<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)

<p>An Integrated Coastal Engineering model (ICEM) has been developed, which models the waves, the coastal circulation and the rates of bed level changes simultaneously. The wave model simulates the combined effect of refraction, diffraction, shoaling, reflection and breaking and the circulation model simulates the wave driven currents in the coastal zone. Finally, the morphological model simulates the sediment transport loads and the morphological changes after solving the combined wave current boundary layer. The waves, currents and sediment transport loads are recalculated for every so-called morphological time step. The ICEM is capable of modeling both the short and long term effects of coastal structures such as groins, detached breakwaters, seawalls, etc. The ICEM is calibrated and verified using field data in the Mediterranean coast of Egypt. The model is applied to similar areas in Crete, where the wave climate and bathymetric data are available. The best protection scheme is defined for each area. From the engineering point of view, this research provides an effective design tool for coastal protection projects. It also can provide an assessment on the effectiveness of the existing coastal protection projects.</p> / Doctor of Philosophy (PhD)

<p>Structural frames designed or proportioned to resist seismic forces, must possess adequate ductility to redistribute internal forces or have needed energy absorbing capability. This research investigation touches on a number of aspects that deal with or relate to the above characteristics, while the principal aim is to assess and compare the rotation capacity and energy absorption of locally web stiffened beams with unstiffened beams.</p> <p>An approach which allows for the prediction of the initiation of local buckling in the design of wide-flanged beams under moment gradient, is first presented. The method described represents a refined moment-rotation model that includes the effects of strain hardening. This same approach helps define more accurately the appropriate slenderness limits of a beam's plate-elements in relation to the required rotation capacity at maximum moment.</p> <p>The study then addresses the interaction effects of a steel member's plate slenderness values and its lateral slenderness on rotation capacity at ultimate deformation. It is shown that members with slenderness values close to the limits specified by codes of practice may not be able to redistribute moments adequately under seismic loading.</p> <p>To further ascertain and assess the ductility and energy dissipation capabilities of W-shaped beams, a series of test specimens subjected to monotonic and quasi-static cyclic loading was conducted. The specimens were meant to represent beams in ductile moment resisting frames undergoing cyclic lateral loads. Of direct relevance to seismically designed moment resisting steel frames, the experimental results of this research effort clearly highlight the superiority of herring-bone style stiffened specimens over unstiffened specimens. To provide further supporting evidence, as well as insights into the behaviour of herring-bone stiffeners, an inelastic large deformation analytical study was undertaken using cubic-quadratic shell finite elements. This work allowed a parametric study to be undertaken on the effects of stiffener thickness on strength and ductility properties. Based on these, and the experimental results, preliminary design guidelines have been proposed. Another important objective was to assess and document the strength and energy deterioration occurring under conditions of low cycle fatigue and which involve local buckling.</p> <p>The results of a series of W-shaped test specimens subjected to fatigue type of loading under constant amplitude are presented. This work has permitted strength and energy deterioration and damage models to be developed for the W-shape steel beams. A generalized model which uses plate slenderness values together with lateral slenderness is proposed for predicting the rate in strength deterioration per reversal and cumulative damage after a given number of reversals.</p> <p>The research investigation concludes with a review of some of the concepts used in damage assessment; simple damage parameters such as ductility ratio and realistic mathematical models reflecting the deterioration of steel beams due to maximum response, and, dissipated energy are then discussed. Damage models are then presented that combine maximum response with repeated effects in low-cycle fatigue loading. The proposed models calibrated through the use of cyclic tests on steel beams, are then used to yield deterministic parameters that predict adequate ductility values for steel beams under cyclic loading. This phase of the work was completed by having the damage models incorporated into a non-linear dynamic analysis of a sample building and ends with the recommendation of employing a new "adequate ductility" design parameter.</p> / Doctor of Philosophy (PhD)

<p>A new shell element for the analysis of thin and thick plate and shell structures has been formulated along with the compatible beam element. The new elements are referred to as the consistent shell element and the consistent beam element. By combining the consistent shell element and the consistent beam element a finite element model for the analysis of reinforced concrete structures has been formulated. The scope of the study is broadened further through the modification of the new elements to allow for the analysis of laminated fiber-reinforced composite beams and shells.</p> <p>Many of the currently available beam and shell elements exhibit spurious variations of the transverse shear stress(es). To obtain improved responses when thin beams or shells are analysed the reduced integration technique has typically been employed. This approach is not acceptable since the reduced integration technique cannot be applied with complete confidence. In the present study it is found that the unsatisfactory behaviour of these elements is due to an inconsistency in their formulation. In the formulation of the new elements a consistent formulation has been ensured. The new elements behave very well in the analysis of both thin and thick beams and shells and contain no spurious zero energy modes. In addition, they provide a quadratic variation of the transverse shear stress(es), and a cubic variation of the displacement(s) through their thicknesses. Therefore, the shear correction factor k, which is usually required to correct for the assumption of constant transverse shear strain through the thickness is not required. Both elements include material non-linearity. Special attention has been given to the efficient implementation of the consistent shell element by employing a sub-matrix formulation in conjunction with a modified frontal solution algorithm. The numerical results show the new elements to be highly accurate and computationally efficient.</p> <p>The reinforced concrete finite element model employs a rational elasto-plastic constitutive relationship for concrete, discrete bar elements for modelling of reinforcement, joint elements for bond slip between concrete and reinforcement, beam elements for supporting girders and shear connector elements along the concrete/girder interface. The numerical results show that the model accurately predicts the behaviour of reinforced concrete slabs, including punching shear failure under point loads. The constitutive model employed has been found to be reasonably objective with respect to refinement of the finite element mesh.</p> <p>The consistent laminated beam element and the consistent laminated shell element, have been formulated for the analysis of laminated fiber-reinforced composites. Special attention has been given to the approximation of stresses through the thickness of the laminate because of their importance in predicting delamination failures. This has been achieved by allowing the transverse shear strain(s) to be discontinuous at the interface of two layers while still maintaining continuity of the global displacements across the interface. The numerical results show that the elements provide very accurate predictions of stresses through the thickness of both thin and thick laminates.</p> / Doctor of Philosophy (PhD)

