Critical Analysis of FRP-NSM double-shear pull-out tests. Abstract

Transcription

1 Critical Analysis o FRP-NSM double-shear pull-out tests Inês COSTA * PhD student ISISE - University o Minho Departent o Civil Engineering, Capus de Azuré, Guiarães, Portugal ines.costa@civil.uinho.pt* Joaqui BARROS Full Proessor ISISE - University o Minho Departent o Civil Engineering, Capus de Azuré, Guiarães, Portugal barros@civil.uinho.pt Abstract The study o the bond behaviour between ibre reinorced polyer (FRP) systes and concrete is an issue that nowadays attracts any researchers. The scientiic counity dedicated to the research o FRP reinorceent has been conducting nuerous experiental progras aiing to assess the local bond-slip law o the FRP-adhesive-concrete connection. This paper reports the relevant results obtained by the Structural Coposite Research Group o Minho University in the scope o an international Round Robin Test. The suitability o the recoended test setup to derive a local bond constitutive law or odelling the bond behaviour o Near Surace Mounted reinorceent systes is discussed based on a deep interpretation o the results. Keywords: Bond behaviour; Double-Shear pull-out test; Fibre reinorced polyer (FRP); Local bondslip law; Near Surace Mounted (NSM) * Corresponding Author. Tel: ; Fax: E-ail address: ines.costa@civil.uinho.pt (Inês G. Costa). 1

2 1 Introduction The local bond-slip law has long been deined or coon steel reinorceent, and its analytical solution has also been well deined [1]. However, the consideration o a local bond-slip law to describe the behaviour o a reinorceent syste is recognized to be a reductive approach that neglects several iportant aspects o the bond-slip response especially, in this case, the tri-aterial interaction between FRP, adhesive and concrete. Nonetheless, it is coon practice to use this type o approach to characterize the FRP-adhesive-concrete syste interaction by neglecting the deorability o the concrete substrate. The concrete deorability can be later taken into account using other nuerical tools. The undaentals o this local bond-slip law are suarized in Figure 1 and Eq. 1, and are based on the assuption that the applied axial orce is purely balanced by the tangential orce produced, considering that the concrete substrate reains undeored. where x is the position, easured ro the end o the bond length bc d 2 ( ) s x s 2 χτ ( x) = 0 dx (1) l, s( x ) is the slip at the position x, τ ( s) is the tangential stress in correspondence to this slip value, s. In reality, this slip corresponds to the displaceent o the loaded-end o the bar in relation to its initial position beore loading, caused by the deoration o the adhesive, the existent interacial discontinuities and the stiness degradation during the loading process. For sipliication purposes, the geoetric and aterial properties o the bonded eleent are aggregated in one unique ter, χ, deined in Eq. 2 where Σ is the perieter o the bar cross section, elastic odulus. χ Σ = (2) A E A is the cross-sectional area o the bar, and E its Several authors have recently suggested that the sae principles can be applied to FRP bars, although the laws presented by soe authors do not consider the yielding plateau, usually assued or steel aterials. Two o the ost siple stress-slip laws adopted to solve the dierential equation o bond are the non-linear (Figure 2) and the bi-linear law (Figure 3) [2-3]. Both o these laws can be written in atheatical ters, as presented in Eqs. 3 and 4. 2

3 α s τ ( s) = τ 0 s s s s α ' s τ ( s) = τ s s where τ is the axiu bond stress, evaluated at s, α and ' α are the paraeters deining the growth and decay rate o the bond stress, respectively. (3a) (3b) s τ s = τ τ. + τ 0 s s (4a) ( ) ( ) 0 0 s s s τ ( s) = τ 1 s s s u su s where τ 0 is the initial shear strength due to cheical adhesion between adhesive and surrounding aterials and cohesion within the adhesive itsel, and s u is the ultiate slip. (4b) These local bond-slip laws enable the deterination o the slip distribution o a given bonded length or both non-linear and bi-linear laws (Eqs. 3 and 4, respectively). However, in the case o the nonlinear approach, a closed-or solution o the dierential equation o bond can only be derived to estiate the bond length corresponding to the irst branch o the local bond-slip curve, l bc, i.e. the length obilized until the axiu value ( ; ) s τ is reached at the loaded section. This bond length is o ajor iportance in the design o FRP-NSM systes since it occurs or slip values in the interval o 0.2 to 0.5 [3, 4], and this range is copatible with the liitations iposed by the Service Liit State (SLS) due to axiu crack width [5]. This solution is, however, unable to provide the ultiate pull-out load or the bond conditions aditted since the post-peak branch o the local bond-slip law contributes to the inal load value. For this reason, the slip unction is assessed only ro the irst branch o the curves previously presented (Eq. 5). ( 1 α ) ( + α ) 1 2 ( 1 α ) 2 χτ s( x) = x α 2s 1 τ s τ s x = χ x τ s ( ) 0 cosh 1 (5a) (5b) The deterination o the bond length corresponding to the irst branch o the local bond-slip curve, l bc, is now sipliied and corresponds to the position at which s( x) = s (Eq. 6). 3

