ACI statistical UPV Martí Ros

ACI Structural Journal/July-August 2011 461

ACI Structural Journal, V. 108, No. 4, July-August 2011.MS No. S-2010-065.R1 received June 11, 2010, and reviewed under Institute

publication policies. Copyright © 2011, 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 May-June2012 ACI Structural Journal if the discussion is received by January 1, 2012.

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

The positive effect of fibers on the bond of reinforcing bars inconcrete is widely recognized. Different authors, however, come todifferent conclusions regarding particular points.

This research analyzes the results of a series of pullout tests toobtain statistically supported conclusions regarding the bondperformance of normal-strength steel fiber-reinforced concrete(SFRC). To do so, the experimental program was conceived byobserving statistical criteria (design of experiments [DOE]technique), and the results were studied using the analysis ofvariance (ANOVA).

It has been shown that the role fibers play in the bond ofreinforcing bars in concrete is of the same importance as that ofconcrete cover or reinforcing bar diameter. It is especiallyremarkable that the mere fact of adding fibers—regardless of theamount—considerably increases the ductility of the bond failure,thus underlining the role of fibers in bond performance aspassive confinement.

Keywords: bond; pullout test; statistical approach; steel fiber-reinforced concrete.

INTRODUCTIONThe fact that fibers have a positive effect on the bond of

steel reinforcing bars in concrete is widely recognized andsupported by the literature. Such a positive effect is observedeven with low fiber contents1 and is being gradually assumedby codes. The new Spanish code for structural concrete,EHE-08,2 recognizes that fibers improve bond conditions andstates that this may be taken into account when determiningdevelopment lengths (or “anchorage lengths” following theterminology of Eurocode 23). A very similar statement isfound in ACI 408R-034 with respect to the expressionsprovided by ACI 318-085 for determining development lengths.

Fibers improve concrete bond capacity by confining thebars—their role being similar to that of stirrups—and bywidening the range of crack widths within which thisconfinement remains active.1 Improvement in terms of bondcapacity can be regarded as a result of the improvement ofmatrix properties due to the fibers.6

There are relatively few studies available that deal with thebond of reinforcing bars in steel fiber-reinforced concrete(SFRC). Several authors1,6,7 agree that fibers improve bondcapacity mainly in terms of ductility, whereas their influenceon bond strength (peak bond stress) is of little importancewhen compared to that.

Different authors, however, come to different conclusionsregarding particular points. First, whereas some investigationsconclude that the effect of fibers on bond strength is notsignificant,8 others state that this is true only when the modeof failure is due to pullout but not when there is splitting. Asa matter of fact, when there is splitting, the effect of fibers isimportant.9,10 In addition, some authors state that addingfibers does not significantly affect the bond strength innormal-strength concretes6,11 (compressive strength values

of up to 40 to 50 MPa [5801 to 7252 psi]). Also, when itcomes to compressive strength values of 90 to 100 MPa(13,053 to 14,504 psi), some authors relativize the effect offibers and conclude that they do increase bond strength butby no more than 15%.6 This raises the question of whether itwould really be useful to take the effect of fibers on bondinto account when determining development lengths or lapsplice lengths.

Several studies on the bond of reinforcing bars in SFRCconsider no more than two factors among the following:fiber content, compressive strength, concrete cover, andreinforcing bar diameter. It is quite rare to find allcombinations of the different values of these factors tested,and conclusions are usually obtained by comparing bondstrength values or bond stress-slip curves in a one-to-onemanner. Therefore, any disagreement between the conclusionsof different studies may be considered, taking into accountthe difficulty of these being generalized.

As a result, the aim of this research was to comprehensivelystudy the effect of four different factors on SFRC bondcapacity and ductility. Keeping this purpose in mind, theexperimental program was conceived to obtain reliable andstatistically supported conclusions while minimizing theamount of laboratory work.

RESEARCH SIGNIFICANCEThe significance of this research concerns the bond

performance of reinforcement in SFRC and the ductility ofbond failure by means of a statistically reliable approach.

This research comprises a series of pullout tests carried outon SFRC prismatic specimens and comprehensively studiesthe effect of several factors (fiber type and content, concretecover, and reinforcing bar diameter) on bond capacity. Theconclusions drawn from this study are statistically reliable,which is not typical in studies that deal with the bond ofreinforcement in concrete.

EXPERIMENTAL INVESTIGATIONMixture design

One composition of the concrete matrix was consideredthroughout all the research; the required average compressivestrength was 30 MPa (4350 psi). This centered the researchon a normal-strength concrete that can be regarded as typicalin most applications.

