ASSESSMENT OF NON LINEAR BOND LAWS FOR NSM SYSTEMS IN CONCRETE ELEMENTS

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1 ASSESSMENT OF NON LINEAR BOND LAWS FOR NSM SYSTEMS IN CONCRETE ELEMENTS Franceca CERONI Aitant Profeor Univerity of Sannio Benevento, Italy Joaquim BARROS Full Profeor Univerity of Minho Guimarãe, Portugal Maria PECCE Full Profeor Univerity of Sannio Benevento, Italy Marco IANNICIELLO Mater in Civil Engineering Univerity of Sannio Benevento, Italy Abtract In thi paper the numerical FEM model developed to imulate the behaviour of the NSM trengthening ytem for concrete element i preented. The plane model introduce the non linear bond law of the ytem by an interface element between the compoite reinforcement and the concrete conidered linear. The reult of two experimental program are analyed and ued to calibrate the parameter of the bond hear-lip relationhip by mean the numerical model. The procedure i baed on the invere analyi of the experimental data in order to have the better fitting of the global pull-out load-diplacement curve. Keyword: Bond-lip law, FEM model, NSM technique 1. Introduction Over the lat year, the ue of fibre reinforced polymer (FRP) material for repair and trengthening of concrete tructure ha progreively increaed, due to the everal advantage related to thee compoite when compared to the teel [1] [2]. In the lat decade, a trengthening technique deignated by near urface mounted (NSM) ha been propoed to increae the flexural and hear trength of RC member precluding the debonging failure. NSM ytem are compoed by FRP rod and trip that are intalled into pre-cut groove open on the concrete cover of the element to be trengthened [3] []. Several reearche have tudied the NSM technique, performing experimental tet to characterize both the load-carrying capacity and the bond trength of thee ytem [5] [6] [7] [8]. The experimental reult evidence that the load-carrying capacity of NSM ytem i trongly influenced by the bond performance, which i trictly dependent of the material, urface configuration and type of the FRP reinforcement. The objective of thi reearch i to derive a bond tre-lip relationhip, τ, for the modelling of the bond behaviour between NSM FRP bar/trip and concrete by uing a finite element approach (FEM). Uing the τ propoed by Sena Cruz and Barro [7], the bond behaviour of everal pecimen teted by Bilotta et al. [9] and Macedo et al. [1] were imulated by performing FEM analyi in order to derive the value of parameter of the bond law that aure the bet fitting of the force-end lip relationhip obtained experimentally. Some of the reult are preented herein. 2. Experimental reult 2.1 Experimental program The reult of two experimental program of bond tet on variou type of NSM ytem carried out by the Author uing different type of tet et-up have been conidered in thi Page 1 of 8

2 paper. The meaningful data of both program, dicued in detail in [9] [1], are ummarized in the following and individuated a program 1 and 2. The pecimen of program 1 teted in [9] are made of primatic concrete block (dimenion b c = 16 mm, h c = 2 mm, L c = mm) trengthened with FRP bar or trip bonded according to the NSM technique (Figure 1). Three bond tet have been performed on equal pecimen for each FRP typology; in particular, 6 different type of bar/trip have been embedded into a groove longitudinally cut in the cover of the prim after concrete hardening (Figure 1). The ame bond length wa ued for all the pecimen (L b = 3 mm). Five train gauge 7 mm paced have been glued on the NSM urface before applying the adheive. metallic pipe NSM FRP concrete 3 2 teel bar F ection ection 1 ection ection 2 3 LVDT 1 LVDT 2 adheive CFRP 22 xi 5 1 L Lb concrete 15 teel plate bolt Figure 1. Set-up of experimental program 1. Figure 2. Set-up of experimental program 2. The main tet variable were: type of reinforcement (bar or trip), type of fiber (gla, baalt, carbon), Young modulu (6-182 GPa), bar diameter (d = mm). Furthermore, the bar have different urface treatment: and coated round baalt bar with diameter 6 and 8 mm (B-6-SC and B-8-SC), ribbed round gla bar with rib cut in the hardened bar with diameter 8 mm (G-8-RB), mooth round carbon bar with diameter 8 mm (C-8-S), and mooth carbon trip with thickne 2.5 mm and width 15 mm (C-2.5x15-S). The round bar were introduced into quare groove of 1 and 1 mm edge for the bar of 6 and 8 mm diameter, repectively and, thu, the hape ratio k i defined a ratio of groove edge to-bar diameter; by contrat, the trip wa introduced into a rectangular groove of 25 mm x 8 mm cro ection, and k i defined a ratio of groove-totrip width. The value of k, are alway greater than 1.5, which i the minimum value uggeted to avoid the plitting failure of the epoxy [8]. Epoxy adheive wa ued to bond the bar and the trip into the groove. All pecimen have been cat in the ame batch; the mean cylindrical compreive trength at 28 day after the cating wa f cm = 19 MPa and the mean Young modulu wa 18.6 GPa. In the experimental program 2 carried out by Macedo et al. [1] the pull-out configuration repreented in Figure 2 wa ued. Primatic concrete pecimen with dimenion of 15x15x6 mm 3 were adopted and everal bond length were analyzed. The depth and width of the groove wa 22 mm and 5 mm, repectively. One diplacement tranducer (LDTV1) wa ued to meaure the diplacement between the left edge of concrete pecimen (ection ) and the firt FRP point bonded to concrete (ection 1); in the following it will be referred a diplacement at loaded end, d l. A econd diplacement tranducer (LDTV2) wa ued to regiter the diplacement at free end, d fr, by meauring the diplacement between the Page 2 of 8

