an experimental study on ion of frp plates bonded to concrete

8/8/2019 An Experimental Study on ion of FRP Plates Bonded to Concrete

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An experimental study on delamination of FRP platesbonded to concrete

C. Mazzotti *, M. Savoia, B. FerracutiDISTART Structural Engineering, Viale Risorgimento 2, University of Bologna, 40136 Bologna, Italy

Received 18 April 2006; received in revised form 7 April 2007; accepted 9 April 2007Available online 14 June 2007

Abstract

Results of an experimental campaign on FRPconcrete delamination are presented. Specimens with different bonded lengths andplate widths have been tested. Strain gauges along the FRP plate have been used to measure longitudinal strains. For long bondedlengths, progressive debonding along the specimens has been followed. Starting from experimental data, average shear stressslips datahave been computed. By post-processing these data, non-linear interface laws for two different plate widths have been calibrated.Increase of maximum shear stress with decreasing plate width has been observed, whereas no signicant plate width effect on fractureenergy and delamination force has been found. Experimental tests have been simulated by adopting a numerical bond-slip model and theabove mentioned non-linear law for the FRPconcrete interface. Numerical results in good agreement with experimental results havebeen obtained, both at low and very high loading levels. 2007 Elsevier Ltd. All rights reserved.

Keywords: FRP; Concrete; Delamination; Interface; Experimental study

1. Introduction

When using FRP plates or sheets to strengthen r.c.beams, FRPconcrete bonding plays an important role.Since delamination is a very brittle failure mechanism, itmust be avoided in practical applications. In reinforcedconcrete beams externally strengthened for bending, deb-onding may occur close to plating extremities due to loadtransfer from concrete to FRP plate (end debonding),

along the beam length for the same reason (intermediatedebonding) [1,2]. In these cases, mode II cracking occurs(tangential relative displacement between two materials).Debonding may be also due to diagonal shear cracks orto the presence of appreciable irregularities of concrete sur-face. In this case, mixed mode cracking is typicallydetected, with both tangential and normal displacements(with signicant contribution of normal-peeling-stresses).

In the case of shear strengthening, debonding of FRPsheets glued to beam lateral faces is the typical failure mode[3], with mode II cracking and bonding lengths typicallyshorter than effective bonding length.

Denition of a correct interface law is then important topredict ultimate failure load due to delamination, especiallyin the case of short bonded lengths. FRPconcrete inter-face law is also required to estimate the effectiveness of strengthening under service loadings. Stress concentrations

close to exural cracks in concrete [4] or plate end must becompared with maximum shear stress [5], in order to pre-serve durability of the anchorage.

Bond behaviour depends on mechanical and physicalproperties of concrete, composite and adhesive. In [6],some recently proposed interface laws are reviewed, anda new (simplied) law is proposed by the authors makinguse of a rened Finite Element analysis [7]. This studyclearly shows that, from the experimental point of view,evaluation of maximum delamination force or appliedforceplate displacement curves only is not sufficient to

0950-0618/$ - see front matter 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.conbuildmat.2007.04.009

* Corresponding author. Tel.: +39 051 2093251; fax: +39 051 2093236.E-mail address: [email protected] (C. Mazzotti).

www.elsevier.com/locate/conbuildmat

Available online at www.sciencedirect.com

Construction and Building Materials 22 (2008) 14091421

Construction and Building MATERIALS
mailto:[email protected]:[email protected]


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provide data to dene a shear stressslip interface law.Very accurate tests with measure of strains or displace-ments (depending on the adopted measurement technique)along the FRP plate are needed, together with advancedpost-processing techniques of experimental results.

