Non-uniqueness of FRP bond stress-slip relationships in the presence of steel. Mehdi Taher Khorramabadi and Chris J. Burgoyne

Non-uniqueness of FRP bond stress-slip relationships in the presence of steel Mehdi Taher Khorramabadi and Chris J. Burgoyne 1 1 Biography: Mehdi Taher Khorramabadi works for Read Jones Christopherson (RJC) Consulting Engineers in Canada. In 0, he received his PhD in strengthening of concrete structures at the Structures Group, University of Cambridge, Cambridge, UK. In 00, he received his MS in rehabilitation of structures from Dresden University of Technology, Dresden, Germany, and in 00, his BS in civil engineering from Amirkabir University, Tehran, Iran. His research interests include bond behavior between fiber-reinforced polymer (FRP) and steel and substrate material, strengthening methods of reinforced concrete structures using FRPs, and their failure modes. Chris J. Burgoyne is a Reader in Concrete Structures at the University of Cambridge. He is a member of ACI Committee 0, Fiber Reinforced Polymer Reinforcement. His research interests include advanced composites applied to concrete structures. 1 1 1 1 1 1 0 1 ABSTRACT The literature is not consistent about whether bond stress-slip relationships at the reinforcement concrete interfaces are unique or are location and length dependent. Experiments based on a new bond test method showed that the local relationships for Near Surface Mounted (NSM) FRP reinforcement are only unique when the same boundary conditions apply, and also that the average relationships are not location independent. The presence of steel has a significant effect on the bond characteristics of nearby FRP. Attention is drawn to significant differences between the bond behavior in the cracked and anchorage regions in a beam and the need for these to be taken into account when designing strengthened members. Keywords: bond behavior; cracked region; anchorage region; local bond stress-slip model; debonding; FRP; NSM 1

1 1 1 1 1 1 1 1 0 INTRODUCTION It has been a challenge to find a material law to predict the bond behavior of steel or FRP to concrete. Material laws should be the same everywhere: the relevant question for bond is whether the bond-stress-slip relationships is a material law. A commonly held view is that the interface layer does not know where it is in the member, which would imply that the bond relationship should be unique and the same everywhere, and could be implemented in the form of a ( τ s ) relationship. However, the argument to be presented here is that the local conditions, including the strain state in the concrete, affect the interface and alter this relationship. These conditions can be expressed in terms of the boundary conditions of the region being studied. A similar argument would apply for Externally Bonded Reinforcement (EBR), NSM and even steel, although only NSM is considered here. This discussion has been reflected in the literature, but never fully resolved. Some researchers have accepted that the local bond stress against slip relationship ( τ s ) is an appropriate material law but there are contradictory reports that bring its uniqueness into question. Nilson and Jiang et al. 1, believe that the shear bond stress-slip relationship (for steel) is local in nature, and varies depending on the location. Somayaji and Shah (for steel) concluded that the relationship between the local bond stress-slip is not unique but is a function of the distance of the section from cracked face. The fib report showed from experimental results on FRP that the local bond stresses vary from point to point and that there is no unique bond stress slip relationship that can describe the behaviour along the bar. 1 In contrast, others - have assumed that the bond stress-slip relationship is a material property and hence location-independent. Tassios and Yannopoulos say (for steel) Admittedly, there is a unique relationship between local bond stress and local slip at every point of a bar inserted in a mass of concrete. Some researchers take an intermediate view, assuming that the relationship is unique under certain conditions. Dai et al. assume that at any location of a FRP sheet concrete bond interface

under the boundary condition of zero FRP-end slip, which can be approximately attained using a longer bond length, there exists a unique τ s relationship and a unique relationship between the strain of FRP sheets and interfacial slip. Mirza and Houde tested reinforced concrete ties 1 1 measuring strains along the embedded -mm (0.-in.) steel bar with strain gauges. Local bond stress was inferred from differences between adjacent gauges. The bar slips were evaluated using an empirical equation relating the steel stress and section geometry to slip. They concluded that the bond stress-slip relationship is unique and thus applicable directly at any point along the bar. But then they added that The bond stress-slip behaviour past the peak point was dependent on the distance from the end face. Based on the experimental investigations,1 that are described below, it is found that a unique local bond stress-slip relationship exists between the reinforcement and the concrete when the same boundary conditions apply. It is independent of location and bond length. None of the aforementioned researches considered the effects of different boundary conditions. 1 1 1 1 1 1 0 1 RESEARCH SIGNIFICANCE This paper explores the contradiction in the literature regarding the uniqueness of the bond stress- slip relationships, and answers the question of whether the bond stress-slip relationship is unique or location-dependent. A new test method is implemented that simulates different boundary conditions in a single specimen. The paper considers the conditions that need to be considered when applying bond models to real problems; these have been overlooked in the past. The paper shows that a commonly held view that the τ s relationship is unique - is wrong. It does not purport to quantify all the parameters that might be relevant to bond in general. METHODOLOGY In the present paper, the uniqueness of the local bond stress-slip relationships is investigated using the results of experiments conducted by the authors. The data of the same experiments were used