3 lat FRP bonded point (ection 2) and the concrete point located at ection 3. Strain gauge glued to the CFRP were ued to etimate the train variation in the bonded region. To ae the influence on the ytem performance of the bond length and the depth at which the CFRP trip i located into the groove, 1 pullout tet were performed uing 5 different value of bond length, L b ; therefore for each couple of pecimen with ame L b, 2 different poition of the trip into the groove, x i, were conidered (Figure 2). The generic denomination of erie i LbY_xZ, where Y and Z are the CFRP bond length (, 7, 9, 12 and 15 mm) and it poition in the groove (6 and 12 mm), repectively. To evaluate the concrete propertie, three compreive tet on cylinder pecimen at 28 day after cating were performed and gave a mean value of 25. MPa and 29. GPa for the compreive trength, f cm, and Young modulu, E c, repectively. 2.2 Experimental reult For each NSM ytem of program 1 and 2, Table 1 and 2 include the following relevant reult: ultimate tenile trength f fu, Young modulu E f, axial tiffne E f A f, groove hape factor k, failure mode, imum load F, and the loaded end lip at F, d. The mechanical propertie of FRP indicated in thee table are the average value obtained by experimental tenile tet on five pecimen according to [11]. In program 1 the diplacement d were calculated by integrating the train meaured along the bonded length, while in program 2 they were obtained by the difference between the LVDT1 meaure, d l, and the elatic elongation of the unbounded part of the FRP trip. Table 1. Main experimental data and reult for program 1. Specimen f fu E f E f A f K Failure F d [MPa] [GPa] [kn] [-] mode (a) [kn] [mm] B-6-SC-1 E/C B-6-SC-2 E/C B-8-SC-1 E/C B-8-SC E/C B-8-SC-3 E/C G-8-RB-1 E/C G-8-RB E/C G-8-RB-3 E/C C-8-S-1 E/C+CL C-8-S E/C+CL C-8-S-3 E/C+CL C-2.5x15-S-1 E/C C-2.5x15-S E/C C-2.5x15-S-3 E/C (a) E/C: debonding at the epoxy-concrete interface, CL: detachment of a concrete layer Table 2. Main experimental data and reult for program 2. f fu E f E f A f K Failure F d Specimen [MPa] [GPa] [kn] [-] mode (a) [kn] [mm] Lb_x6 S Lb_x12 S Lb7_x6 S Lb7_x12 S Lb9_x6 S Lb9_x12 S Lb12_x6 S Lb12_x12 S Lb15_x6 S Lb15_x12 S (a) S: Splitting of adheive Page 3 of 8

4 3. The numerical analyi 3.1 The FEM model The numerical imulation were carried out with FEMIX v. FEM-baed computer program [12]. To imulate the boundary condition of the tet pecimen of program 1, in the FEM model (Figure 3a) the inferior part of the pecimen wa retrained with upport, precribing the diplacement in direction 3 (Figure 3b). The tet wa modeled a a plane tre problem. Due to tructural ymmetry condition only half part of pecimen wa conidered. Four-node Lagrangian plane tre element with a 2x2 Gau-Legendre integration cheme were ued to imulate the concrete and the CFRP trip; the thickne of 2 mm and 15 mm were aigned for the concrete and CFRP, repectively. The adheive wa imulated by fournode line finite interface element with two-point Lobatto integration rule. The tangential tiffne of thee interface element i defined once the parameter that define the local τ - law are known. In regard to the normal tiffne, a contant value of 1.e+6 N/mm 3 i conidered. The CFRP trip and concrete were modeled a linear elatic material, conidering the Young modulu value determined in the experimental tet, and a Poion coefficient of. and.2 for the CFRP and concrete, repectively. The load wa applied in two point, and the arc-length method wa ued with the controlling diplacement at loaded end of CFRP, by applying a diplacement increment of.1 mm in direction 3 (Figure 3b). 8 F F Loaded point F = (F/ + F/) 2 Integration point CFRP trip Diplacement Concrete z = 1 mm average Lb = 3 z z = 1 mm Bond tre z = 5 mm average dir. 3 z = 5 mm Interface element dir. 2 Support (a) (b) Figure 3. Finite element idealization of C-2.5x15-S erie: (a) complete meh; (b) zoom on the top ide. 3.2 The bond law of the interface element In the preent work the determination of the local bond tre-lip relationhip for both trip and bar i baed on the approach from [7]. The non linear bond law, τ, can be defined a follow: Page of 8

