Retrofitting of Reinforced Concrete Beams with CARDIFRC Research PhD/2003 Retrofitting of... · Retrofitting of Reinforced Concrete Beams with CARDIFRC Farshid Jandaghi Alaee1 and

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Retrofitting of Reinforced Concrete Beams with CARDIFRCFarshid Jandaghi Alaee1 and Bhushan Lal Karihaloo, F.ASCE2

Abstract: A new retrofitting technique based on a material compatible with concrete is currently under development at Cardiffsity. It overcomes some of the problems associated with the current techniques based on externally bonded steel plates~fiber-reinforced polymer! laminates which are due to the mismatch of their tensile strength and stiffness with that of the concrete sbeing retrofitted. This paper will describe briefly the technology necessary for preparing high-performance fiber-reinforced concre~HPFRCC!, designated CARDIFRC. They are characterized by high tensile/flexural strength and high energy-absorption capa~i.e.,ductility!. The special characteristics of CARDIFRC make them particularly suitable for repair, remedial, and upgrading activiti~i.e.,retrofitting! of existing concrete structures. The promising results of several studies using CARDIFRC for retrofitting damaged cflexural members will be presented. It will be shown that damaged reinforced concrete beams can be successfully strengthrehabilitated in a variety of different retrofit configurations using precast CARDIFRC strips adhesively bonded to the prepared suthe damaged beams. To predict the moment resistance and load-deflection response of the beams retrofitted in this manner amodel will be introduced, and the results of the computations will be compared with the test results to evaluate the accuracy of th

DOI: 10.1061/~ASCE!1090-0268~2003!7:3~174!

CE Database subject headings: Retrofitting; Beams; Steel fibers; Bonding; Composite materials.

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Introduction

Existing concrete structures may, for a variety of reasonsfound to perform unsatisfactorily. This could manifest itselfpoor performance under service loading, in the form of excesdeflections and cracking, or there could be inadequate ultimstrength. Additionally, revisions in structural design and loadcodes may render many structures previously thought to be sfactory, noncompliant with current provisions. In the present enomic climate, rehabilitation of damaged concrete structuremeet the more stringent limits on serviceability and ultimstrength of the current codes, and strengthening of existingcrete structures to carry higher permissible loads, seem tomore attractive alternative to demolishing and rebuilding.

The performance of current techniques of rehabilitationstrengthening~the collective term retrofit, which implies the adition of structural components after initial construction, captuboth rehabilitation and strengthening! using externally bondesteel plates and fiber-reinforced plastic~FRP! laminates has beeextensively investigated~Ahmed and Gemert 1999; El-Refaet al. 1999; Fanning and Kelly 1999; Yagi et al. 1999!. The tech-nique of retrofitting using externally bonded steel platesgained widespread popularity, being quick, causing minimaldisruption, and producing only minimal change in section sHowever, several problems have been encountered with this

1PhD Candidate, School of Engineering, Cardiff Univ., QueeBuildings, P.O. Box 925, Cardiff CF24 0YF, Wales, UK.

2Professor, School of Engineering, Cardiff Univ., Queen’s BuildinP.O. Box 925, Cardiff CF24 0YF, Wales, UK~corresponding author!.E-mail: [email protected]

Note. Discussion open until January 1, 2004. Separate discusmust be submitted for individual papers. To extend the closing datone month, a written request must be filed with the ASCE ManagEditor. The manuscript for this paper was submitted for review andsible publication on November 27, 2001; approved on July 2, 2002.paper is part of theJournal of Composites for Construction, Vol. 7, No.3, August 1, 2003. ©ASCE, ISSN 1090-0268/2003/3-174–186/$18.

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nique, including the occurrence of undesirable shear failures,ficulty in handling heavy steel plates, corrosion of the steel, athe need for butt joint systems as a result of limited workablengths~Jones et al. 1988; Ziraba et al. 1994; Hussain et al. 199!~Fig. 1!.

FRP materials as thin laminates or fabrics would appearoffer an ideal alternative to steel plates. They generally have hstrength to weight and stiffness to weight ratios and are checally quite inert, offering significant potential for lightweight, coseffective and durable retrofit~Nanni 1995; Bu¨yukozturk andHearing 1998!. Retrofitting using FRP is also vulnerable to undesirable brittle failures due to a large mismatch in the tensstrength and stiffness with that of concrete~Fig. 2!.

