Title. Author(s)Ueda, Tamon; Dai, Jianguo. CitationProgress in Structural Engineering and Materials, 7( Issue Date Doc URL. Rights.

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1 Title Interace bond between FRP sheets and concrete subst behaviour Author(s)Ueda, Tamon; Dai, Jianguo CitationProgress in Structural Engineering and Materials, 7( Issue Date Doc URL Rights Copyright 2005 John Wiley & Sons, Inc., PROGRESS I Vol.7-1, p Type article (author version) File Inormation PSEM7-1.pd Instructions or use Hokkaido University Collection o Scholarly and Aca

2 Interace bond between FRP sheets and concrete substrates properties, numerical modeling and roles in member behaviors Tamon Ueda (1) and Jianguo Dai (2) (1) Proessor, Division o Structural and Geotechnical Engineering, Hokkaido University Sapporo, Japan (2) Post-doctoral Fellow, Division o Structural and Geotechnical Engineering, Hokkaido University Sapporo, Japan SUMMARY The success o most o strengthening or retroitting technologies or concrete structures by using external bonded FRP sheets highly depends on the interace bond between FRP sheets and concrete substrates. This paper reviews current studies on evaluating the bond properties o FRP sheet-concrete interaces, and in particular, ocuses on several newly developed bond models or describing the bond characteristics o FRP sheet-concrete interaces under various loading conditions. This paper also gives several examples that apply those interacial bond models to the design o dierent retroitting cases. Analytical solutions are discussed that consider the local interacial delamination and slip behaviour, which can improve the prediction o strength and deormation perormances, as well as clariy the ailure mechanisms o concrete members upgraded with FRP composites. Moreover, the improvement in structural perormances o retroitted concrete members is discussed by relating them to the optimum microscopic properties o the interace bond and the properties o retroitting materials. Key words: Fiber Reinorced Polymer (FRP), sheet bonding, interace bond, bond models, anchorage design, optimized interace properties 1. INTRODUCTION With the development o the technology o upgrading the existing concrete structures by using externally bonded FRP composites, a number o issues related to conventional structural behaviors o the concrete structures ater being upgraded have been studied in the past decade. Among them is a keen interest to clariy the mechanisms o the interace bond between FRP composites and concrete substrates, because the bonding interace is relatively weak in comparison with the neighboring materials in the whole upgraded system. In most o strengthening cases, the interace bond is critical in transerring stresses rom 1

3 the existing concrete structures to the externally bonded FRP composites. When a structural element is encircled in FRP composites the mechanical role o interace bond becomes less important, but it still has the unction o keeping the integrity and durability o the composite FRP-concrete systems. Thereore, a good understanding on the interace bond is a prerequisite or achieving more reliable but rational design or concrete structures externally bonded with FRP composites. Generally, there are two interace bonding systems or FRP upgrading, namely plate bonding and sheet bonding. A higher quality control is possible with FRP plate bonding system, compared with the sheet bonding system that has a greater potential or construction laws, because the mixing o resins and the curing o FRP composites are carried out in ield conditions. Kaiser and Karbhari [1,2] has given a detailed summary o the potential laws that can occur during preparation o the concrete surace, o the adhesive and o the FRP composites, as well as o the whole bonding procedures, with a view to improving the quality control and monitoring o the bonding process. The sheet bonding system is currently more popular, because it has high conormability to the surace onto which sheet is bonded and oers maximum lexibility and convenience or construction. Current applications o the sheet bonding system include lexural strengthening, shear strengthening and column wrapping. In the column wrapping case, the interace bond ailure is not a major concern. Instead, the racture o FRP sheets is the dominant ailure mode, and it has been recently suggested that FRP materials with a high racture strain capacity (elongation larger than 5%) can be used [3-5]. However, or concrete members strengthened with FRP sheets or lexure and shear, debonding o the FRP rom concrete substrate can lead to overall structural ailures (see Figures 1 and 2). In the shear strengthening cases, the debonding o FRP sheets rom the concrete substrates are similar to those observed in pull-out shear bond tests. In the lexural strengthening cases, the debonding modes are various, and the corresponding ailure mechanisms are more complex. Besides the conventional concrete compression ailure or FRP racture, the ailure modes o FRP upgraded concrete members in lexure have been well documented in many literatures [6-9]: (1) Plate-end ailure (also called concrete cover delamination), which is a very brittle ailure manner and arises rom the normal and shear stress concentrations occurring at the ends o FRP near supports. Because this debonding leads to a catastrophic ailure o the strengthened concrete members, its ailure mechanisms have been heavily studied in the past decade [10-19]. The main reasons leading to this ailure are the distance between the ends o the FRP and the beam supports 2

4 and the use o relatively thick FRRP plates. However, when sheet bonding system is used, plate-end ailure has not been widely reported, because FRP sheets are think and are usually extended to the supports. (2) Anchorage ailure, which is due to the insuicient anchorage length o FRP sheets. (3) Mid-span debonding, where the interace debonding initiates rom the tips o mid-span lexural cracks or lexural-shear cracks o RC members. To avoid the mid-span debonding ailure, most present design guidelines recommend limits on the strains in the FRP sheets, although their approaches or determining these limits may be dierent [8, 9, 20]. Mid-span debonding results rom the interaction o the steel reinorcement, concrete cover and the FRP sheets. So it is closely related to bond between steel reinorcement and concrete, crack spacing, dowel action on the FRP sheets, and, most o all, the interace slip and delamination behaviours between the FRP sheets and the concrete substrates. For the sheet-bonding system, mid-span debonding is a critical ailure mode.. To date, it can be said the macro-mechanical behaviour o RC members upgraded with FRP sheet, such as the undamental ailure modes and their eects on the strength capacity and ductility, have been well established, based on a large number o experimental and analytical studies in the past decade. However, to achieve a reined design or concrete structures to be upgraded with FRP sheets, urther study is needed on the undamental issues, such as interacial bond racture mechanisms, selection o bonding or strengthening material, and design detailing. For reliable, but rational and cost-eective use o FRP materials reined upgrading designs should ollow perormance-based design concepts, or which the accuracy o predicting the perormances o FRP upgraded concrete members relies on accurate material laws, as well as advanced analytical methods. The Japan Concrete Institute (JCI) established a technical committee on retroitting technology (2001 to 2003) that ocused on the interace bond properties between existing concrete structures and retroitting materials or both adhesive bonding and overlaying retroitting technologies [21]. The objective o the committee was to gain insight into the micro- and macro-interacial bonding mechanisms, the selection o the optimum interace materials and upgrading methods, the improved prediction o the perormances o upgraded concrete structures, and, inally, the improvement o current upgrading techniques rom both a construction and material point o view. This paper also relects part o achievements o this technical 3

