Composites: Part B 58 (2014) 618–624

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Composites: Part B

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Bond strength and effective bond length of FRP sheets/plates bondedto concrete considering the type of adhesive layer

1359-8368/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.compositesb.2013.10.075

⇑ Corresponding author. Tel.: +20 100 8816623; fax: +20 88 218 5566.E-mail addresses: heshamdiab2@yahoo.com, Diab@aun.edu.eg (H.M. Diab),

omar_farghal222@yahoo.com (O.A. Farghal).

Hesham M. Diab ⇑, Omer A. FarghalCivil Engineering Department, Faculty of Engineering, Assiut University, P.O. Box 71515, Assiut, Egypt

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

Article history:Received 13 May 2013Received in revised form 7 September 2013Accepted 25 October 2013Available online 9 November 2013

Keywords:A. FibresB. FractureB. StrengthC. Analytical modellingFlexible adhesive

Recent experimental results of the FRP–concrete bonded joint using flexible adhesive showed that themost popular analytical models available in the literature underestimate the bond strength and the effec-tive bond length of these experiments. Most of these existing models need to be modified to consider thetype of adhesive layer. Consequently, the bond strength model proposed by Chen and Teng (2001) hasbeen modified to consider the type of adhesive layer. An extensive database consisting of about 100 testresults of FRP–concrete joint has been assembled to examine the validity of the proposed model takingthe type of adhesive layer into consideration. The modified bond strength model is accurately capable ofpredicting the bond strength and the effective bond length.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Determination of bond capacity of the FRP–concrete interface isan important subject, and has attracted extensive research till now[1–4]. Based on the extensive tests, researchers concluded that thebond capacity is affected mainly by mechanical and physical prop-erties of concrete, thickness and stiffness of the FRP, thickness ofthe adhesive, and the bonded length [5–7]. However, someresearchers [8,9] concluded that thickness of the adhesive has anegligible effect on mean and peak shear stresses.

Indeed, a number of researchers investigated the effect of flex-ible adhesive on the bonding of FRP sheets [10–12]. Dai and Ueda[11] considered the effect of adhesive layer stiffness by consideringdifferent thicknesses of the adhesive layer, and consequently theyconcluded that the use of adhesive with lower stiffness may lead tohigher bond capacity. However, the thickness of the adhesive layercannot be easily defined and it is believed to be too small to bemeasured experimentally. Moreover, Dai et al. [12] provided asummary report on the flexible bonding system. The contents in-cluded the bond characteristics of FRP/concrete joints, strengthand ductility of FRP strengthened RC beams. The conclusion wasthat the flexible bonding system with sufficient long anchoragecan achieve higher bond capacity and a ductile failure. However,the authors couldn’t determine the percentage of increase in thebond capacity in comparison to others types of adhesive. On the

other hand, Xia and Teng [10] studied the interfacial behavior ofFRP laminates bonded to steel member using different adhesivetypes. It was concluded that properties of adhesive have a signifi-cant effect on the bond capacity of FRP–steel joints.

The force induced in FRP sheets is transferred to concretemainly through shear stress in the adhesive in a short length nearthe applied load which is called effective bond length. As the effec-tive bond length exceeds, an increase in the applied load can beachieved. Also, as a result of increasing the effective bond length,shear stress concentration reduces. As a consequence no debond-ing occurs at concrete interface [13]. Moreover, increasing thebonding length of FRP sheets than the effective bond length no fur-ther increase in failure load can be achieved. Therefore, determina-tion of the effective bond length is considered an important issueto determine the maximum bond capacity of the FRP–concreteinterface. Consequently, most theoretical bond strength modelspredict the maximum capacity of FRP bonding system based onthe predicted effective bond length.

Many analytical models have been proposed in order to predictthe effective bond length and the ultimate bond strength of theFRP-strengthened system. It is interesting to note that most of theexisting models, which are in reasonable agreement to experimentalresults [5–7], neglect the adhesive layer properties. Furthermore,most existing models were developed from the results of single ordouble test methods of FRP-bonded concrete blocks using normaladhesive (one kind of epoxy) and therefore, the corresponding appli-cability to the structural system remains challenged.