<p>Combined sewer systems are designed to bypass excess flows directly to the receiving water during rainstorm events. This is commonly achieved by means of diversion structures incorporating side spillways, oblique weirs or orifices.</p> <p>The simulation of diversion devices by the EXTRAN Block of the Stormwater Management Model is examined. Results for the weir algorithm were not satisfactory. Therefore, a new procedure is written to compute the overflow and the water surface profile along the side weir. The hydraulics of flow over side weirs is reviewed in detail. The momentum approach is used in computing the water surface profile. The coefficient of discharge is estimated from a newly proposed relationship. A method for predicting the formation of a hydraulic jump along the weir section is derived from the momentum balance between the upstream and downstream side of the jump.</p> <p>A computer program called OVRFLO3 is developed to compute the overflow and the water surface profile. Validation tests show good agreement with observations.</p> <p>Finally, OVRFLO3 is adjusted to fit the SWMM package. The new Block is called SIDWEIR.</p> / Master of Engineering (ME)

<p>The finite element method of simulating tunnel excavations in squeezing ground requires experimental data on multiaxial creep relationships and related characteristics of rock and concrete as input. A servo-controlled test frame, for applying multiaxial stress states to cubical specimens through three independent actuators, was developed. This test system allows the simulation of typical stress levels and stress paths involved during rock excavation, with continuous monitoring of loads and displacements through a data acquisition system. The overall equipment development required considerable design and assembly effort. A testing programme for concrete specimens was completed to evaluate the equipment. Finally, conclusion and recommendations were made which provide the necessary information and guidance for future testing to develop multiaxial creep relationships for rocks known to have significant time-dependent behaviour.</p> / Master of Engineering (ME)

<p>Conical steel shells are fairly widely used as elevated water tanks. However, the current code of practise in North America for the design of such reservoir structures provides an obsolete method for ascertaining their adequacy to resist hydrostatic loadings. Moreover, there are no provisions available for handling liquid-filled conical tanks subjected to seismic forces. The lack of appropriate design methods could not have been demonstrated more vividly when in December of 1990, an elevated conical water tower failed by buckling when being filled for the first time. The steel vessel, located in Fredericton, New Brunswick, is claimed to have "exploded" by eyewitnesses.</p> <p>The work of this thesis, then, was motivated by this failure. It involves non-linear stability analysis of liquid-filled conical steel vessels possessing geometric imperfections and residual stresses, and which can be subjected to hydrostatic and seismic loading. To achieve this, a finite element formulation is developed based on a consistent shell element which is free from spurious shear modes known to exist in the isoparametric shell elements. The consistent shell element employed also exhibits excellent performance in the analysis of plates and shells in the small displacement range. This element is extended to include both geometric and material non-linearities as well as non-linear dynamic analysis. The non-linear finite element model developed is general and can be applied to any thin or thick shell problem. Numerical testing of the non-linear model through static and dynamic analysis of different plate and shell problems indicates the continued excellent performance of the consistent shell element in the non-linear range.</p> <p>Hydrostatically loaded conical steel vessels are modelled using the consistent shell element. Static stability analyses of conical shells with different geometric imperfection patterns are undertaken and the results indicate that the presence of axisymmetric imperfections leads to the lowest limit load for the structure. The sensitivity of the hydrostatically loaded conical vessels to geometric imperfections and residual stresses is investigated by considering three cases: (i) analysis of perfect vessels, (ii) same as case (i) but with axisymmetric geometric imperfections of the order of the thickness of the shell, (iii) same as case (ii) but with the addition of residual stresses due to welding. The results from these analyses indicate that the liquid-filled conical shells are significantly sensitive to geometric imperfections, and that yielding precedes elastic buckling for tanks having practical dimensions.</p> <p>The non-linear dynamic (stability) analysis of elevated liquid-filled conical vessels subjected to both horizontal and vertical accelerations, but free from rocking motion, is then considered. The boundary integral method is used to formulate the fluid added-mass matrix resulting from the impulsive component of the hydrodynamic pressure. This is added to the mass matrix of the shell structure to perform free vibration as well as nonlinear time history analyses for elevated liquid-filled conical tanks treated as either perfect or axisymmetrically imperfect. Tanks with different dimensions and imperfection levels are subjected to an appropriately scaled real input ground motion. Some of these elevated structures exhibit inelastic behaviour and generally develop a localized buckle near the bottom of the vessel which leads to the overall instability of the structure. In general, time history analyses indicate that liquid-filled conical tanks, often possessing apparently adequate safety factors under hydrostatic loading, may not be safe under seismic loading. Therefore, a proper modelling procedure along with time dependent analysis must be followed in order to design such tanks safely. The finite element model developed in this thesis is a means provided for such a purpose.</p> / Doctor of Philosophy (PhD)