Title. Author(s)Dai, Jianguo; Ueda, Tamon; Sato, Yasuhiko. CitationJournal of Composites for Construction, 9(1): Issue Date Doc URL.

Transcription

1 Title Development o the Nonlinear Bond Stress-Slip Model Simple Method Author(s)Dai, Jianguo; Ueda, Tamon; Sato, Yasuhiko CitationJournal o Composites or Construction, 9(1): Issue Date 2005 Doc URL Type article (author version) Note It is the author's manuscript version and not the pu File Inormation JCC9-1.pd Instructions or use Hokkaido University Collection o Scholarly and Aca

2 Manuscript number: CC/2003/022424, Journal o Composites or Construction, ASCE Development o the Nonlinear Bond Stress-Slip Model o Fiber Reinorced Plastics Sheet-concrete Interaces with a Simple Method By Jianguo Dai 1, Tamon Ueda 2 and Yasuhiko Sato 3 Abstract In this paper, a new analytical method or deining the nonlinear bond stress-slip models o Fiber Reinorced Plastics (FRP) sheet-concrete interaces through pullout bond test is proposed. With this method, it is not necessary to attach many strain gages on the FRP sheets or obtaining the strain distributions in FRP as well as the local bond stresses and slips. Instead, the local interacial bond stress-slip models can be simply derived rom the relationships between the pullout orces and loaded end slips. Based on a series o pullout tests, the bond stress-slip models o FRP sheet-concrete interaces, in which dierent FRP stiness, FRP materials (Carbon FRP, Aramid FRP, Glass FRP), and adhesives are used, have been derived. Only two parameters, the interacial racture energy and interacial ductility index, which can take into account the eects o all interacial components, are necessary in these models. Comparisons between analytical results and experimental ones show good accordance, indicating the reliability o the proposed method and the proposed bond stress-slip models. Keywords: Fiber Reinorced Plastics, Concrete, Adhesives, Interace shear, Bond Stress, Slip, Fracture Mechanics INTRODUCTION Bonding FRP sheets externally to strengthen the existing deicient reinorced concrete (RC) structures has become a popular technology in the past decade. With the rapid development o this new technology, many issues related to the structural perormances o FRP strengthened RC elements have been studied. Among them the study on the interacial bond between the externally bonded FRP sheets and concrete may be the most undamental one because it plays a key role on the composite perormances and the durability o RC structures ater being strengthened. In order 1 Post-doctoral Fellow, Division o Structural and Geotechnical Engineering, Hokkaido University, Sapporo, , Japan, daijg@eng.hokudai.ac.jp 2 Assoc. Pro., Division o Structural and Geotechnical Engineering, Hokkaido University, Sapporo, , Japan, ueda@eng.hokudai.ac.jp 3 Research Associate, Division o Structural and Geotechnical Engineering, Hokkaido University, Sapporo, , Japan, ysato@eng.hokudai.ac.jp 1

3 to evaluate the interacial bond mechanisms quantitatively and carry out numerical simulation or FRP sheets strengthened RC structures, deining an accurate bond stress-slip (τ~s) relationship has become a main task among the bond issues studied in the past. The conventional way o inding a τ~s relationship or FRP sheets bonded to concrete depends on the strain distributions o FRP and local bond stresses measured by many strain gages mounted on FRP sheets. However, it is diicult or us to apply this way or FRP sheet-concrete interaces because o the diiculty in arranging many gages in a short eective load transer length. The highly scatter nature o local τ~s relationships is another diiculty we ace. Particularly, local bending o FRP sheets whose bending stiness is small introduces signiicant bending strains in FRP and coarse aggregates in a concrete surace layer are causes o the scatter. Thereore, the objectives o this study are as ollows: 1. To develop a simple but rigorous analytical way to derive the local τ~s relationship based on the relationship between the pullout loads and slips at the loaded end in a pullout test rather than the observations on the strain distributions o FRP sheets and local bond stress behaviors. 2. To propose the nonlinear interacial τ~s relationships or FRP sheet-concrete interaces based on the experimental studies and the proposed method, in which the eects o all interacial materials including concrete, FRP, and adhesive layer can be taken into account. LITERATURE REVIEW A airly large amount o bond tests or the FRP sheet-concrete interaces under shear have been carried out in the past. Test methods include single lap pullout test method (Chajes et al. 1996, Täljsten et al. 1997, Bizindavyi et al. 1999), double lap pull-out bond tests (Nakaba et al. 2001, Yoshizawa et al. 2000, Sato et al. 2000, Brosens and Gemert 1997, Sato et al. 1997), shear bending tests (Leung 2001, Lorenzis et al. 2001), and bond tests or the critical strain energy release rate (Karbhari and Engineer 1996, Fukuzawa et al. 1997). Through those experimental studies, the bond mechanisms o FRP sheet-concrete interaces have been clariied in the ollowing aspects: (a) Bond strength: The bond strength o FRP sheet-concrete interaces has been studied most intensively. The FRP sheet-concrete interace ails mostly at a thin layer beneath the concrete surace. As a result, the concrete surace condition and strength are critical actors aecting the interacial bond strength. The concrete surace treatment methods have been studied experimentally (Chajes et al. 1996) and quantiied in details by using 3D proile method to evaluate the concrete surace roughness index (Mitsui et al. 2000). At present sandblasting is the most common 2