4 l l bc = s s χτ 2( 1+ α ) ( 1 α ) 2 τ + τ cosh 1 0 bc = χτ τ 0 (6a) (6b) The deterination o the paraeters necessary or using these expressions ( s, τ, α or τ 0 ) is especially interesting when it is based on the data derived ro an experiental progra like the one presented in this paper, since those paraeters would be aected by the respective adhesive deorability o each FRP-adhesive syste instead o being explicitly considered in the equation, even though this deterination is not in the scope o this paper. This deterination is relatively coplex since the local bond-slip law is only one o the paraeters deining the global behaviour o the FRP- NSM syste, and the deorability o the concrete substrate or the oration o cracks ay drastically alter the bond-slip distribution o the bonded connection. The experiental progra carried out has the particularity o gathering data ro several saples with dierent values o χ, i.e. speciens reinorced with FRP systes o dierent aterial and geoetric properties, tested under the sae conditions. 2 Experiental Progra 2.1 Specien and Test Coniguration The pull-out speciens used in this experiental progra are scheatized in Figure 4. Each specien was coposed by two concrete blocks ( ) connected only by eans o two identical FRP bars, bonded in opposite aces o the concrete blocks. Each concrete block had two 16 steel rods with an ebedent length o 380, responsible or ensuring the load transerence ro the concrete blocks to the FRP bars. To proote debonding in a speciic region, the FRP bond length adopted in one block was larger than in the opposing block (see Figure 4). These concrete blocks will be herein designated botto and top blocks, respectively. The test was controlled by the total oveent between the two blocks, which was easured by the internal LVDT o the testing achine, herein labelled as LVDT1. Sall tabs were glued in the FRP s loaded-end, aking an angle o 90º with the ibres o the FRP, and creating an extension to the outside o the slit. A steel piece was astened in those tabs providing the conditions or the easureent o the FRP loaded-end slip by LVDTs 2 and 3, supported on the concrete block, and always placed in the let 4

5 side o the FRP, where concrete deoration is expected to be negligible (see Figure 5). In this experiental progra strains were also recorded along the sallest bond length ( l b = 300 ) by using three strain gauges (SG) placed 10, 80 and 220 ro the loaded-end (Figurer 4) in order to iniize the aount o daage in the bonded length caused by this installation. The two FRP reinorceents were expected to be stressed siultaneously and to ail on the sallest bond length. During the control tests it was veriied that the existence o the steel rods was causing the oration o undesired longitudinal cracks and, or that reason, two passive conineents were placed near the extreities o the concrete blocks to avoid concrete splitting (Figure 5). These double-shear pull-out tests were perored in a universal testing rae o 1000 kn tension/copression capacity at a constant displaceent ratio o 0.5 /in (easured by LVDT1), and the applied load was easured with a 1000 kn load cell. 2.2 Material Properties Concrete The concrete used in all the speciens was a C25/30 strength class, ordered ro a ready-concrete copany. The eective copressive strength and Young s odulus o the concrete were deterined in cylinders o 150 diaeter by 300 o height, ollowing the recoendations o the appropriate Portuguese standard [6]. The tensile strength was obtained by testing beas with according to Rile recoendations [7]. The average properties obtained at 28 days and at the age o testing are presented in Table FRP In this experiental progra several types o FRP aterials were tested using the setup described in Section 2.1, and the ain characteristics o each type can be ound in Table 2. The aterials were labelled according to their ain characteristics: type o iber (Basalt B, Carbon C, Glass G), diaeter or cross section, and also aspect o the inishing (Sand Coated SC, Ribbed Rb, or Sooth S). For exaple, the saple B-6-SC reers to a 6 basalt FRP bar with a sand-coated inish, while C S is a sooth carbon lainate with cross section. The Young s odulus, E, and tensile strength,, were estiated according to ISO standard [8], even though the preparation o the speciens obeyed to the RRT Test Procedure recoendations [9]. 5

6 The values o the cross sectional area, A, reported in Table 2, result ro the eective diensions o the speciens, and although they were not used in any calculation, they are presented to deonstrate that these values can dier signiicantly ro the noinal diensions Adhesives In this experiental progra, each FRP bar/lainate required a speciic bonding agent and, thereore, our types o adhesives were used. Dubbell-shaped speciens o adhesive were oulded at the tie o reinorceent and kept at roo teperature. These speciens were tested according to ISO recoendations [10] ater copleting the pull-out tests. The easured cross sectional area, the obtained tensile strength, a, and Young s odulus in tension, E a, are presented in Table 3. A a, and 2.3 Specien Preparation The preparation o the speciens was perored observing the existent recoendations or the installation o NSM reinorceents. The slits, into which the dierent FRPs were bonded to the concrete through the adhesive, were opened respecting the recoended geoetry, depicted in Figure 6, where d, w and t are the diaeter, the width and the thickness o the circular, square and rectangular cross section type bars. Since the noinal diensions indicated by the suppliers o soe FRPs are relatively dierent ro the actual diensions o these bars, especially in the case o bars with dierent surace treatent, soe grooves had to be enlarged to provide an adequate adhesive thickness. The real diensions o the inal grooves were, thereore, easured and the average diensions obtained (depth and width) are presented in Table 4, where the groove or the circular and square cross section type bars, while groove. d slit and w slit are the width o Σ slit is the inner perieter o the The reinorcing procedure was initiated by cleaning the grooves with copressed air, and the surace o the FRPs with a degreasing agent. Special care was adopted while peroring the reinorceent task to ensure that the steel rods and FRPs were perectly aligned, avoiding any possible eccentricities. The dierent adhesives applied were ixed according to the recoended proportions, and the speciens were let to cure at roo teperature or at least 30 days. The real age o the FRP reinorceent at tie o testing is indicated in Table 4, and all data is presented or each o the three speciens o each aterial. 6

