The Method of Moments (MoM) has been widely used for the full-wave electromagnetic analysis of planar multilayered media. However, the MoM is a computationally intensive process and requires considerable computer resources to perform the analysis. Thus, several efficient numerical techniques both in the spectral domain and spatial domain are investigated and further developed in this research. Two fitting procedures, i.e., the Rational Function Fitting Method (RFFM) and the Discrete Complex Image Method (DCIM), are investigated and developed in order to obtain closed-form spatial-domain Green's functions (GFs). Because the subtraction of the surface-wave pole contribution plays an important role for the accurate estimation of the spatial-domain GFs via DCIM, an efficient and accurate surface-wave pole location method is developed to find all the surface-wave poles for general multilayered media. The RFFM can be realized through either the Total Least Square Algorithm (TLSA) or the Vector Fitting (VECTFIT) method. Both the RFFM using VECTFIT and DCIM are detailed in step by step procedures. An efficient and low cost algorithm combining the advantages of DCIM and TLSA is also developed to evaluate the closed-form Green's functions for general multilayered media. A prototype version of the Full-Wave Layered-Interconnect Simulator (UA-FWLIS) was developed by analytically calculating the MoM reaction elements via Cauchy's residue theorem and the Complementary Incomplete Lipschitz-Hankel Integrals in stripline structures. After applying RFFM via VECTFIT to the G-functions, which are directly related to the spectral-domain GFs for microstrip structures, a procedure that is similar to the one used in the previously developed UA-FWLIS for stripline structures can be applied to calculate the MoM reaction elements analytically when the two reaction cells are close (< 0.1λ₀) in the spectral domain via the Electrical Field Integral Equation (EFIE). When the two reaction cells are far enough away (> 0.10.1λ₀), a simple expression for the reaction element can be obtained in the spatial domain via the Mixed Potential Integral Equation (MPIE) by a summation of a few complex image terms for the evaluation of the vector and scalar GFs. An efficient hybrid spectral-spatial method is thus developed to extend UA-FWLIS to microstrip structures. The method is validated by several numerical examples.

The primary focus of this research is to evaluate the time-dependent crack growth in rocks using lab tests and numerical modeling and its application to geologic hazard problems. This research utilized Coconino sandstone and Columbia granite as the study materials and produced the subcritical crack growth parameters in both mode I and II loadings using the rock materials. The mode I loading test employs three different types of fracture mechanics tests: the Double Torsion (DT), the Wedge Splitting (WS), and the Double Cantilever Beam (DCB) test. Each test measured the mode I crack velocity. The DT test indirectly measured the crack velocity using the load relaxation method. The WS and DCB tests directly measured the crack velocity by monitoring using a video recording. The different mode I subcritical crack growth parameters obtained from the three tests are discussed. For the mode II loading test, this study developed a new shear fracture toughness test called the modified Punch-Through Shear (MPTS). The MPTS test conducted at different loading rates produced the mode II subcritical crack growth parameters. These fracture mechanics tests were calibrated and simulated using the distinct element method (DEM) and the finite element method (FEM). DEM analysis employed the particle flow code (PFC) to simulate the mixed mode crack growth and to match with the failure strength envelop of the triaxial compressive tests. FEM analysis employed the Phase2 program to analyze the crack tip stress distribution and the FRANC2D program to calculate the modes I and II stress intensity factors. The fracture mechanics tests and numerical modeling showed well the dependency of the mode II subcritical crack growth parameters according to confining pressure, loading rate, and the mode II fracture toughness. Finally, the UDEC modeling based on DEM is utilized in this study to forecast the long-term stability of the Coconino rock slope, as one of geologic hazards. The fracture mechanics approach is implemented in the program using the modes I and II subcritical crack growth parameters obtained from the lab tests and numerical modeling. Considering the progressive failure of rock bridges due to subcritical crack growth, the UDEC results predicted the stable condition of the Coconino rock cliff over 10,000 years. This result was validated by comparing it with the previous planar failure case.

