The investigation reported in this thesis was the initial phase of an experimental programme initiated in 1969 at Auckland University to study the application of hydrometallurgical techniques to the recovery of base-metals from New Zealand sulphide ores. The principal aim was to design and build a suitable autoclave for conducting pressure leaching experiments and with this to evaluate the sulphuric acid leaching kinetics of a bulk lead-zinc-copper-iron concentrate, under a range of experimental conditions that might have process potential. The effects of temperature, oxygen partial pressure, initial acid concentration, excess or deficiency of acid, initial particulate surface area, agitation, catalyst additions (cupric and ferric sulphate) and time on the rate of leaching of sphalerite, galena, chalcopyrite and pyrite were investigated. Galena was found to dissolve with the formation of hydrogen sulphide and lead sulphate. The hydrogen sulphide inhibited the dissolution of both sphalerite and chalcopyrite but not galena. The effect of experimental variables on the rate of oxidation of hydrogen sulphide to sulphur are reported. This reaction was found to take place on the surface of sulphide particles between adsorbed species and the rate determining step was the oxidation of adsorbed ferrous ions by dissolved oxygen. Scanning electron micrographs are presented which show that the lead sulphate forms as a non-coherent crystalline layer on the galena surface. Conversion reaction kinetics were consistent with rate control by liquid phase diffusion in the pores of this layer. The rate of conversion was independent of oxygen partial pressure, initial acid concentration and hydrodynamics but was directly proportional to the initial particulate surface area. A very low temperature dependence was exhibited. Sphalerite was found to exhibit linear leaching kinetics up to extractions of eighty percent after reaction inhibiting hydrogen sulphide had been removed by oxidation. The rate of linear leaching was directly proportional to oxygen partial pressure and surface area but independent of acid concentration and hydrodynamics. The ultimate sulphide oxidation products were elemental sulphur and sulphate ions with the former usually accounting for over ninety percent of the reacted sulphide sulphur. The dissolution reaction producing sulphur was electrochemical in nature and the cathodic reaction involving the discharge of oxygen was found to be rate controlling. Soluble iron catalysed this reaction and a mechanism is proposed that involves the chemisorption of ferrous ions and dissolved oxygen at the mineral surface. Scanning electron micrographs are presented which show that certain crystal faces are preferentially attacked and that dissolution occurs by a pitting action. They also explain why sphalerite dissolution is severely curtailed at temperatures exceeding the meltinq point of sulphur. For extractions exceeding eighty percent the dissolution rate decreased rapidly due to a decrease in cathodic area and to the agglomeration of residues. Chalcopyrite and pyrite dissolved much more slowly than sphalerite and were extensively coated by elemental sulphur because the oxidation of hydrogen sulphide was catalysed on their surfaces. Some practical implications of the leaching results are discussed.

Elastic Solutions can be used to predict stresses and displacements in loaded soil media provided the non-linear stress-strain behaviour of the soil is recognised and allowance made for it in calculating displacements. This thesis examines the methods of elastic analysis suitable for examining problems in Soil Mechanics and the determination of suitable stress-strain parameters. The use of the Finite Element method in Soil Mechanics is reviewed, and a computer program for examining linear elastic plane stress and plane strain problems is presented. The program has been used to examine a range of problems involving infinitely long excavations of rectangular cross-section in the surface of a stratum overlying a rigid base. The excavations were analysed for a uniform vertical loading in the base of the excavation and for lateral wall loads representing the effect of the release of the insitu stresses during excavation. Cases in which the lateral movement of the walls is completely restrained are also considered, and the effect of wall restraint on the vertical displacements due to the vertical base loading is shown to be small. Results obtained by the author suggest that care should be exercised in the use of the Finite Element method to analyse problems involving loaded rigid footings or the stresses behind rigid retaining walls, and that the solutions in these cases may be inaccurate. The solutions available for surface loadings on layered elastic strata are reviewed and results obtained from a Fourier Series approach are presented for a range of problems involving surface loadings on a single rigid base elastic stratum. Uniform vertical and horizontal strip loadings and rigid strip footings with vertical, horizontal and moment loadings are considered. A uniform vertical strip load on the surface of a multilayer stratum overlying a half space or rigid base is also analysed. The computer programs and full mathematical derivations for the strip loading cases are presented, and the extension of the solutions to rectangular loadings is discussed and the basic mathematical derivations outlined. The application of the Fourier Series solutions to the calculation of consolidation settlements is discussed. Work by other investigators suggests that a hyperbolic model may be suitable for approximating soil stress-strain curves and that fundamental stress-strain behaviour should be examined in tests in which the bulk stress remains constant during the application of the shear stress. Equipment designed to carry out slow drained triaxial tests in which the bulk stress is constant during the shearing phase is described, and the results of a short series of tests used to proof test the equipment are presented.