5 committee related to the interace bond between FRP sheets and concrete substrate. In general, the research topics on the FRP sheet-concrete interaces can be addressed by the ollowing: : 1. Parametric studies on interace bond, which include eects o all interace components: concrete, bonding layer and FRP sheets; 2. Test method or evaluating the interace bond properties; 3. Bond strength and anchorage design; 4. Failure mechanisms o interace bond and bond modeling; 5. Eects o interace bond on member behavior o concrete structures ater retroitting; 6. Optimized design o interace bond; and 7. Durability o interace bond. This paper ocuses mainly on the interace bond, including its evaluations, modeling and inluence on member behaviour o FRP upgraded concrete structures rom point o view o mechanics. It should be mentioned that durability o interace bond is another very important issue, which is the ocus o a technical committee o RILEM. 2. REVIEW ON THE FUNDAMENTAL BOND PROPERTIES OF FRP SHEET-CONCRETE INTERFACES AND THE EVALUATION METHODS 2.1 Bond o FRP Sheet-Concrete Interaces under Shear The most important role o the bond interace between FRP sheets and concrete is to transer shear stresses rom existing concrete structures to externally bonded FRP sheets or both shear strengthening and lexural strengthening cases (see Figs 1,2 ). Thereore, the shear bond properties o FRP sheet-concrete interaces have been extensively studied. Various test methods including single-lap-type, double-lap-type, bending-type, and inserted-type (see Figs 3-6) have been developed to characterize the local interacial shear bond behaviors by studying the strain distribution in the FRP sheets or to evaluate the average interacial bond strength. The evaluated interace characteristic parameters include average shear bond strength, eective bond length, maximum shear bond stress, interacial racture energy, as well as the local bond stress-slip relationship. All studied experimental parameters can be summarized as shown in Table 1. Bond length o FRP sheets [22-27] 4

6 Many researchers have studied the eects o sheet bond length. While bond strength increase as the sheet bond length is increase, when the sheet bond length is increases beyond a certain extent, the bond length does not increase any urther. Thereore, the average bond length decreases with the increase o sheet bond length. In other words, there exists an eective bond length. Besides the premature debonding phenomenon caused by shear stress concentration, the existence o eective bond length is another actor that causes the tensile strength o FRP materials not to be ully utilized. Nevertheless, owning the dierent deinitions given by dierent researchers and the dissimilar materials used in their tests, the eective bond lengths can vary signiicantly, such as 45 mm [22], 75 mm [23], 100 mm [24], 93 mm [25], 63.5~134.5 mm [26] and 275 mm [27]. Bond width o FRP sheets [28-29] It has been shown that the sheet width does not inluence the average bond strength o interaces when the width o sheets ranges rom 50 mm to 200 mm. However, when the sheet bond width is less than 50 mm, the smaller the sheet width, the higher average shear bond strength that the interace can achieve. Stiness o FRP sheets There are many reports on the eects o the stiness o FRP sheets (elastic modulus thickness). Clearly, the bond strength increases with the stiness o FRP sheets. Meanwhile, a higher FRP stiness will result in s longer anchorage length. Strength o concrete [25-26, 28-32] Concrete strength is thought to be a actor aecting the interace bond signiicantly. But it is, in act, rather diicult to veriy its eects in experimentally. Only when the concrete strength is greatly can can its eects become visible. Yoshizawa et al. and Lorenzis et al. indicated that the dependence o the interacial racture energy on the concrete compressive strength ' c is negligible [25, 30]. However, Chajes et al. and Horiguchi reported that the bond strength is proportional to and, respectively [31,32]. Brosens et al. reported that the bond strength is proportional to the square root o concrete tensile strength [28]. Nakaba et al. and Sato et al. reported that the maximum interacial bond ' 0.19 c ' 0.20 c stresses are proportional to and, respectively [26, 29]. ' 1/ 2 c ' 2 / 3 c Surace treatment o concrete Test results by Chajes et al showed that surace preparation o the concrete inluences the bond strength. 5

7 They ound that the using by mechanical abrading (similar to sandblasting) higher average interacial bond strength could be achieved [31]. Mitsui et al. conducted a urther quantitative study on the eects o surace condition. They evaluated the surace roughness index o concrete by changing the treatment methods, which were sandpaper polishing, disk sander grinding, sandblasting and chipping. They observed the three-dimensional proile o the concrete surace, using an optical displacement meter and obtained measurements o the maximum depth, supericial area and so on [33]. They concluded that the methods o sandblasting and chipping could lead to higher bond strength. Regarding the eects o concrete surace cleanness, it has been conirmed that the bond strength will decrease markedly i the concrete surace is greasy. But whether or not the moisture o concrete surace aects the bond strength or not depends on the type o bonding adhesives used. It should be noted that in practice it is diicult to control the roughness o concrete surace quantitatively. Experimental database, shown later herein, indicates that there is a wide scatter o bond strength caused by concrete surace condition, even when dierent workers (laboratories) ollow a same surace treatment method. But as a minimum, a clean concrete substrate with open pore structures is needed to achieve a good bond between the adhesive and concrete, or, in other words, to ensure that the bond ailure occurs in the concrete. Properties o bond layers [34-35] It has been ound that bond layers with lower elastic moduli, but good ductility, can lead to higher interace bond strengths. The mechanical properties o bond layers can be adjusted through changing the elastic modulus o either bonding resin or putty. However the eective bond length increases when the elastic modulus o bond layers decreases. It was also reported that using ordinary primer with a viscosity o 2,000 mpa.s is better than using high permeability primer with a viscosity o 90 mpa.s. The latter primer leads to lower bond strength. Interace deects [21] The liting o bonded sheet can simulated the interace deects that can be induced during bonding construction. It has been reported that a mm liting area o FRP sheets in specimens prepared or pull-out shear bond tests, which was equivalent to 6 % to 13% o the whole sheet bonding area, has no signiicant eects on the overall pull-out bond strength. 2.2 Bond o FRP Sheet-concrete Interaces under Tension In comparison with shear bond test, tensile tests or FRP sheet-concrete interaces are easier to perorm 6

