### Abstract:

A numerical model for the cathodic protection of steel in reinforced concrete is
developed. Parameters are set to represent a three-dimensional section of a bridge
beam exposed to the atmosphere and coated with a thermally sprayed zinc anode.
Both diffusion of oxygen and conduction of charge within the concrete are considered
explicitly through a two-dimensional finite element model. The diffusivity and
conductivity are represented as functions of concrete moisture content.
Electrochemical reactions considered at the rebar-concrete interface are reduction of
oxygen, oxidation of iron, and evolution of hydrogen in a constant-potential cathodic
protection circuit. Reaction-kinetic parameters for actively corroding steel (not
passivated steel) are used. Reactions at the zinc-concrete interface are not considered
explicitly.
The effectiveness of protection is found to vary significantly with both
concrete moisture content and position on the rebar. For spatially uniform pore
saturation, the drier the concrete is, the greater the corrosion current and the greater
the non-uniformity. Protection is significantly more effective at the "front" of the
rebar (closest to the zinc anode) than at the "back" (closest to the center of the beam).
Corrosion current is greater under drying conditions than under wetting conditions.
The numerical model is applied towards interpretation of the "100-mV polarization
decay criterion" that is often used to assess the effectiveness of cathodic protection. It
is found that the polarization decay predicted from relaxation of oxygen concentration
gradients was comparable in magnitude to that observed experimentally, but depends
on location on the rebar.
A numerical model for the transport of ions in porous concrete under cathodic
protection is presented. In this initial model, transport of the ions zinc, calcium,
chloride and hydroxide is described by a one-dimensional Nernst-Planck equation at
constant current density with generation of zinc ions at the anodic interface, generation
of hydroxide ions at the cathodic interface, and no chemical reactions in the bulk of
the concrete. The equations are solved numerically by two methods: the point
method, in which concentrations and electric potentials are solved for directly through
finite-difference approximations of the differential equations and the box method, in
which the domain is divided into discrete volume elements with flux balances for each
chemical component and for charge. A base grid of 41 nodes is used. Results for the
system after 96 and 9600 days of cathodic protection are discussed.
Both numerical methods yielded concentration profiles that are virtually
indistinguishable. Numerical noise in the box method leads to values in the first and
second derivatives of the electric potential that tend to oscillate around the central
values represented by the same smooth curve of the point method. In contrast, the
point method shows greater apparent numerical deviation from electroneutrality which
is largest near the boundaries and decays towards the center in damped oscillations.
The deviations decrease with smaller size of grid elements and higher order difference
approximations. The magnitude of the charge density in the bulk of the concrete
calculated from the second derivative of the electric potential through Poisson's
equation is shown to be negligible compared to the overall electroneutrality calculated
from the concentrations of ions. At 96 days, the relative contributions of migration
and diffusion to the overall flux are shown to vary widely with position and species;
migration can neither be neglected nor can a "corrected" Fick's law approach be used.
Zinc ions are found to have moved approximately 15 mm into the bulk of the concrete
at 96 days.