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Numerical modelling of non-destructive testing of buried waveguides

Abstract : Various elements of civil engineering structures are elongated and partially embedded in a solid medium. Guided waves can be used for the nondestructive evaluation (NDE) of such elements. The latteris therefore considered as an open waveguide, in which most of waves are attenuated by leakage losses into the surrounding medium. Furthermore, the problem is difficult to solve numerically because of its unboundedness. In aprevious thesis, it has been shown that the semi-analytical finite-element method (SAFE) and perfectly matched layers(PML) can be coupled for the numerical computation of modes. It yields three types of modes: trapped modes,leaky modes and PML modes. Only trapped and leaky modes are useful for the post-processing of dispersion curves. PML modes are non-intrinsic to the physics. The major aim of this thesis is to obtain the propagated and diffracted fields, based on modal superpositions on the numerical modes. First, we show that the three types of modes belong to the modal basis. To guarantee the uniqueness of the solutions an orthogonality relationship is derived on the section including the PML. The forced response can then be obtained very efficiently with a modal expansion at any point of the waveguide. Modal expansions are also used to build transparent boundaries at the cross-sections of a small finite-element domain enclosing a defect, thereby yielding the diffracted field. Throughout this work, we study whether solutions can be obtained with modal expansions on leaky modes only, which enables to reduce the computational cost. Besides, solutions are obtained at high frequencies (which are of interest for NDE) and in tridimensional waveguides, which demonstrates the generality of the methods. The second objective of this thesis is to propose an imaging method to locate defects. The topological imaging method is applied to a waveguide configuration. The general theoretical framework is recalled, based on constrained optimization theory. The image can be quickly computed thanks to the modal formalism. The case of a damaged waveguide is then simulated to assess the influence on image quality of the emitted field characteristics (monomodal, dispersive or multimodal)and of the measurement configuration.
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Matthieu Gallezot. Numerical modelling of non-destructive testing of buried waveguides. Acoustics [physics.class-ph]. École centrale de Nantes, 2018. English. ⟨NNT : 2018ECDN0040⟩. ⟨tel-01963534⟩

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