Very few experimental studies can be found in literaturewhich can be useful to calibrate a FRPconcrete interfacelaw. Among them, the following studies can be quoted:Chajes et al. [8] performed delamination tests using CFRPplates 25.4 mm wide and different bond lengths (from50.8 mm to 203.4 mm); Taljsten [9] conducted severaldelamination tests considering both steel and compositeplates; FRP plates were also considered by Aiello andPecce [10]; Miller et al. [11] adopted a particular bendingset-up to perform delamination tests on carbon-ber sheetsglued to concrete; Brosens [12] and Xiao et al. [13] adopted

symmetric setups by gluing two CFRP sheets to two con-crete specimens subject to traction test whereas Yao et al.[14] proved the reliability of the near end supported sin-gle-shear test. In all these tests, failure load and strainsalong the FRP plate were measured. In [6], an interestingcomparison between predictions of experimental testresults making use of different interface laws proposed inthe literature ( [15,16] and others) can be found. Moreover,in [17] it is shown that classical bilinear interface law maysignicantly overestimate debonding force for short bond-ing lengths. Finally, as described in [6] and with some addi-tional details in the following Section, the adopted setupfor delamination tests may have some signicant effect inexperimental results.

In the rst part of the present paper, results of an exper-imental campaign on FRPconcrete end debonding arepresented. Eight specimens with different bonded lengthsand widths have been tested. A number of closely spacedstrain gauges has been used to measure strains along theFRP plate. Starting from experimental data, average shearstresses between two subsequent strain gauges and corre-sponding shear slips have been computed. These data havethen been used to calibrate a fractional non-linear interfacelaw. The (estimated) value of maximum transmissible loadby an anchorage of innite length is used to dene the

value of fracture energy of interface law. This quantity is

assumed as a constraint in the calibration procedure of unknown parameters of interface law. Mode II fractureenergy, in fact, is an important condition to be satisedto predict the correct value of maximum transmissible loadthrough the interface. Moreover, the softening branch of the law, where experimental results are typically very scat-tered, is strongly inuenced by the value of fracture energy.

Results obtained by gluing the plate starting from thefront side of concrete specimen (conventional set-up) orat a given distance from it are compared ( Figs. 1 and 2).Moreover, the effect of plate width on parameters of inter-face law (delamination force per unit width, fractureenergy, peak shear stress and shape of interface law) hasbeen investigated.

Nomenclature

BL plate bonded lengthE a elastic modulus of adhesiveE c elastic modulus of concrete

E p elastic modulus of CFRP platesF max maximum transmissible force by an anchorageof innite length

G f fracture energy of interface lawbc concrete block widthbp plate widthc1, c2 parameters involved in the denition of k b

f cm mean compressive stress f ctm mean tensile strengthhp plate thickness

k b width factorn exponent of non-linear interface laws plateconcrete slip s slip corresponding to peak shear stressx distance from beginning of bonded platee plate longitudinal strains peak shear stress

Fig. 1. Setup A FRP plate bonded starting from the front side of concrete block: (a) tensile stresses from FE model (in the elastic range); (b)

specimen after debonding.

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Finally, a bond-slip numerical model, originally pre-sented in [18], has been used to simulate the experimentaltests. Concrete and plates are considered as elastic materi-als and the proposed non-linear interface law is adoptedbetween two materials. Numerical results are found to bein good agreement with experimental results.

2. Geometry and mechanical properties of specimens

2.1. Specimen preparation

The mode II end debonding of CFRP plates bonded toconcrete surface has been investigated by performingexperimental tests according to pushpull single-shear testscheme and by varying plate width and bonded length.Two plate widths (50 and 80 mm) and four bonded lengths(50, 100, 200 and 400 mm) have been considered for a totalnumber of eight specimens.

Concrete specimen dimensions were150 200 600 mm.They were fabricated by using normal strength concrete,poured into wooden forms and externally vibrated. Thetop was steel-troweled.

Specimens were demoulded after 24 h and covered withsaturated clothes for 28 days; after that, they were stored atroom temperature and variable humidity inside thelaboratory.

Mean compressive strength f cm = 52.6 MPa, mean valueof elastic modulus E cm = 30700 MPa and Poisson ratiom = 0.227 have been obtained (according to Italian stan-dards [19]) from compression tests and mean tensilestrength f ctm = 3.81 MPa from splitting tests.

For composite plates, CFRP Sika CarboDur S plates 50

and 80 mm wide and 1.2 mm thick have been used. Accord-

ing to technical data provided by the producer, plates havecarbon-ber volumetric content equal to 70% and epoxymatrix. Mean elastic modulus E p = 195200 MPa has beenobtained from tensile tests.

