In this research, a novel, unique systematic procedure was implemented to investigate the influence of the fracture networks and confining stresses on the jointed coal mass strength (JCMS). Both a laboratory experimental scheme and a numerical modeling scheme were carried out at the 3-D level. The laboratory experiments were performed to achieve the following three goals. Firstly, the geomechanical properties for the intact coal and coal discontinuities were estimated through the laboratory geomechanical property tests. Secondly, naturally existing fracture networks in the cubic coal blocks were first detected by the industrial Computed Tomography (CT) scanning technique and then quantified by the fracture tensor based methodology. Thirdly, polyaxial tests were conducted on the same cubic coal blocks to obtain the JCMS values under different confining stresses. With respect to the numerical modeling, PFC^3D and 3DEC software packages were used to simulate the polyaxial compression tests for intact and jointed cubic coal blocks, respectively. From more than twenty intact rock strength criteria, nine criteria were selected for this research. The intact coal strength data bank obtained from PFC^3D modeling was used to evaluate the applicability of nine different intact rock strength criteria. A modified grid search (MGS) procedure is proposed and used to find the best fitting parameter values and calculate the coefficient of determination (R²) values for each criterion. These criteria are compared in detail using the following features: R² values, σ₁ - σ₂ plots for different σ₃, shapes on the deviatoric planes, linearity or nonlinearity on the meridian planes. The regression analysis and the MGS procedure were found to be equivalent in finding the best fitting parameter values for a certain intact rock strength criterion. Through the comparisons, the modified Wiebols-Cook and modified Lade criteria were found to provide the highest R² values and fit the intact coal strength data best on the σ₁ - σ₂ coordinate plane and meridian planes. Based on the appearances on the deviatoric plane, the nine intact rock strength criteria are categorized into three types: the single shear stress criteria, the octahedral shear stress criteria and the criteria incorporating the maximum principal shear stress and partial intermediate principal shear stress. The relative positions of the different criteria on two specific meridian planes are also discussed. The geometric model of the jointed coal block was first set up by incorporating the fracture network constructed from the CT scanning into the intact coal block using a modified fictitious joint procedure. The numerical parameter values of intact coal and coal discontinuities were then calibrated and validated through a trial and error procedure using the laboratory test results of some selected samples. Next the JCMS data bank was consummated by performing a four-phase numerical investigation on several jointed coal blocks having selected fracture networks and five additional artificial fracture networks under different confining stress combinations. Finally, a new empirical coal mass strength criterion was developed to estimate the JCMS values at the 3-D level. The developed new model is capable of capturing the scale effect and anisotropic strength behaviors. It can also be applied to rock masses having approximately orthogonal fracture systems or for masses where fracture system can be reduced to an equivalent orthogonal fracture system.The following new contributions were made in this dissertation to advance the existing state-of-art on the dissertation topic: (a) A new, unique methodology as shown in Fig. 1.1 incorporating the following aspects was used to develop a new 3-D coal mass strength criterion: a complete set of geomechanical property tests, fracture network detection and quantification, polyaxial compression tests, numerical decomposition techniques; (b) A new procedure was developed to construct the fracture network in the coal cubes starting from CT scans to perform numerical modeling using 3DEC. In this procedure, a modified fictitious joint framework was also proposed to extend the applicability of the original fictitious joint framework, which allows incorporating a large quantity of non-persistent joints with acceptable numerical calculation effort; (c) A new 3-D coal mass strength criterion was developed to incorporate the fracture network and 3-D confining stress system to capture the anisotropy and scale effect of coal mass strength. The proposed criterion not only includes the influence of the intermediate principal stress, which is ignored by some existing strength criteria, but also includes the intensity and orientation and size probability distributions of the fracture system explicitly by a fracture tensor based methodology, which is far more advanced than most of the current criteria that are based on rock mass classification systems having only scalar indices; (d) A modified grid search procedure was proposed and used to evaluate the applicability of nine different intact rock strength criteria. The best intact rock strength criteria applicable for the intact coal data obtained through PFC^3D modeling were found by performing the most detailed intact rock strength criteria evaluation incorporating σ₁ - σ₂ - σ₃ plots and behaviors on the deviatoric and meridian planes, which improves the understanding of the available intact rock strength criteria.

