BOND BETWEEN NEAR-SURFACE MOUNTED FRP RODS AND CONCRETE IN STRUCTURAL STRENGTHENING. Laura De Lorenzis 1, Antonio Nanni 2

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1 BOND BETWEEN NEAR-SURFACE MOUNTED FRP RODS AND CONCRETE IN STRUCTURAL STRENGTHENING Laura De Lorenzis 1, Antonio Nanni 2 KEYWORDS: Bond, Concrete, External Reinforcement, Fiber Reinforced Polymers, Rods, Slip, Strengthening ABSTRACT The use of Near Surface Mounted (NSM) Fiber Reinforced Polymer (FRP) rods is a promising technology for increasing flexural and shear strength of deficient reinforced concrete (RC) members. As this technology emerges, the structural behavior of RC elements strengthened with NSM FRP rods needs to be fully characterized, and bond is the first issue to be addressed. Bond is of primary importance since it is the means for the transfer of stress between the concrete and the FRP reinforcement in order to develop composite action. The objective of this research program was to investigate bond between NSM FRP rods and concrete. Some of the factors expected to affect bond performance were addressed, namely: bonded length, diameter of the rod, type of FRP material, surface configuration of the rod, size of the groove. Results are presented and discussed in this paper. INTRODUCTION The use of Near Surface Mounted (NSM) Fiber Reinforced Polymer (FRP) rods is a promising technology for increasing flexural and shear strength of deficient reinforced concrete (RC) and prestressed concrete (PC) members. Advantages of using NSM FRP rods with respect to externally bonded FRP laminates are the possibility of anchoring the reinforcement into adjacent RC members, and minimal installation time (Alkhrdaji et al., 1999). Furthermore, this technique becomes particularly attractive for flexural strengthening in the negative moment regions of slabs and decks, where external reinforcement would be subjected to mechanical and environmental damage and would require protective cover which could interfere with the presence of floor finishes. 1 Ph.D. Candidate, Department of Innovation Engineering, University of Lecce, Via per Monteroni, Lecce, Italy. 2 Jones Professor of Civil Engineering, University of Missouri Rolla, Rolla, MO. 1

2 Although the use of FRP rods for this application is very recent, NSM steel rods have been used in Europe for strengthening of RC structures since the early 50's. The earliest reference that could be found in the literature dates back to 1949 (Asplund, 1949). Nowadays, FRP rods can be used in place of steel and epoxy paste can replace cement mortar. The advantage is primarily the resistance of FRP to corrosion. This property is particularly important in this case due to the position of the rods very close to the surface, which exposes them to the environmental attacks. The method used in applying the rods is described as follows. A groove is cut in the desired direction into the concrete surface. The groove is then filled half-way with epoxy paste, the FRP rod is placed in the groove and lightly pressed. This forces the paste to flow around the rod and fill completely between the rod and the sides of the groove. The groove is then filled with more paste and the surface is leveled. Very limited literature is available do date on the use of NSM FRP rods for structural strengthening. Laboratory studies and field applications are reported in Alkhrdaji et al. (1999), Crasto et al. (1999), Hogue et al. (1999), Tumialan et al. (1999), Warren (1998), Yan et al. (1999), De Lorenzis (2000). Yan et al. (1999) performed experimental tests to characterize the bond strength of NSM FRP rods. As this technology emerges, the structural behavior of RC elements strengthened with NSM FRP rods needs to be fully characterized and bond is the first issue to be addressed. Bond is of primary importance since it is the means for the transfer of stress between the concrete and the FRP reinforcement in order to develop composite action. The bond behavior has influence on the ultimate capacity of the reinforced element as well as on serviceability aspects such as crack width and crack spacing. The objective of this experimental program was to investigate bond between NSM FRP rods and concrete. Some of the factors expected to affect bond performance were addressed, namely: bonded length, diameter of the rod, type of FRP material, surface configuration of the rod, size of the groove. A series of specimens was tested to assess the influence of each of the above mentioned factors on the bond behavior. DESCRIPTION OF SPECIMENS AND TEST MATRIX A beam pull-out test was adopted for this project, based on merits of test methods and previous work on bond between CFRP sheets and concrete (Nanni et al. 1995, Miller, 1999). The specimens were unreinforced 2

3 concrete beams with an inverted T-shaped cross-section, chosen to provide a larger tension area for concrete while minimizing the overall weight of the beam. A larger tension area for concrete was needed to increase the cracking moment resistance of the specimen. Furthermore, the position of the bonded length of the rod had to be chosen appropriately in order to prevent flexural cracking before bond failure. For different applied load levels, the maximum tensile stress in the concrete cross-section was computed as a function of the distance of the bonded length from the support. This distance was then chosen such that the maximum tensile stress in the concrete, at a load level corresponding to the envisioned bond failure load, was conveniently lower than the concrete modulus of rupture. The dimensions of the beams are given in Figure 1. The specimen had a steel hinge at the top and a saw cut at the bottom, both located at mid-span. The purpose of the hinge and saw cut was to allow control of the internal force distribution. During loading of the specimen, the saw cut caused a crack to develop at the center of the beam and extend up to the hinge. Therefore, the compressive force in the beam at mid-span was located at the center of the hinge and the internal moment arm was known and constant for any given load level above the cracking load. Each beam had a NSM FRP rod applied to the tension face and oriented along the longitudinal axis of the beam. One side of the beam was the test region, with the NSM FRP rod having a limited bonded length and being unbonded in the remaining part. The rod was fully bonded on the other side of the beam, to cause bond failure to occur in the test region. The variables examined in the experimental test matrix were the following: bonded length. Four different bonded lengths were selected, equal to 6, 12, 18 and 24 times the diameter of the rod; diameter of the rod. Rods No. 3 and No. 4, having nominal diameter 3/8 in. (9.5 mm) and 1/2 in. (13 mm) respectively, were examined; type of FRP material. Both CFRP and Glass FRP (GFRP) rods were used; surface configuration of the rod. For the CFRP rods, the effect of two different surface conditions, deformed and sandblasted, was examined; 3