to investigate the average bond stress-slip relationships elsewhere 1. In those experimental tests, the bond behavior was investigated at the FRP-concrete interface of a reinforced concrete tie. Crack inducers were placed at different locations to study the effects of cracks on the bond behavior. Some of the specimens were reinforced with both steel and NSM FRP to investigate the interaction between FRP and steel, both when the steel is elastic and when it yields. The experimental local and average bond models in different regions are compared. 1 1 1 1 1 1 1 1 0 1 Boundary conditions in the cracked and anchorage regions A conventional method to test the bond behavior of a bonded FRP reinforcement is to pull the FRP bar from a constrained concrete block (shown in Fig. 1a); the FRP is loaded at one end and is free at the other end (unloaded end). This method mimics the boundary conditions of an FRP bar in the regions between the flexural crack nearest to the support and the end of the FRP in a flexurally FRP-strengthened RC beam; this is often referred to as the anchorage region. In the flexurallycracked regions of a strengthened beam, the boundary conditions are similar to those in a concrete tie (shown in Fig. 1b). The strain, slip and bond stress distributions in both the cracked and anchorage regions are compared in Fig. 1. In conventional bond tests, the axial stress in the FRP is maximum at the loaded end and zero at the unloaded end. The FRP end slip is initially zero, but eventually slip propagates through from the loaded-end even though there is no strain at the FRP-end. This differs from the conditions between two cracks in a tension member, where slip remains zero at a point where the bond reverses. The bond stress in a conventional test is initially zero away from the loaded end, but eventually stresses develop as the strain propagates along the bar. Even though the strain at the unloaded-end is always zero, the strain difference along the FRP bar produces bond stress in the region close to the FRP-end. This condition is not the same as in the regions between cracks since there is a point between the cracks at which bond stress is always zero, where the direction of the bond stress changes. Thus, the conventional test does not provide boundary conditions that mimic the behavior between cracks.

In a conventional bond test (Fig. 1a), depending on the exact set up, the boundary conditions are taken from the following list: ( 1 ) : ε ( ) : s ( ) : ε ( ) : s ( ) : ε ( ) : s ( x = 0) = ( 0) ( x = 0) ( x = L) = ( L) ( x = L) ( x ) i ( x ) i = ε = s = s = s i i ds dx 0 ds dx L = 0 = ε L (1) where the reference point (x = 0) is taken at the unloaded-end, ε and s are the reinforcement (FRP or steel) strain and slip, respectively. T f is the applied FRP force at the loaded-end at x = L. x i is the location of the point i with the known strain ε i measured by strain gauge. s 0 and s L are the measured slip at the FRP-end and loaded-end, respectively. Due to the nature of the conventional bond tests, the FRP strain at the FRP-end is always zero (ε(x=0) = 0). In the cracked regions (Fig. 1b), the boundary conditions (Eq.) are different 1) : ε () : s () : τ () : ε () : s () : ε ( x = 0) = ( 0) ( x = 0) ( x = 0) ( x = L) = ( L) ( x = L) ( x ) i = ε = 0 = 0 = s i ds dx ds dx L = ε ( 0 = ε L () 1 1 Under ideally symmetric conditions, the slip s and bond stress τ at a point midway between the two cracks ought to be zero (x = 0).

It should be noted that if the slip at the end, or the strain at a particular location is not measured, then not all of these conditions can be used. Taher Khorramabadi,1 SUMMARY OF BOND TESTS proposed a test method and carried out experiments that mimic the 1 1 1 1 1 1 1 1 0 1 conditions in both the anchorage and the cracked regions in a single specimen in the presence/absence of internal steel: a brief description of the test method is presented below. Three specimens of the tests that were conducted by Taher Khorramabadi are considered in the present paper. Specimens consisted of 00 mm (in.) long concrete ties with 0x1 mm (.x. in.) rectangular cross sections strengthened with steel bar and carbon fiber-reinforced polymer (CFRP) strips that were laid longitudinally (Fig. a). Additional anchorage bars were provided in the end regions, extended outside the specimen to connect to the test rig. The specimens were tested under uniaxial tensile loading (Fig. b). To ease further referencing to different parts of the specimens, the regions at both ends, where the anchored bars were embedded, are termed the anchorage regions and the region between, without anchored bars, is termed the central region. The specimens were coded for identification in the following format: Bd-n s Sn f F-f cu where Bd, S, F stand for Bond test series, Steel bars, and FRP strips, respectively. n s and n f are the number of the steel bars and the CFRP strips in the central region, respectively. f cu is the concrete cube strength of the specimen. Fig. C shows the cross-sections of the Specimens. Bd-1SF- & Bd-1SF- were reinforced with a mm (0. in.) ribbed central steel bar and with two 1. mm 1 mm (0.0 in. 0. in.) FRP strips, embedded in epoxy inside mm 1 mm (0. in. 0. in.) slots cast into the concrete on opposite faces of the ties along their full length. Specimen Bd-1S0F- was reinforced with two FRP strips only on opposite faces of the ties along their full length. The central mm (0. in.) steel bar continued through the full length of the Bd-1SF- & Bd-1SF- specimens. The anchorage