Recent studies [14–17] have shown that the adhesive layer inaddition to many other parameters, which were previously

H.M. Diab, O.A. Farghal / Composites: Part B 58 (2014) 618–624 619

mentioned, play a relevant role in the behavior of adhesive joints.Ascione and Mancusi [18,19] have proposed a model to predict theeffective bond length and the ultimate bond strength of the FRPadhesive joints. This model showed a good accuracy in comparisonto the experimental results. It is worthwhile to note that this mod-el takes into account the axial stiffness of the composite laminateand the cohesive interface parameters of the interfacial bondingwhich they significantly depends on the interfacial fracture energy.Therefore, a reliable and efficient model should be establishedthrough a comprehensive understanding of the contribution ofadhesive layer type on FRP–concrete strengthening systems.

2. Experimental program

The experimental program conducted in this study is aimed atstudying the effective bond length and the bond strength of FRPsheets bonded to concrete using a flexible epoxy adhesive whichhas a low elastic modulus. These experimental results used to val-idate the existing bond strength models and the modified bondstrength model proposed by the authors.

The double-shear specimens consist of two concrete prisms withdimensions of 100 � 100 � 200 mm3 and100 � 100 � 250 mm3.The two prisms are connected through FRP sheet strips externallybonded to the opposite sides of the prisms. Deformed steel bars of22 mm in diameter are inserted in the cast exiting 50 mm fromone end of each prism in the way to apply the pull load in the test set-up. The 28-day compressive strength of concrete was about40.0 MPa. Two types of FRP sheets have been considered: CarbonFRP and Basalt FRP. The mechanical properties of the FRP sheets pro-vided by manufacturers are described in Table 1.

The concrete surface of the prisms was roughened using amechanical grinder to remove the surface laitance and exposethe coarse aggregate. Dust and any loose particles were blownoff by means of compressed air and then the surface has beencovered with a layer of epoxy primer. Such a primer has an elas-tic modulus of 2.45 GPa. After Harding the primer, the FRP sheetshave been applied to the concrete surface using a flexible type ofepoxy adhesive, CN-100; in the case of more than one layer ofFRP, a layer of adhesive was applied between every couple ofconsecutive sheets. The CN-100 epoxy adhesive has an elasticmodulus of 0.39 GPa, a tensile strength of 11.8 MPa, and an elon-gation of 50%. These properties are provided by themanufacturer.

Specimens have been prepared in laboratory conditions and thetest temperature was about 24 �C. One of the two prisms has beenmechanically anchored with steel plate to prevent any slippage inthe FRP sheets during test. However, on the other prism the bond-ing system of the FRP sheets has been monitored using a number ofstrain gauges mounted on the FRP sheets as shown in Fig. 1. Theglobal slip, which is defined as the relative displacement betweenthe two concrete prisms, was measured using four clip straingauges that were attached on free sides of concrete prisms. Detailsof these instruments are available elsewhere [20]. Table 2 summa-rizes the number of specimens, their parameters and their results.

The specimens were labeled within alphanumeric designation(Table 2) depending upon the type of the FRP sheets, adhesive layerand number of FRP sheet layers. The number following the hyphenrepresents the number of specimen. Two types of FRP sheets were

Table 1Summary of mechanical properties of different fiber sheets.

Types of fibers Fiber aerial weight (g/m2) Thickness (mm) Mo

Carbon fiber 300 0.167 230Basalt (BUF7-300) 300 0.17 91.

considered in this study: carbon fiber reinforced polymer, CFRP,and basalt fiber reinforced polymer, BFRP.

2.1. Experimental results and discussions

The obtained experimental results for the different specimensare listed in Table 2. This study is only concerned with the bondstrength and the effective bond length of FRP sheets bonded tothe concrete surface using flexible adhesive and more details aboutthe experiment results can be found elsewhere [20]. The effectivebond length (Le exp) is defined as the distance from the free endof the specimen to the position where 97% of the strain value isreached [21]. The interfacial fracture energy, Mode II, Gf, representsthe total external energy supply, per unit of area, required to cre-ate, propagate and fully break a crack along the FRP–concreteinterface. The fracture energy of the FRP–concrete interface isdetermined from the following equation:

Gf ¼P2

2b2f Ef tf

ð1Þ

where P is the tensile force of one lap FRP laminate, bf, Ef ,and tf arewidth, longitudinal elasticity modulus, and thickness of the FRPsheets, respectively.