8 in order to veriy the interace bond quality. Three types o tensile test methods have been reported in the past (Figs 7-9). Fig.7 shows a direct tensile test method, which is adopted by the Guideline on Upgrading o Concrete Structures with FRP sheet o Japan Society o Civil Engineering (JSCE) and the Design and Construction Guideline o Continuous Fiber Reinorce Concrete Structures o Architectural Institute o Japan (AIJ). This method is convenient because it checks the interace bond quality qualitatively, by observing, or example, whether or not the racture has occurred in the concrete. Figs 8 and 9 are three-point bending and wedge splitting, tests respectively [36-38]. They can be used to evaluate the Mode I racture energy, as well as the tension sotening diagram o FRP sheet-concrete interaces. Based on the two test methods, the bond properties o FRP sheet-concrete interaces under tension can be discussed parametrically and quantitatively. It was reported that under static loading condition and ordinary environmental condition, the Mode I racture energy o FRP sheet-concrete interace is mainly aected by the concrete surace condition, e.g. whether or not the coarse aggregates have been exposed suiciently. The selection o adhesives has a minor role, because the ashesives are more critical in shear than in tension. A three-point bending test has also been used or evaluating the bond degradation o FRP sheet-concrete interaces ater exposure to severe environmental and atigue loading [39]. 2.3 Bond o FRP Sheet-Concrete Interace under Combination o Shear and Tension A more representative interace bond ailure or concrete structures retroitted with FRP should be a combined mode, recognizing that the FRP sheet-concrete interaces are subjected to shear and tension simultaneously. Few experimental and analytical studies have been perormed to evaluate the interace ailure under mix-mode loading conditions. Karbhari and Engineer developed a bond test method to evaluate the bond between FRP composites and concrete under mix-mode loading conditions by producing dierent interace peeling angles [40]. However, their main purpose was to enable the determination o both Mode I (tension) and Mode II (shear) components o interacial racture energy and to allow a quantitative comparison o interace adhesion mechanisms and energies. They did not orientate their studies to any particular application o FRP strengthening technology or concrete structures. There is a new application o FRP strengthening technology in Japan, which is to bond FRP sheets on the bottom surace o tunnel linings or elevating bridges or the purpose o preventing deteriorated concrete 7

9 blocks rom alling. In those strengthening cases, FRP sheet-concrete interaces are under mix-mode loading, as shown in Fig.10. Two types o test methods have been applied to determine the bond properties o interaces under these loading conditions [41-43]. One is beam-type dowel test or FRP sheet-concrete interaces, in which one-directional FRP sheets are bonded on the bottom o a notched concrete beam (see Fig.11). The other is a slab-type shear punching test, in which bidirectional, rather than unidirectional FRP sheets are attached on the bottom o a concrete slab (see Fig.12). Two undamental bond characteristics o FRP sheet-concrete interaces under the dowel action have been obtained rom both two test types: (1) the peeling angle (see Fig.10) is constant during the interace debonding procedure; and (2) the vertical orce per unit width FRP sheet-concrete interace can bear is a constant value during the interace debonding procedure. The two conclusions can be used or bond modeling and retroitting design, as shown in the ollowing sections. Also, the analysis in the later part shows the outcomes rom both two test methods are equivalent. Another widely reported mix-mode ailure mode o FRP sheet-concrete interace is in FRP strengthened RC beams in lexure [6, 9, 44-45]. The interace debonding may initiate rom the tip o a shear-lexural crack, where the peeling is caused simultaneously by crack opening in longitudinal direction and crack sliding in vertical direction. Up to now no appropriate bond model has been published to describe this mix-mode ailure, nor its associated design detailing. In general, this ailure mode may be suppressed by limiting diagonal cracking, which in turn may be achieved through shear strengthening with transverse strips [8]. During experimental tests o RC beams lexurally strengthened with FRP sheets, it is diicult to measure the vertical sliding o a lexural-shear crack or the dowel deormation acting on FRP sheets. Consequently, whether or how much the vertical sliding o crack aects the lexural strengthening eiciency o FRP sheets is not clear. In the author s laboratory, experiments were perormed to investigate whether or not the lexural strengthening eiciency o FRP sheets is aected by the ratio o transverse reinorcements. Two RC beams lexurally strengthened with same amount o FRP sheets were designed to ail in lexure. Steel stirrups were over-provided or both two beams, but in dierent ratios. Test results indicated that the strengthened RC beam with a larger amount o transverse reinorcements achieved about 10% higher lexural capacity than the other beam. and also showed better ductility, although both beams ailed in lexure due to debonding o FRP sheets [46]. Thereore, the eects o 8