4 size of the groove. For some types of rods, specimens with three different sizes of the groove were tested. The groove width was maintained equal to the groove depth in all the tested specimens, so that the term size is used in the following to refer to either the groove depth or width. Concrete strength and type of epoxy were not varied, although they are significant parameters. Concrete with 4000-psi (27.6 MPa) nominal compressive strength and a commercially available epoxy paste were selected as representative systems. The average concrete strength, determined according to ASTM C39-97 on three 4-in. (102- mm) diameter by 8-in. (203-mm) cylinders for each concrete batch, ranged from 3880 to 4100 psi (26.7 to 28.2 MPa). The mechanical properties of the epoxy paste, as specified by the manufacturer, were: 2000 psi (13.8 MPa) tensile strength (ASTM D638), 4% elongation at break (ASTM D638), 8000 psi (55.2 MPa) compressive yield strength (ASTM D695) and 400 ksi (2757 MPa) compressive modulus (ASTM D695). Tensile strength and modulus of elasticity of the CFRP deformed rods were determined from laboratory testing. The average values resulted to be 272 ksi (1875 MPa) and ksi (104.8 GPa) with a standard deviation of 6.9 ksi (47.6 MPa) and 700 ksi (4.8 GPa), respectively. The manufacturer specified for the GFRP No. 4 rods a tensile strength of 116 ksi (799 MPa) and a Young s modulus of 6000 ksi (41.3 GPa). Properties of the CFRP No. 3 sandblasted rods were: 225 ksi (1550 MPa) tensile strength and ksi (164.7 GPa) Young s modulus. Table 1 summarizes all specimens that were tested together with the designation used to identify them. Six specimens with GFRP No. 4 deformed rods were tested. The first series consisted of three specimens (G4D6a, G4D12a and G4D18a) with the same groove size (5/8 in., 16 mm) and three different bonded lengths (6, 12 and 18 d b ). The value of the groove size was chosen as the smallest possible from a practical standpoint. Subsequently, two more specimens were tested (G4D12b and G4D12c), characterized by a bonded length of 12 d b and two different values of the groove size, namely, 3/4 in. (19 mm) and 1 in. (25 mm). After testing of these two specimens, a groove size of 1 in. (25 mm) was identified as the recommendable size for embedment of a No. 4 GFRP deformed rod. Therefore, an additional specimen was tested (G4D24c), with 1-in. (25-mm) groove and a bonded length of 24 d b. Longer bonded lengths are more capable to represent the non-uniform interface conditions and to make negligible the unavoidable end effects. The same test matrix was followed for the twelve specimens with CFRP No. 3 deformed and sanblasted rods. The groove size reflected the use of a smaller diameter rod. 4

5 Four specimens with CFRP No. 4 sandblasted rods were tested, with a groove size of 3/4 in. (19 mm) and four different bonded lengths (6, 12, 18 and 24 d b ). No different groove sizes were investigated, since testing of the specimens with No. 3 sandblasted rods had shown no influence of the groove size on ultimate load and failure mode. PROCEDURE The epoxy paste was allowed to cure for at least 15 days (full cure time at room temperature) prior to testing of the beams. The beams were loaded under four-point bending with a shear span of 19 in. (483 mm). Each beam was instrumented with two LVDTs, one placed at mid-span to measure deflection of the beam and the other one used to monitor the slip of the rod at the end of the test region. Three or four strain gages were applied on the surface of the FRP rods within the bonded length and an additional one was applied in the unbonded region. No strain gages were applied to the specimens with a bonded length of six diameters. Testing was performed by loading the beam in displacement controlled mode until failure. RESULTS General Results The test results in terms of ultimate pull-out load, average bond strength and failure mode are summarized in Table 1. The expression pull-out load has been adopted to refer to the tensile load directly applied to the NSM rod after cracking of the beam, which could be computed with accuracy from the value of the external applied load as a result of the specimen configuration. The ultimate pull-out load has been also expressed as a percentage of the ultimate tensile load of the FRP rod, to give an idea of how efficiently the rods can be used when bond is the controlling factor. The failure mode is indicated for all the specimens in the last column. A detailed description of the failure modes is reported in the next section. The load vs. mid-span deflection curves were used to check the overall behavior of the specimen during loading. Three types of load vs. mid-span deflection behavior were observed, depending on the failure mode. For the specimens failed by splitting of the epoxy cover, the load vs. mid-span deflection curve appeared very similar to that shown in Figure 2-curve a, relative to specimen G4D12a. The instant of cracking is clearly visible at a load level of 2930 lbs (13.0 kn), after which the applied load starts increasing again until failure occurs in a sudden 5

