Construction and Building Materials 37 (2012) 791–800

Contents lists available at SciVerse ScienceDirect

Construction and Building Materials

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

Simulation of concrete cover separation failure in FRP plated RC beams

Sahar Radfar, Gilles Foret ⇑, Navid Saeedi, Karam SabUniversité Paris-Est, Laboratoire Navier, Ecole des Ponts ParisTech, IFSTTAR, CNRS, 6 et 8 avenue Blaise-Pascal, Champs-sur-Marne, 77455 Marne-la-Vallée cedex 2, France

h i g h l i g h t s

" This study presents test results of 12 FRP strengthened RC beams and 3 control beams." Strengthened beams exhibited higher load capacity, lower ductility than reference beams." All strengthened beams failed by concrete cover separation which is a brittle failure." Numerical results also predict peeling-off failure for all strengthened beams." The thicker the FRP sheets, the higher the stiffness is and the lower the load capacity is.

a r t i c l e i n f o

Article history:Received 4 January 2012Received in revised form 24 July 2012Accepted 4 August 2012Available online 14 September 2012

Keywords:Peeling-offConcrete cover separationStrengtheningFinite element analysisExperiments

0950-0618/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.conbuildmat.2012.08.020

⇑ Corresponding author. Tel.: +33 1 64 15 37 13; faE-mail addresses: sahar.radfar@enpc.fr (S. Radfar),

navid.saeedi@enpc.fr (N. Saeedi), karam.sab@enpc.fr (

a b s t r a c t

The flexural strength of a reinforced concrete beam can be increased by bonding a FRP sheet to the ten-sion face. Nevertheless, this type of reinforcement may cause a premature debonding failure. This paper isconcerned with the failure by concrete cover separation; in other words by peeling-off. Four series of FRPplated RC beams and one group of control beams were tested in a four-point bending setup where eachgroup consisted of three beams. All strengthened beams failed by peeling-off. As a part of this studynumerical analyses using the commercial program; Abaqus have been carried out in order to predict thistype of failure. Comparisons between the predictions of the numerical model and test results show a verygood agreement indicating that the ultimate load, the beam behavior and the failure mode can be closelypredicted by using the proposed model.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The infrastructures in developed countries are aging and in addi-tion changes in their using purposes, increase of load level, con-structional faults and damages or deterioration demand adequatemaintenance and the upgrading of existing structural members.In other words, if structural members in a bridge or a building arerendered incapable of resisting the applied loads due to poor con-struction, marginal design or inferior materials, one solution is toincrease the load capacity of the affected members by strengthen-ing them. Externally-bonded fiber reinforced polymers and steelplates are now routinely used for strengthening the structuresand this method is a viable solution to costly replacement of dete-riorating structures. The advantage of strengthening by bonding isthat it increases the life of reinforced structures and that can limitthe stress concentrations in comparison to the assembly by bolting.Nowadays FRP sheets are used more than the steel plates because of

ll rights reserved.

x: +33 1 64 15 37 41.gilles.foret@enpc.fr (G. Foret),K. Sab).

numerous advantages such as minimum increases in structural sizeand weight, high strength-to-weight ratio, ease of site handling andexcellent corrosion resistance. A large number of researches showthat FRP-plated RC beams may fail by one of these failure modes:(a) flexural failure by FRP rupture, (b) flexural failure by crushingof compressive concrete, (c) shear failure, (d) concrete cover sepa-ration (also referred as ‘‘end-of-plate failure through concrete’’,‘‘concrete rip-off failure’’, ‘‘debond at rebar layer’’, ‘‘concrete coverdelamination’’ and ‘‘local shear failure’’), (e) plate end interfacialdebonding and (f) intermediate crack induced interfacial debond-ing. Among these failure modes, the first three are roughly the sameas those in conventional RC beams while the others are known aspremature failures because they prevent the strengthened RCbeams from attaining their ultimate flexural capacity; furthermore,these types of failure are brittle and unique to beams bonded with asoffit plate. Fig. 1 shows the failure modes of a FRP/steel strength-ened reinforced concrete beam.

Extensive research has been carried out on strengthening the RCbeams and their conventional failure. Shahaway et al. [1] haveexperimentally investigated the increase in strength and stiffnessof the beams provided by the bonded laminates. According to this

Fig. 1. Failure modes of a FRP/steel strengthened reinforced concrete beam.