2.1.1. Bond strength of the FRP sheetsLoad carrying capacity is an important reference for selecting

the optimum bonding adhesive. There is a clear reinforcement ac-tion which is achieved by applying flexible adhesive with differenttypes of FRP sheets. Fig. 2 shows experimental ultimate bondstrength versus predicted ultimate bond strength. The bondstrengths were calculated using the most accurate and appropriatebond strength models proposed by Chen and Teng [5], Neubauerand Rostasy [6], and Wu et al. [7]. Details of these models can befound in their references. It is worthwhile to mention that thesemodels underestimate the bond strength of the different speci-mens except for one specimen which has a low FRP stiffness, i.e.BFRPL2 and BFRPL1. Also, it seems that the accuracy of the bondstrength model mainly depends on the type of adhesive layer asshown in Fig. 2. These obtained results emphasized that the flexi-ble adhesive layer can be successfully used to increase the bondcapacity of the FRP–concrete interface.

2.1.2. Interfacial fracture energyEq. (1) can be used to predict the interfacial fracture energy Gf

(Mode II). The values of interfacial fracture energy for each speci-men are shown in Table 2. It is observed that the interfacial frac-ture energy of specimens of flexible adhesive layer falls withinthe range between 0.82 and 2.25 N/mm. On the other hand, previ-ous studies concluded that the interfacial fracture energy of FRP–concrete interface using ordinary adhesive falls within the rangebetween 0.68 and 1.09 N/mm [22]. Consequently the fracture en-ergy also mainly depends on the properties of adhesive layer.

3. Proposed bond strength model

Analytical models used to predict the bond strength, availablein the literature, are evaluated on the basis of 351 bond tests per-

dulus of elasticity (MPa) Tensile strength (MPa) Rupture strain (%)

� 103 3400 1.480 � 103 2100 2.6

Fig. 1. Specimen details and instrumentation.

Table 2Specimens’ data and key results from bond tests.

Specimen Type of FRP sheets No. of FRP sheets Ultimate load (kN) Fracture energy (N/mm) Effective bond length

BFRPL1-1 Basalt FRP sheets 1 24.23 1.94 110BFRPL1-2 1 21.90 1.58BFRPL1-3 1 17.40 1.00BFRPL2-1 2 19.89 0.65 210BFRPL2-2 2 22.25 0.82BFRPL2-3 2 23.60 0.91BFRPL3-1 3 32.45 1.16 >250BFRPL3-2 3 44.19 2.15BFRPL3-3 3 36.80 1.49CFRPL1-1 Carbon FRP sheets 1 43.8 2.50 200CFRPL1-2 1 41.6 2.25CFRPL1-3 1 37.65 1.85CFRPL2-1 2 48.4 1.52 250CFRPL2-2 2 44.62 1.30

0 10 20 30 40 50Pu Exp. (kN)

Neubauer & Rostasy 1999-CFRPNeubauer & Rostasy 1999-Basalt

0

5

10

15

20

25

30

35

40

45

50

Chen & Teng 2001-CFRPChen & Teng 2001-Basalt

Pu p

r.(k

N)

Wu et al. 2009-CFRPWu et al. 2009-Basalt

Fig. 2. Pu predicted versus Pu experiment for different types of FRP compositesusing flexible adhesive.

620 H.M. Diab, O.A. Farghal / Composites: Part B 58 (2014) 618–624

formed by Toutanji et al. [23]. It is found that the formula proposedby Chen and Teng [5] better predicts the experimental measure-ments for all types of composite materials. Even though, this modelfails to correctly predict bond strength of specimens carried out inthis study for the case of the FRP sheets bonded to concrete usingflexible adhesive. This model and the others showed underesti-mate values as mentioned previously. This study confirms thatthe type of the adhesive layer is able to increase the bond capacityof FRP–concrete interface. Therefore, the type of adhesive layershould be considered through all existing models. In this studythe most accurate bond strength model introduced by Chen andTeng [5] will be modified to consider the type of adhesive layer

based on the limited number of experiments available in thisstudy. The bond strength of an FRP–concrete interface of a simpleshear joint based on the Chen and Teng’s model is represented asfollows;

