Experimental and numerical study of reinforced concrete specimens strengthened with composite plates

Composites: Part A 35 (2004) 885–893 www.elsevier.com/locate/compositesa

Experimental and numerical study of reinforced concrete specimens strengthened with composite plates Mickael Muller, Evelyne Toussaint, Jean-Franc¸ois Destrebecq, Michel Gre´diac* Laboratoire d’Etudes et de Recherches en Me´canique des Structures, Universite´ Blaise Pascal Clermont II, 24, avenue des Landais, BP 206, 63174 Aubie`re Cedex, France

Abstract The present paper deals with the refined analysis of reinforced concrete specimens strengthened with composite plates and subjected to tension tests. A particular attention is paid to the characterization of cracks that develop in the concrete when tensile tests are carried out. A non-contact optical method based on image correlation is used to determine the displacement field onto the surface of the specimens during the tests. Both unstrengthened and strengthened specimens are tested in purely axial tension. The latter ones are first precracked, then repaired with composite plates bonded onto the concrete. The influence of the composite plates is studied in terms of distribution and width of cracks, especially in the vicinity of the composite. A model for the prediction of crack width in a repaired specimen is proposed. This model is validated by experiments and 3D finite element simulations. q 2004 Elsevier Ltd. All rights reserved. Keywords: A. Laminates; B. Anisotropy; C. Laminate mechanics; Optimization

1. Introduction Civil concrete structures are generally designed for a service life ranging between 50 and 100 years. As a matter of fact, the longevity of a structure depends on its constitution and service conditions. Several parameters may reduce this lifespan like increased service load, creep, environmental or fatigue effects [1 – 4]. Economical reasons do not always allow the destruction and the construction of a new structure to replace a damaged one. In order to fulfill new service conditions and/or to reduce time effects, a solution consists in adding an externally bonded material. This additional material relieves stresses in the concrete member. A solution was proposed about 40 years ago which consisted of fixing steel plates onto the soffit of concrete structures [5]. This technique is, however, difficult to use and needs in practice some important handling. Besides, it is not always possible to reach the damage part of the structure with cumbersome systems to support steel plates. Another way to repair concrete structures is to use composite materials. This method is younger than the previous one since the first * Corresponding author. Tel.: þ33-4-73-40-75-29; fax: þ33-4-73-40-74-94. E-mail addresses: [email protected] (M. Gre´diac), [email protected] (E. Toussaint) 1359-835X/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2004.01.009

attempts were performed in the 1980s. The use of composite materials overcomes the problems of transporting, handling and bonding heavy plates. Fiber reinforced polymer materials exhibit a high strength-to-weight ratio and corrosion resistance. Mechanical properties of such composites are greater than those of steel, especially in terms of tensile and fatigue strengths. Designing both additional composite material and joint with concrete are critical points because reinforcements support a part of the loading of the structure in order to relieve it. Some simplified models have been proposed within the framework of the theory of beams to design the reinforcement. In this case, the composite is considered as an additional and external material [6]. Such a framework is, however, too rough to take into account some specific local phenomena which take place in repaired structures like the transfer length and the bridging of the cracks [7,8]. The question of the transfer length is critical since it governs the range of a shear stress peak in the concrete near the end of the composite reinforcement [9]. This is a consideration at the ultimate limit state, since it may cause the sudden collapse of a repaired structure. This issue has received considerable attention from a number of authors. Therefore, it will not be discussed more in the present work. The issue of the crack bridging is another challenge,