10 mix-mode ailure o FRP sheet-concrete interace are inluenced by the amount o transverse reinorcement, and should be considered in a reined design. It is clear that the contribution o the interace dowel resistance to the shear capacity o strengthened RC beams is negligible. However, the dowel action on FRP sheets may aect the eiciency o shear stress transer in FRP sheet-concrete interace and result in a premature interace debonding, and, consequently, a decrease o the maximum tensile stress achieved in FRP sheets. To determine the eects o dowel action on the interace shear orce transer in the anchorage area, the authors perormed mix-mode tests or the FRP sheet-concrete interaces. In the tests, a dowel orce was directly imposed onto FRP sheets through a vertical bar connected to the loading system o a universal test machine, which is similar to that in Fig.11. However, by setting a reaction ramework inside the test machine, as shown in Fig.13, a pullout orce could be introduced into FRP sheets, as well as a bending orce on the concrete beams can be achieved by adding the dowel orce and bending load simutaneously [47]. In the experiments, two layers o FRP sheets (FRP stiness is 50.6 kn/mm) were attached to concrete beams with an anchorage length o 400 mm. Fig.14 shows the eects o the overall lexural strengthening eiciency o dowel orces imposed on FRP sheets. The lexural strengthening eiciency is deined as the ratio o the maximum bending load a concrete beam achieved under dowel eects to that a reerence beam achieved without the dowel eect. It has been ound that the lexural strengthening eiciency is not signiicantly aected, even i the dowel orce is added till the 90% o the interace dowel orce capacity. In other words, i the dowel orce locally imposed on FRP sheets does not exceed the interace dowel orce capacity, its aects on the overall shear orce transer o the interace are not signiicant. As shown in the next section, the dowel orce acting on FRP sheets is in act the vertical component o tensile orce in FRP sheets during the interace debonding. In order to decrease the dowel orce while achieve a high tensile stress (lexural strengthening eiciency) in FRP sheets, the peeling angle between the concrete surace and FRP sheets should be controlled. Fig.15 shows the change o interace crack mouth open displacement (interace CMOD) between the FRP sheets and the concrete at the location where the dowel orce was added with the increase o bending loads. It can be seen that the CMOD decreases with the increase o bending orce, meaning that the increase o tensile stress in FRP sheets can be achieved by limiting the interace opening displacement in vertical direction i anchorage length is not suiciently long. On the other side, i the CMOD, which equals the dowel deormation induced by diagonal cracks in 9

11 an FRP strengthened beam, is ixed, the negative eects o dowel deormation on the lexural strengthening eiciency can be eliminated by increasing the additional anchorage length, which can consequently decrease the interace peeling angle. In the experiments, the authors also monitored the bending loads corresponding to the initial debonding o the FRP sheets rom the concrete substrates near the location where the dowel orce was added (see Fig.14). It can be seen the initiation o the interace debonding is signiicantly aected by the dowel orce imposed. Although this kind o local debonding does not aect the ultimate shear orce transer capacity o an FRP sheet-concrete interace, as already discussed, the stiness o strengthened concrete beams has been ound to decrease by 20% when 90% o the maximum dowel orce that the interace can bear was applied to FRP sheets compared with the stiness o the reerence beam. 3. BOND MODELING AND FUNDAMENTAL APPLICATIONS IN RETROFITTING ENGINEERING 3.1 Modeling or Interace Bond under Shear The bond stress-slip (τ~s) relationship is the most important law to describe the interace perormance o two bonding materials. A number o τ~s relationships have been proposed by dierent researchers. However, even the shapes those τ~s relationships or FRP sheet-concrete interaces dier greatly. For example, many conigurations or the τ~s relationships, including cut-o type, bilinear type, elasto-plastic type, and Popovic type have been reported [22, 25-26, 29-30]. Those dierences indicate the diiculty in deining a reliable local τ~s model or an FRP sheet-concrete interace rom conventional pull-out bond test results. The reasons may be as ollows. First, the eective bond length o FRP sheet-concrete interaces is rather short, and it is diicult to arrange many strain gages in an active, but short, load transer length. Second, the FRP sheets have rather small bending stiness, so that the strains observed on the surace o FRP sheets have a larger scatter due to local bending deormations. Third, the interace between FRP composites and concrete easily exceeds the peak shear bond stress, even i there is a low tensile stress level in FRP sheets, so the interacial τ~s relationship is highly nonlinear [48]. To solve those diiculties, the authors developed a new dierential solution or deriving the local τ~s constitutive law or an FRP sheet-concrete interace [49]. Based on that solution, it is not necessary to record the local bond behaviors o an FRP sheet-concrete interace during a pullout bond test. Instead the 10

12 local τ~s relationship can be derived rom the relationship between the pullout loads and slips at the point o loading. The proposed local τ~s relationship has two parameters, one o which is the interace racture energy and another is interacial ductility actor. Its expression has been obtained based on a lot o experimental results as ollows: τ (1) = 2BG (exp( Bs) exp( 2Bs)) where G is the interacial racture energy (N/mm); B is termed as interacial ductility actor by the authors (mm -1 ). G and B have been determined through regression o the experimental data as ollows: G ( Ga / ta) c ( E t = ) (2) ( E t ) ( Ga / ta B = ) (3) where E t is the stiness o FRP (kn/mm); G a is the shear modulus o adhesive bond layer (GPa); t a is the thickness o adhesive bond layer (mm); and c is the compressive strength o concrete (MPa). The proposed τ~s relationship can consider the eects o all interacial components: stiness o FRP, concrete and adhesive. One advantage o this above τ~s relationship is its simplicity on expression and the rigorous analytical procedure. Another advantage is that parameters such as the peak bond stress and the corresponding slip value, which in act are diicult to be calibrated during pull-out tests, can be determined mathematically as ollows: s max = 0.693/ B (4) τ = 0.5BG max (5) For most o the requently used adhesives, Equation 1 can be urther simpliied by averaging a lot o experimental curves and neglecting the minor eects caused by stiness o FRP as shown in Figure 9. Then the Equation 1 becomes: τ = 10.7 (exp( 10.4s) exp( 20.8s)) (6) ' c 3.2 Anchorage Design or Tensile Force in FRP sheets A undamental issue in studying the shear bond between concrete and any reinorcing material is the anchorage design. The bond o externally bonded FRP sheets to concrete is signiicantly dierent rom that o reinorcing bars in concrete. The anchorage design criteria or the bond o reinorcing bars in RC 11

