<p>The objective is the development of two reIated mathematical models to provide minimum cost designs of water distribution and waste-water collection networks.</p> <p>This wealth of literature is classified in terms of problems formation and method of solution. This places individual contributions in perspective and serves to identify the major shortcomings of existing techniques. These are:-</p> <p>1- Inability to handle large network systems efficiently. 2- lnadequate treatment of the hydraulics of the system. 3- Absence of a satisfactory discrete solution.</p> <p>The results presented are considered to be more comprehensive than any other technique reported in the literature to the author's knowledge. The major contributions presented are:-</p> <p>(i) Both problems are formulated in the form of a nonlinear programming problem and in terms of practical engineering variables and solved by application of the MINOS package.</p> <p>(ii) A standard data format is suggested which allows user input to be defined in a very compact and logical form.</p> <p>(iii) Pre-and Post-processors are developed which free the user from the complicated and extremely error-prone tasks of creating the necessary input data and interpreting the resultant output files of the MINOS package.</p> <p>(iv) For distribution networks, a comparison is presented between the explicit use of a network analyser (coupled with an efficient optimization package) and the implicit incorporation of the analysis stage within the linear and nonlinear constraints of a comprehensive nonlinear model. The latter method is shown to have significant advantages.</p> <p>(v) For collection networks, a model formulation is presented which properly represents the hydraulics of part full flow in circular sewers. The problem size is reduced by the introduction of an equality constraint which correlates velocity and discharge under these conditions. The accuracy of the method is checked by comparison with a more rigorous but significantly more expensive problem formulation.</p> <p>(vi) Methods are suggested whereby pumps, reservoirs, pressure reducing valves and minor loss devices can be easily and correctly incorporated in a distribution network design.</p> <p>(vii) Techniques involving variable transformation and the partitioning of basic, nonbasic and superbasic variables are developed which greatly increase the efficiency of solution.</p> <p>(viii) For both types of network, the models are augmented to allow a very good discrete solution to be obtained in terms of pipe diameter. A heuristic argument is presented which suggests that the solution for distribution networks must be very close to optimal although optimality cannot be rigorously proven. For collection networks it is shown that discretization may frequently be infeasible unless at least one of the constraints is relaxed in the form of a 'soft' constraint.</p> <p>(ix) Both types of network design are demonstrated using problems of substantial size. For distribution networks a method is demonstrated whereby the analysis or design problem can be solved as special cases of the more general optimization problem.</p> / Doctor of Philosophy (PhD)

<p>When new construction projects are postponed or cancelled because of socio-economic concerns, greater emphasis is placed on enhanced operational planning -- to get the most at the least cost, from the existing projects. Of the approaches that made significant improvement in the operation of energy production systems is the co-ordination between hydro and thermal power plants. In this research, the problem of "Long-term Optimal Operation of Hydro-Thermal Power Systems" is addressed. Considering the uncertainty in reservoir in flows, the problem is defined as a "two-stage stochastic linear network programming with recourse". To avoid dimensionality problem generally associated with the employment of dynamic programming in large scale applications, Bender's decomposition approach is employed as the solution algorithm basis for the defined problem. Using the "General Algebraic Modelling System", a modelling code, the "Hydro-Thermal Co-ordinating Model (HTCOM)" is developed. In HTCOM, each sequence of hydrologic inflows generates a subproblem which is solved deterministically. The solutions of all subproblems are next co-ordinated by a master problem to determine a single feasible optimal policy for the original problem. This policy includes optimal reservoirs releases as well as allocation of energy generation at different power plants in the subsequent time period. The objective minimizes the expected total cost of meeting the energy demands while satisfying the system constraints over the long-term horizon of one to three years. To demonstrate the applicability of HTCOM, a real world case study named the "Khozestan Water and Power Authority (KWPA)" in Iran is employed as a system of two multipurpose reservoirs with five hydro-thermal power plants and transactions of energy. The KWPA system components are operating policies are stimulated as the network flow model and an integrated solution procedure is planned to determine the optimal operation policies. This procedure included the development of three specialized models: - HTCOM-I: to investigate the potential improvements of the current system; -HTCOM-II: to provide the required confidence in using the model in future simulations by evaluating the actual savings; and -HTCOM-III: to simulate the system operation under uncertainty, and determining the optimal operation policies for the next month. The results of employing all three cods in the KWPA system conclude that the selected approach for formulating the problem, the adopted algorithm based on Benders' decomposition technique, and the models (developed in the GAMS environment) are suitable, capable to handle stochasticity of inflows, and considerably cost-efficient.</p> / Doctor of Philosophy (PhD)