Top surfaces of concrete blocks have been grinded witha stone wheel to remove the top layer of mortar, until the

aggregate was visible (approximately 1 mm). Plates havebeen bonded to the top surface of blocks by using a1.5 mm thick layer of two-components Sikadur-30 epoxyadhesive. From tensile tests, mean strength 30.2 MPa andmean elastic modulus E a = 12840 MPa have been obtainedfor the adhesive. No primer before bonding has been used.Curing period of specimens was between 10 and 15 dayprior to testing.

2.2. Position of bonded surface along the specimen

In order to investigate sensitivity of bond failure to theposition of bonded surface along the specimen, a series of FE numerical investigations have been performed beforeexperimental tests. Two different positions of bonded sur-face on the concrete specimen have been considered (seeFig. 1), i.e., close to the front side of concrete block (whereforce is applied) or at a certain distance from it.

This study showed that if CFRP plate is bonded close tothe front side of the concrete specimen (Setup A), very hightensile stresses occur in this concrete portion ( Fig. 1a). As aconsequence, adopting this test setup, an early failure typ-ically occurs due to concrete splitting of a prism with trian-gular section ( Fig. 1b, see also [14]). Shape of concreteprism is independent of bonded length, with edges of the

section about 35 mm long; similar results can be found alsoin [3]or, in the case of steel or composite bars embedded inconcrete, in [20] or [21], respectively.

On the contrary, when plate bonded length starts farfrom the front side (Setup B), tensile stresses are muchsmaller with respect to previous case ( Fig. 2a) due to theconnement effect of concrete, and a more regular growth

Fig. 2. Setup B FRP plate bonded far from the front side of concreteblock: (a) tensile stresses from FE model (in the elastic range); (b)specimen after debonding.

Fig. 3. Cracking pattern close to main exural cracks in FRP-strength-

ened reinforced concrete beam.

C. Mazzotti et al. / Construction and Building Materials 22 (2008) 14091421 1411


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of delamination along the specimen can be followed duringtest (Fig. 2b).

In the present experimental investigation, plate bondedlength starts 100 mm far from the front side of specimen.In this way, the interface behaviour is not affected byboundary effects and it is then more representative of mate-

rial behaviour. On the contrary, in the authors opinion,tests on plates glued close to the front side of the specimen(Setup A) provides for information on FRP bonding inproximity of cracks, such as those in concrete due to exurein FRP-strengthened beams. Comparison of Figs. 1b and 3clearly shows that failure mechanisms are very similar.

The results of the present study adopting Setup B will bethen compared in Section 6.4 with others obtained by theauthors [22], with identical concrete specimens, FRP platesand adhesives, but with plate bonding starting at the frontside (Setup A).

3. Experimental setup and instrumentation

The experimental setup is depicted in Fig. 4a. Concreteblock was positioned on a rigid frame with two steel reac-

Fig. 4. (a) Geometry of FRPconcrete specimens, scheme and (b) picture

of experimental setup (Setup B).

Table 1Distance (mm) of strain gauges from the beginning of the anchorage, fordifferent values of bonded length (BL)

BL x1 x2 x3 x4 x5 x6 x7 x8 x9 x1050 10 20 30 40100 10 20 30 40 50 60 70 80 90200 10 20 30 40 50 60 80 100 140 190400 10 20 40 70 110 150 210 270 330 390

0

400

800

1200

1600

BL =50 mm ( )

0

500

1000

1500

2000

2500

BL =100 mm

( )

BL =200 mm

( )

BL =400 mm

( )

0

500

1000

1500

2000

2500

0 100 200 300 4000

500

1000

1500

2000

2500

x (mm)

0 40 80 120 160 200 x (mm)

0 20 40 60 80 x (mm)

0 10 20 4030 50 x (mm)

Fig. 5. Delamination tests (Setup B, bp = 50 mm) Longitudinal strains in

FRP plates along the bonded lengths. Load levels are reported in Table 2 .