4 surace treating method that is being adopted in many researches and accepted in practical sites. Chajes et al. (1996), Horiguchi (1997) and Sato et al. (2000) studied the eects o concrete strength c and concluded that the average interace bond strengths, which are the ultimate pull-out orces divided by bond areas between FRP sheets and concrete, are linearly proportional to 1/2 c, 2/3 c, and 1/5 c respectively. Besides the concrete property, the FRP and adhesive properties aect the interace bond strength as well. In general, using higher FRP stiness (Brosens and Gemert 1997, Bizindavyi et al. 1999, Yoshizawa et al. 2000, Lorenzis et al. 2001, Nakaba et al. 2001) and soter adhesives (Nishida et al. 1999, Dai et al. 2002) can increase the average bond strength. Chen and Teng (2001) reviewed the current models or predicting the bond strength o FRP sheet-concrete interace with dierent bond lengths. They classiied all the models into three categories: empirical models based directly on the regression o test data, model based on racture mechanics, and models meant directly or design purpose, which generally make use o some simple assumptions. (b) Interacial racture energy: The interacial racture energy G, which is the area underneath the interacial bond stress-slip curve, is an important parameter or the bond characteristics. Based on dierent types o interacial bond stress-slip relationships, Yuan et al. (2001) proved that the maximum interacial bond orce can be expressed as a unction o the G and FRP stiness (elastic modulus thickness). Due to the clear physical meaning o the G, it is very useul to apply it in numerical analysis or deriving bond strength and anchorage length models as well as or clariying the debonding ailure mechanisms o FRP sheet-concrete interaces in more comprehensive ways (Yin and Wu 1999, Wu and Yin 2002). The G is usually expressed as a unction o concrete tensile strength (Brosens and Gemert 1999). However, the eects o adhesive layer on the G have been hardly reported. (c) Eective bond length: There exists an active bonding zone named as the eective bond length L e, along which most o the interacial load is transerred between FRP sheets and concrete. When the bond length o FRP sheet-concrete interaces exceeds the L e, the bond strength will not increase signiicantly any longer. With a ew exceptions (Maeda et al. 1997), it was reported that the eective bond length increases with the stiness o FRP sheets. Nevertheless, due to the dierent deinitions given by dierent researchers and the dierent materials used in their tests, the eective bond length was reported in a airly big range, such as 45 mm (Sato et al. 1997), 75 mm (Miller and Nanni 1999), 93 mm (Lorenzis et al. 2001), 100 mm (Ueda et al. 1999), 63.5~134.5 mm (Nakaba et al. 2001), and 275 mm (Brosens and Gemert 1997). Yuan et al. (2001) gave a theoretical expression or the eective bond length (deined as the bond length undertaking the 97% o whole interacial load) based on the assumed 3

5 interacial racture energy and interacial bilinear τ~s relationship. (d) Bond stress~slip (τ~s) relationship: As the most undamental constitutive laws that characterize the bond o FRP sheet-concrete interaces, several empirical τ~s relationships have been proposed as ollows: 1. Elasto-plastic model by Sato et al. (1997) and Lorenzis et al. (2001); 2. Bilinear model based on the interacial racture energy G (Yoshizawa et al. 2000). 3. Model based on Popovic s expression by Nakaba et al. (2001). 4. Shear sotening model by Sato et al. (2000). Above-mentioned models conigure the shapes o the τ~s relationships in dierent ways (see the comparison in Fig. 1). The concrete strength is assumed as a constant value 35MPa or all models shown in Fig. 1 or the comparing purpose. Although the elastic modulus o the adhesives in those studies or model developing are similar, it can be seen that airly big dierences exist among those models. Those dierences may be due to the dissimilar interacial material properties (e.g. FRP stiness) or the bonding skills (the deviations o concrete surace conditions or the adhesive s thickness) applied in dierent studies. Besides that, the airly big scattering among the experimentally observed bond stress-slip relationships at dierent interacial locations (to be shown in the next section) may be another actor, which aects the decisions on the shapes o the τ~s relationships and the calibration o the needed empirical parameters. The FRP sheet-concrete interace is composed o FRP sheets, adhesive layer, and concrete, each one o which aects the interacial mechanical properties. To consider these eects, calibrating many empirical parameters in an unknown τ~s relationship without consideration o their corresponding physical meanings is a very complex task. Up to now it can be said that the interacial bond mechanisms between FRP sheets and concrete have been clariied qualitatively in some extent. However, in order to carry out accurate quantitative simulation or the FRP sheet-concrete interaces, the way o determining a τ~s relationship should be urther improved. EXPERIMENTAL OUTLINE A single-lap pullout test setup (see Fig. 2) including: a thick steel basement ixed to strong loor through our prestressed high strength bolts, a steel box connected to the steel basement through two lines o steel bolts, concrete block with the size o mm, FRP sheets externally bonded to the concrete block, and connectors between the end o the FRP sheets and actuator, was applied in the study. In the concrete block, our plastic pipes 4

6 with diameter o 30 mm were pre-set vertically, so that the concrete block could be ixed on the steel box symmetrically and stably through our steel bolts. The connectors between the FRP sheets and the actuator contain two directional hinges, ensuring that the end o the FRP sheets can be rotated reely to avoid bending or torsion eect. The width o FRP sheets is 100 mm. In order to exert uniorm tensile orces to the FRP sheets, two steel plates were adhered to both sides o FRP sheets. Two additional bolts were used to enhance the bond between FRP sheets and steel plates to avoid the bond ailure in FRP sheet-steel plate interaces ahead o that in FRP sheet-concrete interaces. The attached area o FRP sheets to steel plates is mm. In order to avoid local damage o the concrete block, an un-bonded length (50 mm) was set by using vinylon tape to separate the concrete surace rom the FRP sheets. It is very important to keep the midline o the FRP sheets vertically, on which the center o actuator is located. To achieve this purpose, the location o the concrete block was careully adjusted on the steel box. During the pullout test procedures, the displacement control loading system was applied. LVDT transducers were set at both the loaded and ree ends o the bond area to obtain the relative slips between the FRP sheets and concrete. The load cell and the transducers were connected to the data logger then the load and slip signals were recorded simultaneously by a computer. Four types o adhesives (including one type o primer) and three types o FRP sheets were applied in the study. The mechanical properties o adhesives and FRP sheets and the inormation o manuacturers are shown in Table 1 and Table 2 respectively. Due to the obvious non-linearity when the adhesive becomes soter (see the tensile stress-strain relationships o adhesives in Fig. 3), the initial elastic modulus adhesives is deined as the average secant modulus while the strain lies between and (JIS 1995). Both the elasticity modulus and thickness o bond layer aect the interacial bond properties (Lee et al. 1999, Tripi et al. 2000, Dai et al. 2002). Thereore, the property o bond layer can be quantiied using its shear stiness (shear modulus/thickness) as ollows: G t a a G p Gad =, G t + G t p ad ad p G p E p =, (1 + γ ) 2 p G ad Ead = (1) (1 +γ ) 2 ad where: G a is the shear modulus o adhesive layer; t a is the thickness o adhesive layer; E P, E ad ; t p, t ad and γ p, γ ad are the elasticity modulus, thickness and Poisson ratio o primer and adhesive layer respectively. As indicated in Eq.1, the shear stiness o bond layer is that o a combined layer o primer and adhesive. To obtain the accurate geometrical inormation about the adhesive layer, the FRP sheets attached with ailed concrete 5