6 fashion. When failure occurred at the interface between epoxy paste and FRP rod (pull-out), the load dropped to a value smaller than the cracking load and remained constant while deflection kept on increasing until the test was stopped (Figure 2-curve b). This behavior is due to the presence of friction between the rod and the surrounding paste, which keeps on resisting a certain amount of load even after the other bond-resisting mechanisms are lost. This phenomenon is clearly absent when splitting leads to the total or partial loss of the epoxy cover. Finally, specimen C3D12c experienced failure by cracking of the concrete surrounding the groove, that led to gradual dropping of the load, as shown in Figure 2- curve c. Average bond stress vs. free-end slip diagrams were also plotted. Those of the specimens with GFRP rods are illustrated in Figure 3. For this type of rebar, an 18-diameter bonded length was enough to prevent the free end from slipping before bond failure. In the case of CFRP sandblasted rods, free-end slip was recorded prior to failure when the bonded length was 18 d b, while no slip occurred in the specimen with 24-d b bonded length. In the case of CFRP deformed rods, the rod's free end started slipping before failure even in the specimen with the longest bonded length. Failure Modes Specimens with Deformed Rods For all the specimens with deformed rods, with the only exception of specimen C3D12c, failure occurred by splitting of the epoxy paste in which the NSM rods were embedded, accompanied or not by cracking of the concrete surrounding the groove. During testing, a crackling noise revealed the progressive cracking of the epoxy paste, until the epoxy cover was completely split and the load suddenly dropped. Although this overall behavior was common to all the specimens, some differences could be observed as bonded length and groove size were changed. In specimens G4D6a, G4D12a, C3D6a and C3D12a, having the minimum groove size, failure occurred by splitting of the epoxy paste which disintegrated in very small pieces, while no damage was visible in the surrounding concrete and the deformations on the bar surface were also intact. Very similar was the aspect of specimens G4D18a and C3D18a, having the minimum groove size and a bonded length of 18 bar diameters. In this case, some damage in the concrete surrounding the rod was visible and, for GFRP rods, In the case of GFRP, the 6

7 deformations on the rod s surface in the region close to the loaded-end had been partially sheared off. In specimens G4D12b, G4D12c and C3D12b, due to the larger groove depth, a higher level of damage was observed in the concrete at the sides of the groove (Figure 4). The epoxy paste, rather than disintegrating in small pieces, developed longitudinal and inclined cracks that propagated in the concrete. Also, since specimen G4D12c was able to sustain a load slightly higher than G4D18a, shearing-off of the rod s lugs occurred also in specimen G4D12c. Specimen C3D12c experienced a different mode of failure. Inclined cracks propagated in the concrete surface at one side of the groove and led to a gradual dropping of the load. Visual inspection after failure revealed also the presence of inclined cracks in the epoxy close to the rod s loaded end. This specimen had the largest value of the ratio cover thickness to rod diameter among all the specimens with deformed rods. The cover was thick enough to offer a higher resistance to splitting, so that the controlling failure mechanism shifted to cracking of the surrounding concrete. Finally, in specimens G4D24c and C3D24b, inclined and longitudinal splitting cracks formed in the epoxy paste and the inclined cracks propagated in the concrete surrounding the groove (Figure 5). The rod s deformations were extensively sheared-off in specimen G4D24c and damaged in localized areas in specimen C3D24b. The failure mode by splitting of the epoxy cover is similar in its mechanics to splitting of the concrete cover for reinforcing rods embedded in concrete. The radial components of the bond stresses are balanced by circumferential tensile stresses in the epoxy cover which may lead to the formation of longitudinal splitting cracks (Tepfers, 1979). The load at which splitting failure develops is influenced by the surface characteristics of the rods, the tensile strength of the cover material and the thickness of the cover, which in turn depends on the depth of the groove in which the rods are embedded. Epoxy has typically a much higher tensile strength than the concrete, however, the cover thickness of NSM reinforcement is very low compared to that of reinforcing bars in concrete, which makes this mode of failure critical for NSM reinforcement. The concrete material surrounding the groove is also subjected to tensile stresses along inclined planes, and the tensile strength of the material may be eventually reached causing fracture along these planes. Whether failure in the concrete occurs before or after the formation of splitting cracks in the epoxy or even the complete fracture of the epoxy cover, depends on the groove size and the tensile strength of the two materials. 7

8 Internal cracks in the epoxy paste were observed in all the specimens after failure. These secondary cracks indicate the trajectories along which the compressive forces leave the surface of the bars and spread out into the surrounding material. Unlike in the case of reinforcing bars embedded in concrete, in NSM reinforcement these inclined cracks may form not only as secondary cracks in the internal surface of the epoxy paste, but also, due to the small cover thickness, as primary cracks that can lead to bond failure. Specimens with Sandblasted Rods Different failure modes were observed in the specimens with CFRP sandblasted rods. Specimens C3S6a and C4S6a failed by splitting of the epoxy cover. In specimen C3S6a, the epoxy paste disintegrated in small fragments, while the cover of specimen C4S6a broke up in two pieces along a longitudinal splitting crack. Inclined cracks in the epoxy underneath the rod and inclined white lines on the rod surface were visible tracks of the bond stresses. Specimens C3S12a, b and c all failed at the interface between epoxy and CFRP rod. This failure mode has been referred to as pull-out in Table 1. The degree of micro-deformation on the surface was not enough to provide mechanical interlocking and bond was primarily guaranteed by chemical adhesion and friction after onset of slip. As a result, the rod was pulled out as soon as adhesion was lost. No sign of damage was visible in the test side of these specimens after failure. All the other specimens experienced a mixed failure mode between the previous two. After failure, either the epoxy cover appeared partially damaged (C3S18a) or a longitudinal splitting crack has developed close to the rod s loaded end (C4S12a). Effect of the Tested Variables Among the two different rod surface conditions examined in this experimental study, deformed and sandblasted, the former appeared to have a greater tendency to induce splitting failure, as expected. However, comparing the average bond strength of specimens with CFRP deformed and sandblasted rods having the same values of all the remaining parameters, it can be concluded that deformed rods are more efficient than sandblasted rods from the standpoint of the bond performance. 8