It is generally accepted that some areas of the earth's surface are more prone to earthquake occurrence than others. Furthermore, within these earthquake-prone area the distribution of earthquake epicentres is non-uniform. Ttis has led to a system of regional zoning for earthquake resistant design in most countries. Observations of localised damage resulting from earthquakes has only recently led to the general acceptance of the fact that the degree of damage may be influenced by the characteristics of the soils in the affected area. Where the damage is related to gross instability of the soil resulting in large permanent deformations, association of the damage with local soil conditions is readily apparent. A somewhat less obvious effect of soil conditions on building damage is that subsurface soil layering can influence the intensity of ground shaking, and the frequency content of the surface motion, even though the soils underlying structures may remain perfectly stable during an earthquake. The frequency characteristics of the surface motion are important as the existence of a predominant ground frequency may lead to resonance of structures during prolonged shaking. In Chapter 2 a brief resume of existing knowledge of the occurrence, origin and nature of earthquakes is presented. Basic wave models and wave types are outlined.

A description of the development and design of a two channel solar radiometer is given. Particular attention has been paid, in the choice of receiving system and the design of its components, to the avoidance and reduction of interference. The system used is a two receiver multiplying interferometer with the addition of phase switching. A computer controlled phase cancelling system is used to make the interferometer fringe track the source (i.e the sun), thereby producing a rectified output. An outline of the design of comb-line filters is given. These low loss transmission filters are used at the receiver inputs to attenuate strong out of band interfering signals. Operational amplifiers are used to gain stabilize the RF preamplifiers. Very low sensitivity of gain to temperature change is shown to result from the use of this technique. The system incorporates an analogue magnetic tape recorder so that signals of interest can be replayed for paper strip chart recording at high speed. The recording system has the feature that time of day information is recorded automatically in conjunction with the receiver signals.

It is recognised that saturation of an unbound granular basecourse may lead to the premature failure of flexible asphalt pavements. Basecourse saturation results in increased flexural strains in the asphaltic layer and increased rutting leading to cracking of the surface layer. To obtain a physical and quantitative understanding of the deformation characteristics of saturated granular basecourse materials and the associated failure mechanisms of the pavement structure, laboratory testing equipment was developed including an automated kneading compactor, dynamic triaxial apparatus and a constant head permeameter. Tests were carried out on 250 mm diameter compacted samples of a basaltic aggregate having a maximum particle size of 38 mm. Dynamic tests were performed on both unsaturated and saturated samples. Characterisation tests established variations in resilient moduli and Poisson’s ratio with deviator and confining stress for use in multi-layer elastic analyses. The results of a testing program where samples were subjected to stress states simulating traffic loading, indicated that saturation approximately doubles resilient deformations and increases creep rates by as much as a factor of 10. These changes are caused by loss of capillary stress on saturation and increases in dynamic pore water pressures as a result of applied lateral pressures. A fundamental relationship between the creep rate and the resilient strain amplitude was established, and provides a simple key for the comparative study of different aggregates and the assessment of rut depths in design applications. To assess the effects of dissipation on the magnitude of the dynamic pore water pressures in a pavement structure, a permeability study was carried out on compacted basecourse samples. The permeability characteristics measured were used in a computer analysis to establish the effects of dissipation. Graphs were established showing the effects of permeability and traffic speed on the pore water pressure response. The permeability tests also showed that fines were transported at hydraulic gradients in excess of l resulting in clogging of pore channels and large reductions in permeability. Comparative analyses were carried out to assess the response of saturated and unsaturated pavement sections using the deformation characteristics established in conjunction with a multi-layered elastic computer program. Results of the analyses indicated that the increase in rut depth due to basecourse creep deformation may be 100 times larger for a saturated pavement compared to an unsaturated pavement.

