Proceedings of International Symposium on Bond Behaviour of FRP in Structures (BBFS 2005), Dec, 79, Hong Kong, China, 4554 Chen and Teng (eds) © 2005 International Institute for FRP in Construction Design Proposals for the Debonding Strengths of FRP Strengthened RC Beams in the Chinese Design Code L. P. Ye ^{1}, X. Z. Lu ^{1} and J. F. Chen^{ 2} ^{1 }Department of Civil Engineering, Tsinghua University, Beijing, China, 100084, Email: ylp@tsinghua.edu.cn, luxinzheng@263.net ^{2 }Institute for Infrastructure and Environment, The University of Edinburgh, UK. Email: J.F.Chen@ed.ac.uk ABSTRACT Debonding failures are very common in FRP strengthened RC structures so they must be carefully considered in design. In the last few years, significant new understandings of the debonding behaviour of both flexurally and shear strengthened RC beams have been achieved based on recent research on the behaviour of FRPtoconcrete interface. These new understandings are reflected in the national design standard of China, Standard for FRP in Civil Engineering, which is being drafted. This paper summarises relevant specifications adopted for such debonding failures in the new Chinese standard. KEYWORDS FRP, strengthening, design specifications, debonding, flexural, shear 
Introduction The technique of externally bonding fibre reinforced polymer (FRP) composite plates or sheets (referred as either FRP sheets or FRP plates interchangeably hereafter for brevity) to reinforced concrete (RC) structures was introduced into China in 1997. After extensive research and promotion since then, it has now become a major method for retrofitting concrete structures. At present, over 600,000m^{2} FRP sheets are used to retrofit or repair concrete structures every year in China. This popularity of FRP in China means that there is a strong demand for design standards and specifications. Consequently, the first specification for FRP in Civil Engineering in China, ¡°Technical specification for strengthening concrete structure with carbon fibre reinforced polymer laminate CECS146¡± (CECS146 2003) (referred as the specification hereafter for brevity), was published in 2003. A national standard, ¡°Standard for FRP in Civil Engineering¡± (referred as the standard hereafter for brevity), is currently being developed. When an RC structure is strengthened with externally bonded FRP, the bond between FRP and concrete plays a crucial role in guaranteeing the effectiveness of the strengthening. Because of the high strength of FRP materials, most failures of FRP strengthened RC members are caused by debonding along FRPtoconcrete interfaces. herefore, appropriate considerations must be given to debonding failures in design. This paper presents the design methods proposed in the specification and the standard for debonding failures in flexurally and/or shear strengthened RC beams. The debonding failures concerned in this paper are limited to cases where the FRP sheets are properly installed with appropriate adhesives by qualified personnel following a proper construction procedure. In such cases, debonding failures usually occur in the concrete about 2~10mm away from the concreteadhesive interface. It is assumed that any debonding in the adhesive or delamination of FRP is caused by poor construction or substandard materials. Such failures should be prevented by careful selection of materials, quality assurance of supplied materials and by following appropriate construction and inspection procedures. These details are not discussed in this paper. DEBONDING FAILURES IN FLEXURALly Strengthened members A large number of experimental studies (e.g. Teng et al. 2002a, 2003a, b, Lu 2004) have shown that, without any additional anchorage, there are mainly three debonding failure modes in RC beams strengthened with a tension face FRP sheet (Figure 1). 1) Plate end debonding/concrete cover separation; 2) Critical diagonal crack debonding (CDC debonding); 3) Intermediate crack induced debonding (IC debonding).