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tion elements in order to prevent horizontal and verticaldisplacements; front reaction element was 60 mm height.The extremity of the plate was mechanically clampedwithin a two steel plate system. A hinge allowed for rota-tion around the vertical axis. Traction force was appliedto the steel plate system by means of a mechanical actuator

(Fig. 4b); tests were then performed by controlling the dis-placement of plate free end.A load cell was used to record the applied traction force

during test. Along the CFRP plate, a series of four-to-tenstrain gauges (depending on plate length) was placed, inthe centerline, to measure longitudinal strains. For eachbonded length, distance x i of strain gauges from the begin-ning of bonded length is reported in Table 1 . For bothplate widths (50 and 80 mm), the same strain gauge posi-tions were adopted.

4. Results of delamination tests

4.1. Strains along CFRP plates

Tests have been carried out by performing a rst cycle of loading up to 4 kN of traction force with subsequentunloading, followed by a monotonic loading at a rate of about 0.1 kN/s. In the nal stage of the test, i.e., duringdelamination with attainment of maximum force, plateend displacement rate was about 50 l m/s and tests wereconducted under control of loaded end displacement.

Results from specimens with 50 mm width CFRP platesare presented rst. For different bonded lengths (50, 100,200, 400 mm), longitudinal strains along the plate at vari-

ous loading levels are reported in Fig. 5ad. Levels of applied force corresponding to different curves are givenin Table 2 . Strains at x = 0 are calculated from values of applied force as e 0 = F /E p Ap .

Analogous results from tests on CFRP plates with80 mm width are reported in Fig. 6ad; values of appliedforce are reported in Table 3 .

Some remarks can be drawn concerning experimentalresults for both plate widths (50 and 80 mm). For bondedlengths from 100 mm to 400 mm, FRP strains show anexponential decay starting from the loaded section ( x = 0)for low-to-medium values of applied force, whereas theyare almost constant close to loaded end, for high force levelsdue to onset of delamination phenomenon. These resultsare similar to those already reported in other papers [23].

On the contrary, for the 50 mm bonded length, decayprole of strains along the anchorage is almost linear,also for low levels of applied force. These prolesindicate a more uniform distribution of shear stresses

along the anchorage. In fact, the 50 mm bonded length

Table 2Levels of applied force (kN) corresponding to FRP strain proles in Fig. 5(bp = 50 mm)

BL F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11

50 4 8 10 12 13 14100 4 8 12 16 18 20 22 22.3200 4 8 12 16 18 19.8 19 18

400 4 8 12 16 20 22 23 21 20 19 18

0 10 20 30 40 500

400

800

1200

1600

0 20 40 60 80 1000

400

800

1200

1600

2000

0 40 80 120 160 2000

500

1000

1500

2000

2500

0 100 200 300 4000

500

1000

1500

2000

2500

BL =50 mm

x (mm)

x (mm)

x (mm)

x (mm)

( )

BL =100 mm

( )

BL =200 mm

( )

BL =400 mm

( )

Fig. 6. Delamination tests (Setup B, bp = 80 mm) Longitudinal strains inFRP plates along the bonded lengths. Load levels are reported in Table 3 .



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is signicantly smaller than effective anchorage length(minimum length assuring maximum FRP anchoringforce), which is l e = 175 mm according to Italian GuideLines [5].

For all specimens, failure was caused by shearing of alayer of concrete 12 mm thick (see Fig. 2b). Thicknessof concrete attached to the adhesive was uniform underthe whole plate, so assessing no boundary effects close tothe initial section of the anchorage occurred.

Finally, a sufficiently stable delamination was observedfor long bonded lengths (BL = 200, 400 mm). In strain pro-les reported in Figs. 5 and 6, experimental data measuredduring delamination (corresponding to slightly decreasingvalues of applied force) are indicated by hollow squaremarkers.

4.2. Maximum transmitted forces by the anchorage

Values of maximum transmitted force at failure as a func-tion of bonded length are reported in Fig. 7aandbfor50and80 mm plate widths, respectively. Interpolation curves have

been also calculated to obtain values of maximum transmis-sible force F max by an anchorage of innite length. ValuesF max,50 = 22.8 kN and F max,80 = 36.2 kN have beenobtained for two different plate widths. In the same gures,results obtained from numerical simulations using thebond-slip model described in Section 7 are also reported.

