A utilização de concreto projetado como suporte de túneis é uma prática amplamente difundida no mundo inteiro. Este tipo material possui a característica de começar a agir estruturalmente desde pequenas idades. Apesar disso, os correntes processos de dimensionamento de suportes negligenciam o desenvolvimento de suas propriedades com o tempo, em acoplamento aos efeitos tridimensionais da região onde se localiza a frente de escavação. O presente trabalho tem a finalidade de relatar os procedimentos utilizados na análise da influência de alguns parâmetros da interação maciço - suporte, sobre os esforços solicitantes e os deslocamentos radiais finais do suporte de um túnel, tanto para o caso de concreto projetado, com suas propriedades dependentes do tempo, quanto para materiais com propriedades constantes. São elaboradas soluções adimensionais para o problema da quantificação de esforços solicitantes no suporte e de deslocamentos radiais na interface entre maciço e suporte. Além disso, é proposta uma forma de se determinar, através destas soluções adimensionais, coeficientes de alívio de tensões que auxiliam em simulações bidimensionais de escavações subterrâneas. / The utilization of shotcrete as tunnel support is a widely diffused practice in the whole world. This kind of material has the feature of beginning to act structurally since early ages. Nevertheless, the current processes of support design neglect the development of its properties after some time in connection to the 3D effects of the region where the face of the tunnel is located. The present work relates the procedures adopted in analyzing the influence of some ground-support interaction parameters on the support internal forces and interface radial displacements of a tunnel, not only when shotcrete is used, with its time-dependent properties, but for materials with constant properties as well. Dimensionless solutions are developed for the support thrust and radial displacement quantification problem. Moreover, through this dimensionless solution, a way of quantifying stress relief factors, which are intermediate steps in 2D simulations of underground excavations, is proposed.

[pt] Nesta dissertação apresenta-se uma formulação para a análise numérica de cascas espessas axissimétricas, sob os carregamentos de pressão e força distribuida ao longo de um paralelo, utilizando-se a técnica de elementos finitos enriquecidos. As discretizações dos campos de deslocamento axial e radial são consideradas no domínio do elemento verificando-se as seguintes restrições: tensões nulas nas faces interna e externa da casca e uma combinação das soluções analíticas para cascas espessas cilíndricas e esféricas. A formulação resulta em um modelo com seis graus-de-liberdade generalizados por ponto nodal para elementos unidimensionais, considerando- se como referencia a superfície média da casca. Na imposição de condições de continuidade e de fixação associados aos graus-de-liberdade empregou-se o método de penalidades. A formulação foi implementada e alguns testes numéricos são apresentados para demonstrar sua aplicabilidade em comparações com outras soluções analíticas ou numéricas. / [en] This work presents an element formulation for the analysis of axisymmetric thick shells under pressure and line loads using Enriched Finite Element technique. Axial and radial displacement fields are considered in the formulation under the conditions of zero stresses at internal and external surfaces of the shell and, a combination of analitical solutions for radial displacements of cilindrical and spherical thick wall shells. The formulation results in a six generalized degree-of-freedom uni-dimensional model refered to the element nodal points at the shell mid-surface. Continuity between adjoining elements and clamped boundary conditions associated to the element degrees-of-freedom are imposed by the use of a penalty method. The formulation has been implemented and some numerical analysis results are shown to demonstrate its aplicability, as compared to other analytical or numerical solutions.

Este trabalho apresenta um ambiente de simulação de escoamentos com simetria radial e superfícies livres, baseado no sistema Freeflow. O sistema é formado por três módulos: um modelador de moldes, um simulador e um visualizador de escoamentos. O simulador implementa o método GENSMAC para a solução das equações de Navier-Stokes em coordenadas cilíndricas, utilizando diferenças finitas em uma malha diferenciada. São introduzidos os efeitos da tensão superficial e do ângulo de contato nas simulações com simetria radial. Alguns resultados de simulações utilizando este sistema e uma validação do código são apresentados, comparando simulações com soluções analíticas e experimentais, e estudando a convergência do método. / This work presents an environment for the simulation of axisymmetric free surface flows, based on the Freeflow system. The system contains three modules: a geometric model modeller, a simulator and a visualizator. The simulator implements the GENSMAC method for the solution of the Navier-Stokes equations in cylindrical coordinates, using finite differences in a staggered grid. The effects of surface tension and contact angle are introduced in the axisymmetric simulations. Some results from simulations using this system and a validation of the code are presented, comparing the simulations with analytical and experimental solutions, and studying the convergence of the method.