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which has not been properly faced until now to the knowledge of the authors. Crack control, i.e. appropriate design in order to limit crack spacing and width, is necessary to prevent harmful ingress and corrosion of the steel reinforcement during the expected service life of the structure. This is a consideration at the serviceability limit state, which requires specific investigations in the case of reinforced concrete members repaired with composite plates. The aim of the present paper is to bring a contribution to this research effort. Several models have been developed and validated to describe the evolution of cracks in repaired concrete structures. Some authors proposed models with simplified assumptions [10], but refined studies allowing their validation are rather scarce in the literature. On the other hand, the mechanical response of a crack bridged by a bonded composite plate remains somewhat obscure. The objective of this work is to examine the kinematic field in the vicinity of bridged cracks. The attention is focused on the proper prediction of crack widths in reinforced concrete members strengthened with composite plates. Refined tests are necessary since the materials involved exhibit very different mechanical behaviors. Moreover, phenomena are localized. The concrete is brittle, the composite presents a very high fracture strength and a longitudinal modulus five times higher than the concrete one. The glue between concrete and composite is much more flexible and its thickness is small. Besides, the glue mainly carries shear stress. The composite works in very unusual conditions because stress peaks are assumed to take place in the vicinity of the cracks. Refined observations in this zone would be very relevant to understand these phenomena and to establish predictive models. Non-contact techniques have proved profitable to elucidate the mechanism of stress transfer in composite-plated members. Such a technique [11] has been recently used to measure crack widths in a repaired structure [12]. Many studies have already been carried out to investigate static or quasi static behaviors of repaired structures. Tension tests on concrete members reinforced with composite plates have seldom been carried out [13, 14]. On the contrary, bending tests are widespread because they correspond to a type of loading that exists in practice [7,10,12,15 –18]. As a matter of fact, the state of stress is much more complex in bending specimens, whereas it is more ‘homogeneous’ in axially tensioned specimens. Another difference is that non-contact measurements can be easily taken from all four faces of a specimen in the case of a purely axial test. For these reasons, and because the concern here is the opening of cracks bridged by an external composite reinforcement, tension tests have been preferred in the present work. The main features of the non-contact method used during the tests are briefly described below.

2. Principle of the image correlation method Non-contact optical methods are very attractive to investigate concrete structures. Indeed, they provide displacement or strain fields. These methods can be used in laboratory or in situ. In the present work, a non-contact method is used to measure the displacement fields from the faces of the tested specimens. The technique used for displacement measurements is the image correlation method proposed by Sutton [19]. This method is based on the comparison between two different images captured at two different levels of loading. The former image is analyzed as a function f ðx; yÞ that represents an initial grey level distribution. This function becomes f p ðxp ; yp Þ in the deformed image. It is defined by f p ðxp ; yp Þ ¼ f p ðx þ uðx; yÞ; y þ vðx; yÞÞ

ð1Þ

where uðx; yÞ and vðx; yÞ are the components of the displacement fields onto the surface under investigation. The two functions are compared using a grey level correlation coefficient. An iterative process based on an optimization of the correlation coefficient calculates the deformation of a virtual mesh attached to the investigated surface. This procedure provides discrete values of the vector of displacement. A continuous displacement field is obtained by interpolating between node values. This technique of image correlation has been implemented in a software called KISDEF developed by Vacher [20]. This software has been used for the present work. The smallest distance between two independent points is the spatial resolution; it is about 10 pixels in the present study. The smallest detectable measurement is the resolution; it can be defined as the standard deviation of the noise. It depends on the quality of the material (camera, lighting). In the present study, it has been found to be equal to about 0.05 pixels.

3. Experimental setup 3.1. Specimen preparation The specimens consist of concrete prisms (80 £ 80 £ 500 mm3) reinforced with four re-bars parallel to the longitudinal axis (Fig. 1). The re-bars are standard deformed bars 6 mm in diameter. Their specified yield stress

Fig. 1. Layout of a reinforced concrete specimen strengthened with composite plates.

M. Muller et al. / Composites: Part A 35 (2004) 885–893 Table 1 Material properties

Young modulus (GPa) Poisson ratio Density (kg/m3)

Concrete

Steel

Composite

Adhesive

36 0.2 2400

200 0.3 7800

165 0.32 1500

13 0.3 1800

is 500 MPa. Note that their length exceeds the specimen length. The concrete was prepared with the following material proportions: free water/cement ¼ 0.59 and cement/sand/coarse aggregate/fine aggregate ¼ 1.2/2.15/2.46/0.24. Because of the dimensions of the specimens, the coarse aggregate was of 8 mm maximum size. The compressive strength of the concrete was about 35 MPa at 28 days. The specimens were demoulded 24 h after cast. Then they were kept until testing day in a plastic foil. Composite plates were bonded onto two opposite faces of some of the concrete prisms. The plates were 80 mm wide, 340 mm long and 1.35 mm thick. They were cut from Sika Carbodur S 812 carbon/epoxy plates. They contained 68% fraction of high strength fibers and 32% of epoxy resin. The longitudinal modulus of the composite was 165 GPa and the tensile strength was 2800 MPa. The material characteristics are shown in Table 1. The surfaces to be bonded were prepared as suggested by the composite supplier. The surface of the concrete was brushed to remove laitance, grease and other dirt. The composite plates were cleaned and grease was removed with Sikadur cleaner. Then, the plates were symmetrically bonded onto the concrete prism with a two-part cold-curing epoxy resin adhesive. The resin and the hardener were mixed with a ratio in mass resin/hardener equal to 3/1. The adhesive was applied to both components to ensure there was sufficient excess to avoid a starved join and to prevent the formation of air bubbles by the spread of adhesive from one surface to the other. A suitable device was used [21] to achieve the desired thickness of 1 mm. Grey levels of investigated surfaces must be as random as possible to use the image correlation method. Hence, the surface of the samples had to be as random as possible in terms of grey levels. This was the case of the concrete surface because it exhibited a natural contrast in term of grey levels. On the contrary, the composite surface was uniformly black. To improve the contrast, spots of white painting were sprayed on the surface by using an atomizer. An important condition consisted in using matt painting to avoid any reflection. 3.2. Tension tests The specimens were tested at the age of 4 months. They were equipped with two fixings specially designed to carry the load from the grips of the testing machine to the re-bars (Fig. 1). The four steel bars were welded to a thick steel