4.3. Fracture energy of interface law

It can be demonstrated that the following relation holdsbetween maximum transmissible force F max by an anchor-age of innite length and mode II fracture energy G f of interface law:

F max bp ffiffiffiffiffiffiffiffi2 E phpG f p ; 1where E p , hp , bp are elastic modulus, thickness and width of FRP plate, respectively. Eq. (1) has been derived for a gen-eral non-linear interface law [9,24], with reference to a pureshear bond-slip model with plane deformation for bothconcrete and plate. Eq. (1) was previously derived by Wuet al. [25] considering a bilinear interface law and by Bro-sens [12] in the case of a power law.

Making use of Eq. (1), values of fracture energy

G f,50 = 0.5251 N/mm and G f,80 = 0.5171 N/mm have beenobtained for 50 mm and 80 mm plate widths, respectively.According to these results, tests on plates of different widthprovided for very similar values of fracture energy. Accord-ing to studies reported in the literature (see Section 6.3),some difference was expected. In the authors opinion,inuence of plate width on fracture energy was not evidentin the present tests due to small aggregate size of concrete.

5. Post-processing of experimental results

Measures of FRP strains along the plate have been usedto calculate shear stress and slip distributions along thebonded lengths. The procedure illustrated in [16,24] isadopted, to which the reader is addressed for additionaldetails.

Local x-axis has the origin at the initial bonded section,where load is prescribed, and xm = BL at the free end of theplate.

Considering an elastic behaviour for the compositeplate, average shear stress ^s i 1=2 between two subsequentstrain gauges is written as a function of the difference of measured strains.

Moreover, assuming for sake of simplicity perfect bond-ing at the last strain gauge position (no slip at x = xm ) and

neglecting concrete strain with respect to FRP counterpart,

Table 3Levels of applied force (kN) corresponding to FRP strain proles in Fig. 6 (bp = 80 mm)

BL F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F11 F12

50 4 8 12 16 20 21 22100 4 8 12 16 22 26 28 30 30.5200 4 8 12 16 22 26 30 32 33400 4 8 12 16 22 26 30 34 37 36 34 32 30

0 200 400 600Bond length (mm)

0

5

10

15

20

25

M a x

i m u m

l o a d

( k N )

exp. resultsinterp. curvenum. data


0

10

20

30

40

M a x

i m u m

l o a d

( k N )

exp. resultsinterp. curvenum. results

Fig. 7. Delamination loads vs. bonded length: experimental results,interpolation curve and numerical results from bond-slip model; (a)bp = 50 mm, (b) bp = 80 mm.



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9 for 50 and 80 mm plate widths, respectively. Curves referto values calculated for loading levels reported in Tables 2and 3. When computing shear stresses and slips, someirregular values in FRP strain proles for high loading lev-els have been removed.

Comparing the data, some interesting conclusions for

both plate widths can be drawn:(a) Stiffness of initial branch (slip 6 0.02 mm) is almost

independent of bonded length. The only exceptionis represented by results obtained from the smallestbonded length (50 mm). In this case, length of theanchorage is so small that actual interface slip doesnot vanish at the end of the plate (i.e., at x = xm ).Hence, the procedure adopted to obtain slip prolesalong the plate underestimates the actual slip. Forthis reason, these data have not been used to calibratethe interface laws (see the next section).

(b) Curves exhibit a maximum value of shear stress fora FRPconcrete slip of about 0.04 mm; for higherslips, an evident softening behaviour has beenfound, with shear stress decreasing for increasingvalues of slip. Experimental results are in this regionvery scattered.

6. Calibration of a non-linear interface law

6.1. The interface law

When a plate is bonded to a concrete specimen and issubject to axial load up to failure (i.e., in tangential direc-

tion with respect to the interface), Mode II shear failureoccurs [26]. In fact, only a small layer of concrete closeto interface is subject to very high shear stresses (few milli-metres depth), and criterion of the maximum release raterequires that fracture propagates along it.