Figure 1. Debonding failure modes in flexurallystrengthened RC beams Plate End Debonding/Concrete cover separation FRP plate end debonding or concrete cover separation is believed to be caused by the significant stress concentration at the FRP plate end arising from geometrical and flexural stiffness discontinuities. This failure mode has received extensive attentions in early studies on FRP strengthening of RC structures. Linear elastic analysis indicates that very large normal and shear stresses exist in the adhesive layer at the plate end (Teng et al. 2002a, 2002b). Many factors including the elastic modulus and the thickness of the adhesive layer affect the values of these stresses. It shall be noted that these large stresses are present only in a small region: they are reduced to very small values several times of the thickness of FRP plate away from the plate end. Because the thickness of the FRP plate is only a few millimetres in most cases, the actual size of the stress concentration region is very small. Since the debonding always occurs within the concrete, the actual stress distributions at the FRPtoconcrete interface are much more complicated than those from a linear elastic analysis due to concrete cracking. This led to the development of several design proposals considering the nonlinear interfacial behaviour. However, there are still large discrepancies between all strength models based on either linear elastic or nonlinear interfacial stress analyses and test results (Smith and Teng 2002a, b). Further research has shown that the plate end debonding/concrete cover separation can be easily prevented by using additional anchors such as FRP Ujackets or nails at the FRP plate ends (Figure 2). The installation of such anchors at the plate ends is very convenient in practice. Therefore, both the specification and the standard proposed the following clause to avoid plate end debonding/concrete cover separation: ¡°The tension face FRP plates/sheets should be extended to the supports. FRP Ujackets should be installed at the ends of FRP plates/sheets. The width and thickness of FRP Ujackets should not be less than half of the width and thickness of the tension face FRP plates/sheets.¡±
(a) FRP Ujacketing (b) Nail anchors Figure 2 Additional anchors for preventing plate end debonding If there are difficulties in installing such plate end anchors, it was recommended that the conservative model proposed by Smith and Teng (2002b) be used to calculate the debonding strength. But the strength of FRP may not be fully used in such cases. Critical Diagonal Crack Debonding The main cause of CDC debonding failure is the low shear capacity of the beam. An effective method for preventing CDC debonding is thus to avoid shear failure of a beam by increasing its shear capacity. RC beams are usually designed following the principle of ¡°strong shear weak bending¡± to avoid the brittle shear failure. This principle also applies to FRP strengthened concrete beams, i.e. the shear capacity of a strengthened beam should be larger than its flexural capacity after flexural strengthening. Both the specification and the standard adopt this principle to avoid the CDC debonding. Furthermore, additional FRP Ujackets are also required to ensure the shear capacity of the flexurally strengthened beam even if its shear strength is adequate and to increase the ductility in an intermediate crack induced debonding failure (IC debonding). Further details are given in the following sections. Intermediate Crack Induced Debonding For an FRP strengthened RC beam designed to satisfy the principle of ¡°strong shear weak bending¡± and various detailing requirements, flexural cracks will inevitably occur under service load. The initiation and development of flexural cracks result in large interfacial stresses at the FRPtoconcrete interface at both sides of a flexural crack which may lead to interfacial debonding failure. Such debonding failure is referred as Intermediate Crack induced debonding, or IC debonding (Teng et al. 2003b). An IC debonding is caused by the widening of a flexural crack. The contribution of unprestressed FRP to the flexural strength takes place mainly after the yielding of the flexural steel reinforcement which leads to rapid propagation of flexural cracks and large interfacial slips between the FRP and the concrete on both sides of the flexural crack. No efficient method is available yet to avoid IC debonding failures. If the thickness of the FRP plate is significant, IC debonding cannot be avoided even when additional anchors such as U jacketing are used (e.g. Lu 2004, Teng et al. 2002a). Therefore, IC debonding should be considered as one of the controlling failure modes in the strengthening design of RC beams using tension face FRP sheets. The flexural strength should be calculated by considering the effective FRP tensile stress at IC debonding failure. Based on recent research on the mechanics of IC debonding (Lu 2004, Lu et al. 2004), the effective FRP strain at IC debonding can be calculated as:
in which E_{f } (MPa) is the elastic modulus of the FRP plate; t_{f} (mm) is the thickness of the FRP plate; L_{d} (mm) is the distance from the plate end to the section where the FRP plate is fully used (Figure 3); b_{w} is the FRPtoconcrete width ratio; b_{f} is the width of the FRP plate; b_{c} is the width of the concrete beam; and f_{t} (MPa) is the average tensile strength of the concrete.