An imperative task for successful underground mining is to ensure the stability of underground structures, since it influences the safety, and in turn, the production capacity and economic performance of the mine. This is more so for deep excavations in soft rock which may be under significantly high stresses. In this thesis, stability studies on two tunnels, a horseshoe-shaped and an inverted arch-shaped tunnel, have been presented. The tunnels, running at a depth of 1325 m, are part of the Xiezhuang Coal Mine, in the Xinwen mining area, in China. Using the available information on stratigraphy, geological structures, in-situ stress measurements and geo-mechanical properties of intact rock and discontinuity interfaces, a three-dimensional numerical model has been built using the 3DEC 3-Dimensional Distinct Element Code to simulate the stress conditions around the tunnels. Based on available discontinuity geometry constraints, the rock mass has been modelled as a mixture of a discontinuum medium close to the tunnels and as an equivalent-continuum in the far field. Due to the unavailability of field measurements for rock mass mechanical parameters, the parameters have been estimated by incorporating the available intact rock mechanical properties and field deformation monitoring data into a strength reduction model calibration procedure. This back-analysis (calibration) has been carried out through a pseudo-time dependent support installation routine which incorporates the effect of time through a stress-relaxation mechanism. The results from the back-analysis indicate that the rock mass cohesion, tensile strength, uniaxial compressive strength, and elastic modulus values are about 35-45 % of the corresponding intact rock property values. Additionally, the importance of incorporating stress relaxation before support installation in numerical modeling has been illustrated, for the first time in literature, through the increased support factors of safety and reduced grout failures. The calibrated models have been analyzed for different supported and unsupported cases in an attempt to quantify the effect of supports in stabilizing the tunnels and to estimate the adequacy of the existing supports being used in the mine. A direct outcome is that the findings indicate that longer supports may be better suited for the existing geo-mining conditions around the tunnels since they have fractured zones that are larger than the supports currently in use at the mine. The effects of supports have been demonstrated using changes in deformations and yield zones around the tunnels, and changes in the average factors of safety and grout failures of the supports. The use of longer supports and floor bolting has provided greater stability for the rock masses around the tunnels. A comparison between the closure strains in the two differently shaped tunnels indicates that the inverted arch tunnel may be more efficient in reducing roof sag and floor heave for the existing geo-mining conditions. Additional analyses focusing on parametric sensitivity studies on the rock and joint mechanical properties show that the tunnel stability is highly sensitive to changes in cohesion and internal friction angle of the intact rock, and changes in joint basic friction angle. Tunnel stability is seen to not be very sensitive to changes in intact rock tensile strength and joint shear stiffness for the tunnels being studied. Finally, support optimization studies conducted by studying the effect of changing cable diameters and grout uniaxial compressive strengths on support factors of safety and grout failures show the trade-off that is necessary in selecting cable strength vis-à-vis grout strength. The results indicate that simply increasing either one of cable or grout strength parameters without considering their interactions and compatibilities could be detrimental to the stability of the support system.