The elastic and geometric stiffness matrices are developed from 1st principles for a beam-column element which is to be used in the linear elastic stability analysis of frameworks. The element formulation is extensively tested against classical and experimental results for beams, columns, and frames. A practical application of the element is demonstrated by using it to investigate the lateral stability of a number of rigid jointed trusses. The bracing requirements of these trusses are compared with the requirements of the bracing to pinned columns, which are the same size as the compression chord of the trusses, and have either a constant or stepwise parabolic distribution of axial load. It is found for most bracing cases, that the critical load and the bracing requirements for a truss, can be closely estimated from an analysis of a column with a "parabolic" axial load distribution.

The investigation reported in this thesis is part of a programme of research concerning the flow behaviour of paper pulp suspensions commenced at the University of Auckland in 1969. A primary aim of the research was to supply the industry with reliable pipe friction data for the pulps manufactured in New Zealand mills. Secondly, it was hoped to increase the fundamental understanding of the mechanisms of flow of the suspensions in pipes and so devise a more satisfactory method of correlation than the one used at present. Pipe friction data were obtained for two N.Z. groundwood pulps, two N.Z. Kraft pulps and one imported Kraft pulp in 1, 2, 3 and 4 inch pipes for a wide range of consistencies and velocities. The data were of the same form as previously reported in the literature, but for a given set of conditions the friction losses were lower for the N.Z. pulps. For Kraft pulps the curves of head loss versus velocity exhibited the usual maxima and minima, but for groundwoods the decrease in head loss from the maximum to the minimum and the subsequent rise were replaced by an approximately level portion. The data in the regime before the maxima in the head loss curves for Kraft pulps were correlated to allow extrapolation to the larger pipes used in the paper mill. This regime incorporates the majority of practical flow situations for consistencies over two per cent. The limits of the regime were approximately defined by values of the dimensionless friction factor. The correlation method used was a slight modification of that employed by previous authors. The data for groundwood pulps were correlated in a similar way. The head losses predicted by the new correlations were consistently lower than those calculated from previous equations. Observation of the flow in perspex pipes confirmed the mechanisms of flow proposed by some previous authors, but disagreed with the mechanisms proposed by others. The mechanisms of flow of groundwood pulps were found to be essentially similar to those of Kraft pulps except that the groundwoods exhibited a plug cleavage phenomenon at very low velocities. The different shapes of friction curve for the two types of pulp were attributed directly to their macroscopic properties. A flow model was developed on the basis of the observed flow behaviour in pipes in which the suspensions move as a fibre/water plug surrounded by a sheared water annulus. The model assumed that the annulus formed as a result of the action of the hydrodynamic shear stress on the fibre network comprising the plug. The analysis resulted in an expression relating the average velocity and the longitudinal pressure gradient in the pipe and also incorporated the pipe radius, the viscosity of the suspending medium μ and a pseudo shear modulus for the fibre network G. The plug flow model was found to apply to the data in the regime before the maximum in the head loss curve. The relation between the pressure gradient and the pipe diameter as predicted by the model was slightly erroneous for some pulps, although it was the same as that in the standard empirical correlation used in design by the industry. This led to the conclusion that the deflection of fibre ends on the plug surface also contributed to the formation of the annulus, as proposed by previous authors. The relative importance of the two mechanisms of annulus formation was used to explain the occurrence of the maxima and minima in the head loss curves for chemical pulps. The plug flow model was found to be closely related to both the direct correlation method used in the past and to the standard pseudoplastic model for non-Newtonian pipe flow. The model was also applied to analogous flow in a rotational viscometer. The values of the pseudo shear modulus G calculated from the rotational viscometry data were the same as those calculated from pipe flow data under certain conditions. However, limitations in the equipment and the effect of gravitational settling restricted the results to a narrow range. The behaviour of the pulp suspensions in batch settling tests varied markedly from pulp to pulp. There was a high correlation between the pseudo shear modulus G obtained from pipe flow data and the final height of the suspension in a settling test. Likewise there was a relationship between the effective viscosity of the suspending medium μ (as modified by the proportion of fines in the pulp) and the initial settling rate in a batch test. This suggested that a simple and accurate method of determining pipe friction data from batch settling test data is possible. Settling tests also showed that air content and the presence of acidic and basic ions, but not the viscosity of the suspending medium, increased the strength of fibre networks. A further correlation method to incorporate all flow regimes was suggested from the results of the present investigation and from indications in the literature that fibre networks behave like Bingham plastics when they are sheared.