7 3 Results 3.1 Failure Modes The aspect o the speciens ater testing is reported in Figure 7. In all photos the speciens are positioned according to Figure 5, eaning that l b is 300 in the upper block, and 350 in the lower block. The ajority o the speciens ruptured by debonding o the FRP-adhesive group, accopanied by substantial cracking in the surrounding concrete and a relatively sall level daage in the adhesive layer (see Figure 7). This indicates that the bond strength o FRP-adhesive group is higher than the strength provided by the racture o the surrounding concrete, having been the concrete racture the governing inal ailure echanis. However, in the series with the largest FRP cross section (C S), the spalling o the concrete in the plane o the steel rods was unavoidable, as illustrated in Figure 7i, which prevented an eective obilization o the FRP bond length in all the three speciens. Due to the occurrence o concrete splitting in a great nuber o speciens, it was realized that this setup can lead to stress ields, conceptually reproduced in Figure 8, that do not correspond to the stress ields in real case applications (Figure 9). In these speciens, the steel bars introduce bond stresses o opposite direction o the bond stresses applied by the FRP reinorceent, which is not observed in the strengthening o RC eleents, or both shear and lexural conigurations. This eect is believed to have inluenced the inal deoration/slip o the FRP reinorceent, thereore being questionable the applicability o the bond-slip law derived ro these tests or the odelling o the bond behaviour o FRP strengthened RC structures. Soe authors have reported that the presence o steel reinorceent in the speciens contributes or a ore realistic prediction o the NSM reinorceent properties [11]. According to this work [11], the presence o reinorceent, associated with the typically low perorance o the concrete cover can be, in soe cases, unavourable to the global perorance o the FRP-concrete bond connection. However, the level o daage introduced by these bond stresses should not be as unavourable as the case depicted in Figure 8. In act the opposite bond stresses applied by the steel and FRP reinorceents to the surrounding concrete introduces shear distortions ore intense than in real cases (Figure 9), where the reinorceents introduce in the surrounding concrete bond stresses that are either parallel or convergent. Tests like pull-out bending are ore suitable to assess the bond behaviour o 7

8 FRP bars or the lexural strengthening o reinorced concrete eleents, while direct pull-out tests are recoended or deriving the local bond law to siulate the contribution o NSM bars or the shear strengthening [12]. 3.2 Pull-out Load The load in each FRP was estiated to be hal o the total load easured in the load cell. The stress level applied ranged between 20 and 90% o the ultiate resistance, revealing that in all speciens the resisting bond length was too short to obilize the ull resistance o the FRP connection. In Table 5 the ollowing values are presented or each specien: - F ax : is hal o the total load easured in the achine s load cell; - ax : is the applied tensile stress, obtained by dividing F ax by the noinal cross section o the bar, A ; - % : corresponds to the percentage o stress obilized, i.e., the axiu applied stress divided by the FRP s tensile strength; - Σ : is the average noinal FRP perieter; - Σ slit : is the average easured slit perieter; - τ a and τ a c : are the average bond stress at rupture, in the FRP-adhesive and adhesive concrete interace, respectively. These values are deined by Eqs. 7 and 8, and calculated considering the sallest bond length, l b = 300. F ax τ a = (7) lb Σ F ax τ a c = (8) lb Σ slit 3.3 Strain Distribution The strain distribution recorded in all tests was very well captured, as it can be observed in Figure 10. Note that initially the strains decrease rapidly towards the ree-end o the FRP. By increasing the load the dierence o strain between consecutive strain-gauges decreases and rupture usually occurs shortly ater. For levels o stress under 0.6 ax, the strain gauges recorded siilar evolutions in speciens o the sae FRP aterial. It is worth entioning that, o the 72 strain-gauges installed, only SG 80 in specien C S-1 did not work during the test up to ailure. 8