792 S. Radfar et al. / Construction and Building Materials 37 (2012) 791–800

study, there exist an optimum number of CFRP layers below whichthe improvement in performance is not guaranteed, in otherwords, a few number of CFRP layers cannot control cracking atthe bottom of the beam and that result in initiating a prematurebond failure. With the increase in the number of CFRP layers, themoment capacity and stiffness increase and deflection decreases.The non-strengthened RC beams exhibit several widely spacedcracks as compared with the closely spaced cracks for the strength-ened laminated beams. Wang and Chen [2] proposed an analyticalmodel based on a conventional moment–curvature analysis forconcrete T-beams externally bonded with FRP laminates to theirsoffit and sides subjected to flexure, but their model does not pre-dict the premature failures. Hu et al. [3] performed numerical anal-yses to predict the ultimate loading capacity of FRP strengthenedRC beams which failed in a conventional manner. They also inves-tigated the influences of fiber orientation, beam length and rein-forcement ratios on the strength of the beams. Literature reviewof current attempts to explain the premature plate debondingmechanism contains three categories: an analytical approach, anempirical approach and a numerical approach. The empirical ap-proach tries to establish a relationship between plate debondingand various geometrical or force parameters and the analyticaland numerical approach try to predict the plate debonding failure.The empirical approaches lead to the control of plate geometrysuch as the width to thickness ratio to prevent plate debonding,for example for strengthening concrete beams with steel plates,it’s recommended that the ratio of the plate width to thickness isabove 60 according to McDonald [4] and above 50 according toSwamy et al. [5]. The researchers have also developed some theo-retical models to predict the premature failures of reinforced con-crete beams or plates strengthened in flexure by gluing steel/FRPplates to their tension sides [6–8]. Smith and Teng [9] have donea comprehensive review of plate debonding strength models pub-lished prior to their work in the following failure modes: plate endinterfacial debonding and concrete cover separation. Among thesemodels it’s easy to distinguish three categories of strength models,namely shear capacity based models, concrete tooth models, inter-facial stress based models. They conducted an experimental studywith an extensive database [10] which showed the deficiencies ofthose models and they also proposed a simple and conservativemodel based on the shear capacity approach; in this approachthe debonding failure strength is related to the shear strength ofthe concrete with no or only partial contribution of the steel shearreinforcement. Yao and Teng [11,12] continued the work of Smithet al. by an experimental study on plate end debonding failures andthey also gathered some test results available in literature. Further-more, they developed a shear capacity based predictive modelwhich can be improved for such failures. The second strength mod-el mentioned above is concrete tooth model which is based on theformation of teeth between adjacent cracks in the concrete coverand each tooth behaves like a cantilever under horizontal shearstresses at the base of the beam; when the tensile stress at the rootof a tooth exceed the tensile strength of the concrete the peeling-

off occurs. Raoof et al. [13,14] have conducted a theoretical (con-crete tooth model) and also an experimental study on externallyplated R.C. beams. They established a concrete tooth model andfrom the results they concluded that the models proposed for thedebonding failure of uncracked beams are conservative and cansafely be used for the analysis of beams in actual structures whichare precracked to some degree. In addition, they stated that theultimate plate peeling moment can be significantly lower thanthe associated failure moment of the unplated R.C. beam whichshows the importance of peeling failure in design. Unlike thisinvestigation, Benjeddou et al. [15] announced through an experi-mental study that CFRP plating increase the mechanical perfor-mance of the repaired RC beams and this technique can at leastrestore the mechanical performance of cracked or damaged RCbeams. Gao et al. [16,17] improved the concrete tooth model andthey proposed a failure diagram to show the relationship and thetransition among different failure modes for a given strengthenedRC beam. As cited, the third strength models are the interfacialstress based models, these models make use of interfacial stressesand a concrete failure criterion like the work of Saadatmanesh andMalek [18] in which it’s assumed that concrete cover failure is re-lated to high stresses at the plate end; therefore, the closed-formsolutions [19] for interfacial stresses are employed to predict fail-ure. Saxena et al. [20] has done a critical study about differentexisting models for the prediction of debonding failure. Based ontheir work, in addition to strength models mentioned above, thereis another approach to prevent debonding in design whose aim isto limit the debonding strain in FRP to a certain value but the re-sults of this approach are highly conservative. In numerical analy-ses of premature failure of concrete beams, one of the mostimportant parameters is the modeling of concrete behavior whichis discussed in detail in the following sections. Yang et al. [7] sim-ulated the concrete cover separation failure using a discrete crackand a linear elastic fracture mechanics model. Based on this inves-tigation the length of the plate has an important effect on the fail-ure mode; in other words, if all parameters are the same a beamstrengthened with a short plate is more likely to fail in concretecover separation mode. Lundqvist et al. [21] investigated numeri-cally and experimentally the minimum anchorage length of FRPneeded to prevent premature failure. They used the commercialFE program Abaqus and concrete was simulated by a damagedplasticity model. The failure load was defined as the load level atwhich the simulation fails to converge. They concluded that defin-ing an exact critical anchorage length is difficult to estimate andfurther investigations are needed. Si-Larbi et al. [22] proposed anew strengthening system using a cementitious matrix internallyreinforced with preloaded FRP rods. They have done a numericalstudy using the FE software ANSYS in which concrete was modeledwith the smeared crack approach. According to their experimentalresults the premature failure, peeling-off, occurred in some of thestrengthened beams. Aram et al. [23] have carried out an exhaus-tive study about flexural strengthened RC beams. They reviewedexisting international codes and guidelines and compared with

Fig. 2. Test setup before and after failure.

Table 1Details of concrete beams.

Groupno.

No. Beam geometry Longitudinalsteel

FRP geometry

a(mm)

t(mm)

d(mm)

Ø (mm) bp

(mm)tp

(mm)

1 1, 2, 3 100 150 24 2Ø6 100 1.22 4, 5, 6 100 150 24 2Ø6 100 0.63 7, 8, 9 100 150 24 2Ø6 – –4 10, 11,

1270 105 24 2Ø6 70 1.2

5 13, 14,15

80 120 24 2Ø6 80 0.6

S. Radfar et al. / Construction and Building Materials 37 (2012) 791–800 793

the analytical and numerical solutions especially for failure byinterfacial debonding and they suggested that an appropriate fail-ure criterion must be introduced into the codes and guidelines inorder to include concrete cover separation failure.

Although there is a large number of experimental and numerical re-searches on the fiber-reinforced polymer (FRP) strengthening of con-crete structures, a full understanding of the premature failures aresomewhat lacking. In other words, a primary technique for analyzingstrengthened RC beams has yet to be agreed upon. This paper is con-cerned with the failure by concrete cover separation in other wordsby peeling-off which is far more common than plate end interfacialdebonding. This mode involves the tearing-off of the concrete coveralong the level of tension steel reinforcement starting from a plateend. The first step for a successful, safe and economic design of flexuralstrengthening using FRP composite at the bottom of the beam is thento predict such failure and to take it into account in design.