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plate at both ends. A steel rod was tightened at one end to the steel plate by a nut and the other end was gripped in the jaw. A 200 kN Zwick testing machine was used to load the samples in tension. A ball and socket joint fixed at the top jaw ensured the axiality of the loading. The tests were monitored by the control of the displacement of the grip at a rate of 0.4 mm/s. 3.3. Displacement measurement The optical system used for the non-contact measurement method consisted of a 12 bits dynamic Philips camera. The CCD camera had 106 joined pixels (1024 £ 1024 pixels). The camera was fixed onto a multidirectional adjustable support at a distance about 500 mm from the specimen. A personal computer was connected to the camera in order to process image acquisition and data treatment with the KISDEF program described above. Two lamps provided uniform light to the specimen with good contrast. The zoom of the camera was adjusted in such a way that 10 pixels corresponded to 1.02 mm for the unstrengthened specimen and to 1.4 mm for the strengthened specimen. The values were different because the tuning of the zoom lens of the camera was not the same for both tests. The images were captured by the camera and stored on the hard disk of the personal computer. The images corresponded to the surface of the samples at different levels of loading. The KISDEF program automatically calculated the displacement fields by comparison of two images: the one was a reference image that corresponded to the unloaded specimen. The other image corresponded to the loaded specimen.

4. Specimens without composite 4.1. Tests results 4.1.1. Crack detection Specimens without composite plates were subjected to five cycles of loading/unloading. The maximum applied load was 40 kN. This was sufficient to observe concrete cracks without an elastic deformation in the reinforcing steel (yield limit of the re-bars corresponded to a load of about 60 kN). Typical results obtained for one of the tested specimens are discussed in the present section. A close picture of the tested specimen (Fig. 2) shows that two cracks have formed in the zone under investigation (underlined with dashed lines). The longitudinal component of the field of displacements given by the non-contact measurement method onto the concrete surface at a given loading level is presented in Fig. 3. The two cracks, hardly visible by the naked eye, are detected with the optical system. They appear as discontinuities in the displacement fields. The distance between the two cracks is presently

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displacement field calculated with the optical method is the sum of a mechanical displacement and a measurement noise that mainly depends on the quality of the camera and on lighting conditions. In order to overcome this difficulty, the following procedure has been defined to determine the crack width and location. First, a difference in the longitudinal displacement is calculated pixel to pixel along a given longitudinal line. The abscissa where this difference is maximum corresponds to the location of the crack. Then, starting from the crack, a difference pixel to pixel of the longitudinal displacement is calculated until this difference becomes smaller than a limit (5 mm in the present case). This is repeated on both sides of the crack. The width of the crack corresponds to the difference between the longitudinal displacements of the two relevant points.

Fig. 2. Tensile cracks in a RC specimen (detail).

about 60 mm. The vertical steps shown in the displacement field correspond to crack openings. Between cracks, the strains remain limited in the concrete (within elastic range), leading therefore to a nearly uniform field of displacements. 4.1.2. Determination of crack width The displacement field shown in Fig. 3 may be used to measure the crack widths. The height of the steps in this figure corresponds to the openings of the cracks. The magnitude of the steps is about 0.88 pixels, which corresponds to a crack width of about 90 mm. An important difficulty encountered in the determination of the width of cracks is the measurement noise. Indeed, any

Fig. 3. View of the longitudinal displacement field on the surface of a cracked specimen.