The key advantage of CARDIFRC mixes for retrofitting is thaunlike steel and FRP, their tensile strength, stiffness, and coecient of linear thermal expansion are comparable to that ofmaterial of the parent member.

Several studies have previously been undertaken at Carinto the feasibility of using CARDIFRC for the rehabilitation anstrengthening of damaged RC flexural members~Karihaloo et al.2000, 2002; Alaee et al. 2001a,b!. This paper, without repeatingthe results reported in those papers, expands on those stuapplying this technique on different types of beam~with and with-out shear reinforcement! and introducing an analytical modelFirst, the material selection resulting from a rheological studconducted recently at Cardiff, is outlined, and the applicationthese materials for retrofitting of beams is then discussed. Folloing that, to predict the behavior of the beams retrofitted with thtechnique, an analytical model is introduced. Finally, the resuof the computations are compared with the test results, andaccuracy of the model is evaluated.

CARDIFRC

A rheological study was recently carried out in Cardiff to optmize high-performance fiber-reinforced concrete mixes. The a

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Fig. 1. Failure of beams retrofitted with steel plates:~a! by platedebonding and~b! by ripping off of the concrete cover~after Zirabaet al. 1994!

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Table 1. Mix Proportions for Optimized CARDIFRC Mix I andMix II ~per m3!

Constituents~kg! Mix I Mix II

Cement 855.00 744.00Microsilica 214.00 178.00Quartz sand

9–300mm 470.00 166.00250–600mm 470.00 —212–1,000mm — 335.001–2 mm — 672.00

Water 188.00 149.00Superplasticizer 28.00 55.00Fibers

26 mm 390.00 351.00213 mm 78.00 117.00

Water/cement 0.22 0.20Water/binder 0.18 0.16

Table 2. Typical Material Properties of CARDIFRC Mix I andMix II

Material properties Mix I Mix II

Indirect tensile strength~MPa! 24 25Fracture energy~J/m2! 12,210 12,380Compressive strength~MPa! 207 185

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was to achieve good workable mixes with a very low wabinder ratio and a high volume fraction of steel fiber, in order tthe resulting material, in its hardened state, will be very ducwith a relatively high tensile strength. As a result of many tmixes and testing, the mixes shown in Table 1 are the optimones. Two different mixes~designated CARDIFRC, Mix I andMix II ! of high-performance fiber reinforced concrete differimainly by the maximum size of quartz sand used in the mix hbeen developed using novel mixing and fiber dispersion prdures. These procedures are described in the patent applicGB 0109686.6.

Brass-coated steel fibers diameter 0.16, 6, or 13 mm longused to prevent corrosion. The optimized grading of quartz sleads to a considerable reduction in the water demand witloss in workability. All materials used in Table 1 are availacommercially.

A volume fraction of 6% short and long fibers is used, coprising 5% short fibers and 1% long fibers for Mix I, and 4.5short fibers and 1.5% long fibers for Mix II. The specimens whot-cured at 90°C for seven days. The strengths attainedbeen found to be the equivalent of standard 28-day water cu

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at 20°C. Table 2 shows the material properties of the optimizmixes. The Young modulus of CARDIFRC is around 50 GPa.

Test Beams

Two types of beams differing only by the reinforcement weused for Stages I and II of the experimental program. The beain Stage I were reinforced in flexure only with a single 12 mrebar, whereas in the beams tested in Stage II, stirrupconsisting of 6 mm deformed steel bars placed at 65 mspacing—were also provided in the shear spans of the beams~Fig.3!. As no shear reinforcement was provided in the beams testeStage I, both modes of failure, i.e., shear and flexural werepected. However, the beams tested in Stage II were designesuch a manner to fail in flexure. All the beams were made fromstandard concrete mix and were 1,200 mm long, 100 mm wand 150 mm deep. The beams were removed from their moafter one day and water cured at ambient temperature~20°C! fora minimum of 28 days. The mechanical properties of concretesteel can be found in Table 3.

