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ARTICLE

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Experimental and numerical study on the effect of repairing reinforced concrete cracked beams strengthened with carbon fibre reinforced polymer laminates P. Duarte, J.R. Correia, J.G. Ferreira, F. Nunes, and M.R.T. Arruda

Abstract: This paper presents experimental and numerical investigations on the effect of repairing cracks in reinforced concrete (RC) beams prior to strengthening them with carbon fibre reinforced polymer (CFRP) laminates. The experimental campaign comprised flexural tests on three types of full-scale RC beams with T-shaped cross-section: (i) two reference un-strengthened beams, (ii) two CFRP-strengthened beams previously loaded and cracked, and (iii) two CFRP-strengthened beams, previously loaded, cracked and repaired with epoxy resin. The repair and strengthening techniques consisted of respectively injecting the cracks with epoxy resin and applying CFRP laminates according to the externally bonding reinforcement technique. In the numerical study, the structural response of all beams tested was simulated using the finite element software ATENA, which features a smeared cracked model constitutive relationship for concrete. A parametric study was carried out in which the influence of material parameters, namely the fracture energy, on the beams structural response was assessed. Experimental results showed that repairing cracks by means of epoxy injection before strengthening them with CFRP laminates provided a considerable increase of stiffness, but only a slight increase of ultimate strength, as failure was triggered by the debonding of the strengthening system at the anchorage zones. In the numerical study a very good agreement with experimental data was obtained. For the repaired and strengthened beams, such agreement was obtained by increasing concrete's fracture energy when compared to that of the reference beams. Key words: reinforced concrete, beams, epoxy, CFRP laminates, repair, strengthening, experimental tests, nonlinear numerical models. Résumé : Cet article aborde des études expérimentales et numériques sur l’effet de la réparation des fissures dans les poutres en béton armé avant de les renforcer avec des stratifiés de polymères renforcés de fibres de carbone (PRFC). La campagne d’études comprenait des essais en flexion sur trois types de poutres en béton armé pleine échelle ayant des sections en T : (i) deux poutres non renforcées servant de contrôle, (ii) deux poutres renforcées au PRFC qui ont été préalablement chargées et fissurées et (iii) deux poutres renforcées au PRFC qui ont été préalablement chargées, fissurées et réparées au moyen d’une résine époxyde. Les techniques de réparation et de renforcement étaient respectivement d’injecter de la résine époxyde dans les fissures et d’appliquer des stratifiés de PRFC en suivant la technique de renforcement collé a` l’externe. La réponse structurale de toutes les poutres a` l’essai a été simulée dans l’étude numérique en utilisant le logiciel par éléments finis ATENA, qui comporte une relation constitutive d’un modèle d’une fissure diffuse pour le béton. Une étude paramétrique a été réalisée pour évaluer l’influence des paramètres des matériaux, principalement l’énergie de fracturation, sur la réponse structurale des poutres. Les résultats expérimentaux montrent que la réparation des fissures par injection époxyde avant de les renforcer par des stratifiés de PRFC augmente considérablement la rigidité, mais augmente seulement légèrement la résistance a` la rupture, puisque la défaillance est déclenchée par le décollement du système de renforcement aux zones d’ancrage. L’étude numérique a montré une très bonne corrélation avec les données expérimentales. Une telle corrélation a été obtenue pour les poutres réparées et renforcées en augmentant l’énergie de fracturation du béton par rapport aux poutres de contrôle. [Traduit par la Rédaction] Mots-clés : béton armé, poutre, époxyde, stratifiés de PRFC, réparation, renforcement, essais expérimentaux, modèles numériques non linéaires.

1. Introduction Reinforced concrete (RC) structures may suffer several types of defects that may jeopardize their service life and (or) structural reliability. Alongside excessive deflections and reinforcement corrosion, excessive cracking is one of the most common defects affecting RC flexural members and is often caused by overloads due to changes of use. Under these circumstances, to sustain higher loads, compared to those considered in the original design, proper strengthening systems need to be applied on the damaged structure.

The most conventional techniques used to strengthen RC members are concrete jacketing and steel plate bonding. The first technique involves enlarging the cross-section of the concrete member to be strengthened and adding steel bar reinforcement (Júlio et al. 2003, 2006; Dias-da-Costa et al. 2012). The second technique involves bonding steel plates to the surface of concrete elements after carefully preparing both surfaces (Vilnay 1988; Oehlers et al. 1998; Gomes and Appleton 1999). In the last few decades, the use of fibre reinforced polymer (FRP) materials to strengthen RC members has consistently increased.