9 Up to 0.6 ax.the variation o strain along the bond length has a concave coniguration, but at 0.9 ax.becoes, in general, convex, especially in carbon systes with sooth surace. This suggests that the debonding process progresses aster in these FRP systes, which ight be caused by the sooth characteristics o these eleents. In ost series the two branches that copose the strain variation along the bond length have uch dierent slopes. However, this is not the case o C S speciens because the expected strain evolution process was preaturely interrupted due to the concrete racture caused by the relatively high tensile orces applied in these tests (see Figure 7i). The other iportant reark concerns G-8-Rb. In all three speciens, or a load level o 0.9 ax, the strain recorded in SG 10 decreases signiicantly. Ater a careul analysis o the data, it was realized that at about that load level, all the strain-gauges located at that position started to gradually unload. This act is believed to be related to an internal sliding between the ibres and the coating since it was expected to record strain values in the loaded-end o approxiately 3.3, 6.7 and 10 or 30%, 60% and 90% o ax, respectively. O all the tests perored, C S exhibited the highest eectiveness, since rupture was attained at approxiately 90% u in all speciens, with no evident strain approxiation between SG 10 and SG 80 (except in the case o Specien 1, where at 0.90 ax the strain ield was alost constant in all easuring points, revealing that the eective bond length had already shited to the vicinity o the ree end). 3.4 Load-Slip Relationship As entioned previously, the loaded-end slip was onitored during the tests by eans o LVDTs 2 and 3. However, the results obtained by these LVDTs proved that in soe cases lexural phenoena were recorded during the tensioning process (see Figure 11), since they recorded slip values o opposite signal. For this reason, the loaded-end slip was estiated by ultiplying the values recorded in the strain-gauges by the respective inluence length (Eq. 9, where ε SG 10, ε SG 80 and ε SG 220 are the strains in the strain gauges at 10, 80 and 220 ro the loaded end, Figure 4). Note that this approxiation does not intend to reconstruct with precision the load-slip curve, but to observe the relative dierences between the tested FRP reinorceent systes. Moreover, the slip easured during the test is dierent ro the local slip deined in Section 1. During the pull-out test, discrete cracks in the concrete induce localized strain increents that are not copatible with initial assuptions o local bond-slip law, i.e., that the concrete substrate is undeorable. In reality, the ree- 9

10 end slip ay not be zero at tie o rupture and this act would require the addition o that value in Eq. 9. In any case, even i the nuber o strain-gauges was suicient to reconstruct the precise slip curve o this relatively long joint, the value o the ree-end slip would probably be negligible when copared to the loaded-end slip. i i 45 SG SG80 SG [] (9) 220 s = x ε = ε + ε + ε The results obtained by this approxiation related quite well, in each test, with at least one o the LVDTs. When asyetric behaviour was not too pronounced, the load-slip relationship deterined ro both approaches related airly well in ters o shape (see Figure 11, specien C-6-Sc-2, LVDT2 located in the sae ace as the instruented FRP). These graphs evidence that the average signal o the LVDT2 and LVDT3 has higher probability o assuring stable tests in the post peak sliding phase, i it is used to control the load to be applied under the raework o a closed-loop test controlling equipent. However, even in this case, the position o these LVDTs should be careully selected in order do not register parasitic deorational eects, as will be highlighted later in this section. The position o LVDTs 2 and 3 indicated in Figures 4 and 5 was changed ater analysing the results o the irst two tested series (C S and C-6-SC). The LVDT was initially placed near the border o the specien (Position 1 in Figure 12), and was later oved closer to the border o the groove (Position 2 in Figure 12). This odiication was otivated by the negative slips easured while testing (visible in Figure 11), caused by incontrollable rotations o the concrete block. Note that a rotation o one block correspondent to 1 degree, which is nearly iperceptible, can result in a parasite displaceent ( s par ) either positive or negative. In Figure 12 is illustrated the case o this parasite displaceent in both positions o the LVDTs. Both bars and lainates have relatively sall lexural resistance and so, the FRP bar/lainate tends to aintain a vertical alignent. On the other hand, the LVDT rotates jointly with the concrete block and since the LVDT is only able to easure perpendicular displaceents, it is possible to easure a axiu s par o approxiately 1 in Position 1 or 0.4 in Position 2 (calculated or the special case o an 8 bar, inserted in a 12 groove). These values, although iperceptible to the naked eye, can cause the initial negative slips reported in Figure 11. Note that the initial slip values o FRP reinorceents are usually very sall since the connection is rather sti and, in this case, the parasite displaceent can increase aster than the slip itsel, causing extraneous readings. I this critical analysis o the setup was not done, and only the results ro Figure 11a were presented, it could be assued that one o the bars was initially copressed, and the other one tensioned, although the concrete blocks were at all ties being oved apart and consequently, always tensioning the FRP reinorceents. In soe tests, the griping o the 10

11 steel rods was in one rod stronger than in the other, causing this rotation to becoe even ore pronounced, increasing the parasite displaceent even urther. However, given the nuber o actors that can cause undesired rotations, it is very unlikely that those events can be isolated and properly subtracted ro the loaded-end slip easured. Another signiicant phenoena easured by the LVDTs, is related to the shiting o the resisting bond length. Observing the obtained results (Figure 11b), it is believed that there are two bond coponents that contribute or the bond resistance: the FRP-adhesive bond coponent and the adhesive-concrete bond coponent. The FRP-adhesive bond coponent is the irst to be obilized, and it is initially ore active in the loaded-end zone. For high levels o stress, the daage introduced in this zone (zone I, see Figure 13) is likely to cause alost iperceptible ree elastic deoration ( s e ) in the reinorcing bar. This causes the resisting bond length to shit successively and later, other zones will exhibit the sae strain level as the loaded-end (Figure 13). This act can have special signiicance in double-shear tests like the ones presented, since a unique load is being recorded and evenly divided by the two FRPs. Reeber that the tests were perored under displaceent control and, in this case, i in one side o the block the FRP is experiencing a larger slip (due to the elastic deoration, s e ) the longitudinal stress distribution will becoe uneven. In that situation, or the sae iposed deoration, the load absorbed by the FRP in the daaged ace will be lower than hal o the applied load, and the opposite FRP reinorceent, as it is still bonded to the surrounding concrete, will bear ore than hal o the load. However, as the exact stress level in each bar is not known, dierent stress-slip relationships can be observed in opposing FRPs. Additionally, this elastic deoration can occur in any bond length and easily decrease the longest bond length ( l b = 350 ) to a shortest length, which ay justiy the existence o debonding in the largest bond lengths (see Figure 7). The evaluation o the slip based on strain distribution is recognized to be a rough process to estiate the slip, but given the uncertainties associated with the rotations occurred on the speciens, it is believed to lead to ore reasonable slip results than the ones obtained by the LVDTs. Additionally, it is well known that the strain proile along the bond length is greatly non-linear and thereore, the accuracy o this slip estiation is highly dependent on the nuber o onitored zones. The relationship between the strain-based slip and the FRP axial stress in the loaded end or all the speciens is presented Figure