In this paper, experimental work and numerical analyses of fourtypes of reinforced concrete beams have been carried out. Experi-ments were performed on strengthened RC beams to investigatethe behavior and to determine the ultimate failure load. A series of4 RC beams strengthened with FRP sheets at the bottom were testedto failure under a four-point bending load. All of the beams collapsedby peeling-off. Furthermore, numerical analyses were performed topredict the behavior and ultimate load-carrying capacity of RCbeams strengthened by FRP applied at the bottom of them. Numer-ical simulation of a peeling-off problem is a highly nonlinear prob-lem with material nonlinearities and local large displacements.The material nonlinearity is caused by: cracking of the concrete,compression concrete and plasticity of reinforcement. The geomet-rical non-linearity is taken into account because we model a type offailure which results in large displacements as it can be seen in Fig. 2.Furthermore, the numerical results before and at failure confirm thishypothesis and we can observe local geometrical nonlinearities. Thefinite element package Abaqus has been used for the simulation ofconcrete cover separation failure by applying a fracture mechanicsbased finite element analysis. A three-dimensional finite elementmodel has been adopted. Solid elements (brick) have been used tosimulate the behavior of concrete beams, shell elements to simulatethe behavior of FRP sheets and truss elements to simulate the steelreinforcements. The proposed finite element model has been vali-dated by comparing numerical results with experimental oneswhich mean that the method can successfully simulate the concretecover separation failure in FRP strengthened RC beams.

2. Experimental work

2.1. Specimen design

The test specimens consisted of 15 RC beams classified into five groups accord-ing to the different characteristics namely width and height of the beam and thick-ness of external reinforcement (FRP sheet). Among these beams, one group was notstrengthened and used as reference specimens and four groups were strengthened

externally with carbon FRP composite strips glued with epoxy adhesive to the ten-sion face of the RC specimens. In each group the beams have the same characteris-tics in order to have reproducible tests. All the beams were 1200 mm long and theywere designed in a way that the failure mode would be peeling-off. They wereinternally reinforced in flexure with two bars on the bottom side of the beam. Shearreinforcement for the beams consisted of FRP composite plates glued to the sides ofthe beams in the shear span. Beams geometry are shown in Table 1 where a, t, d, Ø,bp, tp denote the width of RC beam, depth of RC beam, distance from beam tensionface to centre of steel tension reinforcement, diameter of tension steel reinforce-ment, FRP width and FRP thickness.

2.2. Test setup and instrumentation

Specimens were simply supported and tested under four-point bending with anet span of 1.0 m and a shear span of 0.6 m. The supports were placed on bottom ofconcrete beams and elastomeric pads were placed between the steel supports andthe beams. The load was applied with steel cylindrical rollers as line load across thetop width of the beams. The beams were tested monotonically to failure by a dis-placement controlled electromechanical MTS machine at a constant displacementrate of 1 mm/min. One LVDT (DCTH400) was used to measure the midspan deflec-tion and two were used to measure the support displacement originating from elas-tomeric pads settlements. Test setup including beam geometry and reinforcementas well as the loading and support arrangement before and after the failure is illus-trated in Fig. 2.

2.3. Material properties

The specimens were built with concrete having a 28 days compressive cylindri-cal average strength of 40.4 MPa and tensile average strength of 2.7 MPa. Compres-sion and Brazilian tests were carried out on 11 � 22 cm and 16 � 32 cm cylindricalconcrete specimens in order to define the compressive and tensile strength ofconcrete beams. These mechanical characteristics are given in Table 2 for differentspecimens where f 0c and f 0t represent compressive and tensile strength respectively.The internal flexural reinforcement consisted of ribbed steel bars with a yield stressof 500 MPa. The FRP flexural reinforcement consisted of several unidirectional car-bon epoxy composite laminates that were placed and shaped into a flat plate andthat were processed by heat and pressure to densify and consolidate the structure.The thickness of each FRP layer was 0.15 mm and the fibers of laminate layups wereparallel to the longitudinal direction of the beams. The FRP shear reinforcementswere 1.2 mm thick and consisted of prefabricated carbon epoxy composite.Mechanical properties of FRP materials are reported in Table 3 where f 0t is tensilestrength, E and G are Young modulus and shear modulus associated with the

Table 2Properties of concrete.

Specimen no. f 0c (MPa) f 0t (MPa)

1 45.0 3.12 42.3 2.73 42.6 2.44 35.9 3.05 36.1 2.36 40.5 2.8

Table 3Mechanical properties of FRP reinforcements.

FRP EL

(GPa)ET = EN

(GPa)GLT = GLN

(GPa)GTN

(GPa)mLT = mLN mTN f 0t

(MPa)

Shear reinforcements 160 6 4 2.4 0.3 0.25 2800Flexural reinforcements 120 8 4.5 3.2 0.3 0.25 2000

Fig. 3. Load–deflection curve of reference beams.

Fig. 4. Load–deflection curve of reinforced beams.

794 S. Radfar et al. / Construction and Building Materials 37 (2012) 791–800

material’s principal directions ‘‘L, T, N’’ which signify the longitudinal, transversaland normal directions. The FRP strips were bonded to the specimens by Sikadur-30 adhesive after sandblasting and cleaning to guarantee a good bond betweenthe adhesive and the concrete.

