Strengthening Slabs Using Externally-bonded Strip Composites

Composites: Part B 39 (2008) 1125–1135

Contents lists available at ScienceDirect

Composites: Part B

journal homepage: www.elsevier .com/locate /composi tesb

Strengthening slabs using externally-bonded strip composites: Analysisof concrete covers on the strengthening

Amen Agbossou a,*, Laurent Michel b, Manuel Lagache a, Patrice Hamelin b

a Laboratoire Optimisation de la Conception et Ingénierie de l’Environnement (LOCIE), Polytech’Savoie, Université de Savoie, 73376 Le Bourget du Lac Cedex, Franceb Laboratoire de Génie Civil et Ingéniérie Environnementale (LGCIE), Université CBL Lyon I, 82 Boulevard N. Bohr, 69622 Villeurbanne Cedex, France

a r t i c l e i n f o

Article history:Received 22 November 2007Accepted 6 April 2008Available online 20 June 2008

Keywords:A. Carbon fibreA. PlatesB. Interface/inter-phaseC. Damage mechanicsC. Finite element analysis (FEA)

1359-8368/$ - see front matter � 2008 Elsevier Ltd. Adoi:10.1016/j.compositesb.2008.04.002

* Corresponding author. Tel.: +33 (0) 479 758 850;E-mail address: [email protected] (A

a b s t r a c t

This study pertains to the experimental and theoretical behaviour of slabs strengthened by fibre rein-forced polymer (FRP). The experimental results show that FRP significantly increases punching failurestress, resulting in a reduction of slab rotation around the loading column. The theoretical investigationpresents a finite element model for the bending of strengthened slabs. The developed model considersthe concrete as a 3D multi-layered non-linear material and explicitly takes into account the steel rein-forcement and the FRP strips. The proposed model is then used to analyse the effects of a concrete coveron the reinforcement and repairs. In the analysed cases, the results show that an average reduction in theconcrete shear modulus, between steel rod and FRP, of more than 30% leads to significant reductions ofstress and slab stiffness.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Due to the increasingly severe conditions (legal and used) of ci-vil engineering structures, the reinforcement and repair of workswith composite material is increasingly recommended [1]. Thereare many studies on the strengthening of works done with fibrereinforced polymer (FRP). Most of these concern beams [2,3]. Thesestudies analyse: (i) the effects of bonded fibre-reinforced compos-ites in the strengthening of structural materials and on techniquesfor bonding, (ii) the structural strengthening of concrete using un-stressed or prestressed composite, (iii) environmental durability,time-dependent behaviour and fatigue, and (iv) design and specifi-cation for the structural strengthening of beams. None of thesestudies considers the effect of the concrete, between the steel rodsand the FRP, on the behaviour of the strengthened structure.

The first section of this study analyses the strengthening ofslabs using externally-bonded FRP composites, as well as indicatesthe relation between the bending behaviour and the mechanicalproperties of concrete between FRP and steel rods.

In the second section, the experimental results are presented,illustrating the effect of FRP on the stiffness and punching stressof slabs. In Section 3, a theoretical analysis is developed, simulatingthe bending behaviour of slabs reinforced by FRP strips. In thisanalysis, the concrete of the area between FRP strips and lowersteel reinforcements is regarded as multi-layer non-linear con-crete. Finally, the proposed model is used to analyse the effects

ll rights reserved.

fax: +33 (0) 479 758 144.. Agbossou).

of the layer of concrete covering the steel on the bending behaviourof FRP-strengthened slabs.

2. Experimental analysis

2.1. Experiment preparation and test scheme

Four steel-reinforced concrete slabs of 1.25 m � 1.25 m � 0.1 mwere made in laboratory conditions.

The concrete was made to class C30. Table 1 presents the ratioof components in the concrete mixture and the actual mechanicalproperties. The compression tests were carried out on 16 � 32 testsamples in accordance with standard NF P 18-406. The tensilestrengths were obtained by following NF P 18-408.

The steel reinforcement was made from ST65 C welded squaremesh (S = 636 mm2, s = 100 � 100, £s = 9 mm � 9 mm) for thelower side and ST35C welded square mesh (S = 385 mm2, s =100 � 100, £s = 7 mm � 7 mm) for the upper side. The elastic limitof steel was 500 MPa. The minimum cover of steel rebars was25 mm. Plastic wedges were used for spacing. The steel truss wascentred following the symmetry axis of the slab in both directions.

The composite reinforcement was made of ROCC� UD carbonsheet developed by GTM.