Bed topography identification in open channel and glacier flows is of paramount importance for the study of the respective flows. In the former, the knowledge of the channel bed topography is required for modelling the hydrodynamics of open channel flows, fluvial hydraulics, flood propagation, and river flow monitoring. Indeed, flow models based on the Shallow Water Approximation require prior information on the channel bed topography to accurately capture the flow features. While in the latter, usable bedrock topographic information is very important for glacier flow modellers to accurately predict the flow characteristics. Experimental techniques to infer the bed topography are usually used but are mostly time consuming, costly, and sometimes not possible due to geographical restrictions. However, the measurement of free surface elevation is relatively easy. Alternative to experimental techniques, it is therefore important to develop fast, easy-to-implement, and cost-effective numerical methods. The inverse of the classical hydrodynamic problem corresponds to the determination of hydraulic parameters from measurable quantities. The forward problem uses model parameters to determine measurable quantities. New one-shot and direct pseudo-analytical and numerical approaches for reconstructing the channel bed topography from known free surface elevation data is developed for one-dimensional shallow water flows. It is shown in this work that instead of treating this inverse problem in the traditional partial differential equation (PDE)-constrained optimization framework, the governing equations of the direct problem can be conveniently rearranged to obtain an explicit PDE for the inverse problem. This leads to a direct solution of the inverse problem which is successfully tested on a range of benchmark problems and experimental data for noisy and noiseless free surface data. It was found that this solution approach creates very little amplification of noise. A numerical technique which uses the measured free surface velocity to infer the channel bed topography is also developed. The one-dimensional shallow water equations along with an empirical relationship between the free surface and the depth averaged velocities are used for the inverse problem analysis. It is shown that after a series of algebraic manipulation and integration, the equation governing the inverse problem simplifies to a simple integral equation. The proposed method is tested on a range of analytical and experimental benchmark test cases and the results confirm that, it is possible to reconstruct the channel bed topography from a known free surface velocity distribution of one-dimensional open channel flows. Following the analysis of the case of one-dimensional shallow water flows, a numerical technique for reconstructing the channel bed topography from known free surface elevation data for steep open channel flows is developed using a modified set of equations for which the zero-inertia shallow water approximation holds. In this context, the shallow water equations are modified by neglecting inertia terms while retaining the effects of the bed slope and friction terms. The governing equations are recast into a single first-order partial differential equation which describes the inverse problem. Interestingly, the analysis shows that the inverse problem does not require the knowledge of the bed roughness. The forward problem is solved using MacCormack’s explicit numerical scheme by considering unsteady modified shallow water equations. However, the inverse problem is solved using the method of characteristics. The results of the inverse and the forward problem are successfully tested against each other. In the framework of full two-dimensional shallow water equations, an easy-to-implement and fast to solve direct numerical technique is developed to solve the inverse problem of shallow open channel flows. The main underlying idea is analogous to the idea implemented for the case of one-dimensional reconstruction. The technique described is a “one-shot technique” in the sense that the solution of the partial differential equation provides the solution to the inverse problem directly. The idea is tested on a set of artificial data obtained by first solving the forward problem. Glaciers are very important as an indicator of future climate change or to trace past climate. They respond quickly compared to the Antarctica and Greenland ice sheets which make them ideal to predict climate changes. Glacier bedrock topography is an important parameter in glacier flow modelling to accurately capture its flow dynamics. Thus, a mathematical technique to infer this parameter from measured free surface data is invaluable. Analogous to the approaches implemented for open channel flows, easy-to-implement direct numerical and analytical algorithms are developed to infer the bedrock topography from the knowledge of the free surface elevation in one space dimension. The numerical and analytical methods are both based on the Shallow Ice Approximation and require the time series of the ablation/accumulation rate distribution. Moreover, the analytical method requires the knowledge of a non-zero glacier thickness at an arbitrary location. Numerical benchmark test cases are used to verify the suitability and applicability of the algorithms.