Fig. 3. Internal reinforcement and load configuration in Stage I

Fig. 2. Failure modes in FRP retrofitted concrete beams:~a! steelyield and FRP rupture;~b! concrete compression failure;~c! shearfailure; ~d! debond of layer along rebar;~e! delamination of FRPplate; and~f! peeling due to shear crack~after Buyukozturk andHearing 1998!

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Table 3. Parameters Assumed for Modeling the Behavior of Concrete and Steel

Stage

Concrete

SteelIn compression In tension

f cm ~MPa! Ec ~GPa! Ec1 ~GPa! «c1 ~—! «cu ~—! f ctm ~MPa! GF ~N/mm! W1 ~mm! Wc ~mm! f y ~MPa! Es ~GPa!

I 45 35.6 20.7 0.0022 0.00315 4.0 0.0725 0.017 0.128 544 20II 47 36.1 21.4 0.0022 0.00330 3.5 0.0675 0.015 0.128 500 20

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Stage I

Of the 32 beams used in Stage I, four were tested to failurcontrol beams to compare with the performance of those retrted with CARDIFRC strips. They were loaded in three-pobending over a span of 1,100 mm. Ten transducers~five on eachside! were used to record the deflection of the beams at varpoints along its span. The transducers were SOLATRON tACR-25 and DCR-15 LVDTs. An aluminum frame~yoke! wasdesigned with two bars and a total of ten slots, to accommothe transducers. One bar was placed on each side of the bemidheight, as shown in Fig. 4. As expected, two control beafailed in shear, one in flexure and the fourth in a combinationshear and flexure modes. The average failure load was 29.48

The remaining 28 beams were preloaded to approxima75% of the above failure load to induce flexural cracking.addition to parameters such as the material~Mix I or II ! andthickness of retrofit strips~16 or 20 mm!, four different configu-rations of retrofitting were investigated. Retrofitting with:• One strip bonded on the tension face@Fig. 5~a!#,• Three strips~one bonded on the tension face and the others

the vertical sides! @Fig. 5~b!#,• One strip bonded on the tension face and four rectang

strips on the vertical sides@Fig. 5~c!#, and• One strip bonded on the tension face and four trapezo

strips on the vertical sides@Fig. 5~d!#.In total, ten different combinations of retrofitting were achievwith the 28 damaged beams tested in Stage I, as detailed in T4 and 5.

Stage II

Of the 14 beams produced for Stage II, three were tested witany repair as control beams. These beams were tested to faunder four-point bending over a span of 1,100 mm~Fig. 4!. Thespacing between the applied loads was 400 mm. As expectethe control beams in this stage failed in pure flexure and taverage failure load was 42.03 kN. The remaining 11 beams wpreloaded in the same manner as the control beams to app

Fig. 4. Arrangement for testing beams:~a! side view, ~b! crosssection, and~c! plan

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mately 75% of the failure load~31 kN!. To improve the flexuralbehavior of the damaged beams three configurations of retroting strips were investigated in this stage. Retrofitting with:

• One strip bonded on the tension face@Fig. 6~a!#,• One strip bonded on the tension face and four short strips

the vertical sides covering the supports and the ends oftension strip@Fig. 6~b!#, and

• One strip bonded on the tension face and four short and tcontinuous strips on the vertical sides, fully covering the suports and the tension strip@Fig. 6~c!#.

It should be mentioned that the last configuration@Fig. 6~c!# canbe realized by bonding a strip to the tension face and two loncontinuous strips on the vertical sides covering fully the suppoand the sides of the tension strip. The solution chosen heredictated by the fact that the precast strips were shorter~1,030 mmlong! than the overall span of test beams~1,200 mm!.

Only Mix I was used as the retrofitting material in Stage II. Ain the previous stage, this material was used for retrofitting tbeams in two different thicknesses, i.e., 16 and 20 mm. In tosix different combinations of retrofitting were achieved in thstage, as detailed in Table 6.