9 When failure was by splitting of the epoxy cover, increasing the groove size led to a higher bond strength. For specimens G4D12, the ultimate load increased 8% and 24% as the groove size increased from 5/8 in. (16 mm) to 3/4 in. (19 mm) and 1 in. (25 mm), respectively. For the specimens C3D12, the ultimate load increased 15% and 8% as the groove size increased from 0.5 in. (13 mm) to 3/4 in. (19 mm) and 1 in. (25 mm), respectively. The smaller increase in the second case corresponded to a different mode of failure, as previously discussed. As the groove size increases, the thickness of the epoxy cover increases, so offering a higher resistance to splitting. The ultimate load increases correspondingly, and failure may eventually shift from the epoxy to the surrounding concrete. For specimens C3S12, increasing the groove size did not influence the failure load, since pull-out was the controlling mechanism. However, in specimens with longer bonded lengths splitting cracks developed and accelerated pull-out failure. Therefore, it is expected that increasing the groove size would have been beneficial also for specimens with sandblasted rods. The ultimate load increased, as expected, with the bonded length of the rod. For the specimens with GFRP No. 4 deformed and CFRP sandblasted rods, the average bond strength was found to decrease as the bonded length increased. On the contrary, for specimens with CFRP No. 3 deformed rods, the average bond strength resulted approximately constant with the bonded length, which indicates an even distribution of bond stresses along the bonded length at ultimate. ANALYSIS OF RESULTS Elastic Modulus of the Rods After the mid-span cross-section had cracked, the specimen configuration allowed to compute the tensile load in the rod from the externally applied load using equilibrium. On the other hand, strain at the rod loaded end was monitored by an electric strain gage. Therefore, at each load level after cracking, the elastic modulus of the rod was calculated dividing the tensile load by the loaded-end strain and by the nominal cross-sectional area of the rod. As the crack reached the top hinge, the value of the elastic modulus computed as described stabilized. The average of all values in the stable range (i.e., variation less than 5%) is used as the reference elastic modulus. Once the reference elastic modulus had been computed, the tensile load in the rod became known at every load level, also 9

10 before cracking, from the values of elastic modulus and loaded-end strain. For the purpose of data analysis, it was decided to use, for each specimen, the reference elastic modulus pertaining to that specimen and not the grand average, so that, after stabilized cracking, the values of tensile load calculated by equilibrium from the external load coincided with those computed from the strain readings. The elastic modulus computed for the specimens in which the strain gage in the unbonded region was properly functioning up to failure is reported in Table 2, where it is compared with the value known by manufacturer specifications or experimental testing. It can be seen that reasonable agreement exists between the average of the two sets. Analysis of Strain Data The data from the strain gages was used to plot strain vs. location graphs. In these graphs, the strain in the rod along the bonded length is plotted for different values of the pull-out load. All points were obtained from the readings of the strain gages, except for the strain at the end of the bonded length, which was assumed to be equal to zero. From the strain-location data many useful information can be drawn. Equilibrium of a piece of rod of length dx (Figure 6), along with the assumption of linearly elastic behavior of the rod, leads to the following: d b dε b ( x) τ ( x) = Eb (1) 4 dx where d b, E b, ε b are diameter, Young s modulus and strain of the rod, respectively, while τ is the bond stress and x is the coordinate along the bonded length. Given that strain measurements are available at discrete points along the bonded length, and indicating with ε bi the strain reading at the location expressed by the coordinate x i, (1) may be approximated as follows: xi + x j d ε b bj ε bi τ ( ) = Eb (2) 2 4 x x j i 10

11 Recalling the definition of slip as the relative displacement between reinforcement and parent material, and recalling also that: ε du b b = dx and ε du e e = dx, (3) where u b and u e are the displacements of the FRP reinforcement and of the epoxy, respectively, it follows that: ds dx = ε ε b e ε b (4) where the epoxy strain, ε e, is assumed to be negligible when compared to the FRP strain, ε b. Thus: x s( x) = s(0) + ε b ( x) dx (5) or, in the case of discrete strain readings, 0 i j= 1 ( x x ) s( x ) = s(0) + ε (6) i bj j j 1 Figures 7 through 9 illustrate an example of strain, slip and bond stress vs. location curves obtained as explained above from the strain readings of specimen C3D18a. In all figures, each curve is relative to a certain load level indicated as percentage of the ultimate load. This was done to allow comparison between different specimens in spite of the different failure load. The left end (location equal to zero) and the right end of the x axis correspond to the free end and to the loaded end of the bonded length, respectively. The strain distribution along the bonded length, highly non-linear at moderate load levels, tends to approach an almost linear shape as the applied load increases. This means that, as load increases, bond stresses become more evenly distributed along the bonded length as a result of changes in the nature of bond. When ribbed reinforcement is used, the primary bond mechanism changes from chemical adhesion to mechanical interlocking as soon as the ribs are brought into bearing. The radial components of the bond stresses produce internal microcracks in the epoxy resin that have been visually observed in all specimens after failure. Microcracking and the consequent slip between reinforcement and parent material tend to make the bond stress more evenly distributed. Figure 9 shows that, while at low loads the bond stresses at the rod s free end are close to zero, as the load increases the peak of the bond stresses gradually shifts towards the free end and the whole bonded length contributes to resist the pulling force. 11

