published_or_final_version / Civil Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / abstract / Civil Engineering / Doctoral / Doctor of Philosophy

Three-dimensional acoustic propagation in shallow water waveguides is studied using the longitudinally invariant finite element method. This technique is appropriate for environments with lateral variations that occur in only one dimension. In this method, a transform is applied to the three-dimensional Helmholtz equation to remove the range-independent dimension. The finite element method is employed to solve the transformed Helmholtz equation for each out-of-plane wavenumber. Finally, the inverse transform is used to transform the pressure field back to three-dimensional spatial coordinates. Due to the oscillatory nature of the inverse transform, two integration techniques are developed. The first is a Riemann sum combined with a wavenumber sampling method that efficiently captures the essential components of the integrand. The other is a modified adaptive Clenshaw-Curtis quadrature. Three-dimensional transmission loss is computed for a Pekeris waveguide, underwater wedge, and Gaussian canyon. For each waveguide, the two integration schemes are compared in terms of accuracy and efficiency. / text

Advection-dispersion is generally solved numerically with methods that treat the problem from one of three perspectives. These are described as the Eulerian reference, the Lagrangian reference or a combination of the two that will be referred to as Eulerian-Lagrangian. Methods that use the Eulerian-Lagrangian approach incorporate the computational power of the Lagrangian treatment of advection with the simplicity of the fixed Eulerian grid. A modified version of a relatively new adaptive Eulerian-Lagrangian finite element method is presented for the simulation of advection-dispersion. Advection is solved by an adaptive technique that automatically chooses a local solution technique based upon a criterion involving the spatial variation of the gradient of the concentration. Moving particles (the method of characteristics; MOC) are used to define the concentration field in areas with significant variation of the concentration gradient. A modified method of characteristics (MMOC) called single-step reverse particle tracking is used to treat advection in areas with fairly uniform concentration gradients. As the simulation proceeds, the adaptive technique, as needed to maintain solution accuracy and optimal simulation efficiency, adjusts the advection solution process by inserting and deleting moving particles to shift between MMOC and MOC. Dispersion is simulated by a finite element formulation that involves only symmetric and diagonal matrices. Despite evidence from other investigators that diagonalization of the mass matrix may lead to poor solutions to advection-dispersion problems, this method seems to allow "lumping" of the mass matrix by essentially decoupling advection and dispersion. Based on tests of problems with analytical solutions, the method seems capable of reliably simulating the entire range of Peclet numbers with Courant numbers that range to 15.

This research is an investigation into two different aspects of the faulting process. The first part of the study focuses on the initial stages of fault formation, while the second analyzes the deformation produced by an existing fault. The section on fault formation is an attempt to determine whether slip on an existing fault has a significant effect on the formation of subsequent faults. A two-dimensional elastic finite element technique is used to examine the system of stresses produced by slip on an initial fault, assuming that deformation occurs either elastically or by brittle failure. A Mohr-Coulomb failure criterion is used to determine the most likely region of secondary fault initiation. A strain energy criterion is then used to find the preferred direction of fault propagation. The study on fault formation is subdivided into two sections representing two idealized tectonic environments: purely extensional and purely compressional. The section on extensional fault formation explains the prevalence of grabens in extensional tectonic regimes as a consequence of the stress perturbations due to slip on an initial normal fault. Slip on the initial fault produces a region of high proximity to failure at the surface of the downthrown block. A secondary fault would be expected to initiate in this region. The direction of propagation of this fault that most effectively relieves the shear stress (and therefore minimizes the total strain energy) is toward the initial fault, resulting in an antithetic orientation, or graben. The width of the graben is found to be controlled by the depth of the initial normal fault, rather than the depth to a change in material properties. The study of compressional fault formation indicates that, except for steeply-dipping faults, the presence of an initial thrust fault tends to suppress the formation of other faults in its vicinity. However, if a secondary fault initiates near an initial thrust fault, the direction in which it propagates will be influenced by the presence of the initial fault. The way in which it is influenced is dependent on the fault dip. The final part of this study examines the deformation produced by repeated earthquake cycles on the San Andreas fault in southern California. A three-dimensional, time-dependent kinematic finite element model is used to investigate the influence of slip distribution and rheological parameters on the predicted horizontal and vertical deformation. The models include depth-varying rheological properties and power-law viscoelastic behavior. The predicted deformation patterns are fairly sensitive to the parameters used in this study. Of particular importance is the calculation of vertical uplift rate since, in many cases, models that cannot be distinguished from each other on the basis of horizontal deformation may produce distinctive vertical uplift patterns.

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In the research undertaken a finite element formulation has been developed for an elastodynamic problem using a least squares approach. The special requirements of the problem demanded a study of suitability of various elements. The emergence of the final element is a result of both theoretical and numerical study of three different elements. The approximation function is assumed on the basis of the order of the governing differential equations. Then the square of the error resulting from the approximate solution is minimized over the entire domain as well as the boundaries in the same functional. The element equation emerging from the formulation does not yield a singular stiffness matrix, since the boundary conditions are already taken into account in the element equation. The formulation presented in this thesis is only for the normal propagation of phi-wave. A finite element code has been developed based on the new formulation.

No description available.

No description available.

No description available.