1 1 1 1 1 1 1 1 0 1 regions were reinforced internally with two 1 mm (0. in.) and one mm (0. in.) steel bars. By increasing the two 1 mm (0. in.) steel in the anchorage regions, the central steel can yield. Thereafter, any load increment would be carried only by the CFRP at the cracked section and by the concrete, CFRP, and steel (if locally unyielded) between two cracks. That mimics the situation in the cracked regions of a strengthened RC beam. The anchorage bars, which extended beyond the specimen, were gripped in a 000kN (0kips) vertical testing machine as shown in Fig. b. Uniaxial tensile tests were conducted under displacement control at a mean rate of 0.0 mm/s (0.00 in/s). Data were recorded every 0. second. Notches were preformed as crack inducers in the central region of Specimens Bd-1SF- and Bd-1S0F- to simulate the flexural cracks of a beam (Fig. 1b). The notches were cast by placing mm mm (0. in. 0. in.) wooden strips on the four faces of each section. The anchorage regions had conditions similar to those of a conventional bond specimen and the anchorage region of a beam (Fig. 1a). The notch spacing was chosen to ensure that no intermediate crack formed up to the designed failure load. To investigate the effects of the notches on the stresses and minimum crack spacing, Bd-1SF- was cast with only two notches at the middle of the central region on the two faces with no FRP strips (Fig. C). Notches were cast around the other two specimens at three sections (Fig a). Specimen details and material properties are presented in Tables 1 &. Specimens Bd-0SF-, Bd-1SF- were fully instrumented (Fig. a & b). Fig. a shows the labeling used to identify locations along the specimen (A O). The force T and the overall extension were measured within the test machine. The strains were measured in central steel bar and one FRP strip in each specimen using -mm strain gauges ( mm apart in the central zone and 0 mm in the anchorage regions). The crack widths at the locations of the notches were measured by two Linear Resistance Displacement Transducers (LRDTs) placed on opposite sides of the FRP so that any possible asymmetric displacement could be monitored. FRP-end slips at the ends of the specimens were monitored by LRDTs. The average concrete strains in the high concrete strain regions in the central region were measured by portal gauges.

1 1 1 1 1 1 1 1 0 1 OBSERVED FAILURE MODES A detailed description of the specimen behavior and failure modes can be found elsewhere,1. The load-elongation behaviors obtained from the crosshead movement of the test machine are shown in Fig. and Fig. shows the specimens after failure. The initial response of the Bd-1SF- & Bd-1SF- specimens reinforced with FRP strips and conventional steel reinforcing bars was generally linearly-elastic; after the first cracks formed it remained cracked-elastic until the central steel yielded, at which point the stiffness reduced further. The response became nonlinear when either herringbone cracks (sometimes referred to as Goto cracks) were observed in the concrete around the FRP or debonding initiated. Diagonal cracks formed in the anchorage region close to the end notches. Subsequently, the debonding propagated at FRP-epoxy and epoxy-concrete interfaces from the toe of the secondary cracks towards the specimen s end in the top anchorage region, as shown in Fig. a. The specimens failed as debonding reached the FRP-end. The response of the specimen without central steel was linear-elastic up to opening of the middle notch, after which herringbone crack formation started in the central region. The response became nonlinear as diagonal secondary cracks formed in the anchorage region close to the end notches and debonding initiated from the secondary crack toes, primarily at the FRP-epoxy interface but also in the epoxy-concrete interface, shown in Fig. b. The debonding propagated into the bottom anchorage region and the specimen failed as debonding reached the FRP-end. It was observed that when notches were present in the central regions, herringbone cracks formed regardless of steel presence (Fig. a and b). When no notch was cast in the faces where the FRP was placed, debonding occurred and no herringbone crack formed in the central region. Splitting cracks occurred at the end of the specimen immediately before failure (Fig. c).