This thesis describes the development of a bus crew scheduling method, based on a set partitioning model, for the Christchurch Transport Board, New Zealand. It also examines in detail the effects of the high degree of degeneracy in scheduling set partitioning models. Degeneracy can cause severe computational difficulties because it inflates the number of simplex iterations needed to solve the set partitioning linear programme. In this thesis, it is shown that a maximum-pivot leaving variable criterion can considerably improve the performance of the simplex method, but that this alone is insufficient. Experiments with several degeneracy-resolving techniques have been performed on a class of highly degenerate problems arising from an air crew rostering application, and the results are discussed. Before the set partitioning model can be applied to scheduling, the problem size must be heuristically reduced. Therefore the overall Christchurch system is divided into several subsystems which are solved sequentially. Also, a three-stage method has been developed which essentially considers each type of duty individually. At the first stage, meal-breaks are allocated carefully to reduce the effects of the loss of interaction among the subproblems. A further heuristic reduction technique is then applied to each subproblem, not only to reduce its size but also to improve its integer properties. The resulting solution method has been applied to the Christchurch weekday scheduling problem. A special technique for the Sunday scheduling problem has also been developed. The two methods are described and the promising results which have been achieved are discussed. / Whole document restricted, but available by request, use the feedback form to request access.

The coefficients in a mathematical model of a physical problem typically correspond to the material parameters of the problem. In heterogeneous media the material parameters may vary with position, dependent variable value and/or time. The governing equation of a physical problem in heterogeneous media is therefore likely to involve variable coefficients. For this reason the solution of variable coefficient partial differential equations (PDEs) is an important engineering problem. In this thesis ways of solving linear variable coefficient PDEs using the boundary element method have been investigated. The application of the boundary element method to these equations is hampered by the difficulty of finding a fundamental solution. In the literature several methods have been proposed to overcome this problem. A survey of these methods has been undertaken in this study from which it is concluded that the most promising approach is the dual reciprocity boundary element method (DR-BEM). The DR-BEM is tested in this thesis for a range of elliptic variable coefficient PDEs. The results of these test problems indicate that the DR-BEM is a promising method for solving elliptic variable coefficient PDEs. However, in some cases, such as problems in highly heterogeneous media, it is found that a large number of internal solution nodes are necessary to ensure accurate results. This can make the DR-BEM computationally expensive. Some new approaches for improving the efficiency of the DR-BEM are proposed. For problems in highly heterogeneous media a subregion approach is recommended. The use of the DR-BEM for linear parabolic variable coefficient PDEs is also investigated. It is found that by combining the DR-BEM with the coupled finite difference – boundary element method a wide range of parabolic problems can be solved without requiring domain integration. This time-stepping approach can become expensive for variable coefficient PDEs (particularly for large-time solutions) as it requires the solution of a large number of associated elliptic problems with large numbers of internal nodes. Also, it is found that for some problems in highly heterogeneous media the error at each time-step can accumulate leading to poor large-time solutions. To avoid these limitations semi-analytic approaches for solving parabolic equations are investigated. A new semi-analytic method - the separation of variables dual reciprocity method (SOV-DRM) - is proposed which constructs the solution as an eigenfunction expansion. The eigenvalues and eigenvectors are determined using the DR-BEM. This method allows parabolic problems to be solved without requiring time-stepping or domain integration. This method is found to produce accurate results for a range of problems including some problems involving heterogeneous media. Two other semi-analytic methods are also investigated. These methods are implemented and compared with the SOV-DRM. It is concluded that each method has specific strengths and weaknesses and that the choice of method is largely problem dependent.