Title no. 108-S44

Statistical Approach to Effect of Factors Involved in Bond Performance of Steel Fiber-Reinforced Concreteby Emilio García-Taengua, José R. Martí-Vargas, and Pedro Serna-Ros

ACI Structural Journal/July-August 2011462

The concrete composition was the same for all specimensproduced and tested in this study—only the fiber contentvaried. Accordingly, the high-range water-reducing admixturecontent was adjusted in each case, depending on the fibertype and content, to keep the slump values in the range of 10 to15 cm (4 to 6 in.). The contents of all other components werekept constant.

Table 1 summarizes the composition of the concrete matrix.Both the cement type and the water-cement ratio (w/c) can beconsidered as usual in regular construction. The coarseaggregate-sand ratio is nearly 1 to have good levels ofcohesion to work with different levels of admixture and notrisk segregation. This was necessary because different fiber

contents would require variations in the admixture content, asworkability was required to always be the same.

Factors and levels consideredTable 2 shows the situations or parameters considered by

three different codes (EHE-08,2 Eurocode 2,3 and ACI 318-085)in the expressions for determining the development length ofthe reinforcing bars. These were taken into account whendeciding the factors to be considered in this research.

As mentioned previously, the compressive strength wasfixed to a required average value of 30 MPa (4350 psi). It hasnot been considered as a factor because its effect on bond isvery well known and quantified.4

The nominal yield strength of reinforcement was not afactor either because steel reinforcing bars with a yieldstrength of 500 MPa (72,500 psi) were used in all cases; thisis the most common currently used steel type.

Lightweight concretes, epoxy-coated bars, and the applicationof transverse pressure were not included in this research,according to its objectives. Consequently, no factors wereconsidered regarding these.

The parameters considered (factors) in this study alongwith their different values (levels) are summarized in Table 3.

Two types of cold drawn hooked-end steel fibers thatdiffer in slenderness and length were used. In relation tofiber contents, three different values were considered witha maximum value of 70 kg/m3 (4.37 lb/ft3) (0.89% involume); this maximum content was chosen bearing inmind that fiber contents in typical applications are rarelygreater than 1% in volume.

Three different nominal reinforcing bar diameters wereused—all of these are typical in normal buildings in theprecast concrete industry.

Concrete cover C in the pullout specimens was defined asshown in Fig. 1; the unsymmetrical concrete cover reflectsthe most common situation of reinforcing bars in realconcrete elements. The distance between the bar and theopposite surface was not less than 125 mm (4.94 in.) in anycase, which corresponds to good confinement for a 25 mm(0.99 in.) reinforcing bar according to Model Code MC-90.13

This choice allows for the possibility of extending theresearch to 25 mm (0.99 in.) reinforcing bars in the future.

Three different values were considered for the concrete cover:• C1 = 30 mm (1.2 in.), which is the minimum value

required by EHE-082 for reinforcing bars in a precastelement with a compressive strength of 30 MPa(4350 psi);

• C2 is the average of C1 and C3; and• C3 is five times the nominal diameter of the reinforcing

bar, which corresponds to a good confinement accordingto Model Code MC-90.13

Design of specimensPrismatic pullout specimens were produced and tested in

this study; their cross sections are shown in Fig. 1. Theirdimensions vary and depend on the reinforcing bar diameterand the concrete cover value. The cross-section dimensionsof all specimens are summarized in Table 4.

The longitudinal dimensions, total length, and embedded lengthwere defined according to the RILEM recommendations14,15

for the pullout test. According to these recommendations:• The total length of the specimen should be 10 times the

nominal diameter of the reinforcing bar but never lessthan 200 mm (7.9 in.). As the largest diameter considered

Emilio García-Taengua is a Civil Engineer and PhD Candidate at the UniversitatPolitècnica de València, Valencia, Spain, where he received his degree in civilengineering. His research interests include self-consolidating concrete properties androbustness, bond properties of steel fiber-reinforced concrete, and statistics applied toconcrete technology.

José R. Martí-Vargas is an Associate Professor of civil engineering at the UniversitatPolitècnica de València, where he received his degree in civil engineering and PhD.His research interests include the bond behavior of reinforced and prestressedconcrete structural elements, fiber-reinforced concrete, durability of concrete structures,and strut-and-tie models.

