The aim of the work described in this thesis was two-fold; to investigate the effects of fly ash on the fatigue resistance of cement mortars when included as a partial cement replacement, and to seek to improve the understanding of cyclic fatigue crack growth mechanisms in cementitious materials. Mortar mixes were prepared with similar compressive cube strengths using a range of three fly ash contents from 0% to 25% (by mass of cement). Samples prepared using these mixes were tested in a double torsion facility under cyclic loading, and the rates of crack growth measured and recorded. These crack velocities were plotted against the applied stress intensities on log-log scales in so called V-K diagrams. An advantage of using the double torsion system was that the applied stress intensity was constant for constant load conditions and changing crack length, unlike many other configurations. However, the amount of scatter inherent in the system, and in testing cementitious materials, is large. This has meant that comparison between sets of data has had to be carried out on the basis of comparing the positions of clouds of data, rather than comparing the slopes of best fit lines. Another advantage of the OT system is that some of the parameters pertaining to the test can be changed whilst the test is in progress. This means that the effects of changing, say, load amplitude or cyclic frequency can be observed on the same specimen. Parameters that were considered in the test matrix . included the following: fly ash content, sample age, cyclic frequency and amplitude, maximum applied stress intensity, relative humidity and temperature of the environment, drying preparation of the sample and the type of fluid in which the samples were tested. The relative effects of all of these variables were compared in a series of V-K plots and trends were noted. It was apparent that the influence of the presence of fly ash was dependent on the age at which tests were conducted. At early ages the fly ash was found to increase fatigue resistance and toughness, whilst at greater ages the fatigue resistance of the mixes containing fly ash were slightly less resistant to fatigue crack growth. This was thought to be due to the spherical shape of the fly ash particles resulting in a blunting effect on cracks. The relative size of the particles at these ages are similar to other flaws in the matrix (eg capillary pores). At greater ages the continued hydration of the cement reduces the average size of flaws in the matrix, but not all of the larger fly ages_ particles take part in the reaction. Electron microscopy indicated that the bond between the gel and the large fly ash particles was poor, resulting in their effectively acting as flaws that were now large in relation to other flaws in the matrix, thus reducing toughness and fatigue resistance. In all of the tests there appeared to be a reasonable correlation between sample toughness and fatigue resistance, which is consiste-nt with a crack growth mechanism controlled by some form of environmentally assisted cracking (EAC) described by the V-K model. This is in contrast to the inverse relation observed in metals in which crack growth is governed by a non-linear plasticity mechanism described by the Paris relationship .. The results of tests carried out in a variety of environments and over a range of load cases also pointed to an EAC mechanism dominating, yet there was a slight Paris type influence apparent. Another indication of the EAC mechanism dominating was the agreement between the measured relationship between static and cyclic fatigue crack growth rates, and a theoretical relationship for such a mechanism proposed by Evans and Fuller. Some models to describe the mechanisms of crack growth in cementitious materials have been proposed. The first approach was to consider the mechanisms at an extreme microscopic level, where it has been proposed that pa number of mechanism may be acting including: EAC, brittle shear failure, creep, slippage and wedging. The relative dominance of each mechanism is governed by the condition prevailing at the element being considered. At a slightly larger dimensional scale, these localised mechanisms would combine to become apparent in experimental results as two overall mechanisms, namely EAC and another called here pseudo-plasticity (PP). PP may be considered to ~e a result of all of the micro level mechanisms acting together that manifests as a form of non-linear plasticity behaviour. The proposed model incorporating EAC and PP helps to explain the observed behaviour of EAC dominance but with a portion of plasticity being apparent. Further work is required in order to be able fo quantify the relative effects of the different mechanisms for a variety of environmental and loading states.

