## Building System under Investigation
### Numerical Model and Material Parameters  
In this research, structural modeling is performed while applying the ABAQUS nonlinear finite element software [47]. The middle frame (see Figure 2) is selected for planar modeling due to the symmetry of the analyzed structure. In the numerical, the concrete and rebars are modelled separately, and concrete and rebars of beam, column, and joint are simulated while using the Solid (C3D8R) and Truss (T3D2) elements, respectively. The rebars are embedded in the concrete to simulate the interaction between rebars and concrete, meanwhile the ideal bond is assumed and the influence of bond-slip between rebars and concrete is neglected. In addition, the influence of infill wall and soil-structure interaction are also neglected. It should be mentioned that the representative values of slab weight and gravity load are converted into the model density, in order to simplify the modeling of the RC frame. Figure 3 shows the planar three-dimensional (3D) numerical model of intact RC frame. In this numerical model, the total number of structural elements is 43,863, which includes 37,125 C3D8R elements and 6738 T3D2 elements. Figure 3: The planar three-dimensional (3D) numerical model of intact RC frame. Figure 2: Geometries and reinforcement details for RC frame (all dimensions in mm): (**a**) plan view; (**b**) reinforcement details of the beam and column section; (**c**) elevation view. In the numerical analysis, the rebars material adopt the dynamic hardening bilinear elastoplastic constitutive model based on the Von-Mises yield criterion. The concrete damage plasticity (CDP) constitutive model in ABAQUS material library is employed to take into account the strain hardening/softening behavior of concrete materials. The CDP model is based on the isotropy assumptions, while using elastic damage combined with tensile and compressive plasticity in order to replace the inelastic behavior of concrete, and considers the degradation of elastic stiffness, due to plastic strain in the process of tension or compression and the stiffness recovery under cyclic loading [52]. Figure 4 shows the stress-strain relations of CDP model under uniaxial cycle loading. Their constitutive relations under uniaxial tension and compressive can be expressed, respectively, by the following Formula [52],  
\[\sigma_{t} =(1-d_{t})E_{0}(\varepsilon_{t}-\varepsilon_{t}^{pl}) \tag{1}\] \[\sigma_{c} =(1-d_{c})E_{0}(\varepsilon_{c}-\varepsilon_{c}^{pl})\]  
where, \(\sigma_{t}\) and \(\sigma_{c}\) are the tensile and compressive stress of concrete. respectively; \(E_{0}\) is the initial (undamaged) elastic stiffness; \(\varepsilon_{t}^{pl}\) and \(\varepsilon_{c}^{pl}\) are equivalent plastic strain tensors in tensile and compressive conditions; \(d_{t}\) and \(d_{c}\) are the tensile and compressive damage factors respectively, where their values range from 0 (undamaged) to 1 (complete damaged). The two damage variables could consider the strength degradation of concrete materials [4] and they can be computed according to China current code [50]. In addition, in order to consider the complex degradation mechanisms of concrete materials under uniaxial cyclic conditions, the weight factors (stiffness recovery factor) \(w_{t}\) and \(w_{c}\), which can control the recovery of the tensile and compressive stiffness upon load reversal are defined in the CDP model. The default values for the stiffness recovery factors \(w_{t}\) and \(w_{c}\) are 0 and 1 in ABAQUS program, respectively [52], which means that the tensile stiffness does not recover and the compressive stiffness completely recovers under reverse loading. Table 2 summarizes the material input parameters of concrete and rebars constitutive models. In addition, the five plasticity parameters of the CDP model [52], such as dilation angle (\(\psi\)), eccentricity (\(\epsilon\)), strength ratio (\(f_{\text{b0}}/f_{\text{c0}}\)), \(K\), and viscosity parameter, are set to 30.0, 0.1, 2/3, 1.16, and 0.0005, respectively.