2.4. Test results

All the beams were loaded up to complete failure. As it’s shown in Figs. 3 and 4the scatter in the results was small, indicating a good quality control and repeatabil-ity of the experiments. Conventional ductile flexural failure due to yielding of theinternal tensile steel reinforcement occurred for the control beams. Fig. 3 illustrates

the load–deflection curves of control beams at midspan. It’s easy to distinguishthree phases in this figure. Initially, the displacement increases almost linearly withthe load, the slopes of curves are similar and Young’s modulus has its greatest value.In addition, micro-cracks exist in the aggregate–mortar interface but they are con-trolled by friction. In the second stage, the cracks propagate and steel bars take thetraction and we notice here the non-linearity and irreversibility in beam property.Furthermore, the displacement increases faster than load which means a drop inYoung’s modulus in other words, a reduction in the beam stiffness. At last level,there is nearly no more increase in load but displacement grows by steel yieldingup to failure. In fact the nonlinear response of reinforced concrete is caused by threemajor material effects namely cracking of the concrete, plasticity of the reinforce-ment and of the concrete in compression.

Peeling failure of the concrete cover along the steel reinforcement occurred forall the FRP strengthened RC beams, it was brittle and explosive and caused totalfailure of beam. The load–deflection curves of strengthened RC beams are shownin Fig. 4. Failure loads of test specimens are summarized in Table 4. The averageultimate load of the reference beams is 25.03 kN. The average ultimate load ofthe strengthened beams (with the same geometry of reference beams) is 49.5 kN,98% higher than that of the unstrengthened beams, but as expected, the ductilityof the strengthened members decreases due to the application of the FRP. If wecompare the curves of the first and second group in which the difference is justthe thickness of FRP sheet, we realize that the failure load is approximately thesame but the stiffness of the beams of the second group (with thinner FRP) aftercracking is smaller. By comparing the failure load of reference beams with thebeams of first and second group we understand that strengthening has a great influ-ence on failure load but it causes a brittle rupture which is not good. Therefore, ifwe want to use this method of strengthening we should at least be able to predictsuch type of failure.

3. Numerical study

It has been always difficult to develop a definitive technique foranalyzing reinforced concrete which is the most used compositematerials in construction. For many structural materials such assteel and aluminum which have well-defined constitutive proper-ties, the finite element method works very well but when the con-stitutive behavior is not so straightforward like concrete in whichdiscrete cracking occurs, the task is more difficult. Despite this fact,the finite element method continues to be a predominant strategyto conduct structural analysis and it’s more economical than labo-ratory or field testing. The objective of this part of the study is toestablish a reliable, convenient and accurate methodology for ana-lyzing FRP strengthened RC beams which can correctly representglobal beam behavior and accurately predict stress and strain dis-tribution through the thickness of beams. The numerical analysisconsists of a three dimensional nonlinear finite element analysisby means of the commercial FE program Abaqus.

3.1. Material properties and constitutive models

3.1.1. Steel reinforcing barA uniaxial stress–strain relationship is sufficient as the constitu-

tive model of steel reinforcement because it is generally assumedthat the steel reinforcement transmits force axially. The mostcommonly used model for steel reinforcement is the linearly elas-tic-perfectly plastic type. The mechanical properties of steel are asfollows: E = 200 GPa, re = 500 MPa, t = 0.3 where E, re, t denote themodulus of elasticity, yield strength and Poisson’s ratio of the steelbars respectively.

3.1.2. Fiber-reinforced plasticsThe behavior of the FRP laminates is considered as elastic linear

up to failure. The values of mechanical properties are given in theprevious section.

3.1.3. ConcreteThe quasi-brittle behavior of concrete is very difficult to model

because of many parameters like concrete heterogeneity, differentbehavior of concrete in traction and compression, randomly dis-tributed microcracks, etc. Describing the mechanical behavior of

Table 4Experimental results at failure of test specimens.

Groupno.

No. Failure load(kN)

Standard deviation(kN)

Coefficient of variation(%)

Deflection at failure(mm)

Standard deviation(mm)

Coefficient of variation(%)

1 1, 2, 3 50.10 1.68 3.4 4.46 0.33 7.42 4, 5, 6 48.85 2.62 5.4 5.92 0.73 12.33 7, 8, 9 25.03 0.45 1.8 12.16 0.85 74 10, 11,

1226.36 1.76 6.7 7.61 1.24 16.2

5 13, 14,15

29.83 0.72 2.4 7.15 0.43 6.1

Fig. 5. Tension-stiffening law for concrete in tension.

S. Radfar et al. / Construction and Building Materials 37 (2012) 791–800 795

concrete is presented today in many ways like discrete or smearedcrack approaches, plasticity, damaged plasticity and fracturemechanics. These methods have been successfully used by theauthors in numerical analyses of FRP strengthened concrete[7,21,22]. However, modeling the mechanical behavior of concretein not fully resolved and remains an area of research. Therefore, it’snecessary to develop a method which is not only reliable to modelthe complex behavior of concrete but it’s also simple to facilitatethe modeling of large concrete structures.

3.1.3.1. Concrete in compression. One of the commonly used con-stitutive models for concrete is an elastic–plastic material byusing a yield function [3,24,25]. It is known that under multiaxialcompression, concrete behaves like a ductile material and canflow on the yield or failure surface before reaching its crushingstrains, thus it is possible to idealize the concrete as a plasticmaterial with a proper failure criterion [26]. Such idealizationsseem to be acceptable in many practical situations but it’simportant to notice the fact that at local level, the mechanismsinvolved in this case correspond to the microcracking. In thisstudy a macro-level approach for concrete fracture is assumedin which concrete is supposed to be an equivalent isotropiccontinuum. The material model for concrete is developed withinthe framework of the theory of plasticity, in detail; the Drucker–Prager yield function formulated in stress space with associatedflow is adopted. The evolution of the yield surface is controlled

Fig. 6. FRP Strengthened RC beams: geometr

by the hardening variables (appropriate criterion) in tensionand compression. An important advantage of our approach isits robustness and the facility of calculation convergence incomparison to other methods like smeared crack model whereoften stress locking or other numerical problems cause thesolution not to converge, though it does not predict explicitlycrack initiation and evolution.

