## 4 Predictive Model for Bearing Capacity of Columns with Stirrup Corrosion
### Axial Bearing Capacity of Damaged Concrete Sections  
The corrosion of stirrups will cause damage to the section of the compressed column, especially to the peripheral section of the stirrups. According to the deterioration phenomenon of the test column after accelerated corrosion and damage during the bearing capacity test, it can be assumed that the bearing capacity section area of the rectangular stirrup-restrained concrete column consists of \(A_{\text{c1}}\) and \(A_{\text{c2}}\). (See more details in Figure 12). \(A_{\text{c1}}\) is the constrained area and \(A_{\text{c2}}\) is the concrete cover cracking area caused by corrosion. The depth of the cracking area reached the inner side of the main reinforcing steel bars. The lateral deformation was restrained by the rectangular stirrups. The rectangular stirrups were subjected to bending and tension action in the range of the straight section, so they had little constraint effect on the concrete, while the constraint reaction near the corner was stronger, which increased the strength of the concrete in the core restraint \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Specimen Number** & \(\rho_{\text{vc,th}}\) /\% & \(\rho_{\text{vc,ex}}\)/\% & \(N_{\text{cu,test}}\)/\& **Reduction/\%** \\ \hline GZ0 & 0 & 0.00 & 1500 & 0.0 \\ GZ5 & 5 & 4.95 & 1100 & 26.7 \\ GZ10 & 10 & 9.26 & 950 & 36.7 \\ GZ15 & 15 & 12.57 & 900 & 40.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Test results for ultimate bearing capacity. Figure 12: Division of bearing capacity in the cross-sectional area of stirrup-restrained concrete columns. area \(A_{\rm c1}\)[28, 29]. However, when the stirrups were corroded, the diameter of the stirrups became thinner and the tensile and flexural stiffness decreased. When the stirrups were subjected to axial pressure, the circumferential deformation increased with the increasing degree of corrosion. In addition, the corrosion products on the surface of the stirrups played a lubricating role between the stirrups and the concrete, thus reducing the bonding property. The corners of the corroded stirrups were easily pulled apart, which reduced the constraint ability of the core concrete. In addition, there was a stronger restraining effect on the concrete in the plane in which the corroded stirrups were located, while there was less restraining effect on the concrete between two adjacent stirrups. All of these factors reduced the effect of the corroded stirrups on the strength improvement of the core concrete. Therefore, in the prediction model of the bearing capacity of axial compression columns with stirrup corrosion, the effect of stirrup corrosion on the increase in the strength of the core concrete was not considered. Instead, the concrete strength in the core restraint area \(A_{\rm c1}\) was still used as the concrete axial compressive strength. In the concrete cover cracking area (\(A_{\rm c2}\)), the test column surface was divided into several sub-areas with corrosion-induced cracks, thus destroying the integrity of the area and resulting in damage to the test column section that decreased the ultimate bearing capacity. The damage level of the concrete cover cracking area was related to the area of corrosion cracking, with more serious damage occurring in larger areas of corrosion cracking. Therefore, the damage degree parameter \(\lambda\)\({}_{\rm c}\) was introduced and defined as the ratio of the crack area \(A_{\rm c}\) to the column surface area \(A\):  
\[\lambda\)\({}_{\rm c}=\frac{A_{\rm c}}{A} \tag{2}\]  
where: \(A_{\rm c}=W_{\rm ave}\times l_{\rm c}\), \(W_{\rm ave}\) is the average width of the corrosion-induced cracks on the column surface and \(l_{\rm c}\) is the total length of the corrosion-induced cracks on the column surface.