<p>In cold climates, temperatures higher than the ambient have been observed near the bottom of water lakes in the vicinity of thermal discharges. Concern has been expressed about the adverse effects of such abnormally warm water on the winter ecology of lake bottoms. It is expected that the existence of a density extremum in water at 4° C and the resulting nonlinear relation between density and temperature gives rise to densimetric flows which are markedly different from those in the linear range.</p> <p>This thesis presents experimental and numerical investigations that give some insight into the phenomenon of the thermal bar and the manner in which it may infIuence nearshore transport processes in the vicinity of a thermal outfalI in a cold climate. The investigations are restricted to an idealized model where the lock exchange mechanism is selected due to the fact that its behaviour is close to that expected in the prototype situation.</p> <p>The experimental investigation provides dramatic proof that the existence of an extremum in the density-temperature relation has a profound influence on the behaviour of densimetric flows in general and lock exchange behaviour in particular. Three zones in the vicinity of a thermal bar are clearly demonstrated viz. (i) the thermal overflow region. (ii) the thermal bar, and (iii) the thermal underflow region. The experiments provide data on the horizontal scale at which sinking takes place.</p> <p>A numerical model has been constructed to develop a means of modelling the behaviour of a thermal bar at the outfall of a steam electric generating station cooling water system. The numerical model employs a finite-difference scheme where the resulting algebraic finite difference equations are soIved using an alternating direction implicit method and a sparse-matrix package. The numericaI modeI has been verified by comparing it to numerical solutions of four different cases of the idealized problem of steady laminar flow in an enclosed rectangular cavity with differentially heated end walIs. Moreover, additional acceleration techniques are introduced to improve the numerical solution procedure. The numerical model is employed to solve the actual problem of simulating lock exchange flows created between two water bodies having different temperatures around the temperature of maximum density (i .e. having temperatures above and below 4° C). The general behaviour which has been observed experimentally is also confirmed numerically. The sensitivity of the associated parameters is examined. The relative extension of the thermal bar is correlated with relevant system parameters. Difficulty was experienced in obtaining numerical results for the same (high) Rayleigh numbers as were used for the physical experiments. Despite this, an encouraging degree of consistency was observed between simulated and observed behaviour.</p> <p>The important aspect of the study is to draw attention to the adverse effects of the sinking phenomenon (thermal bar), which may occur in the vicinity of man-made warm effluents as well as in natural bodies of water during the spring warming period. The study is significant in terms of the horizontaI scaIe at which sinking takes place, for the design of power station once-through-cooling water systems that must operate in cold climate winter conditions.</p> / Doctor of Philosophy (PhD)

<p>The fact that considerable quantities of solids, toxic metals and hazardous contaminants are washed off urban surfaces has been well documented in recent literature.</p> <p>It is generally recognised that urban runoff models predict runoff quantity quite well. However, due to lack of understanding of the various processes involved in pollutant buildup, washoff and routing and insufficient, and faulty data collection, urban runoff models depict runoff quality poorly. This research therefore attempts to introduce new concepts and algorithms, based on the physical processes involved, to improve runoff quality prediction. The problem has been segmented into three broad areas: a) pollutant buildup, b) pollutant washoff and, c) routing and fate of pollutants.</p> <p>The interaction of addition and removal processes in pollutant buildup has been further disaggregated. Estimates are made of the daily mass balance of pollutants over a dry period, considering meteorological and geographical effects. Additions from atmospheric dustfall, vehicles, population and special activities; removal due to biological decay, vehicle and wind created eddies and intentional removals (street sweeping) are formulated individually. Scavenging of aerosols and gases and washoff from canopies during precipitation are also modelled and added to conventional washoff. Expressions for the impact of raindrops, shear due to overland flow, and vehicle-induced eddies are used to develop a new washoff equation which is compared to conventional washoff equations. An established pollutant routing algorithm is modified to minimise summation error. All these pollutant concentration prediction algorithms are interfaced with one of the most comprehensive models, the Storm Water Management Model Version 3 (SWMM3), preserving the runoff quantity prediction algorithms. Provision has been made for variable time steps for both runoff quantity and quality. The modified SWMM3 is called CHGQUAL in the present work. CHGQUAL was applied to the Chedoke Creek Catchment in Hamilton, Canada, for verification, calibration and validation. The pollutional parameters used in the study are suspended solids(SS), biochemical oxygen demand (BOD), total nitrogen (TKN) and total phosphorous (TP). The CHGQUAL computed pollutant concentration results were statistically compared to both SWMM3 results and observed data.</p> <p>The new runoff water quality algorithms showed improved predictability for the test catchment. The CHGQUAL model can readily be applied to other catchments.</p> / Doctor of Philosophy (PhD)

