published_or_final_version / abstract / toc / Mathematics / Master / Master of Philosophy

Abstract A small opencast coal mine has been developed over previous underground workings in the Malvern Hills, inland Canterbury, New Zealand. The coal measure strata dip at ~45° to the southeast, and consist of finely laminated mudrocks with multiple coal seams of varying thickness. Production is in the range 10,000 to 15,000 tonnes per annum from two principal seams with an aggregate thickness of ~4.5m. The open pit has been designed with footwall batters parallel to bedding, vertical bench separation of 15m, and the highwall formed to a nominal 4V:1H. Preliminary examination of the open pit mine site in 2003 indicated that footwall failures involved de-lamination due to drying out on exposure, and buckling and/or shearing along bedding surfaces. During mine development it became apparent that the batters formed easily where thin (less than 0.3m thick) coal seams were present in the sequence. In the 2004 campaign the pit floor was lowered, with a new batter and bench formed to expose the 3m thick Main Seam coal. The day after completion of this batter, a large buckle failure occurred involving the entire length of the pit (85m along strike), and a 2m thick intact slab with a total volume of ~3700m³ translated down dip 6.2m on the base of a thin coal seam to form a pronounced buckle at the toe. Even though footwall batters are cut to the angle of dip, which is entirely realistic geotechnically, the de-coupling and buckling that occurred compromised the safety and economics of the whole operation. Buckling failure in moderately dipping soft rock sequences has been identified in footwall slopes of coal mining operations. Models used in the literature to simulate similar footwall failures include: the Euler solution using column and beam buckling theory to calculate the kinematic feasibility of a slab-buckle, conceptual modelling using a base friction table, and numerical modelling using distinct element analysis. Back analysis of the Malvern Hills failure was necessary to investigate the controls on the footwall stability, and for future mine design. Engineering geological description of the pit and slab materials was done, and an engineering geological model created. Samples of the slab material and failure surface were collected by coring and trenching, with testing of these materials to establish the required parameters for use in the Euler solution. Back analysis using three different forms of the Euler solution provided unrealistic results that overestimated the overall length of a stable slope by more than 10 times. An engineering geology reassessment was undertaken, and a number of inadequacies in the Euler solution methodology were identified particularly in relation to pore pressure and elasticity considerations. Given that the Malvern Hills toe-buckle slab failure displays both elastic and plastic deformation components in the soft mudrocks, and the slab itself cannot be considered as homogenous, reservations must exist about conventional predictive analytical techniques for pit slope failures of this type. No further large scale slab-buckle failures have developed at the mine site, in part because of the slow rate of coal extraction, but precautionary drainage of the footwall slopes has been undertaken to improve overall batter stability. The location of the slab-buckle failure on a critically positioned pre-sheared thin coal seam with full hydrostatic head is considered the most probable cause, rather than inherent instability of the generic bench and batter arrangement adopted. The adoption of a precedent based engineering geology approach to future mine design is considered the most appropriate solution in the circumstances.

This dissertation covers the process of modelling and subsequently developing a flight dynamics controller for a quad–rotor unmanned aerial vehicle. It is a theoretical study that focusses on the selection of a controller type by first analysing the problem on a system level and then on a technical level. The craft is modelled using the Newton– Euler model, accounting for multiple reference frames to account for the interpretation of orientation as seen by on–board sensors. The quad–rotor model and selected controllers are characterized and compared. The model is verified through simulation by comparison to a validated model. A series of generic control loops are derived and used as reference for the implementation of the controllers. A Simulator is developed and used to do a comparative study of the various controller types and the control approach. Finally a full simulation is done to demonstrate the interaction between the controllers. / Thesis (MIng (Computer and Electronical Engineering))--North-West University, Potchefstroom Campus, 2012.

