Cathodic Protection of Steel in Reinforced Concrete

Cathodic protection (CP) is a common strategy for retarding the corrosion of reinforcing steel in concrete structures, such as bridges and parking garages. By the use of CP the potential of the corroding surface is lowered, thereby decreasing the rate of undesired anodic corrosion reaction.

This example models the cathodic protection of a steel reinforcing bar (rebar) in concrete. The corrosion cell consists of a zinc anode, the concrete, acting as electrolyte, and the steel surface. Iron oxidation, water reduction (hydrogen evolution) and oxygen reduction are considered on the steel surface, whereas oxygen and charge transport are accounted for in the concrete electrolyte.

The anode and the steel surface are connected electrically via a potentiostat that controls the cell voltage.

Concrete is a porous material, and an effect of this is that its transport properties for ions and gases vary with the moisture content. Therefore the electrolyte conductivity and oxygen diffusion coefficient are modeled to vary with the concrete pore saturation level using empirical data.

The corrosion rate for various moisture contents is investigated.

The model example is based on a paper by Muehlenkamp and others (Ref. 1).

For a more detailed description for how to build this model, including screen shots, see the Introduction to the Corrosion Module.

Model Definition

Geometry

Figure 1 shows the model geometry. The geometry modeled represents a two dimensional cross section of a repeating unit cell in a larger structure where three symmetry planes (top, bottom and right) have been used in order to reduce the model geometry. The zinc anode has been coated onto the concrete by thermal spraying and is assumed to be permeable to air.

Figure 1: Model geometry. One electrolyte domain and two electrode surfaces.

Concrete domain equations

Use a Tertiary Current Distribution Nernst Planck interface to model the electrochemical currents. The electrolyte conductivity depends on the pore saturation level according to Figure 2.

Figure 2: Electrolyte conductivity (S/m) as function of the concrete pore saturation level.

The oxygen diffusivity depends on the pore saturation level according to Figure 3.

Figure 3: Oxygen diffusivity (m2/s) in the concrete as function of pore saturation.

boundary conditions

Choose the electrical potential of the Zn anode as ground for the system. By assuming the kinetics of the Zn anode to be very fast the polarization is neglected in the model, setting the electrolyte potential to

Set the concentration of oxygen at the Zn anode to atmospheric conditions according to

Consider three different electrode reactions on the steel rebar boundary: iron oxidation, oxygen reduction, and hydrogen evolution:

Model the reaction kinetics for these reactions with an Electrode Surface node in the Tertiary Current Distribution, Nernst Planck interface, on which the external electric potential of the steel bar,

, is set to the applied cell potential of -1 V.

The electrode kinetics of the steel bar reactions are described by Tafel expressions according to

using the parameters shown in Table 1, where the overpotential for each reaction is calculated as

Table 1: Electrode reaction parameters.
Parameter	Unit	Zn	Fe	O2	H2
Equilibrium potential, Eeq	V	-0.68	-0.76	0.189	-1.03
Exchange current density, i0	A/m2	-	7.1·10-5	7.7·10-7	1.1·10-2
Tafel slope, A	V/decade	-	0.41	-0.18	-0.15

The oxygen reduction reaction causes a flux of oxygen at the steel surface according to Faraday’s law.

Use atmospheric concentration as initial value for the oxygen concentration variable.

Study

Solve the model using a parametric sweep over a stationary study step, solving for a range of pore saturation values from 0.2 to 0.8.

Results and Discussion

Figure 4 shows the electrolyte potential for a pore saturation level of 0.8. The electrolyte potentials is lower toward the back (the right side) of the rebar.

Figure 4: Electrolyte potential for a pore saturation (moisture) level of 0.8.

Figure 5 shows the oxygen concentration in the electrolyte for a pore saturation level of 0.8. The concentration is very low close to the rebar, indicating that the oxygen reduction kinetics should be mass transport limited for this pore saturation level. The concentration is lower toward the back of the rebar.

Figure 5: Oxygen concentration for a pore saturation (moisture) level of 0.8.

An important factor for the corrosion rate of the rebar is the operating electrode potential, which is the difference between the electric potential (here the potential applied by the potentiostat) and the electrolyte potential. Figure 6 shows the operating electrode potential for various pore saturation levels for three different points (front, middle and back) of the rebar surface. The potential drops considerably at a pore saturation level of 0.65.

Figure 6: Operating electrode potential for three points at the rebar-concrete interface.

Figure 7 shows the local oxygen concentration at the rebar for various pore saturation levels. The concentration drops significantly toward higher saturation levels. This is an effect of the decreasing diffusivity of oxygen in the concrete for higher saturation levels.

Figure 7: Local oxygen concentration at the rebar-concrete interface.

The local oxygen reduction current densities at the rebar are shown in Figure 8. The magnitude of the oxygen reduction current density is highest around a pore saturation level of 0.6 – 0.65. Up to this point the current densities are increasing due to increased electrolyte conductivity, but for higher pore saturation levels the current densities decrease due to decreased oxygen diffusivity.

Figure 8: Local oxygen reduction current densities at the rebar-concrete interface.

The hydrogen evolution current densities are shown in Figure 9. Hydrogen evolution is very limited below a PS level of 0.65, which is the saturation level at which the electrode potential gets below the equilibrium potential (1.03 V) for the hydrogen evolution reaction, see Figure 6.

Figure 9: Local hydrogen evolution current densities at the rebar-concrete interface.

Finally, the iron oxidation current densities are shown in Figure 10. Corrosion current densities are higher for low PS levels, which is in line with the higher electrode potential for low PS levels (Figure 6). It should be noted that the magnitude of iron oxidation current density is considerably smaller than oxygen reduction and hydrogen evolution current densities at the steel rebar indicating the effectiveness of zinc coating onto the concrete in protecting the steel rebar from corrosion.