<p>Coagulation is a common water treatment step primarily designed to aggregate and thereby help remove true particulate (turbidity causing) matter. Organic compounds of natural origin (i.e. humic and fulvic acids) have also been observed to be removed by Coagulation. This research was designed primarily to identify the limiting mechanisms responsible for the removal of natural organics by the coagulation process. This identification is thought to be crucial in the optimization of this important water treatment step as it may help to maximize the benefits obtained from coagulants.</p> <p>The examination of the literature related to this topic suggests two possible removal routes:</p> <p>(i) a reaction whereby the fulvic acids form an original compound with the coagulating ion Al³⁺ or one of its hydroxy complexes.</p> <p>(ii) the adsorption of the fulvic acid molecules or jons onto the surface of a solid precipitating independently of these compounds.</p> <p>These two possibilities are examined in detail on theoretical grounds, and two following pieces of information are defined as being discriminatory with respect to the two removal routes:</p> <p>(i) The shape of the isotherm, as defined in typical adsorption studies.</p> <p>(ii) The ligand number or OH/Al ratio of the precipitate, accessible by processing the dissolved Aluminum data with respect to pH.</p> <p>These considerations lead to an experimental design allowing the convenient evaluation of these characteristics. An array of nine treatment dosages and four operating pH is applied on two raw waters, using four Aluminum based coagulants.</p> <p>The results suggest that under these experimental conditions (dosage between .1 and 1 mM Al/L pH between 5 and 8.5), the Fulvic acids are removed by Adsorption onto Al(OH)₃, regardless of the type of coagulant. Increasing pH and the presence of SuIfate in the coagulant were found detrimental to this adsorption. Increasing OH/Al ratio in the coagulant is detrimental at low pH, low dosage, and becomes beneficial at neutral to mildly alkaline pH conditions. A two stage treatment scheme was found efficient at neutral to mildly alkaline pH, using Alum.</p> / Doctor of Philosophy (PhD)

<p>A research program is presented to investigate the behaviour of rectangular hollow section (RHS) T-joints in the elasto-plastic range of loading. The study includes the determination of both rotational and punching shear stiffnesses and strengths of the RHS T-joints due to branch moment or punching shear or a combination of both. The determined joint characteristics are then incorporated into an elasto-plastic analysis of Vierendeel trusses composed of RHS members.</p> <p>Two different joint types have been analyzed, the double chord T-joint and the single chord type. In both cases, the joint is modelled by the chord top flange treated as a thin plate loaded on the perimeter of a rigid inclusion and restrained by coupled translational and rotational springs along its longitudinal edges. These springs simulate the restraining effect of the side walls and connecting bottom flange. Transverse edges, some distance from the joint, are taken as simply supported.</p> <p>The proposed finite element formulation incorporates rectangular plate, beam and boundary spring elements. The formulation considers both bending and in-plane actions. Material nonlinearities of the joint are assumed to be adequately represented by the Von-Mises yield criterion and the associated flow rule. While geometric nonlinearities have been neglected, this assumption is reasonable for the range of deformations deemed important in this study.</p> <p>A parametric analysis has been undertaken for each of the double chord and single chord joints under either branch moment or punching shear. Each analysis considers the effect of each of five non-dimensiononal geometric parameters. One of the parameters, considered, is used to study the stiffening effect of a reinforcing flange plate. Results of the analysis are presented in the form of non-dimensionalized load-deformation (M-Φ and P-δ) curves.</p> <p>A standardization procedure has been used to develop generalized (M-Φ and P-δ) formulae, based on the parametric analyses. In addition, formulae for the joint stiffness and strength, in terms of its geometry, are presented for each case.</p> <p>When the joints are analyzed under combined loading, the branch moment and punching shear are applied in different ratios. The results are presented in the form of interaction equations.</p> <p>Next, the joint characteristics have been incorporated in an elasto-plastic finite element analysis of Vierendeel trusses. The effect of the joint flexibility on the truss behaviour is investigated. Also considered is a comparison between trusses possessing single chords and those possessing double chords.</p> <p>Another aspect of this investigation is to predict upper bound capacities for the double chord joints due to branch moment or punching shear. The yield line theory has been utilized for this purpose.</p> <p>The experimental part of the study involves the testing of ten double chord joints. Results of these tests along vith other available experimental data are used in examining the validity of the analytical models that have been developed.</p> / Doctor of Philosophy (PhD)