Pu ¼ 0:427bbbLbf Le

ffiffiffiffiffiffiffiffibaf 0c

qð2Þ

Le ¼ffiffiffiffiffiffiffiffiffiEf tfffiffiffiffi

f 0cp

s; bb ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2� bf =bc

1þ bf =bc

s; bL ¼ 1 if L P Le;

bL ¼ sinpL2Le

if L � Le ð3Þ

where Ef, tf, bf are longitudinal elasticity modulus, thickness andwidth of FRP sheets, respectively; f 0c ; bc are the concrete compressivestrength and width of concrete block, respectively; Le, L are theeffective bond length and bond length, respectively. Experimentalresults showed that the flexible adhesive layer increases the effec-tive bond length which results in the redistribution of shear stressesalong the bonded length and in turn increases the bond capacity ofFRP–concrete interface. Therefore; a coefficient ba is proposed to theeffective bond length and to the bond strength equations of Chenand Teng’s model [5]. From the regression of the limited test dataavailable in the present study, the factor ba is represented as:

ba ¼ffiffiffiffiffiffiffiffiffiffi

Ea

2:45

rð4Þ

where Ea is the weakest elastic modulus of adhesive layer or epoxyprimer in GPa used to bond FRP sheet to concrete prism.

Table 3Details of specimens and test results.

No Ref Lb (mm) fc (MPa) Ef⁄tf (GPa) Er (GPa) Pu exp/width (N/mm) Chen and Teng’s model Proposed model

Le Pr Pu pr Pex/Ppr Le Pu Pex/Ppr

1 Chajes et al. [24] 76.2 36.8 110.2 5.2 333.1 134.8 270.8 1.2 92.8 278.3 1.22 76.2 48.0 110.2 5.2 390.9 126.1 303.3 1.3 86.8 303.9 1.33 76.2 48.7 110.2 5.2 418.7 125.6 305.1 1.4 86.5 305.3 1.44 76.2 44.5 110.2 2.2 414.5 128.5 293.5 1.4 135.5 290.3 1.45 76.2 44.5 110.2 0.2 352.5 128.5 293.5 1.2 415.6 186.8 1.96 76.2 44.5 110.2 0.2 378.3 128.5 293.5 1.3 415.6 186.8 2.07 76.2 44.5 110.2 1.6 414.0 128.5 293.5 1.4 159.8 277.8 1.58 76.2 44.5 110.2 1.6 440.8 128.5 293.5 1.5 159.8 277.8 1.69 101.6 37.1 110.2 1.6 504.2 134.5 324.4 1.6 167.1 318.3 1.610 152.4 37.1 110.2 1.6 469.2 134.5 349.9 1.3 167.1 386.3 1.211 203.2 37.1 110.2 1.6 455.3 134.5 349.9 1.3 167.1 390.1 1.2

12 Maeda et al. [25] 76.2 40.8 24.8 2.4 116.1 62.3 170.0 0.7 63.0 170.9 0.713 152.4 40.8 24.8 2.4 184.1 62.3 170.0 1.1 63.0 170.9 1.114 304.8 43.3 24.8 2.4 239.0 61.4 172.5 1.4 62.0 173.4 1.415 76.2 42.4 61.5 2.4 200.0 97.2 254.7 0.8 98.2 254.9 0.816 152.4 42.4 61.5 2.4 146.1 97.2 270.2 0.5 98.2 271.6 0.517 152.4 42.7 49.6 2.4 325.0 87.1 243.2 1.3 88.1 244.4 1.318 711.2 42.7 24.8 2.4 200.0 61.6 171.9 1.2 62.3 172.8 1.2

19 Taljsten [26] 101.6 86.0 200.1 6.6 346.0 146.9 514.6 0.7 89.7 454.5 0.820 203.2 92.8 200.1 6.6 549.9 144.1 592.8 0.9 88.0 463.2 1.221 304.8 99.7 200.1 6.6 701.9 141.6 603.5 1.2 86.4 471.6 1.522 406.4 99.7 200.1 6.6 538.0 141.6 603.5 0.9 86.4 471.6 1.1

