## 3 NSAS-Based Underground Structure
### Soil and Boundary Conditions  
For the analyzed underground structure with the control of the NSAS isolation system imbedded in the soil, numerical models were developed using ABAQUS [27]. For the sake of accuracy, the finite-element simulation techniques that were proven in previous studies were employed [28; 29]. The mechanical properties of concrete and reinforced steel are represented by the classic concrete damaged plasticity model [30] and the bilinear plastic model [31], respectively. The classic Davidenkov model was proposed by [PERSON] and [PERSON] [32], and has been proven to be an effective model for describing the dynamic stress-strain relationship of soil [33]. Therefore, a constitutive model based on the classical Davidenkov method was developed and utilized to simulate the dynamic behavior of the surrounding soil. Details and validation of this model can be found elsewhere [34]; briefly, the tangent shear modulus G \({}^{t+\Delta t}\) for initial loading is  
\[G^{t+\Delta t}=\frac{\partial\tau_{\text{oct}}^{t+\Delta t}}{\partial\gamma_{ \text{oct}}^{t+\Delta t}}\ =\ G_{\text{max}}\left[1-\left[1+\frac{2\cdot A\cdot B}{1+\left|\frac{\gamma_{ \text{act}}}{\gamma_{0}}\right|^{2B}}\right]\cdot H\left(\left|\gamma_{\text{ oct}}\right|\right)\right]_{t+\Delta t} \tag{6}\]  
For unloading and reloading, it is  
\[G^{t+\Delta t}=\frac{\partial\tau_{\text{oct}}^{t+\Delta t}}{\partial\gamma_ {\text{oct}}^{t+\Delta t}}=G_{\text{max}}\left[1-\left[1+\frac{2\cdot A\cdot B }{1+\left|\frac{\gamma_{\text{act}}-\gamma_{\text{oct},c}}{2\gamma_{0}} \right|^{2B}}\right]\cdot H\left(\left|\frac{\gamma_{\text{oct}}-\gamma_{ \text{oct},c}}{2}\right|\right)\right]_{t+\Delta t} \tag{7}\]  
where superscripts \(t+\Delta t\) and \(t\) represent the tangent shear modulus at the end of the current and previous increments, respectively; \(G_{\text{max}}\) is the maximal shear modulus of the soil; \(\tau_{\text{oct}}\) and \(\gamma_{\text{oct}}\) are the shear stress and strain of soil, respectively; \(\gamma_{\text{oct},c}\) is the shear strain in the last load reversal, and \(H(\gamma)\) is a shape function given by  
\[H(\gamma)=\left\{\frac{\left(\gamma^{\prime}/\gamma_{0}\right)^{2B}}{1+\left( \gamma^{\prime}/\gamma_{0}\right)^{2B}}\right\}^{A} \tag{8}\]  
where \(A\), \(B\) and \(\gamma_{0}\) are fitting parameters of the model. To intuitively illustrate this model, its dynamic shear stress-shear strain curves are plotted in Figure 5, taking \(\gamma_{0}=0.1\%\) as an example. Figure 4: Model of soil–underground structure interaction system controlled by conventional isolation system (CIS) and by NSAS combined with an isolator. In the finite-element simulation, a typical artificial constrained boundary [26], shown in Figure 6, was utilized to deal with the static-dynamic boundary-coupling conditions by using the classical procedure of finite-element software. In the geostatic step, the horizontal direction of the side boundary was constrained; then, reaction forces on the side boundaries were outputted after the geostatic step had been completed. Before conduct dynamic analysis, the side boundaries were converted by applying the horizontal outputted reaction forces in the direction of the side boundary, and the vertical direction was constrained. Referring to the design code [35], a stratum wherein shear-wave velocity is greater than 300 m/s can be selected as the artificial bedrock. At the same time, for the bottom boundary condition [36], the distance between the bottom of the soil and the underground structure should not be less than three times the height of the underground structure, which is selected in this study. The side boundary of soil is simulated by analyzing soil with 10 times the width of the soil depth, which was proven in previous studies to be effective in preventing propagating waves that reflect back to the model [28]. To simulate the contact behavior at interfaces during an earthquake, frictional surfaces were adopted as interfaces between the soil and the underground structure [37].