In this paper we present some numerical results concerning the identification of material parameters in linear elasticity by dealing with small deformations. On the basis of a precise example different aspects of the parameter estimation problem are considered. We deal with practical questions such as the experimental design for obtaining sufficient data for recovering the unknown parameters as well as questions of treating the corresponding inverse problems numerically. Two algorithms for solving these problems can be introduced and extensive numerical case studies are presented and discussed.

In this paper we present some numerical results concerning the identification of material parameters in linear elasticity by dealing with small deformations. On the basis of a precise example different aspects of the parameter estimation problem are considered. We deal with practical questions such as the experimental design for obtaining sufficient data for recovering the unknown parameters as well as questions of treating the corresponding inverse problems numerically. Two algorithms for solving these problems can be introduced and extensive numerical case studies are presented and discussed.

Cette thèse porte sur l’étude de la déformation de surface (petite et grande déformation) pouvant être détectée en utilisant la méthode de l’interférométrie "InSAR " pour le traitement des images SAR (Synthetic Aperture Radar, bande C : λÉ = 5.6 cm) et signal associé à synthèse d'ouverture. Les nouveaux développements des techniques de traitement InSAR permettent le suivi de la déformation en surface avec une précision de l'ordre millimétrique. Les traitements dites conventionnels de l'InSAR utilisent une paire d'images SAR ("Maitre" et "Esclave") afin de mesurer la différence de phase entre les deux prises de la même scène d'image à des moments différents. Les incertitudes dans les mesures obtenus à partir du traitement conventionnel de l'InSAR sont nombreuses : la décorrelation dans le signal en raison du délai du à l'atmosphère, la contribution topographique et les positions orbitales sont les handicaps majeurs de cette technique. En 2001, Ferretti et al. ont introduit une nouvelle méthode appelée Permanent Scatterer (PS-InSAR) également connue sous le nom de Persistent Scatterer. Pour cette méthode, nous utilisons une série d'images, dont une dite esclave pour construire des interférogrammes avec la même image dite « Maître ». Cette méthode permet d'améliorer le signal de visé (LOS) en terme de correlation pour chaque pixel (PS) en utilisant les meilleurs réflecteurs donnant une corrélation maximale (à partir de l'amplitude et/ou la phase) dans le temps et dans l'espace. Un grand nombre d'algorithmes a été élaboré à cet effet en utilisant le même principe (des variantes) décrit auparavant. En 2002, Berardino et al. publient un nouveau algorithme développé pour le suivi de la déformation en surface en se basant sur les interférogrammes produits à partir des couples d’image SAR ayant une petite séparation spatial (SBAS) de la ligne de base.Dans cette thèse, les techniques InSAR sont appliquées pour différents cas d’étude allant de la petite déformation en surface telle que: 1) Un affaissement dans une zone de puits de pétrole, 2) des glissements de terrain dans une zone urbaine, et 3) la déformation lente à travers les zones de failles des zones sismiques. Afin d'étudier la petite déformation j'opte pour l’utilisation des deux algorithmes (PS et SBAS) dit de traitement multi-temporelle de l’InSAR incorporés dans le logiciel StaMPS (Hooper, 2008). Ainsi, j’ai pu calculer la méthode de combinaison ou hybride entre PS et SBAS et ce, pour toutes les études de cas présentées dans cette thèse. Par ailleurs, certains logiciels en libre accès sont utilisés tout au long de cette thèse tel que, Roi-pac (Rosen et al., 2004) pour aligner les images SAR ainsi que Doris (Kampes et al., 2003) pour calculer interférogrammes à partir de images SAR.[...] / This thesis aims at the study of small to large surface deformation that can be detected using the remote sensing interferometric synthetic aperture radar (InSAR) methods. The new developments of InSAR processing techniques allow the monitoring of surface deformation with millimeter surface change accuracy. Conventional InSAR use a pair of SAR images (“Master” and “Slave” images) in order to measure the phase difference between the two images taken at different times. The uncertainties in measurements using the conventional InSAR due to the atmospheric delay, the topographic changes and the orbital artifacts are the handicaps of this method. The idea of InSAR method is to measure the phase difference between tow SAR acquisitions. These measure refere to the ground movment according to the satellite position. In interferogram the red to blue colors refere to the pixel movement to or far from the satellite position in Line-Of-Sight (LOS) direction. In 2000’s, Radar spacecraft have seen a large number of launching mission, SAR quisitions and InSAR applicability have seen explosion in differents geophysical studies due to the important SAR datas and facility of data accessibity. This SAR-mining needs other type and generation of InSAR processing.In 2001, Ferretti and others introduce a new method called Permanent Scatterer InSAR (PS) that is based on the use of more than one Slave image in InSAR processing with the same Master image. This method allows enhancing the LOS signal for each pixel (PS) by using the best time and/or space-correlated signal (from amplitude and/or from phase) for each pixel over the acquisitions. A large number of algorithms were developed for this purpose using thesame principle (variantes). In 2002, Berardino et al developed new algorithm for monitoring surface deformation based on the combination of stack of InSAR results from SAR couples respecting small baseline (SB) distance. Nowadays, these two methods represent the existing time series (TS) analysis of SAR images approaches. In addition, StaMPS software introduced by Hooper and others, in 2008 is able to combine these two methods in order to take advantages from both of this TS approaches in term of best signal correlation and reducing the signal noise errors. In this thesis, the time series studies of surface changes associate to differents geophysical phenomena will have two interest: the first is to highlight the PS and SBAS results and discuss the fiability of obtained InSAR signal with comparation with the previous studies of the same geophysical case or observations in the field and in the second time, the combined method will also validate the results obtained separately with differents TS techniques. The validation of obtained signal is assured by these two steeps: Both of PS and SBAS methods should give relatively the same interferograms and LOSdisplacement signal (in term of sign and values), in addition these results will be compared with the previous studies results or with observations on the field.In this thesis, the InSAR techniques are applied to different case-studies of small surface deformation [...]