Methane gas hydrates have attracted significant international interest as a potential future energy resource, but also as a geotechnical hazard for offshore operations related to hydrocarbon recovery. In this context, the abilities to detect the presence of hydrate in marine sediments and to quantify the amount of hydrate contained therein, have become increasingly important over the years. Detection and quantification of hydrates are done on the basis of seismic surveys, which measure indirectly the bulk dynamic properties of large volumes of sediment in situ. Seismic data are then interpreted using an effective medium model, which employs theoretical assumptions to relate wave velocities to gas hydrate content of the sediment. Wave velocity can then be used to infer hydrate concentration levels. A host of such effective medium models exists in the literature. Many of these models have been calibrated on and tested on specific sites, and are not readily transferable to other settings. In addition, many models ignore the existence of heterogeneities of the host sediment, or the inhomogeneous distribution of hydrate within it. These, however, are factors that may have a significant impact on the seismic signature of the sediment-hydrate system, and thus on the predicted quantity of hydrate. This paper presents a review of existing effective medium models and identifies general areas for improvement. A new numerical modelling method is outlined that enhances existing effective medium approaches, by taking explicitly into account different hydrate morphologies within the host sediment.

This thesis concerns the computation of bed adjustments of equilibrium in alluvial meandering streams. It is assumed that the channel centerlines follow sine-generated curves, the banks are rigid, and the steady-state flow is turbulent and sub-critical. The flow width is assumed to remain constant in the streamwise direction, and the flow width-to-depth ratio is large (>=15, say). The bed material is cohesionless and homogeneous. The purpose of the thesis is to develop and test a numerical model for the computation of bed development, given the aforementioned idealized conditions. The model comprises: 1- an initial bed topography generator, to generate the bed at time t = 0 of the calculations; 2- the vertically-averaged hydrodynamic model of Zhang (2007) to calculate the flow fields; and 3- a sediment transport model to relate the bed deformation to the flow. Both the initial bed topography generator (expression of the deformed bed surface) and the numerical sediment transport model based on the sediment transport continuity equation are original and developed entirely by the author. The resulting model is computationally very efficient. In contrast to previous works on the theoretical determination of bed deformation, the beds at the beginning of the calculations may represent any stage of the development process, and not necessarily the initial flat bed. The bed deformation was tested for several test cases, devised on the basis of laboratory runs available in the literature. These include Run ME-2 by Hasegawa (1983) in a 30-degree-channel, Run 3 by Binns (2006) in a 70-degree-channel and the run by Termini (1996) in a 110-degree-channel. The erosion/deposition patterns of the computed equilibrium bed topographies were found to be in reasonable agreement with their measured counterparts. However, as evidenced by the difference plots included in this thesis, in detail there are substantial differences between the computed and measured equilibrium beds, especially in the regions near the banks. As a by-product of the present thesis, the functions representing the parameters required by the hydrodynamic model of Zhang (2007) were also evaluated. In particular, the present results suggest that the coefficient Alpha-q appearing in the expression of the local friction factor (used in the flow model of Zhang 2007) depends on the flow width-to-depth ratio and bed roughness to a much larger extent than previously thought. Considering this, a generalization of the expression of Alpha-q due to El-Tahawy (2004) (and adopted by Zhang 2007 in her model) is proposed. Future work should be carried out to address the application of the present model to real river conditions, including generalizations to irregular meandering plan shapes, unsteady-state flows and non-homogenous bed materials. / Thesis (Ph.D, Civil Engineering) -- Queen's University, 2008-12-19 21:32:06.645

