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A mathematical model is developed for quantification of aquifer deformation due to ground-water withdrawal and, with some modifications, is potentially applicable to petroleum reservoirs. A porous medium saturated with water is conceptually treated in the model as a nonlinearly viscous fluid continuum. The model employs a new three-dimensional extension, made in this thesis, of Helm's poroviscosity as a constitutive law governing the stress-strain relation of material deformation and Gersevanov's generalization of Darcy's law for fluid flow in porous media. Relative to the classical linear poroelasticity, the proposed model provides a more realistic tool, yet with greater simplicity, in modeling and prediction of aquifer movement. Based on laboratory consolidation tests conducted on clastic sedimentary materials, three phases of skeletal compaction are recognized. They are referred to as "instantaneous compression", "primary consolidation" and "secondary compression" according to Terzaghi and Biot's theory of poroelasticity. Among the three modes of consolidation, material behavior during the secondary compression phase has a nonlinear stress-strain relationship and is strongly time-dependent, exhibiting a phenomenon often known as "creep". In poroelasticity, the primary and secondary compressions have been conceptually considered as two separate physical processes that require two sets of material parameters to be evaluated. In contrast, the proposed poroviscosity model is a unified theory of time-dependent skeletal compression that realistically describes the physical phenomena of sediment compression as one single transient process. As a general model, two sets of governing equations are formulated for Cartesian and cylindrical coordinates, respectively, and allow for mechanical anisotropy and the assumption of principal hydraulic directions. Further simplifications of the governing equations are formulated by assuming mechanical isotropy, irrotational deformation and mechanical axisymmetry, which are more suitable for field applications. Incremental forms of the governing equations are also provided. / Ph. D.

Newtonian theory was applied, in this analysis, to the elliptic cone segment at angles of attack and sideslip. Closed form expressions for the aerodynamic coefficients and static stability derivatives were obtained. Expressions for the full and half conic bodies were given and approximate expressions were given for the half cone case. The circular cone results were obtained as a special case of the general results. Comparisons of the theoretical calculations with experimental results at hypersonic speeds were made of the aerodynamic coefficients and static derivatives for several conic segments. Generally, good agreement was observed for specified ranges of fineness ratios and angles of attack. / Master of Science