7 were processed ater the pullout tests. Then the thickness o every bonding layer (primer and adhesive layer) was measured under a microscope (see Fig. 4). Ater that the shear stiness o adhesives could be calculated through Eq.1 (see the values in Table 3). Ready-mixed concrete with the tested compressive strength o 35 MPa was prepared in order to keep a same strength or all specimens. Moreover, in order to observe the whole peeling-o procedures, the bond length o 330 mm was applied. Wet-lay-up bonding system was applied in the study. However, to avoid the decreasing o the tensile strength o FRP sheets induced by the resin matrix with low elasticity modulus (e.g. CN-100), the resins used in FRP layers and the adhesive layers were dierent (see Fig. 4 ). Adhesive FR-E3P, which is commercially used as the resin matrix and the bonding adhesive o carbon iber sheets, was applied as the resin matrix o FRP in all specimens. The primer FP-NS was used in the bonding procedures o all specimens. Ater the adhesive bond layer was cured or 24 hours, resin FR-E3P was used to orm FRP layers as shown in Fig. 4. The details o the specimens can be ound in Table 3. ANALYSIS ON TEST RESULTS Description o the Methodology Generally, in order to obtain the local bond stress-slip relationships o FRP sheet-concrete interaces rom the direct pullout bond test, many strain gages should be attached with a small interval (10 mm~20 mm) on the suraces o FRP sheets (JCI TC ). As a result, the strain distribution o FRP sheets along the interaces corresponding to every step load can be obtained. Fig. 5 shows the sketch o a single lap pullout bond test setup. Supposed that the interval o gages is a constant value Δx, the local bond stress can be obtained using the ollowing expression: E t i i i = ( ε ε 1 τ ) (2) Δx where τ i is the average interacial bond stress in the section i; ε i and ε i-1 are the strain values o the i th and i-1 th gages arranged on a FRP sheets respectively; E and t are the elastic modulus and thickness o the FRP sheets respectively. The local slip is caused by the strain dierence between FRP sheets and concrete. The strain o concrete can be neglected and the ree end slip can be regarded approximately as zero in the case o using a long bond length. So the local slip can be expressed as: 6

8 s i i 1 Δx = ( ε ε j + ε i ) 2 j= 1 (3) where s i is the local slip between FRP sheets and concrete at the section i; ε 0 is the strain o FRP sheets at the ree end o bond area. ε j (j=1,i) is the strain value o the j th gage arranged on the FRP sheets. Fig. 6 is a paradigm o obtained strain distributions o specimen CR1L1 (with adhesive FR-E3P and one layer o FRP sheet) in the authors previous study (Dai et al. 2002). Upon Eq.2 and Eq.3, the local τ~s relationships at dierent locations rom the loaded point in a pullout test can be derived as shown in Fig. 7. Obviously, airly big irregular dierences among those τ~s relationships are observed at dierent interacial locations. The similar experimental observations can be ound in other literatures (Yoshizawa et al. 2000, Nakaba et al. 2001, Sato et al. 2000). This airly big variation probably is the main reason why dierent shapes o bond stress-slip relationships were proposed or why researchers preer a simpliied bilinear bond stress-slip model even though numerous o pullout bond tests or FRP sheets-concrete interaces have indicated that more reasonable conigurations are needed. All the actors such as the distribution o ine and coarse aggregates along the concrete surace, the concrete volume attached to FRP sheets ater the initial damage o concrete, and the local bending o FRP sheets or the local mixed-mode ailure o concrete can contribute to the inal scattering. It is not convincing to pick up one o these local τ~s relationships to represent the overall one. In order to clariy the local interacial bond mechanisms exactly, simulating the bonding among coarse aggregates, mortars, adhesives and FRP sheets at a microscopic level may be a more precise way. However, it is much more diicult to get the microscopic-level constitutive model o the interace. The authors (Dai and Ueda 2003) proposed a back calculation method, which tried to minimize the dierences between the experimentally observed strain distributions and the analytical ones, to calibrate the unknown parameters needed or an assumed bond-stress slip curve optimally. Nevertheless, the analytical results on the unknown parameters rely much on the selected shape o the τ~s relationships. In the ollowing part, an improved method on how to obtain interacial τ~s relationships without the necessity to record the strain distributions o FRP sheets is to be discussed. At any location o an FRP sheet-concrete bond interace under the boundary condition o zero ree 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 o FRP sheets and interacial slip (Shima et al. 1987). The latter can be expressed as ollows: 7

9 ε = (s) (4) where ε is the strain o FRP sheets at any location; s is the corresponding slip at that location. A irst order dierential calculus o ε to x yields the ollowing equation: dε d ( s) ds d ( s) d ( s) = = ε = ( s) dx ds dx ds ds (5) Thereore, or FRP sheet-concrete interaces, the interacial bond stress can be expressed as: dε d ( s) τ = E t = E t ( s) (6) dx ds where E t is the stiness o FRP sheets (elastic modulus thickness). It can be seen rom Eq.4 to Eq.6 that the bond stress-slip relationship can be determined i the relationship between local strain o FRP sheets and local slip is deined. During the pullout test, the pullout orces and the slips at the loaded end can be measured accurately through load cell and displacement transducer. As a result, the relationship between the strains o FRP sheets and the slips at the loaded end, in other word, the unction o (s) can be obtained directly rom the simple pullout tests. Fig. 8.a to Fig. 8.e are the experimentally observed relationships between the strains o FRP sheets and the interacial slips at the loaded ends o FRP sheet-concrete interaces, which include cases o dierent FRP stinesses, dierent adhesive types and dierent types o FRP materials. It is ound that the exponential expression (see Eq.7) can it the experimental results very well (the values o correlative actors R 2 between the strains in FRP sheets and the slips at loaded ends lie between and or all specimens as shown in Table 3). ε = ( s) = A(1 exp( Bs)) (7) where A and B are experimental parameters (the values or each specimen are given in Table 3). Thereore: d ( s) / ds = AB exp( Bs) (8) Once Eq.7 and Eq.8 are substituted into Eq.6, the bond stress-slip relationship can be obtained as ollows: 2 τ = A BE t exp( Bs)(1 exp( Bs)) (9) The interacial racture energy G is deined as: 8