1 1 1 1 1 1 1 1 0 1 LOCAL BOND STRESS-SLIP RELATIONSHIPS Equilibrium equations can be established to describe the relationship as given by Eq. between the strain in the FRP strip and bond shear stress τ, acting at the FRP-substrate interface EA dε τ = () Σ dx where dε is the change in strain over dx and Σ p is the effective perimeter of the section at which the bond stress is calculated. E and A are modulus of elasticity and area of the material under consideration, respectively. The slip s(x) at a distance x along the FRP strip is defined by Eq. as the relative displacement between strip and substrate material (e.g. concrete) s ( x) s ( x) s ( x) f p = () s f (x) is the displacement of the FRP strip at point x and s c (x) is the displacement of the concrete at point x. The difference in displacement between two points on the concrete at the concrete-frp interface is much less than the difference in displacement between corresponding points on the FRP strips. This is equivalent to stating that the concrete displacements are negligible and the slip at each interface point is equal to the displacement of the corresponding section of the strip. Therefore, s c ( x) s ( x) = () Differentiating Eq. twice and substituting into Eq. gives the familiar equation d s dx ( x) f Σ p = τ () EA Equation is the general differential equation for bond slip response as a function of x that relates the second order derivative of the bond slip to the local bond stress. Assumptions in the governing bond differential equation: FRP has a linear elastic constitutive law in the longitudinal direction. The displacement of the FRP is significantly higher than that in the concrete at the FRPconcrete interface.

The axial stiffness of the epoxy layer is significantly lower than that of the FRP strip and is neglected, but its shear strength is higher than the bond. There exists a bond characteristic at the FRP-concrete interface that can be analytically described by a relationship between the local bond stress acting at the interface, and the slip between FRP and concrete -, 1. Regardless of the type of problem (cracked or anchorage region), the bond stress function τ is unknown in Eq.. In order to solve the equation with two of the boundary conditions explained in the previous section, certain assumptions are necessary. It will be assumed that the local τ is a function of local slip s; a parametric relation between τ and s (Fig. ) will be assumed (Eq. & Eq.): τ = τ m s s 1 α s s 1 () 1 τ = τ m s s 1 α s > s 1 () 1 1 1 1 1 1 1 0 1 where τ m is the maximum bond resistance, s 1 is the FRP slip at which peak bond stress reaches, α and α are curve fitting parameters. At large slips, the bond stress approaches zero asymptotically. Equation is the ascending branch of the well known BPE model 1, which was originally proposed for modeling the τ s relationship of a steel bar to concrete. Equation is identical to Equation, with exception that exponent α is negative as proposed by De Lorenzis et al. 1. They modeled the descending branch of the ribbed bars which failed at the epoxy concrete interface. τ s relationship of Glass Fiber Reinforced Polymer (GFRP) Equations & have been used previously by Cruz 1 for specimens that failed either in the concrete-adhesive or in the adhesive-laminate interfaces; good fits were obtained with their experimental results. The boundary conditions that can be implemented to solve the bond Equation depend on the type of the problem and the available experimental data. In this paper, the first two equations of Eq. were taken as the boundary conditions in the cracked regions of the bond specimens; the slip is

zero midway between the cracks ( x = 0 in Fig. 1b or Section G-G in Fig. ) and the strain ε 0 at this point has been measured with a strain gauge. The chosen boundary conditions in the anchorage regions were the fifth and the sixth equations of Eq.1 as strain and slip at one point along the bonded length. The slip can be calculated by integrating the FRP strain from the FRP-end up to strain gauge i. For instance, at Section E E 1 1 1 1 1 1 1 1 0 1 in Fig., ε i and s i were the measured strain and slip at point E, respectively. The strain was measured directly by strain gauges at E and the slip was calculated from the strain integration along CE plus the measured slip at the FRP-end from the transducer. In calculating the slip, it is assumed that the strain between each pair of the strain gauges varies linearly. Depending on the assumed bond stress-slip model and boundary conditions, the solution of Eq. can be complex. The four unknown parameters ( τ m, s 1, α, α ) of the τ s relationship can be found through an optimization process; it has been carried out here using the built-in solvers in Matlab and the results have been checked against the limited number of cases for which there are closed-form solutions (1). Initial guesses are made for a set of parameters, and then Eq. is solved with two of the boundary conditions. Since it is assumed that the local τ s relationship is unique, the solution of the bond equation must be valid for any point along the bonded length. Therefore, in each iteration, the solution of the bond equation is checked against the measured strains at different points. The set of four parameters that minimizes the error function at the other boundary conditions defines the correct local τ s relationship. In the cracked regions, the error function Eq. was defined as the sum of the squares of the difference between the experimental and theoretical strains at the middle of the segment and at the cracked sections. These are the points at which the strains were measured experimentally. For example, along the segment FGH the error function was defined as: Er = n [ ( Gi ) ( ε Gi ) ) + ( ε Hi ) ( ε Hi ) ) ] exp theo exp theo i= 1 ε ()

