Keywords: fibre-reinforced plastics strengthening, spectral elements, debonding, damage identification.

Advanced composite materials are increasingly used in the strengthening of reinforced concrete (RC) structures. The use of externally bonded strips made of fibre-reinforced plastics (FRP) as a strengthening method has gained widespread acceptance in recent years since it has many advantages over the traditional techniques, especially because of the high strength and modulus of elasticity, improved durability, and low weight of the composite material. Failure of FRP-strengthened RC beams may take a variety of forms including all those associated with conventional concrete beams. However, unfortunately, this strengthening method is often associated with a brittle and sudden failure caused by some form of FRP bond failure. This kind of failure is produced in the form of cover delamination, i.e., along the plane of the steel reinforcement, or FRP delamination, i.e., in the plane along the FRP-concrete interface. Furthermore, failure may be originated at the termination of the FRP material and propagate towards the midspan or in the vicinity of flexural cracks in the RC beam and propagate towards the FRP termination. Hence, flexural cracking of the RC beam has a major influence on the overall response of the strengthened member, and it affects the distribution of the stresses in the various constituents of the strengthened member. In addition, this failure mode will affect the dynamic response of the beam by altering its natural frequencies. As a result, considerable analytical, numerical and experimental efforts should be made to capture these phenomena. An optimization method based on spectral elements is proposed here for detection of local debonding in RC beams externally strengthened with FRP. Although the proposed approach is not a conventional finite element (FE) method, its structure is perfectly adaptable to the displacement-based FE technique. For its application, the dynamic field equations are transformed to the frequency domain by using a discrete Fourier transform (DFT) and then solved exactly or almost exactly in the frequency domain.

The two main characteristics of the proposed approach are its simplicity and its ability in accurate high-frequency modelling. A first approach to identify debonding damage based on the proposed model has been implemented in a model updating framework. More future studies should be carried out about its applicability as a damage detection tool.

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