# Seismic Resilience of CRC- vs. RC-Reinforced Buildings: A Long-Term Evaluation
## 3 Prediction of Material Properties
### Steel Reinforcement Bars  
To determine the changes in the properties of steel reinforcement over time, particularly concerning its residual area due to corrosion, we utilize the expiration proposed by [PERSON] et al. [9]. This expiration assumes that the corrosion current density remains consistent across a set of \(n\) reinforcing bars of identical diameter, all equally affected by corrosion. The model allows the users to determine the cross-sectional area of these reinforcing bars at any given time t (years) through a series of equations (Equations (7)-(9)). This framework enables calculating the reduction in diameter of a corroding reinforcing bar after a specific duration, thereby providing a quantitative measure of the impact of corrosion on the structural behavior.  
\[\varnothing(t)=\varnothing_{0}-2P_{X}=\varnothing_{0}-2i_{corr}k\cdot(t-t_{in}), \tag{7}\]  
where \(\varnothing(t)\) (mm) denotes the residual diameter, \(\varnothing_{0}\) (mm) denotes the initial diameter of the steel, given time \(t\) (years) after corrosion initiation, \(t_{in}\) (years) denotes the time for corrosion to initiate on the rebar surface, and \(P_{x}\) (mm) denotes the average value of attack penetration. \(P_{x}\) specifically refers to the decrease in the radius of the reinforcing bar due to corrosion; see Equation (8).  
\[P_{X}(mm/year)=2i_{corr}\Big{(}\mu A/cm^{2}\Big{)}\cdot t_{p}(years), \tag{8}\]  
Finally, Equation (9) is employed to determine the residual area of steel reinforcement affected by corrosion.  
\[A_{S}(t)=\frac{n\cdot\pi[\varnothing_{0}-2i_{corr}k\cdot(t-t_{in})]^{2}}{4}, \tag{9}\]  
where \(t_{p}=(t-t_{in})\) denotes the \"propagation time\", which is the duration in years after the onset of corrosion. tin is defined from Equations (1)-(5) and found to be 20 years, indicating that the corrosive effects on the steel reinforcement begin 20 years after the construction has been completed. This delay accounts for the time it takes for corrosive substances to penetrate the concrete cover and reach the reinforcing steel, where the corrosion process is initiated. The factor k = 0.0116 is used as a conversion factor to translate the corrosion current density \(i_{corr}\) (uA/cm\({}^{2}\)) into a rate of steel loss in mm/year.  
Figure 4 presents the trend in the reduction ratio of the reinforcement area for n = 3, each with a diameter of 16 mm. This reduction ratio is calculated based on the predictive  
Figure 3: The predictive expansion and loss of compressive strength (X top refers to compressive strength degradation) of concrete over time (X bottom relates to time), analyzed by [PERSON] et al. [31].  
model discussed earlier, considering the effects of corrosion over time, specifically after the corrosion initiation period tin and during the propagation time \(t_{p}\).  
\[RAA(\%)=0.2585\cdot t,\quad t>20\ years \tag{10}\]  
An R-squared value of 0.9988 was obtained, showing a high level of predictive accuracy. It should be noted that we assumed that the mechanical properties of steel do not deteriorate over years, as presented in Table 1.