23 De Lorenzis et al. [28] 101.6 48.2 37.6 0.7 325.7 73.5 267.1 1.2 135.9 334.8 1.024 101.6 48.2 37.6 0.7 349.4 73.5 267.1 1.3 135.9 334.8 1.025 203.2 48.2 37.6 0.7 311.7 73.5 267.1 1.2 135.9 363.1 0.926 203.2 48.2 37.6 0.7 279.3 73.5 267.1 1.0 135.9 363.1 0.827 304.8 48.2 37.6 0.7 335.4 73.5 267.1 1.3 135.9 363.1 0.928 304.8 48.2 37.6 0.7 296.8 73.5 267.1 1.1 135.9 363.1 0.829 101.6 41.5 75.1 0.7 519.2 108.0 362.2 1.4 199.6 354.4 1.530 101.6 41.5 75.1 0.7 450.1 108.0 362.2 1.2 199.6 354.4 1.331 203.2 41.5 75.1 0.7 405.4 108.0 363.8 1.1 199.6 494.6 0.832 203.2 41.5 75.1 0.7 548.1 108.0 363.8 1.5 199.6 494.6 1.133 304.8 41.5 75.1 0.7 489.5 108.0 363.8 1.3 199.6 494.6 1.034 304.8 41.5 75.1 0.7 444.8 108.0 363.8 1.2 199.6 494.6 0.935 101.6 25.0 37.6 0.7 289.0 86.7 226.5 1.3 160.3 258.4 1.136 101.6 25.0 37.6 0.7 273.2 86.7 226.5 1.2 160.3 258.4 1.137 203.2 25.0 37.6 0.7 389.7 86.7 226.5 1.7 160.3 308.0 1.338 203.2 25.0 37.6 0.7 255.7 86.7 226.5 1.1 160.3 308.0 0.839 304.8 25.0 37.6 0.7 417.7 86.7 226.5 1.8 160.3 308.0 1.440 304.8 25.0 37.6 0.7 302.1 86.7 226.5 1.3 160.3 308.0 1.0

41 Brosens and Gemert [27] 150.0 56.0 39.2 3.1 297.4 72.4 226.3 1.3 64.4 213.4 1.442 150.0 56.0 39.2 3.1 284.5 72.4 226.3 1.3 64.4 213.4 1.343 150.0 56.0 78.5 3.1 378.5 102.4 320.1 1.2 91.0 301.8 1.344 150.0 56.0 78.5 3.1 446.3 102.4 320.1 1.4 91.0 301.8 1.545 150.0 56.0 117.7 3.1 418.3 125.4 392.0 1.1 111.5 369.6 1.146 150.0 56.0 117.7 3.1 480.8 125.4 392.0 1.2 111.5 369.6 1.347 200.0 56.0 39.2 3.1 231.6 72.4 226.3 1.0 64.4 213.4 1.148 200.0 56.0 39.2 3.1 309.6 72.4 226.3 1.4 64.4 213.4 1.549 200.0 56.0 78.5 3.1 400.1 102.4 320.1 1.3 91.0 301.8 1.350 200.0 56.0 78.5 3.1 445.4 102.4 320.1 1.4 91.0 301.8 1.551 200.0 56.0 117.7 3.1 436.0 125.4 392.0 1.1 111.5 369.6 1.252 200.0 56.0 117.7 3.1 534.6 125.4 392.0 1.4 111.5 369.6 1.453 150.0 56.0 39.2 3.1 272.6 72.4 188.9 1.4 64.4 178.1 1.554 150.0 56.0 39.2 3.1 260.8 72.4 188.9 1.4 64.4 178.1 1.555 150.0 56.0 78.5 3.1 326.7 102.4 267.2 1.2 91.0 251.9 1.356 150.0 56.0 78.5 3.1 376.1 102.4 267.2 1.4 91.0 251.9 1.557 150.0 56.0 117.7 3.1 382.9 125.4 327.3 1.2 111.5 308.6 1.258 150.0 56.0 117.7 3.1 381.1 125.4 327.3 1.2 111.5 308.6 1.259 200.0 56.0 39.2 3.1 273.8 72.4 188.9 1.4 64.4 178.1 1.560 200.0 56.0 39.2 3.1 328.5 72.4 188.9 1.7 64.4 178.1 1.861 200.0 56.0 78.5 3.1 393.2 102.4 267.2 1.5 91.0 251.9 1.662 200.0 56.0 78.5 3.1 413.3 102.4 267.2 1.5 91.0 251.9 1.663 200.0 56.0 117.7 3.1 431.5 125.4 327.3 1.3 111.5 308.6 1.464 200.0 56.0 117.7 3.1 427.3 125.4 327.3 1.3 111.5 308.6 1.4

