Academic literature on the topic 'Anisotropic medium'

Les tunnels profonds sont souvent construits dans les roches sédimentaires et métamorphiques stratifiées qui présentent habituellement des propriétés anisotropes en raison de leur structure et des propriétés des constituants. Le présent travail vise à étudier les tunnels profonds dans un massif rocheux anisotrope élastique en portant une attention particulière sur les effets des couplages hydromécaniques par des approches analytiques et numériques. Une solution analytique pour un tunnel creusé dans un massif rocheux anisotrope saturé est développée en tenant compte du couplage hydro-mécanique dans le régime permanent. Cette solution analytique est utilisée pour réaliser une série d’études paramétriques afin d'évaluer les effets des différents paramètres du matériau anisotrope sur le comportement du tunnel. Dans un deuxième temps la solution analytique est élargie pour décrire le comportement du tunnel pendant la phase transitoire hydraulique. Afin de compléter ces études analytiques qui prennent en compte seulement un couplage unilatéral (dans le sens que seul le comportement hydraulique influence le comportement mécanique et pas l’inverse) de l’analyse numérique avec un couplage complet, ont été réalisés. Une application de la solution analytique sur la méthode de convergence-confinement est aussi bien abordée qui peut prendre en compte l'influence du front de taille du tunnel sur le travail du soutènement ainsi que sur le massif. La solution obtenue peut servir comme un outil de dimensionnement rapide des tunnels en milieux poreux en le combinant avec des approches de dimensionnement comme celle de convergence confinement<br>Deep tunnels are often built in the sedimentary and metamorphic foliated rocks which exhibits usually the anisotropic properties due to the presence of the discontinuity. The analysis of rock and liner stresses due to tunnel construction with the assumption of homogeneous and isotropic rock would be incorrect. The present thesis aims to deal with the deep tunnel in anisotropic rock with a particular emphasis on the effects of hydraulic phenomenon on the mechanical responses or reciprocal effects of hydraulic and mechanical phenomena by combining analytical and numerical approach. On that point of view, a closed-formed solution for tunnel excavated in saturated anisotropic ground is developed taking into account the hydromechanical coupling in steady-state. Based on the analytical solution obtained, parametric studies are conducted to evaluate the effects of different parameters of the anisotropic material on the tunnel behavior. The thesis considers also to extend the analytical solution with a time-dependent behavior which takes into account the impact of the pore pressure distribution on mechanical response over time, i.e., one way coupling modeling. In addition, some numerical analysis based on fully-coupled modeling, i.e., two ways coupling, are conducted which are considered as the complete solution for the analytical solution. An application of the closed-form solution on convergence-confinement method is as well referred which can take into account the influence of the tunnel face on the work of the support as well as the massif. The obtained solution could be used as a quick tool to calibrate tunnels in porous media by combining with design approaches such as convergence-confinement method

The linear Boltzmann equation for the transport of neutral particles is investigated with the objective of generating benchmark-quality calculations for homogeneous infinite media. In all cases, the problems are stationary, of one energy group, and the scattering is both isotropic and anisotropic. In the transport problems considered, the Green's function is generally the quantity of interest. The solution is obtained through the use of the Fourier transform method. The numerical inversions use standard numerical techniques, such as Gauss-Legendre quadrature, summation of infinite series, and Euler-Knopp acceleration. The most basic source of neutral particles is the point-beam source, or Green's function source. The Green's function in an infinite medium with isotropic scattering is treated as explained in chapter two. The Green's function in an infinite medium with anisotropic scattering is treated using two different mathematical methods as explained in chapters three and four. The results for both cases is shown in chapter 5.

There are by now many applications of methods based on near- infrared radiation (NIR) used for optical imaging and therapeutic purposes in medical settings. Such optical techniques are appealing in not requiring potentially harmful ionizing radiation, being non-invasive, and generally being easily implementable. Since photons are randomly scattered by cell components, successful use of NIR requires knowledge of the photon trajectories expressed in statistical terminology. Until now the necessary analysis has been based on diffusion theory assuming that the scattering coefficient is an isotropic material property. We analyze the properties of the penetration depth when this assumption is violated. By penetration depth will be meant the depth attained in the turbid medium, given its ultimate emission at the planar surface at a time T , as a function of the degree of anisotropy of the scattering coefficient. Our analysis will be based on a continuous-time random walk formalism. Properties of both time-gated and continuous-wave experiments will be derived.