12 The behavior is different in the case of specimens with sandblasted reinforcement. Although a certain amount of internal microcracking of the epoxy was found also in these specimens, this was not sufficient to allow the bond stresses to redistribute along the bonded length. Linear Analysis of the Bonded Joint The differential equation governing bond is as follows: 2 d s 2 dx d b 4 E b τ ( s( x)) = 0 (7) Equation (7) comes from equilibrium and compatibility relations on a finite element of rod of length dx, along with the assumptions that the FRP rod is linearly elastic and the concrete strain is negligible if compared to that of the FRP. The analysis of the bonded joint in the linear elastic range can be conducted by means of a simple shear lag approach. At moderate load levels, a linear bond stress-slip behavior can be adopted: τ = K s (8) where K is the so called slip modulus and s is the slip. Solving (7) with the τ-slip relationship given by (8) yields the following equation for the strain distribution along the FRP bar: σ appl sinhαx ε b ( x) = (9) E sinhαl b b where σ appl is the tensile stress applied to the rod, l b is the bonded length and: 4K α = (10) E b d b The slip modulus K has been evaluated by best fitting between the theoretical strain distribution given by (9) and the experimental strain values. In other words, K was computed at each load level by minimizing the percent error, evaluated as follows: Err = N i= 1 ( ε theor bi maxε i ε exp bi exp bi ) (11) 12

13 where ε theor bi and ε exp bi are the theoretical and experimental strain, respectively, at the location of the i th strain gage, and N is the total number of strain gages. For most specimens, the agreement between experimental strains and theoretical curves is generally good for load levels up to approximately 40% of ultimate. As an example, Figure 10 shows theoretical and experimental strain distributions at moderate load levels for specimen C3D18a. The theoretical curves were plotted for the value of K that minimizes the average of the errors at the 10% to 40% load levels, that is K=448 ksi/in. (121.5 MPa/mm). The average Err for this value of K is 4.0%. Local Bond Stress Slip Relationship The local τ slip relationship can be obtained by combining the two curves τ(x) and s(x) expressed by equations (1) and (5). A τ vs. x curve and an s vs. x curve can be obtained for each value of the applied load, therefore, a τ vs. slip diagram corresponding to each value of applied load can be drawn. At a given load level, the τ vs. slip diagram covers the range of slip between the free-end slip and the loaded-end slip at that load level. The entire curve can be obtained as the envelope of the partial curves at all load levels between zero and ultimate. In the case of discrete strain readings, equations (1) and (5) are approximated by (2) and (6). It is obvious that, given the small number of strain gages and the influence exerted on their readings by the unavoidable local effects, given also that derivation performed on experimental data increases their degree of irregularity, the experimental τ vs. slip diagrams are often very irregular. Therefore, rather than as curves, the τ -slip data was plotted as points at ten load levels between 10% and 100% of ultimate. The experimental τ -slip points for specimen C3D18a are reported in Figure 11. Once a local τ slip relationship is obtained, the next step is to find an analytical expression capable to model such relationship. For steel and FRP reinforcing bars in concrete, various equations have been previously proposed (Eligehausen et al., 1983, Cosenza et al., 1997, Focacci et al., 2000). Each of them contains a certain number of unknown parameters, which need to be calibrated by comparison with experimental data. In the present study, a modified version of the Bertero-Popov-Eligehausen (BPE) relationship proposed by Cosenza et al. (1997) 13

14 has been used for specimens with deformed rods. Such relationship has a first ascending branch coinciding with the BPE model, and a second linear softening branch: α s α τ ( s) = τ m = C s s for s < s m (12a) m τ ( s) = τ m + p ( s sm ) for s m < s < su (12b) where s u has been assumed as the value of slip at which the bond stress becomes equal to zero. For specimens with sandblasted rods, the following relationship has been used: α s α τ ( s) = τ m = C s s for s < s m (13a) m τ s) = τ + p ( s s ) for s m < s < s f (13b) ( m m τ = ( s) τ f for s f s > (13c) where the third constant branch represents friction. The unknown parameters contained in the models, calibrated by best fitting of the experimental results, are reported in Table 3. When more than one specimen of the same type was tested and gave good strain readings, the reported values are the average of those of the single specimens (e.g. C3Da is the average of C3D12a and C3D18a). For C3S specimens, results of specimens C3S12c and C3S24a were averaged, since no changes were observed in specimens C3S12 due to the different groove size. It may be noted that specimens with sandblasted rods tend to have low values of s m compared with those with deformed rods, and high values of α (close to 1.00), which indicates that their ascending branch is close to the linear shape. Specimens with deeper grooves have generally higher values of τ m, except for the case of C3Dc which failed by concrete cracking. However, the reported parameters need to be calibrated over a wider experimental base to confirm and more precisely quantify these trends. An example of local bond stress vs. slip diagram is reported in Figure 11. Calculation of Bond Failure Load and Anchorage Length Once the analytical τ slip relationship is known, it can be used to analytically solve all problems related to the bond behavior, particularly, to calculate the anchorage length of NSM FRP rods. 14

