# Seismic Response and Mitigation Analysis of a Subway Station in the Site with Weak Interlayers
## 2 Seismic Response of the Subway Station in the Site with Weak Interlayers
### Finite Element Model  
The numerical simulation method is a research method in the civil engineering field, which is verified by some studies [39; 40]. In this study, a two-dimensional model of the soil and subway station structure is established by using the finite element software ABAQUS [41]. The soil model has a width of 119 m and a height of 40 m. The specific values for the soil parameters are listed in Table 1 and the elastic modulus can be calculated using Equations (1) and (2). Here, \(\rho\) represents the density of the soil layer, \(V\)s stands for the shear wave velocity of the soil layer, and \(\
u\) represents the Poisson's ratio of the soil layer. \[G=\rho{V_{s}}^{2} \tag{1}\]  
\[E=2(1+\
u)G \tag{2}\]  
During the modeling process, the selection of soil layer damping deserves careful consideration as it is a pivotal factor. In this study, the Rayleigh damping model was chosen. Using the frequency analysis module in the ABAQUS software, we determined the first \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Condition**} & \multirow{2}{*}{**Interlayer Position (m)**} & **Relationship between** & \multirow{2}{*}{**Thickness of Interlayer**} & **Shear Wave** \\  & & **Interlayer and Underground** & & **(m)** & **Velocity (m/s)** \\ \hline
1 & Layered soil site & & & \\
2 & 2 & Upper & 2 & 80 \\
3 & 6 & Top & 2 & 80 \\
4 & 12 & Middle & 2 & 80 \\
5 & 19 & Bottom & 2 & 80 \\
6 & 22 & Lower & 2 & 80 \\
7 & 12.5 & Middle & 1 & 80 \\
8 & 12.25 & Middle & 1.5 & 80 \\
9 & 11.75 & Middle & 2.5 & 80 \\
10 & 11.5 & Middle & 3 & 80 \\
11 & 12 & Middle & 2 & 90 \\
12 & 12 & Middle & 2 & 100 \\
13 & 12 & Middle & 2 & 110 \\
14 & 12 & Middle & 2 & 120 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List of operating conditions. Figure 2: Schematic diagram of the soil-underground structure working condition. and second natural frequencies of the soil layers. Subsequently, the Rayleigh damping coefficients of the soil layers were calculated using Equations (3) and (4). \[\alpha=\frac{2D\times w_{1}\times w_{2}}{w_{1}+w_{2}} \tag{3}\]  
\[\beta=\frac{2D}{w_{1}+w_{2}} \tag{4}\]  
In the equation, where \(w_{1}\) and \(w_{2}\) represent the first and second natural frequencies of the soil layers, \(D\) is the damping ratio, set as 0.1 [42]. The concrete's constitutive model employed is the plastic damage model proposed by [PERSON] et al. [43], which is an improvement based on the model introduced by [PERSON] et al. 's work [44]. This model is grounded in the principles of fracture energy within concrete and introduces two key variables: tensile damage and compressive damage factors. These factors are employed to represent the stiffness degradation in concrete under tension and compression, respectively. The C40 concrete is used for the main structure of the station, with a density of 2500 kg/m\({}^{3}\), an elastic modulus of 3.25 \(\times\) 10\({}^{4}\) MPa, and a Poisson's ratio of 0.2. The other corresponding parameters are listed in Tables 3-5. The materials for the station's column include C50 concrete. The column is uniformly spaced along the alignment, with a 7 m interval. The material properties of the column are equivalently determined following established principles [38]. As a result of this equivalency, the column has a density of 250 kg/m\({}^{3}\), an elastic modulus of 3.45 \(\times\) 10\({}^{3}\) MPa, a Poisson's ratio of 0.2, a peak compressive strength of 1.83 MPa, and a peak tensile strength of 0.13 MPa. Reinforcement is simulated using truss elements, employing an ideal elastic-plastic constitutive model. The initial elastic modulus is set at 200 GPa, with a Poisson's ratio of 0.3 and a yield stress of 335 MPa.