## 2 The Proposed Model
### Axial Compression Point  
The cross section of a corroded RC column under axial compression can be decomposed into four different regions (Figure 3), i.e., the cracking area of unconfined concrete \(A_{1\mathrm{c}}\), cracking area of confined concrete \(A_{2\mathrm{c}}\), no cracking area of confined concrete \(A_{3\mathrm{c}}\) and the longitudinal reinforcement area considering the buckling effect \(A_{1\mathrm{,red}}\)[29]. Figure 1: Moment–axial force curve. Figure 2: The flowchart of the proposed method. The bearing capacity model and strength contribution of the areas can be expressed as  
\[N_{0}=\psi f_{c}A_{1c}+\psi f_{cc}A_{2c}+f_{cc}A_{3c}+\beta\big{(}A_{1,red}f_{y} \big{)}, \tag{1}\]  
\[A_{1c}=(2b\delta+2H\delta)-4\delta^{2}, \tag{2}\]  
\[A_{2c}=bH-\Big{[}(2b\delta+2H\delta)-4\delta^{2}\Big{]}-[(b-2\delta-2\varphi_{ st}-2\varphi_{1})(H-2\delta-2\varphi_{st}-2\varphi_{1})], \tag{3}\]  
\[A_{3c}=(b-2\delta-2\varphi_{st}-2\varphi_{1})(H-2\delta-2\varphi_{st}-2\varphi _{1}), \tag{4}\]  
where \(f_{cc}\) and \(f_{c}\) represent the compressive strength of the confined concrete and unconfined concrete, respectively; \(\psi\) is the strength attenuation factor of concrete under compression; \(\beta\) is the yield strength attenuation factor of longitudinal reinforcement considering the buckling effect; \(\varphi_{st}\) and \(\varphi_{1}\) are the diameters of the uncorroded stirrup and longitudinal bar, respectively; \(H\) and \(b\) are the height and width of the rectangular column, respectively; and \(\delta\) denotes the thickness of the concrete cover. The attenuation factor \(\psi\) describes the characteristics of concrete expansion cracking caused by corrosion of steel bars, which leads to reduction of the concrete compressive strength. The mathematical model can be given as [30]  
\[\psi\!\!=\!\frac{f_{c}^{*}}{f_{c}}=\frac{1}{1+k^{2\pi\eta_{bars}(\eta_{s}-1)X} }, \tag{5}\]  
where \(f_{c}^{*}\) is the reduced compressive strength of concrete; \(k\) is the coefficient related to bar roughness and diameter, as suggested in [30], \(k=0.1\); \(v_{rs}\) is the volume expansion ratio of corrosion products; \(n_{bars}\) denotes the number of bars in the compression area; \(\varepsilon_{0}\) is the peak strain of normal concrete, \(\varepsilon_{0}=0.002\); and \(X\) is the corrosion depth, which describes the uniform corrosion characteristics of steel bars. According to [31], the reduction in the diameter of a corroding reinforcing bar after \(t\) years \(X\) (mm) can be predicted by  
\[X=0.0116i_{corr}t, \tag{6}\]  
where \(i_{corr}\) denotes the corrosion current density (\(\mu\)A/cm\({}^{2}\)). Due to [PERSON]'s effect, transverse deformation occurs when concrete is subjected to an axial load. When the axial strain is large enough, the transverse strain is restrained by stirrups, which improve the strength and ductility of concrete. The reinforcement characteristic value is an indispensable  
Figure 3: The bearing capacity model of corroded reinforced concrete (RC) column under axial compression. \(A_{1c}\): cracking area of unconfined concrete; \(A_{2c}\): cracking area of confined concrete; \(A_{3c}\), no cracking area of confined concrete; \(A_{1,red}\): the longitudinal reinforcement area considering the buckling effect; \(H\) and \(b\): the height and width of the rectangular column, respectively; \(s_{1}\): the lateral spacing of longitudinal reinforcement; \(\delta\): the thickness of the concrete cover. one among the many factors that affect the confined concrete. As suggested in [32], the compressive strength of the confined concrete can be calculated by  
\[f_{cc}=(1+1.79\lambda_{v})f_{c}, \tag{7}\]  
where \(\lambda_{v}\) is the reinforcement characteristic value. When the corrosion of stirrups is not included,  
Figure 2:0  
Figure 2:1  
where \(\mu_{v}\) is the stirrup ratio without considering the corrosion of stirrups; \(f_{s,y}\) is the yield strength of uncorroded stirrups; \(C\) is the length of stirrups; and \(s\) is the space between stirrups.