Fig. 5. Configurations of retrofitting in Stage I:~a! beam retrofittedwith one strip on tension side;~b! beam retrofitted with one stripunderneath and two side strips;~c! beam retrofitted with one stripunderneath and four rectangular side strips; and~d! beam retrofittedwith one strip underneath and four trapezoidal side strips

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Table 4. Test Results~Three-Point Bending! and Analytical Model Predictions of Stage I Beams

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Table 5. Test Results~Four-Point Bending! and Analytical Model Predictions of Stage I Beams

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Casting of Strips

The retrofit materials, CARDIFRC Mix I and Mix II were cast asflat strips in 1,030 mm long and 100 mm wide steel molds withwell-oiled base and raised border whose height could be adjustto give 16 or 20 mm thick plates. The molds were filled on avibrating table at 50 Hz frequency and smoothed over withfloat. To ensure a uniform thickness~within 1 mm! a glass panelwas located on top of the raised border. The strips were leftcure in the molds for 24 h at 20°C before demolding. The retrofistrips were then hot-cured at 90°C for a further nine days~includ-ing one day for raising and one day for lowering the temperature!.

Fig. 6. Configurations of retrofitting in Stage II:~a! one strip bondedon tension face;~b! one strip bonded on tension face and four shorstrips on vertical sides covering supports and ends of tension strand ~c! one strip bonded on tension face and four short and twcontinuous strips on vertical sides, fully covering supports antension strip sides

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The short rectangular and trapezoidal side strips, were cut fthe long cast strips to the required size using a diamond saw

Adhesive Bonding

To improve the bond between the retrofit strips and the damabeams, all contacting surfaces were carefully cleaned and rouened. An angle grinder was used to create a grid of groovesproximately 3 mm deep at a spacing of 50 mm on the contacsurfaces of the damaged beams.

The retrofit strips were bonded to the prepared surfaces ofdamaged concrete beams with a commercial thixotropic epadhesive. The two parts of the adhesive were thoroughly miand applied to the tension side of the damaged beam with arated trowel to a uniform thickness of 3 mm. The strips weplaced on the adhesive and evenly pressed. To ensure good asion, pressure must be applied to the strips during the hardeof the adhesive~24 h! in accordance with the manufacturer’s reommendation.

For the retrofitted beam with more than one strip, the bewas turned on its side to which the strip was bonded in the samanner as above. After another 24 h, this procedure was repeon the other side of the damaged beam. In practice, to engood adhesion between the strips and the damaged beam precan be applied using G-clamps.

Test Results

Stage I

Of the 28 beams retrofitted in Stage I, 22 beams were tested insame manner as the corresponding control beams, i.e., in thpoint bending over a span of 1,100 mm. The remaining six beai.e., the beams retrofitted with one continuous and four 20 mthick rectangular strips were tested over the same span, bufour-point bending. The spacing between the applied loads400 mm. In all cases, the load was controlled by the movemen

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Table 6. Test Results~Four-Point Bending! and Analytical Model Predictions of Stage II Beams

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the actuator~stroke control!. The rate of loading was 0.01 mm/sthe beginning of all tests, but it was increased to 0.02 mm/s wthe midspan deflection exceeded about 3 mm. In some casebeams were deliberately unloaded after the attainment ofmaximum load and then reloaded. Therefore, the stiffness obeam during reloading could be compared with the initial sness and the damage accumulated in the beam could be evalTables 4 and 5 show the test results of control and retrofibeams.

Of the seven beams retrofitted with one strip only on thesion face, four beams failed in flexure, two in shear, and onecombination of flexure and shear. All the beams failed at loadleast equal to the average failure load of the control beams.six beams retrofitted with three 16 mm strips all failed in pflexure. Their failure was characterized by the formationopening of a single flexural crack around the midspan of the b@Fig. 7~a!#. This configuration of retrofitting not only increasethe load carrying capacity by more than 60% over that ofcontrol beams, but also improved significantly the serviceabof the beams in terms of a significant reduction in the numberthe width of the cracks. For instance, the midspan deflectiothe retrofitted beams at a load level of 20 kN was only about 1

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Fig. 7. Flexural cracking in beam retrofitted with:~a! three 16 mmthick strips and~b! four trapezoidal strips on sides and continuoustrip on tension face

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fsgFig. 9. Load-deflection response of retrofitted beams:~a! Stage Ibeams retrofitted with one continuous and four rectangular 16thick strips under three-point bending and~b! Stage II beams retro-fitted with only one 20 mm thick strip on tension face under foupoint bending

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of that of the control beams. Fig. 8 compares the typical lodeflection response of the beams retrofitted with three continustrips with that of the control beams.

