# Seismic Resilience of CRC- vs. RC-Reinforced Buildings: A Long-Term Evaluation
## 3 Prediction of Material Properties
### Reinforced Concrete  
#### 3.5.1 Concrete Compressive Strength  
This section explores the phenomenon of corrosion penetration and its subsequent impact on the compressive strength, stiffness, and ductility of RC elements. It is worth noting, as highlighted by [PERSON] [33; 34], that the influence of steel bar creep on the compressive strength of RC elements is relatively small, especially when compared to the creep of CFRP, which significantly affects both compressive strength and ductility. The focus of this section is primarily on reducing compressive strength as a fundamental cause of deterioration in concrete structures. Addressing this critical issue involves the exploration of methodologies to accurately predict the compressive strength of corroded concrete, with specific emphasis on RC beams. Herein, we adopted an empirical equation highlighted in the studies by [PERSON] and [PERSON] [4], as presented in Equation (11). \[\beta=\frac{f_{cu}^{*}(t)}{f_{cu}}=\frac{1}{1+k\cdot\frac{2\pi X\cdot n_{bars}}{ b\cdot c_{2}}}, \tag{11}\]  
where \(f_{cu}^{*}(t)\) denotes the entire cross-section of the corroded compressive strength, \(f_{cu}\) denotes the uncorded compressive strength, \(k\) is a variable, where setting \(k\) as 0.1 refers to medium rebar corrosion levels, \(X\) denotes the corrosion penetration length, \(b\) the width of the cross-section, \(\varepsilon_{c2}\) the strain at the peak, and \(n_{bars}\) the number of steel reinforcements in the compressive zone. The research conducted by [PERSON] and [PERSON] [4] emphasizes the critical need to accurately reflect the reductions in compressive strength to areas specifically impacted by corrosion. These areas ensure that estimations of the structural capacity loss remain accurate and grounded in the actual extent of corrosion damage. This methodology helps prevent the underestimation of a structure's remaining load-bearing capability. Figure 6 shows the differential in compressive strength reduction across various sections. Figure 5: The trend of CFRP SR over time, highlighting the linear decrease in material strength, as provided by [32]. Carbonation penetration in reinforced concrete structures is a time-dependent process that intensifies with concrete aging [35; 36]. This carbonation process is notably more rapid in concrete of lower strength, where the porosity tends to be higher, facilitating the ingress of carbon dioxide. The adverse effect of carbonation on concrete strength is significant, as it not only reduces the alkalinity of the concrete, thereby endangering the protective oxide layer on the reinforcing steel, but also directly impacts the concrete's structural durability. Equations (12)-(15) quantify the relationship between the depth of carbonation penetration and its detrimental effects on the concrete's compressive strength:  
\[X=K\cdot\sqrt{t}\,, \tag{12}\]  
where \(X\) denotes the depth of corrosion penetration measured in (mm) and \(K\) denotes the carbonation coefficient (mm/year-1/2). \(K\) quantifies the rate at which carbonation progresses through the concrete over time, and t denotes the exposure time to CO\({}_{2}\) (years). In the study conducted by [PERSON] et al. [35], the compressive strength of concrete was meticulously computed and subsequently utilized to estimate the carbonation coefficient, as presented in Equation (13). \[K=847f_{cu}^{s}-1.435, \tag{13}\]  
The research conducted by [PERSON] and [PERSON] [4] significantly advanced the understanding of concrete durability by establishing a correlation that links the ultimate strength of concrete to its age, considering the varying diffusion rate \(K\) of carbon. Their work recognized that the diffusion rate of carbon increases as the concrete's strength decreases over time, highlighting a critical aspect of concrete aging and deterioration. In our analysis, we evaluated this relationship by integrating Equations (11)-(13), which collectively help define the compressive strength (\(f_{cu}\)). This relationship is explicitly expressed through Equations (14a) and (14b).