The only -reliable approach open to designers of pipeline systems conveyin,g non-Newtonian slurries in the turbulent flow regime has been large scale-pipe-tests. This thesis addresses this design problem, with particular emphasis on the theoretical modelling of the laminar/turbulent transition and turbulent flow behaviour of these slurries in pipes. The literature and theory pertinent to-the flow of slurries in pipes-is examined. The development of nonNewtonian Reynolds numbers and laminar/turbulent transition criteria are presented and existing theoretical models for predicting turbulent flow are reviewed. Three test facilities were built for the establishment of a data base ofnon-Newtonian slurry behaviour - a tube viscometer and t~o pumped recirculating pipe test rigs. The experimental investigation covered wide ranges of diameter (5mm to 200mm nominal bore), mean pipe velocity (O,lm/s to lOm/s), slurry relative density (1,02 to 1,65), volumetric concentration (2% to 37%), solids relative density (2,4 to 2,8) and particle size range (d85 = 24 to 120μm). The experimental results are analysed using theoretical models from the literature. Rheological characterisation was successfully performed using the approach ofl...azarus & Slatter (1988) and the yield pseudoplastic rheological model. The-laminar/turbulent analyses showed that the Metzner & Reed (1955) Reynolds number and the intersection method (Xu et al, 1993) gave the best results. However, the intersection method cannot explain flow behaviour. An increasing trend in the value of the stability criterion (Ryan & Johnson, 1959)withincreasing Hedstrom number is evident- this value was previously believed to be constant. The turbulent flow predictions of the Torrance (1963) and Wilson & Thomas (1985) models are similar and produce good results in the-early turbulent region but diverge from the data as the shear stress increases. These models are also shown to be sensitive to changes in rheology. Predicted thicknesses of the laminar sub-layer are less than the size of the.- larger particles showing that the continuum approximation is being compromised in the wall region. New models for the prediction of the laminar/turbulent transition and turbulent flow are developed from widely accepted fundamentals. The laminar/turbulent transition is modelled using a new Reynolds number formulation which takes into account the full viscous_force and the unsheared plug caused by the presence of a yield stress. A particle roughness effect has been observed and turbulent flow is modelled using a new roughness Reynolds number to correlate the roughness function. A new pipe Reynolds number is developed and found to be a reliable predictor of the laminar/turbulent transition and the increase in the value of the stability criterion can be-predicted using this new Reynolds number. Turbulent flow predictions using the new turbulent model are accurate and better than previous models, particularly in the rough wall region. The new analysis is based on physical behaviour and contributes to the understanding of the mechanisms involved.

An anisotropic damage model is proposed for the constitutive description of microcracking processes in brittle rock under a general loading path. Experimental data and micromechanical models are reviewed to quantify the effect of microcracking on the material stiffness and the mechanisms of microcrack formation in brittle rocks under compression are discussed. The sliding crack concept is adopted as the micromechanical basis of the anisotropic damage model. Undamaged material is represented with a linear elastic constitutive equation. Damage initiation is defined by a Coulomb friction law, which excludes damage at low deviatoric stress levels. The formulation of the directional damage extends the arguments of continuum damage models for tension cracking to general, tension and compression, stress states. This is achieved by the definition of damage in a subdomain of the total strain and the characterisation of the directional microcra.cking by a fourth order tensor internal variable, the damaged secant stiffness of the 'crack' strain subdomain. Induced anisotropy results from the reduction of components of the initial stiffness tensor in the direction of the positive principal 'crack' strains. Evolution of the damage magnitude is determined by the principle of maximum damage dissipation in terms of the undamaged energy norm of the positive part of the 'crack' strain tensor. Versatile evolution functions, based on the Weibull probability density function, are proposed for compression and extension damage modes. Unloading and reloading criteria are developed which are consistent with the sliding crack concept and introduce hysteretic behaviour. A numerical solution scheme is presented and the model is implemented in a nonlinear finite element program. The material constants are determined in a straightforward procedure from standard rock mechanics test results. The physical interpretation of the material parameters is highlighted in a sensitivity study. Backpredictions of dilatancy, induced anisotropy and ultimate strengths of Witwatersrand Quartzite subjected to triaxial stress path tests show good agreement with experimental data. The finite element analysis of mining simulation experiments in small Quartzite blocks verified the applicability of the model for a complex load path involving the sequential removal of elements. The extent and direction of damage, the predicted strains and the final excavated span are in good agreement with observations. The model was applied to Indiana Limestone in diametral compression and three-point tests in a compression/tension stress field. A quasi-linear constitutive rel~tion was required to account for stiffening of the highly porous material in compression. Predicted load - deformation response and damage energy release rates which compare well with experimental data. A two-dimensional analysis of the Dinorwig power station cavern demonstrates the potential of the anisotropic damage model to predict the magnitude and direction of damage and the associated deformation in a full scale engineering problem involving different rock types, geological features and an excavation and construction sequence.

