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Reflection Coefficients in the TM Mode

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Reflection Coefficients in the TM Mode Research institute Research Group GeMMe Department ArGEnCo Faculty of Applied Sciences University of Liege, Belgium Thesis committee Prof. Luc Courard Université de Liège Advisor Prof. Frédéric Nguyen Université de Liège Co-advisor Prof. Eric Pirard Université de Liège President Prof. Jean-Paul Balayssac INSA Toulouse Prof. Andrzej Garbacz Politechnika Warszawska Prof. Jan van der Kruk Forschungszentrum Jülich Prof. André Plumier Université de Liège Funding This research has been supported by the F.R.S.-FNRS research fellow grant FC 84664. Copyright © 2014 Audrey Van der Wielen Citation: Van der Wielen, A. (2014). Detection and characterization of thin layers into concrete with Ground Penetrating Radar. PhD Thesis, University of Liège, Belgium, pp. XXX. Abstract The Ground Penetrating Radar (GPR) is a nondestructive technique increasingly used for the inspection of concrete structures. The method is well suited to study multilayer media, because only a part of the incident energy is reflected at each interface. But the quantitative determination of the thickness and properties of thin embedded layer remains an application under development, in particular when the tests are performed with contact antennas of high frequency. The aim of this work is to contribute to the development of a fast method for the thin layers determination, based on measurements performed with commercial antennas, by proposing an analytical estimation of the reflection coefficient. As a first step, the equations allowing to estimate the reflection coefficient on a simple interface were developed, taking into account the wave spherical reflection in the near field and the lateral wave propagation. Similarly, for thin layers, equations taking into account the multiple reflections on the interfaces can be developed with different approaches. On the basis of the comparison of these equations with simulations of wave propagation, a hybrid model was defined: it allows approaching the reflection coefficient by the most adapted method depending on the thickness and the permittivity of the thin layer. This model was then compared to reflection coefficients obtained by FDTD numerical simulations and laboratory tests. The reflection coefficients were obtained by comparing each measurement to a measurement performed on a metallic sheet embedded at the same depth. The tests were conducted on concrete slabs containing air layers of variable dimensions. Exploiting the spectral analysis of the laboratory tests performed with a single antenna, the use of the model allowed determining the permittivity of the layers and their thickness with respective errors of 0% and 20%. When tests with two antennas (CMPs) were performed, the precision was inferior because additional phenomena appear, including different waves propagating at the surface. Therefore, the proposed method can be applied directly in some precise cases (when a reference measurement on a metallic sheet can be performed), but could be extended to numerous other situations by means of the quantification of the surface phenomena. In this case, it could be applied unaltered, possibly completed by an inversion program, or used as a first step of a more sophisticated method (modelling or full waveform inversion), in order to reduce the space of parameters to investigate. Résumé Le Ground Penetrating Radar (GPR) est une technique d’inspection non destructive de plus en plus utilisée pour inspecter les structures en béton. La méthode est bien adaptée pour étudier des milieux présentant plusieurs couches, car seule une partie de l’énergie incidente est réfléchie à chaque interface. Mais la détermination quantitative de l’épaisseur et des propriétés des couches minces enfouies reste une application en cours de développement, notamment lorsque les essais sont pratiqués avec des antennes de contact à hautes fréquences. L’objectif de ce travail consiste à contribuer au développement d’une méthode rapide de détermination de couches minces sur base de mesures réalisées avec des antennes commerciale, en proposant une estimation analytique du coefficient de réflexion. Les équations permettant d’estimer le coefficient de réflexion sur une interface simple ont été développées dans un premier temps, en tenant compte de la réflexion sphérique des ondes en champ proche et de la propagation de l’onde latérale. De même, pour les couches minces, des équations prenant en compte les multiples réflexions sur les interfaces peuvent être développées de différentes façons. Sur base de la comparaison de ces équations avec des simulations de propagation d’onde, un modèle hybride a été défini : il permet d’approcher le coefficient de réflexion par la méthode la plus adaptée en fonction de l’épaisseur