where n is the number of the available data at each point, subscripts exp and theo stand for experimental and theoretical data, respectively. Since point G was located midway between F and H, the effect of point G was given increased weighted by a factor of. For the segments in the anchorage regions, the error function was defined as the square of the difference between the experimental and theoretical strain at the end closest to or at the cracked section (Eq.). For example, along the segment CD the error function was defined as Er = n ( ( Di ) ( ε Di ) ) exp theo i= 1 ε () 1 1 1 1 1 1 1 1 0 1 Experimental results and discussion The parameters of the assumed local FRP bond stress-slip models (Eq. & Eq.) in the central regions can now be found, with and without steel, as well as in the anchorage regions. They were determined at the epoxy-concrete interface. The bond model obtained in the regions between the cracks (Table ) is termed cracked-region bond model. The bond model obtained in the anchorage regions (Table ) is termed anchorage-region bond model. The results are grouped into three categories: Cracked-region bond models in the presence of steel (Fig. a) Cracked-region bond models in the absence of steel (Fig. b) Anchorage-region bond models (Fig. ) The local bond stress-slip relationships within each of these individual groups are unique, but they differ between the groups:- They are independent of the distance from the cracked sections, since for each region a local bond stress-slip relationship has been found that satisfies the strains at any point along its length. For example in the FGH region (Fig. a), where H is at the crack and G is at the midway between the zero slip section (F) and crack H, a bond stress-slip relationship has 1

1 1 1 1 1 1 1 1 0 1 been found (Fig. a) that predicts the strains at F, G, and H with a very small deviation from the experimental results. The local relationships are length independent; for example the length FH is twice the length of either FG or GH but all three regions share the same bond stress-slip relationship. The area below the curves represents the dissipated energy D L at the FRP-concrete interface. D L for each segment up to 1 mm (0.0 in.) slip is calculated in Tables and. There is some variation in the energy dissipation within each of Figures and, due to material inhomogeneity, but it is clear that the energy dissipated in the anchorage regions (Fig. ) is always significantly higher than that dissipated in the central zone (Fig. ). This is shown more clearly in Fig.. This finding is in agreement with the researchers - who concluded that local bond stressslip is unique. However, none of them tested the local bond behavior with other boundary conditions with the same material properties. They investigated either the anchorage region or the cracked region boundary conditions, but not both. The effects of different boundary conditions can be seen in Fig.. The effects due to the presence of steel can be studied by comparing the results between specimens with and without steel in the central region. The average curves from each specimen are compared in Fig.. It can be seen that at the same slip, local bond stresses in the specimen with steel (Model 1) are higher than the local bond stresses in the specimen with FRP only (Model ). The slope of the FRP bond stress-slip model is higher for the specimen without steel when compared with the specimen with steel, because the FRP has to pick up all the tensile stress while the concrete strains remain small. However, its slope gradually decreased as it reached the peak stress. The peak bond stress in the specimen with steel was between. MPa (0.1 ksi) and. MPa (0.1 ksi) at the slip between 0.0 mm (0.00 in.) and 0. mm (0.00 in.). Peak bond stress and slip values were higher than in specimen without steel in 1

1 1 1 1 1 1 1 1 0 1 which the peak stress was.00 MPa (0. ksi) at 0.0 mm (0.00 in.). Beyond its peak, bond stress gradually decreased as the slip was increased. The dissipated energy D L at the bond between FRP and concrete in the specimen with steel was 0% higher than in the specimen without steel. In the anchorage region, in contrast The average of the local peak bond stresses in the anchorage regions was.1 MPa (1. ksi), which was more than twice as high as the values obtained in the cracked regions (Fig. ). The slip s 1 at which the peak bond stress was observed in the anchorage region was about 0. mm (0.01 in.) while that observed between the cracks was 0.0 mm (0.00 in.). The dissipated energy D L for the anchorage regions is calculated in Table for the area below the curves shown in Fig., where the average value is more than. times higher than the D L in the cracked regions. Therefore, the results of the conventional pull-out tests (anchorage region) do not reflect bond characteristics in cracked regions, and thus overestimate bond strength. The JSCE 1 states that the pull-out tests given in JSCE-E 1 have been claimed to be incapable of measuring bond strength accurately, owing to differences in the stress conditions in actual members. The pull-out test referred to here is the test method for determining the bond strength of Continuous Fibre Reinforcing Material (CFRM) used in place of steel reinforcement or pre-stressing tendon in concrete by pull-out testing. In this test method, the tendon with a minimum length of four times its diameter is placed at the centre of a cubic or cylindrical concrete specimen, and tendons are pulled out while constraining the specimen at the loaded face. A schematic view of the local bond stress-slip models obtained here in the cracked and anchorage regions in the bond tests is shown in Fig.. The peak bond stress in the anchorage region was significantly higher than between the cracks. This could be due to the formation of the herringbone cracks between the existing cracks (preformed notches) as shown in Fig.. The number of these small cracks is much lower away from the main 1