Pedro Serna-Ros is a Professor of civil engineering at the Universitat Politècnica deValència, where he received his degree in civil engineering; he received his PhD fromthe École Nationale des Ponts et Chaussées, Paris, France. His research interestsinclude self-consolidating concrete, fiber-reinforced concrete, and the bond behaviorof reinforced and prestressed concrete.

Table 1—Composition of concrete matrix

Cement type CEM II/B-M 42.5 R*

w/c 0.60

Cement content 325 kg/m3 (20.29 lb/ft3)

Coarse aggregate-sand ratio 0.90

Sand type River limestone (0/4)

Coarse aggregate type Crushed limestone (7/12 and 12/20)*Cement type designation according to EN 197-1:2000.12

Table 2—Parameters influencing development length in selected building codes

ACI 318-085 Eurocode 23

EHE (Spain)2

Compressive strength of concrete X X X

Nominal diameter of bar X X X

Yield strength of reinforcement X X X

Position of the reinforcement X X X

Lightweight/normal concrete X X X

Epoxy-coated/non-epoxy-coated bars X — —

Concrete cover X X —

Confinement by transverse reinforcement X X —

Confinement by transverse pressure — X —

Table 3—Parameters considered (factors) and their values (levels)

Type of fibersType A (slenderness/length = 65/60)Type B (slenderness/length = 80/50)

Fiber content 0, 40, and 70 kg/m3 (0, 2.50, and 4.37 lb/ft3)

Nominal diameter of bar 8, 16, and 20 mm (0.31, 0.63, and 0.79 in.)

Concrete cover C1 = 30 mm (1.18 in); C2 is average; and C3 = 5 × diameter


was 20 mm (0.79 in.), all specimens had a length of200 mm (7.9 in.); and

• The embedded length should be five times the nominaldiameter of the reinforcing bar.

Table 5 and Fig. 2 show the longitudinal dimensions of thepullout specimens for the three different reinforcing bardiameters considered, where the reinforcing bar positionvaries as a result of factoring in the concrete cover.

Design of experiment: statistical approachStudies that aim to analyze how different factors affect

bond capacity usually proceed by varying only one factor ata time and comparing results. This approach is not the best,however, because it does not take into account that the effectof a factor on bond capacity can vary depending on thevalues of other factors.16,17 The technique globally known asdesign of experiments (DOE)17-19 allows the amount oflabor to be optimized and the conclusions to be reliable on astatistical basis. Therefore, DOE-based experiments make itpossible to study the effect of several factors on one (ormore) parameters on the basis of the analysis of variance(ANOVA).18,19 Taking these factors into consideration, thisexperiment was planned by applying DOE techniques andstatistical considerations.

If all possible combinations of the different factors andlevels considered (refer to Table 3) had to be analyzed, itwould have required 54 different specimens to be producedand tested. By using orthogonal arrays and derived factorialplans,17-19 the number of specimens to be tested would beaffordable, and the statistical inference in relation to theeffect of the factors considered on the response variableswould be completely reliable. As a result, this researchcomprised nine different combinations, which are summarizedin Table 6.

To obtain more experimental results and, as a result, to makeconclusions more reliable, each test was not carried out only once:three specimens of each combination were produced and tested.

In addition, four cube specimens with sides measuring100 mm (3.94 in.) and four prismatic notched specimens (inagreement with EN 1465120) were produced in each case tocontrol both the compressive and residual flexural strengths.

Therefore, 27 pullout specimens, 36 cube specimens, and36 prismatic notched specimens were produced and tested.

Mixing and specimen production and testingThe mixing, producing, and testing of the specimens were

carried out in all cases by following exactly the samesequence and by controlling the time for all operations.Components were added to the mixture following thissequence: aggregates, cement, water, fibers, and high-rangewater-reducing admixture. The moisture in the aggregateswas also strictly controlled to pour the exact amount of totalwater required. This procedure was performed to avoid anypossible uncontrolled interference that might affect the results.

Immediately after mixing, workability was monitored andcontrolled by means of the slump test following EN 12350-2.21

Specific molds for the pullout specimens were designedand purposely produced because both the position of the barand the dimensions of the specimen were different in each

Fig. 1—Definition of concrete cover.

Fig. 2—Longitudinal section of generic pullout specimen.

Table 4—Dimensions of specimens’ cross section for different reinforcing bar diametersDiameter D,

mm (in.) Factor levelCover C,mm (in.)

D + C + 125,mm (in.)

Side S,mm (in.)