Figure 3 Definition of L_{d} It may be noted that the concrete tensile strength in Eq. 1 is the average strength from tests. In the Chinese concrete design code, the design tensile strength is about half of the average strength. This can lead to overconservative designs when the concrete design tensile strength is used. Consequently, the standard proposes some modifications to the coefficients in Eq. 1 to balance safety and economy. Furthermore, although FRP Ujackets cannot completely prevent the occurrence of IC debonding, they may increase the ultimate failure load to certain extent. According to Zhuang (2005), properly installed FRP Ujackets can increase the FRP strain at an IC debonding failure by about 30%. Because of the limitation of available experience, the standard proposes that the contribution of U jackets to the IC debonding strength should not be considered if they do not meet the detailing specifications. However, any use of FRP Ujackets is beneficial because they can significantly improve the ductility in an IC debonding failure. Finally, the standard adopts the following equation to calculate the FRP strain at IC debonding
where, f_{td} (MPa) is the design tensile strength of concrete; l is a factor considering the anchorage of the tension face FRP plate. l =1.0 in all cases, but = 1.3 (which may be increased to 1.5 if the designer has sufficient experience) when FRP Ujackets are used and meet the following detailing requirements: ¡°FRP Ujackets are installed within the whole length of L_{d} as in Figure 3. The height of Ujackets is not smaller than half of the beam height. It is preferable that the Ujackets are extended to the full height of the beam or to the bottom of the slab. The width and thickness of Ujackets shall not be smaller than half of the width and thickness of the tension face FRP plate respectively¡± (Figure 4).
Figure 4 FRP Ujackets for flexural strengthening At IC debonding failure, the extreme fibre of the compressive concrete may not reach its ultimate strain e_{cu}. The concrete strength in the compression zone cannot be fully developed in this case and the compression force resisted by the concrete will be overestimated if the compressive stress block used in the design of normal RC beams is adopted. Based on some theoretical analyses, the standard adopts a factor w to consider the reduction of the compressive concrete strength in such a case. Consequently, the bending moment capacity at IC debonding failure for an RC beam with tension face FRP plates is calculated according to the following equations:
where, b is the width of a rectangular crosssection; h_{0} is the effective height of the section which is the distance from the top of the beam to the centroid of the tensile reinforcements; x is the height of the rectangular concrete compressive stress block; A_{s} is the crosssectional area of the tensile steel reinforcements; A_{f} is the crosssectional area of the tension face FRP plate; f_{c }is the design compressive strength of concrete; f_{y} is the design strength of steel reinforcement; s_{f,md} is the design strength of FRP for the ultimate limit state; f_{fd }is the FRP design tensile strength; and e_{fe,m2} is the effective FRP strain at IC debonding failure which can be obtained from Eq. 2 and should be not be smaller than 0.5e_{fe,m1} in which e_{fe,m1} is the FRP strain when the outmost concrete fibre reaches the crushing strain as given by
A comparison with 80 IC debonding test data (Figure 5) shows that the adopted design model is accurate and conservative.
Figure 5. Adopted design model for IC debonding versus test data

DEBONDING FAILURE IN SHEAR STRENGTHENED RC Beams As summarized by Chen and Teng (2003a), common methods for the shear strengthening of concrete beams include side bonding, Ujacketing and wrapping (Figure 6). Ujacketing and side bonding are more commonly used in practice because complete wrapping has difficulties such as the need to cut holes through concrete slabs.