5 τ ( ) = m lin τ ( ) = τ α τ ( ) = τ if lim if lim if > where τ i the hear trength and it correponding lip, repectively, α and α are parameter defining the hape of the curve and m lin i the initial tiffne of the bond law (Figure a). The oftening branch of the bond law can tend aymptotically toward a reidual or a zero hear tre. The trend of the influence of the characteritic of a local bond-trelip law on the pull-out behavior of a pecimen in a bond tet (repreented by the pull-out force-diplacement relationhip, F - d) are repreented in Figure b. τ τ 6 5 α ' (1) DESCENDING branch of τ - Linear branch mlin lin (a) 3 ASCENDING branch of τ LINEAR branch of τ (b) Figure. (a) Local bond tre-lip relationhip; (b) qualitative correlation between τ- and F-d relationhip in a bond tet. 3.3 The influence of bond law parameter on the pull out load The bond law depend on five parameter, but the following one have relevant influence on the bond behaviour: - the peak value of bond tre-lip curve, τ, and it correponding lip, ; - the parameter that define the hape of the pot-peak branch of τ relationhip, α. Each one ha a different impact on the trength of the ytem, a howed in Figure 5. In thi graphic the parameter ξ i given by the following expreion: where, τ and parametric tudie, repectively (i.e. ' τ α ξ = = = ' τ α ' α repreent the minimum value of, τ and 5 =.8mm, τ =1.25MPa and ' α =.2). (2) ' α ued in the 3 2 F / F τ α' ξ Figure 5. Evaluation of the impact of, τ and α on the F. Page 5 of 8

6 F i the imum pullout force when uing thee value. Figure 5 how that the parameter that mot affect the imum pull-out force value i the local bond peak tre, τ ; in fact, when ξ = 8, the ratio F / F i about 5.. Experimental-numerical comparion.1 The invere analyi The differential equation of bond wa olved for ome of the pecimen teted in [9] [1] auming the bond law given by Eq. (1). The firt aement of the bond law parameter for pecimen of program 1 wa tried uing the experimental τ relationhip obtained by mean the train gauge meaurement. In particular, the hear tre wa calculated by uing the meaure of the firt two train gauge placed at 1 and 8 mm from the beginning of FRP bonded length and, thu, the experimental meaure refer to the abcia z = 5 mm. The correponding lip wa calculated by integrating the experimental meaure of train along the bond length. However, the reult were not atifactory when the force-diplacement curve, F - d, were numerically determined and compared with the experimental one. Therefore, an invere analyi baed on the comparion of the experimental pull-out force-diplacement curve, F - d, with the numerical one, wa performed to ae the two parameter and α, while the τ, lim and α were fixed by conidering the local experimental bond law. The parameter ult i defined when the imum pull-out force i attained. In Table 3 the value of the parameter are lited for each NSM ytem together with the theoretical and the mean experimental failure load. In Figure 6 the whole numerical and experimental F - d curve are compared. A good compliance can be oberved both in term of F - d curve and of imum load. The value of the parameter of the bond law are thoe that aure the bet fitting of the average F - d curve of the three pecimen that compoe each erie. Finally, in Figure 7 the τ bond law derived from the train gauge meaure, and the one determined from invere analyi addreed to the optimization of the curve F - d are compared for two experimental cae. The hear tre i evaluated by conidering the perimeter at the concrete-rein interface for the pecimen of program 1 (failure at the concrete-rein interface) and the perimeter at the reinforcement-rein interface for pecimen of program 2 (plitting failure). The graph evidence a quite good predictive performance up to bond trength, and a ignificant deviation between both approache in the τ decending branch. Thi deviation could be due to the larger uncertainne of the experimental meaure when the bond law attain the pot-peak branch. Table 3. Main parameter of the bond law aeed by invere analye. Specimen E f lin τ α α' ult F,th F,exp [GPa] [mm] [mm] [MPa] [-] [-] [mm] [kn] [kn] B-6-SC B-8-SC G-8-RB C-8-S C-2.5x15-S Lb7_x Lb9_x Page 6 of 8