15 In order to predict the failure load of a bonded joint for which the τ slip relationship is known, the following procedure can be used. Differential equation (7) can be solved numerically for increasing values of the free-end slip, that is, for a certain number of boundary conditions of the type: s(0) = s f ds = ε b (0) = 0 dx x= 0 (14) To each value of free-end slip corresponds a value of strain at x=l b, that is, at the rod s loaded end. If s f (i) is the free-end slip at the i th iteration and ε (i) the corresponding loaded-end strain, the free end slip must be incremented bl until is ε ( i +1) < ε (i). At this point, the values of free-end and loaded-end slip are those at bond failure, and the bl bl loaded-end strain, multiplied by elastic modulus and cross-sectional area of the rod, gives the bond failure load. Figure 12 illustrates the failure load and the free-end and loaded-end slip at failure as functions of the bonded length, expressed as number of diameters. Although the curves have been obtained using the parameters of specimens C3Da, the comparison with the experimental results in Figure 12-a shows reasonable correlation also with the failure load of specimens C3Db and C3Dc. It can be also seen that the maximum load that the bonded joint can sustain is equal to 11.4 kips (50.7 kn), that is, only 38% of the ultimate tensile load, and that the minimum bonded length required to anchor the rod under this load is approximately 35 diameters. Figure 12-b shows that, as the bonded length increases, the loaded-end slip at failure increases and the free-end slip decreases. If the bonded length is long enough, bond fails before the rod s free end starts slipping. The load at onset of slip has been also plotted. It can be computed by solving equation (7) with boundary conditions: s(0) = 0 ds = ε (0) = 0 b dx x= 0 (15) For the τ slip relationship adopted herein, equation (7) with the above boundary conditions has a closed-form solution. From the design standpoint, the anchorage length of the rod has to be such that the free end does not slip under the design load, therefore, the load at onset of free-end slip has more practical interest of the bond failure load. Furthermore, it is often desired to anchor the rod using only the ascending portion of the τ slip relationship. The maximum tensile stress that can be applied to the rod to satisfy this condition is (Cosenza et al., 1997): 15

16 σ = 1 8 E d b b τ m sm 1+ α and the corresponding minimum bonded length is: σ 1 d b 1+ α l m = (17) 4 τ 1 α m The computed values of σ 1and l m are reported in Table 3. The low values of σ 1 / f u, f u being the tensile strength, indicate that the efficiency in the use of the FRP material is very limited, bond being the controlling factor. However, anchoring the rod only in the ascending branch of the τ slip law is probably too conservative, as visible in Figure 12-a where the point corresponding to P1 = A b σ 1 is the inflection point of the light curve. (16) CONCLUSIONS The following conclusions can be drawn from the experimental investigation on bond of NSM FRP reinforcement in concrete: the bond test method adopted in this experimental program appears to be an efficient protocol for investigation of bond. It gives reliable data while maintaining a manageable specimen size. Furthermore, specimen details as the saw cut and the top hinge at mid-span allow to analyze the data with accuracy; three different failure modes were experienced during the experimental tests, namely, splitting of the epoxy cover, cracking of the concrete surrounding the groove and pull-out of the FRP rod. In some cases, combined failure modes were registered; the surface condition of the FRP rods influences the bond strength. Deformed rods appear to be more efficient than sandblasted rods from the standpoint of the bond performance; increasing the groove size, and thus the cover thickness, leads to higher bond strength when failure is controlled by splitting of the epoxy cover. Conversely, it does not have any effect when pull-out failure occurs; the only specimen that failed by cracking of the concrete surrounding the groove had the largest value of the ratio cover thickness to rod diameter among all the specimens with deformed rods. When failure occurs by splitting of the epoxy cover or by pull-out of the rod, the ultimate load is expected to be independent 16

17 from the concrete tensile strength. However, if the groove is deep enough to cause failure occur in the concrete, the concrete tensile strength becomes a significant parameter; from the experimental results involving three different groove sizes, the optimum groove sizes appear to be 3/4 in. (19 mm) and 1 in. (25 mm) for embedment of NSM rods No. 3 and No. 4, respectively. This conclusion is based on testing of specimens with deformed rods. The effect of the groove size for specimens with sandblasted rods having bonded lengths greater than 12 rod diameters needs to be investigated; the distribution of bond stresses at ultimate is not uniform. Therefore, the anchorage length has to be calculated by solving the differential equation of bond with the local bond stress slip relationship of the NSM rods. Such relationship was obtained for the tested specimens by best fitting between the τ slip points obtained by the strain data and parametric laws proposed by previous researchers; as the efficiency in the use of this strengthening technique is affected by bond performance, deeper groove sizes and different epoxy resin with higher tensile strengths need to be studied. Furthermore, the influence of the concrete strength on the bond behavior needs to be assessed. Finally, a wider experimental base is needed to confirm and more precisely quantify the trends indicated by the present study. ACKNOWLEDGEMENTS The authors would like to acknowledge the NSF Industry/University Cooperative Research Center on Repair of Building and Bridges with Composites (RB 2 C) for support to this project. APPENDIX: REFERENCES Alkhrdaji, T.; Nanni, A.; Chen, G.; and Barker, M. (1999), Upgrading the Transportation Infrastructure: Solid RC Decks Strengthened with FRP, Concrete International, American Concrete Institute, Vol. 21, No. 10, October, pp Asplund, S.O. (1949), "Strengthening Bridge Slabs with Grouted Reinforcement", Journal of the American Concrete Institute, Vol. 20, No. 6, January, pp