The Normal Accident Theory (NAT) attempts to understand why accidents occur in systems with high-risk technologies. NAT is characterized by two attributes: complexity and coupling. The combination of these attributes results in unplanned and unintended catastrophic consequences. High-risk technology systems that are complex and tightly coupled have a high probability of experiencing system failures. The mining industry has experienced significant incidents involving haulage operations up to and including severe injuries and fatalities. Although the mining industry has dramatically reduced fatalities and lost time accidents over the last three decades or more, accidents still continue to persist. For example, for the years 1998 - 2002, haulage operations in surface mines alone have accounted for over 40% of all accidents in the mining industry. The systems thinking was applied as an approach to qualitatively and quantitatively evaluate NAT in mining haulage operations. A measurement index was developed to measure this complexity. The results from the index measurements indicated a high degree of complexity that exists in haulage transfer systems than compared to loading and unloading systems. Additionally, several lines of evidence also point to the applicability of NAT in mining systems. They include strong organizational management or safety system does not guarantee zero accidents, complexity is exhibited in mining systems, and they are interactive and tightly coupled systems. Finally, the complexity of these systems were assessed with results indicating that a large number of accidents occur when there are between 4 or 5 causal factors. These factors indicate the degree of complexity necessary before accidents begin to occur.

This thesis considers the development of settlement landscapes in the Iron Age across two adjacent regions, the upland eastern Cotswolds and lowland upper Thames valley. Previous studies have focused on the differences in settlement form, economic practice and social development and therefore the possible dichotomy of heartland and hinterland landscapes. It is clear, however, that this is due to an imbalance of research brought about as a result of the natural landscape, interests of antiquarians and archaeologists and modern settlement focus and development. A new dataset of cropmark and geophysical survey material is presented as a way of redressing the imbalance. The focus within this study on banjo enclosures also provides an opportunity to analyse what remains a relatively enigmatic and understudied site-type that appeared during the Middle and Late Iron Age. The results illustrated and discussed here provide the chance to outline new narratives that take into account both practical and non-functional interpretations. From this, more is elucidated regarding these sites within the context of Middle and Late Iron Age settlement landscape developments. By integrating this new dataset within the wider context of the upper Thames and immediate environs a number of further and more general questions have been raised. These focus on the chronology of settlement development, the appearance and growth of exchange networks and the changing significance of open and enclosed settlements throughout the period. Differences have been used in the past to symbolise alternative social systems apparent across two settlement landscapes. However, as a result of the evidence presented here these perceptions are no longer viable as an interpretive framework. Instead, aspects of chronological development, settlement space and sphere of influence and interaction are discussed in relation to the evidence from Midlands and central southern Britain.

Ground-Penetrating Radar (GPR) is a non-destructive electromagnetic investigative tool used in many applications across the fields of engineering and geophysics. The propagation of electromagnetic waves in lossy materials is complex and over the past 20 years, the computational modelling of GPR has developed to improve our understanding of this phenomenon. This research focuses on the development of accurate numerical models of widely-used, high-frequency commercial GPR antennas. High-frequency, highresolution GPR antennas are mainly used in civil engineering for the evaluation of structural features in concrete i. e., the location of rebars, conduits, voids and cracking. These types of target are typically located close to the surface and their responses can be coupled with the direct wave of the antenna. Most numerical simulations of GPR only include a simple excitation model, such as an infinitesimal dipole, which does not represent the actual antenna. By omitting the real antenna from the model, simulations cannot accurately replicate the amplitudes and waveshapes of real GPR responses. Numerical models of a 1.5 GHz Geophysical Survey Systems, Inc. (GSSI) antenna and a 1.2 GHz MALÅ GeoScience (MALÅ) antenna have been developed. The geometry of antennas is often complex with many fine features that must be captured in the numerical models. To visualise this level of detail in 3d, software was developed to link Paraview—an open source visualisation application which uses the Visualisation Toolkit (VTK)—with GprMax3D—electromagnetic simulation software based on the Finite-Difference Time-Domain (FDTD) method. Certain component values from the real antennas that were required for the models could not be readily determined due to commercial sensitivity. Values for these unknown parameters were found by implementing an optimisation technique known as Taguchi’s method. The metric used to initially assess the accuracy of the antenna models was a cross-corellation of the crosstalk responses from the models with the crosstalk responses measured from the real antennas. A 98 % match between modelled and real crosstalk responses was achieved. Further validation of the antenna models was undertaken using a series of laboratory experiments where oil-in-water (O/W) emulsions were created to simulate the electrical properties of real materials. The emulsions provided homogeneous liquids with controllable permittivity and conductivity and enabled different types of targets, typically encountered with GPR, to be tested. The laboratory setup was replicated in simulations which included the antenna models and an excellent agreement was shown between the measured and modelled data. The models reproduced both the amplitude and waveshape of the real responses whilst B-scans showed that the models were also accurately capturing effects, such as masking, present in the real data. It was shown that to achieve this accuracy, the real permittivity and conductivity profiles of materials must be correctly modelled. The validated antenna models were then used to investigate the radiation dynamics of GPR antennas. It was found that the shape and directivity of theoretically predicted far-field radiation patterns differ significantly from real antenna patterns. Being able to understand and visualise in 3d the antenna patterns of real GPR antennas, over realistic materials containing typical targets, is extremely important for antenna design and also from a practical user perspective.