(a) Side bonding (b) Ujacketing (c) Wrapping Figure 6 Common methods for the shear strengthening of RC beams Extensive research has shown that FRP fracture and FRP debonding are the two main failure modes in RC beams strengthened in shear (Chen and Teng 2003a, b). The FRP fibres intersecting a major shear crack are vulnerable to debonding failure when the crack widens. For almost all beams strengthened with side bonding and most beams strengthened with U jacketing, the shear capacity of the strengthened beam is controlled by debonding failure unless the ends of the FRP are properly anchored (Chen and Teng 2003a, b). Most existing design models use the superposition principle to calculate the shear capacity of RC beams shear strengthened with FRP, i.e.
in which V_{FRP} is the FRP contribution to the shear capacity and V_{RC} is the shear capacity of the original RC beam. It may be noted that the superposition principle is not precisely applicable here as V_{RC} and V_{FRP} may not reach their peak values simultaneously (Ye et al. 2002, Teng et al. 2002a) but it is still widely adopted for convenience and the same is adopted in the standard. The major task here is thus to determine the FRP contribution to the shear capacity V_{FRP}. The value of V_{FRP} may be estimated from the summation of forces in the FRP stripes intersecting the critical shear crack at the ultimate limit state:
where e_{fi} , E_{fi} and A_{fi} are the strain, elastic modulus and crosssectional area of the i^{th} FRP strip; A_{f} is the total crosssectional area of FRP intersecting the critical shear crack; a is the angle between the FRP fibre direction and the longitudinal axis of the beam; e_{fe} is the average strain for FRP intersecting the shear crack at the ultimate limit state.
Figure 7 FRP Strain distribution along the critical shear crack If the critical shear crack has an angle q with the longitudinal axis of the beam, Eq. 6 can be rewritten as:
where the factor of 2 applies when FRP is bonded on both sides of the beam; h_{fe} is the effective bond height of FRP as defined in Figure 8; and w_{f} and s_{f} are the width and the centertocenter spacing of FRP stripes respectively.
Figure 8 Effective bond height h_{fe} Experimental and analytical studies have shown that the average strain of FRP intersecting the shear crack e_{fe} is mainly controlled by the following factors: the strength of concrete, the FRP strengthening method, the bond length and stiffness of FRP plates, and the shape of shear cracks. Lu et al. (2004) recently investigated the average FRP strain e_{fe} at debonding failure using a rigorous FRPtoconcrete interface bondslip model (Lu et al. 2005a). They considered 4 typical shear crack shapes and found that Chen and Teng¡¯s (2003b) model developed based on their bond strength model (Chen and Teng 2001) is in good agreement with the numerical results (Lu et al. 2005b). Nevertheless, Lu (2004) proposed the following alternative but simpler model
where _{ } is the FRP strain when the bond length is infinite and K_{v} is the FRP bond length effect factor that is expressed as:
in which the bond length ratio l is the ratio of the FRP effective bond height h_{fe} to the FRP effective bond length L_{e} which is expressed as
The FRP strain _{ } for an infinite bond length is given as (Lu et al. 2005a):
During the process of developing the standard, the factors in the above equations were modified to consider the difference between the average and design concrete strengths whilst some simplifications were made. Assuming that the angle of the critical shear crack is 45¡ã, the standard finally adopts the following design model:
where t_{ave} is the average bond strength between FRP and concrete; and the shear strengthening method factor f = 1.0 for sidebonding and 1.3 for Ujacketing.
Figure 9 Effective FRP bond area The proposed design equation (Eq. 9) for calculating V_{FRP} has been compared with 35 Ujacketing and 34 sidebonding test data. Figure 10 shows that the simple design model is in good agreement with test data and conservative.