8 (0.31)

C1 30 (1.18) 163 (6.42)

180 (7.09)C2 35 (1.38) 168 (6.61)

C3 40 (1.57) 173 (6.81)

16 (0.63)

C1 30 (1.18) 171 (6.73)

230 (9.06)C2 55 (2.17) 196 (7.72)

C3 80 (3.15) 221 (8.70)

20 (0.79)

C1 30 (1.18) 175 (6.89)

250 (9.84)C2 65 (2.56) 210 (8.27)

C3 100 (3.94) 245 (9.64)

Table 5—Longitudinal dimensions

Reinforcing bar nominal diameter, mm (in.)

Total length LT,mm (in.)

Embedded length LE,mm (in.)

8 (0.31) 200 (7.87) 40 (1.57)

16 (0.63) 200 (7.87) 80 (3.15)

20 (0.79) 200 (7.87) 100 (3.94)

Table 6—Pullout specimens produced and tested

IDFiber type

Fiber content,kg/m3 (lb/ft3)

Reinforcing bar diameter, mm (in.)

Concrete cover

L1 65/60 40 (2.50) 16 (0.63) C1

L2 — 0 (0) 8 (0.31) C2

L3 65/60 70 (4.37) 20 (0.79) C3

L4 65/60 40 (2.50) 8 (0.31) C3

L5 — 0 (0) 20 (0.79) C1

L6 65/60 70 (4.37) 16 (0.63) C2

L7 80/50 40 (2.50) 20 (0.79) C2

L8 — 0 (0) 16 (0.63) C3

L9 80/50 70 (4.37) 8 (0.31) C1

464 ACI Structural Journal/July-August 2011

case. Sleeves were used to control the embedded length, asshown in Fig. 3.

Concrete was placed into the mold in two stages. First,concrete was placed until it filled half the mold; then it wasvibrated for no more than 4 to 5 seconds using an internalvibrator. After that, the mold was filled and the vibration wasrepeated. To minimize the possibility of fiber orientation, thevibrator was immersed in concrete far enough from the

reinforcing bar. The specimens were demolded and stored ina moist room 24 hours after casting.

Both the pullout specimens and the control specimenswere tested 28 days after casting. During the pullout tests(Fig. 4), relative displacements (slip values) were measuredat the unloaded end by means of a linear variable differentialtransformer (LVDT). Every test was carried out by keepingthe load/time ratio between 2 to 4 kN/min (450 to 900 lbf/min)before the peak load was reached and by keeping the slip/time ratio between 0.4 to 0.6 mm/min (0.016 to 0.024 in./min)after the peak load in all cases. The test was finished whenthe slip reached values of 14 to 15 mm (0.5 to 0.6 in.).

Response variables: parameters measuredand analyzed

Response variables are the results related to bond capacityand ductility determined from the bond stress-slip curves, asshown in Fig. 5. They are the following:• τmax: bond strength or peak bond stress in MPa (psi);• τav: average bond stress in MPa (psi), as defined for the

beam test by EN 1008022—that is, the average of the valuesof the bond stress that corresponds to the slip values of0.01, 0.1, and 1 mm (0.0004, 0.004, and 0.04 in.);

• smax: slip that corresponds to the peak bond stress inmm (in.);

• A80: area under the curve in mm/MPa (in./psi) measuredup to the slip value (in the postpeak region) that correspondsto 80% of the peak bond stress; and

• A50: area under the curve in mm/MPa (in./psi) measuredup to the slip value (in the postpeak region) that correspondsto 50% of the peak bond stress.

Bond stress values (either τmax or τav) are defined based onthe assumption of a uniform stress distribution and aredetermined as follows

(1)

where P is the load (either peak or average), D is the nominalreinforcing bar diameter, and L is the embedded length.

The aforementioned parameters, particularly areas A80 andA50, were first defined for bond stress-slip curves thatcorrespond to pullout failures. When specimens experiencedsplitting, the bond stress values after failure were taken as zero.

CONTROL TEST RESULTSThe average compressive strength determined from the

cubes was 33 MPa (4785 psi), which is in agreement with therequired average compressive strength.

Table 7 shows the average values of all the bending testresults (each value is the average of four individual values),determined according to EN 1465120:• The variable fct,L is the limit of proportionality.

τP

πDL-----------=

Fig. 3—Detail of wooden mold for pullout specimen.

Fig. 4—Pullout test.

Fig. 5—Definition of parameters for ductility A80 and A50.

