# Regional Seismic Damage Simulation of Corroded RC Frame Structures: A Case Study of Shenzhen City
## 5 Degradation Analysis of Building Interstory Backbone Curve Parameters
### Results of Simulation  
The simulated interstory backbone curves of the first story of all cases are presented in Figure 9. The results show that with an increased degree of corrosion, the initial stiffness, ductility, and load carrying capacity, in all cases, decrease. Note that the results exhibit a similar pattern, because the trilinear backbone curve is adopted to simulate the curvature-bending moment response of RC components. Meanwhile, the responses of corroded components are simulated by reducing the key mechanical parameters of RC components in an uncorroded state according to Equations (12)-(15). Therefore, the backbone curves of both corroded and uncorroded frames exhibit similar trilinear patterns.  
After obtaining the backbone curves of all cases, the reduction factors of backbone curve parameters among cases with different degrees of corrosion are computed according to the method presented in Section 4. The calculated parameter reduction factors are shown in Figure 10.  
The above results show that reduction factors of building interstory backbone curve parameters decrease with an increase in degree of corrosion, which corresponds to the experimental results (Figure 6). Moreover, the PCC can also affect backbone curve parameters. For example, the larger the PCC, the smaller the stiffness and carrying capacities. The above results show that both PCC and degree of corrosion can affect the building interstory backbone curve parameters. Therefore, bivariate linear regression is used to analyze the reduction factors and the reduction equations are shown in Equations (16)-(19).  
\[\alpha_{i}=-0.00595\;\omega-0.49567\;i+1, \tag{16}\]  
\[\beta_{i}=-0.01174\;\omega-0.78526\;i+1, \tag{17}\]  
\[\delta_{i}=-0.00179\;\omega-1.83327\;i+1, \tag{18}\]  
\[\gamma_{i}=-0.01888\;\omega-0.74122\;i+1, \tag{19}\]  
where \(\omega\) is the PCC and \(i\) is the degree of corrosion of corroded components.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**ID**} & \multirow{2}{*}{**Bays**} & \multirow{2}{*}{**Span (m)**} & \multirow{2}{*}{**Story Height (m)**} & \multicolumn{2}{c}{**Proportion of**} & \multirow{2}{*}{**Degree of Corrosion**} \\  & & & & & & \\  & & & & & & \\ \hline F-1-0 to F-1-20 & 1 & 6 & 3.3 & 100.00\% & 0\%, 5\%, 10\%, 15\%, 20\% \\ F-2-0 to F-2-20 & 2 & 6 & 3.3 & 88.89\% & 0\%, 5\%, 10\%, 15\%, 20\% \\ F-3-0 to F-3-20 & 3 & 6 & 3.3 & 75.00\% & 0\%, 5\%, 10\%, 15\%, 20\% \\ F-4-0 to F-4-20 & 4 & 6 & 3.3 & 64.00\% & 0\%, 5\%, 10\%, 15\%, 20\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters of simulation cases.  
Figure 10: Reduction factors of building interstory backbone curve parameters: (**a**) Reduction factor of initial stiffness; (**b**) Reduction factor of peak carrying capacity; (**c**) Reduction factor of peak displacement; (**d**) Reduction factor of ultimate carrying capacity.  
Figure 9: First story backbone curves of all cases: (**a**) One-bay building (PCC = 100.00%); (**b**) Two-bay building (PCC = 88.89%); (**c**) Three-bay building (PCC = 75.00%); (**d**) Four-bay building (PCC = 64.00%).  
From the above analyses, the reduction rules of interstory backbone curve parameters of corroded RC frame structures are obtained. For the THA-based building seismic damage simulation of corroded RC frame structures using a MDOF shear model, the initial uncorroded interstory backbone curve parameters of the MDOF shear model obtained through the method of [PERSON] et al. (2018) can be adjusted using Equations (16)-(19) (Figure 3).