## 3 Results and Discussion
### Corrosion Effect on Bond Strength  
Figure 13 illustrates the local bond-slip relationship for the PC-bars. The black line is the bond-slip without corrosion (0 years), while the red line represents the bond-slip at 75 years. The dotted lines between these two solid lines show the bond-slip relationship corresponding to points in time from 10 years to 60 years. In the case without corrosion, the PC-bar began to slip when the bond stress reached 4.62 MPa. At 75 years, the bond stress decreased to 31.3% of the initial value due to cracks around the corroded PC-bar and concrete. Figure 13 also depicts the bond-slip relationship by using FIB Model Code 2010 [38] and Cairns [39]. The bond strength by using Cairns was similar to that of this study; however, Cairns did not examine the bond strength reduction with the progress of the corroding of the rebar. Furthermore, the bond strength by using the FIB Model Code 2010 was very conservative compared to the results of this study. The explanation  
Figure 12: Relationship between corrosion degree and concrete compressive strength.  
is that the FIB Model Code 2010 equation was derived from the average value of their test results for various compressive strengths of standard concrete, rebar diameters, and anchorage depths.  
The following equations were proposed for the bond strength of corroded PC-bar as a function of the corrosion degree:  
\[\tau_{b,corr}=(1.1\,e^{-7.335\psi})\tau_{b,0}\text{ for }\psi\ >\ 1.3\% \tag{14}\]  
\[\tau_{b,corr}=\tau_{b,0}\text{ for }\psi\ \leq\ 1.3\% \tag{15}\]  
where \(\tau_{b,corr}\) is the bond strength of a corroded PC-bar; \(\tau_{b,0}\) is the initial PC-bar bond strength; and \(\psi\) is the corrosion degree.  
The ratio of the bond strength of the corroded PC-bar to its initial bond strength was defined as the bond strength reduction ratio. Figure 14 shows the relationship between the corrosion degree and the bond strength reduction ratio. The bond strength decreased inverse-exponentially against the corrosion degree after the corrosion degree reached 1.3%. Figure 14 also compares the bond strength reduction ratio in this study to those in previous studies ([PERSON] et al. [15] and [PERSON] [5]). [PERSON] et al. proposed the bond strength as a function of corrosion degree as follows:  
\[u_{b}=24.7\psi^{-0.55}\text{ for }\psi\ >\ 2.0 \tag{16}\]  
\[u_{b}=16.87\text{ for }\psi\ \leq\ 2.0 \tag{17}\]  
where \(u_{b}\) is the bond strength and \(\psi\) is the corrosion degree in %. [PERSON] proposed the bond strength as an exponential function with corrosion degree as a variable, which is expressed as follows:  
\[\tau_{b,corr}/\tau_{b,0}=1.2e^{-0.076\psi}\ \leq\ 1.0 \tag{18}\]  
where \(\tau_{b,corr}\) is the bond strength of a corroded rebar; \(\tau_{b,0}\) is the initial bond strength; and \(\psi\) is the corrosion degree in %.  
Figure 13: Local bond–slip relationship.  
[PERSON] et al. discovered a smaller bond strength reduction ratio, while [PERSON] discovered a larger bond strength reduction ratio than the results of this study. [PERSON] et al. conducted pull-out tests on specimens using deformed rebar and regular concrete, while [PERSON] considered high-strength concrete and bent rebar with confinement effects. Differences in specimen specifications (i.e., the concrete strength, the shape of the rebar's surface, and the confinement effect) caused differences in bond strength between their study and the present study. Furthermore, the concrete rupture failure mechanism influenced the bond strength between the deformed rebar and the concrete due to the influence of the rebar ribs and the subsequent bond-slip failure mechanism. In contrast, the bond strength between concrete and plain-surface PC-bar was only affected by the bond-slip failure mechanism.