The effect of chamber length and Reynolds number on the stability and behavior of the flow field generated by a precessing jet nozzle was studied using stereoscopic particle image velocimetry (StereoPIV). An algorithm was developed to determine the mode of the flow based on the distribution of axial velocity. The optimal chamber length for precession to occur was found to be between 2 and 2.75 chamber-diameters. There is no precession at a chamber length of one diameter, and the occurrence of precession was found to be strongly related to Reynolds number. Conditionally averaged velocity distributions for the flow in precessing mode were calculated. The effect of initial condition on downstream behavior of axisymmetric jets was examined. Variations in spread and decay rates were found for jets issuing from different nozzles. Self-similar solutions for axisymmetric jets are therefore not universal, and are instead dependent upon initial conditions at the source.

This study considers the elastostatic contact problem of a semi-infinite cylinder. The cylinder is compressed against a layer lying on a rigid foundation. There is a sharp-edged circular hole in the middle of the foundation. It is assumed that all the contacting surfaces are frictionless and only compressive normal tractions can be transmitted through the interfaces. The contact along interfaces of the elastic layer and the rigid foundation forms a circular area of which outer diameter is unknown. The problem is converted into the singular integral equations of the second kind by means of Hankel and Fourier integral transform techniques. The singular integral equations are then reduced to a system of linear algebraic equations by using Gauss-Lobatto and Gauss-Jacobi integration formulas. This system is then solved numerically. In this study, firstly, the extent of the contact area between the layer and foundation are evaluated. Secondly, contact pressure between the cylinder and layer and contact pressure between the layer and foundation are calculated for various material pairs. Finally, stress intensity factor on the edge of the cylinder and in the end of the sharp-edged hole are calculated.

In this paper, we study the partial Fourier method for treating the Lamé equations in three-­dimensional axisymmetric domains subjected to nonaxisymmetric loads. We consider the mixed boundary value problem of the linear theory of elasticity with the displacement u, the body force f \in (L_2)^3 and homogeneous Dirichlet and Neumann boundary conditions. The partial Fourier decomposition reduces, without any error, the three­dimensional boundary value problem to an infinite sequence of two­dimensional boundary value problems, whose solutions u_n (n = 0,1,2,...) are the Fourier coefficients of u. This process of dimension reduction is described, and appropriate function spaces are given to characterize the reduced problems in two dimensions. The trace properties of these spaces on the rotational axis and some properties of the Fourier coefficients u_n are proved, which are important for further numerical treatment, e.g. by the finite-element method. Moreover, generalized completeness relations are described for the variational equation, the stresses and the strains. The properties of the resulting system of two­dimensional problems are characterized. Particularly, a priori estimates of the Fourier coefficients u_n and of the error of the partial Fourier approximation are given.

No description available.

This work considers a cracked semi-infinite cylinder and a finite cylinder. Material of the cylinder is linearly elastic and isotropic. One end of the cylinder is bonded to a fixed support while the other end is subject to axial tension. Solution for this problem can be obtained from the solution for an infinite cylinder having a penny-shaped rigid inclusion at z = 0 and two penny-shaped cracks at z = &plusmn / L. General expressions for this problem are obtained by solving Navier equations using Fourier and Hankel transforms. When the radius of the inclusion approaches the radius of the cylinder, the end at z = 0 becomes fixed and when the radius of the cracks approaches the radius of the cylinder, the ends at z = &plusmn / L become cut and subject to uniformly distributed tensile load. Formulation of the problem is reduced to a system of three singular integral equations. By using Gauss-Lobatto and Gauss-Jacobi integration formulas, these three singular integral equations are converted to a system of linear algebraic equations which is solved numerically.

