| Name: | Description: | Size: | Format: | |
|---|---|---|---|---|
| 7.13 MB | Adobe PDF |
Authors
Advisor(s)
Abstract(s)
Nesta tese analisam-se os eléctrodos de terra, primeiro em solo homogéneo e depois em solo com dois estratos. Em solo homogéneo são estudados em pormenor varas e cabos enterrados, analisando a distribuição de potencial à superfície, obtendo-se, desta forma, as tensões de passo e de toque. As fórmulas para o cálculo da resistência também são comparadas inclusive as da legislação nacional. Finalmente eléctrodos planos como quadrados, chapas e grelhas também são consideradas. Em solo de dois estratos é analisado pormenorizadamente o método da matriz, que é o mais simples de todos, evidenciando as singularidades do método numérico, onde ocorrem e como as superar. O método mais usado para o cálculo da resistência nesta tese é o método dos momentos, que se obtém por dupla integração do método da matriz. As singularidades deste são rastreadas no processo de integração, permitindo identificar assim as regiões de singularidade do método dos momentos, a sua localização, sugerindo-se também alternativas para evitar a impossibilidade de calcular as grandezas em estudo. O terceiro método numérico usado foi o método dos elementos finitos, aplicado à formulação diferencial do problema, dada pela equação de Laplace, método este que não sofre os efeitos das imagens, geradoras das singularidades nos métodos anteriores, sendo usado para validar as alternativas de superação das singularidades referidas dos outros métodos. O conhecimento do solo, obtendo-se modelos de solo homogéneo, de solo de dois estratos e de solos de três estratos também foi considerado, apresentando-se os métodos mais comuns para se obterem modelo de solo de duas camadas e divulgando também o método de Pirson que permite obter modelos de três estratos. Dada a dificuldade em medir a resistividade em zonas urbanas, esta pode ser obtida a partir da medida de resistência de uma vara durante o enterramento, tendo-se desenvolvido métodos por optimização para obter tais modelos de solo, usando-se para tal o método do gradiente e o método de Newton. Os ensaios de campo que foram feitos são finalmente analisados, enfatizando o eléctrodo em serpentina para o qual se propõe uma nova metodologia de cálculo.
The present thesis analyzes the ground electrodes, first in homogeneous soils and then in two layer soils. In soils with constant resistivity, ground rods and wires are first considered, by computing surface potentials and then step and touch voltages. The resistance calculation is made by comparing several formulae including those from Portuguese standards. Finally two dimension electrodes are considered, such as squares, grids and plates. In soils with two layers the matrix method, which is the simplest method, is carefully considered showing the singularities of the method, where they occur and how to avoid them. The method of moments is the reference method in the thesis to compute ground electrode resistance, which is obtained through the double integral of the matrix method expressions. In this computation the singularities of this method are tracked through the integration process, allowing the identification of the singularities of the method of the moments, their location, and how to avoid the regions were calculations are impossible. The third numerical method herein used was the finite element method (FEM), using the differential operator, since Laplace equation is representative of the phenomenon under study. FEM is image independent, so it does not have the singularities detected in the other methods, allowing its use to validate the options to avoid singularities. The knowledge of the soil was also considered in order to obtain models for one layer, two layers and three layers soils. The most common methods to obtain a two layer soil are presented and Pirson’s method for a three layer soil is also considered. Since resistivity measurements in cities are difficult to be made, they can be obtained by measuring a rod resistance during the burying process and using optimization techniques, such as the gradient method or the Newton method, to compute a soil model. Finally field measurements are presented, focusing on the sinusoidal electrode for which a new algorithm to compute the electrode resistance is proposed.
The present thesis analyzes the ground electrodes, first in homogeneous soils and then in two layer soils. In soils with constant resistivity, ground rods and wires are first considered, by computing surface potentials and then step and touch voltages. The resistance calculation is made by comparing several formulae including those from Portuguese standards. Finally two dimension electrodes are considered, such as squares, grids and plates. In soils with two layers the matrix method, which is the simplest method, is carefully considered showing the singularities of the method, where they occur and how to avoid them. The method of moments is the reference method in the thesis to compute ground electrode resistance, which is obtained through the double integral of the matrix method expressions. In this computation the singularities of this method are tracked through the integration process, allowing the identification of the singularities of the method of the moments, their location, and how to avoid the regions were calculations are impossible. The third numerical method herein used was the finite element method (FEM), using the differential operator, since Laplace equation is representative of the phenomenon under study. FEM is image independent, so it does not have the singularities detected in the other methods, allowing its use to validate the options to avoid singularities. The knowledge of the soil was also considered in order to obtain models for one layer, two layers and three layers soils. The most common methods to obtain a two layer soil are presented and Pirson’s method for a three layer soil is also considered. Since resistivity measurements in cities are difficult to be made, they can be obtained by measuring a rod resistance during the burying process and using optimization techniques, such as the gradient method or the Newton method, to compute a soil model. Finally field measurements are presented, focusing on the sinusoidal electrode for which a new algorithm to compute the electrode resistance is proposed.
Description
Keywords
Resistência de terra - Tensão de passo Resistência de terra - Tensão de toque Resistência de terra - Método de cálculo