The development of a three dimensional B-Spline based method, which is suitable for the steady-state potential flow analysis of free surface piercing bodies in hydrodynamics, is presented. The method requires the B-Spline or Non Uniform Rational B-Spline (NURBS) representation of the body as an input. In order to solve for the unknown potential, the source surface, both for the body as well as the free surface, is represented by NURBS surfaces. The method does not require the body surface to be discritized into flat panels. Therefore, instead of a mere panel approximation, the exact body geometry is utilized for the computation. The technique does not use a free surface Green's function, which already satisfies the linear free surface boundary conditions, but uses a separate source patch for the free surface. By eliminating the use of a free surface Green's function, the method can be extended to considering non-linear free surface conditions, thus providing the possibility for wave resistance calculations. The method is first applied to the double body flow problem around a sphere and a Wigley hull. Some comparisons are made with exact solutions to validate the accuracy of the method. Results of linear free surface conditions are then presented.

Shallow foundations are widely used in different types of soils for supporting the loads from the lightly loaded superstructures of various civil infrastructures both on level and sloping ground. Design of shallow foundations in geotechnical engineering practice is widely based on the principles of saturated soil mechanics because they are relatively simple. However, the soil near the ground surface (i.e., vadose zone) in which the shallow foundations are typically placed is in an unsaturated state. The water content variation in unsaturated soils is influenced by hydrological events such as the snow melt, rainfall infiltration, evaporation, and the plant transpiration. Due to this reason, the hydro-mechanical properties (i.e., coefficient of permeability, shear strength and volume change) of unsaturated soils are sensitive to the variation in soil suction associated with water content changes. These properties in turn have a significant impact on the bearing capacity and settlement behavior of the shallow foundations. Therefore, it is rational to investigate shallow foundations’ behavior extending the principles of unsaturated soil mechanics. During the last two decades, there has been a significant interest towards investigating shallow foundations based on unsaturated soil mechanics. Laboratory, field, and model studies highlight that matric suction variation in unsaturated soils has a significant influence on the bearing capacity and settlement behavior of shallow foundations. However, the focus of most of the presently available studies in the literature consider mostly vertical loading conditions on level soil ground. There are limited studies related to the design of shallow foundations on sloping ground and subjected to inclined and eccentric loading conditions. Also, there are only few studies that consider the effect of the steady state and transient flow conditions on the foundation bearing capacity evaluation. Therefore, one of the key objectives of this thesis is directed toward developing rational tools for investigating shallow foundations considering the steady state and transient flow conditions associated with water infiltration and evaporation in unsaturated soils. Comprehensive investigation studies are undertaken to interpret the influence of the steady state and transient flow conditions on the shallow foundations related to: (i) bearing capacity on the sloping ground in different types of soils including expansive soils, and (ii) bearing capacity under the inclined and eccentric loading conditions with homogeneous soil properties and considering spatial variation of soil properties. Succinct details related to investigated studies are summarized below: (1) An analytical method is proposed for quantifying the bearing capacity of the shallow foundations on unsaturated soil slopes considering different rainfall infiltration conditions. The proposed method is a novel tool for considering the simultaneous influence of several parameters that include the flow rates, the infiltration duration, the foundation set-back distance and the ground water table depth on the foundation bearing capacity. (2) Another analytical method is proposed for evaluating the foundation bearing capacity under inclined and eccentric loading considering both the steady state and transient flow conditions. Semi-empirical equations are proposed for describing the failure envelops in vertical and horizontal (V - H) loading space and in the vertical and moment (V - M) loading space. These equations are capable to describe the variation of failure envelops considering the influence of the groundwater table depth variation, internal friction angles, surface flux boundary conditions and different infiltration durations. (3) The influence of infiltration on the combined performance of both the foundation and the slope in cracked expansive soils is evaluated with the aid of a numerical technique. A semi-empirical model that describes the elastic modulus and the matric suction is implemented into the numerical model. Bimodal soil water characteristic curve is used as a tool for understanding the influence of surface cracks in the numerical study in a simplified manner. The influence of the rainfall intensity, rainfall duration, foundation setback distance and foundation loading on the combined performance of foundation and slope were investigated. Results combined with some suggestions for rational design procedures are presented that can be useful for geotechnical engineers in practice applications. (4) Numerical analyses are conducted for shallow foundations under vertical and combined loading subjected to different flow conditions. A numerical code procedure is exclusively developed as a part of this study to: (i) consider the variation of soil properties along with the matric suction fluctuations in the commercial software ABAQUS with the aid of a user developed subroutine USDFLD; (ii) incorporate the spatial variability of soil properties into the finite element model. Comparisons are provided between the numerical study and other methods such as the experimental investigations, the analytical methods, and the semi-empirical equations for bearing capacity failure envelopes. In addition, comparisons are also made between the failure envelopes and the failure mechanisms contour using the model considering soil spatial variability and homogeneous soil properties. The proposed methods in this thesis are simple to use for evaluating bearing capacity of shallow foundations that are subjected to steady state and transient state flow conditions considering two scenarios: (i) foundation on sloping ground (ii) foundation under inclined and eccentric loading. The results from the above studies reveal that it is the relationship between the soil permeability and the rainfall characteristics that mainly control the water infiltration rates. The soil suction and the effective degree of saturation are influenced by the water infiltration rates and have a significant impact on the foundation as well as the slope behavior. More importantly, the investigations undertaken in this thesis contribute towards addressing the research gaps related to the behavior of foundations in unsaturated soils. Various scenarios considered in this thesis include the influence of unsaturated flow have not been considered earlier in the literature. The results of the studies summarized in this thesis are expected to be useful for practicing geotechnical engineers in the optimal design of shallow foundations extending the principles of unsaturated soil mechanics for various soils. Moreover, the proposed methods can be used for interpreting the foundation behavior for their entire life span service. In addition, these methods can be employed to rationally explain the field-measured data and can also be used in the forensics analyses of failed slopes and shallow foundations.