10 0 G = τ ds (10) By substituting Eq.9 into Eq.10, the ollowing equations can be obtained: G 1 2 = A E t (11) 2 Then the ollowing expression or A is obtained: 2G A = (12) E t For FRP sheets bonded to concrete under pullout load, the theoretical maximum interacial pullout orce can be expressed as ollows: Pmax = b E t ε max = b E t lim A(1 exp( Bs)) = b E t A (13) s where b is the bond width o FRP sheets with concrete; and ε max is the maximum strain o FRP sheets corresponding to the maximum pullout orce. The comparisons between the calculated maximum pullout orces based on the regressed A (see Eq.13) and the experimental ones are shown in Fig. 9. It can be seen that good agreement can be reached. The agreement implies that the theoretical maximum interacial pullout orce predicted based on the assumption o zero end slip boundary condition can be reached through using the bond length o 330mm in the experiment With the substitution o Eq.12, Eq.13 can become: P = b 2E t G (14) max b E t A = Based on energy method or orce equilibrium method, Eq.14 was derived by many researchers (Täljsten et al. 1997, Yuan et al. 2001) and now is applied widely in predicting the ultimate bond orces o FRP sheet-concrete interaces. And also, through experimental study, the authors ound that Eq.14 is applicable or all types o FRP materials regardless o the dierences in their elastic modulus (Dai et al. 2002, Dai and Ueda 2003). The shear stress lows can spread to the concrete in the vicinity o both sides o FRP sheets i the FRP sheets are attached to concrete whose width is wider than theirs. That makes the eective interacial contact areas wider than the real ones. The authors observed the eects o bond width o FRP sheets (rom 1 cm to 20 cm) on the average bond strength in the previous studies (Sato et al. 2000). The experimentally obtained bond orce per unit width o 9

11 FRP sheets (P max /b ) is generally high when the width o FRP sheets used in the tests is narrow. When the bond width exceeds 10 cm, the value o P max /b becomes almost constant. An additional width 2Δb (Δb is taken as 3.7 mm) can be added to the original bond width b or calculating the interacial bond strength and quantiying the bond width s eects ( Sato et al., 2000). Here a same 2Δb is introduced into Eq.14. Through that the back-calculated G rom obtained P max will not depend on the FRP sheet width used in the test. Thereore, Eq.14 can be modiied as ollows: P = ( b + 2Δb ) 2E t G (15) max From Eq.15 it can be known that the interacial load carrying capacity is determined by the interacial racture energy and FRP stiness. Increasing both the racture energy and FRP stiness (by increasing either the amount or elastic modulus o FRP materials) can improve the ultimate interacial load carrying capacity. Similarly, the usable strain (strength) o FRP sheets is determined by the interacial racture energy and the FRP stiness as well (see Eq.12). High interacial racture energy can increase the usable strength or strength eiciency o FRP sheets; however, high FRP stiness cannot. Thereore, in order to utilize the FRP materials more eiciently in consideration o their decreasing but still higher costs, besides ensuring the concrete surace quality, more eects should be put on to ind optimum adhesive layer to improve the interacial racture energy. Discussion on the Interacial Fracture Energy and the Bond Stress-slip Relationships With Eq.9 and Eq.12, the interacial τ~s relationship can be rewritten as: τ = 2BG (exp( Bs) exp( 2Bs)) (16) in which only two parameters, the interacial racture energy G and another interacial material constant B are needed or deining the bond stress-slip relationship. Let, 2 dτ / ds = 2B G (exp( Bs) 2 exp( 2Bs)) = 0 (17) The slip s max corresponding to the maximum bond stress τ max, at which dτ/ds=0, can be determined as ollows: s = ln 2 / B / B (18) max = By substituting Eq.18 into Eq.16, the maximum bond stress τ max can be obtained as well: τ max = 0.5BG (19) For every specimen in the present study, the material constant B and the interacial racture energy G can be 10

12 obtained according to the processes proposed in the previous section (see the results in Table 3). Then the values o τ max and s max are calculated and shown in Table 3. For the normal adhesive (FRP-E3P), Nakaba et al. (2001) observed experimentally that the values o s max lie between and mm, with which the analytical results (0.053~0.077 mm) based on the present method show good agreement. Based on the above-mentioned process, all the ound bond stress-slip relationships derived rom pullout tests are shown in Fig. 10. When the FRP racture ailure happens, the obtained τ~s relationships are excluded because the peeling o process is interrupted and the interacial racture energy cannot be calculated correctly. To get a uniied τ~s model in consideration o the eects o all interacial materials, the ollowing paragraphs give results o regression analysis or the two important parameters G and B based on experimental results. The interacial racture energy G is aected by the properties o concrete, adhesives and the FRP stiness. It has been mentioned that, in the case o long bond lengths, G can be calculated based on either the value o A obtained rom the regression analysis o the FRP sheet strain-slip curves at loaded ends (see Eq.11) or directly rom the ultimate pullout orces (see Eq.14). Thereore, the authors collected more experimental data o the ultimate pullout orces published by other researchers (Nakaba et al. 2001, Yoshizawa et al. 2000) to evaluate the eects o concrete strength and FRP stiness on G based on more experimental databases. Only those data with bond lengths exceeding 300mm has been selected. Through Eq.15 the eects o bond width on the G can be eliminated. Fig. 11.a, Fig. 11.b and Fig. 11.c show the eects o concrete strength, FRP stiness and adhesive properties on the G respectively. Since the other researchers did not study the eects o adhesives, Fig. 11.c only shows the test results o the present study. It can be ound that the shear stiness o adhesive layer aects the interacial racture energy most (see Fig. 11.c). The eect o the concrete strength is much less than that o the adhesive (see Fig. 11.a) but slightly greater than that o the FRP stiness (see Fig. 11.b). The lower shear stiness adhesives can improve the interacial racture energy signiicantly due to their good toughness (Dai et al. 2002,Dai and Ueda 2003). Through regressing, the expression or the interacial racture energy can be obtained as ollows: G ( Ga / ta) c ( E t = ) (20) The values o another interacial parameter B are obtained rom the regression analysis o the FRP sheet strain-slip curves at the loaded end o each specimen in the present study. The eects o FRP stiness and adhesives on B are shown in Fig. 12.a and Fig. 12.b respectively. It can be seen that B increases insigniicantly with the FRP stiness (see Fig. 12.a) whereas increases remarkably with the shear stiness o adhesive layer (see Fig. 12.b). Through a 11