<p>In this study the two problems of rainfall estimation and forecasting using data from weather radars and rain-gauges are studied. A GIS multi-component interface is developed for the analysis of weather radar precipitation data. This interface performs different operations, such as loading and redelivering radar and satellite data, projecting geographical features into the radar coordinate system, and overlaying data from multi-sensor into a common coordinate system. Additional features include accumulating radar rainfall depths, radar comparison with rain-gauge data, animating storm evolution on top of geographical features, and tracking and forecasting rainfall fields. Accurate measurements of rainfall duration, timing, location, and intensity are important for different water resources applications. Weather radars can provide valuable information on the space-time variations of rainfall. However, there are uncertainties in the radar measurements of precipitation. Thus rain-gauges are used to calibrate Z-R relations, which are used to convert from radar reflectivity Z to rainfall rate R. Sampling errors cause differences between rainfall estimated by radar and that estimated by rain-gauges. These errors constitute a limitation for use of radar data for high resolution applications such as urban applications. A methodology is developed to address and correct the effects of these errors. The results prove that correction for these errors reduces the variation between the two sensors. In addition, given that the radar is properly calibrated, correction for sampling errors can provide temporally detailed radar rainfall fields that can be used for high resolution hydrological applications. The comparisons between two Canadian radars (King City and Exeter) show that there is good agreement between rainfall fields estimated by the two radars. The comparisons between radar rainfall intensities estimated by the two radars and the corresponding rain-gauge intensities show that the classical Z-R equation used by the National Canadian Radar Network is biased and can lead to serious underestimation of rainfall. An optimum Z-R relation is calibrated using surface rain-gauge data to be used for unbiased rainfall estimation by the two radars. A new radar-based model is developed for quantitative short-term forecasting of rainfall fields. The new model is called the AARS (Automated Adaptive Rainfall Simulator). The AARS model employs an optimization strategy for performing the cross-correlation analysis that reduces the run time significantly and makes the technique attractive for real-time applications. In addition, the model tracks and forecasts the changes in rainfall intensities in space and time and produces forecasted rainfall fields for the specified lead time. The AARS model employs the adaptive exponential smoothing algorithm for real-time parameters estimation. Performance comparisons between the AARS model and the Canadian short-term prediction model SHARP (Short-Term Automated Radar Prediction) show that the AARS is superior in terms of tracking run time and slightly better in terms of accuracy for forecasting lead times up to 30 minutes. The application of the AARS model for rainfall forecasting in Hamilton-Wentworth Region shows promising results for forecasting lead times less than 60 minutes.</p> / Doctor of Philosophy (PhD)