Two epoxy components, CAB and GTM ROCC, were used toimpregnate and bond carbon fibre reinforced polymer (CFRP) stripson slabs according to the recommendations of the manufacturer.The number of CFRP strips used was decided according to thedesired strength of the slab. Therefore, n-layers (n = 1, 2, 3)

mailto:[email protected]

http://www.sciencedirect.com/science/journal/13598368

http://www.elsevier.com/locate/compositesb

Table 1C30 concrete formulation

Cement CPA52.5 (kg/m3)

Water(l/m3)

Sand(kg/m3)

Rock(kg/m3)

Compressionstrength (MPa)

Tensile strength(MPa)

350 192 850 1020 36 3.3

1280

1200

100×100 ST35C

ST65C e

F

1126 A. Agbossou et al. / Composites: Part B 39 (2008) 1125–1135

represented the number of CFRP strips used in x (0�) and y (90�)direction. The symbol [0n/90n] represents strengthening withn-layers of CFRP in x (0�) and n-layers in y (90�) direction. Thethickness and the width of each strip layer were 1 and 5 mm,respectively. Table 2 presents the mechanical properties of theanalysed slabs.

The CFRP strips were positioned during a preliminary layout.Regularly-spaced CFRP strips were bonded to the lower face of

the slab after the surface had been sandblasted (Fig. 1). The spacingbetween the middle of each parallel strip was 10 mm. The bondingwas done according to the manufacturer’s recommendations. Theresin was applied to the concrete and then CFRP bonding was usedas a primer. Excess resin was removed by passing a roller with uni-form pressure (Figs. 1–3).

The slabs were placed on four 1.2 m lines with simple supportsat the slab edges (Fig. 2). A 500 kN hydraulic jack was used to applythe load locally to a surface 10 � 10 cm in the centre of the slab.

Table 2(a) Mechanical properties and (b) presentation of the analysed slabs

CFRP Concrete Steel

(a)Elastic modulus (GPa) 79.94 ± 4.6 30 200 ± 4Poisson’s ratio – 0.2 0.3Tensile failure stresses (MPa) 925 ± 48 2.5 500Crushing failure stresses (MPa) – 35.4 500Density (kg/m3) – 2500 7850Stress–strain relations Linear elastic. Non-plastic r ¼ Eb

e1þð1þe=e0Þ2

with e0 ¼ 2 fcEb

Elastic–plastic (perfect plasticity)Layer thickness (mm) 1 Down ST 65C Up ST 35CLayer width (mm) 5Layers spacing (mm) 15

(b)Slab R0: no CFRP Slab R2: reinforced slab after initial pre-cracking: two layers in x direction, two layers in y direction, [02/902]Slab R1: one layer in x direction,

one layer in y direction [01/901]Slab R3: three layers in x direction, three layers in y direction [03/903]

Fig. 1. CFRP slabs: (1) marking; (2) the carbon strips are impregnated and bonded on the concrete slab; (3) removing excess resin by rolling; (4) additional layering.

Fig. 2. Loading system and slab sizes.

Fig. 3. Location of the strain gauges on: (a) steel reinforcement; (b) CFRP material.

A. Agbossou et al. / Composites: Part B 39 (2008) 1125–1135 1127

Slab R2 was pre-cracked before being reinforced in order toevaluate the effect of externally- bonded CFRP reinforcement onslab behaviour.

Load, displacement, as well as steel and composite strains weremeasured during the slab loading. Two LVDT transducers (dis-placement range of ±100 mm) were used to monitor displacement.The first (LVDT1) was located on the top face of the slab, close tothe jack. The second (LVDT2) was on the lower face, to monitorthe central deflection of the slab. A 1000 kN transducer located un-der the jack measured the load.

Steel strain was measured by means of three 120 X strain gaugeswith a 10 mm grid length located on the lower steel rebars. Theywere used to measure strain in both directions of the steel truss(Fig. 3a). Then, strain gauges were placed on the CFRP strips in themiddle of the slab in both directions (Fig. 3b). Five strain gaugeswere bonded onto the CFRP close to the critical punching perimeter.

2.2. Test results

2.2.1. Flexing behaviour: bending stiffness of strengthened slabsFig. 4 shows the maximal load displacement curves and the load

strain curves, which illustrate the effects of externally-bondedstrip composites on the behaviour of the slab. Table 3 presentsthe main values of the experimental results.

The composite reinforcement permits a significant increase inslab stiffness. Indeed, the mid-span deflection of R1 and R3-typeslabs are reduced respectively by 35% and 45% (Fig. 4). An initialobservation is that the cracking load of RC slab is increased by40% for slab R1 and by 48% for slab R3. For slab R2, the crackingload does not increase significantly.