13 similar regressing way, the expression or B can be obtained as ollows: ( E t ) ( Ga / ta B = ) (21) Thereore, the τ~s relationships o FRP sheet-concrete interaces with dierent properties o FRP, adhesives and concrete strength can be determined through the two calibrated parameters G (Eq.20) and B (Eq.21). Fig. 13.a shows the eects o FRP stiness on the τ~s relationships. It can be seen that both the initial stiness o the τ~s relationships and the maximum bond stresses increase slightly with the increasing o FRP stiness. Similar eects o FRP stiness on the maximum bond stress were included in the models proposed by Sato et al. (2000) and Lorenzis et al. (2001) in dierent extent. Tripi et al. (2000) also ound that relative displacements between the FRP sheets and concrete are slightly aected by the elastic modulus o the sheets in their moiré intererometric analysis. The eects o FRP stiness on the interacial stiness and maximum bond stress may be caused by the dierent strain condition in the thin concrete layer next to the adhesives. In the case o using same adhesives, higher FRP stiness brings lower strain level in the concrete. The dependency o G and B on the FRP stiness exists but is rather small (see Fig. 11.b and Fig. 12.a). Thereore, in the case o using common adhesives such as FR-E3P, the expressions G = c and B=10.4mm -1 can be obtained or the τ~s relationship (Eq.16) by averaging all experimental values without consideration o the FRP stiness eects and assuming that the shear stiness o the adhesive is the same (see Fig. 10.a). Fig. 13.b gives a group o τ~s relationships with dierent shear stiness o adhesives but the same FRP stiness (50.6 kn/mm) and concrete strength (35MPa). The comparisons between the experimental τ~s relationships and predicted ones in cases o using adhesives other than FR-E3P are shown in Fig. 10.b and Fig. 10.c. It is obvious that the maximum interacial bond stress increases with the shear stiness o adhesives. When the FRP stiness is same, this increase is caused by high strain gradients in FRP sheets in the case o using high modulus adhesives (Nishida et al. 1999, Dai et al. 2002). In the present model, the maximum bond stress decreases with the shear stiness o adhesive due to the signiicant decreasing B, although the interacial racture energy G can increase with the decreasing o adhesives shear stiness (see Eq.19). In act, the value B can be regarded as an index o ductility o the τ~s relationships, which is mainly aected by the adhesive properties. Better ductility means slower sotening ater the peak bond stress. Smaller B means lower initial interacial stiness but better interacial ductility and vice versa. In other words, it is diicult to obtain higher 12

14 interacial stiness and ductility simultaneously. This shortcoming is caused by the inherent properties o adhesives. However, it gives us a possibility to optimize the interace design according to the desirable structural perormances. Fig. 14 gives comparisons o the ultimate interacial loads predicted by the present proposed τ~s model and the experimental data selected rom the pullout tests o FRP sheet-concrete interaces with bond lengths exceeding 30cm (Yoshizawa et al. 2000, Nakaba et al and present study). The reasonable scattering o all data around the line o P ana. /P exp. =1.0 indicates the good accuracy o the present models on predicting the bond capacity o FRP sheet-concrete interaces. As discussed above, the ultimate interacial load is only related to FRP stiness and the G (the area under the τ~s relationship) regardless o the shape o the τ~s relationship. Thereore, it is a good choice to use G, which can be back-calculated rom many published ultimate interacial loads, as a control parameter when coniguring any unknown τ~s relationship. The use o G at least can ensure the accuracy o predicting the ultimate interace bond capacity in the case o long bond length. However, the issues o predicting the initial interacial peeling, evaluating the interacial load-deormation behaviors or determining the eective anchorage length depend on not only the use o G, but also the accurate coniguration o τ~s relationship. Based on the present and other researchers τ~s relationships as shown in Fig. 1, Fig. 15 gives an example o comparing the predicted strain-slip relationships at the loaded end o a FRP sheet-concrete interace, o which the FRP stiness, concrete strength and adhesive stiness are 50.6 kn/mm, 35 MPa and 1.14 GPa/mm (FR-E3P) respectively. It can be seen that the present model and Nakaba s model give good prediction on the whole period o pullout test (beore and ater initial peeling). Nakaba s model gives slight underestimation on the initial interacial stiness. Yoshizawa s simpliied bilinear model gives a good prediction on the initial interacial stiness but shows a big deviation when the strain o FRP becomes higher. Sato s model gives a good prediction on the maximum strain but shows a big deviation during initial ascending period. The assumption o elasto-plastic bilinear τ~s relationships (Sato (Yuichi) and Lorenzis) shows comparatively less accuracy. CONCLUSIONS: Based on the experimental and analytical studies, the ollowing conclusions can be drawn up: 1. A simple method to determine the local bond stress-slip relationships o FRP sheet-concrete interaces is developed. With this method, it is not necessary to put many gages on the surace o sheets as conventional ways applied in previous studies or recommended in the present bond test speciications to 13