18 Eligehausen, R.; Popov, E. P.; and Bertero, V. V. (1983), Local Bond Stress Slip Relationships of Deformed Bars Under Generalized Excitations, Report No. 83/23, EERC, University of California, Berkeley, CA, 162 pp. Cosenza, E.; Manfredi, G.; and Realfonzo, R. (1997), Behavior and Modeling of Bond of FRP Rebars to Concrete, Journal of Composites for Construction, Vol. 1, No. 2, pp Crasto, A.; Kim, R.; and Ragland, W. (1999), Private Communication. De Lorenzis, L. (2000), Strengthening of RC Structures with Near-Surface Mounted FRP Rods, MSc Thesis, Department of Civil Engineering, University of Missouri Rolla, Rolla, MO, 175 pp. Focacci, F; Nanni, A.; and Bakis, C.E. (2000), Local Bond-Slip Relationship for FRP Reinforcement in Concrete, Journal of Composites for Construction, Vol. 4, No. 1, pp Hogue, T.; Cornforth, R.C.; and Nanni, A. (1999), Myriad Convention Center Floor System Reinforcement, Proceedings of the Fourth International Symposium on Fiber Reinforced Polymer Reinforcement for Reinforced Concrete Structures, C.W. Dolan, S. Rizkalla and A. Nanni, Editors, American Concrete Institute SP-188, pp Miller, B. (1999), Bond Between Carbon Fiber Reinforced Polymer Sheets and Concrete, MSc. Thesis, Department of Civil Engineering, University of Missouri Rolla, Rolla, MO, pp Nanni, A.; Bakis, C.E.; and Boothby, T.E. (1995). Test Methods for FRP Concrete Systems Subjected to Mechanical Loads State-of-the-Art Review, Journal of Reinforced Plastics and Composites, Vol. 14, No. 6, pp Tepfers, R. (1979), Cracking of Concrete Cover Along Anchored Deformed Reinforcing Bars, Magazine of Concrete Research, Vol. 31, No. 106, Cement and Concrete Association, Wexham Springs, Slough, England, pp Tumialan, G.; Tinazzi, D.; Myers, J.; and Nanni, A. (1999), Field Evaluation of Masonry Walls Strengthened With FRP Composites at the Malcolm Bliss Hospital, Report CIES 99-8, Center for Infrastructure Engineering Studies, University of Missouri-Rolla, Rolla, MO. Warren, G.E. (1998), Waterfront Repair and Upgrade, Advanced Technology Demonstration Site No. 2: Pier 12, NAVSTA San Diego, Site Specific Report SSR-2419-SHR, Naval Facilities Engineering Service Center, Port Hueneme, CA. 18

19 Yan, X.; Miller, B.; Nanni, A.; and Bakis, C.E. (1999), Characterization of CFRP Bars Used as Near-Surface Mounted Reinforcement, Proceedings 8 th International Structural Faults and Repair Conference, M.C. Forde, Ed., Engineering Technics Press, Edinburgh, Scotland, 1999, 10 pp., CD-ROM version. 19

20 Laura De Lorenzis, ACI member, received her MS in May 2000 from the University of Missouri-Rolla, Department of Civil Engineering. She is currently a PhD candidate in the Department of Engineering Innovation of the University of Lecce, Italy. Antonio Nanni, FACI, is the V & M Jones Professor of Civil Engineering and Director of the University Transportation Center (UTC) at the University of Missouri-Rolla. Dr. Nanni is an active member in the technical committees of ACI, ASCE, ASTM and TMS. 20

21 List of Tables Table 1 Description of the Specimens and Test Results Table 2 Elastic Modulus Data Table3 Calibrated Parameters in the τ slip relationships and Values of σ 1 and l m 21

22 List of Figures Figure 1 Test Specimen Figure 2 Load vs. Mid-Span Deflection Curves Figure 3 Average Bond Stress vs. Free-End Slip for Specimens with GFRP Deformed Rods Figure 4 Specimen C3D12b after Failure (Splitting of Epoxy + Concrete Cracking) Figure 5 Specimen C3D24b after Failure (Splitting of Epoxy +Concrete Cracking) Figure 6 Free-body Diagram of Bar with Length dx Figure 7 Strain vs. Location (C3D18a) Figure 8 Slip vs. Location (C3D18a) Figure 9 Bond Stress vs Location (C3D18a) Figure 10 Theoretical and Experimental Strain Distribution at Moderate Loads (C3D18a) Figure 11 Bond Stress vs. Slip (C3D18a) Figure 12 Theoretical Bond Failure Load and Slip for Specimens C3Da 22

