Construction and Building Materials 24 (2010) 2285–2293

Contents lists available at ScienceDirect

Construction and Building Materials

journal homepage: www.elsevier .com/locate /conbui ldmat

Deflection behavior of concrete beams reinforced with PVA micro-fibers

Sameer Hamoush a, Taher Abu-Lebdeh a,*, Toney Cummins b

a Department of Civil, Architectural, and Environmental Engineering, North Carolina A&T State University, Greensboro, NC 27411, United Statesb Concrete and Materials Division, US Army Corps of Engineers, Vicksburg, MS, United States

a r t i c l e i n f o a b s t r a c t

Article history:Received 27 October 2009Received in revised form 6 March 2010Accepted 1 April 2010Available online 27 April 2010

Keywords:DeflectionMoment–curvatureStress–strainMicro-fibers reinforced concreteFlexural strengthStrain-softeningDuctilityToughness indexLoad–deflection curve

0950-0618/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.conbuildmat.2010.04.027

* Corresponding author. Tel.: +1 336 334 7737; faxE-mail address: taher@ncat.edu (T. Abu-Lebdeh).

This paper presents experimental and theoretical investigations on the stress–strain and load–deflectionbehavior of Poly Vinyl Alcohol (PVA) microfiber reinforced concrete composites. The actual stress–strainrelationships in both compression and tension were established by performing a series of compressionand tension tests on PVA micro-fibers reinforced concrete specimens. The proposed deflection modelwas developed by using the well known moment–curvature and conjugate beam methods. Comparisonswith the experimental data indicated that the model can be efficiently used to predict the load–deflectionbehavior of the microfiber reinforced concrete beams. Flexural results indicated that the addition of PVAmicro-fibers significantly increases toughness and ductility.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Concrete is a brittle material that has low tensile strength andlow strain capacity. In fact, many deterioration and failures inthe concrete structures are due to the brittle nature of this mate-rial. However, these disadvantages may be avoided by addingmicro-fibers to the plain concrete. Incorporating micro-fibers pro-vides a practical means of enhancing the ductility of concretematerials. The addition of fibers to a brittle concrete matrix sub-stantially improves its tensile strength and reduces the tendencyof cracking, which leads to enhanced ductility and toughness. Fur-ther, adding fibers to plain concrete greatly enhance its post-peaktension-softening behavior under tensile load. The fibers cross thepaths of potential cracks and transmit stress between the fibersand the matrix through the interfacial bond.

Significant research efforts have gone into attempts to improvethe ductility of concrete materials. Li and Zhang [1] conducted astudy on engineered cementitious composite (ECC), a special typeof high performance fiber reinforced concrete composites (HPFRCC)with extreme tensile ductility. The ultimate tensile strain capacityof the ECC material could reach 3–5% (which is several hundredtimes that of normal concrete). Li and Zhang [1] presented experi-mental and theoretical analyses on monotonic and fatigue perfor-

ll rights reserved.

: +1 336 334 7126.

mance of ECC in pavement overlay system. They observed thatboth the load carrying ability and deformability of ECC overlay weresignificantly higher than that of plain concrete overlaid systems.The fiber reinforced ECC significantly decreased the relative mi-cro-cracking failure in pavement overlay systems and increasedthe fatigue life of the pavement structure under traffic type loading.Yang and Li [2] examined the rate dependence in engineeredcementitious composites (ECC) and uncovered the source of therate dependence. Their results show strong rate dependence inPVA–ECC tensile properties, and indicated that both first crackingstrength and ultimate tensile strength increase with increasingstrain rate.

Plain concrete lacks the ability to carry load in the post-peak re-gime. Addition of microfiber to plain concrete increases ductilitywhich leads to a significant increase in the material’s toughnessor consuming energy. This is due to the fact that after the brittlecement matrix fractures, additional energy must be consumed topull the fibers out of the fractured paste for the crack to continueto open. This additional energy consumption enhances toughness.Kim et al. [3] investigated the post-peak behavior of reinforcedconcrete beams and concluded that concrete beams exhibit a soft-ening response that is gradually decreases with increasing dis-placements due to a strain softening. Read and Hegemier [4]examine the effects of strain-softening on the stress wave propaga-tion in softening material. They found that, for incrementally linearmodels, strain-softening occurs when the matrix of tangent

Table 1Properties of PVA structural micro-fibers.