4.1.3. Evolution of the crack width vs load The evolution of the width of one crack vs load is studied for two cycles of loading of the specimen (Fig. 4). During the first cycle of loading, the crack has appeared at F ¼ 20 kN. This value is consistent with the expected behavior of the specimen (see Section 4.2). At unloading, the crack width decreases at a linear rate with the load. A residual width of the crack of about 24 mm is observed after unloading. It is generally assumed that the opening of cracks is resulting from a slip between the concrete and the re-bars. Unfortunately, this mechanism could not be observed during the tests, since the optical method used allowed measurements from the external faces of the specimens only. Based on this assumption, the residual width could be explained as resulting from a partially unrecoverable slip between the two materials. Similarly, the hysteresis observed during the second loading cycle could be related to this mechanism. At the beginning of the second cycle, the crack width does not increase at once. In fact, the crack begins to open again between 5 and 10 kN (note that images have been recorded every 5 kN). On unloading, the crack width is very similar for the two cycles. Three more loading cycles have been applied to the specimen (not represented in Fig. 4).

Fig. 4. Evolution of one crack width in a reinforced concrete specimen under cyclic loading.

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and for the load that caused the cracking of the crosssection, respectively. e s2 is given by

e s2 ¼

Fig. 5. Evolution of crack widths in a precracked reinforced concrete specimen.

The crack widths measured at F ¼ 40 kN are very similar to values obtained at the same level of loading during cycles one and two (Fig. 4). 4.1.4. Crack width in a precracked specimen The method has been used to study the crack spacing and crack width distribution in a precracked specimen. Five cracks were observed in the zone under investigation. By using the procedure described above, it was possible to determine the location and the width of each pre-existing crack. The distance between neighbor cracks was found to be randomly distributed between 60 and 90 mm with an average spacing equal to 71.4 mm. Fig. 5 represents the evolution of crack widths vs loading force. Since the optical method is based on a comparison of images, only the increase Dw in the opening of the cracks can be measured, but not the initial opening (i.e. actual residual width) in the unloaded specimen. Larger crack opening corresponds to larger crack spacing. On the contrary, lower opening corresponds to lower spacing. This result is consistent with the usual assumption about reinforced concrete behavior. 4.2. Prediction model for crack width and spacing

N Es A s

ð4Þ

where N is the actual longitudinal tensile force applied to the member, Es is the Young’s modulus of the steel and As is the total cross-sectional area of the steel bars. Based on these equations, the evolution vs loading of the width of the crack located at mid-length of the tested specimen is estimated. The mean distance to neighbor cracks, measured during the test, is equal to 80 mm. The calculated value of the loading that has caused the cracking of the specimen, i.e. F ¼ 18:9 kN, is estimated on a basis of the tensile stress in the uncracked cross-section equal to the tensile strength of the concrete, i.e. 2.7 MPa. The comparison between predicted and experimental crack width is shown in Fig. 6. It is seen that the values predicted by the present model are in fair agreement with experimental values. In Section 4.3, this model will be introduced in a finite element model of a cracked specimen in order to analyze its tensile behavior. 4.3. Numerical simulation The theoretical model presented above has been implemented in a 3D FEM model in order to simulate the behavior of a cracked specimen. CAST3M software [23] was used to this purpose. Since the theoretical model applies to cracked specimen, concrete blocks between cracks are modeled separately from each other. Taking advantage of the symmetry, only one eighth of a concrete block is modeled (Fig. 7). Appropriate limit conditions are applied to the planes of symmetry. The cracked section is taken into account as a non-cohesive interface. To simulate the loading conditions, the load is applied to the re-bar in the cracked section. Eight-nodes cube elements are used to mesh the specimen. The modeled re-bars have the same cross-sectional

The objective of this section is to calculate the width of cracks in reinforced concrete specimens subjected to tensile loading. According to CEB – FIB Model Code [22], an average value wm for crack width in the tensile zone of a reinforced concrete member is given by the following equation wm ¼ je s2 Dlm

ð2Þ

where Dlm is the average crack spacing, e s2 is the strain in the tensile reinforcement in a cracked cross-section and j is a coefficient defined as follows   ssr 2 j¼12 ð3Þ ss where ss and ssr are tensile stresses in the re-bars calculated in a cracked cross-section for the actual value of the loading

Fig. 6. Crack opening in an unstrengthened specimen—comparison between theory, experiments and FEM simulation.