Only one beam was retrofitted by three 20 mm thick striDue to the over-strengthening of the midspan by the retrofit strthis beam failed suddenly in shear. The energy released by cring was so large that the beam split into two parts.

To prevent shear failure of the beams retrofitted with threemm strips, two systems of repair with one continuous strip afour rectangular/trapezoidal strips@Figs. 5~c and d!# wereadopted. As with the other retrofitting configurations, the contious strip was bonded to the tension face, whereas the rectangtrapezoidal strips partly covered the sides of the beam closethe supports. The main objective of using trapezoidal strips wacheck whether or not the gradual change in the cross sectiothe side strips improves the behavior of the beams and decrethe stress concentration. Two damaged beams were repairedone continuous and four trapezoidal 20 mm thick strips. Thbeams failed in flexure with the opening of a flexural crack inmiddle of the beam@Fig. 7~b!#.

Of the 12 damaged beams retrofitted by one continuousfour rectangular strips, six beams~with 16 mm thick strips! weretested in three-point bending and the remaining six~with 20 mmthick strips! in four-point bending. The typical load-deflectioresponse of the beams tested in three-point bending can be fin Fig. 9~a!. It should be noted however, that these beams whave a deflection capacity of only 3 mm under an accideoverload. The dominant cracks in four of these beams were nevertical and formed in the middle of the beams. These obsetions are typical of a flexural failure. In the other two beams,dominant crack formed in the middle third of the beams, initiatiwhere the side retrofit strip stopped and extending up to the pof loading. There were signs that the flexural and shear streinfluenced the dominant crack, so that the beams failed in a cbined shear-flexure mode. In three-point bending, the shear fin all the sections of a beam is the same as at the supports. Ifailure under the influence of the shear stress occurs in the mithird of the beam, then the failure will be ductile. However, ifoccurs at the supports where there are no retrofitting strips, thwill be a brittle failure. The difference between the behaviorthe beams retrofitted with trapezoidal and rectangular stripsfound to be negligible.

To confirm that the shear-flexural failure of the two bearetrofitted with one continuous and four rectangular 16 mm thstrips was because they were tested in three-point bendingbeams retrofitted with the same configuration but with 20 mthick strips, were tested in four-point bending. For this config

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ration of loading, five beams failed in pure flexure with openof pre-existing cracks and the appearance of some vertical crin the middle third of the beams. Only one beam failed in sheaits left support where there was no side strip to strengthensection in shear.

Stage II

The beams retrofitted in Stage II were tested in the same maas their corresponding control beams, i.e., in four-point bendover a span of 1,100 mm. The four beams that were retrofiwith one strip only on the tension face all failed in flexure. Hoever, in most of the beams~three out of four! some signs of sheadistress in the form of tiny diagonal cracks were observed atend of the strips near the supports. These cracks propagatewards the nearest loading point and caused a local drop inload. The load-deflection response of the beams retrofitted20 mm thick strips can be found in Fig. 9~b!. It should be notedagain, that these beams will have a deflection capacity of aro3 mm under an accidental overload.

To overcome this problem, the anchorage area of the tenstrip was strengthened in shear by covering the sides of the bat the supports and near the ends of the strip by additional s

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Fig. 10. Stress-deformation diagrams assumed in model for:~a! steel;~b! concrete in compression;~c! concrete in tension; and~d! CARDIFRCin tension. Constant A depends on aspect ratio and volume fraction of fiber and fracture toughness of cementitious matrix.

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strips. As mentioned before, two types of retrofitting strips winvestigated. Four beams were retrofitted with one strip bonon the tension face, and four short strips on the vertical sicovering the supports and the ends of the tension strip@Fig. 6~b!#;and three beams were retrofitted with one strip bonded ontension face and four short and two continuous strips on thetical sides, fully covering the supports and the tension strip s@Fig. 6~c!#. In fact in the second configuration, further improvment in flexural behavior of the beams was also expected.seven beams failed in pure flexure with the opening of a p

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existing crack after it had penetrated into the retrofit strip in thmiddle third of the beam. No shear cracks or drop in the loawere observed thus confirming the usefulness of the coveringsides of the beams.