Received 20 March 2013. Accepted 30 December 2013. P. Duarte, J.R. Correia, J.G. Ferreira, F. Nunes, and M.R.T. Arruda. Instituto Superior Técnico / ICIST, Technical University of Lisbon, Department of Civil Engineering, Architecture and Georesources, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal. Corresponding author: J.R. Correia (e-mail: [email protected]). Can. J. Civ. Eng. 41: 222–231 (2014) dx.doi.org/10.1139/cjce-2013-0124

Published at www.nrcresearchpress.com/cjce on 7 January 2014.

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Duarte et al.

The FRP materials can be used as either (i) precured systems (including laminates and rebars), (ii) wet lay-up systems (including sheets and fabrics) or (iii) pre-impregnated (prepreg) systems. The most common strengthening techniques for applying FRP materials are the following: (i) the externally bonded reinforcement (EBR) technique, according to which the FRP systems are externally glued on the surface of the structural member to be strengthened, in the same way as steel plates; (ii) the near surface mounted (NSM) technique (Soliman et al. 2010), in which the laminates are inserted into grooves opened on the concrete cover of the RC structural member to be strengthened; and (iii) the mechanically fastened fibre reinforced polymer (MF-FRP) technique (Napoli et al. 2013), where pre-cured FRP systems are mechanically fixed to the surface of the structural member to be strengthened using closely spaced fastening pins. Among the different types of FRP strengthening systems available, carbon fibre reinforced polymer (CFRP) laminates have already proved to be a competitive alternative to the above mentioned strengthening techniques in the flexural and shear strengthening and seismic retrofitting of RC members, mainly due to their higher strength-to-weight ratio and resistance to corrosion (David et al. 1998). The application of CFRP laminates on RC structures is also very simple and efficient, owing to their lightweight. As drawback, CFRPs present linear elastic behaviour up to failure and are susceptible to elevated temperature (Firmo et al. 2012; López et al. 2013). In addition, when CFRPs are applied according to the EBR technique, premature delamination of the strengthening systems may occur due to stress concentrations at the anchorage zones, thereby preventing the full exploitation of the CFRP material. When applying CFRP strengthening systems to RC members, most technical guidelines recommend repairing cracks wider than 0.3 mm before applying the CFRPs, as those cracks may affect the performance of the strengthening system through delamination or fibre crushing. Furthermore, smaller cracks may also require injection when the RC members are exposed to aggressive environments to delay the reinforcement corrosion (ACI Committee 440 2002). In spite of the above mentioned recommendations, actually adopted in the current engineering practice, there are very few studies reported in the literature concerning the effects of pre-cracking and crack repair on the performance of RC structures strengthened with CFRP laminates. David et al. (2003) conducted an experimental study regarding the flexural behaviour of RC members strengthened with CFRP strips applied according to the EBR technique. Four-point bending tests were carried out to evaluate the influence of the number of CFRP layers and the effect of pre-cracking. Results showed that while the use of multiple CFRP layers increases both stiffness and ultimate strength (as expected), the pre-cracking had no significant influence on such parameters. Regarding the crack pattern, the control beam showed concentrated cracks between the loaded sections, while strengthened beams showed a much more uniform distribution of cracks along their span. In this study, the effect of crack repair was not investigated. Hawileh et al. (2011) studied the flexural behaviour of precracked and retrofitted small-scale RC beams using epoxy injection and CFRP laminates. The experimental campaign comprised the test of three different small-scale (1.84 m long) specimens: (i) a reference control beam (non-strengthened), (ii) an uncracked strengthened beam, and (iii) a pre-cracked, retrofitted and strengthened beam. Results obtained showed that retrofitting a specimen before applying the CFRP laminates increases both the stiffness and the ultimate strength. However, the authors did not evaluate the effect of pre-cracking on the performance of the strengthening system. Ekenel and Myers (2007) studied the effect of environmental conditioning after crack injection with and without CFRP strengthening systems. Several types of specimens were tested:

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RC control beams, RC beams repaired with epoxy injection, RC beams strengthened with CFRP fabrics, and RC beams both repaired with epoxy injection and strengthened with CFRP fabrics subjected to different environmental conditions. Results obtained showed that, as expected, the epoxy injection provides remarkable increase of stiffness when compared to control specimens in un-strengthened beams. Additionally, in strengthened beams, crack injection provided an increase in both initial stiffness and ultimate strength, together with lower crack opening. Unfortunately, the beams tested were of very reduced dimension, with a span of only 0.81 m. Nikopour and Nehdi (2011) investigated the experimental behaviour of RC beams subjected to cyclic loading, repaired with epoxy resin and shear strengthened using FRP sheets. Results showed that those rehabilitation techniques provide significant mechanical improvements regarding ultimate shear capacity and ductility. The simultaneous application of epoxy injection and FRP sheets proved to be a very effective technique. In what concerns numerical investigations on the structural response of repaired and CFRP-strengthened RC members, namely using damage and fracture models, studies reported in the literature are very scarce (none of the above cited studies included numerical simulation of the experiments). Such types of studies are very important for practice oriented engineers, since when rehabilitation of damaged structures with CFRPs is performed, many questions remain regarding the structural response of the rehabilitated members. The main difficulty is the adoption of a correct constitutive relationship when the member has been subjected to a prior load that caused extensive cracking. Although some studies have been performed about the effect of FRP strengthening in RC slabs (Schladitz et al. 2012), the effect of the repair (crack injection) has not been duly taken into account yet. This paper presents further experimental and numerical investigations about the effects of pre-cracking and repairing cracks by epoxy injection on the performance of CFRP strengthening systems applied in RC beams. The experimental programme, described in section 2, comprised flexural tests on full-scale RC beams in which the above mentioned rehabilitation procedures were applied. Results are analysed in terms of load vs. deflection and moment vs. curvature behaviours, initial stiffness, crack development, ultimate strength and failure modes. The numerical study, presented in section 3, included the simulation of the beams tested using finite element (FE) software ATENA, which features a smeared cracked model constitutive relationship for concrete. The FE models were used to conduct a parametric study in which the constitutive relationships of the concrete material, namely the value of its fracture energy, were assessed. The numerical and experimental responses were compared to evaluate which concrete material parameters better simulate the overall response of the tested beams. In particular, the study aimed at evaluating the value of concrete's fracture energy that allowed simulating the structural response of rehabilitated beams with best accuracy.

2. Experimental investigations 2.1. Test programme The experimental programme was carried out at Instituto Superior Técnico (IST) and comprised (i) material characterization tests of the concrete and steel bars used in the beams, and (ii) full-scale 4-point bending tests on the following three different types of beams (Table 1): two reference un-strengthened beams – B1 and B2; two beams strengthened with CFRP laminates without prior loading and crack repair – B3 and B4; two beams strengthened with CFRP laminates with prior loading and crack repair by means of epoxy injection – B5 and B6. Published by NRC Research Press

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Table 1. Experimental series. Series

Specimens

Epoxy crack repair

Reference Strengthened Repaired and strengthened

B1 and B2 B3 and B4 B5 and B6

No No Yes

CFRP reinforcement No Yes Yes

To accomplish the above mentioned initial conditions for each type of beam, the chronologic sequence of the experimental programme was set as follows: (i) loading up to failure of beams B1 and B2; (ii) applying damage load (defined as described in section 2.4) to beams B3 to B6; (iii) repairing cracks of beams B5 and B6 by means of epoxy resin injection (under static loading); (iv) unloading and bonding the CFRP laminates on the bottom face of beams B3 to B6; (v) loading up to failure of beams B3 to B6. The above mentioned sequential tests allowed evaluating the effect of repairing cracks in RC beams prior to bonding the CFRP laminates, by comparing results from beams B3 and B4 with those from beams B5 and B6. 2.2. Specimen description, materials, and test setup The RC beams tested presented a T-shaped cross section with the dimensions and steel reinforcement as depicted in Fig. 1. The nominal length of the beams was 3.30 m and the concrete cover was set as 20 mm. Tables 2 and 3 summarize the properties of the materials used in the experimental programme. The RC beams were produced using standard Portland cement concrete (average compressive and splitting tensile strengths at the age of 28 days of fc = 31.0 MPa and fct = 2.6 MPa, respectively) and A500NR steel bars with diameters of 12 mm (average yielding and failure stresses of fsy = 535 MPa and fsu = 646 MPa) and 8 mm (fsy = 583 MPa and fsu = 691 MPa). An epoxy resin (Sikadur-52) was used to repair concrete cracks, being injected with a manual pump. The CFRP strengthening laminates, supplied by S&P (CFK 150/2000), have sectional area of 80 × 1.4 mm2, length of 2.5 m (covering 83% of the beams' clear span), elasticity modulus of Ef = 165 GPa (S&P 2007). The CFRP laminates were adhesively bonded to the RC beams using an epoxy resin (S&P 220), without any anchorage system. The test setup is shown in Fig. 2. The load was applied by an Enerpac hydraulic jack with a capacity of 3000 kN and measured with a Novatech load cell with a capacity of 4000 kN. The vertical deflections were measured with three TML and APEK displacement transducers (with precision of 0.01 mm) placed under the mid-span and the loaded sections of the beam. To measure the beams' axial deformations at mid-span, four TML electrical strain gauges were adhesively bonded to the top and bottom longitudinal steel reinforcement as depicted in Fig. 1. Tests were conducted under load control at an average speed of 1 kN/s. Data was acquired at a rate of 0.5 Hz using an 8 channel HBM Spider8 data logger and registered in PC. 2.3. Test procedure The reference control beams (B1 and B2) were first loaded monotonically up to failure with the objective of assessing the flexural behaviour (stiffness and strength) of the un-strengthened beams and determining their damage load. This load was defined to meet the crack width criteria (0.3 mm) along the loaded span without causing the steel reinforcement to yield. Crack widths were measured at different load levels with a crack microscope on a representative crack located close to mid-span.