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bonding procedure and control of the adhesive joint thickness were processed as explained above in Section 3.1. The length of the composite plates was designed in such a way that the two cracks closest to specimen ends were not bridged by the composite. All intermediate cracks were bridged. The camera was adjusted in order to monitor the behavior of the two first cracks at the one end of the specimens. The load was increased at a constant rate of displacement of the grip until the peeling-off of the concrete cover occurred in the zone of anchorage of one composite plate. Then, the loading was relieved until complete unloading of the specimen. 5.2. Test results Fig. 7. FEM model for an unstrengthened specimen (each cube represents 33 ¼ 27 cube finite elements).

area as the actual ones (Fig. 7). Mechanical properties used for the calculations are those measured for the materials used (Table 1). All materials are supposed to behave in their elastic range. The theoretical model is introduced in the FEM model by relaxing nodal connections between concrete and re-bars over a length counted from a crack equal to jDl=2; Dl being the distance between neighbor cracks. Coefficient j depends on the level of loading, according to Eq. (3). Calculations were, therefore, repeated for different values of j ranging from 0 to 0.78, which correspond to F values ranging from 18.9 kN (force at cracking) to 40 kN. The relative displacement between the two lips of the crack was considered as its opening. The corresponding calculated values are plotted in Fig. 6 for the crack already studied above. This figure shows a fair agreement between analytical, numerical and experimental values of the crack width. This confirms the applicability of the non-contact optical method for measuring crack opening and the validity of the FEM model presented above. Therefore, these two ways may be used to study the cracking activity in a reinforced concrete specimen strengthened with external composites plates.

Attention here is focused on results concerning the crack behavior of the same specimen as studied above. The longitudinal component of the field of displacement measured by means of the non-contact method is presented in Fig. 8 at F ¼ 35 kN (just before peeling-off). Two cracks are visible in this figure. The wider one (i.e. the higher step in the longitudinal displacement) is the one closest to the specimen end. As explained above, this crack was not bridged by the composite. The next crack is located in the repaired zone of the specimen. Its width is less than the previous one (about 28 mm, instead of 100 mm for the unbridged crack). This difference could be observed during the test since the first crack was visible by naked eye whereas the other one was not. The evolution vs load of the widths of the two cracks is plotted in Fig. 9. For reasons discussed in Section 4.1.4 about precracked specimens, Dw represents the increase in width of the cracks starting from the initial width (i.e. residual width in the unloaded specimen) since this initial width cannot be measured by means of the optical method. Fig. 9 clearly shows that the two investigated cracks behave in different ways. The behavior of the unbridged one is very

5. Specimens repaired with composite plates 5.1. Test arrangement The aim of this second part of the study was to analyze the influence of composite reinforcements on the crack behavior in repaired specimens. The specimens used in the previous part of the study were strengthened with pairs of composite plates bonded onto two opposite faces (Fig. 1). The specimens were unloaded during the application of the composite plates. Preparation of the concrete surface,

Fig. 8. Longitudinal displacement field on the surface of a precracked specimen repaired with composite plates just before peeling-off.

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the specimen (about 100 mm). As discussed above, the average width of the second one is much smaller, about 28 mm. But its width is not uniform; it ranges from about 5 mm next to the composite to 35 mm in the middle of the concrete face. This clearly enlightens the bridging effect of the composite reinforcement onto cracks. It is worth keeping in mind that this conclusion is drawn from purely axial tests where cracks propagate through the full depth of the concrete specimen. Bending tests could possibly lead to different conclusions since cracks develop generally according to a more complex pattern in the latter case [21]. 5.4. Proposition of a modified expression for wm Fig. 9. Evolution vs loading of the crack widths in a strengthened RCspecimen.

similar to that of cracks in the unstrengthened specimen (Fig. 5). The crack does not re-open before the load reaches 5 kN. Then the crack width increases in a pretty linear manner with the intensity of the load. Similarly, the bridged crack starts to open for F $ 5 kN. Then its width increases at a much lower rate than the former one. Above 35 kN, the width of the bridged crack increases suddenly at a much higher rate. This is due to the peeling-off of the concrete. As a matter of fact, the tensile force supported by the composite reinforcement is transferred to the concrete through the adhesive joint [9]. This mechanism yields a complex stress concentration in the concrete beneath composite end. If the concrete strength is exceeded, a crack forms and propagates within the concrete cover between reinforcing bars and composite plates, thus leading to brittle failure by peeling-off.