15 obtain the local bond stress-slip relationships. Instead, they can be simply derived rom the pullout orce ~ loaded end slip curves, which can be measured accurately during the pullout bond tests. 2. Based on the proposed method and the experimental studies, the bond stress-slip relationships or FRP sheet-concrete interaces are proposed. Only two parameters, which are the interacial racture energy G and another constant called as interacial ductility index B are needed in the models. The two parameters, G and B aect the ultimate interacial load carrying capacity and the coniguration o the bond stress-slip relationship respectively. With these two parameters, the eects o all interacial materials can be taken into account. 3. Experimental results show that the interacial racture energy is hardly aected by FRP stiness, but aected by the mechanical property o adhesives most and then by the concrete strength. With the decreasing o the shear stiness o adhesive, the interacial racture energy and the interacial ductility can be improved although the maximum interacial bond stress decreases. That leads to the improvement o the interacial load transer capacity. The FRP stiness has a slight eect on the bond stress-slip relationships. The maximum bond stress increases and the interacial ductility decreases slightly with the increasing o the FRP stiness. However, in comparison with the eects o adhesives and concrete, the eects o FRP stiness on the bond stress-slip relationships are insigniicant. RECOMMENDATION FOR FUTURE STUDY Concrete properties aect the interacial bond behaviors by both its surace condition and strength. The dependency o interacial ductility actor B on the concrete strength needs to be observed in uture study. In addition, concrete surace treatment in laboratory may be dierent rom that in the ield. The problem on how the concrete surace condition aects the interacial parameters o G and B needs to be solved quantitatively based on more solid databases. ACKNOWLEDGEMENTS The authors would like to express their sincere thanks to Mr. Makoto Saito and Mr. Akira Kobayashi o Nippon Steel Composite Co. Ltd. or their kind oering o experimental materials. 14

16 REFERENCES Bizindavyi, L. and Neale, K. W. (1999). Transer Length and Bond Strength or Composites Bonded to Concrete. Journal o Composites or Construction, ASCE, 3(4), Brosens, K. and Gemert, D. Van. (1997). Anchorage Stresses between Concrete and Carbon Fiber Reinorced Laminates. Non-Metallic (FRP) Reinorcement or Concrete Structures, Proceedings o Third International Symposium, Vol.1, Brosens, K. and Gemert, D. Van. (1999). Anchorage Design or Externally Bonded Carbon Fiber Reinorced Polymer Laminates. ACI, SP , Chajes, M. J., Finch, William. W., Januszka, T. F. and Thomson, T. A. (1996). Bond and Force Transer o Composite Material Plates Bonded to concrete. ACI Structural Journal, 93(2), Chen, J.F. and Teng, J.G. (2001). Anchorage Strength Models or FRP and Steel Plates Bonded to Concrete. Journal o Structural Engineering, Vol. 127, No.7, Dai, J.G., Sato, Y. and Ueda, T. (2002). Improving the Load Transer and Eective Bond Length or FRP Composites Bonded to Concrete. Proceedings o the Japan Concrete Institute, Vol.24, Dai, J.G. and Ueda, T. (2003). Local Bond Stress Slip Relations or FRP Composites-concrete Interaces. Proceedings o FRPRCS-6, Edited by Tan, K. H., Vol. l, Fukuzawa, K., Numao, T., Wu, Z., Yoshizawa, H., and Mitsui, M. (1997). Critical Strain Energy Release Rate o Interace Debonding Between Carbon Fiber Sheet and Mortar. Non-Metallic (FRP) Reinorcement or Concrete Structures, Proceedings o Third International Symposium, Vol.1, Horiguchi, T. (1997). Eect o Test Methods and Quality o Concrete on bond strength o CFRP Sheet. Non-Metallic (FRP) Reinorcement or Concrete Structures, Proceedings o Third International Symposium, Vol.1, JCI TC 952 on Continuous Fiber Reinorced Concrete. (1998). Technical Report on Continuous Fiber Reinorced Concrete. Japan Concrete Institute (JCI). JIS K7113 (1995). Testing Method or Tensile Properties o Plastics. Karbhari, V.M. and Engineer, M. (1996). Investigation o Bond between Concrete and Composites: Use o a Peeling Test. Journal o Reinorced Plastics and Composites, Vol.15,

17 Lee, Y. J., Boothby T. E., Bakis, C.E., and Nanni, A. (1999). Slip Modulus o FRP Sheets Bonded to Concrete. Journal o Composites or Construction, ASCE, 3(4), Leung, C. K. Y. (2001). Delamination Failure in Concrete Beams Retroitted with a Bonded Plate. Journal o Materials in Civil Engineering, ASCE, 13(2), Lorenzis, L. De., Miller, B., and Nanni, A. (2001). Bond o Fiber-Reinorced Polymer Laminates to Concrete. ACI Material Journal, 98(3), Maeda, T., Asano, Y., Sato, Y., Ueda, T., and Kakuta, Y. (1997). A Study on Bond Mechanism o Carbon Fiber Sheet. Non-Metallic (FRP) Reinorcement or Concrete Structures, Proceedings o Third International Symposium, Vol.1, Mitsui, M., Fukuzawa, K., Numao, T. and Fuda, I. (2000). Relations between Surace Roughness Indexes and Bond strength between CFRP sheets and Concrete. Journal o Society Material Science. Japan, 49(6), (In Japanese). Miller, B. and Nanni, A. (1999). Bond between CFRP Sheets and Concrete. Proc. o ASCE 5 th Materials Congress, Edited by L.C. Band, Cincinnati, OH, May 10-12, Nakaba, K., Kanakubo, T., Furuta, T., and Yoshizawa, H. (2001). Bond Behavior between Fiber-Reinorced Polymer Laminates and Concrete. ACI Structural Journal, 98(3), Nishida, H., Simomura, T., Kamiharako, A., and Maruyama, K. (1999). Bond Behaviors between the FRP Sheets and concrete. Proceedings o JCI, 21(3), (in Japanese). Sato, Y. (Yuichi), Kimura, K., and Kobatake, Y. (1997). Bond Behaviors between CFRP Sheet and Concrete. Journal o Structural Construction Engineering, AIJ, No.500, (in Japanese). Sato, Y., Asano, Y., and Ueda, T. (2000). Fundamental Study on Bond Mechanism o Carbon Fiber Sheet. Concrete Library International, JSCE, No.37, June 2001, Shima, H., Chou, L., and Okamura, H. (1987). Bond stress-slip-strain relationship o deormed bars embedded in massive concrete. Concrete Library International, JSCE, No.10, Täljsten, B. (1996). Strengthening o Concrete Prisms Using the Plate-bonding Technique. International Journal o Fracture, 82, Täljsten, B. (1997). Deining anchor lengths o steel and CFRP plates bonded to concrete. International Journal o Adhesion and Adhesives, 17(4),