Afterwards, beams B3 to B6 were loaded up to the damage load obtained in the tests on reference beams. Beams B5 and B6 were repaired under static loading according to the following procedure: (i) In all cracks that were possible to inject (with average openings of about 0.3 mm), two holes per crack were drilled intersecting the crack plane (on each side of the beam), Fig. 3a; (ii) The resin components were mixed according to the manufacturers' ratio until a homogenous mixture was obtained; (iii) The manual pump was cleaned every time a new mixture was prepared by pumping acetone through the hose; (iv) Steel packers were introduced in each drilled hole and tightened to ensure the mechanical grasp, Fig. 3b; (v) The epoxy resin was injected with an applied pressure of 2 to 3 bar, Fig. 3c. The injection was considered to be complete once the resin covered most of the crack's surface or when the resin stopped reaching new areas after several attempts. The beams were then left loaded for about 24 h, period of time considered enough for the resin to attain sufficient degree of curing. Beams B3 to B6 were then unloaded and turned upside-down to bond the CFRP strengthening laminates. The laminate area was outlined and needle scalers were used to roughen and remove the superficial layer of the concrete, exposing the first layer of aggregates. Then, the surface of the laminate was cleaned with acetone to ensure the best possible bonding conditions. The thickness of the bonding resin is an important parameter for the best performance of the strengthening system: a very low thickness may compromise the bonding of the laminate, while a high thickness may increase stress concentrations at anchorage zones. Therefore, and according to the manufacturers' recommendations, a 3 mm thickness of resin was applied. Figure 3 illustrates the process of strengthening the RC beams. In the tests of beams B3 to B6, the load as well as the vertical displacements and the longitudinal strains were also measured during the preliminary loading and unloading stages. Also the crack development along each test was monitored. Detailed description of these results can be found in Duarte (2011).

2.4. Results and discussion 2.4.1. Load– deflection behaviour Figure 4a illustrates the load vs. midspan deflection curves of all beams tested. The load corresponds to the force applied by the hydraulic jack (total load). Beams B1 and B2 presented the typical behaviour of RC flexural members, with their load vs. deflection curves sequentially exhibiting (i) an elastic un-cracked branch (up to a load of roughly 15 kN), (ii) an elastic cracked branch (up to a load of about 100 kN), and (iii) a plastic yielding path. Based on the load vs. deflection curves, the average values of 7.6 kN/mm, 103.9 kN, and 118.5 kN were obtained respectively for the stiffness (K, computed within the elastic cracked branch, for loads between 30 and 80 kN), yielding load (Py), and ultimate load (Pu) of the reference beams. The load vs. deflection curves of beams B3 to B6 presented in Fig. 4 are also typical of CFRP-strengthened RC beams. Results obtained show that all strengthened beams were considerably stiffer than the reference ones in the elastic cracked branch, with such stiffness progressively decreasing until a sudden load decrease occurred (due to the debonding of the strengthening system), without showing any plastic branch. Beams B3 and B4 (only strengthened) showed an average elastic stiffness in the cracked branch of 12.5 kN/mm, which corresponds to an increase of 65% when compared to the reference beams and their strength was also considerably higher, with an average ultimate load of 158.9 kN (increase of 34.1%). Beams B5 and B6 (repaired and strengthened) presented the highest stiffness and ultimate load with average values of 16.7 kN/mm and 167.1 kN, respectively Published by NRC Research Press

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Fig. 1. (a) Geometry of the beams’ cross section and position of strain gauges and (b) reinforcement detailing.

Table 2. Mechanical properties of concrete, steel reinforcement, and CFRP laminates. Material

Designation

Elastic modulus (GPa) a

Concrete Steel reinforcement

C25/30 A500NR

30 210b

CFRP laminates

S&P CFK 150/2000

165b

Strength (MPa) fc = 31.0 fsy,⌽12 = 535 fsy,⌽8 = 583 ft,0.6 = 1000b

fct = 2.6 fsu,⌽12 = 646 fsu,⌽8 = 691 ft,0.8 = 1300b

aEstimated bProvided

based on compressive strength. by manufacturer.