Table 7—Results of four-point bending tests, MPa (psi)

Concrete fct,L fR1 fR2 fR3 fR4 fRmax

No fibers 4.13 (598.85) — — — — —

Type 65/60, 40 kg/m3 3.51 (508.95) 2.95 (427.75) 3.78 (548.1) 4.01 (581.45) 4.00 (580) 4.14 (600.3)

Type 65/60, 70 kg/m3 3.72 (539.40) 4.68 (678.60) 5.76 (835.20) 6.03 (874.35) 5.93 (859.85) 6.22 (901.90)

Type 80/50, 40 kg/m3 3.47 (503.15) 3.62 (524.90) 5.15 (746.75) 4.70 (681.50) 4.73 (685.85) 5.33 (772.85)

Type 80/50, 70 kg/m3 3.52 (510.40) 6.17 (894.65) 6.44 (933.80) 6.03 (874.35) 5.61 (813.45) 6.55 (949.75)

Note: 1 kg/m3 = 0.06243 lb/ft3.


• The variables fR1, fR2, fR3, and fR4 are the residual flexuraltensile strengths corresponding to the crack mouthopening displacement (CMOD) values of 0.5, 1.5, 2.5,and 3.5 mm (0.02, 0.06, 0.10, and 0.14 in.), respectively.

• The variable fRmax is the maximum residual flexuraltensile strength in the postcrack region.

These results were taken as informative. The more fibersthat are added to concrete, the greater the residual flexuralstrength values are. It should be noted that in concretes with40 kg/m3 (2.50 lb/ft3) of fibers, residual flexural strengthvalues are significantly improved when 80/50 fibers are usedinstead of 65/60 fibers. These results detect differences in theproperties of the matrix and, consequently, fiber type isexpected to influence bond capacity.

PULLOUT TEST RESULTS AND DISCUSSIONFigure 6 shows a typical bond stress-slip curve, as obtained

from one of the L3 specimens. Table 8 shows the averagevalues of all the pullout test results (each one is the average ofthree values corresponding to three different specimens).

All results were analyzed using ANOVA, which detectsfactors that have a statistically significant influence on theresponse variables of the experiment.

Table 9 summarizes the effects of the factors consideredon all response variables of the pullout tests. The followingcriteria were followed:• Effects corresponding to confidence levels of 95% (p-values

up to 0.05) were considered “very significant” andmarked with XX; and

• Effects corresponding to confidence levels of 90% (p-valuesbetween 0.05 and 0.10) were considered “significant”and marked with X.

As Table 9 shows, all the factors considered significantlyinfluence bond capacity one way or another. Although theinfluence that concrete cover and bar diameter have on bondis well known, these parameters were considered to give theresearch a more comprehensive approach and to better showthe fibers’ contribution. Bearing that in mind, these resultsshow that the role that fibers play in bond is not less importantthan that of concrete cover or bar diameter.

The results of the ANOVA carried out for each one of theresponse variables are reliable because of the following17-19:• Orthogonal arrays were used to design the experiment

so there was no interference between different effects;• The total number of results (3 x 9) minus the total number

of levels considered is a large enough value (greaterthan 4) to consider the ANOVA robust; and

• All circumstances not considered as factors were controlledand kept constant: if any of them had been influential, it

would have equally affected all the results and, as aconsequence, not the results of the ANOVA.

The results obtained from these analyses are valid for theconcrete, factors, and levels considered in this research.These results would have to complement those of otherexperiments, however, to be completely valid in general(different mixture designs or different levels of variation).

The ANOVA is just a first step. After that, graphicalanalysis by means of the calculation and interpretation of theleast significant difference (LSD) intervals makes it possibleto detect general tendencies in the effect of the factorsconsidered on the response variables of the experiment.18,19

Furthermore, to quantify the effect of fibers on thedifferent parameters of the pullout test, regression analysesin multi-factor scenarios have been carried out based on theexperimental data obtained and summarized in Table 8,which has led to correlation expressions whose R2 values arebetween 55 and 75%. They have been used to determine theeffect that the addition of fibers has on bond parameterswhen concrete cover is 2.5 times the reinforcing bar diameter.This information is summarized in Table 10, where eachpercentage is the expected average increase of a bondparameter (τmax, smax, τav, A80, and A50) under different

Fig. 6—Bond stress-slip curve corresponding to one L3specimen.

