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51314-3743-Methodological Approach to the Average Potential Method to Obtain a Generalized Equation for the Resistance of Vertical Electrodes-II

Picture for Methodological Approach to the Average Potential Method to Obtain a Generalized Equation for the Res
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Product Number: 51314-3743-SG
ISBN: 3743 2014 CP
Author: Rogelio de las Casas
Publication Date: 2014
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Erling D. Sunde obtained an equation for the resistance of vertical electrodes underground in a groundbed configuration. In his approach he regarded that the top of the electrode was at the earth surface. Sunde used the Average Potential Method (APM) and the method of images to obtain this equation; where all the anodes have the same length.W. Von Baeckmann et al also presented an equation for vertical electrodes where the distance from the top of the electrode to the ground surface is taken into account. They also consider that all the vertical electrodes have the same length and the distance from top of the electrode to soil is a non-zero constant value for all the electrodes.In this paper we are obtaining a generalized equation for vertical electrodes where the APM in a matrix form is used and the final equation will contain Sunde’s equation as particular case. This new approach regards dissimilar length of anodes and dissimilar distance from the top of the anodes to soil surface.The average potential method calculate the potential of the electrode to remote earth regarding uniformity of current distribution on the electrode axis averaging the potential value at a point in the electrode surface over the entire electrode length through an integration process. The influence of parallel electrodes is also included with an integral-matrix approximation as interference factor that increases the total groundbed resistance.Keywords: vertical groundbed resistance equation potential theory interference factor between vertical electrodes cathodic protection design.
Erling D. Sunde obtained an equation for the resistance of vertical electrodes underground in a groundbed configuration. In his approach he regarded that the top of the electrode was at the earth surface. Sunde used the Average Potential Method (APM) and the method of images to obtain this equation; where all the anodes have the same length.W. Von Baeckmann et al also presented an equation for vertical electrodes where the distance from the top of the electrode to the ground surface is taken into account. They also consider that all the vertical electrodes have the same length and the distance from top of the electrode to soil is a non-zero constant value for all the electrodes.In this paper we are obtaining a generalized equation for vertical electrodes where the APM in a matrix form is used and the final equation will contain Sunde’s equation as particular case. This new approach regards dissimilar length of anodes and dissimilar distance from the top of the anodes to soil surface.The average potential method calculate the potential of the electrode to remote earth regarding uniformity of current distribution on the electrode axis averaging the potential value at a point in the electrode surface over the entire electrode length through an integration process. The influence of parallel electrodes is also included with an integral-matrix approximation as interference factor that increases the total groundbed resistance.Keywords: vertical groundbed resistance equation potential theory interference factor between vertical electrodes cathodic protection design.
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