Bonding between FRP plate and concrete is typicallyrepresented by an interface law. The interface law mustreproduce an almost linearly elastic behaviour for smallslips with a maximum value for shear stress and a softeningbranch for higher slips.

In Ref. [17], a fractional law has been proposed:

s p s s

s

n

n 1 s= sn ; 2

similar to that proposed by Popovics [27] for constitutivelaw of concrete under compression and later adopted alsoby Nakaba [15] to interpolate experimental results fromdelamination tests. In Eq. (2), s , s are maximum shearstress and corresponding slip, whereas n > 2 is a parametermainly governing the softening branch.

Fracture energy of the law can be written in the form:

G f Z 1

0s p spd sp g f ns s; 3

where g f is an analytical function of exponent n:

g f n p1

n 1 12n 1

sin2p =n: 4

6.2. Calibration of interface laws parameters

In the present study, experimental results are used tocalibrate an interface law according to Eq. (2). Both shearstressslip data ( ^s i 1=2,

^

si 1=2) and mode II fracture energyG f are used to evaluate the three unknown parameters of interface law in Eq. (2), i.e., s , s, n.

A least square minimization between theoretical andexperimental shear stressslip data is performed, adoptingas a constraint in the minimization procedure the valueof fracture energy obtained from Eq. (1), i.e.,

mins ; s;n X

J

i1s is ; s; n s exp;i

2; 5a

subject to constraint G f g f ns s F 2max;exp2 E phpb2p ; 5b

where J is the total number of experimental data andF max,exp is the (asymptotic) value of maximum transmissi-ble force by an anchorage of innite length (according toSection 4.2).

This procedure is very simple since, from Eq. (5b), thepeak slip s can be written as an explicit function of theremaining parameters s , n; the optimization procedure thenreduces to a two-parameter minimization.

6.3. Effect of plate width

The calibration process has been applied to experimen-tal data obtained for both 50 and 80 mm plate widths.The values of parameters are reported in Table 4 , togetherwith fracture energies of the laws. In Fig. 10a and b, thetwo interface laws are reported and compared with shearstressslip experimental data. Even though experimentalresults are very scattered, the interface laws seem toapproximate quite well the interface behaviour also in thesoftening branch.

Results obtained for two different plate widths can becompared. Delamination force per unit width, fractureenergy and peak shear stress are typically considered asa function of plate and concrete specimen widths. Twomain different formulas to take this effect into accounthave been proposed in the literature. Starting from aset of experimental results obtained from homogeneous

Table 4Parameters and mode II fracture energy of interface laws for differentplate widths

Plate width bp (mm) Parameters of interface law Fracture energy

s MPa smm n G f (MPa/mm)

50 9.14 0.033 4.1876 0.5251

80 6.63 0.038 3.7518 0.5171

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before failure). First of all, it can be veried that adoptingSetup A (bonding starting at the front side of the specimen)stiffness of the interface in the linear range is lower than in

Setup B, denoted by a less sharp decay of strains alongFRP plate. Moreover, the last strain prole before failureadopting Setup B indicates almost complete delamination,which is experimentally detected, with a small decrease of applied load with respect to maximum load. On the con-trary, with Setup A, due to the splitting of the concretewedge at the front side of the specimen, FRP-delaminationcannot be followed experimentally.

Moreover, delamination loads as a function of bondedlength obtained with two different setups are compared in

Fig. 13a. For 50 mm bonded length, delamination loadreduction when plate bonding starts from the front sideof concrete specimen is very signicant (about 60% lesswith respect to Setup B). On the contrary, for long bondedlengths, boundary effect affects only slightly the value of delamination load. Theoretically, for bonded length

approaching innity, maximum transmissible force shouldbe the same, independently of setup adopted for tests. Inthe present case, even for the 400 mm bonded length, nostable delamination was obtained with Setup A and corre-sponding asymptotic value of delamination load was thenslightly lower than obtained with Setup B. Since maximumtransmissible force is needed to estimate fracture energy of interface law according to Eq. (1), Setup B is then moreappropriate.