No description available.

Les courants de gravité, écoulements issus de la présence d’un contraste de densité dans un fluide ou de la présence de fluides de densités différentes, sont rencontrés dans de nombreuses situations naturelles ou industrielles. Quelques exemples de courants de gravité sont les avalanches, les marées noires et les courants de turbidité. Certains courants de gravité peuvent représenter un danger pour l’homme ou l’environnement, il est donc nécessaire de comprendre et de prédire leur dynamique. Cette thèse a pour objectif d’étudier l’évolution de courants de gravité de masse fixée, et notamment l’influence d’une forme initiale non-axisymétrique sur la dynamique, effet jusque-là peu abordé dans la littérature. Pour cela, une large gamme de paramètres est couverte, incluant le rapport de masse volumique entre le fluide ambiant et le fluide dans le courant, le rapport de forme initiale, la forme de la section horizontale de la colonne de fluide (circulaire, rectangulaire ou en forme de croix), le nombre de Reynolds (couvrant jusqu’à 4 ordres de grandeur) et la nature du fluide lourd (salin ou chargé en particules). Deux campagnes d’expériences ont été menées et complétées par des simulations numériques hautement résolues. Le résultat majeur est que la propagation du courant et le dépôt de particules (lorsque particules il y a) sont fortement influencés par la forme initiale de la colonne de fluide. Dans le cas de la colonne initialement rectangulaire le courant se propage plus vite et dépose plus de particules dans la direction initialement de plus courte dimension. Ce comportement non-axisymétrique est observé dans une large gamme des paramètres étudiés ici. Pourtant les modèles analytiques existants et notamment le modèle dit de boîte (box model) qui prédit avec succès le comportement des courants de gravité/turbidité dans les cas plan et axisymétrique ne sont pas capables de reproduire ce phénomène. C’est pourquoi une extension du box model a été développée ici, et est en mesure de décrire la dynamique de courants de gravité de masse fixée dont la forme initiale est arbitraire. Le cas plus général d'un courant de gravité évoluant sur un plan incliné a été abordé et une dynamique intéressante a été observée. / Gravity currents are buoyancy driven flows that appear in a variety of situations in nature as well as industrial applications. Typical examples include avalanches, oil spills, and turbidity currents. Most naturally occurring gravity currents are catastrophic in nature, and therefore there is a need to understand how these currents advance, the speeds they can attain, and the range they might cover. This dissertation will focus on the short and long term evolution of gravity currents initiated from a finite release. In particular, we will focus attention to hitherto unaddressed effect of the initial shape on the dynamics of gravity currents. A range of parameters is considered, which include the density ratio between the current and the ambient (heavy, light, and Boussinesq currents), the initial height aspect ratio (height/radius), different initial cross-sectional geometries (circular, rectangular, plus-shaped), a wide range of Reynolds numbers covering 4 orders of magnitude, as well as conservative scalar and non-conservative (particle-driven) currents. A large number of experiments have been conducted with the abovementioned parameters, some of these experiments were complemented with highly-resolved direct numerical simulations. The major outcome is that the shape of the spreading current, the speed of propagation, and the final deposition profile (for particle-driven currents) are significantly influenced by the initial geometry, displaying substantial azimuthal variation. Especially for the rectangular cases, the current propagates farther and deposits more particles along the initial minor axis of the rectangular cross section. This behavior pertaining to non-axisymmetric release is robust, in the sense that it is observed for the aforementioned range of parameters, but nonetheless cannot be predicted by current theoretical models such as the box model, which has been proven to work in the context of planar and axisymmetric releases. To that end, we put forth a simple analytical model (an extension to the classical box model), well suited for accurately capturing the evolution of finite volume gravity current releases with arbitrary initial shapes. We further investigate the dynamics of a gravity current resulting from a finite volume release on a sloping boundary where we observe some surprising features.