In a time when the world is becoming more environmentally conscious, and is looking for simple, efficient, economical, and environmentally friendly solutions to sewage and sludge treatment, the dual digestion system presents itself as an attractive alternative to other sludge treatment systems. The dual digestion system comprises an autoheated thermophilic (55-65°C) aerobic first stage and a mesophilic (37°C) anaerobic second stage. Past research into the dual digestion system has given rise, inter alia, to the following claims (de Villiers, et al, 1991): a) sludge disinfection and stabilisation occur in one process - disinfection .in the thermophilic aerobic first stage and stabilisation in the anaerobic second stage. b) the stability of the anaerobic stage is considerably 'improved by the increase in H2C03 * alkalinity and pH in the aerobic stage. c) in the aerobic stage the sludge is aerobically or thermally pretreated (conditioned) making it more readily digestible under anaerobic conditions, thereby allowing significantly reduced retention times from 25 t~ 30 days for normal digestion, to 8 to 10 days. Messenger (1991), in a full scale investigation at the Potsdam Wastewater Treatment Plant in Milnerton, Cape Town, verified claims (a) and (b), but was unable to verify claim ( c) above. It was the intention in this investigation to verify this claim at full scale using the existing dual digestion plant at Milnerton. However, after 9 months of starting up the plant, the fiberglass aerobic tank failed structurally along one of its seams. This failure was so extensive that the plant could not be started up again and the research project was terminated. The failure of the aerobic reactor necessitated continuing this thesis investigation in the laboratory. With regard to claim (c) above, no conclusion could be reached by past research as to whether the conditioning of the sludge was caused simply by the heating of the sludge or by the biological action of the thermophilic bacteria on the sludge. Therefore, it was the initial intention of the laboratory investigation to operate 3 anaerobic units using 3 different feed sludges viz: 1) autotheral thermophilic aerobic sludge, 2) sludge heat treated to thermophilic temperatures, and 3) primary sludge as a control. By comparing the anaerobic performance of feed sludge types (1), (2) and (3) above, with progressively reduced retention times, it was hoped to establish which feed type displayed superior anaerobic digestibility ie. which feed type could be treated at the lowest anaerobic retention time. The difference in digestibility between feed types (1) and (2) would indicate whether the heating only, or the aerobic biological heating, conditioned the sludge. However, difficulties were experienced in starting up and operating an autothermal thermophilic aerobic reactor at laboratory scale and this part of the investigation had to be abandoned. Consequently, experimentation continued using only feed sludge types (2) and (3) above. The objectives of the investigation were modified since it would no longer be possible to establish the difference in anaerobic digestibility between the heat treated sludge and the thermophilic aerobic sludge. The objectives of this investigation , therefore, became to: (1) determine whether or not the exposure of the sludge to thermophilic temperatures caused the conditioning of the sludge (2) determine how the performance of the anaerobic digester fed heat treated primary sludge compared with a digester fed untreated primary sludge In order to fulfill the objectives above, four 14 litre anaerobic digesters were operated using the two different feed types (feed types (2) and (3) above). The heat treatment of the primary sludge took place in stainless steel reactors that were operated at a retention time of 1.5 days and a temperature of 65°C. These parameters were selected to simulate the heating conditions in the aerobic reactor that was operated as part of the dual digestion system at Milnerton. The anaerobic digesters were all operated at a temperature of 37°C while the retention times were progressively reduced until they failed. The purpose of this was to establish the minimum retention for the anaerobic digestion of the two feed types mentioned above and, therefore, to determine if there was any difference in digestibility between the two sludge types. From these results it would be possible to determine if the heat treatment process had any conditioning effects on the primary sludge that enhanced anaerobic digestion.