Table 3. Physical and mechanical properties of the epoxy resins used for crack injection (SIKA Portugal SA 2007) and CFRP bonding (S&P 2008). Resin

Density (g/cm3)

Viscosity (mPa·s)

Thermal expansion coefficient (°C−1)

Compressive strength (MPa)

Tensile strength (MPa)

Bonding strength (MPa)

Elastic modulus (GPa)

Pot-life (min)

Crack injection CFRP bonding

1.10 1.75

430a —

8.9×10−6 —

52b >90

37b >30

>4 >3

1.8b —

25a 60a

aat

room temperature (20 °C). seven days at 23 °C.

bafter

Fig. 2. Test setup (dimensions in metres).

(increases of 120% and 41.0% when compared to reference beams B1 and B2, and 33% and 5.1% when compared to the unrepaired beams B3 and B4). However, one should note that deflections on the brink of failure were very similar for both repaired and unrepaired strengthened beams. It is also worth mentioning that beams B5 and B6 presented some residual deflection after being repaired and unloaded (Duarte 2011). Such effect is probably explained by the fact that the epoxy resin filled the cracks providing some axial restriction (wedge effect) when unloading. As expected, in all strengthened beams, after the debonding of the strengthening system occurred, the load–deflection behaviour approached that of the non-strengthened beams. Table 4 summarizes the results obtained for each series in terms of average stiffness (KExp) and ultimate load (Pu,Exp). For both properties, the percentage variation (⌬) of beams B3 to B6 compared to the reference beams is also listed.

2.4.2. Moment– curvature behaviour The moment–curvature curves obtained from the measured values of axial strains in the steel rebars are illustrated in Fig. 4b. The curves are plotted up to the instant when one of the strain gauges stopped responding. In general, the moment vs. curvature curves (local behaviour of the half-span cross-sections, monitored with strain gauges) obtained for the different types of beams are in agreement with the corresponding load vs. deflection curves (global behaviour of the flexural members), exhibiting the same behavioural stages (note that the moment–curvature curves of the strengthened beams do not present the sudden decrease branch after maximum load is attained, since strain gauges stopped responding earlier). For the reference beams, when concrete cracks, together with the change of slope of the moment–curvature curve there is a sudden increase of curvature due to the stress transfer to the bottom rebars Published by NRC Research Press

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Fig. 3. Stages of the repair and strengthening processes: (a) hole drilling, (b) packer introduction, (c) resin injection, and (d) CFRP laminate bonding.

from the surrounding concrete. As for the load vs. deflection curves, the moment vs. curvature curves of the strengthened beams show a significantly higher stiffness compared to nonstrengthened beams. 2.4.3. Crack evolution and failure modes Figure 4c presents the evolution of crack widths as a function of the applied load. As already mentioned, based on crack width measurements of reference beams, the damage load was set as 90 kN. For such load level, crack width was roughly 0.3 mm, compatible with the viscosity of the epoxy resin used. For beam B1, the first to be tested, cracks were measured only up to a load level of 60 kN for safety reasons. Since the crack evolution of this beam is similar to that of beam B2 it seems plausible that it presented the same behaviour up to failure. For beam B2, the final crack measurement of about 1.0 mm (not plotted in Fig. 4) was made for a load of 100 kN. For beams B3 to B6, the presented crack widths were measured after (i) applying the cracking load, (ii) strengthening and (or) repairing, and (iii) unloading such beams, hence the initial widths of those specimens are not null. Also the repaired beams presented higher widths for the initial loads. This result occurred mainly due to the presence of epoxy resin inside the cracks and the subsequent residual deflections. Results presented in Fig. 4c show that the repaired beams presented higher widths for the initial loads. This result occurred mainly due to the presence of epoxy resin inside the cracks and the subsequent residual deflections. Yet, the crack repair appeared to have no influence on the crack width development as the crack behaviour of the strengthened beams was very similar. Nevertheless, when comparing such development with that of the reference beams, the effect of the strengthening system is noticeable, providing much lower crack width growth. On the brink of failure, in the strengthened unrepaired beams a considerable amount of new cracks was noticed arising in the lower part of the beams' web, reducing the crack spacing (Fig. 5a), while in the repaired beams the number of new cracks in this region was considerably lower (Fig. 5b). Failure of beams B1 and B2 occurred due to concrete crushing at the central span. After some damage progression (Fig. 6a), during which the applied load maintained a roughly constant value with increased deflection, the beams were unloaded as failure was considered to be reached. In both types of strengthened beams (unre-

paired and repaired), failure was caused by the sudden debonding of the CFRP strengthening system due to concrete pull-out at the anchorage zone (Fig. 6b and 6c). 2.4.4. Summary Results obtained in the flexural tests are very clear regarding the effect of crack repair on the stiffness increase of strengthened beams; compared to beams B3 and B4, the stiffness of beams B5 and B6 increased 33%. However, the 5% increase in ultimate load was much less significant. This is most likely related with the fact that failure of these beams was not related to cracking as it was caused by the debonding of the CFRP strengthening system at the anchorage zone.