12 It is visible ro the results in Figure 14 that SC speciens presented a ore ductile behaviour, i.e., a higher slip at rupture, due to the supericial characteristics o these FRP aterials. On the other hand, C S speciens presented a ore ragile behaviour, due to their lower aspect ratio, Σ A, associated with the preature concrete ailure, due to the relatively high applied load. Note that in soe cases, as it happened in speciens 2 and 3 o C S series, interediate plateaus were recorded since slip increased without stress increent. This inoration is believed to be related either to the phenoena represented in Figure 13 or, to daage induced by adjustents o the speciens in the testing rae, causing daage in the reinorceent interace and subsequent loss o stiness. The inoration provided in this chapter indicates that the post-peak sliding phase is virtually ipossible to obtain with this test setup. Soe attepts can be ade to assure stable tests in this phase such, controlling the applied load ro the signal corresponding to the average slip recorded in LVDT2 and LVDT3. Even in this case, the slip should not include parasitic coponents and thereore, the supports o the LVDTs should be ixed in the plane ored by both FRP eleents, in a zone o negligible deoration. 4 Analysis o the results / Discussion One o the purposes o this experiental progra was to obtain the paraeters that deine the local bond-slip law i.e., the values o s, τ and α or τ 0. However, this can only be perored executing inverse analysis with sophisticated FEM-based siulations [12], which is not in the scope o the present paper. To peror an appropriate odel calibration these FEM-based siulations should consider the concrete nonlinear behaviour due to cracking. To appraise the predictive perorance o a odel, not only the loaded-end slip should be well captured, but also the strain evolution during the loading process. Since in this experiental progra the loaded-end slip was not easured with the desired accuracy, the data ro the three strain gauges should be careully considered to calibrate the local bond-slip law. Even so, analysing the available data, three signiicant eects can be observed in this experiental progra. The irst eect is related to the axiu average bond stress (Eq. 8) that shows to be o the sae agnitude o the concrete tensile strength (last colun o Table 5). When debonding in the adhesiveconcrete interace occurs, usually accopanied by tearing o a concrete layer, it is coon to observe average bond stress levels o this agnitude, or slightly superior, both in externally bonded 12

13 reinorceents [13] and NSM reinorceents [14-15]. On the other hand, when debonding occurs in the FRP-adhesive interace the average bond stress values reported are usually higher [4,16-17]. According to Bianco et al. [11], this average bond stress is expected to decrease with the bond length but no additional inoration is usually ound regarding the coparison o dierent FRPs bonded using a constant bond length. These results can be intuitively observed in Figure 15 where, the individual specien average bond stress in the slit, τ a c (Eq. 8 and Table 5), is represented. The illed circles represent the standard deviation produced by each group o three speciens, with centre in the average value. Note that nearly all results are contained in the range o the concrete tensile strength values obtained by aterial testing. In Figure 15 ct, L represents the average lexural tensile strength considering all the speciens tested (at 177 and 188 days), σ ct, L is the correspondent standard deviation and ct, L, in and ct, L, ax are the iniu and axiu values observed. The second eect is in soe way related to the irst and has already been observed by other authors [18]. According to the results obtained, in ters o obilized stress and or the constant bond length analysed, the inluence o the aterial properties sees to be negligible. Note in Figure 16, that all readings suggest that the axiu tensile stress that can be applied to the FRP reinorceents increases alost linearly with Σ A (deined in section 3.2). Eq. 8 shows that τ a c is proportional to σ ( Σ A ) (assuing that Σ Σ alost constant, a constant value is expected or the ( A ) ). Thereore, since the last coluns o Table 5 show that slit τ a c is σ Σ ratio, as Figure 16 is revealing. Bianco et al. (2009) [19] have developed a atheatical odel that was based on the assuption that during the pullout o a NSM FRP syste the ollowing possible ailure odes can aect the ultiate behaviour o this reinorceent: loss o bond (debonding); concrete sei-conical tensile racture; ixed shallow-sei-cone-plus-debonding and FRP tensile racture. The developed odel ulils equilibriu, kineatic copatibility and constitutive laws o both the intervening aterials and the bond between the, but in the present phase its use or design purposes is still quite laborious. I the average bond strength applicable to a given FRP syste proves to be constant and equal to the tensile strength o the surrounding concrete, this would sipliy the estiation o the resisting bond length o one FRP bar. Using this approach, ro Eq. 8, and assuing τ a c as being the lexural tensile strength o the concrete, ct, 13