Hydraulic spool valves are found in most hydraulic circuits in which flow is to be modulated. Therefore their dynamic performance is critical to the overall performance of the circuit. Fundamental to this performance is the presence of flow reaction forces which act on the spool. These forces can result in the necessity of using two stage devices to drive the spool and in some cases have been directly linked to valve and circuit instabilities. As such, a great deal of research and design has concentrated on ways to reduce or compensate for flow forces. In one particular series of studies conducted on flow divider valves, it was established that a rim machined into the land of the spool reduced the flow dividing error by approximately 70-80%, and it was deduced that the main contribution to this error was flow forces. Direct verification of the claim regarding flow force reduction was not achieved and hence was the motivation for this particular study. <p> This thesis will consider the reaction (flow) force associated with a conventional spool land and one with a rim machined into it, and a modified form of the rimmed land referred to as a sharp edge tapered rim spool land. The rim and the sharp edge tapered rim were specially designed geometrical changes to the lands of the standard spool in order to reduce the large steady state flow forces (SSFF) inherent in the standard spool valve. In order to analyze the flow field inside the interior passages of the valve, three configurations of the spool were considered for orifice openings of 0.375, 0.5, 0.75 and 1.05 mm. Computational Fluid Dynamics (CFD) analysis was used to describe the fluid mechanics associated with the steady state flow forces as it provided a detailed structure of the flow through the valve, and to identify the flow mechanism whereby flow forces are reduced by the machining of a rim and tapered rim on the land of the spool. For all openings of the spool, the sharp tapered rim valve provides the largest reduction in SSFF. It was also observed that for all cases studied, the inflow SSFFs were smaller than for the outflow conditions. <p>The prediction of the steady state flow force on the rim spool was investigated in a flow divider valve configuration, and the results from the CFD analysis indicated a reduction by approximately 70%.

Hydraulic spool valves are found in most hydraulic circuits in which flow is to be modulated. Therefore their dynamic performance is critical to the overall performance of the circuit. Fundamental to this performance is the presence of flow reaction forces which act on the spool. These forces can result in the necessity of using two stage devices to drive the spool and in some cases have been directly linked to valve and circuit instabilities. As such, a great deal of research and design has concentrated on ways to reduce or compensate for flow forces. In one particular series of studies conducted on flow divider valves, it was established that a rim machined into the land of the spool reduced the flow dividing error by approximately 70-80%, and it was deduced that the main contribution to this error was flow forces. Direct verification of the claim regarding flow force reduction was not achieved and hence was the motivation for this particular study. <p> This thesis will consider the reaction (flow) force associated with a conventional spool land and one with a rim machined into it, and a modified form of the rimmed land referred to as a sharp edge tapered rim spool land. The rim and the sharp edge tapered rim were specially designed geometrical changes to the lands of the standard spool in order to reduce the large steady state flow forces (SSFF) inherent in the standard spool valve. In order to analyze the flow field inside the interior passages of the valve, three configurations of the spool were considered for orifice openings of 0.375, 0.5, 0.75 and 1.05 mm. Computational Fluid Dynamics (CFD) analysis was used to describe the fluid mechanics associated with the steady state flow forces as it provided a detailed structure of the flow through the valve, and to identify the flow mechanism whereby flow forces are reduced by the machining of a rim and tapered rim on the land of the spool. For all openings of the spool, the sharp tapered rim valve provides the largest reduction in SSFF. It was also observed that for all cases studied, the inflow SSFFs were smaller than for the outflow conditions. <p>The prediction of the steady state flow force on the rim spool was investigated in a flow divider valve configuration, and the results from the CFD analysis indicated a reduction by approximately 70%.

