# Seismic Response Analysis of Reinforced Concrete Frame Structures Considering Slope Effects
## 2 Establishment of Soil-Structure Interaction Model
### Establishment of a Reinforced Concrete Frame Structure Model Considering Soil-Structure Interaction  
According to Chinese current norms [17], a reinforced concrete frame structure with six layers and three spans was designed. Three different slope ratios of 1:1, 1:2, and no slope were considered, respectively, in the design of the slope foundation.  
Fortification intensity (planned basic acceleration) was VIII degree (0.2 g). The ground motion group was group 2. The site classification was class II. The primary reinforcement bar grade of the beam and column was HRB335. The stirrup grade was HPB235. The concrete grade was C35. The X-direction dimension of the soil was 104.4 m. The slope height was 18 m. The ratios of the slope were 1:1 and 1:2, respectively. The horizontal distance from the superstructure to the top of the hill was 3 m. The superstructure side-span was 6 m, and the middle span was 2.4 m. The structure's bottom layer was 3.9 m, and the standard layer height was 3.3 m. The size of the beam section was 0.25 m \(\times\) 0.5 m. The section size of the column and pile was 0.6 m \(\times\) 0.6 m. The pile length was 6 m. Figure 3 is the structure diagram, and Figure 4 shows the reinforcement information of the beam section and column section.  
Figure 2: Schematic diagram of soil spring.  
This study used PIMY and PDMY from OpenSees to simulate the soil material. The two constitutive relations of the material were elastoplastic materials with multiple yield surfaces. Concrete01 from OpenSees was used to simulate the foundation beams, columns, and piles. The Steel02 constitutive model was adopted for longitudinal reinforcement in beams, columns, and piles. In addition, this study used PySimple1 and TzSimple1 materials from OpenSees to realize the characteristics of the \(p\)-\(y\) unit and the t-z unit in springs. Displacement-based beam-column elements were used to model beams, columns, and piles. The soil element adopted the four-node plane strain element. And the pile-soil interaction was simulated by the \(p\)-\(y\) zero-length element. Beams, columns, and piles were made of the same type of material. Tables 1 and 2 show the specific parameters of the materials of beams, columns, and piles. This research is based on actual slope engineering when considering soil parameters. Additionally, the property of each soil layer was assumed to be uniform. The details of the soil are provided in Table 3[18]. The finite element model is shown in Figure 5.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Structure Type** & \(f_{\text{c}}\)**/MPa** & \(\varepsilon_{\text{co}}\) & \(f_{\text{cu}}\)**/MPa** & \(\varepsilon_{\text{cu}}\) \\ \hline Non-Core & 29.76 & 0.002 & 0 & 0.004 \\ Concrete & 32.57 & 0.0022 & 20.76 & 0.0124 \\ \hline \hline \end{tabular} Where \(f_{\text{c}}\) is concrete compressive strength (with positive value), \(\varepsilon_{\text{co}}\) is concrete strain at maximum strength (with positive value), \(f_{\text{cu}}\) is concrete crushing strength (with positive value), \(\varepsilon_{\text{cu}}\) is concrete strain at crushing strength (with positive value).  
\end{table}
Table 1: Concrete parameters.  
Figure 4: Section reinforcement drawing. (**a**) Side-span beam; (**b**) middle-span beam; (**c**) column.  
Figure 3: Structure diagram.