Table 8—Results of pullout tests: average values

ID τmax, MPa (psi) smax, mm (in.) τav, MPa (psi) A80, MPa × mm (in psi) A50, MPa × mm (in psi)

L1 6.24 (904.8) 1.34 (0.05) 3.46 (501.7) 13.24 (75.6) 25.37 (144.8)

L2 8.36 (1212.2) 1.01 (0.04) 4.78 (693.1) 20.27 (115.7) 39.77 (227.0)

L3 18.44 (2673.8) 1.67 (0.07) 8.99 (1303.5) 86.93 (496.3) 159.00 (907.7)

L4 7.78 (1128.1) 1.64 (0.06) 3.59 (520.6) 20.27 (115.7) 35.30 (201.5)

L5* 10.17 (1474.6) 0.26 (0.01) 3.54 (513.3) 2.08 (11.9) 2.08 (11.9)

L6 6.83 (990.4) 1.92 (0.08) 4.10 (594.5) 24.50 (139.9) 34.40 (196.4)

L7 11.79 (1709.6) 2.60 (0.10) 4.03 (584.4) 52.00 (296.9) 95.27 (543.9)

L8 5.76 (835.2) 1.71 (0.07) 2.48 (359.6) 16.27 (92.9) 25.32 (144.5)

L9 5.62 (814.9) 2.30 (0.09) 1.76 (255.2) 24.20 (138.2) 35.38 (202.0)*Mode of failure is pullout in all cases except L5 (splitting).

Table 9—Analysis of variance: summary of resultsConcrete cover Bar diameter Fiber type Fiber content

τmax XX XX XX X

smax XX — XX XX

τav XX XX XX X

A80 XX XX — XX

A50 XX XX — XX

Notes: X is significant effects (p-values between 0.05 and 0.10); and XX is very significant effects (p-values up to 0.05).


circumstances (fiber content, fiber type, and reinforcingbar diameter).

The following sections show and discuss the LSD intervalplots for the factors considered in this research and theinformation summarized in Table 10. LSD intervals for theaverage bond stress are not shown because they follow thesame tendency as the peak bond stress.

Effect of concrete coverAs shown in Table 9, the effect of concrete cover on bond

is very strong and affects all response variables. Figure 7shows the LSD interval plots related to the values of concretecover. The tendency with respect to concrete cover valuesincreases and is practically linear for all response variables:the more concrete cover, the more bond capacity and ductility.

Effect of reinforcing bar diameterThe reinforcing bar diameter affects all response variables,

except the slip that corresponds to the peak bond stress (refer

to Table 9). Figure 8 shows the LSD interval plots related tothe values of reinforcing bar diameter. Although this factorhas a strong influence on bond capacity and ductility, thedifference with respect to the effect of concrete cover is thatthe tendencies are no longer linear. It seems that the differencebetween small and medium diameters is not important. It isimportant, however, between medium and large diameters.

Effect of fiber typeThe fiber type affects bond capacity (bond peak stress, the

slip that corresponds to the peak stress, and average bond stress)but not at all ductility parameters (areas) (refer to Table 9).

Figure 9 shows the LSD interval plots related to the fibertypes. By using 65/60 fibers, the bond strength achieved isgreater than by using 80/50 fibers; in particular, a greaterpeak bond stress (and also average bond stress values) wereobserved at smaller slip values. In relation to the fact that theimprovement of ductility when fibers are added is notsensitive to the fiber type, Table 10 gives an interesting

Table 10—Quantification of effect of fibers on bond parametersFiber type: 65/60 Fiber type: 80/50

Reinforcing bar diameter, mm (in.)

0→40 kg/m3 (0→2.50 lb/ft3), %

40→70 kg/m3 (2.50→4.37 lb/ft3), %

0→40 kg/m3 (0→2.50 lb/ft3), %

40→70 kg/m3 (2.50→4.37 lb/ft3), %

τmax

8 (0.31) 47.8 13.6 5.7 18.9

16 (0.63) 27.7 9.1 3.3 11.2

20 (0.79) 21.0 7.3 2.5 8.6

smax

8 (0.31) 9.4 30.1 78.6 18.5

16 (0.63) 10.0 31.9 83.7 19.1

20 (0.79) 10.3 32.9 86.5 19.5

τav

8 (0.31) 84.1 14.6 69.1 30.6

16 (0.63) 52.8 11.0 32.2 18.3

20 (0.79) 94.1 9.8 25.4 15.2

A80

8 (0.31) — 82.5 — 70.1

16 (0.63) — 47.3 — 42.9

20 (0.79) — 32.3 — 30.2

A50

8 (0.31) — 83.9 — 76.5

16 (0.63) — 45.0 — 42.8

20 (0.79) — 29.9 — 28.9

Fig. 7—LSD interval plots related to concrete cover.


