to testing, however, turned the funnel to the side.

The test results shown in Fig. 9 indicate that an increase in the moving speed of the chute along the beam axis led to an increase in flexural strength. An equivalent bending strength as high as approximately 30 MPa (4.4 ksi) was observed in

the beams with straight fibers (2.5% volume fraction) and twisted fibers (1.5% volume fraction) cast using a high chute moving speed. This strength was approximately 30% higher than that of beams cast using a medium chute moving speed. The reason for such a high bending strength was the strong fiber alignment resulting from the fast layer-casting opera-tion, which was not as pronounced for the case of a medium chute moving speed. The use of a low speed led to a nearly 50% lower strength compared to that in beams cast using a medium speed (Fig. 9(c)). In this case, a combination of a snake-like flow behavior (Fig. 6(b)) and the creation of small funnels (similar to that shown in Fig. 6(a)) seemed to cause

Fig. 8—Comparison of cracking pattern and bending behavior for “large” unnotched and notched UHP-FRC specimens cast following middle casting method.

ACI Materials Journal/May-June 2012 385

a tendency for the fibers to align perpendicularly to the beam longitudinal axis.

All beams cast following a middle casting procedure, whether medium or large, showed the same crack propa-gation and opening pattern. Instead of cracks propagating straight upward from the extreme tension side toward the compression zone, the critical cracks clearly bent and followed the perimeter of the funnel generated during the casting process (Fig. 8(a) to (c)). A visual investigation of the failed specimens confirmed a tendency for the fibers to align with the concrete flow, which in this case translated into fibers aligning toward a vertical plane.

In terms of bending response, the beams cast first in the middle exhibited a lower peak flexural strength compared to the beams cast in layers using a high chute speed. When compared to beams cast in layers using a medium chute speed, the peak flexural strength was comparable for the case of UHP-FRC-S1.5 but approximately 40% lower for UHP-FRC-T1.5. In both cases, however, the peak equivalent bending strength was approximately 15 MPa (2.2 ksi).

Effect of support typeTo investigate the effect of friction developed at supports

intended to work as rollers, five additional series of medium

beam specimens were tested (Table 4) using high-friction supports (Fig. 1(b) and 2(b)) and the results were compared to those shown in Fig. 9 using low-friction supports (Fig. 1(e) and 2(d)). For each support condition, beams were cast in layers following various chute moving speeds, as indicated in Table 4.

As expected, the use of high-friction supports led to a significantly higher bending strength compared to that of beams with low-friction supports. The increase in bending strength ranged between approximately 30 and 60%, leading to sfl = 28 MPa (4.1 ksi) and sfl = 39 MPa (5.7 ksi) for beams with a volume fraction of steel straight fibers of 1.5% and 2.5%, respectively (Fig. 10).

Figure 11(a) illustrates the external and internal actions in a beam subjected to four-point bending. Friction at the supports is considered by a horizontal reaction force FH, which depends on the friction coefficient m and the applied vertical load F. The support friction thus induces a compression force in the beam equal to FH. Because as beam deflections increase beyond flexural cracking, only a small compression zone is required to balance the resultant tension force due to fiber tension and the compression force due to friction at the support; therefore, it is reasonable to assume that the internal resultant compression force acts at a

Fig. 9—Effect of casting method on bending behavior of “medium” specimens.

Fig. 10—Influence of support friction on bending behavior for various layer casting speeds: lF is low-friction and hF is high friction.

386 ACI Materials Journal/May-June 2012

distance of 0.9h from the beam extreme tension fiber. Based on this, the increase in beam moment strength due to support friction can simply be calculated as

0.9 0.92HF HFM F h h= × = m × (3)

The equivalent bending strength under no axial restraint can be estimated by subtracting the additional moment MFH from the total applied moment M at the critical section, which, for beams subjected to three- and four-point bending, is equal to FL/4 and FL/6, respectively, where L is the beam span length. The equivalent bending strength is thus calcu-lated as follows

2

0.92

6

fl

FM h

bh

− m ×s = (4)

where h = b = L/3. Applying Eq. (4) with a friction coef-ficient m = 0.4 leads to a decrease in the equivalent bending strength of 36% and 24% for beams subjected to four-point and three-point bending, respectively, compared to the total applied moment.

To further evaluate the effect of support friction on bending behavior, a backward analysis (Fig. 12; Wille 2008) was performed. A finite element (FE) model of a 152 x 152 x 508 mm (6 x 6 x 20 in.) beam with a 457 mm (18 in.) span was constructed. The beam model contained a notch at midspan and was loaded under three-point loading in accordance with RILEM TC 162-TDF. Due to the pres-ence of the notch and the loading conditions, cracking was expected to develop at midspan, as was confirmed by experi-ments (Fig. 8(d) to (f)). Therefore, cracking at midspan was considered by 25 spring elements whose properties were determined, on a step-by-step basis, such as to match the response from the simulations with the experimentally obtained results. It should be mentioned that the concentra-tion of nonlinear material behavior in the spring elements did not allow the consideration of the spread of the fracture process zone. Ideal elastic behavior with a Poisson’s ratio of 0.2 and an elastic modulus of 60 GPa (8700 ksi) was assigned to the FEs used to simulate the half beam.

