# Regional Seismic Damage Simulation of Corroded RC Frame Structures: A Case Study of Shenzhen City
## 4 Statistical Analysis of Experimental Results of Corroded RC Components  
To date, the mechanical properties of corroded beam and column components have been studied experimentally by numerous researchers. In this section, experimental data of corroded slender RC components are collected and the backbone curve parameters (i.e., initial stiffness, peak carrying capacity, peak displacement, and ultimate carrying capacity) of these components are analyzed statistically to reveal the degradation characteristics of key backbone curve parameters. The flexural capacity of slender RC components can be affected by various design factors, for example, reinforcement ratio, section dimension, material strength, and axial load ratio. To eliminate the influence of different design factors, components with the same design factors but different degrees of corrosion are categorized into groups. For each group, the reduction ratio of backbone curve parameters of the corroded to uncorroded components is calculated. Note that the reduction ratio is a dimensionless value, which is useful to reflect the degradation of mechanical properties induced by corrosion. The adopted backbone curve parameters and the calculation methods are elaborated as follows:  
1. For the reduction factor of initial stiffness \(\alpha_{i}\) (Equation (8)), the initial stiffness is calibrated according to Tran and Li [48], which is obtained by calculating the secant stiffness at the point when the applied load reaches 0.75 times of the peak carrying capacity. \(\alpha_{i}\) is the ratio of the backbone curve initial stiffness \(K_{i}\) of a corroded component with the degree of corrosion \(i\) to the initial stiffness \(K_{0}\) of an uncorroded component with the same design details, as illustrated in Figure 5a. \[\alpha_{i}=K_{i}/K_{0}\] (8)2. For the reduction factor of peak carrying capacity \(\beta_{i}\) (Equation (9)), the peak carrying capacity can be obtained by calculating the maximum value of the applied load. In Equation (9), \(F_{i}\) is the peak carrying capacity of a component with the degree of corrosion I, and \(F_{0}\) is the peak carrying capacity of an uncorroded component (Figure 5a). \[\beta_{i}=F_{i}/F_{0}\] (9)
3. For the reduction factor of peak displacement \(\delta_{i}\) (Equation (10)), the peak displacement is the corresponding displacement of the peak carrying capacity. \(\delta_{i}\) is the ratio of the peak displacement \(\Delta_{\text{pi}}\) of a component with the degree of corrosion \(i\) to peak displacement of an uncorroded component \(\Delta_{\text{p0}}\) (Figure 5a). \[\delta_{i}=\Delta_{\text{pi}}/\Delta_{\text{p0}}\] (10)
4. The reduction factor of ultimate carrying capacity \(\gamma_{i}\) (Equation (11)) is the ratio of the ultimate carrying capacity \(F_{\text{ui}}\) of a component with the degree of corrosion of \(i\) to that of an uncorroded component \(F_{\text{u0}}\) (Figure 5a). In literatures, the ultimate point is usually defined as the point when the carrying capacity decreased to 0.85 times that of the peak carrying capacity [24; 49]. For the collected test results, some specimens exhibited small strength degradation and the test was terminated when the carrying capacity was still larger than 0.85 times the peak carrying capacity. Note that the terminated displacement is larger than 1.3 times the peak displacement for all components, the point at 1.3 times the peak displacement is defined as the ultimate point, and the corresponding carrying capacity is defined as the ultimate carrying capacity (Figure 5a). The calibrated backbone curve for an example specimen is illustrated in Figure 5b.