Finally, interface laws calibrated by post-processingexperimental results obtained from Setups A and B arecompared in Fig. 13b. The two curves are very different:maximum shear stress predicted from Setup A tests isabout one-half of that obtained from Setup B, whereas cor-responding slips are quite similar. Hence, in the authorsopinion, two different setups should be suitably chosenaccording to specic purpose of the investigation: gluingplates starting from the front side of the specimen (SetupA) provides for information on FRP bonding in proximityof cracks (see Fig. 3), such as transverse cracks in concrete

0 40 80 120 160 2000

500

1000

1500

2000

2500 BL =200 mm

x (mm)

( )

0 100 200 300 4000

500

1000

1500

2000

2500 BL =400 mm

x (mm)

( )

Fig. 11. FRP plate bonded starting from the front side of concrete block(Setup A, see Fig. 1) strains in FRP plates along the bonded lengths(bp = 50 mm; see [22] for further details).

BL =400 mm ( )

0 100 200 300 4000

500

1000

1500

2000

2500 Setup A

Setup B

x (mm)

Fig. 12. Strains along FRP plate for tests performed according to Setup Aand Setup B: curves refer to 12 kN applied force and to the last recorded

data before failure due to debonding.


0

5

10

15

20

25

M a x

i m u m

l o a d ( k N )

Setup A: exp. resultsSetup A: interp. curveSetup B: exp. resultsSetup B: interp. curve

0 0.2 0.4 0.60

2

4

6

8

10

Setup A

Setup B

(MPa)

s (mm)

Setup A Setup B

Fig. 13. (a) Delamination loads vs. bonded length, with FRP platebonded starting from the front side of concrete block (Setup A) or 100 mmfar from it (Setup B); (b) FRPconcrete interface laws by post-processing

experimental results.



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due to exure in FRP-strengthened beams; on the contrary,tests with plate bonding far from concrete edge (Setup B)provides for experimental data more suitable for the cali-bration of a shear stressslip interface law, as well as topredict failure due to end debonding.

7. Numerical simulation of tests

Experimental tests have been numerically simulated, inorder to verify the accuracy of the proposed plateconcreteinterface law.

A bond-slip kinematic model has been adopted, origi-nally presented in [18] and more recently in [17], to whichthe reader is addressed for additional details. The modelis based on the assumption of pure extension for concreteand FRP plate. Interaction between two materials is mod-eled by the non-linear interface law reported in Eq. (2), col-lecting all non-linear compliance contributions of concretecover and adhesive. As a consequence, concrete and FRPplate are considered as elastic materials. A nite differencediscretization is used for governing equations, whose vari-ables are axial displacements and stress resultants of con-crete and plate.

Some comparisons between experimental and numericalresults are reported in Fig. 7 (delamination forces) andFigs. 1417 (FRP strain proles).

Strain distributions in FRP plate along the bondedlength are given in Figs. 14a, b and 15a, b for 50 mmand 80 mm plate widths, respectively. Loading levels arereported in Tables 2 and 3 . The higher load level is closeto failure load obtained experimentally.

Numerical results are generally in good agreement withexperimental data (considering the unavoidable scatteringof experimental results at high load levels). For all bondedlengths, the behaviour for low loads is well predicted, soassuring that stiffness of initial (elastic) branch of interfacelaws is correctly evaluated. Moreover, the bond-slip modelis able to follow the growth of delamination at constantload along the bonded length.