<p>A review of fracture mechanics, fracture toughness and creep behavior of ice is presented. An expression for evaluating the energy releases rate (J-integral) for fracture of ice under creep is developed and incorporated in the finite element program for implicit, incremental, non-linear creep analysis.</p> <p>It is assumed that the energy release rate due to fracture of ice at any creep stage is dependent on the recoverable strain energy and not affected by the non-recoverable work done during creep. A zone classification of the finite element mesh around the crack tip and the equivalent elastic displacements for the stress state at a given creep stage are used to compute the fracture toughness of ice. This is then compared with the prescibeed values of K(ic) (the crack initiation fracture toughness) or K(ia) (the crack arrest fracture toughness) for either the crack initiation or crack propogation, respectively.</p> <p>Two examples are analyzed using the method mentioned above.</p> <p>(i) A rectangular plate with symmetric edge cracks, under plane strain and subjected to uniform tension.</p> <p>(ii) A double slope ice mass with uniform thickness, and an initial crack at the knee, subjected to gravity load.</p> <p>It is assumed that the crack path is predetermined and the crack opening is of mode type I. In both examples the displacements, redistribution of stress around the crack tip and the stress intensity factors are computed at various creep stages. For the double slope example, K(i) is compared with K(ic) or K(ia) and the knee crack is propagated through a finite extension accordingly. Finally, the effect of varying the two slope angles on the stress intensity factor and crack propagation for the double slope example is investigated and was found to be sensitive to the difference between the two slope angles.</p> / Master of Engineering (ME)

<p>Detailed descriptions of finite element models for deformation, temperature and instability analyses of large ice masses are presented. Two non-Newtonian, creeping flow models are developed for steady-state creep situations; one enforces incompressibility, the other near incompressibility. The third creep model incorporates a large displacement formulation and an implicit time-marching scheme for transient creep analysis. To allow for basal sliding, a time-dependent sliding element is also developed. In addition to the creep models above, a transient heat transfer model is presented. By stepwise uncoupling of the stress and temperature dependent creep, it is possible to carry out transient thermal creep analysis for surging of the Barnes Ice Cap. An upwind scheme for triangular elements is given for thermal analysis where the influence of thermal advection is required.</p> <p>It is demonstrated that the three finite element creep models predict similar steady-state creep behaviour for simple ice masses with simple boundary conditions. For more complex problems, agreement of the computed velocities by the models is found to be very sensitive to the boundary conditions at the ice-bedrock interface. Results from the finite element simulations suggest that it may be premature to assume that the influence of elastic strains is negligible.</p> <p>The thermal regime of the Erebus Glacier Tongue is studied assuming steady-state conditions. It is shown that the temperature field is mainly influenced by the near horizontal thermal advection. Reasonable velocity fields for the thermal analysis could only be attained by assuming that the ice is not frozen to bedrock at the transition from a land-based glacier to a floating glacier.</p> <p>Finally, a basal instability model is presented. In this model, the basal shear resistance is reduced according to the excess sliding energy dissipated above some threshold value. The time for a surge to propagate is characterized by a lubrication factor incorporated in the basal instability model. It is confirmed that a geothermal flux approaching 1.9 HFU is required to bring most of the south-west ice-bed interface of the Barnes Ice Cap to pressure melting which would allow for basal sliding and instability. Furthermore, it is shown that the temperature changes during a surge are negligible. The numerical examples analyzed and presented indicate the appropriateness of the analytical modelling and versatility of the finite element method for incorporating complex material properties and boundary conditions.</p> / Doctor of Philosophy (PhD)

<p>The angle of incidence is a major variable for calculating transmission loss from field data [A.S.T.M 336-77]. This suggests that the acoustical insulation of residential construction may vary with the relative location of the flight paths and the housing. Alternatively, the Central Mortgage and Housing Corporation assumes in its guideline that the number of reflected paths in normal residential areas is so great as to override any such effect.</p> <p>The first objective of this study is to investigate the effect of the angle of incidence on the acoustical insulation in residential construction. The second objective is to compare the acoustical insulation as calculated from field transmission loss data with the one estimated in the C.M.H.C. guideline.</p> <p>Field transmission loss data were collected for each one-third octave band for 30 rooms in the Toronto airport area. The first objective is studied using data from rooms affected by aircraft noise, where the flight path is perpendicular to the place defined by the element of interest, as well as from rooms affected by road traffic noise. The variation of the acoustical insulation over time is studied. The results suggest that there is a noticeable effect of the angle of incidence for the houses exposed to aircraft noise. The second objective is studied using data from rooms affected by aircraft noise. The acoustical insulation estimated by C.M.H.C. is found to be lower than the one calculated from field transmission loss data.</p> / Master of Engineering (ME)