In most South African nnmicipal water distribution systems approximately 90% of the ' pipes used will be composed of cement type materials and the remainder metal type. This arises for two reasons. ~, cement-type pipes are cheaper than metal-type, ar;d secondly, cement material does not undergo redox reactions in an aqueous environment so that corrosion and its pernicious results cannot occur. However, depending on the chemical characteristics of the water, dissolution of cement-type pipe material may occur with eventual pipe failure. This form of attack is termed aggression and the waters involved are termed aggressive. The chemical characteristics of aggressive waters are usually reflected by low calcium and carbonate species concentrations and perhaps low pH. Waters with these characteristics can leach out calcitlD hydroxide and calcium carbona~ species from the current matrix, thereby damaging-the integrity of the material. Conversely, where the water being transported has high calcium and carbonate species concentrations, the dissolution of calcitlD hydroxide results in a rise in pH, supersaturation with respect to calcium carbonate, and precipitation of this mineral within the cement matrix. This process is termed aqueous phase carbonation. ~ carbonation has occurred, and provided the chemical characteristics of the . transported water are maintained with sufficient calcit1n and alkalinity, the pipe is protected from aggressive attack. When a water brings about such carbonation of cement materials it is said to· be stable with regard to aggression (this does not mean that it is .necessarily stable with regard to corrosion of metals). The chemical quality criteria to attain such stability are sufficiently high dissolved calcium and carbonate species concentrations and that the water is just, or slightly, supersaturated with respect to calcit1n carbonate. Conversely a Wa.ter is aggressive when it is undersa.turated with respect to calciun carbonate. When considering transportation of the brown waters of the South African southern and south-eastern seabJard regions, analysis shows that they characteristically have low calciuo and carbonate species concentrations. and a pH less than about 6,0. As such, these waters are aggressive and aqueous phase carbonation will not occur. Progressive deterioration of the conduit can be expected. However, experience with transportation of these waters in concrete and asbestos cement pipes is variable. In most instances a' very aggressive attack has been observed resulting in significant reduction in the design life of the pipe. Yet, in other instances, pipes have shown relatively little evidence of attack. The greater resistance of some pipes to these so called brown waters has prompted investigation into possible reasons. Recognising that calcium . hydroxide (lime) is significantly more .soluble than calcium carbonate, it would appear that if a degree of carbonation was able to occur prior to comnissioning of the pipe, this could in some measure reduce the rate of aggressive attack on the concrete. Such carbonation could occur fran the gaseous phase via atmospheric carbon dioxide diffusing into the concrete and reacting with calcium hydroxide to fonn calcillll carbonate, i.e. gaseous phase carbonation. If, in fact, this layer of calcium carbonate is able to provide significantly better protection than unca.I"bonated cement to brown water attack, then the ability to create such a layer through the use of accelerated gaseous phase carbonation techniques could have important implications when considering the transportation of natural waters • ..., In this report an experimental study was undertaken to investigate the validity of the above hypothesis, i.e. the ability of a calcium carbonate skin to provide protection to concrete conduits and cement type pipes from / brown water attack. As such the study consists of the following two main objectives, to investigate : A. the effectiveness of a carbonated layer to protect concrete from aggressive white and brown water attack . B. accelerated gaseous }:ilase carbonation. 'lbese two objectives are achieved by splitting this report into the above two sections, namely .A and B.

In this thesis we study the mathematical structure and numerical approximation of two boundary-value problems in small strain elastoplasticity. The first problem, which we call the incremental holonomic problem, is based on a consistent incremental holonomic constitutive law, which in turn derives from the notion of extremal paths in stress and strain space as originally proposed by PONTER & MARTIN (1972); the second problem which we study is the classical rate problem. We show that both problems can be formulated as variational inequalities, with internal variables being included explicitly in the formulation. Corresponding minimisation problems follow naturally from standard results in convex analysis. Perturbed minimisation problems are introduced, in which the original functionals J are replaced by perturbed functionals J e: which depend on a parameter e: > 0 • In the rate problem e: is a penalty parameter; here J e: differs from J by a term e: -l j( •) where j( •) is a penalty functional which allows the non-negativity constraint on the plastic multipliers to be removed. In the incremental holonomic problem the non-differentiable plastic work function wP ( •) is regularised, and replaced by a differentiable function WP(~) • e: In both problems the perturbed functionals form the basis for fintte element approximations, the error in the approximate solutions now depending on both mesh size and on the magnitude of e: • Numerical algorithms are proposed, and implemented in two computer programs. On the basis of preliminary numerical experiments we conclude that the penalty-rate formulation is useful in a limited class of elastic-plastic problems, and that the incremental holonomic formulation has exceptional potential, without any apparent limitations.

With the increase in ship sizes, there has been an increased interest in the prediction of ship motions in shallow water, where the possibility of grounding becomes a problem. Theoretical equations governing the ship's motions have been formulated involving various hydrodynamic coefficients. In this thesis these coefficients have been found experimentally for a range of water depths and wave periods. The methods for solving the equations of motion theoretically are introduced and discussed. The equations of motion are solved using the coefficients, found experimentally, to give results in the form of motion response amplitude operators. These are compared against other authors' results derived either theoretically or experimentally. It was found that the hydrodynamic coefficients increase rapidly with decrease in water depth. Relatively good agreement between the empirical results of this thesis and results of other authors would indicate that the theoretical formulae do represent the coefficients to which they are claimed to approximate, for at least the case of zero or low forward speeds.