7 6 C-2.5x15-S erie 6 C-8-S erie C-2.5x15-S-1 (exp) C-2.5x15-S-2 (exp) C-2.5x15-S-3 (exp) Average (num) 3 2 C-8-S-1 (exp) C-8-S-2 (exp) C-8-S-3 (exp) Average (num) Lb7_x6 (a) Lb9_x6 (b) Experimental Numerical 2 Experimental Numerical G-8-RB erie G-8-RB-1 (exp) G-8-RB-2 (exp) G-8-RB-3 (exp) Average (num) (c) (e) B-8-SC erie 5 B-8-SC-1 (exp) B-8-SC-2 (exp) B-8-SC-3 (exp) Average (num) Figure 6. Experimental v. theoretical pull-out force-diplacement curve for different NSM ytem: (a) carbon trip 2.5 mm x 15 mm; (b) carbon bar 8 mm; (c) carbon trip 1. mm x 1 mm; (d) carbon trip 1. mm x 1 mm; (e) ribbed gla bar 8 mm; (f) and coated baalt bar 8 mm. (d) (f) τ [MPa] C-2.5x15-S-2 Experimental Numerical 1 [mm] (a) τ [MPa] B-6-SC-1 Experimental Numerical 1 [mm] (b) Figure 7. Numerical-experimental comparion of the local bond-law: (a) carbon trip 2.5 mm x 15 mm; (b) baalt bar 6 mm. Page 7 of 8

8 5. Concluion The FEM modelling applied to the technique of NSM trengthening appear efficient to calibrate the parameter of the elected type of bond law. The reult of the calibration point out the global reliability of the hape of the τ relationhip in term of imulating the pullout load-diplacement curve. The potentiality of the developed model allow to analye and to compare the behaviour of the variou type of FRP element in term of imum local hear tre and it correponding lip, bond length effect, tre field and concrete crack pattern. Acknowledgement Some of the experimental activitie were developed within the reearch work of the European Network for Compoite Reinforcement - TR 9.3. The reearch carried i part of the FCT PreLami project PTDC/ECM/1195/29. Reference [1] ACI-, Guide for deign and contruction of externally bonded FRP ytem for trengthening concrete tructure, ACI Technical Report, May 22, 118 pp. [2] CEB-FIB, Externally bonded FRP reinforcement for RC tructure, International Federation for Structural Concrete - Technical report, July 21, 13 pp. [3] BLASCHKO, M., ZILCH, K., Rehabilitation of concrete tructure with CFRP trip glued into lit, Proceeding of the 12th International Conference on Compoite Material, Pari, France, July [] DE LORENZIS, L., NANNI, A., LA TEGOLA, A., Strengthening of reinforced concrete tructure with near urface mounted FRP rod, Proceeding of the International meeting on compoite material - PLAST, Milan, Italy, May 2, 8 pp. [5] DE LORENZIS, L., NANNI, A., Shear trengthening of reinforced concrete beam with near-urface mounted fiber reinforced polymer rod, ACI Structural Journal, Vol. 98, No. 1, January/February 21, pp [6] HASSAN, T., RIZKALLA, S., Invetigation of bond in concrete tructure trengthened with near urface mounted carbon fiber reinforced polymer trip, ASCE Journal of Compoite for Contruction, Vol. 7, No. 3, Augut 23, pp [7] SENA CRUZ, J.M., BARROS, J.A:O., Bond Between Near-Surface Mounted Carbon- Fiber-Reinforced Polymer Laminate Strip and Concrete, ASCE Journal of Compoite for Contruction, Vol. 8, No. 6, November/December 2, pp [8] DE LORENZIS, L., TENG, J.C., Near-urface mounted FRP reinforcement: An emerging technique for trengthening tructure, Compoite Part B: Engineering, Vol. 38, March 27, pp [9] BILOTTA, A., CERONI, F., DI LUDOVICO, M., NIGRO, E., PECCE, M., MANFREDI, G., Bond efficiency of EBR and NSM FRP ytem for trengthening of concrete member, ASCE Journal of Compoite for Contruction, publihed on line, doi: 1.161/(ASCE)CC [1] MACEDO, L., COSTA, I.G., BARROS, J.A.O., Avaliação da influência da propriedade de adeivo e da geometria de laminado de fibra de carbono no comportamento de enaio de arranque (Evaluation of influence of adheive and geometry of laminated carbon fiber on the behavior of tartup tet), Proceeding of Betão Etrutural 28, Guimarãe, Portugal, November 28 [in Portuguee]. [11] ASTM-D339, Specification for Concrete Aggregate, ASTM International, Wet Conhohocken, PA, 23, doi: 1.152/C33-3, URL: [12] SENA CRUZ, J.M., BARROS, J.A:O., Numerical imulation of the nonlinear behavior of RC beam trengthened with NSM CFRP trip, Proceeding of Congre on numerical method in engineering, Porto, Portugal, June 27, 2 pp. Page 8 of 8