13 is to guarantee a suicient development length, with which a reinorcing bar can resist a tensile orce equal to its tensile strength. However, the externally bonded FRP in an FRP sheet-concrete interace seldom can reach its material strength, even over a very long bond length, because o the existence o premature debonding and eective bond length, as reviewed in Section 1. Thereore, the problem o how to precisely determine precisely the ull interacial bond strength at debonding and the necessary eective bond length to achieve that bond strength should be solved. Until now, a number o empirical and analytical models related to average bond length, eective bond length have been proposed in the past [9, 30, 50-53]. However, most o the existing eective bond length models consider only the eects o FRP stiness and concrete strength and neglect the important eects o the interace adhesives, which signiicantly aect the eective bond length and the bond strength [34]. In addition, the eective bond length is usually used in existing bond strength models as a parameter to predict the bond strength o an FRP sheet-concrete interace by judging whether or not its bond length is longer than the eective bond length [50-53]. However, as reviewed in Section 2.1, the eective bond length was reported in a widely scattered range o 45 ~ 275 mm. Indeed, a more reasonable and general approach is to determine the anchorage length based on the bond stress-slip relationship obtained. On the basis o τ~s relationship, as shown in Equation 1, the authors developed a model or predicting the anchorage length o FRP sheet-concrete interaces by analyzing the strain distributions in FRP sheets and the bond stress distribution along the interace [54]. Figure 17 show an example o the predicted shear stress distributions o an FRP sheet-concrete interace under dierent pull-out loading levels. It can be seen that there exists only a limited distance with visible bond stresses, even a very long length is available. That is why FRP sheet-concrete interaces cannot increase their bond strength beyond the eective bond length. Consequently, the eective bond length can be deined as that active bond distance L e indicated in Figure 17, which can be expressed mathematically as ollows: 2E t 1 + α L e = ln( ) (7) B G 1 α where L e is the eective bond length, α is the ratio o the bond orce that the eective bond area can bear to the deined theoretical maximum bond strength. Theoretically there always exists even a tiny shear stress between the FRP and concrete no matter how big the interacial slip becomes, meaning that the interace can never achieve the maximum theoretical bond strength (α always smaller than 1.0). Based on 12

14 experimental observations α can be taken as 0.96 or the purpose o anchorage design. The proposed expression or eective bond length L e can include the eects o concrete, FRP stiness and the adhesive layer as well. The L e increases with the stiness o FRP, but decreases with the increase o interacial racture energy and the B. The B has a higher value when a stier adhesive is used and vice versa. By using a similar solution, a uniied bond strength model or FRP sheet-concrete interaces, which was derived rom Equation 7, was also developed as ollows [54]: P u = αp max (8.1) L b B G exp( ) 1 2 E t α = (8.2) L b B G exp( ) E t P = ( b + 2Δb ) 2E t G (8.3) max Where P u is the bond strength o FRP sheet-concrete interace with a given bond length L b ; L b is the bond length o FRP sheets; b is an additional width, which is given to consider the eects o bond width o FRP sheets on the average interace bond strength and can be taken as 3.7mm based on test results [29]. Another important issue that should be mentioned is the large scatter o bond strength. The bonding perormances o FRP sheet-concrete interaces closely rely on the concrete properties. However, the bond strength o FRP sheet-concrete interaces is in act more sensitive to the condition o concrete surace preparation, because the bond ailure always happens within a thin concrete layer just beneath the adhesive. Even though a standard concrete surace treatment is ollowed, the concrete surace condition may deviate according to the operating skills o the workers. At present, it is diicult to quantiy scientiically and precisely these construction deviations o concrete surace conditions. Also, the bond perormances achieved in construction are not easily obtained because pull-out bond tests are less likely to be perormed ater a concrete structure has been strengthened. However, the accumulation o experimental databases o pullout test results in laboratories to date makes it possible to evaluate statistically the eects o construction deviations on the bond strength. The authors collected a large number o pull-out bond test results or FRP sheet-concrete interaces (220 specimens), which were published by 11 researchers [22-31, 55-56]. Figure 18 gives a comparison 13

15 between all test results and the analytical predictions o the present bond strength model. It shows that the scatter o the bond strength o FRP sheet-concrete interaces is rather large, though the present model gives a good average prediction. Ater the other material actors are considered appropriately, the remaining large scatter can be considered as a kind o construction deviation. Thereore, or a sae interace bond design, a construction deviation actor can be introduced to the present model. According to the databases shown in Figure 18, a reduction actor 0.68 can be added in the present bond strength model (Equations 8.1 to 8.3) i we permit that 5% o the experimental data (the points above the dotted line P pre. /P ana. =1.5 in Fig.18) can be overestimated. According to the square root relationship between the ultimate pullout load and interacial racture energy, a construction deviation actor o k c =0.46 can be considered in the expression or the G (Equation 2) or engineering design purpose. With this approach, the anchorage length is given a saety actor o 1.46 based on the relationship between L e and G as shown in Equation 7. Figure 18 also includes test data o several FRP plate-concrete interaces, or which FRP has a high tension stiness (about 200 kn/mm). It is shown that the analytical model proposed, based on sheet bonding system, always overestimates the bond strength o FRP plate-concrete interaces, implying that sheet bonding system can achieve higher interacial racture energy than the plate bonding system. A possible explanation or this is that FRP sheets have greater conormability to the concrete surace irregularity. 3.3 Modeling or Interace Bond under Tension [38] In general, the racture o FRP sheet-concrete interaces occurs in concrete, because the tensile strength o adhesive is usually higher than that o concrete. The thickness o concrete over which the damage occurs is small in comparison with the dimensions o the whole concrete element. So the interace debonding can be simulated as the interacial cracking, using link elements between FRP and concrete, as shown in Figure 19. The nonlinear damage in the concrete element can be simulated by lumping it into the sotening o the interace element instead o allowing damage in the concrete elements. The crack open displacement o interace is a combination o the cracking in the adhesive layers and concrete, respectively, beore and ater the peak tensile stress o concrete is reached. So the interace tensile stress-open displacement relationship can be expressed as ollows: 14