Figure 13(a) shows the experimentally obtained bending behavior of a layer-cast, notched, large beam (UHP-FRC-S1.5) on low frictional supports along with the backwardly calculated response assuming a friction coefficient m = 0. For comparison, the experimental response of an UHP-FRC-S1.5 beam tested on high friction supports is also shown in Fig. 13(a). As indicated by the label in the figure, the best-fit friction coefficient for this particular beam was 0.4. Because the properties of the spring elements were kept the same as those used for the beam with a friction coefficient m = 0, the predicted response for the beam with high-friction supports could be predicted by solely adjusting the friction coefficient.

The analytically obtained nonlinear tensile behavior of the spring elements and, thus, of the UHP-FRC material, is shown in Fig. 13(b). Neglecting the effect of support fric-tion in the backward analysis would have led to an approxi-mately 30% overestimation of tensile strength. Therefore, it is necessary to either measure the effect of support friction and take it into account when evaluating material behavior, or use a beam test setup with minimal support friction or axial restraint so that the measured bending behavior faith-fully reflects the material behavior and not structural effects.

Fig. 12—Determination of uniaxial tensile behavior of UHP-FRC based on bending test. (Note: 1 kN = 0.2248 kips; 1 mm = 0.0394 in.)

Fig. 11—Influence of friction coefficient m on internal forces in beam subjected to four-point loading.

ACI Materials Journal/May-June 2012 387

To minimize support friction, the authors recommend the use of roller supports that are able to roll on a plane surface, such as that shown in Fig. 2(d). If the test method requires a constant span throughout the test, the use of a bearing roller support (Fig. 2(e)), where the contact friction between the steel surfaces is minimized by the sliding of the inside bear-ings, is recommended.

Summary of effects on equivalent bending strengthA summary of the effect of the various parameters inves-

tigated on the equivalent bending strength is provided in Fig. 14. As can be seen in the figure, the effect of specimen size for the range investigated in this research had only a minor influence on the peak equivalent bending strength of UHP-FRC. Variations in casting method, presence of notch, and support type, however, significantly affected the flex-ural strength exhibited by UHP-FRC test beams, leading, in some cases, to strength variations of over 100% when a single parameter was varied. These variations should be considered when transitioning from material properties obtained through standard tests to those used in structural design based on the casting method used and tendency for fiber alignment in the structural element under consideration. Such differences between standard tests and the actual struc-tural element are currently considered through the K-factor in AFGC-SETRA (2002).

SUMMARY AND CONCLUSIONSA comprehensive experimental study was carried out to

investigate the effect of beam size, presence of notch, and

support restraint on the bending behavior of FRCs. Given the increasing interest of researchers and practicing engineers in applications of UHP-FRCs, which are characterized by very high compressive and tensile strengths and high ductility and durability, the experimental program focused on these materials rather than on regular FRCs. Furthermore, due to the high workability of UHP-FRCs and the associated tendency for fibers to align along the flow direction, different casting methods in accordance with either ASTM C1609/C1609M-06 or RILEM TC 162-TDF were followed to also evaluate the effect of the casting method on bending behavior.

By changing the specimen size, the casting method, and the support system to cover the cases typically considered by the research community in accordance with ASTM C1609/C1609M-06 and RILEM TC 162-TDF, differences in peak equivalent flexural strength as large as 200% were obtained. For example, equivalent bending strengths as low as 10 MPa (1.4 ksi) and as high as 29 MPa (4.2 ksi) were obtained using the same UHP-FRC mixture design with a 1.5% volume fraction of high-strength straight steel fibers.

The influence of support restraint or friction coefficient on bending behavior was analytically evaluated and compared with results from experiments. An increase in the friction coefficient m from 0.0 (considered adequate for the low-fric-tion supports used in this study) to 0.4 (representative of the friction coefficient in the high-friction supports used) was found to lead to an increase in bending strength of approxi-mately 30% for beams subjected to four-point loading. The backwardly calculated tensile material behavior would be overestimated by the same magnitude if the friction support

Fig. 13—Influence of support friction coefficient m on: (a) bending response; and (b) back-wardly calculated tensile behavior.

Fig. 14—Influence of test parameters on equivalent bending strength.

388 ACI Materials Journal/May-June 2012

component is not considered. Therefore, if an overestima-tion of material equivalent bending strength is to be avoided, the use of low-friction supports, such as those evaluated in this research, is essential to minimize beam axial restraint. The test results also indicate that a more specific recommen-dation on the casting method is needed when using highly workable or self-consolidating FRC, given the variability in results between beams constructed following a layer-casting method using various chute speeds, as well as between beams constructed following a layer cast versus a middle casting procedure.

ACKNOWLEDGMENTSThis work was supported by a fellowship within the Postdoc-Programme

of the German Academic Exchange Service (DAAD). The authors would also like to acknowledge the following companies for providing free material: Bekaert, Elkem Materials, Grace Construction Products, and Lehigh Cement Company. The opinions expressed in this paper are those of the authors and do not necessarily reflect the views of the sponsor.

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