It is important to note that when the externally-bonded CFRP isapplied after cracking, the stiffness of the RC slab is also increased(see Fig. 4 slab R2). It should also be stated that CFRP increases theinitial cracking load of slabs (Table 3). In addition, it decreases themaximal bending displacement, while significantly increasing thefailure stress and stiffness of slabs after the concrete cover hasbeen cracked. Therefore the total strain energy (integral of load–displacement curves) tends to decrease with the presence of CFRPstrips and with the increase in the number of strips.

2.2.2. Ultimate behaviour: punching shear failuresThe failure of all slabs occurs by punching. The composite rein-

forcement increases the failure load by approximately 15% forslabs reinforced by one layer (R1: [01/901]) of CFRP strip and byapproximately 30% for slabs reinforced by three layers (R3: [03/903]).

In order to observe the punch cracking pattern in the slabs, eachslab was cut down in the middle, revealing a cross section of theslab.

The punching shear crack pattern consists of one or two maincracks. As in Menétrey [4], the main crack may be divided intothree straight lines, each with a different angle (a1, a2 and a3).The steel rebars decrease these angles. Consequently, the numberof angles depends on the number of steel rebar layers. For a slabwith two punching cracks, the second crack corresponds to astraight line with angle a4.

The analysis of crack patterns in slabs R1, R2 and R3 shows thatthe external bonding of CFRP on the lower surface affects thepunching mechanism (Figs. 5 and 6), which results in a slight mod-ification of angle a2. The value of a2 decreases (for R1 and R3) asCFRP thickness increases (Table 4).

For the initially pre-cracked slab R2, repair with CFRP limits thetwo main crack mechanisms as shown in slabs R1 and R3. A de-tailed analysis of crack patterns in slab R2 shows also that the CFRPmay change the initial cracking failure mode [5].

3. Theoretical analysis

3.1. Finite element model of FRP-strengthened slabs

The main questions regarding this model are: what model touse for reinforced concrete, how to take into account the tensilecracking in concrete and how to associate elements of multi-layer composite with damageable concrete elements. The aimof the proposed models is to take into account the variablemechanical properties of the concrete between the CFRP andthe steel rebars.

There are two methods of calculating damage in concrete: (i)the discrete method (the discrete crack approach), and (ii) the

0

40

80

120

160

2 4 6 8 10 12

Bending displacement in middle of slab (mm)

Load

(kN

)

R0R1

R3

Tensile strain on steel rebar in middle area of slab (%)

Load

(kN

)

0

40

80

120

160

1 2 3 4 5

R3R1

R0

40

80

120

160

0 2 4 6 8


Load

(kN

)

R2 without CFRP = R0 with initial cracking

R2 = R0 with initial cracking + 2 layers of CFRP[02/902]

Fig. 4. Experimental bending behaviour of slabs strengthened by FRP (fibre reinforced polymer).

Table 3Experimental results

R0 R1 R3

Initial stiffness (kN/mm) 27.18 37.21 24.97Stiffness after cracking in concrete cover (kN/mm) 10.69 17.65 26.24Failure load (kN) 121.2 139.5 154.2


smeared crack approach. The discrete method aims to reproducethe propagation of the individual cracks by re-meshing the modelwith developing cracks. The smeared crack approach simulates themacroscopic behaviour of the concrete, by taking into account thereduction of cracks through stiffness and stress transfer (specificdamage laws of concrete). In this study, the models were devel-oped with the second approach. The next section presents two ba-sic models which, together, analyse the behaviour of RC structuresstrengthened with FRP.

Fig. 5. Punching fai

3.1.1. Reinforced concrete model (RCM)Fig. 7 presents the two concrete models that have been

developed.The first reinforced concrete model (RCM1) represents the

beam or the slab as a multi-layer material (Fig. 7a). The second(RCM2 – Fig. 7b) specifically takes into account reinforcement bybar or link elements. In this study, a perfect bond between concreteand steel was assumed. The type of concrete used was element SO-LID65 in ANSYS. This element was used for calculating three-dimensional solids with or without reinforcing bars (rebars). Thesolid is capable of cracking in tension, crushing in compression,creep nonlinearity and large deflection geometrical nonlinearity.The William–Warnke model shows the failure criterion of concretewith five experimental constants [6]. The uniaxial stress–strainrelation was defined by the civil engineering Eurocode.

For the RCM2 model, the reinforcing bar adopted elementLINK8. This three-dimensional element is a uniaxial tension-com-

lure of slab R1.