1 1 1 1 1 1 1 1 0 1 cracks in the anchorage region. The bond model between the cracks considers the stiffness reduction due to the formation of these cracks and model for the anchorage regions takes into account the reduction due to debonding. The average bond stress-slip models of these tests were found elsewhere, 1, where average bond stresses calculated from the strain differences between adjacent strain gauges using Eq. and slip calculated from integration of the measured strains. Fig. shows a schematic average τ s relationship in different regions of the specimens with and without steel. Although none of these curves were identical, in the regions in which steel did not yield or did not exist (FG, CD, BC) the τ s relationships were a typical τ s relationship as observed in a conventional bond test, consisting of one ascending branch followed by a descending branch. However, the average τ s relationships for specimens with steel that yielded (GH) showed very different behavior, with second ascending and descending branches that are not observed in conventional tests. The stress at which the second ascending branch initiated will be a function of the amount of steel bond stress that is present, and therefore, cannot be regarded merely as a property of the FRP-concrete interface. It is clear that the presence of the tension steel does have a significant effect on the relationship between shear stress and slip and this should be taken into account when predicting the response of additional FRP reinforcement. Fig. shows that there is no unique average bond stress-slip model even though there are unique local bond stress-slip models that apply in each region. For example, HG and GF show the average τ s relationships at the cracked section H and at point G which is mm (1.1 in.) further from H, respectively. Comparing these two curves shows that the τ s relationships were a function of the distance from the cracked section. Similar conclusions have been reported by Nilson 1 and the fib report. This result may appear to be counterintuitive: it might be thought that the average behavior is simply the integral of the local behavior. If the local behavior is unique, then so to should the average behavior. However, average slip and average bond stress are difficult to define precisely; they must be based on values of bar force or bar slip at the two ends of the region of 1

1 1 1 1 1 1 1 1 0 1 interest. Both slip and bond stress vary locally in complex ways with position and the form of that variation is very different for the two quantities; high slip can occur at low bond-stress, and viceversa. This means that the average values are quite complex functions of the precise state of the bar and in practice the terms have no useful meaning. The question remains as to why the state of the steel affects the bond between the FRP and the concrete. If the steel is elastic, the steel strains will be small, as will the strains in the nearby concrete. On the other hand, if the steel is yielding, the strains in both the steel and the concrete will be much higher. It can reasonably be supposed that this will have a significant effect on the bond between the concrete and the FRP, especially if the FRP and the steel are not far apart. Thus, the effect can be expected to be higher when dealing with NSM (which is embedded in the concrete cover) than with EBR, (which is on the surface of the cover). In the tests referred to here, sufficient steel was provided in the anchorage region to ensure that it remained elastic, while much less steel was placed in the central zone to mimic the behavior in a beam loaded beyond yield. It is important to note that both steel and FRP bars are normally anchored in regions where the strains are low. In regions where the bending stresses are changing, and the steel is yielding, such as near mid-span in a strengthened beam, there must be a significant change in the stress in the FRP, which requires high bond capacity. But these are precisely the conditions where the bond strength of the FRP is lower. In conclusion, not only does the yielding of the steel affect the average FRP bond stress-slip relationship; the bonded length, the position of the segments with respect to the cracks (between or outside cracks) and the distance from the cracks also influence the relationships. The researchers 1- who concluded that the bond stress-slip relationship is not unique have used the average bond stress-slip relationships. 1

1 1 1 1 1 1 1 1 0 1 CONCLUSION The local bond stress-slip models for different regions were found experimentally; the results show that the local bond behavior differs between the cracked regions and the anchorage regions. Different boundary conditions, including the presence of cracks and steel, were investigated. The bond behavior between the cracks showed lower bond strength due to formation of herringbone cracks and debonding did not form in these regions, although the amount of steel in the anchorage regions was considerably higher than in the central regions at each load level. The peak FRP strain occurred in the central region and not in the anchorage regions. The presence of steel increased slightly the bond strength in the cracked regions, and increased the dissipated energy at the interface by about 0% when compared with the region without steel. This is probably because the steel limited the strain in the concrete, which helps to provide bond to the FRP. When the steel yields, that constraint is weakened. Because of the different boundary conditions, the local bond stresses between the cracks may not reach a level equal to the stresses in the anchorage region. In addition, herringbone cracks may form, in which case the bond stresses drop. The local bond stress-slip models, as well as the average bond models, would thus differ between the anchorage regions and the cracked regions. The local bond stress-slip relationships are unique when the same boundary conditions apply but average bond stress-slip relationships are location and length dependent. Finally, the boundary conditions of the implemented bond models have to comply with the actual boundary conditions of the problem and it is insufficient to treat the bond strength as a material property that is independent of the geometry. The bond models inherently represent the structural behavior of the systems from which they have been derived. REFERENCES 1. Nilson, A. H., Internal measurement of bond slip, ACI Journal Proceedings, Vol., No., 1, pp. -1. 1

