## 2 Background of EIS Corrosion Measurements  
The polarization technique involves the application of an electrical stimulus between two electrodes, i.e., the counter and working electrodes, and the observation of the response, and is extensively used in corrosion science. Among all the polarization techniques, EIS (AC) measurements are based on the frequency domain, thus allowing various types of information, including inductive, capacitive, and diffusion processes on electrochemical cells. The measured impedance is expressed in a complex form consisting of the real (resistance) and fictitious (reactive) parts. \[Z(\omega)=\ Z^{\prime}(\omega)-i\ Z^{\prime\prime}(\omega), \tag{1}\]  
where \(\omega\) is the angular frequency (\(\omega=2\pi\)f, f is the frequency (Hz)), \(\ Z^{\prime}(\omega)\) is the real part, \(\ Z^{\prime\prime}(\omega)\) is the fictitious part, and \(i=\sqrt{-1}\). Two types of formats are typically used to represent EIS data, namely the (1) Nyquist and (2) Bode formats [20]. 1. Nyquist format: The real (\(Z^{\prime}(\omega)\)) and the fictitious (\(Z^{\prime\prime}(\omega)\)) parts are expressed on the x- and the y-axes, respectively. The impedance can be represented with the vector's length (\(|Z(\omega)|\)), and the angle between this vector and the x-axis. This representation cannot express the frequency directly. 2. Bode format: Both the modulus of the impedance and the phase shift on the y-axis are plotted with respect to the frequency on the x-axis. The Bode format explicitly shows frequency information, unlike the Nyquist format. The corrosion of steel in concrete is an electrochemical process, which consists of anode, cathode, and ohmic resistance. The corrosion process in concrete is controlled based on (a) anodic control with iron dissolution, (b) cathodic control with oxygen availability, and (c) ohmic control based on the concrete's resistance. Although the corrosion rate is determined by one dominant factor, both polarization and ohmic resistances are required to calculate the corrosion rate of steel in concrete. The corrosion rate can be calculated using the Stern-Geary equation [21]. \[I_{c}=\frac{B}{\text{R}_{\text{P}}} \tag{2}\]  
where \(I_{c}\) is the corrosion current (mA), and \(B\) is an empirical value as 26 mV for the active state and as 52 mV for passive state. To this end, the EIS technique is beneficial for the estimation of the behavior of steel in concrete as both parameters are measured separately. As shown in Figure 1, the impedance spectra for steel in concrete may ideally consist of two semicircles, including a large one for the low-frequency limit (corresponding to the steel's response), and a small one for the high-frequency limit (corresponding to the concrete's response). In porous materials, the semicircle is typically depressed by the decreasing capacitance at increasing frequencies so that the capacitance element is replaced with a constant phase element (CPE) to improve the fitting in the following equation. \[Z^{\prime\prime}_{CPE}=\frac{1}{C_{0}(i\omega)^{p}} \tag{3}\]  
where \(Z^{\prime\prime}_{CPE}\) is the fictitious impedance, \(C_{0}\) is a coefficient, \(p\) is the exponent \((0<p<1)\), and \(i=\sqrt{-1}\). 3. Reviews for Electrical Equivalent Circuits  
EIS data may contain various types of information, including bulk resistance, diffusion processes, and charge transfers. To explain these, various electrical equivalent circuits have been proposed [5; 7; 8; 11; 22; 23; 24; 25; 26; 27]. Depending on the purpose of the study, the arrangements of elements in the circuits can be diverse; consequently, it is necessary to first review the circuits proposed in the literature, as shown in Figure 2 and Table 1. Complicated circuits,  
Figure 1: Example of electrochemical spectra of steel in concrete.