14 l A b = (9) ψ Σ ct where ψ is a actor that takes into account the size o the slit, and is deined by the ratio between and Σ. This actor is 1.43 or round and square bars and 1.5 or lainates (see Figure 6). Σ slit In ters o FRP tensile stress versus loaded end slip based on strain ield, it was observed that the aspect ratio and Young odulus, all aggregated in the paraeter χ (deined in Eq. 2), appear to be related to the stiness o the connection. This observation is depicted in Figure 17, where the FRP average tensile stress versus load-end slip o the three speciens tested or each series is presented, along with the correspondent range o values observed. Note how, in the case carbon aterials, the speciens with higher values o χ exhibited stier global behaviour. This observation is coherent with the orulation presented in section 1. Note that a higher value o χ, in Eq. 5, would produce a higher total slip, s( x ), and consequently, a higher bond stress, τ ( s), in Eq. 3. This eans that iposing a given load level to a FRP-NSM syste with high χ induces a lower slip in the loaded-end, as observed in Figure 17. It was, however, noticed that glass and basalt bars could not be directly copared with the group o carbon aterials. Note that B-6-Sc and B-8-Sc also reveal a stier response or higher values o χ, but reveal a considerably soter global stress-slip response, due to the saller elasticity odulus o basalt bars. G-8-Rb, also represented in the right plot o Figure 17, exhibits a uch lower value o χ than the basalt bars, accopanied by a stier stress-slip response, suggesting that the global stiness o the specien is, in act, dependent on the elastic odulus o the FRP reinorceent. 5 Conclusions The results obtained by the Structural Coposites Research Group o Minho University in the scope o an international Round Robin Test progra were presented and discussed. Based on a deep interpretation o the results it was veriied that the test setup utilized introduces several uncertainties that put in question the direct use o these results or the deterination o the local bond-stress slip relationship or design purposes. Despite these uncertainties, several iportant conclusions were drawn. It was observed that the average longitudinal tensile stress is proportional to the shape actor o the FRP, which is the ratio between the perieter and the cross sectional area o the FRP ( Σ A ). This observation is logical since or the sae bond length it was expected an increase o the axiu pull-out load with the increase o surace area o the FRP in contact with the adhesive. This act has direct eect on the 14

15 deterination o average bond strength since this proportionality iplies that the average bond strength is constant. Additionally, it was observed that the aterial and geoetric properties o the FRP play an iportant role in the tensile stress versus loaded-end slip response o the connection, since higher values o ( A E ) χ = Σ lead to stier connections. However, this is only noticeable coparing speciens with the sae ibre type, since the larger is relationship. E the stier is the tensile stress-loaded end slip The second order eects (otivated by inherit or induced eccentricities), the use o ultiple bond lengths per test (group testing) associated with aterial heterogeneity itsel, aong others, lead the authors o this work discourage the use o this test setup or the assessent o the basic local bond-slip law paraeters. To iniize these eects, the authors suggest that when executing pull-out tests the LVDTs that easure the loaded-end slip should be attached to the concrete, ixed in two syetrical points, with relation to the FRP. This schee will iniize the existence o parasite displaceents, enabling the LVDT to align with the concrete block in case o undesired rotations. 6 Acknowledgents The irst Author acknowledges the support provided by FCT grant, SFRH/BD/61756/2009. The research carried out is part o the project PreLai, with the reerence PTDC/ECM/114945/ Reerences 1. Russo, G., Zingone, G. and Roano, F. (1990). Analytical Solution or Bond-Slip o Reinorcing Bars in R. C. Joints. Journal o Structural Engineering, Vol. 116, No. 2, ib Bulletin 14. (2001). Externally Bonded FRP Reinorceent or RC Structures. Technical report by Task Group 9.3, International Federation or Structural Concrete, Lausanne, Switzerland. 3. De Lorenzis, L., Rizzo, A. and La Tegola, A. (2002). A odiied pull-out test or bond o nearsurace ounted FRP rods in concrete. Coposites: Part B, Vol. 33, No. 8, Sena-Cruz, J. M. and Barros, J. A. O. (2004). Bond Between Near-Surace Mounted Carbon- Fiber-Reinorced Polyer Lainate Strips and Concrete. Journal o Coposites or Construction, Vol. 8, No. 6, EN (2004). Eurocode 2: Design o concrete structures - Part 1-1: General rules and rules or buildings. European Coittee or Standardization, 225 pp. 15