Classically, the stress field can be expressed by two compo-nents: hydrostatic pressure (p) and Mises equivalent stress (q),the expression of these components are defined in Eqs. (1) and(2). Hydrostatic pressure is related to the volume change ofstressed body and does not depend on shear stress therefore inthe case of pure shear stresses there is just the Mises equivalentstress which has a non-zero value. These two stresses define theelastic and plastic domains in p–q plane.

p ¼ �r11 þ r22 þ r33

3ð1Þ

q¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi12ððr11�r22Þ2þðr22�r33Þ2þðr33�r11Þ2Þþ3r2

12þ3r213þ3r2

23

r

ð2Þ

where rij(i, j = 1,2,3) are the components of stress in the generalstress tensor. The Drucker–Prager model is an extended and modi-fied version of the Mohr–Coulomb model. This model was firstdeveloped in soil mechanics and it was then adopted and used tosimulate concrete [21,27,28]. The Drucker–Prager failure surface isa cone with a circular cross section in deviatoric stress space. Inthe p–q plane, the yield criterion is represented by FDP in Eq. (3)which demarcates the stress states that cause elastic and plasticdeformation. In this model, the yield surface is defined by twomaterial parameters: the internal angle of friction of material /which is the slope of the linear yield surface in the p–q stress plane,and the cohesion d which is equivalent to the shear stress limit incase of pure shear stress. It should be noted that in this study theform of yield surface has a linear form but there are also a hyper-bolic and a general exponential form which suppress the cone sin-gularity. The experimental data available for calibration of themodel parameters (/,d) are the results of compression and Braziliantests on concrete specimens which are given in Table 2 in the pre-vious section, therefore: / = 69.2�, d = 2 MPa. The elastic mechanicalproperties of concrete are: E = 37 GPa, t = 0.2.

FDP ¼ q� ðp tanð/Þ þ dÞ ¼ 0 ð3Þ

y, boundary conditions and loads, mesh.

Fig. 7. Peeling-off crack initiation zone.

Fig. 9. Experimental and numerical load–deflection curves of control beams.

796 S. Radfar et al. / Construction and Building Materials 37 (2012) 791–800

3.1.3.2. Tensile behavior of concrete. The Young’s modulus and thePoisson’s ratio of concrete in traction are the same as the valuesof concrete in compression but the concrete tensile strength ismuch smaller than the compressive strength. In the case of multi-axial traction the failure plane is perpendicular to the direction ofthe greatest tensile stress (principal direction), the failure is fragileand the tensile strength is the same as the tensile strength inuniaxial traction. In design of concrete sections with steel bars,the concrete tensile strength is often neglected as in Eurocode 2but it is naturally expected that the reinforcement could have agreat effect on tension stiffening and on the development of deflec-tions. Tension Stiffening in reinforced concrete represents thecapacity of the concrete to carry the tensile forces after the crackand it’s due to the development of tensile stresses in the concretebetween the neighboring cracks. Therefore, it is better to use theconstitutive models including tension-stiffening for concreteespecially in FRP-plated RC beams. There exist a large number ofmodels for representing this effect. Fig. 5 shows some of concretetension stiffening models. According to these models the behaviorof concrete until the tensile stress reaches the value of tensilestrength is ideally represented with a linear branch while thepost-cracking behavior can be assumed linear, bilinear or parabolic[24,2,21]. In order to model the behavior of concrete in tension,researches have adopted two main approaches: the first oneconsists of the full modeling of constitutive law and the secondone is based on the use of fracture energy. In the present studythe second approach which has more advantages than the firstone is taken into account to determine the total failure of concretebeams by peeling-off. It means that the Drucker–Prager model isalso used for the tensile behavior of concrete and it’s combinedwith the fracture mechanics in order to detect failure in tensilezone.

In Fig. 5, the hatched area (gf) shows the fracture energy inmode I (Gf) per unit width of crack. The fracture energy of concreteGf is the energy required for a tensile crack of unit area to propa-gate. According to the model code of CEB-FIP [29], in the absenceof experimental values Gf can be estimated from the followingequation:

Gf ¼ Gf0

f 0c10

� �0:7

ð4Þ

where f 0c is the compressive strength of concrete (MPa) and Gf0 is thebase value of fracture energy and it depends on the maximum

Fig. 8. Peeling-off

aggregate size of concrete. In the tests presented before, the averagecompressive strength was 40.4 MPa and the maximum aggregatesize was equal to 16 mm, thus Gf0 ¼ 0:03 and Gf = 0.08 N mm/mm2.

3.2. Finite element model

3.2.1. GeneralBefore starting a nonlinear simulation of each problem, there

are some important questions to be answered as follows: 2D or3D modeling, material model, static or dynamic solution, controland stopping parameters, applying of loads, boundary conditions,mesh density, friction coefficient in different contacts, reinforce-ment modeling, failure process, etc. Results and computation timecan considerably differ depending on the way of choosing theseparameters.