Fig. 6. Cracks in slabs’ cross-section.

Table 4Punching angle values

CFRP thickness Slab R0 0 Slab R1 1 mm Slab R2 2 mm Slab R3 3 mm

a1 13� 25� 17� 21�a2 21� 17� 18� 15�a3 35� 32� 36� 38�a4 – 44� – 34�


pression element with three degrees of freedom at each node. Plas-ticity, creep, swelling, stress stiffening, and large deflection capa-bilities are included. The bar was considered an elastic andperfectly plastic material. The strength was defined according tothe data in the test.

Fig. 7. Reinforced concrete models: (a) RCM1 and (b) RCM2 and the developed fibre-rein(d) FRPM2 and (e) FRPM3.

Table 5 compares the two Reinforced Concrete Models, RCM1and RCM2.

3.1.2. Fibre-reinforced-polymer model (FRPM) coupled with reinforcedconcrete model

The first proposed model of FRP (Fig. 7c) is an 8-node structuralelement (3D), designed to replicate thick layered shells and solids.The element (Solid46) allows up to 250 different material layers.Each node of this element has three degrees of freedom to movein directions x, y, and z. The nodes of the composite elements areconnected to those of adjacent concrete elements. The use of thiscomposite element is beneficial, but it often leads to an unsatisfac-tory meshing condition of the basic finite element method. It can,however, be useful for thick FRP.

forced-polymer model (FRPM) coupled with reinforced concrete model; (c) FRPM1,

Table 5Comparison of RCM1 and RCM2

Model Advantages Disadvantages

RCM1 Easy modelling Not very exact solution in areas with non-homogeneous distribution of steels

Low computing time Stresses in reinforcement depend on theused homogenized law

RCM2 Takes into account theexact position of steel parts

Modelling and meshing are complex(necessary on account of nodal locations)

Direct determination ofstresses in reinforcement

High computing time with convergenceproblems


The second FRP model (Fig. 7d) is a 3D element having mem-brane (in-plane) stiffness, but no bending (out-of-plane) stiffness(Shell41). The element (FRPM2) also has three degrees of freedomat each node: translations in nodal directions x, y and z. As for(FRPM1), the nodes of the FRP elements are connected to thoseof the adjacent concrete elements. This element is beneficial andeasy to implement. Unfortunately, its use is limited to a singlelayer of FRP.

The third developed FRP model (Fig. 7e) is a multi-layer com-posite (FRPM3) able to take into account both in-plane stiffnessand bending behaviour. This element (Shell99) allows up to 250layers. It has six degrees of freedom at each node: three transla-tions in the nodal directions and three rotations around axes x, yand z. The nodes of the composite elements are connected to thoseof the adjacent concrete elements. In order to ensure the compat-ibility of the degrees of freedom (dof), one can change the condi-tions of rotation into specific coupling conditions at the point ofinterface of the concrete and FRP. The development of this modelrequires specific programming to ensure element continuity (Fig.7e). The model allows analysis of the failure of multiple layers ofFRP using quadratic failure criteria (such as Tsai-Wu criteria). Inaddition, because of this model’s multiple layers, it can shed newlight on the bonding problems between the concrete and the exter-nally-bonded FRP.

To summarize, the following models are developed and com-bined: (i) RCM1 + FRPM1 (homogenized reinforced concrete + 3D

Fig. 8. Typical meshes of RCM2 + FRP3 of the analysed: (a) beams and (b)

multi-layer thick composite); (ii) RCM1 + FRPM2 (homogenizedreinforced concrete + composite in-plane element); (iii) RCM1 +FRPM3 (homogenized reinforced concrete + multi-layer compos-ite); (iv) RCM2 + FRPM1 (specific modelling of reinforcement inconcrete + 3D multi-layer thick composite); (v) RCM2 + FRPM2(specific modelling of reinforcement in concrete + composite in-plane element); (vi) RCM2 + FRPM3 (specific modelling of rein-forcement in concrete + multi-layer composite).

Fig. 8, shows typical meshes of RCM2 + FRPM3 of the analysedbeams and slabs. The number of elements required for beam anal-ysis was 1458 (880 3D elements, 498 link elements and 80 shellelements). For slabs analysis, 6296 elements (5408 3D elements,728 link elements, 160 shell elements) were used. The total nodesof the slab were 6561. The choice of these numbers was based onpreliminary studies in which different finite element sizes wereused. These numbers represent a good balance for the analyzedbeams and slabs, between the computational time and the numer-ical accuracy of results.