16 6. E365 (1993). Hardened Concrete - Deterination o the odulus o elasticity o concrete in copression. National Laboratory or Civil Engineering Speciication, 2 pp (in portuguese). 7. Rile TC 162-TDF (2002). Test and design ethods or steel ibre reinorced concrete Design o steel ibre reinorced concrete using the siga-epsilon ethod: principles and applications. Materials and Structures, Vol. 35, No. 9, ISO (1997). Plastics - Deterination o tensile properties - Part 5: Test conditions or unidirectional ibre-reinorced plastic coposites. International Organization or Standardization, 12 pp. 9. RRT Test Procedure (2008). FRP RRT: Technical Speciications. European Network or Coposite Reinorceent, 17pp. 10. ISO (1993). Plastics - Deterination o tensile properties - Part 2: Test conditions or oulding and extrusion plastics. International Organization or Standardization, 8 pp. 11. Bianco, V., Shear strengthening o RC beas by eans o NSM CFRP strips: experiental evidence and analytical odeling, PhD Thesis, Sapienza University o Roe, Costa, I. G. and Barros, J. A. O. (2011). Assessent o the bond behaviour o NSM FRP aterials by pullout tests. First Middle East Conerence on Sart Monitoring, Assessent and Rehabilitation o Civil Structures (SMAR2011), Dubai, UAE, 8-10 February, 8 pp. 13. Travassos, N., Ripper, T., Appleton, J. (2005). Bond stresses characterization on CFRP-RC interaces. CFRP units in construction - Third International Conerence July, Lyon, France, 8 pp. 14. Oehlers, D. J., Haskett, M., Wu, C. and Seracino, R. (2008). Ebedding NSM FRP Plates or Iproved IC Debonding Resistance. Journal o Coposites or Construction, Vol. 12, No. 6, Novidis, D., Pantazopoulou, S. J. and Tentolouris, E. (2007). Experiental study o bond o NSM-FRP reinorceent. Construction and Building Materials, Vol. 21, No. 8, Baena, M., Torres, L., Turon, A. and Barris, C. (2009). Experiental study o bond behaviour between concrete and FRP bars using a pull-out test. Coposites: Part B, Vol. 40, No. 8, Costa, I. G. and Barros, J. A. O. (2012) Evaluation o the inluence o adhesive properties and geoetry o carbon iber lainates using pull-out tests. Report 12-DEC/E-08, University o Minho, Guiarães, Portugal. 18. Seracino, R., Saiulnaz, M. R. and Oehlers, D. J. (2007). Generic Debonding Resistance o EB and NSM Plate-to-Concrete Joints. Journal o Coposites or Construction, Vol. 11, No. 1,

17 19. Bianco, V., Barros, J. A. O. and Monti, G. (2009). Bond Model o NSM-FRP Strips in the Context o the Shear Strengthening o RC Beas. Journal o Structural Engineering, Vol. 135, No. 6,

18 List o Figures Figure 1 Generalized stress-slip evolution on bars. Figure 2 Non-linear stress-slip law. Figure 3 Bi-linear stress-slip law. Figure 4 Diensions (in ) and geoetry o the speciens (SG - Strain Gauge). Figure 5 Test setup. Figure 6 Recoended diensions or the grooves o NSM reinorceents. Figure 7 Failure odes o the tested speciens: (a) C-6-SC, (b) G-8-Rb, (c) B-6-SC, (d) B-8-SC, (e) C S, () C S, (g) C-8-S, (h) C S, (i) Detail o the concrete splitting observed in the botto concrete block in C S-1. Figure 8 Conceptual representation o the stress ield introduced by reinorceents in surrounding concrete in the reinorced speciens tested. Figure 9 Conceptual representation o the stress ield introduced by the reinorceents in the surrounding concrete in real FRP reinorced eleents. Figure 10 Strain evolution in the speciens. Figure 11 Exaple o unreliable load-slip results. Figure 12 Exaple o parasite displaceents induced by rotations o the concrete blocks. Figure 13 Evolution o the eective bond length in the presence o elastic deoration zones. Figure 14 Stress-slip curves. Figure 15 Average bond stress at ailure. Figure 16 Relationship between the debonding stress (in the FRP) and the shape actor ( Σ A ). Figure 17 Average stress-slip in carbon ibres (let) and other ibres (right) ( χ in /( 2 GPa)). 18

19 Figure 1 Generalized stress-slip evolution on bars. 19

20 Figure 2 Non-linear stress-slip law. 20

21 Figure 3 Bi-linear stress-slip law. 21

22 Figure 4 Diensions (in ) and geoetry o the speciens (SG - Strain Gauge). 22

23 Figure 5 Test setup. 23

24 Figure 6 Recoended diensions or the grooves o NSM reinorceents. 24

25 (a) (b) (c) (d) (e) () (g) (h) (i) Figure 7 Failure odes o the tested speciens: (a) C-6-SC, (b) G-8-Rb, (c) B-6-SC, (d) B-8-SC, (e) C S, () C S, (g) C-8-S, (h) C S, (i) Detail o the concrete splitting observed in the botto concrete block in C S-1. 25

26 Figure 8 Conceptual representation o the stress ield introduced by reinorceents in surrounding concrete in the reinorced speciens tested. 26

27 Figure 9 Conceptual representation o the stress ield introduced by the reinorceents in the surrounding concrete in real FRP reinorced eleents. 27