65 Diab and Wu [29] 200 40 15.5 3.45 182.0 49.5 133.6 1.4 49.7 133.8 1.466 200 40 15.5 3.45 150.0 49.5 133.6 1.1 49.7 133.8 1.167 200 40 15.5 3.45 165.0 49.5 133.6 1.2 49.7 133.8 1.268 200 40 30.9 3.45 253.0 69.9 188.9 1.3 70.2 189.3 1.369 200 40 30.9 3.45 222.5 69.9 188.9 1.2 70.2 189.3 1.270 200 40 30.9 3.45 231.0 69.9 188.9 1.2 70.2 189.3 1.2

(continued on next page)

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Table 3 (continued)

No Ref Lb (mm) fc (MPa) Ef⁄tf (GPa) Er (GPa) Pu exp/width (N/mm) Chen and Teng’s model Proposed model

Le Pr Pu pr Pex/Ppr Le Pu Pex/Ppr

71 200 40 46.4 3.45 281.0 85.7 231.3 1.2 86.0 231.8 1.272 200 40 46.4 3.45 273.0 85.7 231.3 1.2 86.0 231.8 1.273 200 40 46.4 3.45 262.0 85.7 231.3 1.1 86.0 231.8 1.174 200 40 38.4 3.45 228.5 77.9 210.5 1.1 78.3 210.9 1.175 200 40 38.4 3.45 230.0 77.9 210.5 1.1 78.3 210.9 1.176 200 40 76.8 3.45 322.7 110.2 297.6 1.1 110.7 298.2 1.177 200 40 76.8 3.45 333.0 110.2 297.6 1.1 110.7 298.2 1.178 200 40 9.4 3.45 142.7 38.6 104.3 1.4 38.8 104.5 1.479 200 40 9.4 3.45 131.0 38.6 104.3 1.3 38.8 104.5 1.380 200 40 18.9 3.45 217.0 54.6 147.6 1.5 54.9 147.9 1.581 200 40 18.9 3.45 208.0 54.6 147.6 1.4 54.9 147.9 1.482 200 40 28.3 3.45 258.3 66.9 180.7 1.4 67.2 181.1 1.483 200 40 28.3 3.45 249.0 66.9 180.7 1.4 67.2 181.1 1.4

84 Present study 250.0 40.0 15.5 0.4 242.3 49.5 133.6 1.8 124.0 211.5 1.185 250.0 40.0 15.5 0.4 219.0 49.5 133.6 1.6 124.0 211.5 1.086 250.0 40.0 15.5 0.4 174.0 49.5 133.6 1.3 124.0 211.5 0.887 250.0 40.0 30.9 0.4 198.9 69.9 188.9 1.1 175.3 299.0 0.788 250.0 40.0 30.9 0.4 222.5 69.9 188.9 1.2 175.3 299.0 0.789 250.0 40.0 30.9 0.4 236.0 69.9 188.9 1.2 175.3 299.0 0.890 250.0 40.0 46.4 0.4 324.5 85.7 231.3 1.4 214.7 366.2 0.991 250.0 40.0 46.4 0.4 441.9 85.7 231.3 1.9 214.7 366.2 1.292 250.0 40.0 46.4 0.4 368.0 85.7 231.3 1.6 214.7 366.2 1.093 250.0 40.0 38.4 0.4 438.0 77.9 210.5 2.1 195.3 333.2 1.394 250.0 40.0 38.4 0.4 416.0 77.9 210.5 2.0 195.3 333.2 1.295 250.0 40.0 38.4 0.4 376.5 77.9 210.5 1.8 195.3 333.2 1.196 250.0 40.0 76.8 0.4 484.0 110.2 297.6 1.6 276.2 465.9 1.097 250.0 40.0 76.8 0.4 446.2 110.2 297.6 1.5 276.2 465.9 1.0