explanation if the percentages that compare the concretewith 40 kg/m3 (2.50 lb/ft3) of fibers to its unreinforcedcounterpart are observed. When 65/60 fibers are used, thepeak stress is increased between 21.0 and 47.8%, but smax isincreased by no more than 10.3%. When 80/50 fibers areused, the opposite occurs: the peak stress is increased by nomore than 5.7%, but smax is increased between 78.6 and86.5%. Therefore, 65/60 fibers mainly affect the peak stress,whereas 80/50 fibers affect its position, but both parametersare balanced in approximately the same way. This explainswhy the areas are not differently affected when differentfibers are used. As a matter of fact, this confirms theimportance of previous testing when choosing which fibersare more adequate.

Effect of fiber contentAs shown in Table 9, the effect of fiber content on bond

is strong and affects all response variables. Figure 10shows the LSD interval plots related to the fiber contentsconsidered.

The LSD intervals for the peak bond stress reveal atendency that is noticeably similar to that observed in theplots related to concrete cover values. It seems that ratherlarge fiber contents (nearly 1% in volume), however, arerequired to strongly affect these parameters.

The effect of fibers on the slip value that corresponds tothe peak bond stress is definitely important. The mere fact ofadding fibers—regardless of the amount—increases this

value; that is, adding the fibers displaces the position of thepeak bond stress. Table 10 shows that most of the effect offibers on smax is achieved when 40 kg/m3 (2.50 lb/ft3) offibers are added; the difference between 40 and 70 kg/m3

(2.50 and 4.37 lb/ft3) is of relatively little importance, especiallywith 65/60 fibers. This might be interesting when trying toreduce development lengths by taking the fiber contributioninto account.

Fiber content has a strong effect on areas as well. Bearingin mind that areas somewhat quantify the energy associatedto the material’s fracture, these areas increasing linearly withrespect to fiber content is a consequence of the positiveeffect that fiber content has on both peak bond stress and itsposition. The tendency observed in areas related to the fibercontent is very similar to that of areas related to concretecover. This underlines the role of fibers as passive confinement—similar to concrete cover or stirrups—and foreshadows thepossibility of reducing the development length for reinforcingbars when normal-strength SFRC is used.

CONCLUSIONSThe following conclusions can be drawn based on the

results of this research:1. The effect of fiber type and content, concrete cover, and

reinforcing bar diameter on the bond of reinforcing bars inSFRC has been comprehensively analyzed by applying thestatistical procedures and criteria globally known as DOE.

Fig. 8—LSD interval plots related to reinforcing bar diameter.

Fig. 9—LSD interval plots related to fiber type.


2. The effect of concrete cover on both bond capacity andductility is very strong; it has an increasing and practicallylinear tendency in all bond parameters with respect toconcrete cover.

3. The effect of reinforcing bar diameter on bond performanceis also very important but is not linear at all. The differencesbetween medium and large diameters are very important,whereas there is practically no difference between small andmedium diameters.

4. Although fiber type has been shown not to affect theductility of the failure, it indeed affects bond capacity and theslip corresponding to the peak bond stress. The 65/60 fibersmainly affect the peak and average bond stress, whereas80/50 fibers mainly affect mainly the position of the peak.This confirms the importance of previous testing whenchoosing which fibers are more adequate.

5. The effect of fiber content on bond is very important.Although it seems that rather large fiber contents (nearly 1%in volume) are required to strongly affect peak and averagebond stresses, the mere presence of fibers increases theductility of the failure; the tendency is linear. This underlinesthe role of fibers in bond performance as passive confinement.

6. Considering that fibers improve the bond performanceof normal-strength concrete, further research is needed tosurvey the possibility of modifying the expressions fordetermining the development lengths in SFRC.

REFERENCES1. Cairns, J., and Plizzari, G. A., “Bond Behaviour of Conventional

Reinforcement in Fibre Reinforced Concrete,” Proceedings of the SixthRILEM Symposium on Fibre-Reinforced Concretes (BEFIB 2004),Varenna, Italy, 2004, pp. 321-330.

2. EHE-08, “Instrucción Española de Hormigón Estructural,” Ministeriode Fomento (Spanish Government), Madrid, Spain, 2008, 702 pp. (in Spanish)

3. BS EN 1992-1-1:2004, “Eurocode 2: Design of Concrete Structures—Part 1-1: General Rules and Rules for Buildings,” British Standards Institution,London, UK, 2004, 230 pp.