Material Polyvinyl alcohol

Configuration Chopped fiber, resin-bundled chopped monofilamentfiber

Color White or yellowish whiteSpecific gravity 1.3Lengths 1=4 in. (6 mm), 1/3 in. (8 mm), ½ in. (12 mm), 3=4 in.

(18 mm)Tensile strengths 160,000 psi (1100 MPa) – 203,000 psi (1400 MPa)Chemical

stabilityNon-reactive

Absorption Minimal

2286 S. Hamoush et al. / Construction and Building Materials 24 (2010) 2285–2293

stiffness ceases to positive-definite. Yin and Zhai [5] concluded thatsoftening curves can be obtained from the entire load-deformationcurves in a tensile loading test, and a relation curve for the soften-ing can be formed in terms of the broadness of the crack and theapplied stress. Iyengar et al. [6] presented a method for computingthe ultimate moment of reinforced concrete beam sections withcircular spiral binder confinements in compression. Vebo and Ghali[7] used analytical methods to derive the moment–curvature rela-tionship for slab elements reinforced with top and bottom steelwith load ranges up to ultimate strength.

The present study performs an experimental program and the-oretical analysis on the behavior of concrete reinforced with PVAmicro-fibers. The purpose of the testing program is to establishstress–strain and moment–curvature behavior and to establish amethod to evaluate the deflection of concrete beams reinforcedwith micro-fibers. Twelve concrete cylinders and twelve concretediscs were tested in compression and tension, respectively. Eightmicrofiber reinforced concrete beams, two of which were rein-forced with steel rebars, were tested in four points bending. Anumerical code was also created to determine the inelastic mo-ment curvature. The established moment–curvature plots wereused to evaluate the deflection a long a beam using a new mathe-matical method. Properties of micro-fibers reinforced concreteelement such as compressive strength, flexural strength, load–deflection, first crack toughness, strain-softening behavior, andductility were determined.

2. Experimental investigation

2.1. Description of the experimental program

To provide a better understanding of the performance of con-crete reinforced with micro-fibers, this research performs anexperimental program with focus on the deflection and stress–strain behavior of the material. The specimens were mixed, cured,and tested in accordance with the American Society for Testing andMaterials (ASTM) standards. A total of twelve 150�300 mm (6 in. -12 in.) cylinders and twelve 38 � 150 mm (1.5 in. � 6 in.) discswere tested in compression and tension, respectively. Eight micro-fiber reinforced concrete beams were tested in four points bendingfor flexural and deflection. Six beams had a dimension of102 � 102 � 356 mm (4 in. � 4 in. � 14 in.) and reinforced withPVA micro-fibers only, and two beams 133 � 140 � 1830 mm(51=4 in. � 5½ in. � 72 in.) were reinforced with 2U12 and 2U16steel rebar in addition to micro-fibers. The same mix design wasused for all specimens (beams, compression and tension speci-mens). Specimens were tested in closed-loop controlled MTS test-ing machine, with a 245-kN (55-kip) load cell, and displacementrate of 0.033 mm/min (0.0013 in/min). The two larger beams(133 � 140 � 1830 mm) were tested on MTS testing machine, witha 110-kip (489-kN) load cell and a linear variable displacementtransducer (LVDT) monitored loading head. The loading systemand LVDT were connected in a closed-loop manner. Properties suchas compressive strength, static modulus, flexural strength, mo-ment–curvature, load–deflection behavior, first crack toughness,post-crack behavior, strain-softening behavior, and ductility weredetermined.

2.2. Materials

Specimens for compression, tension, and flexural tests weremade from concrete with micro-fibers, concrete–limestone aggre-gate, concrete–staylite aggregate and concrete–granite aggregatecombinations. For the specimens that were made from concretewith micro-fibers, 3% of type III cement was substituted for the

micro-fibers. The concrete mix design consists of w/c ratio = 0.45and cement-course aggregate-fine aggregate ratio of 1:2:3. Speci-mens were cured in a lime saturated water tank for 28 days atroom temperature (23 ± 2 �C) and relative humidity of 100%. PolyVinyl Alcohol micro-fibers (Table 1) were used in thisinvestigation.