16 σ = kδ ( δ δ p, δ p = ) (9.1) k σ = (δ ) ( δ p δ < δu t < ) (9.2) σ = 0 ( δ > δu ) (9.3) where k is the initial elastic stiness o interace spring (N/mm 3 ). δ is the interace opening displacement (mm); δ p is the interace opening displacement at peak stress (mm) and δ u is the interace open displacement corresponding to zero cohesive stress (mm). To get the tension sotening diagram o FRP sheet-concrete interaces σ=(δ), the authors perormed conventional three-point bending tests on notched composite beams, which included FRP sheet-concrete interaces as shown in Fig.8. Both concrete and mortar substrates were prepared or bonding FRP sheets. Cyclic loading way was applied on all composite beams and the interace tension-sotening diagram was derived through improved J-integral method and then veriied through FEM analysis. Figure 20 shows the experimental relationships between the interacial tensile stress and the open displacement or concrete and mortar bonding substrates, respectively. It was ound that a ollowing uniied expression could model the observed interacial tension sotening diagrams quite well. σ t + δ = 1 δ α (10) u where: α is an interace ductility index, which can be taken as 2.2~2.5 and 3.0 or concrete and mortar bonding substrates respectively. δ u can be taken as 0.3 mm or both concrete and mortar bonding substrates in the case o using normal bonding adhesives (the elasticity modulus o bonding adhesive E a is higher than 1.0GPa). Load-delection curves o notched composite concrete beams can be derived, and include the FRP sheet-concrete interaces, which are represented by link elements between two concrete blocks (see Fig.8) in the FEM analysis. From these curves, the value o E a /t a can be used to determine the initial elastic stiness k o interace spring, where E a is elastic modulus o used bonding adhesives and t a can be measured.experimentally. 3.4 Modeling or Interace Bond under Dowel Action I do not think that ta values are necessary to be shown. Thanks or the rectiication As mentioned in Section 2.3, the FRP sheet-concrete interaces may ail under dowel action, in which 15

17 case the FRP sheet-concrete interaces bear tension and shear eects simultaneously. As shown in the Fig.10, the interace debonding under dowel action is governed by the component o tensile orce T in FRP sheets in the direction o dowel deormation. I the orce induced by a given dowel deormation exceeds the dowel orce capacity o an FRP sheet-concrete interace, the dowel will ail. Thereore, to avoid this kind o dowel ailure, it is important to be able to predict the interace dowel orce capacity. In the loading condition shown in Figure 10, the dowel orce acting on the FRP sheet-concrete can be approximately expressed as ollows: 1 ε = ( 1) cosθ (11) Pd 1 = 2E t ε = 2E t ( 1) sinθ b cosθ (12) where ε is the tensile strain in the FRP sheets. P d is dowel orce imposed on the FRP sheets; T is tensile stress in the FRP sheets; E t is the tension stiness o the FRP sheets; b is the bond width o the FRP sheets; and θ is the interace peeling angle. From a series o dowel tests as shown in Fig.11, the authors derived the relationship between the critical peeling angle and the spalling racture energy o an FRP sheet-concrete interace under a dowel orce as ollows [43]: 2 2 (1 cosθ )(sin θ cos θ + cosθ ) G s = E t 2 (13) 2cos θ where G s is the spalling racture energy o FRP sheet-concrete interace under dowel orce (N/mm). By combining Equations 12 and 13, it can be known that the dowel orce capacity can be predicted i the interace spalling racture energy G s is calibrated. Figure 21 and Figure 22 show, respectively, the relationship between the interace spalling energy G s and the peeling angle θ, and the relationship between the dowel orce P d and interace spalling energy G s. The comparison between the experimental and analytical results shows that the interace debonding ailure under dowel orce (Equations 12 and 13) can be modeled. It is also ound through experiments that the interace spalling racture energy increases with concrete strength, but decreases with increasing the stiness o FRP and adhesive elastic modulus. Increasing the FRP stiness results in a smaller peeling angle (see Figure21), and, consequently, can help decrease the dowel deormation. However, the smaller peeling angle brought by the higher FRP stiness 16

18 means that the dowel deormation o FRP sheets should be more strictly limited when using an FRP with high stiness, i the FRP sheets need to achieve a high tensile stress. 3.5 Spalling Prevention Design o Concrete Structure by Using FRP Sheets FRP sheets are increasingly being used to prevent spalling o concrete blocks rom deteriorated tunnel linings or elevated bridges. Guidelines or anti-spalling design o concrete structures by using FRP sheets can be based on the bond modeling o the FRP sheet-concrete interace under dowel orce. In practic, interace peeling caused by the spalling orce P spalling o deteriorated concrete blocks may propagate in two dimensions, as shown in Figure 23. Punching shear test results or concrete slabs retroitted with bidirectional FRP sheets, in which the tension stiness in x and y directions are equal, showed that the shape o peeled interace under the action o the spalling orce is nearly square. Moreover, the interace peeling angle θ (Fig.23) was ound to be constant during interace debonding process. Based on these two observations, the relationship between the spalling orce and the peeling angle can be obtained through integration as ollows [41]: x( y) spalling P 2( r + L p ) = 2E t x( y) x( y) 1 ( 1)sinθ cosθ (14) where P x*(y) spalling is the interace spalling resistance contributed by the tension stiness in x or y direction; E x(y) t x(y) is the tension stiness o FRP in x or y direction; r is the radius o concrete column used or imposing spalling orce; L p is the largest peeled length along x direction; and θ is the interace peeling angle as shown in Figure 23. It can be seen rom Figure 23 that 2(r+L p ) is the maximum width o the peeled FRP sheets in the x or y direction. By comparing Equation 12 and Equation 14, it can be concluded that the spalling orces per unit width o FRP sheets can bear in unidirectional and bidirectional strengthening cases are the same i the FRP sheets have same tension stiness. In spalling prevention design with bidirectional or multidirectional waved FRP sheets, the sum o FRP tension stiness in two crossed directions can be taken as a design parameter. The bond characteristic parameter o the FRP sheet-concrete interaces under dowel ailure, like the critical peeling angle θ or the interace spalling racture energy G s can be calibrated through the simple inidirectional dowel test, as shown in Fig.11. Wu et al. proposed a value o 0.5N/mm or G s, based on their shear punching test results [41]. It can be seen in Figure 23 that the 17