Analytical Model

To predict the moment resistance and the load-deflection behavof the control and retrofitted beams an analytical model has be

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developed. In this model the strain hardening as well as tensoftening of both concrete and CARDIFRC in tension have btaken into account. The stress-strain relationships of matewere assumed to be according to the test results or the propstress-deformation diagrams of the Model Code CEB-FIP~1993!.Based on this code, steel is assumed to be perfectly elasto-p@Fig. 10~a!#, whereas a parabolic relation is used for concretecompression@Fig. 10~b!#. Table 3 shows the values of the relevaparameters assumed in the model. For concrete, the comprestrength was measured experimentally, and the remaining paeters were calculated from the relations proposed by CEB-The yield stressf y and the modulus of elasticityEs of steel wereobtained from tension test on rebars.

Tensile failure of concrete and CARDIFRC is always a dcrete phenomenon. Therefore, to describe this behavior a ststrain and a stress-crack opening relation should be used founcracked and cracked sections, respectively. For normal conin tension the stress-deformation behavior proposed by CEBwas assumed@Fig. 10~c!#, whereas the behavior of CARDIFRC itension was modeled based on the theory of fracture mechaand a few available test results@Fig. 10~d!#. The parameters assumed for modeling the behavior of concrete and CARDIFRCtension can be found in Tables 3 and 7, respectively. For concthe direct tensile strengthf ctm was estimated from the splittingtest results and the remaining parameters were again calcufrom the relations proposed by CEB-FIP. For CARDIFRC ttensile strength of the matrixf tp was estimated from the splittingtest results of the mix without fibers. However, the specific frture energyGF and the modulus of elasticityE were directlymeasured using the notched beam and prism specimens, retively. The remaining parameters in Table 7 were obtained frofew direct tension tests on dog-bone shape specimens.

The moment resistance of a section retrofitted by CARDIFcan be calculated based on the distribution of stresses causebending. To determine the strain distribution along the heighthe section the following assumptions are made:• Plane sections remain plane after bending. In other words,

distribution of strain through the full height of the beamlinear ~Bernoulli hypothesis! and

• The bond between the retrofit strips and the original beamperfect and there is no sliding at the interface~deformationcompatibility!. This assumption was fully validated by tests

The stress distribution in concrete and CARDIFRC strips canbe assessed directly from the value of strain after cracking, asconstitutive relations are expressed in terms of stress-crack oing rather than stress-strain. Using the following assumptions,evaluation of the crack opening from the strain distribution bcomes possible:• The crack opening at the tension retrofit strip~w! is the prod-

uct of the strain at this level (« f), and an effective length oretrofit strip (Leff) and

• The dominant flexural crack tip is located at the level of tneutral axis. The faces of this crack open in a linear man@Fig. 11~a!#.

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In fact, the strain over the effective length of retrofit strip (Leff)is released in the form of a local crack. To determineLeff , thelength of the strain-free part of the retrofit strip should be calclated. If the tensile stress carried by the cracked strips is ignoin comparison with the tensile stress transferred by the reinforment, the shear stress at the interface is dependent on the sstress applied by the reinforcement, as shown in Fig. 11~b!. As-suming the shear stress at the level of reinforcement is distribuat 45°, a length of retrofit strip (Leff) is stress-free and consequently strain-free. The deformation of this length of strip is lcalized in the crack opening. Therefore, to calculate the craopening of the tension retrofit strip, the strain at this level (« f)can be multiplied by this effective length (Leff), i.e., twice thedistance between the reinforcement and the tension strip. It caseen that by using this method the stress distribution in the rematerial can also be worked out from the strain distribution. Dto the fact that the crack opening displacements~i.e., crackwidths! of the test beams were too small for accurate measument, the crack openings calculated from the above method conot be compared directly with measured values. However,consequences of the above assumptions to the calculation omoment resistance and the load deflection response of the bewill become clear when we compare the model and test reslater in this paper.