2.3. Specimens

As mentioned above, displacement-controlled tests with a dis-placement rate of 0.033 mm/min (0.0013 in./min) were adminis-tered for all compression, tension and flexural tests. Two MTSstrain gauges with 102 mm (4 in.) gage length were attached toeach side of the concrete compression cylinders, and four straingages with 38 mm (1.5 in.) gage length were attached to the tensiondisc specimens (two on each side). For the flexural test specimens,two Linear Voltage Displacements Transducers (LVDT) were used inaddition to the strain gauges that were placed at the top-center (be-tween the load heads) and at the bottom-center of the beam asshown in Fig. 1a and b. High early strength adhesive (LOC-TITE)was applied to attach strain gauges to the concrete specimens.

3. Analytical investigation

In order to analyze a reinforced concrete beam up to the failureload, it is necessary to develop a realistic relationship between mo-ment and curvature. In the present study, a new model is intro-duced to develop the moment–curvature relationship and topredict the deflection at any point along a beam element. Thismodel is based on the stress–strain relationships generated forthe specimens prescribed earlier. It uses a theoretical stress–strainrelationship, as highlighted by Desayi and Krishman [8] and mod-ified by the authors to include the effect of PVA micro-fibers. Thetheoretical stress–strain equations were implemented based onthe testing results of this research.

Further, the moment–curvature relationship was used to char-acterize the non-linearity of the concrete material in the strain-softening region. Strain-softening is considered to occur just beforethe ultimate failure and here where the effect of adding micro-fi-bers becomes even more important. This is because micro-fibersinfluence the toughness of concrete in the post-peak region afterthe concrete has failed and the fibers are the only mechanism leftto consume additional energy. In the compression zone, the addi-tion of micro-fibers increases the ductility in the deformationphase after reaching the maximum stress, while in the tensile zone,the micro-fibers bridge opening cracks and thus influences thepost-crack behavior.

3.1. Mathematical model

The proposed Eqs. (1)–(5) which govern the stress–strainbehavior of micro-fibers reinforced concrete element are function

(a) Concrete beams reinforced with microfibers

(b) Concrete beams reinforced with microfibers plus steel rebars

Fig. 1. Flexural beam specimens. (a) Concrete beams reinforced with micro-fibers. (b) Concrete beams reinforced with micro-fibers plus steel rebars.

S. Hamoush et al. / Construction and Building Materials 24 (2010) 2285–2293 2287

of the concrete peak stress, strains at peak stress, and the ultimatestrain. The model was derived using a quadratic and linear regres-sion for the average stress–strain values for the specimens in com-pression and a linear regression relationship for all tensionspecimens.

In Tension,

r ¼ ftðec=e0Þ; for 0 < ec < e0 ð1Þ

r ¼ ft � 0:14f tec � e0

0:0096� e0

� �; for e0 < ec < 0:0096 ð2Þ

where ft ¼ peak tensile stress; e0 ¼ tensile strain at peak stress;and ec is the concrete strain at the point to be considered.

r ¼ 0:86f t � 0:68f tec � 0:0096etu � 0:0096

� �; for 0:0096 < ec < etu ð3Þ

where etu ¼ 0:0217 (maximum tensile strain)In Compression,

r ¼ 2f 0cec=eo

1þ ½ec=eo�2

" #; for 0 < ec < eo ð4Þ

r ¼ f 0c � 0:187f 0cec � eo

ecu � eo

� �; for eo < ec < ecu ð5Þ

where f 0c is the concrete compressive strength, eo ¼ strain atpeak stress, ecu is the maximum compressive strain, and ec is theconcrete strain at a given point.

Eqs. (1)–(5) were used to determine the concrete compressiveand tensile forces. The model enforced force and moment equilib-rium at each strain increment through an iterative approach. Theultimate strains of 0.00256 for concrete section reinforced withmicrofiber and 0.0041 for concrete reinforced with microfiber plussteel rebars were chosen. However, the model is capable of adopt-ing higher values for the ultimate strain if desired. A FORTRAN pro-gram was written to execute the procedures as shown below. Theprogram uses iterative approach and numerical integration.

1. Select concrete compressive strain in the extreme compressionfiber and assume neutral axis depth (see strain diagram inFig. 2).

2. The steel tensile strains (if any) are determined by similar trian-gles of the strain diagram (Fig. 2). Steel tensile stresses are thendetermined from the stress–strain relationships of the steelrebars.