23 in Structural Strengthening, ACI Structures Journal, Vol. 99, No. 2, March-April 2002, Table 1. Description of the Specimens and Test Results Specimen Code Type of FRP Rod/ Rod Size Surface Configuration Bonded Length (No. of d b ) Groove Size (in) Ultimate Pull-Out Load (lbs) Percentage of Ultimate Tensile Load (%) Average Bond Strength (psi) Failure Mode* G4D6a 6 5/ SOE G4D12a 5/ SOE G4D12b GFRP/ 12 3/ SOE+C Deformed G4D12c No SOE+C G4D18a 18 5/ SOE G4D24c SOE+C C3D6a 6 1/ SOE C3D12a 1/ SOE C3D12b CFRP/ 12 3/ SOE+C Deformed C3D12c No C C3D18a 18 1/ SOE C3D24b 24 3/ SOE+C C3S6a 6 1/ SOE C3S12a 1/ PO C3S12b CFRP/ 12 3/ PO Sandblasted C3S12c No PO C3S18a 18 1/ PO+SOE C3S24a 24 1/ PO+SOE C4S SOE C4S12 CFRP/ PO+SOE Sandblasted 5/8 C4S18 No PO+SOE C4S PO+SOE * SOE = Splitting of Epoxy; C = Concrete Cracking; PO = Pull-Out (1 in. = 25.4 mm; 1 lbs = N; 1 psi = 6.89 kpa) 23

24 Table 2. Elastic Modulus Data Rod Type Bond Tests Tensile Tests* CFRP No. 3 Deformed CFRP No. 3 Sandblasted CFRP No. 4 Sandblasted GFRP No. 4 Deformed Specimen Elastic Modulus E 1 (ksi) Specimen Elastic Modulus E 2 (ksi) C3D12a C3D12c C3D18a Average Average C3S12b C3S12c C3S24a Average Manufacturer Elastic Modulus E 3 (ksi) Difference between the Average Values** (%) N/A 4.8 N/A C4S N/A N/A N/A G4D12a 5134 G4D12b 5626 G4D12c 5496 G4D18a 5988 G4D24c 6213 Average 5691 N/A *From (De Lorenzis, 2000) ; ** Ratio E 1 /E 2 or E 1 /E 3 ; N/A = not applicable or available (1 ksi = 6.89 MPa) Specimen Table 3. Calibrated Parameters in the τ slip relationships and Values of σ 1 and l m τ m (ksi) s m (mil in.) α τ f (ksi) s f (mil in.) p (ksi/mil in.) C3Da C3Db C3Dc G4Da G4Dc C3S C4S (1 in. = 25.4 mm; 1 ksi = 6.89 MPa) σ 1 (ksi) σ 1 /f u (%) l m /d b 24

25 Hinge Groove with NSM Rod 48 Figure 1. Test Specimen (1 in = mm) Load (lbs) Curve a - Failure by Splitting Curve b - Failure by Pull-out Curve c - Failure by Concrete Cracking Deflection (mil in.) Figure 2. Load vs. Mid-Span Deflection Curves (1 lbs = N; 1 in. = 25.4 mm) 25

26 Average Bond Stress (psi) G4D6a G4D12a G4D12b G4D12c G4D18a 0 0 0,5 1 1,5 2 2,5 3 3,5 4 Free-End Slip (mil in) Figure 3. Average Bond Stress vs. Free-End Slip for Specimens with GFRP Deformed Rods (1 psi = 6.89 kpa; 1 in. = 25.4 mm) Bond Breakers Test Zone Figure 4. Specimen C3D12b after Failure (Splitting of Epoxy + Concrete Cracking) 26

27 Test Zone Figure 5. Specimen C3D24b after Failure (Splitting of Epoxy +Concrete Cracking) σ b τ σ b + dσ b dx Figure 6. Free-body Diagram of Bar with Length dx Strain (µε µε) % 20% 30% 40% 50% 60% 70% 80% 90% 100% Location (in.) Figure 7. Strain vs. Location (C3D18a) (1 in. = 25.4 mm) Slip (mil in.) % 20% 30% 40% 50% 60% 70% 80% 90% 100% Location (in.) Figure 8. Slip vs. Location (C3D18a) (1 in. = 25.4 mm) 27

28 Bond Stress (ksi) 1,8 1,6 1,4 1,2 1 0,8 0,6 0,4 0,2 0 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Location (in.) Figure 9. Bond Stress vs Location (C3D18a) (1 ksi = 6.89 MPa; 1 in. = 25.4 mm) 2500 Strain (µε µε) % 20% 30% 40% Location (in.) Figure 10. Theoretical and Experimental Strain Distribution at Moderate Loads (C3D18a) (1 in. = 25.4 mm) 28

29 1,6 1,4 Bond Stress (ksi) 1,2 1 0,8 0,6 0,4 0,2 0 Experimental Best Fitting of Exp Slip (mil in.) Figure 11. Bond Stress vs. Slip (C3D18a) (1 ksi = 6.89 MPa; 1 in. = 25.4 mm) Load (kips) 8 6 P 1 4 Failure Load (Theor.) Failure Load (Exp.) 2 Load at Onset of Slip (Theor.) l m Bonded Length (N of db) 50 (a) Slip at Failure (mil in) Free-end Slip Loaded-end Slip Bonded Length (N of db) (b) Figure 12. Theoretical Bond Failure Load and Slip for Specimens C3Da (1 kip =4.448 kn; 1 in. = 25.4 mm) 29