## 4 Modeling of MD-RC Frame  
### Input Motions  
According to the methodology that is introduced in Section 2, the MD-RC frame models with different damage states (DS) can be obtained through the excitation of mainshocks with different intensities. Subsequently, the seismic performance analysis of the MD-RC frames with and without retrofitting schemes that are subjected to aftershocks is performed. For this purpose, the mainshock-aftershock (MS-AS) seismic sequences should be chosen before the retrofit analysis of the MD-RC frame. More specifically, in order to investigate the influence of earthquake type on retrofit effect, a widely used artificial seismic sequence method (i.e., randomized approach) introduced in literature [53] will be employed in this study. In the randomized approach, irrespective of the source distance (R) and earthquake magnitude (M), the ratios between the peak ground accelerations (\(PGA\)) for the two event cases are given by,  
\[\begin{array}{rl}\frac{PGA_{(2-EVENTS)}}{PGA_{(1-EVENT)}}&=\frac{PGA_{(M-0,2010)}}{PGA_{(M)}}\\ &=\frac{10^{B\ast 0.49+0.23(M-6.03010)-\log\sqrt{R^{2}+8^{2}}-0.0027\sqrt{R^{2} +8^{2}}}}{10^{B\ast 0.49+0.23(M-6.4)-\log\sqrt{R^{2}+8^{2}}-0.0027\sqrt{R^{2}+8^{2}}}} =0.8526\end{array} \tag{2}\]  
Furthermore, in order to construct near-fault MS-AS seismic sequences, six recorded near-fault strong ground motions (include four pulse-like and two non-pulse-like ground motions) are selected from the Pacific Earthquake Engineering Research Center (PEER) NGA-West2 ground motion database as the input motions of the numerical simulation,  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Material Types** & **Constitutive Model** & **Input Parameters** & **Values** \\ \hline \multirow{6}{*}{Concretes (C30)} & \multirow{6}{*}{CDP} & Mass density, \(\rho_{\text{c}}\) (kg/m\({}^{3}\)) & 2400 \\  & & Elastic modulus, \(E_{\text{c}}\) (MPa) & 30,000 \\  & & Poisson’s ratio, \(\
u\) & 0.2 \\  & & Compressive strength, \(f_{\text{c}}\) (MPa) & 20.1 \\  & & Tensile strength, \(f_{\text{t}}\) (MPa) & 2.01 \\  & & Mass density, \(\rho_{\text{s}}\) (kg/m\({}^{3}\)) & 7830 \\  & & Elastic modulus, \(E_{\text{s}}\) (GPa) & 200 (210) \\ \multirow{2}{*}{\
\begin{tabular}{c} Rebars HRB335 \\ (HPB300) \\ \end{tabular} } & \multirow{2}{*}{Bilinear Elastoplastic} & Poisson’s ratio, \(\
u\) & 0.3 \\  & & Yield Strength, \(f_{\text{y}}\) (MPa) & 335 (300) \\ \multirow{2}{*}{
\begin{tabular}{c} Rebars HRB335 \\ (HPB300) \\ \end{tabular} } & \multirow{2}{*}{Bilinear Elastoplastic} & \according to the reference [54]. Table 4 summarizes the information of these selected recorded near-fault ground motions. In this table, the pulse-like ground motion recorded at SVC station in the 1989 Loma Prieta earthquake and JGB station in the 1994 Northridge earthquake are regarded as the mainshock ground motions (remark MS1 and MS2, respectively). Meanwhile, in order to investigate the impact of aftershock types, two pulse-like and two non-pulse-like motion records (i.e., do not contain strong velocity pulses.) are selected as the aftershock ground motions (remark AS1, AS2, AS3, and AS4, respectively). Furthermore, the peak values (i.e., PGA) of the mainshocks and aftershocks are unified as the same sign in order to avoid the polarity influence of MS-AS seismic sequence on the response and behavior of MD-RC frame. In this study, the peak values of mainshocks and aftershocks are uniformly set to be positive in the constructed artificial near-fault seismic sequence.