3. The tensile forces in the steel rebars (if any) are determinedfrom the steel stress and the area of steel.

4. For the selected strain and neutral axis depth, determine con-crete extreme tensile strain from the strain diagram (Fig. 2).The concrete tensile stress is then found from Eqs. (1)–(3). Com-pressive stress is determined from Eqs. (4) and (5).

5. Concrete tensile force is determined by multiplying the tensionarea of the stress diagram (Fig. 2) by the width of the concrete’scross-section. The centroid of the tension area represents thelocation of the concrete’s tensile force. Both, the area and itscentroid were found using numerical integration.

6. The concrete compressive force is determined by multiplyingthe area of the compression part of the stress diagram (Fig. 2)by the width of the concrete’s cross-section. The centroid ofthe compression area represents the location of the concrete’scompressive force.

7. If the compressive and tensile forces are not equal, adjust theneutral axis depth and repeat steps 2–6. It should be noted thatthe calculations are lengthy and hence, the iterative approachmay be used.

8. After the neutral axis depth that satisfies force equilibrium isfound, the internal forces and neutral axis depth are then usedto determine the moment (M) and curvature (U) correspondingto the selected strain (step 1). The moment (M) is the sum of themoments of the compressive and tensile forces about the neu-tral axis, and the curvature is calculated by dividing the selectedstrain value by its corresponding neutral axis depth (x).

9. Repeat steps 1–8 for a range of concrete compressive strain, andplot the entire stress–strain and moment–curvature curves.

Iteration at Initial Strain Capacity of 0.0005

Iteration at Mid Strain Capacity of 0.001

Iteration at Ultimate Strain Capacity of 0.00256

Fig. 2. Iteration at 0.0005, 0.001, and ultimate strain capacity.

2288 S. Hamoush et al. / Construction and Building Materials 24 (2010) 2285–2293

For illustration purpose, the strain, stress, and force distributionsfor concrete strain of 0.0005, 0.001, and at ultimate are shown inFig. 2. The distributions were then used to develop a moment–curva-ture relationship for a typical concrete section reinforced bymicro-fibers and micro-fibers plus rebars. Figs. 3 and 4 show the mo-ment–curvature relationship for specimens reinforced with microfi-ber and specimens with micro-fibers plus steel rebars, respectively.

In order to derive a mathematical model to calculate the deflec-tion of the beam, a classical method, Conjugate Beam Method, was

adopted and shown in Fig. 5. Calculating the moment at a point onthe conjugate beam, the deflection (D) may be expressed as:

Di ¼ h2Xn

i¼1

ðiy00i Þ ð6Þ

where Di is the deflection at any section along the beam, h is thelength of each segment, i is the number of segments and y00i is thecurvature at each section.

Fig. 3. Proposed moment–curvature relationship for specimens. Reinforced withmicro-fibers.

Fig. 4. Proposed moment–curvature relationship for specimens. Reinforced withmicro-fibers plus steel rebars (2 # 4 � 2U12; 2 # 5 � 2U16).

Fig. 5. Conjugate beam method to calculate deflection.

Fig. 6. Average stress–strain of concrete under compression.

Fig. 7. Average stress–strain of concrete under tension.

S. Hamoush et al. / Construction and Building Materials 24 (2010) 2285–2293 2289

4. Experimental results and discussion

4.1. Stress–strain relationship

Compression and tension tests yielded results that were used toconstruct stress–strain curves for all four combinations of the con-crete specimens. For each combination, the average of three cylin-ders in compression and the average of three discs in tension weredetermined and plotted as shown in Figs. 6 and 7, respectively. Thestress–strain variation of plain concrete submitted to axial com-pression (Fig. 6) shows hardly any strain-softening response asthe descending branch after the peak stress is almost vertical. Sud-

den failure occurs when the peak stress is reached in plain concretedue to increase in the brittleness. Further, adding PVA micro-fibersto a plain concrete matrix has little effect on the pre-crackingbehavior; it substantially enhances the post-cracking response.From the compression stress–strain relationship in Fig. 6, it is evi-dent that specimens made from limestone as course aggregate andmicro-fibers as reinforcing component exhibited the ability to car-ry higher strain level, as well as strain-softening behavior beyondtheir peak stress level. Results of the peak stress (fc) and its corre-sponding strain (eo), ultimate strain (eu), and Young’s modulus (E)are listed in Table 2.

