## 3 Description of the Retrofitted Building Models and Ground Motion Datasets
### Structural Modeling  
The two building models were modeled as three-dimensional spatial frames, wherein the floor diaphragms were assumed to be rigid in their own planes without an out-of-plane stiffness. Figure 10 shows the structural modeling. For the numerical analyses, a nonlinear analysis program for spatial frames developed by the authors in a previous study [58] was used. The structural models were based on Model-RuW4-100 from a previous study [44]. As shown in Figure 10b,c, all of the vertical and rotational springs in the basement of the original model were replaced by isolators, and dampers were installed in the isolation layer. The shear behavior of the isolators was modeled using the multi-shear spring model proposed by [PERSON] and [PERSON] [59], while their axial behavior was modeled using a linear elastic spring, as shown in Figure 10d. The shear behavior of the steel dampers was also modeled using the multi-shear spring model, as shown in Figure 10e. No bending stiffness was considered in either the isolators or the dampers. The hysteresis rules of the ESBs and steel dampers were modeled following the normal bilinear rule for simplicity of analysis. Details of the structural modeling of the superstructure can be found in the literature [44]. The damping matrix of the superstructure was then assumed to be proportional to the tangent stiffness matrix of the superstructure, with 2% of the critical damping of the first mode. The damping of the isolators and dampers was not considered, assuming that their energy absorption effects were already included in the hysteresis rules. Note that the force-displacement relationships of all members, including those in the superstructures and in the isolation layers, were assumed to be symmetric in the positive and negative loading directions, as in previous studies [44,58]. It should be mentioned that the foundation compliance and kinematic soil-structure interaction were not considered for the simplicity of the analysis. [PERSON] et al. [60] investigated the performance of a rubber-isolated six-story RC building in soft soil. They concluded that the soil-structure interaction effect is rather negligible in the case of isolated buildings. Based on this, the authors thought the influence of the soil-structure interaction effect to the response of this building would not be significant. Figure 10: Structural modeling: (**a**) Overview of the structural model; (**b**) frame B\({}_{1}\); (**c**) frame Y\({}_{6}\); (**d**) modeling of the isolators (NRBs and ESBs); (**e**) modeling of the steel dampers. Figures 11 and 12 show the first three natural modes of Model-T34 and Model-T44 in the elastic range. Here, \(T_{ie}\) is the natural period of the \(i\)th mode in the elastic range (\(i\) = 1-3), \(m_{ie}{}^{*}\) is the effective modal mass ratio of the \(i\)th mode with respect to its principal direction in the elastic range, \(\psi_{ie}\) is the incidence of the principal direction of the \(i\)th modal response in the elastic range, and \(R_{\rho ie}\) is the torsional index of the \(i\)th mode in the elastic range.