Groundwater is an important resource that is relied on by approximately half of the world’s population for drinking water supply. Source water protection efforts rely on an understanding of flow and contaminant transport processes in aquifers. Bedrock aquifers are considered to be particularly vulnerable to contamination if the overburden cover is thin or inadequate. The objective of this study is to further the understanding of modeling, sampling, and the potential for anthropogenic contamination in fractured bedrock aquifers. Two numerical modeling studies were conducted to examine geochemical groundwater sampling using multi-level piezometers and the role of discretization in a discrete fracture radial transport scenario. Additionally, two field investigations were performed to study the variability of bacterial counts in pumped groundwater samples and the potential for anthropogenic contamination in a bedrock aquifer having variable overburden cover in a semi-urban setting. Results from the numerical modeling showed that choosing sand pack and screen materials similar in hydraulic conductivity to each other and the fractures intersecting the borehole can significantly reduce the required purge volume. Spatiotemporal discretization was found to be a crucial component of the numerical modeling of solute transport and verification of the solution domain using an analytical or semi-analytical solution is needed. Results from the field investigations showed fecal indicator bacterial concentrations typically decrease on the order of one to two orders of magnitude from the onset of pumping. A multi-sample approach that includes collection at early-time during the purging is recommended when sampling fecal indicator bacteria for the purpose of assessing drinking water quality. Surface contaminants in areas with thin or inadequate overburden cover can migrate quickly and deeply into the bedrock aquifer via complex fracture networks that act as preferential pathways. While the presence of fecal indicator bacteria in groundwater samples signifies a possible health risk through human consumption, it was the suite of pharmaceuticals and personal care products that allowed the identification of septic systems and agriculture as the dominant sources of contamination. Land-use planning and source water protection initiatives need to recognize the sensitivity of fractured bedrock aquifers to contamination. / Thesis (Ph.D, Civil Engineering) -- Queen's University, 2011-02-28 17:27:54.806

Water resource infrastructure in cold regions of the world can be significantly impacted by the existence of river ice. Major engineering concerns related to river ice include ice jam flooding, the design and operation of hydropower facilities and other hydraulic structures, water supplies, as well as ecological, environmental, and morphological effects. The use of numerical simulation models has been identified as one of the most efficient means by which river ice processes can be studied and the effects of river ice be evaluated. The continued advancement of these simulation models will help to develop new theories and evaluate potential mitigation alternatives for these ice issues. In this thesis, a literature review of existing river ice numerical models, of anchor ice formation and modeling studies, and of aufeis formation and modeling studies is conducted. A high level summary of the two-dimensional CRISSP numerical model is presented as well as the developed freeze-up model with a focus specifically on the anchor ice and aufeis growth processes. This model includes development in the detailed heat transfer calculations, an improved surface ice mass exchange model which includes the rapids entrainment process, and an improved dry bed treatment model along with the expanded anchor ice and aufeis growth model. The developed sub-models are tested in an ideal channel setting as somewhat of a model confirmation. A case study of significant anchor ice and aufeis growth on the Nelson River in northern Manitoba, Canada, will be the primary field test case for the anchor ice and aufeis model. A second case study on the same river will be used to evaluate the surface ice components of the model in a field setting. The results from these cases studies will be used to highlight the capabilities and deficiencies in the numerical model and to identify areas of further research and model development.

The Alpha Magnetic Spectrometer is an International Space Station Experiment that features a unique nonlinear support system with no previous flight heritage. The experiment consists of multiple straps with piecewise-linear stiffness curves that support a cryogenic magnet in three-dimensional space inside of a vacuum chamber. The stiffness curves for each strap are essentially bilinear and switch between two distinct slopes at a specified displacement. This highly nonlinear support system poses many questions in regards to feasible computational methods of analysis and possible response behavior. This thesis develops a numerical model for a multi-bilinear-spring support system motivated by the Alpha Magnetic Spectrometer design. Methods of analysis applied to the single bilinear oscillator served as the foundation of the model developed in this thesis. The model is developed using MATLAB and proves to be more computationally efficient than ANSYS finite element software. Numerical simulations contained herein demonstrate the variety of response behaviors possible in a multi-bilinear-spring support system, thus aiding future endeavors which may use a support system similar to the Alpha Magnetic Spectrometer. Classic nonlinear responses, such as subharmonic and chaotic, were found to exist.