Fig. 7 shows the indirect tensile stress-average strain relation-ship. The average strain values were determined from the data col-lected from both sides of the tested discs. Three discs of eachcombination were tested and the resulted averages are plotted. Re-sults indicated that when concrete is in tension, the stress–strainrelationship is linear up to the tensile strength, then droppingabruptly to failure. This indicates that cracks begin to form andeven after cracking, the concrete can still resist tensile stresses inparts between adjacent cracks. On the hand, the measured tensilestress–strain relation of the microfiber reinforced concrete speci-mens show remarkable strain capacity (over 0.65%) and peakcrack-bridging stress of about 3.79 MPa (550 psi). Further, the testresults show that the microfiber reinforced concrete specimenswere able to accommodate the highest strain value among alltested specimens. The high strain capacity is attributed to multiplecracking, which is represented by fine cracks perpendicular to theloading axis. However, the distribution of the multiple crackingwas not great enough to cause larger strain-hardening. This is

Table 2Compression test results.

Specimen Peak stress(fc) MPa (psi) Strain at peak stress (eo) Ultimate strain (eu) Modulus of elasticity (E), GPa (psi)

Concrete + limestone 52.6 (7650) 0.0024 0.0035 31.6 (4.6 � 106)Concrete + granite 40 (5800) 0.002 0.002 31.6 (4.6 � 106)Concrete + staylite 33 (4800) 0.0015 0.003 24.8 (3.6 � 106)Concrete + limestone with micro-fibers 33 (4800) 0.0021 0.0075 59.9 (8.7 � 106)

(a) Plain Concrete @ 2500 Res. (b) PVA Microfiber Concrete @ 3500 Res.

Fig. 8. Microscope photograph of concrete fracture surface. (a) Plain concrete @ 2500 Res. (b) PVA Microfiber concrete @ 3500 Res.

2290 S. Hamoush et al. / Construction and Building Materials 24 (2010) 2285–2293

due to the fact that strong bond of the PVA microfiber with the ce-ment paste causes the fiber to rupture instead of being pulled out.It is desirable to have concrete that exhibits strain-hardeningbehavior achieved through multiple cracking of the reinforced ma-trix. However, the strong bond of PVA fibers to the cement pastematrix tends to limit the multiple cracking effects and hence leadsto lower strain-hardening behavior. To achieve larger strain-hard-ening, coated PVA fiber is needed. Such fiber should have the bal-ance between energy dissipation potential (i.e. enough fiberbonding so that pullout energy is not trivial) and fiber rupture pro-tection (i.e. individual fiber load is never greater than the nominalfiber strength). This can be controlled through the amount fibercoating applied to the surface.

Fig. 9. Failure of microfiber concrete specimens. Under compression.

4.2. Modes of failure

All specimens that were not reinforced with micro-fibers exhib-ited brittle failure. These failures started with microcracks in thecement-aggregate interface that then propagated as the load in-creased. The microfiber reinforced specimens, however, exhibitedductile failure. The initial cracks started in the cement matrix,but they did not propagate as fast as in the case of plain concretespecimens. This is due to the reinforcing microfiber’s ability to lim-it cracking from its unique high strength bond with the cementi-tious materials. Microscopic analysis of concrete fracture surface(Fig. 8a) shows that microcracks exist at the aggregate-matrixinterface of the plain concrete specimen even before any load hasbeen applied to the concrete. The formation of such cracks is dueprimarily to the strain and stress concentrations resulting fromthe incompatibility of the elastic moduli of the aggregate and pastecomponents. On the other hand, the strong bond between thebonded fibers and cement paste in the micro-fibers reinforced con-crete specimen reduces such cracks (Fig. 8b). Fig. 9 shows the duc-tile failure of the specimens tested in compression and consistingof limestone aggregate and 3% micro-fibers. The failure of concretespecimens tested in indirect tension is shown in Fig. 10. It was no-ticed that the failure in the plain concrete discs was very brittleand the failure plane was clearly visible to the naked eye(Fig. 10a). On the other hand, ductile failure was observed on the

microfiber reinforce concrete specimens (Fig. 10b). This ductilebehavior and hence, the measured high strain capacity is due tothe fact that micro-fibers stretch more than concrete under load-ing. The composite system of concrete reinforced with microfiberis assumed to work as if it were un-reinforced until it reaches its‘‘first crack strength.” It is from this point that the reinforcing fiberstake over and hold the concrete together. Further, the uniform dis-tribution of the micro-fibers can increase the ductility of the com-posite. This is because, if enough micro-fibers can be distributedinto the cement paste to cross any growing microcrack, the addi-tional energy must be consumed in breaking or pulling the fibers,hence, leads to higher failure load and add toughness to thematerial.