3. Numerical investigations Numerical investigations presented in this section involved the development of finite element models using the commercial software ATENA, developed by Cervenka Consulting. This software has been fully tested with success in the simulation of RC structures using smeared fracture mechanics (Cervenka and Papanikolaou 2008) and recently applied to simulate the behaviour of a wide range of RC members incorporating FRP composites. For instance, this software has been successfully used to simulate the flexural behaviour of RC beams strengthened with CFRPs (Hashemi and Al-Mahaidi 2012; Aram et al. 2008), the strength of RC slabs strengthened with textile reinforced concrete (Schladitz et al. 2012), the ductility of RC beams reinforced with glass fibre reinforced polymer (GFRP) bars (Matos et al. 2012), and the bond splitting failure phenomenon (Ogura et al. 2008). 3.1. Model description 3.1.1. Geometry and type of elements Since physically nonlinear analysis was performed in the present study, to simplify the analysis and the computational costs, only half of the structure was simulated, with a total length of 1.65 m. Due to the test conditions of the experimental campaign, a simple plane stress analysis is adequate to simulate the structural nonlinear behaviour of the beams tested. For this reason, only plane finite elements were used in this analysis to describe the concrete behaviour. Different thicknesses were implemented Published by NRC Research Press

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Fig. 4. (a) Load vs. mid-span deflection curves, (b) moment vs. curvature curves, and (c) crack width evolution.

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Figure 7b illustrates the FE mesh of the reference beams. When generating the mesh for the concrete, plane quadrilateral elements with 4 nodes were used. These are isoparametric elements integrated by Gauss quadrature at 4 integration points for the case of bilinear interpolation, which usually produce good results when the nonlinear behaviour of concrete is simulated. The horizontal steel rebars were positioned in three different vertical levels. The three bottom rebars, with a diameter of 12 mm and subjected only to tension stresses, were positioned 3 cm above the bottom face of the beams. The top rebars, with a diameter of 8 mm, were positioned at depths of 3 cm and 9 cm relatively to the top of the flange. The vertical shear stirrups were implemented using a membrane element (“smeared reinforcement”), with only vertical stiffness, which corresponds to a uniform distribution of shear rebars. The CFRP laminates were implemented directly over the bottom face of the beam, i.e., assuming a perfect bond with the concrete. 3.1.2. Boundary conditions According to the theory of symmetry, in the right end of the beam model the horizontal displacement and the rotation were restricted throughout the edge height. To simulate the pinned support in the left end, and to avoid any stress concentration effects, a rectangular elastic support was adopted. The same simplification was adopted for the applied load. 3.1.3. Constitutive relations For the standard reinforced concrete, a classical smeared crack model was used. This approach was considered to be adequate since for this study no crack concentrations (e.g., notches) existed. The mechanical properties adopted for the concrete were the ones measured in the experimental campaign. Therefore, the following values were used for the smeared cracked model: ft = 2.6 MPa, fc = 31 MPa, Ec = 30 GPa, and ␯ = 0.2. For the shear behaviour a fixed crack model was used, with variable shear retention factor and linear tension-compression interaction. For compression, concrete was simulated using a classical fictitious compression model (Buyukozturk and Teng 1984). This model is based on the assumption that compression failure is localized in a plane normal to the direction of compressive principal stress. In smeared fracture mechanics, the crack direction in the fixed crack model (Cervenka 1985; Darwin and Pecknold 1974) is given by the principal stress direction at the moment of the crack initiation. During further loading, this direction is fixed and represents the material axis of the orthotropy. For this study, since the variation of the axis of orthotropy is low, the use of the fixed crack model was considered to be adequate. A fictitious crack model (such as the fixed crack ones) is based on a tension stress versus crack opening law with certain fracture energy and this formulation has been found to be suitable to model crack propagation in concrete. It is used in combination with the crack band theory to prevent mesh dependency. In the numerical tests performed the exponential crack opening law described in eq. (1) was used to simulate the concrete of the beams, in which ␴ is the normal stress in the crack, w is the crack opening, f tef is the effective tensile strength, c1 and c2 are material parameters that control the level of softening, wc is the crack opening at the complete release of stress, and Gf is the fracture energy.

for the web and the flange, simulated with 2D membrane elements, as shown in Fig. 7a. To comply with the geometry of the cross-section, different thicknesses were adopted for the web and the flange. For the web the plane element was set with thickness of 15 cm and height of 20 cm, whereas for the flange a thickness of 40 cm and a height of 12 cm were defined.