3.2. Numerical and experimental results

3.2.1. Beams with externally-bonded CFRPThis section aims to validate the proposed model by analysing

the behaviour of beams strengthened with composites.To show the usefulness of the developed model compared to the

usual numerical approaches (RCM1), the three-point bending andfour-point bending tests were presented.

First, numerical results (Fig. 9a and b), in the case of three-pointbending tests, were compared for the following models:(RCM1 + FRPM1, 2, 3) and (RCM2 + FRP3). Then, the consistencywas examined between proposed models RCM2 + FRPM3 and theexperimental results for four-point bending tests (Fig. 9c–e).

The properties of the analyzed beams are presented in Table 6.Fig. 9a and b present a numerical comparison of models

RCM1 + FRPM1, 2, 3 and RCM2 + FRPM3, applied to a beam withand without external FRP. The analysis concerns a three-pointbending load. Table 7 shows particular values of the bendingbehaviour of the analysed beam. As expected, the FRP bonded toa beam increases the first crack load and serviceability load. The

slabs with first cracking pattern. (c) Zoom of typical cracking pattern.

0 1 2 3 4 5 6 Bending displacement (mm)

RCM1

RCM1+FRPM1

RCM1+FRPM2 RCM1+FRPM3

RCM2+FRPM3

0 10 20 30 40 50 60Load (kN)

RCM1

RCM1+FRPM1

RCM1+FRPM2

RCM1+FRPM3

RCM2+FRPM3

0

20

40

60

80

100

0 5 10 15 20

Experimen

0

10

20

30

40

50

60

Tens

ile s

tress

in s

teel

0

160

240

320

Bending displacement (mm)

Load

(kN)

Load

(kN)

ba

c d

e

RCM2

Fig. 9. Numerical analysis of three-point bending tests of beams: (a) load versus bending displacement in the middle of the beam; (b) stress in steels versus applied load. Plotof four-point bending tests results compared to numerical results of (c) beam without CFRP; (d) beam with CFRP strengthening; (e) load versus CFRP strain in the middle ofthe beam.


ultimate bending displacement decreases significantly with theuse of FRP.

The relevance of the developed models is the stress analysis ofthe steel and the FRP composites. Table 8 gives the stress valuesin the middle of the beam under a 3-point bending load (48 kN).The stress analysis in the FRP shows that the highest stress is rx

(stress parallel to beam) followed by ry and rxy. It should also beshow that the three composite models (FRPM1, FRPM2, FRPM3)combined with the homogenized concrete model (RCM2) lead tosimilar results for bending displacement and stress in the steeland the FRP.

However, when one compares the results of models RCM1 +FRPM1, 2, 3 and RCM2 + FRPM1, 2, 3 (Fig. 9a and b), differencesare observed in the values of the steel rods. These differences aremainly due to the fact that the RCM1 approach uses the homoge-nized law to determine stress values in the steel, whereas the otherproposed approach directly gives the stress values in reinforce-ment elements.

Fig. 9c–e compare experimental and numerical results in thecase of four-point bending load. The models RCM2 + FRPM1, 2, 3,were used. The results illustrate the accuracy of the FEM approachespecially the model (RCM2 + FRPM3).

However, in the case of slabs, usually less thick than beams,the use of the RCM1 model must be done with careful attentionto the thickness of each layer. For slabs, the difference betweenthe results of the models RCM1 + FRPM1, 2, 3 and RCM2 + FRPM1,2, 3 can become significant. As an illustration, one can considerthe bending of the slab (3 m long and 2 m wide and 100 mmthick).

Fig. 10 shows the stress (rx) in the steel reinforcement in thearea directly under the loading point of the slab. These stress val-ues (rx) as required by the model RCM1 are deducted from theclassical law of mixtures with mechanics of solid rules (homogeni-zation rule). For models RCM1 + FRPM1 and RCM1 + FRPM2, onecan note, as might be expected, a negative value of stress at thebeginning of the slab load, followed by unexpected positive values

Fig. 10. Stresses in the steel reinforcement in the area directly under the loadingpoint of the slab. Comparison of models RCM1 + FRPM1, RCM1 + FRPM3 andRCM2 + FRPM3.