Waves, which arise when restoring forces act on small perturbations, are ubiquitous in fluids. Their counterpart, mean flows, capture the remainder of the motion and are often characterised by a slower evolution and larger scale patterns. Waves and mean flows, which are typically separated by time- or space-averaging, interact, and this interaction is central to many fluid-dynamical phenomena. Wave-mean flow interactions can be classified into dissipative interactions and non-dissipative interactions. The former is important for small-scale flows, the latter for large-scale flows. In this thesis these two kinds of interactions are studied in the context of microfluidics and geophysical applications. Viscous wave-mean flow interactions are studied in two microfluidic problems. Both are motivated by the rapidly increasing number of microfluidic devices that rely on the mean-flow generated by dissipating acoustic waves - acoustic streaming - to drive small-scale flows. The first problem concerns the effect of boundary slip on steady acoustic streaming, which we argue is important because of the high frequencies employed. By applying matched asympototics, we obtain the form of the mean flow as a function of a new non-dimensional parameter measuring the importance of the boundary slip. The second problem examined is the development of a theory applicable to experiments and devices in which rigid particles are manipulated or used as passive tracers in an acoustic wave field. Previous work obtained dynamical equations governing the mean motion of such particles in a largely heuristic way. To obtain a reliable mean dynamical equation for particles, we apply a systematic multiscale approach that captures a broad range of parameter space. Our results clarify the limits of validity of previous work and identify a new parameter regime where the motion of particles and of the surrounding fluid are coupled nonlinearly. Non-dissipative wave-mean flow interactions are studied in two geophysical fluid problems. (i) Motivated by the open question of mesoscale energy transfer in the ocean, we study the interaction between a mesoscale mean flow and near-inertial waves. By applying generalized Lagrangian mean theory, Whitham averaging and variational calculus, we obtain a Hamiltonian wave-mean flow model which combines the familiar quasi-geostrophic model with the Young & Ben Jelloul model of near-inertial waves. This research unveils a new mechanism of mesoscale energy dissipation: near-inertial waves extract energy from the mesoscale ow as their horizontal scale is reduced by differential advection and refraction so that their potential energy increases. (ii) We study the interaction between topographic waves and an unidirectional mean flow at an inertial level, that is, at the altitude where the Doppler-shifted frequency of the waves match the Coriolis parameter. This interaction can be described using linear theory, using a combination of WKB and saddle-point methods, leading to explicit expressions for the mean-flow response. These demonstrate, in particular, that this response is switched on asymptotically far downstream from the topography, in contrast to what is often assumed in parameterisation.