4.3. Flexural behavior of micro-fibers reinforced concrete beams

The flexural tests yielded results that were used to produceload–deflection curves of the concrete beams reinforced with mi-cro-fibers and concrete beams reinforced with micro-fibers plussteel rebars. The load–deflection curves were plotted as shown inFigs. 11–13. The test results show a noticeable increase in thepost-crack energy absorption capacity or toughness (Table 3) due

(a) Plain Concrete Specimen (b) Microfiber Concrete Specimen

Fig. 10. Failure of concrete specimens under tension. (a) Plain concrete specimen. (b) Microfiber concrete specimen.

Fig. 11. Load–deflection relationship for beam specimens reinforced with micro-fibers.

Fig. 12. Proposed load–deflection curve for concrete beams reinforced with micro-fibers.

Fig. 13. Proposed vs. experimental load–deflection curves.

S. Hamoush et al. / Construction and Building Materials 24 (2010) 2285–2293 2291

to the addition of PVA micro-fibers. The contribution of the micro-fibers is mostly apparent in the post-cracking response, repre-sented by an increase in post-cracking ductility, due to the workassociated with pullout of fiber bridging a failure crack. The brittlefailure of the plain concrete beams started with small cracks thatpropagated as the load increased to the maximum load. The mi-cro-fibers reinforced specimens, however, exhibited ductile behav-ior. After reaching the peak load, these specimens did not shear

apart; however, they continued to carry load to complete failure.Tension cracks initially formed on the underside of the beam inthe center portion of the span. As load increases, the cracks prop-agate upward through the cross section, but not as fast as in theplain concrete specimens. As expected, the micro-fibers reinforcedbeams had larger deflections than would be anticipated in plainconcrete beams. Mid span deflections were approximately threetimes larger than that of plain concrete beams. Further, the flexural

Table 3Performance parameters of the microfiber, steel reinforcement concrete beams.

Parameter Beam 1 (2U16rebars)

Beam 2 (2U12rebars)

First cracking strength, MPa(psi)

19.65 (2850) 15.58 (2260)

Flexural strength (MOR), MPa(psi)

31.0 (4500) 22.51 (3265)

Deflection at peak stress, mm(in)

18.5 (0.73) 6.4 (0.25)

Deflection at failure, mm (in) 27.2 (1.07) 10.7 (0.42)Toughness index 6.27 5.42

2292 S. Hamoush et al. / Construction and Building Materials 24 (2010) 2285–2293

test results show that improvements in other properties such asfirst cracking strength and peak load are insignificant.

The effect of micro-fibers combined with steel reinforcement onthe flexural behavior of concrete beams was investigated by testingtwo 133 mm � 140 mm � 1830 mm (51=4 in. � 5½ in. � 72 in.)beams. The two Microfiber concrete beams were reinforced with2U16 and 2U12 (2 # 5 and 2 # 4) rebar and were employed withthird-point loading, displacement-controlled test. Tow Linear Volt-age Displacements Transducers (LVDTs) mounted on both sides ofthe center of the beam were used to measure deflection. The flex-ural behavior of the reinforced concrete beams are shown inFig. 13a and b in terms of load–midpoint deflection curves. Examin-ing the curves, significant ductility can be noted. The ultimate loadsreached were 44 kN (9900 Ib) and 32 kN (7200 Ib), respectively. It isclear that the response is linear until the first crack has formed atapproximately 28 kN (6300 Ib) for beam 1, and 22.3 kN (5000 Ib)for beam 2. Classical reinforced concrete theory predicted tensilereinforcement yielding to commence at approximately 34.7 kN(7800 Ib) and 26.3 kN (5900 Ib) respectively, which is consistentwith the change in slope of the load–deflection response. The corre-sponding flexural strength is 31.0 Mpa (4500 psi) and 22.51 Mpa(3265 psi) respectively. The first cracking strength, flexuralstrength (MOR), deflection at peak stress, ultimate deflection at fail-ure, and toughness index are listed in Table 3. The toughness indexis evaluated by dividing the area under the load–deflection curvefrom first cracking to a deflection equal to twice the first crackingdeflection by the area up to first matrix cracking.