Table 6Mechanical properties of the analysed beams of 0.15 m � 0.25 m � 2.5 m

CFRP Concrete Steel

Elastic modulus (GPa) 79.94 ± 4.6 34.52 200 ± 4Poisson’s ratio – 0.2 0.3Tensile failure stresses (MPa) 1380 3.5 500Crushing failure stresses (MPa) 1130 32.8 500density (kg/m3) 1500 2500 7850Stress–strain relations Linear elastic. Non-plastic r ¼ Eb

e1þð1þe=e0Þ2

with e0 ¼ 2 fcEb

Elastic–plastic; down: 2 �£ 14 mm; up: 2 �£ 8 mmLayer thickness (mm) 1LayerWidth (mm) 150 (beam width)Modulus (GPa) Ex = 117; Ey = 7; Ez = 7

Gxy = 4.2; Gxz = 4.2; Gyz = 2.7mxy = 0.25; mxz = 0.25; myz = 0.3

Distance between external supports 2 m.

Table 7Comparison of first crack load and serviceability load of analysed beam

Loads RCM2 RCM2 + FRPM1 RCM2 + FRPM2 RCM2 + FRPM3

First crack load (kN) 4.5 5.2 5.3 5.3Serviceability (kN) 18.7 32.1 33.5 34.2

Table 8Comparison of the stresses in the middle of the FRP for 48 kN applied load on theanalysed beam

Stress RCM1 + FRPM1 RCM1 + FRPM2 RCM1 + FRPM3

rx (MPa) 424 412 387ry (MPa) 5.77 5.90 5.60rxy (MPa) 0.57 �0.04 0.006


of stress. Whereas for the model RCM2 + FRPM3, the stress is neg-ative and decreases until the slab breaks.

This shows an example of the usefulness of the model RCM2 +FRPM3 compared to the usual models RCM1 + FRPM1 and RCM1 +FRPM2.

The applications of RCM1 + FRPM1, 2, 3 models for slabs oftenshow results, which depend on the estimated thickness of thehomogenized layer. Hence, models RCM2 + FRPM1, 2, 3 are bettersuited for slabs due to their ability to take into account explicit steelreinforcements and composites, without predetermining the layers’thickness. In addition, in order to take into account interface effects,one can introduce the FRP–concrete bond by means of contact ele-ments to the models RCM2 + FRPM1, 2, 3 without any difficulties.

3.2.2. Slabs with externally-bonded CFRPBased on a good correspondence between the experiment and

finite element models for various analysed beams, the RCM2 +FRPM3 model was used for slabs.

Fig. 11 shows a comparison of experimental and numerical re-sults for slabs R0, R1 and R3. Table 9 gives the stiffness results. Thereis a good correspondence between the numerical and experimentalresults for failure stress and stiffness after initial cracking in theconcrete cover. In contrast, for initial stiffness, significant discrep-ancies between numerical and experimental results can be noted.These discrepancies could be due mainly to measuring accuraciesof displacement misfit for the weak displacements measured atthe beginning of the tests. Confirmation of the good correspondencewas obtained by comparing the results of the numerical and exper-imental values of strain gauges on the rebars and the CFRP.

Fig. 11b–f compare the maximal bending displacement and thecracks in two slabs (one with an externally-bonded CFRP strip andthe other without CFRP). These figures display crack symbols atlocations of cracking in concrete elements. The crack elements lo-cated at the bottom of the slab were presented in these figures.Each element can crack in up to three different planes. The thirdcrack, which corresponds to final cracks in the elements, was pre-sented in Fig. 11 for different loading (Fig. 11d–f).

For the same load (Fig. 11d and e), the obvious effect ofstrengthening due to CFRP can be observed through the numberof crack symbols, which are significantly higher in the strength-ened slab (R1). The numerical results (Fig. 11f) show also that CFRPstrips change the distribution of cracks, allowing a larger numberof cracks as a result of increasing slab loading capacity.

Detailed analysis of the numerical results confirms the experi-mental punching failure.

The punching crack patterns are accurately evaluated by calcu-lating the angle w ¼ 2Dmax

L�a of the slab around the loading column.The effect of the CFRP strips (Fig. 12a) is a variation of the punchingload inversely proportional to the w angle. The maximum values ofw are comparable to those of a2 in Table 10. The results in Table 10clearly show a linear relation between punching cone angle a2 androtation w around the loading column. The use of CFRP decreasesthe w rotation value, which exhibits the same variation as thepunching cone angle a2. Therefore, an actual dependence seemsto exist between the rotation around the column, the punchingfailure load and the CFRP properties.

40

80

120

160

200

0 2 4 6 8 10 12

Loa

d (k

N)

R3 exp. + numeric.

R1 exp. + numeric.

R0 exp.+numeric.

a


g

b c

e f

R0 R1

R0 (load = 125 kN) R1(load = 125 kN) R1(load = 160 kN)

d

Fig. 11. Comparison: (a) numerical and experimental results; (b) bending displacement in R0 slab; (c) bending displacement in R1 slab and third crack symbols; (d) in R0 slabat 12.5 kN; (e) in R1 slab at 12.5 kN; (f) in R0 slab at 16 kN; and (g) punching mechanism of slab.