et de la permittivité de la couche mince. Ce modèle a ensuite été comparé à des coefficients de réflexion obtenus par des simulations numériques en FDTD et des essais de laboratoire. Les coefficients de réflexion sont obtenus en comparant chaque mesure à une mesure effectuée sur une feuille métallique enfouie à la même profondeur. Les essais ont été menés sur des dalles de béton contenant des couches d’air d’épaisseur variable. Sur base de l’analyse spectrale des essais de laboratoire réalisés avec une seule antenne, l’utilisation du modèle a permis de déterminer la permittivité des couches et leur épaisseur avec une erreur respective de 0% et 20%. Lorsque des tests à deux antennes (CMPs) sont effectués, la précision est inférieure car des phénomènes additionnels apparaissent, dont différentes ondes se propageant à la surface. La méthode proposée peut donc être appliquée directement dans certains cas précis (lorsqu’une mesure sur une feuille métallique peut être effectuée en comparaison), mais pourrait être étendue à de nombreux autres cas moyennant la quantification des phénomènes de surface. Elle pourrait alors être appliquée telle quelle, éventuellement complétée par un programme d’inversion, ou alors utilisée préalablement à une méthode plus lourde (modélisation ou inversion d’onde complète), afin de réduire l’espace des paramètres à considérer. Acknowledgements First and foremost, I would like to thank my advisors, Luc Courard and Frederic Nguyen, who offered me to work on this project in the first place and supported me during the whole PhD work. They gave me inspired advices and laboratory support and their detailed proofreading of the manuscript helped me to improve the text and structure the chapters. During the last four years, they offered me a total freedom to lead my research, but also involved me into different research, teaching and vulgarization activities. They also encouraged me to take part to various formations and conferences. I am also thankful to the FNRS, for allowing me a research fellow grant, and the ULg for providing an additional funding for the two last months. I am also grateful to every person who has given a few minutes or hours to discuss with me, giving advices allowing to guide my research. Hoping not to forget anyone, I can cite Pierre Gilles and Eric Dondonné, Pierre Tihon, Jonathan Pisane, Jan Van der Kruk, Jamal Rhazi and Bilal Filali, Christophe Geuzaine and Véronique Beauvois and Vlatislav Cerveny. I also think of the members of my thesis committee, Andrzej Garbacz and André Plumier. The experimental part of this thesis would not have been possible without the support of our laboratory team, and especially Amaury. I would also like to thank Lucien Dormal, from the company Ronveaux SA, and Adam Bundhoo , from the company Colas Belgium. The first one provided me with great quality self- compacting concrete slabs for my laboratory tests, and the second one covered my substrate slabs with the optimal asphalt overlay to lead my tests. I would also like to express my deepest gratitude to Carmen Andrade, who welcomed me in the institute Eduardo Torroja in Madrid to carry on my research and the redaction of the thesis. Thanks also to all my colleagues there, who made this stay such a great memory for me. Finally, I would like to thank all the people who have simply supported me during the last four years. I am thankful to my direct colleagues, and especially Astrid, Arnaud, Frederic and Sophie. I also would like to thank the girls of the Wednesday noon running: Julie, Ingrid, Fred and Martine. I may never have started without you! I also wish to say a special thanks to my parents and brother, for their continuously moral and occasionally logistical support. Last but not least, I would like to express my deepest gratitude to the one who was my boyfriend at the beginning of this project, and successively became my fiancé and my husband. François, thank you for your technical help and detailed proofreading, but also for your infinite patience and your indefectible moral support. I don’t think I could have done it without you by my side. Table of contents Introduction 1 Chapter 1 : General context 5 1.1 Pathologies of concrete structures ............................................................................ 5 1.1.1 Steel reinforcement corrosion ........................................................................................ 6 1.1.2 Pathologies leading to concrete disintegration ......................................................... 8 1.1.3 Concrete decay ............................................................................................................... 9 1.1.4 Degradations due to materials incompatibility or non-adhesive interfaces ....... 10 1.2 Non-destructive methods in civil engineering.......................................................
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