To evaluate the moment resistance of the control beamsthe beams retrofitted with different configurations of CARDIFRstrip, which fail in flexure, a program was written. Fig. 12 illustrates the flowchart of this program. First, a strain in the tconcrete fiber and a neutral axis depth are assumed. Thenlinear strain distribution along the height of the beam is definedterms of these assumed values. The depth between the top cpression fiber and the neutral axis is divided into ten sections. Taverage strain over each section is calculated assuming piecelinear fiber strain. The compressive stress can now be found uthe concrete stress-strain relation. Multiplying this by the areathe section gives the compressive force. A similar calculationmade to determine the tensile forces in the concrete in tensionthe retrofit strips, and in the reinforcing steel. As mentioned bfore, to determine the tensile stress of cracked concrete androfit strips the crack opening should also be calculated.

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Fig. 11. ~a! Modeling of flexural crack in middle of beam strengthened with three strips and~b! effective length of strip for calculationof crack opening

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Fig. 12. Flowchart of program for calculating moment resistance of beams

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Having calculated all the forces the neutral axis is adjusuntil the sum of the compressive forces equals the sum oftensile forces. When this is achieved, the moment is determby summing the compressive and tensile forces times theirment arms about a single point. In addition, the curvature ofbeam can also be easily worked out using the strain in theconcrete fiber and the neutral axis depth. This process is repefor different assumed strains in the top fiber of concrete. Tmaximum moment resistance of the section occurs when e

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the moment reduces for an increase in the top fiber strain, ortop fiber concrete strain exceeds the ultimate strain of concretecompression («cu). Fig. 13 shows the relation between the moment resistance of the section and the curvature of the beamthe beams in Stage I.

Due to the fact that all the beams tested are statically deternate, their bending moment diagrams at any stage of loadinguniquely defined. This information can be combined with thmoment-curvature diagram of sections to produce the curvat

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Fig. 15. Comparison of load-deflection response of control beapredicted by model with test results in three cases:~a! when tensilecapacity of concrete is completely ignored;~b! when strain hardeningof concrete is taken into account while tension softening is ignorand ~c! when tension softening and strain hardening of concreteconsidered

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diagram of the beam at different load levels by dividing the beaspan into a number of intervals. The moment-area method is tused to compute the slope and the deflection of any point ofbeam.

Model Results

Stage I

Tables 4 and 5 compare the maximum moment resistance ofbeams predicted by the analytical model with the three- and fopoint bend test results of Stage I, respectively. This comparisoalso made in Fig. 14. It should be emphasized that the presmodel is only applicable to beams which fail in flexure.

The load-deflection response of the control beams is compain Fig. 15 with three model predictions. In the first model predition @Fig. 15~a!#, the tensile capacity of concrete is completeignored. As a result the initial stiffness of the test beams is muhigher than the predicted value. In the second model predict@Fig. 15~b!#, the tensile capacity of concrete up to the peak loadtaken into account but its postpeak tension softening is agignored. As a result the predicted initial response is much cloto the recorded response, but there are still some differences

Fig. 14. Comparison of moment resistance of Stage I beams wpredictions of analytical model

tween the test and model results after the concrete has crackebefore the steel has yielded. In the third model prediction,complete tensile response of concrete including the tensionening is considered. Fig. 15~c! shows that the entire loaddeflection curve predicted by the model is now very close to trecorded in the tests. It can be seen that the load-deflectionsponse of the beams is not accurately predicted, unless theconstitutive behavior of all the contributing materials, includithe tension softening behavior of normal concrete is propetaken into account.

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Fig. 16. Comparison of typical load-deflection response of retrofitbeams with that predicted by model~Stage I!: ~a! beams retrofittedwith one continuous and four rectangular 20 mm strips under fpoint bending and~b! beams retrofitted with three continuous 16 mstrips under three-point bending

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Fig. 18. Comparison of load-deflection response of Stage II bewith model predictions:~a! control beams and~b! retrofitted beamsOf four beams tested, two~1-16-S-1 and 1-16-S-2! were retrofittedwith only one 16 mm strip on tension face, while remaining two hadditionally short retrofit strips bonded on each vertical side nsupports.

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Fig. 15 also shows that the model slightly under-estimatesload carrying capacity of the control beams. It can be due tounder-estimation of the yield stress of steel. Sensitivity anaon the model shows that if the yield stress of steel is increase10%, the moment resistance of the beam is increased by 9.