4. Joint ACI-ASCE Committee 408, “Bond and Development of StraightReinforcing Bars in Tension (ACI 408R-03),” American Concrete Institute,Farmington Hills, MI, 2003, 49 pp.

5. ACI Committee 318, “Building Code Requirements for StructuralConcrete and Commentary (ACI 318-08),” American Concrete Institute,Farmington Hills, MI, 2008, 473 pp.

6. Holschemacher, K., and Weiβe, D., “Bond of Reinforcement in FibreReinforced Concrete,” Proceedings of the Sixth RILEM Symposium onFibre-Reinforced Concretes (BEFIB 2004), Varenna, Italy, 2004, pp. 349-358.

7. Harajli, M. H., “Numerical Bond Analysis Using ExperimentallyDerived Local Bond Laws: A Powerful Method for Evaluating the BondStrength of Steel Bars,” Journal of Structural Engineering, ASCE, V. 133,No. 5, May 2007, pp. 695-705.

8. Dupont, D., and Vandewalle, L., “Influence of Steel Fibres on LocalBond Behaviour,” Proceedings of the Bond in Concrete—From Research toStandards Symposium, Budapest, Hungary, 2002, pp. 783-790.

9. Harajli, M. H.; Hout, M.; and Jalkh, W., “Local Bond Stress-SlipBehavior of Reinforcing Bars Embedded in Plain and Fiber Concrete,” ACIMaterials Journal, V. 92, No. 4, July-Aug. 1995, pp. 343-353.

10. Harajli, M. H., and Mabsout, M. E., “Evaluation of Bond Strength ofSteel Reinforcing Bars in Plain and Fiber-Reinforced Concrete,” ACIStructural Journal, V. 99, No. 4, July-Aug. 2002, pp. 509-517.

11. Ezeldin, A. S., and Balaguru, P. N., “Bond Behavior of Normal andHigh-Strength Fiber Reinforced Concrete,” ACI Structural Journal, V. 86,No. 5, Sept.-Oct. 1989, pp. 515-524.

12. BS EN 197-1:2000, “Cement—Part 1: Composition, Specificationsand Conformity Criteria for Common Cements,” British Standards Institution,London, UK, 2004, 52 pp.

13. CEB-FIP MC-90, “Model Code 1990 (Design Code),” ThomasTelford Ltd., London, UK, 1993, 437 pp.

14. RILEM RC 6, “Bond Test for Reinforcement Steel: 2—Pull-OutTest, 1983,” Recommendations for the Testing and Use of ConstructionMaterials, Reunion Internationale des Laboratoires et Experts des Materiaux(RILEM), 1994, pp. 218-220.

15. RILEM-CEB-FIP, “Bond Test for Reinforcing Steel: 2—Pull-OutTest,” Materials and Structures, V. 3, No. 3, May 1970, pp. 175-178.

16. Khayat, K. H.; Ghezal, A.; and Hadriche, M. S., “Utility of StatisticalModels in Proportioning Self-Consolidating Concrete,” Materials andStructures, V. 33, No. 5, June 2000, pp. 338-344.

17. Plackett, R. L., and Burman, J. P., “The Design of Optimum MultifactorialExperiments,” Biometrika, V. 33, No. 4, June 1946, pp. 305-325.

18. Montgomery, D., Design & Analysis of Experiments, sixth edition,John Wiley & Sons, Inc., New York, 2005, 643 pp.

19. Box, G. E. P.; Hunter, W. G.; and Hunter, J. S., Statistics forExperimenters: Design, Innovation, and Discovery, second edition, JohnWiley & Sons, Inc., New York, 2005, 664 pp.

20. BS EN 14651:2005, “Test Method for Metallic Fibered Concrete—Measuring the Flexural Tensile Strength (Limit of Proportionality [LOP],Residual),” British Standards Institution, London, UK, 2005, 12 pp.

21. BS EN 12350-2:2000, “Testing Fresh Concrete—Slump Test,”British Standards Institution, London, UK, 2000, 8 pp.

22. BS EN 10080:2005, “Steel for the Reinforcement of Concrete—Weldable Reinforcing Steel: General,” British Standards Institution,London, UK, 2005, 74 pp.

Fig. 10—LSD interval plots related to fiber content.

Documents

ACI statistical UPV Martí Ros