# Regional Seismic Damage Simulation of Corroded RC Frame Structures: A Case Study of Shenzhen City
## 2 Methodology  
RC frame structures primarily exhibit shear deformation under lateral load, therefore, the MDOF shear model is adopted in this study. The MDOF shear model has been widely adopted to predict the responses of multistory buildings in regional seismic damage simulations [4; 6; 18; 19]. In the MDOF shear model, the mass of each story concentrates on each mass point, and the mass points are linked to each other by shear springs [34], as exhibited in Figure 2a. Owing to a limited amount of detailed building information for regional simulation, a trilinear backbone curve model (Figure 2b) [5; 18] and a single-parameter hysteretic model (Figure 2c) [35] are adopted to simulate the nonlinear performance of shear springs. Note that the proposed method mainly focuses on corroded RC frame structures. The model adopted in Figure 2 is not applicable to other structural systems, such as RC frame-shear wall structures. Other simplified models such as the MDOF flexural shear model can be used to simulate the seismic performance of high-rise buildings in regional simulations [36]. The framework of regional seismic damage simulation for corroded RC frame structures consists of four modules, as illustrated in Figure 3, and described as follows:  
(1) Corrosion Simulation of Regional Buildings. In this module, a chloride-induced corrosion simulation method is adopted to obtain the degree of corrosion of regional buildings considering the concentration of chloride ion and service year of buildings. The simulated degree of corrosion of longitudinal reinforcement is used to estimate the reduction of key mechanical parameters in the following modules. (2) Statistical Analysis of Experimental Results of Corroded RC Components. The experimental data of corroded components are collected in this study. Subsequently, the backbone curve parameters (i.e., initial stiffness, peak carrying capacity, peak displacement, and ultimate carrying capacity) of RC components with different degrees of corrosion are analyzed statistically to obtain the reduction rule of each key parameter. The obtained reduction rules of component backbone curve parameters can be used to estimate the nonlinear performance of corroded RC components in the following modules. Figure 2: Multi-degree-of-freedom (MDOF) shear model: **(a)** MDOF shear model; **(b)** Trilinear backbone curve; **(c)** Single-parameter hysteretic model. (3) Degradation Analysis of Building Interstory Backbone Curve Parameters. The MDOF shear model is used for the seismic damage simulation of corroded RC frame structures in a city-scale scenario. Therefore, the reduction rules for the interstory backbone curve parameters of corroded RC frame structures are required for the parameter determination of the MDOF shear model. In this module, the component reduction rules obtained in the former module are used for the pushover analyses of corroded RC frame structures. First, typical RC frame structures are designed, and the hysteretic results of beam and column components are simulated using a fiber beam model. Second, a nonlinear Euler beam model is constructed for the studied RC frames and the hysteretic parameters of components are calibrated according to the hysteretic results computed in the first step. Third, the curvature-bending moment backbone curve parameters of each component are adjusted according to the reduction rules obtained in the second module. Fourth, pushover analyses of corroded RC frame structures are performed, and the reduction rules of building interstory backbone curve parameters are obtained through statistical analyses. (4) THA-Based Regional Seismic Damage Simulation of Corroded Buildings. First, set up an earthquake scenario and generate ground motions of the studied region. Second, construct the MDOF shear models of RC frame structures according to building attribute data (number of stories, floor area, year of built, etc.).