This dissertation covers the process of modelling and subsequently developing a flight dynamics controller for a quad–rotor unmanned aerial vehicle. It is a theoretical study that focusses on the selection of a controller type by first analysing the problem on a system level and then on a technical level. The craft is modelled using the Newton– Euler model, accounting for multiple reference frames to account for the interpretation of orientation as seen by on–board sensors. The quad–rotor model and selected controllers are characterized and compared. The model is verified through simulation by comparison to a validated model. A series of generic control loops are derived and used as reference for the implementation of the controllers. A Simulator is developed and used to do a comparative study of the various controller types and the control approach. Finally a full simulation is done to demonstrate the interaction between the controllers. / Thesis (MIng (Computer and Electronical Engineering))--North-West University, Potchefstroom Campus, 2012.

A magnetic study over a 95 m x 150 m area of the Hickory sandstone aquifer in central Texas was carried out as part of multitechnique geophysical investigation that included ground penetrating radar (GPR), electromagnetic (EM), seismic and seimoelectric. In geophysical exploration, the magnetic method can be utilized as an alternative to more expensive methods, such as seismic or it can be used to complement other methods. In this thesis, the magnetic method is applied to estimate the location of a previously mapped fault by Texas A&M geology students, and it is used to estimate the magnetic susceptibility contrast of the targeted fault. The main challenge of this study is imaging shallow faults using the geophysical magnetic method in a fractured aquifer with widely-scattered distribution of iron bearing rocks as in the case of the Hickory sandstone aquifer. A Geometric—G858 Cesium vapor magnetometer was used to collect magnetic data. The data consisted of 19 north-south and 1 east-west lines acquired in October and November of 2012. Elementary data processing such as diurnal correction, regional correction, reduction to pole (RTP) filter, Euler deconvolution, forward modeling and inversion were employed to characterize the faulted zone. This faulted zone separates granite basement rocks from the Hickory sandstone. As a result, this study emphasizes that Euler deconvolution applied to RTP-filtered data increases the interpretability of geological and structural contacts. The results of the magnetic method have been compared to results of GPR, EM and seismoelectric methods. Understanding the magnetic mineralogy of rocks and their properties can improve the geological interpretation of magnetic surveys.

In this thesis, we analyze theoretical properties of the discontinuous Galerkin method (DGM) and propose novel approaches to implementation with the aim to increase its efficiency. First, we derive explicit expressions for the eigenvalues (spectrum) of the discontinuous Galerkin spatial discretization applied to the linear advection equation. We show that the eigenvalues are related to the subdiagonal [p/p+1] Pade approximation of exp(-z) when the p-th degree basis functions are used. Then, we extend the analysis to nonuniform meshes where both the size of elements and the composition of the mesh influence the spectrum. We show that the spectrum depends on the ratio of the size of the largest to the smallest cell as well as the number of cells of different types. We find that the spectrum grows linearly as a function of the proportion of small cells present in the mesh when the size of small cells is greater than some critical value. When the smallest cells are smaller than this critical value, the corresponding eigenvalues lie outside of the main spectral curve. Numerical examples on nonuniform meshes are presented to show the improvement on the time step restriction. In particular, this result can be used to improve the time step restriction on Cartesian grids. Finally, we present a discontinuous Galerkin method for solutions of the Euler equations on Cartesian grids with embedded geometries. Cutting an embedded geometry out of the Cartesian grid creates cut cells, which are difficult to deal with for two reasons. One is the restrictive CFL number and the other is the integration on irregularly shaped cells. We use explicit time integration employing cell merging to avoid restrictively small time steps. We provide an algorithm for splitting complex cells into triangles and use standard quadrature rules on these for numerical integration. To avoid the loss of accuracy due to straight sided grids, we employ the curvature boundary conditions. We show that the proposed method is robust and high-order accurate.

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Conn., Yale Univ., Diss.--New Haven, 2003. / Kopie, ersch. im Verl. UMI, Ann Arbor, Mich.

Univ., Diss--Augsburg, 2005.

Zugl.: Giessen, Univ., Diss., 2008