[pt] O presente trabalho apresenta a implementação computacional pelo método dos elementos finitos de procedimentos para análise de problemas de escavação e de fluxo permanente bidimensional, não confinado, para solos saturados. Tais procedimentos, particularmente indicados para investigação do comportamento mecânico/hidráulico de barragens de terra, vem completar o trabalho iniciado por Parra (1996) para análise do comportamento de barragens sob carregamentos estático e sísmico. Foram implementadas duas técnicas para simulação de escavações, obtendo-se, em ambas, resultados numéricos praticamente idênticos. O procedimento para análise de fluxo permanente foi baseado na proposição de Bathe e Khoshgoftarr (1979), a qual considera a situação de fluxo não-confinado como problema não linear, porém conservando a configuração original da malha de elementos finitos. Os resultados numéricos obtidos neste trabalho foram detalhadamente comparados com os valores publicados na literatura, numéricos ou analíticos, como forma de assegurar a confiabilidade das implementações computacionais. A previsão do comportamento da barragem de terra Macusani, a ser construída no Peru, foi estudada neste trabalho, nos aspectos referentes às fases de escavação, construção, primeiro enchimento do reservatório e determinação da superficie de infiltração de fluxo permanente. Os resultados assim obtidos podem ser eventualmente úteis no detalhamento do projeto final da obra. / [en] This work presents a computer implementation for finite element analysis of excavation problems and unconfined steady state flow through saturated soils. These computer routines are particularly useful for the study of earth dams and they were written with the aim to pursue the development of a numerical model (Parra, 1996) devised to investigate the behavior of earth dams under static and seismic loading. Two techniques were implemented for excavation simulations, with both yielding the some numerical results. For the unconfined fluid flow problem the technique proposed by Bathe and Khoshgoftaar (1979) was adopted, which recasts the problem in a non-linear form but keeps the same basic finite element mesh. The results computed in this research were compared with other analytical and numerical values published in the literature, in order to ensure, as much as possible, the feasibility and efficiency of the computer implementations. The behavior prediction of the Macusani earth dam, to be built in Peru, was also studied in this research, focusing on several aspects related to its planned construction: the excavation, the construction itself and the first reservoir filling. This results may eventually be useful for the final engineering design of the Macusani dam. / [es] El presente trabajo presenta la implementación computacional de procedimentos para análisis de problemas de excavación y de flujo permanente bidimensional, para suelos saturados utilizando el método de elementos finitos. Tales procedimentos, particularmente indicados para la investigación del comportamiento mecánico/hidráulico de represas, completa el trabajo iniciado por Parra(1996) para análisis del comportamiento de represas bajo sobrecarga estática y sísmica. Se implementaron dos técnicas para simulación de excavaciones, obteniendo, en ambas, resultados numéricos prácticamente idénticos. El procedimento para análisis de flujo permanente tubo como base la propuesta de Bathe y Khoshgoftarr (1979), que considera la situación de flujo no confinado como problema no lineal, pero conservando la configuración original de la malla de elementos finitos. Los resultados numéricos obtenidos em este trabajo fueron detalladamente comparados con los valores publicados en la literatura, numéricos o analíticos, para asegurar la confiabilidad de las implementaciones computacionales. La previsión del comportamiento de la represa de Macusani, que será construida en Perú, fue estudiada en este trabajo, especifícamente los aspectos vinculados a las fases de excavación, construcción y determinación de la superficie de infiltración de flujo permanente. Los resultados obtenidos pueden ser eventualmente útiles en el proyecto final de la obra.

abstract: Pseudo-steady state (PSS) flow is an important time-dependent flow regime that quickly follows the initial transient flow regime in the constant-rate production of a closed boundary hydrocarbon reservoir. The characterization of the PSS flow regime is of importance in describing the reservoir pressure distribution as well as the productivity index (PI) of the flow regime. The PI describes the production potential of the well and is often used in fracture optimization and production-rate decline analysis. In 2016, Chen determined the exact analytical solution for PSS flow of a fully penetrated vertically fractured well with finite fracture conductivity for reservoirs of elliptical shape. The present work aimed to expand Chen’s exact analytical solution to commonly encountered reservoirs geometries including rectangular, rhomboid, and triangular by introducing respective shape factors generated from extensive computational modeling studies based on an identical drainage area assumption. The aforementioned shape factors were generated and characterized as functions for use in spreadsheet calculations as well as graphical format for simplistic in-field look-up use. Demonstrative use of the shape factors for over 20 additional simulations showed high fidelity of the shape factor to accurately predict (mean average percentage error remained under 1.5 %) the true PSS constant by modulating Chen’s solution for elliptical reservoirs. The methodology of the shape factor generation lays the ground work for more extensive and specific shape factors to be generated for cases such as non-concentric wells and other geometries not studied. / Dissertation/Thesis / Masters Thesis Chemical Engineering 2017