19 proposed value can give a conservative prediction. In practice, FRP sheets used to prevent the tunnel linings rom spalling, Kojima et al. proposed the ollowing design guideline by using a parameter called the interace spalling strength s p0, which is deined as the interace spalling orce divided by the peeled circumerence o the interace under that orce [42]. Wd γ i 1.0 (15) P spalling P spalling s 0 ( l + γ l ) 2 p = t a a (16) γ m γ b where W d is supposed spalling driving orce in design, P spalling is the spalling resistance or design, γ i is the saety actor or structures, sp0 is the interace spalling strength, γ a is the reduction actor by the curvature o tunnel linings, and l and l are the dimensions o possible spalling blocks in the a t longitudinal and transverse dimension o tunnel respectively. In addition, when FRP sheets with a speciic tension stiness is provided or design, the strength capacity o FRP sheets should be checked by Equations 17 and 18 to prevent sheet rupture. σ γ 1 m (17) t σ 1 = E ε = E ( 1) (18) cosθ where σ is the stress in the FRP sheets when the interace peeling happens, t is the tensile strength o FRP sheets, E is the elastic modulus o the FRP sheets, γ m is the saety actor or the tensile strength o FRP sheets, and θ is the critical peeling angle. It can be seen rom Equations 15 to 18 that two interace parameters are needed or design. One is the peeling angle θ and the other is the interace spalling strength s p0. Based on the bond modeling presented above, with a given spalling energy, G s, θ can be determined based on Equation 12 and s p0 can obtained according to its deinition and Equation 14 as ollows: po = 4 Pspalling 2( r + L p = ) 1 E t 2 x+ y 1 ( 1)sinθ cosθ s (19) where E t x+y is the sum up o the tension stiness o FRP sheets in crossed directions, and, rom Figure 23 18

20 that 2( r + L ) is the circumerence o peeled interace. 4 p Thereore, or the spalling prevention design o concrete structures using FRP sheets, the interace spalling racture energy G s is the only needed bonding characteristic parameter o FRP sheet-concrete interace and it can be calibrated rom a simple unidirectional dowel test, as discussed above. 4. MEBER BEHAVIOR AND BOND PROPERTY 4.1 Numerical Simulation Failures o FRP sheet strengthened concrete members are usually related to the debonding o FRP sheets rom concrete substrates. Consequently, the improvement in predicting the strength, stiness, and ductility behaviors o FRP sheet strengthened concrete members depends upon using interace bond models within appropriate numerical analytical tools. That is also the prerequisite o achieving optimum retroitting design based on desirable perormances. Owing to the special localized delamination and slip phenomena o the FRP composite-concrete interace, it is diicult to use conventional design theory like the iber modeling, which is generally used in beam or column analysis, to evaluate the FRP strengthened RC members precisely. To consider the highly nonlinear interace delamination and slip behavior together with the various types in cracking behaviors, the FEM may be a more useul approach. FEM analytical method with a smeared crack model has been used by many researchers [57-60] mainly or analyzing the perormance o FRP externally strengthened RC beams. Although they can show acceptable agreement between their experimental and analytical results, their proposed interace bond models showed signiicant dierences with those observed in pull-out bond tests, and, hence, a lack o common applicability. It has been recognized that the smeared crack approach is limited in the ability to represent the stress intensity at the delamination tip o FRP laminate strengthened RC beams [61]. For this reason, a racture energy-based criterion is a more suitable solution to describe the bi-material elasticity and the complex stress intensity at the delamination tip governing the propagation o delamination. Wu and Niu perormed two-dimensional FEM analysis (with the ABAQUS Program) based on discrete crack method to clariy the debonding initiation rom the mid-span lexural cracks. In their analysis, they applied energy-based bilinear interacial τ ~ s relationship, which was obtained rom the pull out bond test, in their analysis [62-63]. Kishi et al. perormed three-dimensional FEM analysis (with the DIANA 19

21 Program) on FRP sheet strengthened RC beams. They proposed a mix-mode interacial model, in which both the interacial tension and shear model are assumed as cut-o type, without consideration o the tension and shear sotening [64]. For both two-dimensional and three-dimensional FEM analysis based on discrete method, spacing and localizations o cracks need to be deined by introducing crack elements. The premature interace debonding in FRP strengthened concrete structures is a localized phenomenon and highly depends on the cracking behavior o concrete. Thereore, improvements on both interace bond models and the advanced discrete methods are necessary. In the authors laboratory, a discrete crack approach based on rigid body spring method (RBSM) has been developed [65-66]. The most attractive eature is its ability to simulate the random racture or cracking process o concrete materials. RBSM, with the racture-energy-based nonlinear bond model developed by the authors, was applied to simulate tension stiness behavior o a concrete prism reinorced with a reinorcing bar at its center and externally bonded carbon FRP sheets on two sides (see Figure 24), which was experimentally investigated in a previous study [67]. The simulated results show a good agreement with the experimental ones in average tensile strains in the concrete, steel bar and FRP sheet and bond stresses o the steel bar and FRP sheet. This numerical scheme with RBSM could also analyze a reinorced concrete beam strengthened with FRP sheet in lexure [66]. Using racture-energy-based nonlinear bond models, which have been well veriied in bond element level, the analytical tool is expected to clariy the dierent interacial debonding behaviors in a uniied way. 4.2 Optimal Interace Bond Property or Member Behaviors [21] Good understanding on the bond properties and bond modeling o FRP sheet-concrete interace can help not only to improve the predictions o the load carrying capacity and deormation behavior o FRP strengthened concrete members, but also to ind appropriate interace bonding materials, which can oer suitable interace bond characteristics to optimize the perormances o strengthened RC members. In addition, it is well known that FRP strengthening materials have tensile strength. However, this high strength can seldom be ully utilized in practice owing to the premature debonding. Besides the traditional prestressing and mechanical anchorage systems (or example U-shape wrapping and mechanical bolts) at the ends o FRP sheets, some other novel bonding technologies, such as near surace mounting (NSM) and other mechanical astening or the bond interace as a substitute o adhesive bonding in FRP lexurally strengthened RC members have been developed based on dierent strengthening FRP materials 20