The work described in this thesis is an analytical and experimental study of two-phase gas-liquid horizontal flow in a conduit with particular emphasis on holdup measurements and predictions. Holdup and pressure drop, their inter-relationships, and their flow pattern dependence were investigated. A simple method for flow pattern determination was presented so that the appropriate prediction method may be selected for a particular situation. The results were discussed by comparison with a wide range of experimental data and the relevant literature. Two simple devices for holdup measurements were developed in this work and their behaviours were also found to be flow pattern dependent. The results are as follows: In the analytical study, the original Lockhart-Martinelli formulation was treated analytically for ideal stratified flow giving equations which agree with experimental pressure drop and holdup data and the more rigorously derived relationships of Johannessen and Taitel & Dukler. For ideal annular flow, the derived equations predicted pressure drop in large diameter pipes reasonably well giving results which are in agreement with the modified equation of Baker. Poor prediction was achieved for small diameter pipes. The holdup equations derived for annular flow were also in poor agreement with experimental data although a slight modification resulted in an equation that was not only suitable for holdup prediction, but also may be used to represent the original Lockhart-Martinelli holdup correlation over the entire operating range. A correlation was presented for the frictional pressure drop in annular flow based on laboratory air-water data and geothermal steam-water data. The correlation was found to predict pressure loss values which agreed with data from various different sources. The correlation exhibited a point of inflexion which was believed to be due to the transition from a ripple wave type of interfacial disturbance to one of roll wave-droplet entrainment. An extensive literature survey showed that such a transition at high gas rate occurs at all flow orientations and is governed by a critical liquid rate given by a definite value of the Weber number defined in terms of the liquid phase. The Butterworth form of holdup equation was justified by assuming ideal stratified and annular turbulent-turbulent and viscous-viscous flows. A full set of equations for stratified flow covering the cases of liquid-gas, turbulent-viscous and viscous-turbulent were also derived. It was found that the variation in the coefficients and exponential factors in the Butterworth equation was due to at least three factors: the flow pattern, the flow regimes of the phases, i.e., viscous or turbulent, and the range of the value of the ratio of the liquid holdup to the voidage. Furthermore, experimental data were found to behave according to whether the flow pattern was stratified, slug and plug or annular. Equations for determining these flow patterns were presented, based on the derived stratified flow equations, and were checked to be in agreement with the flow pattern maps of Mandhane et al and Taitel & Dukler, and the experimental flow pattern observations of this work. Since the derivation from the original Lockhart-Martinelli formulation did not yield a completely satisfactory relationship for the holdup and pressure drop in annular flow, such a relationship was examined in terms of the film flow equations, Newton's law of viscosity and the Prandtl’s mixing length. This was also compared with the analysis of Levy of annular-mist flow using the mixing length theory. Throughout the analysis, the results were compared with various sources of laboratory air-water data and geothermal steam-water data, and the discrepancies, if any, were discussed. The rise velocity of Taylor bubbles in conduits was also examined in terms of the film flow equations, the Newton's law of viscosity, the Prandtl’s mixing length theory and the universal velocity distribution equations. The rise velocity of a Taylor bubble as derived by the Prandtl's mixing length theory has the same form as that derived by Dumitriscu and Davies & Taylor who used the classical potential flow theory. The analysis was extended to justify the Armand equation for holdup for slug and plug flows. Thus, to summarise the analytical work presented in this work, given a set of input conditions, the flow pattern may be predicted as one of three: stratified, slug and plug, annular. From a knowledge of the flow pattern, appropriate methods of holdup and pressure drop prediction may be chosen. The interrelationships between holdup and pressure drop for stratified and annular flow have also been shown. In the experimental study, the application of two simple devices, developed in this work, one of which was subsequently patented, for holdup measurement was investigated. Both devices were found to be flow pattern dependent in their behaviour and require calibrations. During the study of these two devices, pressure drop, holdup and flow pattern data were also generated and were used for the comparison with the analytical part of this work.