The Větrníky national nature reserve, located in the South Moravian region north of the village of Letonice, is one of the largest steppe reserves in Southern Moravia. This whole area is characterized by the presence of both stable and active landslides, and the occurrence of suffosion sinkholes has been monitored there in the long-term. The aim of the thesis was to investigate whether it was possible to observe subsurface phenomena, caused by the washing out of fine rock particles by ground water, by means of geophysical methods. This phenomenon is known as suffosion. The measurements took place in the areas where the suffosion manifestation was very distinctive, that is around two sinkholes that were visible on the surface. In order to identify the suffosion structural-geological causes and their manifestations at a given location, the gravimetric and electrical resistivity tomography (ERT) methods were used in the first stage of the research. Measured data was further processed and geologically interpreted. The gravimetric method has proved suitable when identifying rocks affected by suffosion, in which case we assume that their density is lower than the density of the surrounding rocks. Using the ERT method, it was possible, in the vertical profile, to distinguish the sandy-gravelly sediments...

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science. Johannesburg, 2016. / The Jacomynspan Ni-Cu sulphide mineralisation is hosted within a 100m thick steeply dipping tabular, differentiated, sill of mafic to ultramafic composition intruded into country gneissic rocks of the Namaqualand Metamorphic complex. This sill is predominantly composed of tremolite schist (metamorphosed pyroxenite) containing lenticular bodies of harzburgite. The harzburgite generally hosts net-textured mineralisation with up to 50% by volume of the rock. Massive sulphide veins and stringers are occasionally present within the harzburgite. The sulphide minerals are a typical magmatic assemblage of pyrrhotite, chalcopyrite and pentlandite. The sill covers an approximate strike length of about 5km but only a small portion covering 1km x 1km was selected for this study. Physical property studies carried out on the drill core (magnetic susceptibility and conductivity) indicate that the country gneissic rocks are not conductive and neither are they magnetically susceptible. However, the mineralized sill has elevated values of both magnetic susceptibility and relative conductivity compared to its host making it a suitable target for both magnetic and electromagnetic inversion. Drilling done so far on the study area has shown that the well-mineralised harzburgite (hosted within the poorly mineralised ultramafic sill) is not a continuous body but occurs in ‘pockets’. There is therefore need to use the available geophysical and geological datasets to derive a model of these well mineralised pods. This study is therefore intended to assess the feasibility of using electromagnetic (EM) methods together with other geophysical methods and geology in obtaining a model of the harzburgite pods hosted within the less conductive poorly mineralised ultramafic sill in order to guide further drilling. Geosoft’s VOXI Earth Modelling software was used to model the high resolution airborne magnetic data for this study. Cooper’s Mag2dc (www.wits.ac.za) and Stettler’s Magmodintrp software (personal communication, 2015) was also used during modelling of the magnetic data to compliment the modelling from VOXI. The mineralised ultramafic sill was clearly mapped in both the 3D model representation from Mag2dc modelling and VOXI’s 3D unconstrained smooth model inversion for the study area. Based on the physical properties studies carried out on the study area, EM data (both ground and downhole EM) were modelled using Maxwell software. The poorly mineralised tremolite schist was clearly modelled. In order to better constrain the targets, an assumption was made that at late decay times the currents would be focused in the centre of the large EM plate probably giving an indication of the most conductive part of the intrusion. Smaller ‘Resultant EM plates’ of dimensions, 300mx300m that coincide with the centre of the large EM plates (with a conductance above 100S) were constructed in iv Maxwell software and integrated with the DXF file of the Micromine geology model of the well mineralised harzburgite clearly mapping the well-mineralised harzburgite and showing its possible extensions. 2D inversion modelling was conducted on all audio-frequency magnetotelluric (AMT) data for this study area. The modelling results clearly mapped the mineralised intrusion.

Submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg as a requirement for the Degree of Master of Science. Johannesburg, 1992. / The effect of sodium on clays dominates the formation and ecology of granitic eatenas in the Eastern Transvaal Lowveld. This study reviews the process involved and explains the soil, vegetation and erosion patterns in this landscape. Weathering parent rock gives rise to sodium in sufficient amounts to promote clay dispersion. Dispersed, mobile, clays respond to seasonal pulses of laterally moving soil water resulting in alternating zones of clay illuviation and clay deposition down hillslopes [Abbreviated Abstract. Open document to view full version] / AC2017