. Jiang, D. H., Shah, S. P., and Andonian, A. T., Study of the Transfer of Tensile Forces by Bond, ACI Journal Proceedings, Vol. 1, No., 1, pp. 1-.. Somayaji, S. and Shah, S. P., Bond Stress versus slip relationship and cracking response of tension members, ACI Journal Proceedings, Vol., No., 11, pp. 1-.. fib Bulletin No.0, FRP reinforcement in RC structures, 00.. Nammur, J. and Naaman, A. E., Bond stress model for fiber reinforced concrete based on bond stress-slip relationship, Materials Journal, Vol., No. 1, 1, pp. -.. Lees, J. M. and Burgoyne, C. J., Transfer bond stresses generated between FRP tendons and concrete, Magazine of Concrete Research, Vol. 1, No., 1, pp. -.. Focacci, F., Nanni, A., and Bakis, C. E., Local bond-slip relationship for FRP reinforcement in concrete, Journal of Composites for Construction, Vol., No. 1, 000, pp. -1. 1 1 1. Tassios, T. P. and Yannopoulos, P. J., Analytical studies on reinforced concrete members under cyclic loading based on bond stress-slip relationships, ACI Journal Proceedings, Vol., No., 11, pp. 0-1. 1 1 1. Dai, J., Ueda, T., and Sato, Y., Development of the nonlinear bond stress-slip model of fiber reinforced plastics sheet-concrete interfaces with a simple method, Journal of Composites for Construction, Vol., No. 1, 00, pp. -. 1 1. Mirza, S. M. and Houde, J., Study of Bond Stress-Slip Relationships in Reinforced Concrete, ACI Journal Proceedings, Vol., No. 1, 1, pp. 1-. 0 1. Taher Khorramabadi, M.. FRP bond behaviour during intermediate concrete cover separation in flexurally strengthened RC beams. 0. PhD thesis, University of Cambridge. 1

1. Taher Khorramabadi, M., and Burgoyne, C. J., Fiber reinforced polymer bond test in presence of steel and cracks, ACI Structural Journal, V., No., Nov.-Dec. 0, pp. -. 1. George Nammur Jr. and Antoine E.Naaman, Bond stress model for Fiber Reinforced Concrete based on bond stress-slip relationship, Materials Journal, Vol., No. 1, 1, pp. -. 1. Eligehausen R., Popov E.P., and Bertero V.V., Local bond stress-slip relationships of deformed bars under generalized excitations, Earthquake Engineering Research Center, UCB/EERC-/, University of California, Berkeley, 1. 1 1. De Lorenzis, L., Rizzo, A., and La Tegola, A., A modified pull-out test for bond of near- surface mounted FRP rods in concrete, Composites Part B: Engineering, Vol., No., 00, pp. -0. 1 1 1 1. Cruz, J. M. S. and Barros, J. A. O., Bond between near-surface mounted carbon-fiber- reinforced polymer laminate strips and concrete, Journal of Composites for Construction, Vol., No., 00, pp. 1-. 1 1 1. Japan Society of Civil Engineers (JSCE), Recommendations for design and construction of concrete structures using continuous fiber reinforcing materials 1. 1 1 0 1. Japan Society of Civil Engineers (JSCE)-E, Test method for bond strength of continuous fiber reinforcing material by pull-out testing, Japan Society of Civil Engineers, Tokyo, Japan, 1. 1 1. Bruggeling, A.S.G., Structural concrete: theory and its application, Balkema Rotterdam Publisher, 11. 1

LIST OF TABLES AND FIGURES List of tables: Table 1: Details of the bond test specimens Table : Material property Table : Cracked-region local bond stress-slip parameters for FRP (Eq. & Eq.) Table : Anchorage region local bond stress-slip parameters for FRP (Eq. & Eq.) 1 1 1 1 1 1 1 1 0 1 List of figures: Fig. 1: Strain, slip, and bond stress distributions: (a) anchorage region or outside cracks (similar to conditions in a conventional bond test); and (b) cracked region at final cracking stage (between two cracks at final cracking stage) Fig. : Bond test specimens (a) side view (b) Specimen Bd-1SF- in the test rig (c) cross-sections, Dimensions in mm (in.) Fig. : Comparison between total load versus overall elongation of bond test specimens Fig. : Specimens after failure Fig. : Assumed local bond stress-slip relationship Fig. : Cracked-region local FRP bond stress-slip models for specimens with (a) steel and FRP (b) no steel (only FRP) Fig. : Anchorage-region local FRP bond stress-slip relationships Fig. : Examined local FRP bond stress-slip relationships Fig. : Bond models in cracked and anchorage regions Fig. : Effects of location and steel presence on average FRP bond stress-slip relationship 1 0