Shear stress distributions for bonded lengths equal to200 mm and 400 mm and plate width bp = 50 mm arereported in Figs. 16 and 17; smooth lines refer to dataobtained during delamination phase. Numerical and exper-imental results are in good agreement for low-to-mediumloadings. For very high loads, i.e., during plate delamina-tion, results obtained from post-processing experimentaldata are more irregular. In any case, position of maximumshear stress and rate of shear stress distribution along thebonded length are well predicted. As for the value of max-imum shear stress, according to experimental results itdecreases from 12 MPa at the beginning of delaminationto about 45 MPa when a certain length of plate is subjectto delamination. This behaviour suggests that, as physi-cally reasonable, delamination causes damage of concretesubject to high shearing deformation and peak shear stresstends to decrease. Of course, this phenomenon cannot be

captured adopting a local interface law.

x (mm)

( )

x (mm)

( )

0 40 80 120 160 2000

500

1000

1500

2000

2500

0 100 200 300 4000

500

1000

1500

2000

2500

BL =200 mm

BL =400 mm

Fig. 14. Strains along FRP plate: numerical () and experimental ( d , h )results (Setup B, bp = 50 mm); (a) BL = 200 mm, (b) BL = 400 mm.

0 20 40 60 80 1000

500

1000

1500

2000

2500

0 100 200 300 4000

500

1000

1500

2000

2500

BL =100 mm

x (mm)

( )

BL =400 mm

x (mm)

( )

Fig. 15. Strains along FRP plate: numerical and experimental ( d , h )

results (Setup B, bp = 80 mm); (a) BL = 100 mm, (b) BL = 400 mm.



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Finally, delamination failure load obtained numeri-cally as a function of bonded length has been comparedwith experimental results in Fig. 7a and b. Results con-rm that the proposed interface law provides for a goodprediction of failure loads for both plate widths. Forvery long bonded lengths, delamination load obtainednumerically coincides with the asymptotic value deter-mined from experimental results because, as describedin Section 6.2, the value of fracture energy obtained fromEq. (1) has been imposed in the evaluation of parametersof interface law. For very small bonded lengths (50 mm),the experimental load is lower than predicted numeri-cally: when the length of the plate is much smaller thanwidth of concrete prism, assumption of plane deforma-tion necessary for the formulation of a 1 D model isnot valid, and a more complex non-linear 3D modelshould be formulated.

8. Conclusions

Experimental results from FRPconcrete delaminationtests with different plate widths have been presented. Tests

have been performed by gluing plates 100 mm far from the

front side of concrete specimens (called Setup B). Appliedforce and strains along FRP plate have been measured.The (estimated) value of maximum transmissible force byan anchorage of innite length has been used to evaluatethe mode II fracture energy of interface law. Interface shearstressslip laws have then been calibrated starting fromexperimental data, adopting the value of fracture energyas a constraint in the error minimization procedurebetween experimental and predicted values.

Results have been compared with those recentlyobtained by the authors with identical specimens butbonded lengths starting from the front side of concreteprisms (Setup A). It is shown that Setup B is more appro-priate to obtain data for the calibration of a shear stress slip interface law.

The effect of plate width on main parameters of interfacelaw has been also investigated. No signicant effect ondelamination force per unit width and on mode II fractureenergy has been found. On the contrary, the shape of inter-face law changes signicantly: increasing plate width, peakshear stress decreases much more than predicted by formu-las reported in the literature and softening branch is less

brittle.

0 40 80 120 160 200 0 40 80 120 160 2000

4

8

12

BL =200 mm

x (mm) x (mm)

(MPa)

0

4

8

12

BL =200 mm

(MPa)

Fig. 16. Setup B Shear stresses along the interface for BL = 200 mm, bp = 50 mm. Numerical and experimental results at (a) low and (b) high loadinglevels.

(MPa)

0 40 80 120 4000

4

8

12

BL =400 mm

x (mm) x (mm)

(MPa)

0 100 200 300 4000

4

8

12

BL =400 mm

Fig. 17. Setup B Proles of shear stresses along the interface for BL = 400 mm, bp = 50 mm. Numerical and experimental results at (a) low and (b) highloading levels.



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Finally, numerical simulations of tests have been per-formed, and results in good agreement with experimentaldata have been obtained.

Acknowledgements

The authors thank the Sika Italia S.p.A. for providingCFRP plates and adhesives for the specimens. Financialsupports of C.N.R. (PAAS Grant 2001) and Departmentof Civil Protection (Reluis 2005 Grant Task 8: Innovativematerials for vulnerability mitigation of existing structures )are gratefully acknowledged.

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an experimental study on ion of frp plates bonded to concrete

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