## 3 Finite Element Simulations
### Half-Cell Potential Simulation Result  
A half-cell can be simulated as an electrode placed within an electrolyte. To determine the potential difference, a reference electrode can be used on the surface of the concrete. The FE (finite element) model used to simulate the HCP (Figure 1) is the same concrete slab that was utilized for the IE and ER technologies and has a block size of 1.0 m \(\times\) 1.0 m \(\times\) 0.2 m. Cross-section A-A, shown in Figure 2, illustrates the internal steel bar, the cathodic region, and the anodic region (the active corrosion area) within the concrete.  
Figure 1: Finite element 3D model components.  
Figure 2: A-A cross-section.  
The simulation results indicate that the equipotential lines between the anode and cathode are highly sensitive to certain parameters such as shallow delamination and the saturation level of the delamination. To demonstrate the impact of these and other parameters on the electrochemical corrosion process inside concrete, different simulation scenarios are presented. Figure 3a displays the potential distribution within concrete caused by a 15 cm length of steel rebar corrosion with 50% saturation and no delamination. On the other hand, Figure 3b,c show the potential distribution inside concrete with the same parameters but with the presence of 30 mm deep delamination. Figure 3b illustrates a scenario with air-filled delamination (AFD), while Figure 3c illustrates a scenario with water-filled delamination (WFD).  
Figure 3: Potential distribution for 15 cm corrosion length and 0.5 DoS: (**a**) no delamination; (**b**) AFD at 30 mm; (**c**) WFD at 30 mm.  
The half-cell potential (HCP) results are influenced by the physical properties of two materials, the rebar steel where corrosion occurs and the surrounding concrete, as well as the characteristics of the pores that regulate electrolyte flow. The results of the HCP are impacted by all five parameters analyzed in this study. In general, the HCP results are positively correlated with both the corrosion length (CL) and the degree of saturation (DoS). As these two parameters increase, the measured potential becomes more negative. Conversely, HCP results are negatively correlated with increases in the concrete cover (CC) and delamination depth (DD). Figure 4 presents the HCP measurement values for sound concrete with varying corrosion lengths and degrees of saturation at concrete cover thicknesses of 38 mm, 51 mm, 63 mm, and 76 mm. The dashed lines in the figures describe the boundary of the 90% probability of an active corrosion zone according to the standard specification ASTM C876-15.  
In Figure 4a, it can be seen clearly that the corrosion length of 2.5 cm cannot be detected using the HCP as the potential is larger than the threshold for all values of the DoS. Also, the minimum detectable corrosion length is 5 cm with a DoS equal or greater to 0.5, 10 cm with a DoS equal or greater to 0.4, and 15 cm with a DoS equal or greater to 0.3. Furthermore, a  
Figure 4: HCP measurements for sound concrete: (**a**) 38 mm CC; (**b**) 51 mm CC; (**c**) 63 mm CC; (**d**) 76 mm CC.  
corrosion length that is greater than 20 cm can be detected in all values of the DoS. These behaviors change with the change in the concrete cover, as shown in Figure 4b-d.