Le travail présent est axé sur la simulation numérique et l'analyse de l'interaction des ondes de surface de Rayleigh avec des barrières sismiques verticales (murs souterrains, écrans, tranchées, etc.) ainsi que des champs de pieux dans des modèles de matériaux mécaniques élastiques et plastiques linéaires. Le but de la recherche est d'estimer le degré de protection que les barrières verticales et les champs de pieux fournissent contre les vibrations transférées par les ondes de surface de Rayleigh et générées par diverses sources. L'idée principale de ce type de protection est d'éviter que les ondes sismiques ne transmettent l'énergie des vagues dans la zone protégée, diminuant les amplitudes de déplacements, les vitesses et les accélérations aux points situés derrière la barrière (champ de pieux). Les principaux complexes sans dimension sont formulés. L'attention est portée sur les ondes de Rayleigh car elles peuvent être générées à la fois par des sources de vibrations externes (situées à la surface de la Terre) et internes (situées sous la surface de la Terre) et ses ondes peuvent transmettre une portion significative de l’énergie de source de la vibration.Premièrement, des simulations numériques de l'interaction des ondes de Rayleigh avec les barrières sismiques verticales et les champs de pieux sont effectuées en supposant que le sol et les matériaux de barrière se comportent conformément à la loi de comportement linéaire élastique. Cela concerne les vibrations qui induisent des contraintes de cisaillement dans le sol n'excédant pas 0.00001 lors de leur propagation. Les principaux complexes sans dimension sont formulés sur cette base. Des paramètres géométriques et mécaniques de la barrière (champ de pieux) déterminant l'effet de réduction de vibration sont identifiés. Les résultats obtenus révèlent la validité de cette onde de protection contre les vibrations. En outre, l’approche de l’optimisation de la barrière sismique verticale (qui peut également être étendue au champ de pieux) est adoptée sous forme de différences finies pour des conditions de sol particulières et une fréquence de vibration de conception.Plusieurs modèles de comportement du sol sont analysés et leur validité, ainsi que l'applicabilité à l'approximation du comportement dynamique réel du sol, ainsi que le mécanisme de dissipation d'énergie des vibrations, sont identifiés. Sur la base de cette analyse, modèle de Mohr-Coulomb a été choisie car elle dispose d’une base de données expérimentale étendue pour divers sols et reflète de manière appropriée la réduction du module de cisaillement avec l’augmentation de la contrainte de cisaillement ainsi que les effets de dissipation d’énergie. Par la suite, ce modèle est utilisé dans l'analyse de l'interaction des ondes de Rayleigh avec les barrières verticales et les champs de pieux, en tenant compte du caractère non linéaire de la déformation du sol à différents niveaux de déformation de cisaillement. En conséquence, l'influence du niveau de contrainte de cisaillement sur l'efficacité des moyens de protection contre les vibrations considérés est démontrée et les conditions appropriées pour utiliser ces méthodes sont identifiées dans le cadre de cette recherche. / The present work is focused on numerical simulation (FEM) and analysis of surface Rayleigh wave interaction with vertical seismic barriers (underground walls, screens, trenches, etc.) as well as pile fields within the framework of linear elastic and plastic mechanical material models. The aim of the research is to estimate the degree of protection that vertical barriers and pile fields provide against vibrations transferred by surface Rayleigh waves and generated by various sources. The main idea behind this type of protection is to prevent seismic waves form transmitting wave energy into the protected zone, decreasing the amplitude of displacements, velocities and accelerations at the points behind the barrier (pile field). The attention is paid to Rayleigh waves as they can be generated by both external (located on the Earth's surface) and internal (located beneath the Earth's surface) vibration sources and this type of waves can transfer a significant portion of vibration source energy.First, numerical simulations of Rayleigh wave interaction with vertical seismic barriers and pile fields are performed assuming the soil and barrier materials to behave according to the linearly-elastic constitutive law. This regards the vibrations that induce shear strains in the soil not exceeding 0.00001 during their propagation. Based on this, the principal dimensionless complexes are formulated. Geometrical along with mechanical parameters of the barrier (pile field), that determine vibration reduction effect, are identified. The obtained results reveal the validity of this way of vibration protection. In addition to that, the approach towards vertical seismic barrier optimization (which can also be extended to the pile field) is adopted in finite difference form to use for particular soil conditions and design vibration frequency.Several models of soil behaviour are analysed and their validity as well the applicability to approximate real dynamic soil behaviour along with the mechanism of vibration energy dissipation are identified. Based on this analysis, Mohr-Coulomb constitutive model is selected as it has a broad experimental database for various soils and appropriately reflects shear modulus reduction with an increase in the shear strain as well as energy dissipation effects. Afterwards, this model is used in the analysis of Rayleigh wave interaction with the vertical barriers and pile fields accounting for non-linear character of soil deformation at different shear strain level. As a results, the influence of shear strain level on the effectiveness of the considered ways of vibration protections is shown and the appropriate conditions to use these methods are identified within the scope of this research.

Geophysical research has long been interdisciplinary, with many phenomena on the Earth's surface involving multiple, linked processes that are best understood using a combination of techniques. This is particularly true in the case of grain flows on sand dunes, in which the sedimentary stratification with which geologists are concerned arises from the granular processes investigated by physicists and engineers, and the water permeation that interests hydrologists and soil scientists determines the seismic velocities of concern to exploration geophysicists. In this dissertation, I describe four projects conducted for the degree of Doctor of Philosophy, using a combination of laboratory experimentation, fieldwork, numerical simulation, and mathematical modelling to link avalanching on dunes to its effects on stratification, on the permeation of water, and on seismic surveys. Firstly, I describe experiments on erodible, unbounded, grain piles in a channel, slowly supplied with additional grains, and I demonstrate that the behaviour of the consequent, discrete avalanches alternates between two regimes, typified by their size statistics. Reconciling the `self-organised criticality' that several authors have predicted for such a system with the hysteretic behaviour that others have observed, the system exhibits quasi-periodic, system-spanning avalanches in one regime, while in the other avalanches pass at irregular intervals and have a power-law size distribution. Secondly, I link this power-law size distribution to the strata emplaced by avalanches on bounded grain piles. A low inflow rate of grains into an experimental channel develops a pile, composed of strata in which blue-dyed, coarser grains overlie finer grains. Associating stopped avalanche fronts with the `trapped kinks' described by previous authors, I show that, in sufficiently large grain piles, mean stratum width increases linearly with distance downslope. This implies the possibility of interpreting paleodune height from the strata of aeolian sandstones, and makes predictions for the structure of avalanche-associated strata within active dunes. Thirdly, I discuss investigations of these strata within active, Qatari barchan dunes, using dye-infiltration to image strata in the field and extracting samples across individual strata with sub-centimetre resolution. Downslope increases in mean stratum width are evident, while measurements of particle size distributions demonstrate preferential permeation of water along substrata composed of finer particles, explaining the strata-associated, localised regions of high water content discovered by other work on the same dunes. Finally, I consider the effect of these within-dune variations in water content on seismic surveys for oil and gas. Having used high performance computing to simulate elastic wave propagation in the vicinity of an isolated, barchan sand dune, I demonstrate that such a dune acts as a resonator, absorbing energy from Rayleigh waves and reemitting it over an extensive period of time. I derive and validate a mathematical framework that uses bulk properties of the dune to predict quantitative properties of the emitted waves, and I demonstrate the importance of internal variations in seismic velocity, resulting from variations in water content.