There is a growing need to better understand the relationship between time, strain rate, and temperature on the load-deformation behaviour of clay soils in engineering applications. These applications may include: infrastructure constructed in northern regions where climate change is a growing concern; disposal of nuclear waste; and, industrial structures, such as furnaces, foundries, and refrigeration plants. Temperature variations may induce changes in internal pressure in the soil, swelling and shrinkage, and affect the mechanical properties of the soil. This thesis presents thermal numerical modeling for two instrumented field sites in northern Manitoba. Thermal conductivity testing on samples from these sites and field data are used to calibrate these thermal numerical models. Various boundary conditions are examined. The capabilities of the models are evaluated to determine if the models adequately simulate and predict changes in temperature in geotechnical structures. A discussion is presented on the strengths and weaknesses in the models and the predictive capabilities of the models. The thesis then shifts into understanding the concepts of thermoplasticity and viscoplasticity and the mathematics relating these concepts. Mathematical models that describe these concepts are examined and compared with traditional soil mechanics approaches. The concepts of thermoplasticity and viscoplasticity are combined in an encompassing elastic thermo-viscoplastic (ETVP) model using a semi-empirical framework. A sensitivity analysis is used to evaluate quantitatively the response of the model. The model is then validated qualitatively against published laboratory data. Applications of the ETVP model are discussed.

Water resource infrastructure in cold regions of the world can be significantly impacted by the existence of river ice. Major engineering concerns related to river ice include ice jam flooding, the design and operation of hydropower facilities and other hydraulic structures, water supplies, as well as ecological, environmental, and morphological effects. The use of numerical simulation models has been identified as one of the most efficient means by which river ice processes can be studied and the effects of river ice be evaluated. The continued advancement of these simulation models will help to develop new theories and evaluate potential mitigation alternatives for these ice issues. In this thesis, a literature review of existing river ice numerical models, of anchor ice formation and modeling studies, and of aufeis formation and modeling studies is conducted. A high level summary of the two-dimensional CRISSP numerical model is presented as well as the developed freeze-up model with a focus specifically on the anchor ice and aufeis growth processes. This model includes development in the detailed heat transfer calculations, an improved surface ice mass exchange model which includes the rapids entrainment process, and an improved dry bed treatment model along with the expanded anchor ice and aufeis growth model. The developed sub-models are tested in an ideal channel setting as somewhat of a model confirmation. A case study of significant anchor ice and aufeis growth on the Nelson River in northern Manitoba, Canada, will be the primary field test case for the anchor ice and aufeis model. A second case study on the same river will be used to evaluate the surface ice components of the model in a field setting. The results from these cases studies will be used to highlight the capabilities and deficiencies in the numerical model and to identify areas of further research and model development.

The magnetic properties and crystal texture of micron-sized, lithographically patterned ferromagnetic/antiferromagnetic (FM/AF) exchange-coupled elements supporting vortex remanent magnetization states were characterized using experimental and numerical modeling techniques. 10umx10um square elements consisting of Ni80Fe20/Ir20Mn80 bilayers prepared on silicon and glass substrates using e-beam lithography and magnetron sputtering were thermomagnetically annealed under various in-plane cooling fields to induce exchange bias. Longitudinal and time-resolved Kerr effect microscopy were employed to measure the quasi-static hysteresis and dynamic response, while X-ray diffraction analysis was used to probe their crystal texture under different deposition and substrate conditions. The FM layer was found to be critical for the development of the necessary texture and spin alignment in the AF for creating interfacial exchange-bias. The exchange-bias field was found to significantly alter the magnetic behavior of the samples, leading to the stabilization of the vortex structure and asymmetric hysteresis loop shift in the quasi-static regime, as well as precessional frequency reduction of the bottom domain in the dynamic regime. Numerical simulations showed good qualitative agreement with both experimental observations and existing literature, and revealed the origin of the precessional frequency reduction as the different spin-wave eigenmodes excited by different remanent magnetization states. / Graduate