The numerical analysis herein is a three dimensional-nonlinearfinite element analysis of the experimental set-up by means of thecommercial FE program Abaqus. This analysis is a nonlinear staticprocedure with a classical Full-Newton solving method. Fig. 6shows a typical three-dimensional model containing the geometry,boundary conditions, the applied load and the mesh used in thisstudy. Double symmetry of load and geometry were used to modeljust a quarter of the beams and appropriate boundary conditionsare imposed. The symmetry lines are the apparent symmetry linesin the middle of the concrete beams and the symmetry lines in themiddle of their sections. As explained before, the geometrical non-linearity is taken into account in modeling. Full bond is assumedbetween FRP and concrete, i.e. there is full transfer of load betweenFRP and concrete without considering the adhesive layer. It’s alsoassumed that there is no slip between the steel reinforcementand the concrete. The mesh is more refined in the area susceptibleto peeling-off and also in the vicinity of steel bars and it’s coarser inother areas. The concrete is modeled using 10-node tetrahedronsolid elements with quadratic approximation of displacements, re-duced integration, 3D elements with three transitional degrees offreedom per node in three perpendicular directions. Sixnode trian-gular thin shell elements with five degrees of freedom per node

crack surface.

Fig. 10. Failure by concrete cover separation.

a b

dc

Fig. 11. Experimental and numerical load–deflection curves of strengthened beams: (a) Group no. 1, (b) Group no. 2, (c) Group no. 4, and (d) Group no. 5.

S. Radfar et al. / Construction and Building Materials 37 (2012) 791–800 797

with quadratic approximation of displacements are used to simu-late the behavior of FRP sheets. Steel bars are embedded in con-crete and are modeled by threenode quadratic truss (1D)elements. It should be noted that in first simulations concretewas modeled by 20-node hexahedron solid elements and FRPsheets by eightnode rectangular elements. The results were thesame as the presented model but it was much more costly in com-putational time.

3.2.2. Failure detectionAs mentioned before, the concrete cover separation failure is

brittle, therefore, when a crack initiates, it will propagate very soonand that causes the total failure of the beam. Hence, we have fo-cused on the crack initiation for the prediction of the beam failure.Since there is a stress singularity at the end of the FRP plate, it’sbetter to put an energetic criterion rather than a stress one. Thisenergetic criterion which is explained in the previous section isput above a little zone along the beam width at the plate end asit’s shown in Fig. 7. As discussed before, the constitutive modelof concrete is elastic–plastic (Drucker–Prager model), therefore atthe plate end in a certain load a plastic zone appears which showsthe formation of the peeling-off crack. As illustrated in Fig. 8 it’s

possible to define the crack surface (Scr) in this area. The plastic en-ergy dissipated in crack surface is equivalent to the correspondingfracture energy knowing that there are just tensile stresses here.Therefore, it’s necessary to calculate the plastic energy (Ep) in thechosen cuboid in each load increment in order to define the surfaceenergy G0f

� �as in Eq. (5)

G0f ¼Ep

Scrð5Þ

In other words for defining the failure load, we have done a postprocessing of the results. It means that in each step of calculationthe dissipated plastic energy (Ep) is measured and used to calculatethe surface energy G0f

� �. The latter is compared to the fracture en-

ergy. While the calculated surface energy is not reaching the frac-ture energy level, there is no failure but as soon as it reaches thecritical value (Gf) in Eq. (6) we consider the total failure of the beam.

G0f 6 Gf ð6Þ

The size of the chosen cuboid is identified by doing trial and er-ror to have best results. This cuboid is lain along the beam widthwith an edge size of d0/4 to d0/3 where d0 is the concrete cover

Table 5Comparison between the numerical and experimental results.

Group no. No. Failure deflection (mm) Num./exp. Failure load (kN) Num./exp.

Exp. Num. Exp. Num.

1 1, 2, 3 4.46 3.66 0.821 50.10 49.57 0.9892 4, 5, 6 5.92 5.35 0.904 48.85 55.52 1.1374 10, 11, 12 7.61 7.22 0.949 26.36 22.64 0.8595 13, 14, 15 7.15 6.41 0.897 29.83 33.33 1.117

Fig. 12. Effect of element size on load–deflection curve of the beams of the secondgroup.

Fig. 13. Effect of element size on failure load of the second group.

Fig. 14. Effect of failure volume size on failure load.

798 S. Radfar et al. / Construction and Building Materials 37 (2012) 791–800

(d0 = d � /). It should however be noted that the real process of fail-ure is more complicated than is predicted by the present model, asconcrete is not a homogeneous material.

3.3. Numerical results

The numerical results in the following sections are presented interms of the ultimate load carrying capacities, modes of failure anddeformational characteristics of the beams when using the pre-sented model. Fig. 9 shows the load–deflection curve of the controlbeams. As seen in this figure the numerical curve shows the ductileflexural failure as in test control beams. We have calibrated theparameters of Drucker–Prager criterion by using the experimentaldata of reference beams.

According to numerical results all strengthened RC beams failedby peeling-off as seen in Fig. 10 which is in consistent withexperimental results. Fig. 11 shows numerical and experimental

load–deflection relationships of strengthened RC beams. As seenthere is a very good agreement between numerical and experimen-tal results in terms of the ultimate load carrying capacities andmodes of failure. In these figures it is easy to distinguish three inter-vals in curves of second and fifth group (Fig. 11b and d) and two incurves of first and fourth one (Fig. 11a and c). These three phasesrelate to uncracked elastic stage, crack propagation, and the plasticstage respectively. In first and fourth group, the failure occurs beforesteel yielding and therefore there is no third stage in this case. Table 5refers to the numerical results based on the proposed model. In thistable, the ratio of the numerical-to-experimental load capacity anddeflection is given for each beam group. The maximum error in theprediction of failure load is equal to 14.1% which is surely acceptablefor concrete simulation. The maximum error in deflection is 17.9%which may be due to the overestimation of concrete strength in trac-tion after the formation of cracks. The average numerical-to-exper-imental load and deflection ratios and failure modes indicate thevalidation of the proposed model which can be used widely for theprediction of concrete cover separation failure.