Table 1 Details of the bond test specimens Specimen ID Bd-1SF- Notches on four faces at each section No central region reinforcement 1φ + CFRP Bd-0SF- Yes CFRP Bd-1SF- Yes 1φ + CFRP cube concrete strength after days MPa (ksi) (.) (.) (1.) central region Width Height Length m (in.) 0.1 0.1 0. (.. 1.) anchorage region Width Height Length m (in.) Table Material property Material Young s modulus Strength Ultimate GPa (ksi) MPa (ksi) strain (%) 00 (0) CFRP 1 (00) Rupture 1. 00 () Steel 00 (000) Yielding 0.-1. Concrete (00) - - Table : Cracked-region local bond stress-slip parameters for FRP (Eq. & Eq.) Specimen Type Segment τ m MPa (ksi) s 1 mm (in.) α α Er ( - ) D L * N/mm (lb/in.) With steel FGH. (0.) 0.0 (0.00) 0.1-0. 1. 1.(.) JIH. (0.1) 0.0 (0.01) 0.01-0. 0. 1. (.) JKL. (0.) 0.0 (0.00) 0. -0. 1. 1. (.) FED. (0.) 0.0 (0.00) 0. -0.1 1. 1. (.) Ave.. (0.) 0.0 (0.00) 0. -0.0 1. 1. () without steel JIH.1 (0.) 0.0 (0.00) 0.00-0.1 1. 1.1 (.) JKL.0 (0.) 0.00 (0.00) 0. -0. 0.1 1. (.1) Ave.. (0.) 0.01 (0.00) 0. -0. 1.1 1. (.) * D L is the area below the curves shown in Fig. up to 1 mm (0.0 in.) slip only. 1

Table : Anchorage-region local bond stress-slip parameters for FRP (Eq. & Eq.) Specimen Type without steel with steel Segment τ m MPa (ksi) s 1 mm (in.) α α Er ( - ) D L * N/mm (lb/in.) LM.1 (1.) 0. (0.0) 0.001-1. 0.. (.) CD. (1.1) 0. (0.00) - -1.0 0.0 - CD. (1.) 0. (0.00) 0.1-1. 0.1. (.) BC. (1.1) 0. (0.01) 0.1-1.01 0.01.0 (.) Ave.. (1.) 0. (0.0) 0.1-1. 0.. (.1) *D L is the area below the curves shown in Fig. up to 1 mm (0.0 in.) slip only (Segment CD in specimen without steel is not counted in the average values). x x=l Strain gauge x x=l FRP Concrete Tf Supports Tf FRP Concrete Tf i (L) (0) i (L) s s(l) s s(0)=0 s(l) (0)=0 Unloaded-end Loaded end crack crack (a) (b) Fig. 1: Strain, slip, and bond stress distributions: (a) anchorage region or outside cracks (similar to conditions in a conventional bond test); and (b) cracked region at final cracking stage (between two cracks at final cracking stage) 1

Displacement transducer FRP-end T Portal gauge Strain gauge LRDT Top Notch Mid Notch Central steel Bot. Notch FRP b x FRP a 0 0 (.) (.) (.) (1.) A B C D E F G H I J K L M N O Anchorage region Central region Anchorage region anchorage bars 1 T (a) (b) 0 (.) 1 (.) Bd-1SF- & Bd-1SF-, Sec. H-H FRP strip 1.x1 mm (0.0x0.) Slot x1 mm (0.x0.) Cast direction 1 (.) 1 (.) Bd-0SF-, Sec. H-H All specimens, Sec.C-C (1.) (1.) (c) Fig. : Bond test specimens (a) side view (b) Specimen Bd-1SF- in the test rig (c) cross-sections, Dimensions in mm (in.) 1

Fig. : Comparison between total load versus overall elongation of bond test specimens Fig. : Specimens after failure

m (1) () 1 s1 Fig. : Assumed local bond stress-slip relationship s (a) Fig. : Cracked-region local FRP (b) bond stress-slip models for specimens with (a (b) no steel (only FRP) a) steel and FRP

Fig. : Anchorage-region local FRP bond stress-slip relationships Fig. : Examined local FRP bond stress-slip relationships

Bond stress Anchorage-region Cracked-region Debonding Pull-out force Main crack Slip Herringbone cracks FRP Anchorage region Central region Anchorage region 1 Reinforced concrete tie Fig. : Bond models in cracked and anchorage regions Average FRP bond stress (FG) Between two cracks (no steel or steel never yield (BC) Anchorage region (outside crack) (GH) Between two cracks (with steel) (CD) Anchorage region (at crack) FRP slip Fig. : Effects of location and steel presence on average FRP bond stress-slip relationship 1