Dual boundary element formulation for half-space cathodic protection analysis

In this paper, a boundary element formulation is developed and used for the analysis of cathodic protection systems of buried slender structures. The slenderness of the structure brings numerical difficulties into the classical boundary element method. To avoid this problem, the dual boundary element method is implemented: combination of standard and hypersingular integral equations to form a system of equations free from the singularity behavior of the standard approach when the thickness of the body tends to zero. Regularity conditions in infinite domains are analyzed for both standard and hypersingular equations. Besides numerical tests to validate the formulation, a simple experiment is carried out where a galvanized metallic sheet is buried alongside two copper electrodes, in parallel, with the objective of simulating a two-dimensional problem. The soil resistivity properties are measured along the depth and the relation between the current density and the electrochemical potential at the metallic sheet is investigated. The proposed dual approach is applied to model the experiment and results are compared with potential measurements at the ground surface.