3.3.1. Mesh sensitivityFive FE models consisting of tetrahedral elements with edge

sizes of 0.25, 0.5, 1, 2.5 and 3.5 mm in concrete cover at the endof FRP sheet were compared in this study to find out whetherthe concrete model presented above has an effect on failure. Itcan be seen from Fig. 12 that load–deflection curves of the fiveFE models are very close to each other and there is just a little dif-ference in failure load which is shown in Fig. 13. This comparisonreveals that, with the present model, the effect of element sizeon the predicted behavior and failure is small. Hence, the elementsize of 1 mm near the FRP end was used in the numerical simula-tion of all specimens.

3.3.2. Failure zone size dependencyAs explained in the previous section, the failure detection is just

a post processing of numerical results; therefore, it does not

Table 6Effect of the FRP thickness.

Groupno.

No. FRPthickness(mm)

Test crackingload (kN)

Increase in testcracking load (%)

Test ultimateload (kN)

Increase in testultimate load (%)

Numerical ultimateload (kN)

Increase in numericalultimate load (%)

1 1, 2, 3 1.2 12.08 76.6 50.10 100.2 49.57 100.42 4, 5, 6 0.6 13.31 94.6 48.85 95.2 55.52 124.43 7, 8, 9 – 6.84 – 25.03 – 24.74 –

Fig. 16. Effect of the FRP thickness on failure load and modes of failure for a beamwith the same geometry as control beams.

Fig. 15. Effect of the FRP thickness on beam deflection.

S. Radfar et al. / Construction and Building Materials 37 (2012) 791–800 799

change the behavior of beams. In this part, three different volumeshave been taken into account. These volumes have one edge equalto the beam width and two other edges of 4, 5 and 7 mm. The fail-ure loads of these zones are shown in Fig. 14. As seen, there is not agreat difference between different sizes.

4. Discussions

The measured cracking loads for the laminated beams was sig-nificantly higher than that of reference beams, as can be seen in Ta-ble 6 and Fig. 15. This increase might happen due to the increasedstiffness by the laminate restraining effect. The percentage in-crease in the measured cracking load of groups with the samegeometry as control beams was respectively 76.6 and 94.6 forthe beam with eight (thickness of each layer is 0.15 mm) and fourFRP layers.

The ultimate load of the beams increases significantly by FRPstrengthening, as can be seen in Table 6. The ultimate load of

two first test groups was 100.2% and 95.2% higher than that of ref-erence beams respectively. Generally in conventional failures themore the FRP thickness is, the later the beam fails but the FRPthickness has an inverse relationship with beam strength in caseof the concrete cover separation failure due to the stress concentra-tion at the plate end (it should be noted that this statement isdrawn from numerical results and it is not well observed in ourfew experimental results). Therefore, it’s concluded that there isan interval of FRP thicknesses below and beyond which theimprovement in performance is marginal. This interval dependson the size of the repaired member, loading conditions and onmaterial properties. As seen in Fig. 16 a beam with the same geom-etry as control beams and without FRP fails in flexure while if it’sstrengthened by a very thin FRP sheet the ultimate load increasesenormously and the failure load changes to FRP rupture. If the FRPis a little thicker, the failure load will be greater and the rupturemode is concrete cover separation failure, and at last, if the beamis strengthened by a very thick sheet, the failure mode remainsthe same but the ultimate load decreases.

It can be observed from Fig. 15 that for a constant load config-uration the deflection of the beam decreases by increasing the FRPthickness. A comparison of the slope of the curve and the deflec-tions for different beams shows that adding FRP sheets results ina significant increase in beam stiffness.

5. Conclusions

The work presented here focuses on the study of concrete cover sep-aration failure in FRP strengthened RC beams. Test results of 12 RCbeams with external FRP laminates and three control beams (non-strengthened) in 4-point bending set-up have been presented. Thescatter in the test results was small, indicating a good quality controland repeatability of the experiments. A 3D nonlinear finite elementmodel implemented with the general-purpose program ABAQUS hasbeen presented for the simulation of concrete cover separation. In thismodel, the concrete is treated as an elastic–plastic material and thefracture mechanics notions are used to define the failure. By using thisfinite-element model, the various modes of failure (FRP rupture, con-crete cover separation) can successfully be simulated. Furthermore,the model is not only able to capture the failure load but it can also pre-dict the deformational behavior of strengthened RC beams. Compari-sons between the predictions of this model and test results haveshown that the ultimate load and the behavior of the beam at differentload levels can all be closely predicted. Based on the work described inthis paper, the following conclusions are drawn:

� All strengthened beams exhibited a higher load capacity and alower ductility compared with their respective control beams(Fig. 15).� The failure mode of all strengthened beams was peeling-off

which is brittle and explosive.� The thicker the FRP sheets are, the higher is the stiffness of the

beam but the lower is the load capacity of the beam regardingconcrete cover separation failure.

800 S. Radfar et al. / Construction and Building Materials 37 (2012) 791–800

� In the presented model there is almost no dependency on theelement size in predicting the load–deflection behavior andthe failure load.� It may be concluded that the peeling-off in strengthened RC

beams is due to the excessive energy dissipated at the plate end.