Average 1.3 1.2

622 H.M. Diab, O.A. Farghal / Composites: Part B 58 (2014) 618–624

Eqs. (2) and (3) used to predict the effective bond length andbond strength of FRP sheets bonded to concrete can be modifiedto include the adhesive factor, ba, as:

Le ¼ffiffiffiffiffiffiffiffiffiffiffiffiffi

Ef tf

b2a

ffiffiffiffif 0c

ps

ð5Þ

Pu ¼ 0:427bbbLbf Le

ffiffiffiffiffiffiffiffibaf 0c

qð6Þ

3.1. Accuracy of the proposed model

There is plenty of experimental data available on the behaviorof bonded joint of FRP–concrete interface under the axial load,i.e. single or double shear test. However, the properties of adhesivelayer or putty have been neglected in most of these researches andthere is no available data about the adhesive layer. In this study,containing the results of 97 tests on FRP–concrete bonded jointswas built. The data base includes tests reported by Chajes et al.[24], Maeda et al. [25], Talijsten [26], Brosens and Gemert [27],De Lorenzis et al. [28], Diab and Wu [29] and those from the recentstudy. Details of these tests can be found in their references. Theelastic modulus, Ea in Table 3, which represents the weakest mod-ulus of elasticity of either adhesive or primer used to bond FRPsheets, is obtained from its reference except for that reported inthe Maeda et al. [25] was obtained from another study carried bythe same authors [12].

3.2. Predicted bond strength

The predicted bond strength obtained according to both of theChen and Teng’s model and the proposed model are compared withthat obtained experimentally from the present database, seeTable 3. The predicted bond strength (Ppr) per unit width and thepredicted effective bond length (Le Pr) as well as the test-to-pre-

dicted bond strength ratios of each model are given in Table 3.From the table, it can be noticed that both of the two models accu-rately predict the bond strength of the FRP–concrete interface,however the wholly average test-to-predicted bond strength ratioof the proposed model (1.20) is less than that of the Chen andTeng’s model (1.32). Moreover, Fig. 3(a) and (b) shows a compari-son between experimental bond strengths and those predicted bythe two models for two types of adhesive layer, flexible and rigidones. The flexible adhesive is representing the adhesive layerwhich has a modulus of elasticity less than one GPa, similar to thatused by the author and Brosens and Gemert [27]. On the otherhand, the rigid adhesive is repressing the adhesive layer whichhas modulus of elasticity more than 4.0 GPa, similar to that usedby Chajes et al. [24] and Talijsten [26]. Based on the results pre-sented in Table 3 and Fig. 3(a) and (b), the proposed model givesaccurate predictions for FRP sheets bonded to concrete with flexi-ble adhesive and reasonable results for FRP sheets bonded to con-crete with rigid adhesive layer. Indeed, the Chen and Teng’s modelis the most accurate model among the most existing bond strengthmodels for the normal type of the adhesive layer as that reportedby Lu et al. [30]. On the contrary, it is noticed that this modelunderestimates the bond capacity by 40% on the average valuefor the specimens that were carried by both De Lorenzis et al.[28] and the authors in the current study, where the modulus ofelasticity of adhesive is less than one GPa, flexible adhesive. Themodification proposed by the authors improves the accuracy ofthe Chen and Teng’s model to consider all type of adhesive. A un-ique feature of the present model is that, the proposed model canbe used for all types of adhesive taking the properties of adhesiveinto consideration based on the elastic modulus of the weakestlayer of epoxy resin or primer.

3.3. Predicted effective bond length

Even though, there is plenty of experimental data available onthe behavior of FRP bonded to concrete, the properties of adhesive

(a) Specimens using flexible type of adhesive, which its modulus of elasticity less than one GPa

(b) Specimens using rigid type of adhesive, which its modulus of elasticity more than three GPa

Fig. 3. A comparison between test and predicted results using Chen and Teng’s model and the proposed model.

Table 4Experimental and predicted effective bond length of test results.