Based on experimental evidences discussed in Section 5.3, it is possible to propose a modified expression for the analysis of crack width in strengthened reinforced concrete specimens. Let Np and Ns denote the tensile efforts supported by the composite plates and the steel bars, respectively, in a cracked section. Hence Ns ¼ N 2 Np

ð5Þ

Let us assume that the longitudinal strain in the composite may be expressed as be s ; where e s is the actual longitudinal strain in the re-bars and b is a coefficient which allows for the strain distribution between steel bars and composite plates ðb # 1Þ: It is a trivial matter to deduce from the equilibrium of a cracked cross-section that

es ¼ g

N Es As

ð6Þ

5.3. Transverse profile of cracks

where g is a reduction factor defined as follows   Ep Ap 21 g¼ 1þb ,1 Es As

As explained above, cracks are restrained from opening by a bridging effect of the composite plates. This restraint is clearly illustrated in Fig. 10 where the transverse profile of the unbridged crack is compared with that of the bridged one. The width of the former one is about uniform across

Ep and Ap denote, respectively, the longitudinal modulus of elasticity and the cross-sectional area of the composite plates. Assuming that crack width may be estimated by Eq. (2) on the basis of a reduced steel strain (Eq. (6)), it yields wm ¼ gje s2 Dlm

ð7Þ

ð8Þ

where e s2 is given by Eq. (4). Taking the material properties into account (Table 1), the actual value of g is 0.388 in the present work. Coefficient b is presently taken as 1 for the sake of simplicity. 5.5. FEM simulation and comparison with test results

Fig. 10. Comparison between crack width distributions across a strengthened specimen at F ¼ 35 kN.

The FEM model developed above has been completed in order to take the existence of the CFRP-composite reinforcement into account (Fig. 11). Two layers are added to one of the external face of the concrete block; the first one represents the adhesive joint of 1 mm in thickness, the other represents the 1.35 mm thick composite plate. The two layers span the discontinuities introduced to

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Fig. 11. FEM model for a strengthened specimen (each cube represents 33 ¼ 27 cube finite elements).

represent the existing crack in the concrete (see Section 4.3). To simulate the test conditions, the load is applied to a rigid block (not represented in Fig. 11) connected to the re-bar and the composite plate in the cracked section. Eight-nodes cubes are used for the mesh. Material properties are those listed in Table 1. The opening of the cracks corresponds to the relative displacement of the crack lips. It is calculated at the same level as the re-bars. Since the specimen was precracked, the same j value (namely j ¼ 0:78) corresponding to the maximum load intensity previously applied to the specimen (i.e. 4 kN) is considered to relax the nodal connections between concrete and steel. Calculated values of the width of the bridged crack are compared with analytical and experimental values in Fig. 12. It is worth noting that the resolution of the optical method is about 5 mm. This may explain the dispersion observed in the experimental figures. Crack width calculated by the analytical method (with b ¼ 1) and the FEM model are comparable. Both these methods give a save prediction of crack opening in the strengthened specimen. By fitting analytical and numerical models in Fig. 12, it is possible to determine the actual value of b coefficient, i.e. b ¼ 0:897:

Fig. 12. Comparison between analytical, experimental and FEM simulated width for a bridged crack.

† existence of cracks is revealed by discontinuities in the field of displacements. Cracks width corresponds to discontinuity amplitude; † width of crack is measurable beyond a magnitude of 5 mm that approximately corresponds to measurement noise; † crack opening in terms of applied tensile loading is not linear in reinforced concrete specimens. Values predicted by CEB –FIB Model Code are consistent with 3D FEM simulations and with crack width measured by means of the optical method used; † a crack bridging effect is observed in strengthened specimens. Measured widths are much smaller for bridged cracks than for unbridged ones. Looking at crack profile throughout the depth of the specimen, a restraint in crack opening is observed in the vicinity of the composite reinforcements, that shows the existence of a bridging effect by the composites; † a predictive model based on CEB –FIB Model Code is proposed for crack width in strengthened reinforced concrete members. Compared with test results, this model proves conservative. From a comparison with a 3D FEM simulation, a value of 0.9 may be proposed for the reduction factor b:

6. Conclusion Acknowledgements Reinforced concrete specimens have been subjected to tensile tests. After cracking, specimens have been reinforced with composite plates bonded onto two opposite faces. Displacement fields onto the concrete and the composite external surfaces have been measured by means of an optical method. An analytical model has been proposed on the base of CEB – FIB Model Code to predict crack opening in strengthened specimens. Numerical simulations of cracked specimens (strengthened or unstrengthened) have been worked out. The following conclusions can be drawn:

Sika company is gratefully acknowledged for its support during the present study.

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