The nonlinear FE model proposed herein provides researchersand designers a computational tool for design of FRP strengthenedbeams. Through FE modeling, the failure location, the failure modeand the maximum improvement in strength due to the configura-tion of FRP layers can be obtained. Thus, with the proposed model,it is possible to do trial and error to find an effective and reasonableretrofit scheme.

References

[1] Shahaway MA, Arochiasamy M, Beitelman T, Sowrirajan R. Reinforced concreterectangular beams strenthened with CFRP laminates. Compos Part B: Eng1996;27B:225–33.

[2] Wang YC, Chen CH. Analytical study on reinforced concrete beamsstrengthened for flexure and shear with composite plates. Compos Struct2003;59:137–48.

[3] Hu HT, Lin FM, Jan YY. Nonlinear finite element analysis of reinforced concretebeams strenthened by fiber-reinfored plastics. Compos Struct2004;63:271–81.

[4] MacDonald MD. The flexural performance of 3.5 m concrete beams withvarious bonded external reinforcements. Supplemental Rep 728; Transportand Road Research Laboratories (TRRL), Dept. of the Environment; Crowthorne,UK; 1982.

[5] Swamy RN, Jones R, Bloxham JW. Structural behaviour of reinforced concretebeams strengthened by epoxy-bonded steel plates. Struct Eng1987;65(2):59–68.

[6] Limam O, Foret G, Ehrlacher G. RC beams strengthened with compositematerial: a limit analysis approach and experimental study. Compos Struct2003;59:467–72.

[7] Yang ZJ, Chen JF, Proverbs D. Finite element modelling of concrete coverseparation failure in FRP plated RC beams. Constr Build Mater 2003;17.

[8] Nardini V, Guadagnini M, Valluzzi MR. Anchorage strength models for end-debonding predictions in RC beams strengthened with FRP composites. MechCompos Mater 2008;44(3):257–68.

[9] Smith ST, Teng JG. FRP-strengthened RCbeams. I: Review of debondingstrength models. Eng Struct 2002;24:385–95.

[10] Smith ST, Teng JG. FRP-strengthened RCbeams. II: Assessment of debondingstrength models. Eng Struct 2002;24:397–417.

[11] Teng JG, Yao J. Plate end debonding in FRP-plated RC beams – II: Strengthmodel. Eng Struct 2007;29(10):2472–86.

[12] Yao J, Teng JG. Plate end debonding in FRP-plated RC beams – I: Experiments.Eng Struct 2007;29(10):2457–71.

[13] Raoof M, Hassanen MAH. Peeling failure of reinforced concrete beams withfibre-reinforced plastic or steel plates glued to their soffits. Proc Inst Civ Eng –Struct Build 2000;140(3):291–305.

[14] Raoof M, El-Rimawi J, Hassanen MAH. Theoretical and experimental study onexternally plated R.C. beams. Eng Struct 2002;22(1):85–101.

[15] Benjeddou O, Ouezdou MB, Bedday A. Damaged RC beams repaired by bondingof CFRP laminates. Constr Build Mater 2007;21:1301–10.

[16] Gao B, Leung CKY, Kim JK. Prediction of concrete cover separation failure for RCbeams strengthened with CFRP strips. Eng Struct 2005;27:177–89.

[17] Gao B, Leung CKY, Kim JK. Failure diagrams of FRP strengthened RC beams.Compos Struct 2007;77:493–508.

[18] Saadatmanesh H, Malek AM. Design guidelines for flexural strengthening of RCbeams with FRP plates. J Compos Constr 1998;2(4):158–64.

[19] Malek AM, Saadatmanesh H, Ehsani MR. Prediction of failure load of R/C beamsstrengthened with FRP plate due to stress concentration at the plate end. ACIStruct J 1998;95(1):142–52.

[20] Saxena P, Toutanji H, Noumowe A. Failure analysis of FRP-strengthened RCbeams. J Compos Constr 2008;12(1):2–14.

[21] Lundqvist J, Nordin H, Taljsten B. Numerical analysis of concrete beamsstrengthened with CFRP – a study of anchorage lengths. Bond Behav FRPStruct: Proc Int Conf BBFS 2005:247–54.

[22] Si-Larbi A, Agbossou A, Ferrier E, Michel L. Strengthening RC beams withcomposite fiber cement plate reinforced by prestressed FRP rods:experimental and numerical analysis. Compos Struct 2012;94(3):830–8.

[23] Aram MR, Czaderski C, Motavalli M. Debonding failure modes of flexural FRP-strengthened RC beams. Compos Part B: Eng 2008;39:826–41.

[24] Lu XZ, Ye LP, Teng JG, Jiagn JJ. Meso-scale finite element model for FRP sheets/plates bonded to concrete. Eng Struct 2005;27:564–75.

[25] Jiang JF, Wu YF. Identification of material parameters for Drucker–Pragerplasticity model for FRP confined circular concrete columns. Int J Solids Struct2012;49(3-4):445–56.

[26] Chen WF. Constitutive equations for concrete. IABSE Colloq Cph; 1979.[27] Bursi OS, Sun FF, Postal S. Non-linear analysis of steel–concrete composite

frames with full and partial shear connection subjected to seismic loads. JConstr Steel Res 2005;61:67–92.

[28] Salvatore W, Bursi OS, Lucchesi D. Design, testing and analysis of high ductilepartial-strength steel–concrete composite beam-to-column joints. ComputStruct 2005;83:2334–52.

[29] ComitT/EuroInternational/du/Beton. CEB-FIP model code 90. CEB Bulletins;1993.