4.4. Limitations of this study

Almost all research methods have limitations and this study isno exception. Although the above flexural experiments provideddescriptions of deflection and pre- and post-crack response ofmicrofiber reinforced concrete beams, the data were limited to amacroscopic behavior (response of the structural specimens, ormacroscale level). Interaction between the fiber and cementitiousmatrix (mesoscale level) are not considered in this study. However,the mesoscale descriptions of the fiber/matrix interaction areneeded to better understand the fiber failure modes and the result-ing impact on macroscopic ductility. In the literature, numerousworks [9–15] have been published which study the fiber–matrixinterfacial behavior and provide linkage of the microstructure tocomposite to structural performance level. It is generally agreedthat the pull-out work of fibers bridging one or several cracks pro-vides the main source of toughness or energy absorption capacityof fiber reinforced concrete composites, which translates into asoftening load–displacement curve after reaching maximum load.Therefore, this study accepts the correlation between the energyabsorption during fibers’ pullout and toughness of the microfiberreinforced concrete beams. In fact, Kim et al. [15] showed that astrong correlation exists between slip hardening behavior in singlefiber pullout and strain-hardening behavior in tension.

5. Comparison of analytical and experimental results

5.1. Validation of the proposed deflection model

To validate the proposed model, the material properties of theconcrete beam were entered into the FORTRAN code (as describedin Section 3.1) to produce the theoretical moment–curvature rela-tionship. After the moment–curvature was plotted, the momentdiagram was drawn for each load increments of 2.23 kN(500 lbs). The beam was then divided into segments to calculatethe deflection at the middle of the beam. The process was repeateduntil the peak load is reached. The load–deflection relationship wasfound and compared with the experimental results for the aver-ages of all three microfiber specimens and all three concrete withlimestone specimens as shown in Fig. 12. Also, Fig. 13 shows thecomparison between the proposed and experimental load–deflec-tion relationship for the concrete beams reinforced with micro-fi-bers plus rebars. Considering the load–deflection curves; concreteat 30–60% of the peak load contains microcracks that are initiatedat isolated points where the tensile strain concentrations are thehighest. At this load stage, localized cracks are initiated, but theydo not propagate. In the upper half of the pre-peak portion of theload–deflection curve, the crack system multiplies and propagates.In this stage, and near the peak load, the progressive failure of con-crete is primarily caused by cracks through the mortar, thesecracks join bond cracks at the surface of nearby aggregate and formcrack zones of internal damage. It is in this upper region where it isbelieved that micro-fibers can contribute to the increase in thestrength of the concrete. If enough micro-fibers can be distributedinto the cement paste to cross any growing microcrack, then addi-tional energy must be consumed in pulling the fibers. This energycauses higher failure load and add toughness to the material.

6. Summary and conclusions

Microfiber reinforced concrete is a composite material in whichmicro-fibers are incorporated to prevent or control the tensilecracking, increase ductility, and enhance toughness in the strain-softening region. To realize the potential of microfiber blends ina concrete matrix, a concrete containing polyvinyl alcohol (PVA)micro-fibers was designed and the mechanical performance wereevaluated. The micro-fibers delayed the development of micro-cracks and so the composite demonstrated greater strength andcrack resistance than a similar matrix of plain concrete. This is ex-plained by differences in the failure mechanism of the specimens.Further, the stress–strain variation of plain concrete submitted toaxial compression shows hardly any strain-softening response asthe descending branch after peak stress is almost vertical. Addingmicro-fibers to a plain concrete matrix has little effect on its pre-cracking behavior but does substantially enhance its post-crackingresponse, which leads to a greatly improved ductility and tough-ness. In the present study an attempt has been made to predictthe load–deflection characteristics of concrete beams reinforcedwith micro-fibers utilizing the strain softening effects in thestress–strain behavior. The developed model consists of two steps.The first step is to establish a moment curvatures code for any con-crete section using the actual compressive and tensile stress strainrelationships. The second step is to use the moment curvature codein a mathematical model that predicts the deflection at any sectionalong the beam. The actual stress–strains relationships in bothcompression and tension were established by performing a seriesof compression and tension tests prescribed previously.