This thesis aims at the study of small to large surface deformation that can be detected using the remote sensing interferometric synthetic aperture radar (InSAR) methods. The new developments of InSAR processing techniques allow the monitoring of surface deformation with millimeter surface change accuracy. Conventional InSAR use a pair of SAR images ("Master" and "Slave" images) in order to measure the phase difference between the two images taken at different times. The uncertainties in measurements using the conventional InSAR due to the atmospheric delay, the topographic changes and the orbital artifacts are the handicaps of this method. The idea of InSAR method is to measure the phase difference between tow SAR acquisitions. These measure refere to the ground movment according to the satellite position. In interferogram the red to blue colors refere to the pixel movement to or far from the satellite position in Line-Of-Sight (LOS) direction. In 2000's, Radar spacecraft have seen a large number of launching mission, SAR quisitions and InSAR applicability have seen explosion in differents geophysical studies due to the important SAR datas and facility of data accessibity. This SAR-mining needs other type and generation of InSAR processing.In 2001, Ferretti and others introduce a new method called Permanent Scatterer InSAR (PS) that is based on the use of more than one Slave image in InSAR processing with the same Master image. This method allows enhancing the LOS signal for each pixel (PS) by using the best time and/or space-correlated signal (from amplitude and/or from phase) for each pixel over the acquisitions. A large number of algorithms were developed for this purpose using thesame principle (variantes). In 2002, Berardino et al developed new algorithm for monitoring surface deformation based on the combination of stack of InSAR results from SAR couples respecting small baseline (SB) distance. Nowadays, these two methods represent the existing time series (TS) analysis of SAR images approaches. In addition, StaMPS software introduced by Hooper and others, in 2008 is able to combine these two methods in order to take advantages from both of this TS approaches in term of best signal correlation and reducing the signal noise errors. In this thesis, the time series studies of surface changes associate to differents geophysical phenomena will have two interest: the first is to highlight the PS and SBAS results and discuss the fiability of obtained InSAR signal with comparation with the previous studies of the same geophysical case or observations in the field and in the second time, the combined method will also validate the results obtained separately with differents TS techniques. The validation of obtained signal is assured by these two steeps: Both of PS and SBAS methods should give relatively the same interferograms and LOSdisplacement signal (in term of sign and values), in addition these results will be compared with the previous studies results or with observations on the field.In this thesis, the InSAR techniques are applied to different case-studies of small surface deformation [...]

Cette étude a pour objectifs la caractérisation expérimentale des frottements saccadés dans les matériaux granulaires modèles constitués des billes de verre monodisperses en compression triaxiale drainée et l'identification des paramètres de contrôle. Cinq paramètres macroscopiques caractérisent ces frottements saccadés : la chute de déviateur et la contraction volumique, l'intermittence de déformation axiale, le module d'Young et le coefficient de Poisson. Les frottements saccadés affectent simultanément le déviateur et la déformation volumique. Le comportement macroscopique est globalement contractant tandis que le matériau tend vers un état limite critique en grandes déformations, à la manière des sables lâches. Cependant il présente localement, dans les phases de blocage qui suivent immédiatement les ruptures temporaires, le comportement dilatant des sables denses, qui obéit à une relation contrainte-dilatance linéaire et unique. Les frottements saccadés disparaissent au-delà d'une vitesse critique d'écrasement axial, qui dépend de la contrainte de confinement et de la taille des grains. Le module d'Young dynamique par propagation d'ondes varie avec la contrainte de confinement selon une loi de puissance. Le module d'Young quasi-élastique au départ des phases de blocage est constant à l'intérieur du domaine élastique, de même que le coefficient de Poisson. Le suivi par granulométrie laser et par analyse d'images des matériaux après un ou plusieurs essais triaxiaux permet de suivre l'évolution de la taille moyenne et de la forme des grains. Tandis que les instabilités par saccade disparaissent suite à un certain nombre d'essais, on observe, simultanément à une légère diminution du volume moyen, l'apparition progressive de populations d'objets non sphériques par une fusion des grains analogue au frittage. / The objectives of this study are the experimental characterisatino of the stick-slip instabilities in a model granular material and the identification of relevant control parameters. As monodisperse glass beads are subjected to drained triaxial compression tests, five macroscopic parameters characterize the stick-slip phenomenon: the deviator drop, the jump in volumetric contraction, the intermittence of the axial strain, Young’s modulus and Poisson’s ratio. The stick-slip events simultaneously affect the deviator stress and the volumetric strain. While the global material behavior is that of a loose sand, gradually contracting and hardening as it approaches its large strain critical state, its response in the “stick” phases immediately following the “slip” instabilities is similar to that of dense, dilatant sands, with a unique, linear stress-dilatancy relationship. Stick-slip events disappear beyond a critical axial strain rate, depending on the confining stress and on the grain diameter. The Young modulus associated to wave propagation varies with the confining stress according to a power law. The quasi-elastic modulus measured at the beginning of the stick phase is constant inside the elastic domain, as well as the Poisson ratio. The evolution of grain size and shape after one or several triaxial tests is monitored by laser granulometry and image analysis. The gradual vanishing of stick-slip events, on repeating the tests, is likely related to the global decreasing trend of average particle volume and to the formation of non-spherical objects, apparently by some phenomenon analogous to sintering.