# Seismic Resilience of CRC- vs. RC-Reinforced Buildings: A Long-Term Evaluation
## 3 Prediction of Material Properties
### Reinforced Concrete
#### 3.5.3 Reduction in Cross-Sectional Area Due to Corrosion-Induced Cover Cracking  
In this section, we defined the effect of corrosion on cracking and the relationship between corrosion and erosion of the section and residual areas over the years at influenced times. The structure remains unaffected by corrosion for the first twenty years (t = 0 to t = 20 years), as the cover protects the steel reinforcement from corrosive substances. This period is in line with CO\({}_{2}\) and chloride ion diffusion models [39; 40], suggesting that these substances do not reach the steel-to-concrete interface in sufficient quantities to initiate corrosion within this timeframe. However, by the twenty-year mark (t = 20 years), diffusion processes enable CO\({}_{2}\) and chloride ions to penetrate the protective barrier and reach the steel-concrete interface where they initiate the corrosion process. This moment marks a critical shift, leading to the gradual erosion of the protective cover as corrosion advances. From t = 20 to t = 40 years, the build-up of corrosion products causes increasing pressure \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Age** & **As (mm2)** & **As\({}^{\prime}\) (mm2)** & \(f^{\prime}cu\) (MPa)** & **Ec (GPa)** &
\begin{tabular}{c} **Residual Cover—** \\ **Top/Bottom (mm)** \\ \end{tabular} \\ \hline
0 & 602.88 & 602.88 & 37.50 & 30.28 & 30 \\
20 & 602.88 & 602.88 & 37.50 & 30.28 & 30 \\
45 & 559.96342 & 559.96342 & 25.24 & 24.85 & 0 \\
70 & 518.63129 & 518.63129 & 13.67 & 18.28 & 0 \\
95 & 478.8836 & 478.8836 & 9.55 & 15.28 & 0 \\
12 & 440.72035 & 440.72035 & 7.40 & 13.45 & 0 \\
145 & 404.14155 & 404.14155 & 6.07 & 12.19 & 0 \\
170 & 369.14719 & 369.14719 & 5.17 & 11.24 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Properties of RC cross-sections. Figure 8: Predicted long-term behavior of corrosive concrete: (**a**) stress–strain curve; (**b**) modulus of elasticity. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Age** & **As (mm2)** & **As\({}^{\prime}\) (mm2)** & \(f^{\prime}cu\) (MPa)** & **Ec (GPa)** &
\begin{tabular}{c} **Residual Cover—** \\ **Top/Bottom (mm)** \\ \end{tabular} \\ \hline
0 & 100.48 & 100.48 & 37.50 & 30.28 & 30 \\
20 & 97.66656 & 97.66656 & 37.50 & 30.28 & 30 \\
45 & 94.14976 & 94.14976 & 33.75 & 28.73 & 30 \\
70 & 90.63296 & 90.63296 & 33.12 & 28.46 & 30 \\
95 & 87.11616 & 87.11616 & 33.00 & 28.40 & 30 \\
120 & 83.59936 & 83.59936 & 32.78 & 28.31 & 30 \\
145 & 80.08256 & 80.08256 & 32.63 & 28.25 & 30 \\
170 & 76.56576 & 76.56576 & 32.48 & 28.18 & 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Properties of CRC cross-sections. on the surrounding concrete, triggering cracking, especially in the tension areas. By the end of this period (t = 40 years), the structure exhibits full concrete cover cracking. The experimental results and empirical equations presented by [PERSON], [PERSON], and [PERSON] [41] and by [PERSON], [PERSON], and [PERSON] [42] provide a comprehensive picture of the long-term effects of corrosion on RC structures. These findings, as presented in Equations (19)-(21), provide a method of estimating the timeline for concrete cover cracking. These equations depend on the initial concrete cover depth, corrosion rate, and the water-cement ratio. \[i_{corr}(t=1)=\left[37.80(1-W/C)\,^{-1.64}\right]/c \tag{19}\]  
where \(w/c\) denotes the water-cement ratio within the concrete mix and \(c\) denotes the reinforcement-free cover, referring to the thickness of the concrete layer that protects the reinforcement steel from exposure to corrosive substances. To define the corrosion rate over the years, we utilized the methodology presented by [PERSON] and [PERSON] [42]. More specifically, we adopted their recommendation of the time-dependent corrosion rate \(i_{corr}\), starting at \(t_{0}\) = 20 years. \[i_{corr}(t)=\left[i_{corr}(t=1)\cdot 0.85(t-t_{0})\right]^{-0.30} \tag{20}\]  
By adhering to the [PERSON] and [PERSON] guidelines, one can determine and predict when the cover will fully spall, resulting in reduced cross-sectional area.