Table 9Comparison of the theoretical and experimental results

R0 R1 R3

Exp. value Num. value Exp. value Num. value Exp. value Num. value

Initial stiffness (kN/mm) 27.18 128.2 37.21 134.23 24.97 141.78Stiffness after cracking in steel cover concrete (kN/mm) 10.69 10.62 17.65 15.25 26.24 26.19Failure load (kN) 121.2 124.7 139.5 134.3 154.2 199.3


3.3. Effects of concrete cover

3.3.1. Concrete cover considered as inter-phase materialAs slabs and beams have been strengthened over the years,

structures have suffered severe strength and stiffness deteriora-tion of the concrete covering the steel due to tensile micro-cracks or aggressive environmental conditions such as humidity,alkali solutions and salt-water. As shown by Hernandez et al. [7],porosity due to micro-cracks, damages, and aging effects canlead to reduction of the concrete stiffness. They show that a

30% decrease of mortar density due to porosity can introduceapproximately a 14% reduction in concrete stiffness. The reduc-tion in the stiffness of cover concrete could be magnified bythe way durability is affected by the intensity of interactionsof the material with aggressive agents. The pores and capillariesinside cover concrete facilitate the destructive processes thatgenerally begin on the surface. While interacting with its serviceenvironment, concrete often undergoes significant alterationsthat frequently have very adverse consequences on its engineer-ing properties.

R2

R3

R1

0

50

100

150

200

250

5 10 15 20Rotation (0/00)

Load

(kN

)

Load

(kN

)

R0

0

50

100

150

200

250

5 10 15 20Rotation (0/00)

Rdcoating = R0 + Eci concrete cover : i = 1 to 4

Rdcoating+CFRP (01/901)

Rdcoating + CFRP (02/902)a b

Fig. 12. Load–rotation curves of: (a) slabs strengthened with FRP of increasing thickness ‘‘R0, R1, R2” and ‘‘R3”; (b) slabs, with weak modulus of concrete cover, strengthenedby CFRP.

Table 10Comparison of punching angle a2 and theoretical rotation w around the loadingcolumn

Experimental punching angle a2

(�)Rotation w(�)

Punching failure load(kN)

R0 21 19.03 124.7R1 17 14.28 134.3R3 15 12.44 199.3

Fig. 13. Model of concrete cover: four layers with degraded mechanical properties. (b1)discontinuity.


This section presents, numerically, the effect of the concrete’sproperties between the lower steel layer and the CFRP on the effec-tiveness of slab strengthening.

As in previous works on interface in composite material [8,9],the alteration in engineering properties of cover concrete is consid-ered a linear increase of Young’s modulus from the surface towardsthe steel reinforcements. With this assumption, the cover is there-fore considered as four concrete layers with modules (from theoutside towards the interior) Ec1, Ec2, Ec3 and Ec4.

Proposed 3D inter-phase model. (b2) Well known 2D interface with a displacement


In reality, the concrete cover does not degrade uniformly but itsload transfer capability decreases through the formation of discretecracks. However, in order to highlight the problem of FRP strength-ening in a different way, the ‘‘graded cover” assumption (Fig. 13)was adopted.

Such modeling of the concrete cover is motivated by the factthat an interface zone between phases has at least two distinctproperties: strength (related to interfacial failure) and stiffness (re-lated to stress transfer between components). Instead of analysingFRP–concrete interfacial failure (widely studied in literature), oneneeds to focus analysis on inter-phase stiffness properties, whichare important when considering composite mechanical properties.The principle of the proposed 3D model compared to the well-known 2D model is illustrated in Fig. 13b.

The Fig. 13b1 shows a schematic representation of concretecover considered as an inter-phase zone with a gradient in proper-ties between FRP and steel re-rebar zone. The Fig. 13b2 shows auseful simplified 2D model where macroscopic deformations arethe same, but a 2D interface has replaced the 3D inter-phase zone.

The use of theoretical linear variation concrete modulus in theconcrete cover zone could be seen, here, as a method to modelthe deformation of the 3D inter-phase by allowing a displacementdiscontinuity by means of non-linear behaviour of cover concreteduring the load. The magnitude of displacement discontinuityshould be a function of the traction vector in the direction of thediscontinuity and stiffness properties of the inter-phase (coverconcrete – which is a non-linear material in the proposed analysis).Therefore, one can assume in the 3D model (Fig. 13a) that there areperfect bonds between CFRP and concrete, which could be materialwith poor inter-phase mechanical properties.