28 Figure 10 Strain evolution in the speciens. 28

29 (a) Figure 11 Exaple o unreliable load-slip results. (b) 29

30 Figure 12 Exaple o parasite displaceents induced by rotations o the concrete blocks. 30

31 Figure 13 Evolution o the bond length in the presence o elastic deoration zones. 31

32 Figure 14 Stress-slip curves. 32

33 Figure 15 Average bond stress at ailure. 33

34 Figure 16 Relationship between the debonding stress (in the FRP) and the shape actor ( Σ A ). 34

35 Figure 17 Average stress-slip in carbon ibres (let) and other ibres (right) ( χ in /( 2 GPa)). 35

36 List o Tables Table 1 Concrete properties. Table 2 Properties o the FRP systes. Table 3 Properties o the adhesives. Table 4 Average depth and width o the grooves. Table 5 Pull-out load and average bond stresses. 36

37 Table 1 Concrete properties. Age Copressive strength Young s odulus Flexural tensile strength [days] [MPa] [GPa] [MPa] (1.1) [4%] {5} 24.4 (1.1) [4%] {3} 3.31 (0.31) [9%] {4} (1.4) [4%] {4} NT (0.22) [6%] {3} (0.9) [2%] {4} 25.7 (0.5) [2%] {3} 3.47 (0.43) [13%] {3} Average (Standard deviation) [Coeicient o variation] {Nuber o saples} NT stands or Not Tested 37

38 Table 2 Properties o the FRP systes. FRP Saples Cross sectional area Young s odulus Tensile strength [ 2 ] [GPa] [MPa] C-6-SC (2.1) [5%] 177 (8) [5%] 3252 (211) [6%] G-8-Rb (0.4) [1%] 72.3 (3) [4%] 1599 (73) [5%] B-6-SC (0.9) [3%] 54.1 (3) [5%] 1431 (77) [5%] B-8-SC (2.0) [4%] 51.9 (2) [3%] 1333 (79) [6%] C S (0.1) [0%] 172 (4) [2%] 3035 (68) [2%] C S (0.1) [0%] 170 (2) [1%] 1808 (201) [11%] C-8-S (1.8) [4%] 158 (19) [12%] 1316 (452) [34%] C S (1.5) [1%] 159 (5) [3%] 1425 (260) [18%] Average (Standard deviation) [Coeicient o variation] The Young s odulus o all speciens was estiated between 0.5 and 2.5 (strain). Due to the anchorage slippage veriied in these saples, the actual resistance o these aterials is superior to the one reported. 38

39 Table 3 Properties o the adhesives. Adhesive Type Saples Cross sectional area Young s odulus Tensile strength [ 2 ] [GPa] [MPa] I (1.0) [2%] 8.87 (0.38) [4%] 21.7 (6.8) [31%] II (1.6) [3%] 10.7 (0.3) [3%] 33.7 (0.9) [3%] III (1.3) [3%] 7.91 (0.41) [5%] 19.1 (3.0) [16%] IV (1.7) [4%] 7.61 (0.66) [9%] 20.3 (1.8) [9%] Average (Standard deviation) [Coeicient o variation] Due to soe delay in the preparation o the speciens, although 6 speciens were prepared only two speciens were ound suitable or testing. 39

40 Table 4 Average depth and width o the grooves. Specien C-6-SC-1 Age Bonding Agent d slit w slit Σ slit [] [] [] (0.56) [5%] (0.50) [5%] C-6-SC-2 81~82 I (0.41) [3%] 9.71 (0.56) [6%] C-6-SC (1.10) [9%] 9.54 (0.59) [6%] G-8-Rb (1.10) [8%] (0.34) [3%] G-8-Rb-2 34~36 II (1.32) [11%] (0.30) [3%] G-8-Rb (1.14) [8%] (0.30) [2%] B-6-SC (1.06) [11%] 8.78 (0.41) [5%] B-6-SC-2 36~38 II 9.11 (0.89) [10%] 8.90 (0.53) [6%] B-6-SC (1.00) [9%] (0.26) [2%] B-8-SC (1.11) [10%] (0.11) [1%] B-8-SC-2 58~64 II (1.23) [11%] (0.10) [1%] B-8-SC (1.09) [9%] (0.26) [2%] C S (0.87) [6%] 4.66 (0.06) [1%] C S-2 87~88 III (1.23) [8%] 4.64 (0.04) [1%] C S (1.35) [8%] 4.63 (0.05) [1%] C S (2.02) [9%] 7.54 (0.94) [12%] C S-2 62~68 II (1.75) [8%] 7.66 (1.12) [15%] C S (0.40) [2%] 7.74 (0.23) [3%] C-8-S (1.24) [9%] (0.46) [4%] C-8-S-2 35~37 II (0.77) [6%] (0.90) [7%] C-8-S (1.10) [8%] (0.57) [4%] C S (0.85) [5%] (0.62) [4%] C S-2 68~69 IV (1.12) [7%] (0.69) [4%] C S (0.89) [5%] (0.10) [1%] Average (Standard deviation) [Coeicient o variation] 40

41 Table 5 Pull-out load and average bond stresses. Specien F ax ax % Σ Σ slit τ a τ a c [kn] [MPa] [%] [] [] [MPa] [MPa] C-6-SC C-6-SC C-6-SC G-8-Rb G-8-Rb G-8-Rb B-6-SC B-6-SC B-6-SC B-8-SC B-8-SC B-8-SC C S C S C S C S C S C S C-8-S C-8-S C-8-S C S C S C S