Ref. Specimen ID Types of FRP Ef⁄tf (GPa) Ea (GPa) Le exp (mm) Chen and Teng’s model Proposed model

Le Pr Le exp/Le Pr Le Pr Le exp/Le Pr

Wu and Diab [29] CFRPN Carbon 38.4 3.45 75 77.9 1.0 78.3 1.02CFRPN Carbon 76.8 3.45 110 110. 1.0 110.7 1.01GFRPN Glass 9.4 3.45 45 38.6 1.2 38.7 1.22GFRPN Glass 18.9 3.45 50 54.6 0.9 54.9 0.93GFRPN Glass 28.3 3.45 65 66.9 1.0 67.2 1.0BFRPN Basalt 15.5 3.45 50 49.5 1.0 49.7 1.02BFRPN Basalt 30.9 3.45 60 69.9 0.9 70.2 0.93BFRPN Basalt 46.4 3.45 85 85.7 1.0 86.0 1.0

Present study BFRPL1 Basalt 15.5 0.4 110 49.5 2.2 124.0 0.9BFRPL2 Basalt 30.9 0.4 210 69.9 3.0 175.3 1.2BFRPL3 Basalt 46.4 0.4 250 85.7 2.9 214.7 1.2CFRPL1 Carbon 38.4 0.4 200 77.9 2.6 195.3 1.0CFRPL2 Carbon 76.8 0.4 250 110 2.3 276.2 0.9

Average 1.6 1

H.M. Diab, O.A. Farghal / Composites: Part B 58 (2014) 618–624 623

layer or putty have been neglected in most of these researches andthere is no available data about the properties of adhesive and theeffective bond length. The predicted effective bond lengths (Le Pr)via Chen and Teng’s model and the proposed model are comparedwith those obtained experimentally (Le exp) [29] as shown inTable 4. The concept of effective bond length is defined throughthe strain distribution for which the effective bond length is thedistance required for the strain to be vanished as shown in

Fig. 4(a) and (b). Such a figure shows the strain distribution andthe effective bond length for one layer of BFRP sheet bonded toconcrete with two different types of epoxy, ordinary and flexibleadhesive. The comparison between the two FRP strain profilesshows that the effective bond length of FRP sheet mainly dependson the type of adhesive layer. Moreover, Table 4 shows that theeffective bond length of FRP sheets bonded to concrete with ordin-ary adhesive falls within 120 mm which is similar to those already

Fig. 4. FRP-sheet strain distribution along the bonded length of specimens.

624 H.M. Diab, O.A. Farghal / Composites: Part B 58 (2014) 618–624

reported by Mazzoti et al. [22]. On the other hand, the effectivebond length of FRP sheets bonded to concrete with flexible adhe-sive ranges from 100 to 300 mm. Moreover, Table 4 shows thatthe proposed model accurately predicts the effective bond lengthof the FRP sheets bonded to the concrete with different types ofadhesive, ordinary or flexible ones. On the other hand, the Chenand Teng’s model precisely predicts the effective bond length ofspecimens using ordinary adhesive as a bonding material and itcouldn’t predict the effective bond length of specimens using flex-ible adhesive as bonding material. The modification proposed bythe authors considerably improves the accuracy of the Chen andTeng’s model to predict the effective bond length taking into con-sideration the type of adhesive which was neglected in most ofexisting bond strength models.

4. Conclusion

This paper discussed the bond characteristic between FRPsheets bonded to concrete via flexible adhesive. Using differenttype of FRP sheets, the double-shear test shows that the flexibleadhesive layer increases both of the effective bond length andthe ultimate bond strength of FRP sheets. The assessment of theflexible adhesive has been conducted using the test results of 97pull specimens collected from the existing literature. The mostpopular analytical models available in the literature were adoptedto match data obtained experimentally. It is worthwhile to notethat, these models need to be modified to consider the type ofadhesive layer. These models underestimate both of the bondstrength and the effective bond length of the test results. Conse-quently, the most accurate bond strength model introduced byChen and Teng [5] is modified to consider the properties of the

adhesive layer. A unique feature of the new modified model is thatit can be used to accurately predict both of bond strength andeffective bond length of FRP sheets taking into consideration theproperties of bonding materials. The properties of adhesive layerhave been considered based on the elastic modulus of the weakestlayer of epoxy resin or primer.

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