Analytical and computational aspects of solution paths for nonlinear equations are examined, with emphasis on problems in which there are many parameters. The solution to problems of this type is described by an equilibrium hypersurface and methods are presented which allow for the determination of the various features of this surface. These include methods for following numerically any curve on the primary surface, and for determining on such a curve all the singular points (both limit and bifurcation points). Further methods are then presented which allow branching onto secondary paths (subsets of secondary surfaces) from bifurcation points in order to trace out these paths and so determine the bifurcation behaviour of the problem considered. To complete the analysis of the equilibrium surface methods are developed to trace the loci of singular po in ts. The locus of a bifurcation point determines the intersection of the primary and secondary equilibrium surfaces while the loci of limit points allow for the determination of regions of stable and unstable behaviour on the equilibrium surface. These methods are applicable to any system of nonlinear equations but the particular application here is to systems of equations obtained from the finite element approximation of boundary-value problems in elasticity. Attention is restricted to plane boundary-value problems involving incompressible hyperelastic materials. The strain-energy function used to characterise these materials is based on a symmetric function of the principal stretches All of the above ideas are investigated nu me rica lly for the pro bl em of a pressurised rubber cylinder. subjected to axial extension. This problem contains two identifiable loading parameters and exhibits complex limit and bifurcation behaviour, which is studied in some de tail.

Access to finance is an essential factor in the agricultural value chain and enables participants to purchase essential inputs and infrastructure (e.g. machinery and land) necessary for the production process, grading, processing, packaging and distribution of their produce. Finance is also required where there are specific regulatory requirements (such as licencing and certification) to which a participant must adhere, and these may differ from commodity to commodity. With this in mind, it is clear that any farming enterprise that wishes to enter and participate in the agricultural sector will need access to finance to compete effectively. The study examines the financial needs and challenges faced by contract farmers in achieving transformation in the agricultural sector in South Africa. In line with the number of interviews conducted in other qualitative studies, a sample of eight contract farmers from Gauteng, North West, Mpumalanga, KwaZulu-Natal and Free State provinces of South Africa were chosen for the interviews. The study finds that purchase of land, farming infrastructure, farming equipment, working capital for agricultural inputs, and funds for environmental impact assessments are the prevalent financial needs of the sampled contract farmers. Most importantly, the study further documents evidence that business and financial understanding, lack of capital, insufficient collateral, the lending criteria and policies of financial institutions and rigid and non-inclusive products are the major challenges faced by black contract farmers in raising funds to meet their financial needs and their contractual obligations to their sponsors. The study recommends ways in which the farmers believe they could be part of the solution in financially assisting new and emerging farmers and creating a transformed agricultural sector in the country. Farmers believe that this requires a concerted effort by all the stakeholders to close the existing gaps in the current financial mechanisms used to finance farmers in South Africa. It is important that the critical stakeholders (government, development financial institutions and other financial institutions, farmers and their organisations, sponsors and agroprocessors) work closely together so that more can be achieved in the least possible time period. The role of each of the above stakeholders is discussed in the recommendations chapter.

The research explored the long-term relationship between FDI, GDP and host country employment by using sector-wise panel data from 1991 to 2017 in Namibia. The study applied unit root testing and Cointegration test to test for the presence of a cointegration relationship between the variables. Also, a vector autoregression model short-run causality among the variables was examined. In the end, Impulse response functions are estimated. The research found both a short term and long-term causality going from FDI inflow to employment. Impulse responses show that both GDP and employment respond positively to an exogenous shock in FDI inflow. However, the employment response to FDI inflow shock is smaller than that of GDP response. The paper also concludes that FDI has no causal effects on economic growth in Namibia. It means that economic growth is not contributed by the FDI significantly the results in this research have some significant policy implications. Therefore, as the results suggest that the FDI inflow has a positive impact on employment, because of the results, the researcher also recommends that Namibia pursue the policy of attracting foreign firms aggressively and create all the conditions required for attracting foreign direct investment in order to create further employment opportunities.