18 Tripi, J. M., Bakis, C. E., Boothby, T. E., and Nanni, A. (2000). Deormation in Concrete with Externally CFRP Sheet Reinorcement. Journal o Composites or Construction, Vol. 4, No.2, Ueda, T., Sato, Y., and Asano, Y. (1999). Experimental Study on Bond strength o Continuous Carbon Fiber Sheet. ACI, SP , Wu, Z. and Yin, J. (2002). Numerical Analysis on Interacial Fracture Mechanism o Externally FRP-Strengthened Structural Members. Journal o Materials, Conc. Struct. Pavements, JSCE, No.704/V-55, Yoshizawa, H., Wu, Z., Yuan, H., and Kanakubo, T. (2000). Study on FRP-Concrete Interace Bond Perormance. Transactions o Japanese Society o Civil Engineering, No.662/V-49, Yin, J. and Wu, Z. (1999). Interace Crack Propagation in Fiber Reinorced Polymer-strengthened Concrete Structures Using Nonlinear Fracture Mechanics. ACI, SP , Yuan, H., Wu, Z., and Yoshizawa, H. (2001). Theoretical Solutions on Interacial Stress Transer o Externally Bonded Steel/Composite Plates. J. Structural. Mech.Earthquake Eng. JSCE, 18(1),

19 FIGURES: Note: the igures at inal size with desired reduction are provided in another document Fig. 1 (17.78cm wide, suggest 50% reduction) τ(mpa) E t = 25.3kN/mm Lorenzis et al.(2001) Nakaba et al.(2001) Yoshizawa et al.(2000) Sato et al.(2000) E t rom 25.3 to 75.9kN /m m Sato(Yuchi) et al.(1997) E t =75.9kN/mm E t = 50.6kN/mm S(mm) 18

20 Fig. 2 (17.78cm wide, suggest 50% reduction) Load cell Hinges Steel plates FRP sheets Concrete block 19

21 Fig. 3 (17.78cm wide, suggest 50% reduction) σ(mpa) FR-E3P SX-325 CN-100 FP-NS ε 20

22 Fig. 4 (17.78cm wide, suggest 50% reduction) Fiber layer Resin matrix 0.5mm Adhesive layer Bond layer Primer layer Interlocking layer Attached concrete 21

23 Fig. 5 (17.78cm wide, suggest 50% reduction) x ε 0 ε 1 ε 2 ε i Δ x P concrete P L 22

24 Fig. 6 (17.78 wide, suggest 50% reduction) Strain(10-6 ε) kN 6.0kN 14.4kN 19.8kN 21.0kN 23.4kN 21.0kN 24.6kN Location rom loaded end(mm) 23

25 Fig. 7 (17.78cm wide, suggest 50% reduction) τ (MPa) cm rom the loaded end 1.5cm 2.5cm 3.5cm 4.5cm 5.5cm 6.5cm 7.5cm 8.5cm 9.5cm 10.5cm 11.5cm s (mm) 24

26 Fig. 8.a ((17.78cm wide, suggest reduction to 33%) Strain(ε) FRP racture CR1L1-1 exp. CR1L1-1 reg CR1L1-2 exp. CR1L1-2 reg CR1L1-3 exp. CR1L1-3 reg. CR2L1 exp. CR2L1 reg CR3L1 exp Slip(mm) 25

27 Fig. 8.b (17.78cm wide, suggest reduction to 33%) Strain(ε) CR1L2-1 exp. CR1L2-1 reg CR1L2-2 exp. CR1L2-2 reg CR1L2-3 exp. CR1L2-3 reg CR2L2 exp. CR2L2 reg. CR3L2 exp. CR3L2 reg Slip(mm) 26

28 Fig. 8.c ((17.78cm wide, suggest reduction to 33%) Strain(ε) CR1L3-1 exp. CR1L3-2 exp. CR1L3-3 exp. CR2L3 exp. CR3L3 exp. CR1L3-1 reg. CR1L3-2 reg. CR1L3-3 reg. CR2L3 reg. CR3L3 reg Slip(mm) 27

29 Fig. 8.d(17.78cm wide, suggest reduction to 33%) Strain(ε) FRP racture GR1L1 exp. GR1L3 exp. GR1L5 exp. GR2L3 exp. GR3L3 exp. GR1L3 reg. GR1L5 reg. GR2L3 reg Slip(mm) 28

30 Fig. 8.e(17.78cm wide, suggest reduction to 33%) Strain(ε) AR1L1 exp. AR1L1 reg AR1L2 exp. AR1L2 reg AR1L3 exp. AR1L3 reg. AR2L3 exp. AR2L3 reg AR3L3 exp. AR3L3 reg Slip(mm) 29

31 Fig. 9(17.78cm wide, suggest reduction to 50%) (kn) P max ana P ana. max /Pexp. max = P max exp. (kn) 30

32 Fig. 10.a (17.78cm wide, suggest reduction to 33%) τ(mpa) 8 Average All ounded curves rom Exp. G a /t a =1.05GPa/mm(FR-E3P) 6 G =1.19N/m, B=10.4mm s(mm) 31

33 Fig. 10.b (17.78cm wide, suggest reduction to 33%) τ(mpa) 8 6 All ound curves rom exp. Present model G a /t a =0.49GPa/mm(SX-325) G =1.54N/mm,B=5.77mm s(mm) 32

34 Fig. 10.c (17.78cm wide, suggest reduction to 33%) τ(mpa) All ound curves through exp. Present model G a /t a =0.20GPa/mm(CN-100) G =2.10N/mm, B=2.74mm s(mm) 33