The proposed model takes into account the FRP/concrete sepa-ration and yields to solve interface problems in terms of damage inconcrete stiffness and failure.

When the FRP/concrete bond becomes weak, the low slab load-ing leads to interfacial failure of FRP and concrete. Therefore, theeffectiveness of strengthening with the FRP will become consider-ably lower especially for poor mechanical properties of cover.

3.3.2. Numerical analysis of concrete cover considered as n-layermaterial

Three cases of slabs with degraded concrete cover with one ortwo layers of CFRP were analysed. To illustrate the principal conclu-sion, Fig. 13 presents the results of a slab with 2.5 cm of ‘‘graded”concrete cover. The lower concrete cover of the analysed slab wasconsidered as four layers of concrete material in which the modulusincreases from 1 to 4 GPa. The first layer (1 GPa) is the lower facelayer. (Ec1 = 1 GPa, Ec2 = 2 GPa, Ec3 = 3 GPa, Ec4 = 4 GPa). Results(Fig. 12b) show that a reduction in the properties of the concretecover considerably limits the effectiveness of the CFRP.

Obtaining the initial properties of the slab becomes possibleonly with very thick composites. In these cases, failure is not bypunching but by bending. The obvious decrease in slab perfor-mance is mainly due to the low quality of concrete between steeland CFRP. This low quality leads to a weak load transfer of the

externally-bonded composite strips. The other analysed cases oflow quality concrete cover show that, even with a perfect bond be-tween concrete and CFRP, an average decrease in concrete modulusof less than 30% ensures improved effectiveness of the reinforce-ment or repair of the analysed slabs. In reality, such a reduction

d ¼ EInitialModulus�Ewith damage

Modulus

Ewith damageModulus

¼ 30%

� �could be due to high micro-cracks,

aging phenomena and service environment. The service environ-ment effects, coupled with porosity and high micro-cracks in coat-ing concrete could yield to significant reduction of cover concrete.

4. Conclusion

This study presents an experimental and numerical analysis ofthe bending behaviour of reinforced slabs with externally-bondedFRP. The results indicate the effect of the composites on punchingfailure in slabs. They show the influence of the low mechanicalquality of the concrete between steels and CFRP strips on the effec-tiveness of the externally-bonded CFRP strips. One notes for punch-ing that the composites tend to considerably reduce the overallrotation angle of the slab around the loading column and conse-quently tend to increase the stress of punching failure. For lowproperties of the cover, a reduction in the concrete cover modulustends to decrease the effectiveness of thin CFRP strips and leadsto bending failure. These results show that one limiting elementamong others in externally-bonded strip composite could be themechanical quality of the concrete between steel and composite.

Acknowledgements

The authors acknowledge Emily Coffey and Rivers Camp fortheir reading advice on this paper.

References

[1] American Concrete Institute 440.2R-02: Design and construction of externallybonded FRP systems for strengthening concrete structures, American Concr.Inst., USA; 2002.

[2] Ferrier E, Avril S, Hamelin P, Vautrin A. Mechanical behavior of RC beamsreinforced by externally bonded CFRP sheets. Mater Struct, Rilem2003;36(262):522–9.

[3] Teng JC, Chen JF, Smith ST, Lam L. FRP strengthened RC structures. John Wiley &sons; 2002.

[4] Menétrey Ph. Synthesis of punching failure in reinforced concrete. Cem ConcrCompos 2002;24(6):497–507.

[5] Michel L, Ferrier E, Bigaud D, Agbossou A. Criteria for punching failure mode inRC slabs reinforced by externally bonded CFRP. Compos Struct 2007;81(3):438–49.

[6] William KJ, Warnke EP. Constitutive model for the triaxial behavior of concrete.In: Proceedings, international association for bridge and structural engineering,ISMES, Bergamo, Italy, vol. 19; 1975. p. 174.

[7] Hernandez MG, Izquierdo MAG, Ibanez A, Anaya JJ, Ullate LG. Porosityestimation of concrete by ultrasonic NDE. Ultrasonics 2000;38:531–3.

[8] Lagache M, Agbossou A, Pastor J, Muller D. Role of interface on the elasticbehavior of composite materials: theoretical and experimental analysis. JCompos Mater 1994;28(12):1140–57.

[9] Agbossou A, Pastor J. Thermal stresses and thermal expansion coefficients ofn-layered fiber-reinforced composites. Compos Sci Technol 1997;57(2):249–60.

Documents

Strengthening Slabs Using Externally-bonded Strip Composites