Fig. 16~a! compares the typical load-deflection response ofbeams retrofitted with one continuous and four rectangular 20strips @Fig. 5~c!# with the model predictions. The same compason is made in Fig. 16~b! for the beams retrofitted with three 1

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Stage II

Table 6 and Fig. 17 compare the maximum load carrying capaof the Stage II beams~with shear reinforcement! with the modelpredictions. It can be seen that the model predictions are agagood agreement with the test results. Of course, the failure loasome beams retrofitted with 20 mm strips is lower than thatdicted by the model. This is likely to be the result of the poquality of some 20 mm strips used for retrofitting the beams.

The load-deflection response of the control beams in Stagis compared in Fig. 18~a! with the model predictions. It can bseen that up to the load level corresponding to the crackinconcrete in tension, the response predicted by the model andrecorded in the test are identical. However, when concrete crin tension, the model predicts a larger deflection than the msured value. This is because the model assumes the cracketion condition for all sections in the region of the maximum mment. Although this local increase in the deflection wasobserved in the tests, the stiffness of all control beams had

Fig. 17. Comparison of load carrying capacity of Stage II beawith that predicted by analytical model

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creased considerably at this load level. As the load is increathe model predictions again approach the test results, and finaductile failure with the yielding of steel is observed in both thmodel and the test results. The maximum load carrying capaof the control beams is slightly higher than the predicted valueaddition, a local drop in the load is observed just after the attament of the maximum load. This is due to the local instabilinduced by the yielding of steel across the existing flexural crawhich is not included in the model.

Fig. 18~b! compares the load-deflection response of the StII beams with model predictions. Of the four beams tested, t~1-16-S-1 and 1-16-S-2! were retrofitted with only one 16 mmstrip on the tension face, while the remaining two had additionashort retrofit strips bonded on each vertical side near the supp@see, Figs. 6~a and b!#. It can be seen that the load-deflectiopredicted by the model is close to the test results, especiallyfore the maximum load is reached.

Conclusions

The new technique using the CARDIFRC strip bonding systema promising method for improving the flexural and shear behior, as well as the serviceability of damaged concrete beamsdoes not suffer from the drawbacks of the existing techniquwhich are primarily a result of the mismatch in the propertibetween the concrete and the repair material.

The mechanical properties of CARDIFRC Mixes I and II avery similar, therefore there is no real difference in the behavof the beams retrofitted with either of these mixes.

The moment resistance and load-deflection response ofbeams retrofitted using this technique can be predicted anacally, providing that the strain hardening and tension softenresponse of concrete and CARDIFRC are properly taken intocount.

The technique described in this paper may be used when tis a need to improve the durability of existing concrete structuras CARDIFRC mixes are very durable because of their higdense microstructure. Research is currently being undertakestudy the fatigue, shrinkage, and creep properties of CARDIFand the performance of concrete structures retrofitted wCARDIFRC under dynamic, thermal, and hygral loads.

Acknowledgment

This work is supported by U.K. EPSRC Grant No. GR/R1133

Notation

The following symbols are used in this paper:E 5 modulus of elasticity;

Ec 5 modulus of elasticity of concrete;Ec1 5 secant modulus of elasticity of concrete;Es 5 modulus of elasticity of steel;f cm 5 compressive strength of concrete;f ctm 5 tensile strength of concrete;

f t 5 tensile strength of CARDIFRC;f tp 5 tensile strength of CARDIFRC matrix~i.e., mix

without fibers!;f y 5 yield stress of steel;

GF 5 specific fracture energy;

186 / JOURNAL OF COMPOSITES FOR CONSTRUCTION © ASCE / AUGU

,L fmax 5 maximum fiber length in CARDIFRC;P 5 load;

Pu 5 maximum load;d 5 deflection;« 5 strain;

«c1 5 strain of concrete at maximum stress;«ct 5 strain of concrete in tension;«cu 5 ultimate strain of concrete in compression;

s 5 stress;sct 5 stress of concrete in tension;scu 5 ultimate compressive stress of concrete in

compression;v 5 crack opening;

v1 5 crack opening of concrete at knee of tensionsoftening diagram; and

vc 5 maximum crack opening.

References

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