35 Fig. 11.a (17.78cm wide, suggest reduction to 33%) G (N/mm) Yoshizawa et al.(2000) 0.4 Present study Nakaba et al.(2001) 0.2 regressing line G =0.422 ' c c ' (MPa) 34

36 Fig. 11.b (17.78cm wide, suggest reduction to 33%) G / ' c Yoshizawa et al.(2000) Present Nakaba et al.(2001) regressing line G =0.388 ' c (E t ) E t (kn/mm) 35

37 Fig. 11.c (17.78cm wide, suggest reduction to 33%) G / ' c /(E t ) Present exp. Regressing line G =0.446(G a /t a ) ' c (E t ) G a /t a (GPa/mm) 36

38 Fig. 12.a (17.78cm wide, suggest reduction to 33%) B(mm -1 ) Exp. regressing line B=6.947(E t ) R 2 = E t (kn/mm) 37

39 Fig. 12.b (17.78cm wide, suggest reduction to 33%) B/(E t ) (mm -1 ) Exp. Regressing line B=6.846(E t ) (G a /t a ) R 2 = G a /t a (GPa/mm) 38

40 Fig. 13.a (17.78cm wide, suggest reduction to 33%) τ(mpa) E t =25.3kN/mm E t =50.6kN/mm E t =75.9kN/mm G a /t a =1.14GPa/mm ' c =35MPa s(mm) 39

41 Fig. 13.b (17.78cm wide, suggest reduction to 33%) τ (MPa) G a /t a =1.14GPa/mm G a /t a =0.49GPa/mm G a /t a =0.20GPa/mm E t =50.6kN/mm, ' =35MPa c s(mm) 40

42 Fig.14 ((17.78cm wide, suggest reduction to 50%) P ana. (kn) max Nakaba et al. (2001) Yoshizawa et al. (2000) Present P ana. exp. max /P max =1.0 Average=1.0 C.O.V= P exp. max (kn ) 41

43 Fig. 15 (17.78cm wide, suggest reduction to 50%) Strain(ε) Exp. present model Yoshizawa model Nakaba model. Sato(Yuichi) model Lorenzis model Sato model Slip(m m ) 42

44 Figure Captions: Fig. 1 Previous bond stress-slip relationships o FRP sheet-concrete interaces Fig. 2 Pullout test setup Fig. 3 Tensile stress-strain relations o adhesives Fig. 4 Microscopic observation o FRP sheets ater pullout test (CR3L1) Fig. 5 Single lap pullout test Fig. 6 Strain distribution o FRP sheets along bond interace (CR1L1) Fig. 7 Calculated local bond stress-slip relationships at dierent locations rom loaded end (CR1L1) Fig. 8 Experimental and regressed strain-slip curves at loaded ends (a) CFRP, Stiness: 25.3 kn/mm (b) CFRP, Stiness: 50.6 kn/mm (c) CFRP, Stiness: 75.9 kn/mm (d) AFRP, Stiness: 18.6~73.6 kn/mm (e) GFRP, Stiness: 8.7~43.7 kn/mm Fig. 9 Comparison between analytical and experimental maximum pullout loads Fig. 10 Experimentally ound bond stress-slip relationships (a) Adhesive FR-E3P (b) Adhesive SX-325 (c) Adhesive CN-100 Fig. 11 Eects o various parameters on interacial racture energy (a) Concrete strength (b) FRP stiness (c) Adhesive Fig. 12 Eects o various parameters on B (a) FRP stiness (b) Adhesive Fig. 13 Proposed bond stress-slip relationships (a) with dierent FRP stiness 43

45 (b) with dierent adhesives Fig. 14 Comparisons o predicted and experimental ultimate loads o interaces Fig. 15 Predicted strain-slip relationships at loading point by dierent models 44

46 Tables: Table 1 Mechanical Properties o FRP Materials Fiber Type ρ t E t ε u (g/m 3 ) (MPa) (GPa) (mm) (%) Carbon FTS-C Aramid AT Glass FTS-GE Note: ρ = iber density; t = tensile strength; E = elastic modulus; t = thickness; ε u = iber racturing strain; FTS-C1-20 and FTS-GE-30 sheets were oered by Nippon Steel Composite Co. Ltd; AT-90 was oered by Nippon Aramid Co. Ltd. 45

47 Table 2 Material Properties o Adhesives Types o Density Resins/harden Elastic Poisson s Tensile Flexural Gel Viscosity Setting time adhesives (g/cm 3 ) er by weight modulus ratio strength strength time (mpa s/25 C) (h/20 C) (GPa) (MPa) (MPa) (min) CN : SX : FR-E3P : FP-NS (Primer) : >20 < Note: The tests or adhesives were carried out by Sho-bond Co. Ltd., Japan. FR-E3P and FP-NS were oered by Nippon Steel Composite Co. Ltd; SX-325 was oered by Nippon Toho Earth-Tech. Co. Ltd; and CN-100 was oered by Nippon Toho Resin Chemical Co. Ltd. 46

48 Table 3 Details o Specimens and Pullout Bond Test Results Specimen codes G a /t a (GPa/mm) E t (kn/mm) A (ε) B mm -1 G (N/mm) R 2 τ max (MPa) s max (mm) P max kn(exp.) P max kn(ana.) P max (Ana./Exp.) Failure mode* CR1L CF CR1L CF CR1L CF CR1L CF CR1L CF CR1L CF CR1L CF CR1L CF CR1L CF CR1L CF AR1L CF AR1L CF AR1L CF GR1L NA NA NA NA FF GR1L CF GR1L CF CR2L CF CR2L CF CR2L CF AR2L CF GR2L CF CR3L NA NA NA NA FF CR3L CF CR3L CF AR3L CF GR3L NA NA NA NA FF CR1L1 The cccr L plies o FRP sheets Adhesive type; 1,2 and 3 means FR-E3P, SX-325 and CN-100 respectively C: CFRP; A: AFRP; G:GFRP 2: CF-concrete ailure; 3: FF- FRP racture; 47