(a) FRP Ujacketing (b) Side bonding Figure 10 Debonding strengths of FRP shear strengthened RC beams: adopted model versus test data CONCLUSIONS This paper has presented a summary of some recent numerical and experimental research on FRPtoconcrete interfacial behaviour and debonding failures in FRP strengthened RC beams, and how some of these results have been modified for adoption into the Chinese Standard for FRP in Civil Engineering which is being developed. Comparisons of these simplified design models with test data have shown that the adopted design provisions are conservative and correlate well with the test data. ACKNOWLEDGMENTS The authors would like to gratefully acknowledge the financial support provided by the Natural Science Foundation of China (National Key Project No. 50238030) and the Royal Society through Royal SocietyNSFC ChinaUK Joint Project (Grant No. IS 16657). They would also like to thank Professor JinGuang Teng at The Hong Kong Polytechnic University for collaborative research over many years, which has formed an important part of the theoretical basis of the design models described in this paper. References CECS (China Association for Engineering Construction Standardization ) 146 (2003). Technical Specification for Strengthening Concrete Structure with Carbon Fiber Reinforced Polymer Laminate, China Planning Press, Beijing, China. Chen, J.F. and Teng, J.G. (2003a). ¡°Shear capacity of FRP strengthened RC beams: fibre reinforced polymer rupture¡±, Journal of Structural Engineering, ASCE, 129(5), 615625. Chen, J.F. and Teng, J.G. (2003b). ¡°Shear capacity of FRP strengthened RC beams: FRP debonding¡±, Construction and Building Materials, 17(1), 2741. Lu X.Z. (2004). Studies of FRPConcrete Interface. PhD Thesis, Tsinghua University, Beijing, China. Lu X.Z., Ye L.P., Teng J.G., Huang Y.L., Tan Z. and Zhang Z.X. (2004). ¡°Recent research on interfacial behavior of FRP sheets externally bonded to RC structures¡±, Proc. 2^{nd} International Conference on FRP Composites in Civil Engineering, Adelaide, Australia, 389398. Mohamed Ali M. S., Oehlers D. J. and Bradford M. A. (2002). ¡°Interaction between flexure and shear on the debonding of RC beams retrofitted with compression face plates¡±, Advances in Structural Engineering, 5(4), 223230. Oehler, D.J., Park, S.M. and Mohamed Ali, M. S. (2003). ¡°A structural engineering approach to adhesive bonding longitudinal plates to RC beams and slabs¡±, Composites: Part A, 34(12), 887¨C897. Smith S.T. and Teng J.G. (2002a). ¡°FRPstrengthened RC structures, I: review of debonding strength models¡±, Engineering Structures, 24 (4), 385395. Smith S.T. and Teng J.G. (2002b). ¡°FRPstrengthened RC structures, II: assessment of debonding strength models¡±, Engineering structures, 24 (4), 397417. Teng J.G., Chen J.F., Smith S.T. and Lam L. (2003a). ¡°Behaviour and strength of FRPstrengthened RC structrues: a stateoftheart review¡±, Proceedings of the Institution of Civil EngineersStructures and Buildings, 156 (1), 5162. Teng J.G., Zhang J.W. and Smith S.T. (2002b). ¡°Interfacial stresses in reinforced concrete beams bonded with a soffit plate: a finite element study¡±, Construction and Building Materials, 16 (1), 114. Teng, J.G., Chen, J.F., Smith, S.T. and Lam, L. (2002a). FRP strengthened RC Structures, Wiley, Chichester, U.K. Teng, J.G., Smith, S.T., Yao, J. and Chen, J. F. (2003b). ¡°Intermediate crackinduced debonding in RC beams and slabs¡±. Construction and Building Materials, 17(6&7), 447462. Ye, L.P., Yue, Q.R., Zhao, S.H. and Li, Q.W. (2002). ¡°Shear strength of reinforced concrete columns strengthened with carbonfiberreinforced plastic sheet¡±, Journal of Structural Engineering, ASCE, 128 (12), 15271534. Zhuang, J.B. (2005). Experimental Research on RC Beams Strengthened with Prestressed CFRP Sheets. MSc Thesis, Tsinghua University, Beijing, China. 