(1)

␴ f tef

再 冉 ww 冊 冎 exp冉⫺c ww 冊 3

⫽ 1 ⫹ c1

2

c

c

Gf w ⫺ 共1 ⫹ c13兲 exp共⫺c2兲 ; wc ⫽ 5.14 ef wc ft Published by NRC Research Press

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Table 4. Summary and comparison between experimental and numerical results. Stiffness

Ultimate load

Experimental

Numerical

Experimental

Numerical

Beam series

KExp (kN/mm)

⌬ (%)

KNum (kN/mm)

Diff (%)

Pu,Exp (kN)

⌬ (%)

Pu,Num (kN)

Diff (%)

Reference (beams B1/B2) Strengthened (beams B3/B4) Strengthened and repaired (beams B5/B6)

7.6 12.5 16.7

— 64.5 119.7

8.4 11.2 16.1

10.5 10.4 3.6

118.5 158.9 167.1

— 34.1 41.0

110.7 150.7 156.2

6.6 5.2 6.5

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Fig. 5. Crack pattern in beams (a) B3 and (b) B5.

Fig. 6. Failure mode of beams (a) B1 with concrete crushing, (b) B3 and (c) B5 with debonding of CFRP strengthening system.

For the concrete class C25/30, FIB (MC90 1991) indicates an average value of the fracture energy of Gf = 50 N/m for a maximum aggregate diameter of 8 mm, but the scatter of this parameter can be very high (Gdoutos 2005, Hilsdorf and Brameshuber 1991). Beams B1 to B4 were simulated using the above mentioned model and considering such fracture energy. For beams B5 and B6, repaired with epoxy injection and then strengthened with CFRP, the previous smeared crack model was also used, but with higher fracture energy. This option was chosen since, when the repair with epoxy injection is performed, the overall behaviour of concrete becomes stiffer, as shown by the experimental results. It should be noted that the constitutive relationship prior to cracking is maintained — cracking stress and cracking strain correspond to the original material parameters. The main reason for proposing this model is its inherent simplicity and therefore its easier implementation in commercial FE software. Using the above mentioned hypothesis the fracture energy of the concrete of beams B5 and B6 was increased, which basically corresponds to increasing the hardening and promoting some

Fig. 7. FE model of the reference beams: (a) global geometry and (b) mesh geometry (the thick lines represent the steel rebars).

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Fig. 8. Numerical (Ref_Num) and experimental (B1_Exp and B2_Exp) load vs. midspan displacement curves of the reference beams.

stability in stress values after the cracking stress (ft = 2.6 MPa) is reached. A parametric study was performed by increasing the reference fracture energy of the repaired concrete, Gfr = k × Gf (with Gf = 50 N/m), with k varying from 1 up to 100. For the steel rebars, a classical elastoplastic behaviour, with Es = 210 GPa and fyd = 535 MPa, was used. These values were obtained in the experimental campaign. For the CFRP laminates, an elastic model, with Ef = 170 GPa and a maximum admissible strain of ␧adm = 0.4%, was used. The first parameter was measured experimentally (Dias and Barros 2010) and the admissible strain was determined from the average strain at failure, when the CFRP strengthening system debonded. The maximum strain of the CFRP laminates on the brink of collapse was estimated from the strains measured in the upper and lower steel reinforcement rebars, based on Bernoulli's theory. 3.1.4. Type of analysis One of the objectives of this work was to trace the load vs. displacement curve up to the post-failure softening regime. Therefore, to control the post-peak responses during the softening stage, the analysis was performed using applied displacements (Crisfield 1991). Because the load rate used in the experimental campaign was very low, a static nonlinear analysis was adopted. Multiple parameters were used to control the accuracy of the final iteration process of the Newton-Raphson method, namely a relative displacement error and a relative energy error. Beams B1 and B2 were monotonically loaded up to failure. Beams B3 to B6 were first loaded up to about 90 kN, then unloaded and finally reloaded up to failure to simulate the experimental procedure.

3.2. Results and discussion 3.2.1. Reference beams The numerical and experimental load vs. midspan deflection curves of the reference beams are depicted in Fig. 8. Although there are some small differences corresponding to the initial crack propagation stage, numerical and experimental curves are in close agreement. The above mentioned differences stem from the scatter of the maximum tension stress, ft, which typically presents relatively high standard deviation, and the inherent variability of the fracture energy, Gf, that was not determined experimentally. After the crack initiation, the global structural response was quite similar, with the ultimate strength obtained from the numerical model being almost equal to the average experimental failure load. Also the yielding of the steel rebars,