22 [68-70]. However, interace bond properties o FRP strengthened reinorced concrete structures using these novel technologies need to be studies quantitatively such that the interace bond materials can be optimally selected, leading to optimized use o the FRP materials. The predominant local bond characteristic o an FRP sheet-concrete interace is the interacial racture energy G. Numerical analysis has shown that improvement o interacial racture energy may not be necessary or a ductility-orientated member, except when the member is poorly reinorced but strengthened with high stiness FRP sheets [70]. Instead, the improvement o the racture energy o FRP material itsel becomes more important. However, the interace racture energy signiicantly aects the perormances o RC beams strengthened with FRP sheets in lexure and shear. In Japan, design procedure based on veriying the racture energy to calculate the lexural capacity o FRP sheet strengthened RC beams has been adapted in the design recommendation o JSCE [20]. Figure 25 shows an example o analytical results on the lexural capacity o strengthened RC beams by using the interacial racture energy [71]. The material parameters used in calculation are shown in Table 2. It can be seen in Fig.25 that i the racture energy is increased, the lexural capacity also increases, but will stop increasing i compression ailure o concrete occurs. The typical value or the racture energy o FRP sheet-concrete interace is about equal to 1.2 N/mm [30], which means that the lexural capacity o a retroitted RC member can be urther improved i the racture energy can exceed 1.2 N/mm. But on the other hand, it can be seen rom Fig.25 that the lexural capacity will not increase eiciently i the racture energy exceeds 2.0 N/mm. So any value o the interacial racture energy, which is less than 2.0 N/mm, or lexural strengthening is optimum, because the lexural capacity is controlled directly by the interacial racture energy. The maximum lexural capacity can be achieved when the racture energy is 2.0 N/mm. The desired racture energy can be obtained most eectively by selecting an adhesive resin having either an appropriate stiness or an appropriate thickness. For shear strengthening case, a similar analysis can be perormed. To predict the ultimate shear capacity o FRP strengthened member, Kamiharako et al. developed a rigid body model with a single shear crack as shown in Fig.26 based on the ollowing assumptions [73]: the angle θ between the longitudinal axis o the member and the shear crack is 35 0 ; deormation o the member ater shear cracking is represented by rotation o the member; delamination o the sheets bridging a major diagonal crack is described by using a constitutive 21

23 model o the bond between the sheet and the concrete (see Figure 19); concrete blocks on either side o a main shear crack are rigid, and the FRP sheets are elastic; the strain o concrete at compressive zone is deined as unction o the angle ρ shown in Fig.26. The analysis can consider the eects o local interacial bond stress-slip behavior, while the shear orces carried by FRP sheets are evaluated by considering the delamination process o the sheet in each element along the retroitted member or an increasing angle ρ ( see Fig. 26). This analytical method can judge whether the ailure mode is shear compression ailure or sheet rupture. The ultimate shear capacity o retroitted member, V y, is calculated as ollows: V y = V c + V s + V (20) where V c is the shear orce carried by the concrete, V s is the shear orce carried by the web reinorcement, and V is the shear orce carried by the sheet. The shear orces, V c, and V are calculated based on conventional truss models. Based on this rigid body model, the sensitivity o the interace racture energy G on the shear capacity o FRP sheet strengthened RC members was analyzed by using a cut-o bond model as shown in Figure 27 [74], the material parameters used in parameters are shown in Table 3. Figure 28 shows the relationship between the racture energy and the shear capacity o strengthened members in the cases where dierent stiness o FRP (thickness t ) is used. It can be seen that when the thickness o FRP sheets t lies between 0.05 and 0.15 mm, the shear capacity decreases with the increase o interacial racture energy, because the sheet is ruptured beore the interace delaminating in the analysis. However, when the thickness o FRP sheets t exceeded 0.3 mm, the shear capacity can be improved with the increase o racture energy. Though the analysis is qualitative, the ollowing conclusion can be drawn, based upon the analytical results. When the thickness (stiness) o the FRP sheets is very small, the racture energy is not so important; whereas when the thickness (stiness) increases, the improvement in the interace racture energy can improve the signiicantly shear capacity o strengthened members. Our study o the literature persuades us that there are still great gaps in understanding the contribution o interace bond properties to FRP strengthening or a wide range o cases. Engineers and manuacturers lack both experience and adequate data to choose the best materials in many strengthening cases. Even though the new FRP strengthening techniques we are championing are costly now, we are interested in urther work to optimize these new techniques or a given structural perormance and cost-eectiveness. 22

24 Improved knowledge o the interace bond is needed to understand the composite action o the FRP strengthening materials and concretes structures. While it is encouraging or engineers to see emergence o new FRP strengthening techniques, it is paramount to understand the composite action between the FRP and the concrete structure so that the design o the strengthening can be based on perormance-based provisions. 5. CONCLUDING REMARKS Over the last decase, Design guidelines or upgrading concrete structures with FRP sheets have been developed based on undamentals and have now reached a stage where reined design is possible. More attentions need to be paid to the issues o optimal selection o strengthening materials, interace bonding materials, as well as how to utilize eiciently the advantages o FRP materials related to desirable structural behavior. Solutions to these issues depend on improved techniques to predict the the perormance o concrete structures ater upgrading, in which the ocus needs to be advanced modeling o the bond at the FRP sheet-concrete interaces at the micro or element level and also at the member level. This paper has summarized the existing test methods or evaluating bond behavior o FRP sheet-concrete interaces and introduced some updated modeling methods or the bond properties o FRP sheet-concrete interaces under various conditions, as well as the applications o some o those models in FRP strengthening examples. The authors have introduced some o the latest achievements related to the interace bond, which are included in the report o JCI Technical Committee on Retroit Technology, on which the irst author served [21]. It is the authors hope that the descriptions in this paper on modeling the interace bond at the micro-level, the modeling o FRP strengthened members with respect to local bond properties, and the role o the interace bond properties on member behavior will be inormative to researchers, engineers, and material manuacturers and enable them to advance their understanding o FRP retroitting technology. 23

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32 Figures Figure 1 Interace debonding ailure: shear strengthening cases Debonding ailure around anchorage area Debonding ailure around mid-span area Figure 2 Interace debonding ailure: lexural strengthening cases Load FRP Concrete Figure 3 single-lap shear bond test 31

33 Load Concrete Load Rebar Notch FRP Bond length Figure 4 double-lap shear bond test Load Load Concrete FRP Notch Bond length Figure 5 bending-type shear bond test Load Steel plate FRP Figure 6 inserted type shear bond test 32

34 Figure 7 direct tension test Adhesive P FRP sheet Concrete 1 Concrete 2 100mm π gages Separating vinylon tape 350mm Figure 8 three-point bending test Figure 9 wedging splitting test 33

35 Concrete blocks P d Peeling angleθ T FRP sheets Figure 10 Dowel test or FRP sheet-concrete interaces P dowel concrete beam FRP sheet Figure 11 beam-type (one-directional sheet) dowel test Figure 12 slab-type (two-directional sheet) dowel test [4] 34