# Application of Thermal Image Data to Detect Rebar Corrosion in Concrete Structures
## 2 Research Methodology
### Theoretical Considerations
#### 2.1.2 Electrical Resistance of Rebar  
Calculation of Electrical Resistance Using Specific Resistance of Steel  
According to Ohm's Law, the resistance of a conductor is proportional to its length and inversely proportional to its area. The resistance \(R\) can be expressed as in Equation (1). Here, \(\rho\) is the metal's specific resistance at a length of 1 m and a cross-sectional area of 1 m\({}^{2}\). Steel has a specific resistance of \(40\times 10^{-8}\)\(\Omega\)m (at 20 \({}^{\circ}\)C). The length (25 cm) and cross-sectional area (0.7133 cm\({}^{2}\) nominal cross-sectional area, D10 rebar) of the rebar used in the experiments were substituted in this equation to calculate the electrical resistance. Considering the amount of cross-sectional reduction caused by the corrosion ratio, the electrical resistances for each corrosion ratio were compared, and the results showed an electrical resistance of 1.402 m\(\Omega\) in the reference specimen rebar, 1.416 m\(\Omega\) in the 1% corroded rebar, 1.445 m\(\Omega\) in the 3% corroded rebar, and 0.1476 m\(\Omega\) in the 5% corroded rebar. \[R=\rho l/A(\Omega) \tag{1}\]  
Here, \(\rho\) is the specific resistance of a conductor with a length of 1 m and a cross-sectional area of 1 m\({}^{2}\). Calculation of Heat Generation Based on Rebar Corrosion  
According to [PERSON]'s law, heat generation is proportional to the product of the resistance of the conductor, the square of the current, and the time for which it flows. This was used to calculate the heat generated by the rebar (Equation (2)). For this study, the current value was considered to be 200 A, which was used in the experiments. For \(R\), the electrical resistances that were calculated for each corrosion ratio, as described above, were used. The heat generated was calculated as 1.077 cal/s in the 0% corroded rebar, 1.088 cal/s in the 1% corroded rebar, 1.110 cal/s in the 3% rebar, and 1.133 cal/s in the 5% corroded rebar. \[H=0.24I^{2}R\ (\mathrm{cal/s}) \tag{2}\]  
where \(H\) is the heat generated by the current, \(I\) is the current, and \(R\) is the conductor's electrical resistance. Calculation of Temperature Change of Rebar  
A calorie is the amount of heat required to raise the temperature of 1 g of water from 14.5 to 15.5 \({}^{\circ}\)C. To create a formula that applies this to steel, specific heat was used. The specific heat of water is 410 and the specific heat of steel is 45. As such, steel gets heated approximately 9.11 times faster than water. Therefore, the actual rebar's heat generation per second was calculated by dividing the rebar's weight of 140 g, which is calculated from the D10 rebar's unit weight of 0.56 kg/m and length of 25 cm, used in  
Figure 1: Corrosion processes of metal ions and volume expansion owing to corrosion [31]the experiments, by the calculated amount of heat. When the calculations were performed assuming that heating occurred for 210 s, it was found that the temperature increased by 14.71 \({}^{\circ}\)C in the 0% corrooded rebar, 14.86 \({}^{\circ}\)C in the 1% corroded rebar, 15.17 \({}^{\circ}\)C in the 3% corroded rebar, and 15.48 \({}^{\circ}\)C in the 5% corroded rebar. These values were calculated under the assumption that all resistances occurred only in the rebar and there was no heat loss from the rebar during heating. Electrical Resistance Experiments on Corroded Rebar  
The corrosion progression due to potential difference and [PERSON]'s law were used to check the calculated electrical resistance values. The corrosion ratios of 0%, 1%, 3%, 5%, 10%, 20%, and 30% were set as the variables. In this study, a D10 rebar of 25 cm was prepared, which is similar to the rebar used in the preliminary tests. Corrosion was induced in the rebar and its electrical resistance was measured. To measure minor differences in the resistance, a power supply was used to apply a voltage of 5 V to the rebar, as shown in Figure 2. The resulting voltage and current were measured, and [PERSON]'s law were used to calculate the resistance.