## 3 Reinforcement Corrosion Monitoring Techniques
### Corrosion Assessment with Electrochemical Sensors
#### 3.1.3 Polarization Resistance (\(R_{p}\))  
Polarization resistance (\(R_{p}\)) is a well-known, simple and non-intrusive method that allows the determination of the corrosion rate [50; 81; 84; 141; 142; 143; 144; 145]. \(R_{p}\) can be determined by several electrochemical techniques. However, when applied to RCS, specific characteristics should be taken into account due to the high electrical resistance of the electrolyte (concrete). The most common techniques used for \(R_{p}\) measurements, to assess the \(i_{corr}\) of steel in RCS, were galvanostatic [3; 5; 70; 146; 147; 148; 149], potentiostatic pulses [17; 136; 150; 151], cyclic voltammetry (conducted at very low scan rates) [151; 152; 153; 154; 155; 156; 157; 158; 159], and electrochemical impedance spectroscopy (EIS) [160; 161; 162; 163; 164; 165; 166]. The method proposed by [PERSON] and [PERSON] in 1957 is based on the observation of the linearity of the polarization curve together with the corrosion potential. A small potential perturbation (typically 10-20 mV or even 30 mV) is applied to the reinforcing steel (working electrode) and the resulting current is measured. The potential perturbation can be followed potentiostatically by the variation of the known potential (_overpotential_--\(\Delta E\)) expressed with respect to the corrosion potential (_overpotential_ (\(\Delta E\)) = \(E_{appi}\) - \(E_{corr}\)), and the monitoring of current decay (\(\Delta I\)) during a certain period of time. Alternatively, this measurement can be carried out galvanostatically by applying a small fixed current value (\(\Delta I\)) to the reinforcing steel, and monitoring the potential variation (_overpotential_--\(\Delta E\)) for a certain period of time. In each case, the conditions are always selected considering that the \(\Delta E\) falls within the Stern-Geary linear range of 10-30 mV. The \(R_{p}\) is defined as [142]:  
\[R_{p}=\left(\frac{\partial\Delta E}{\partial i}\right)_{\Delta E\to 0} \tag{1}\]  
\begin{table}
\begin{tabular}{c c} \hline
**Risk of Corrosion** & \(\rho\)**/**k\(\Omega\)****m** \\ \hline \hline \(\;The conversion of \(R_{p}\) to \(i_{corr}\), given by the Stern-Geary equation [145], involves the determination of the active corroding area as well as the compensation of the ohmic drop:  
\[i_{corr}=\frac{B}{R_{p}} \tag{2}\]  
where \(B\) is a constant that depends on the Tafel slopes of the anodic (\(\beta_{a}\)) and cathodic processes (\(\beta_{c}\)):  
\[B=\frac{\beta_{a}\cdot\beta_{c}}{2.303(\beta_{a}+\beta_{c})} \tag{3}\]  
Extensive experimental work has been performed in steel embedded in concrete in order to establish \(B\) values to be used in [PERSON]'s equation according each corrosion situation [81; 156; 167; 168; 157]. The constant \(B\), in the case of steel in concrete, ranges between 0.026 V (steel in the active state) and 0.052 V (steel in the passive state) [169]. Table 4 shows the construction steel conditions as a function of the values of \(i_{corr}\) in RCS measured in situ and in laboratory. The \(i_{corr}\) can be converted to corrosion rate (\(V_{corr}\)) expressed in mm year\({}^{-1}\), using [PERSON]'s law. \(V_{corr}\), represents the volumetric loss of metal by unit of area and unit of time and may be expressed in mm year\({}^{-1}\) using [PERSON]'s law and the density of the metal. For the steel 1 uA cm\({}^{-2}\) is equivalent to a corrosion rate of \(1.16\times 10^{-1}\) mm year\({}^{-1}\) for uniform attack (Equation (4)) [130]. \[V_{corr}\;(\text{mm year}^{-1})=0.116\;i_{corr}\;(\text{\mu A cm}^{-2}) \tag{4}\]  
[PERSON] et al. reported in 1985 [151] that the measured \(R_{p}\) must be accurate to avoid under- or overestimated \(i_{corr}\). Theoretically, DC methods such as cyclic voltammetry, potentiostatic transients, galvanostatic transients and AC methods such as EIS will all conduct to the same value of \(R_{p}\) when the appropriate frequencies, times and scan rates are used. In 1995, [PERSON] et al. [170] and [PERSON] et al.