# Seismic Resilience of CRC- vs. RC-Reinforced Buildings: A Long-Term Evaluation
## 3 Prediction of Material Properties
### Normal-Strength Plain Concrete  
Here we focus on the deterioration processes affecting plain concrete structures. While it is known that the degradation of non-reinforced concrete is generally less pronounced compared to that of reinforced concrete, owing largely to the absence of steel reinforcement, which eliminates the risk of corrosion-induced spalling and cracking, the material is not impervious to chemical damage. Among the spectrum of chemical attacks that concrete may face, sulfate attack has emerged as a particularly prevalent threat. Sulfate attack occurs when sulfate ions, commonly present in soil and groundwater, or as byproducts of industrial emissions, penetrate concrete and react with its components, especially the calcium aluminate hydrates in the cement. This reaction leads to the formation of expansive minerals like ettringite and gypsum, which can cause the concrete to crack. This form of chemical degradation is of particular concern in environments with high sulfate concentrations, such as areas near industrial plants, coastal regions, or areas with sulfate-rich soils.  
Significant research efforts have been made to predict the long-term compressive strength (\(f_{cu}(t)\)). A notable example is the study by [PERSON] et al. (2019), which empirically estimated the long-term compressive strength of concrete in a moist environment characterized by 67% air humidity. Their findings, as demonstrated in Equations (1)-(5) provide essential insights into concrete resilience under such conditions.  
\[f_{cu}(t)=\mu_{f}(t)-1.645\cdot\sigma_{t}(t), \tag{1}\]  
where \(\mu_{f}(t)\) and \(\sigma_{f}(t)\) denote the mean value and standard deviation of concrete compressive strength after a specific period \(t\), measured in years; these parameters are crucial in statistical models for quantifying and understanding the variability and reliability of concrete strength over time, as presented in Equations (2) and (3):  
\[\mu_{f}(t) =\xi(t)\cdot\mu_{0}, \tag{2}\] \[\sigma_{f}(t) =\eta(t)\cdot\sigma_{0}, \tag{3}\]where \(\mu_{0}\) and \(\sigma_{0}\) denote the mean value and standard derivation of concrete compressive strength at 28 days (where \(t=0\)), respectively. \(\xi(t)\) and \((t)\) are functions of time that modify the mean and standard deviation over time, respectively, given as  
\[\xi(t)=1.2488e^{-0.0347\left(\text{{Int}}-0.3468\right)^{2}}, \tag{4}\]  
\[\eta(t)=0.0143t+1.6024, \tag{5}\]  
To predict the long-term tensile strength of concrete with compressive strength, [PERSON] et al. (2018) recommend an exponential function. The function provides the relationship between the compressive strength and the tensile strength (\(f_{\text{ts}}(t)\)) of concrete over time, as depicted in Equation (6).  
\[f_{\text{ts}}=1.02\cdot f_{\text{ct}}^{0.36}, \tag{6}\]  
Figure 2 schematically illustrates the changing trends in compressive and tensile strengths of plain concrete as time progresses under standard conditions.  
[PERSON] et al. (2018) present a method of estimating the evolution of strength in unreinforced concrete over time, emphasizing the influence of sulfate content on different concrete mixtures. This model stands out due to its comprehensive examination of how varying levels of sulfate impact concrete durability and structural service life. For our research, we focus on a concrete mixture with the standard sulfate concentration to study its expansion and reduction in compressive strength as time progresses. Our selected mix comprises 300 kg/m\({}^{3}\) cement content, 1% Mg2+ sulfate ions, 0.2% C3A (tricalcium aluminate), and a water-to-cement ratio (W/C) of 0.6. The changes in compressive strength and expansion, as drawn by the [PERSON] et al. model, are depicted in Figure 3, providing the resulting concrete deterioration due to sulfate attack over time.  
Figure 2: Predicted long-term compressive and tensile strengths for plain concrete.