To validate the proposed model, concrete beams reinforcedwith micro-fibers only, and two concrete beams reinforced withmicro-fibers plus steel rebars were tested in flexure. The mid span

S. Hamoush et al. / Construction and Building Materials 24 (2010) 2285–2293 2293

deflection, the top compression stains and the bottom tensilestains were measured. The results from the numerical model werecompared with the test results show good agreement.

Based on the testing program and the work performed in this pa-per, it appears that the addition of micro-fibers to concrete enhancesthe ductile property of the materials and prevents the sudden brittlefailure of the material. This suggests the need to update the equa-tions that the designers are using for calculation in their structuralnotes. Moreover, the following conclusions may be drawn:

1. Although, the addition of micro-fibers does not influence thecompressive strength of concrete, it enhances the ductile prop-erty of the materials, increases toughness, and prevents thesudden brittle failure of the material.

2. The deflection of microfiber reinforced concrete beams has duc-tile behavior and also has a post-peak failure point.

3. Polyvinyl alcohol (PVA) fiber is very suitable fiber to be used asreinforcement of the concrete materials, though the very strongfiber–matrix bond resulting from high chemical bonding causedthe micro-fibers to rupture instead of being pulled out. Largerductility may be achieved by fiber pullout rather than rupture.It is therefore, recommended to conduct experimental programusing coated PVA microfiber with less interface bond. It is also,necessary to develop fiber coating technology to control thefiber–matrix interfacial bonding and produce fiber pullout char-acteristics which are designed to increase energy dissipationwithout causing fiber rupture.

Acknowledgment

The authors would like to thank the US Army Corps of Engineers(ERDC) for funding of this research.

References

[1] Li VC, Zhang J. Monotonic and fatigue performance in bending of fiber-reinforced engineered cementitious composite in overlay system. Cem ConcrRes 2002;32:415–23.

[2] Yang E, Li VC. Rate dependence in engineered cementitious composites. In:Proceedings of international RILEM workshop on HPFRCC in structuralapplications. RILEM; 2006. p. 83–92.

[3] Kim Jin Keun, Lee Tae Gyu. Nonlinear analysis of reinforced concrete beamswith softening. J Comput Struct 1992;44:567–73.

[4] Read HE, Hegemier GA. Strain softening of rock, soil and concrete – a reviewarticle. Mech Mater 1984;3:271–94.

[5] Yin SZ, Zhai Q. An approach to determine concrete-failure softening curves.Eng Fract Mech 1990;35(4/5):719–29.

[6] Iyengar KT Sundra Raja, Desayi Prakash, Reddy K Nagi. Flexure of reinforcedconcrete beams with confined compression zones. Am Concr Inst J1971;68:719–25.

[7] Vebo A, Gali A. Moment–curvature relation of reinforced slabs. ASCE, J StructDiv 1977;103(March):515–30.

[8] Desayi P, Krishman S. Equation for the stress–strain curve of concrete. AmConcr Inst J Struct Eng 1964;61(March):345–50.

[9] Wang Y, Backer S, Li VC. A statistical tensile model of fibre reinforcedcementitious composites. Composites 1989;20(3):265–74.

[10] Li VC, Wang Y, Backer S. A micromechanical model of tension-softening andbridging toughening of short random fiber reinforced brittle matrixcomposites. J Mech Phys Solids 1991;39(5):607–25.

[11] Li VC. Postcrack scaling relations for fiber reinforced concrete cementitiouscomposites. J Mater Civil Eng 1992;4(1):41–57.

[12] Li VC, Stang H, Krenchel H. Micromechanics of crack bridging in fibre-reinforced concrete. Mater Struct 1993;26:486–94.

[13] Stang H, Li VC, Krenchel H. Design and structural application of stress-crackwidth relation in fibre reinforced concrete. Mater Struct 1995;28:210–9.

[14] Maalej M, Li VC, Hashida P. Effect of fiber rupture on tensile properties of shortfiber composites. J Eng Mech 1995;121(8):903–13.

[15] Kim D, El-Tawil S, Naaman AE. Correlation between single fiber pulloutbehavior and tensile response of FRC composites with high strength steel fiber.In: HPFRCC5, Mainz, Germany, 2007. p. 67–76.