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corresponding to the sudden slope variation, occurred nearly for the same deflection. In the numerical model, collapse occurred for a midspan deflection of about 80 mm, only slightly lower than that of the maximum value measured in the experimental tests. Figure 9 illustrates the calculated crack distribution field, and the cracks' directions for the final load step. These numerical results are also in accordance with the structural behaviour observed in the experimental tests, in which the final crack width prior to collapse was higher than 1.0 mm, in accordance with the experimental results of beam B2. 3.2.2. Strengthened beams Figure 10 presents the comparison between numerical and experimental load vs. midspan deflection behaviour of the CFRPstrengthened RC beams. As already mentioned, the numerical results were obtained using the same concrete material model adopted in the reference beams, but this model was initially cracked up to a load similar to the one applied in the experimental analysis. Again, a good correlation was obtained, concerning not only the overall load vs. deflection behaviour, but also the ultimate strength. The collapse of the CFRP strengthening system occurred for midspan deflections of 13 mm and 14 mm in the numerical model and in the tests, respectively. After debonding of the strengthening system, the numerical load–deflection curve of the strengthened beams approached that of the reference one, similarly to what was observed in the experimental tests. 3.2.3. Repaired and strengthened beams As already mentioned, a parametric study was performed to study the structural response of the repaired and strengthened beams as a function of the equivalent material parameters, in particular to inquire about the equivalent material parameters of the concrete used in those beams. Figure 11 presents the load vs. midspan deflection curves of the repaired and CFRP-strengthened beams obtained from the initial material model, in which different fracture energies were assessed, defined as a function of the standard fracture energy, Gfr = k × Gf. The comparison between numerical and experimental results shows that using k = 10 provides the best fit to the experimental results. Despite the numerical and experimental ultimate strengths being slightly different, the global structural response obtained with the numerical model is very similar to experimental behaviour. Also the level of maximum displacement on the brink of maximum load was similar in both cases, being approximately 16.5 mm in the experimental curves (average value) and about 14 mm in the numerical model. Table 4 summarizes the results obtained in the numerical analysis, particularly regarding the beams’ stiffness (KNum) and ultimate loads (Pu,Num), listing also the relative differences compared to experimental data (Diff), attesting to the accuracy of the predictive models proposed.

4. Conclusions The main purpose of the study presented in this paper was to determine the influence of the crack repair through epoxy injection in the mechanical behaviour of reinforced concrete beams strengthened with CFRP laminates. In addition, the authors aimed at developing numerical models capable of simulating the behaviour of such beams with good accuracy and low complexity. Based on the results obtained in the experimental tests and numerical models, the following main conclusions are drawn: 1. As expected, both non-repaired (B3 and B4) and repaired (B5 and B6) strengthened beams presented a considerable improvement in terms of structural behaviour when compared to the reference beams (B1 and B2). Published by NRC Research Press

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Fig. 9. Crack distribution and crack directions of the reference beams for the final load step (colour scale of crack width units in metres).

Fig. 10. Numerical (Str_Num) and experimental (B3_Exp and B4_Exp) load vs. midspan displacement curves of the strengthened beams (numerical results of reference beam are also plotted, Ref_Num).

4.

5.

6.

7.

8. Fig. 11. Numerical parametric study and experimental (B5_Exp and B6_Exp) load vs. midspan displacement curves of the repaired and strengthened beams (1×, 5×,… indicates the ratio between the fracture energy and 50 N/m).

(120%) was considerably higher than that of the non-repaired ones (65%). In terms of cracking behaviour, as expected, the crack width evolution was similar in the non-repaired and repaired strengthened beams, both exhibiting much lower increase of crack width compared to the reference beams. This can be attributed to the increased CFRP tensile reinforcement. From a mechanical point of view, the main interest in repairing the RC beams prior to strengthening them with CFRP laminates was to increase their stiffness. Yet, regarding durability, crack repair also improves the protection against corrosion of steel reinforcement. The smeared crack models and the corresponding constitutive relationships adopted in the numerical investigations for all types of beams provided good agreement with experimentally observed structural behaviour. These models are accessible and easy to use for practice oriented engineers, requiring only a limited number of input parameters. For the non-repaired strengthened beams, a good agreement was obtained by using the original constitutive relation of concrete and considering the effects of prior loading and unloading. For the repaired and strengthened beams, a good agreement with experimental data was obtained by increasing the fracture energy of concrete by 10 times when compared to that of the reference beams.

Acknowledgements The authors wish to acknowledge FCT and ICIST for funding the research. The authors also wish to thank companies S&P Clever Reinforcement for having supplied the CFRP laminates, Secil/ Unibetão for having supplied the concrete, and HTecnic for the kind support in the manufacturing of the beams tested and in the repair and reinforcement execution.

References

2. In terms of strength increase with respect to the reference beams, the repaired and strengthened beams exhibited an improvement (41%) that was only slightly higher than that observed in the non-repaired ones (34%). 3. Regarding the initial stiffness, comparing with the reference beams, the improvement in repaired and strengthened beams

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