# Validation and Parametric Study of a Soil-Structure Interaction Nonlinear Simplified Model
## 3 Improved Penzien Model Validation
### Validation of the Soil-Structure Interaction Simplified Model
#### 3.2.2 Simplified Model Validation
velocity and acceleration response spectra obtained from the MATLAB simplified model were essentially identical to those from the ANSYS model, while the displacement response spectra obtained from the MATLAB simplified model were slightly lower than those from the ANSYS model. This finding was consistent with the conclusions drawn by [PERSON] et al. [42] in the comparison of simplified models and FE models. The discrepancies between the MATLAB and ANSYS models can be attributed to three main factors. Firstly, the modeling methods employed for the soil differed between the two models. In the MATLAB model, the soil was divided into the free field system and the equivalent soil according to the difference between the far field and the near field. The seismic analysis of the free field system enabled the extraction of parameters such as shear modulus, damping ratio, velocity, and displacement for each soil layer, which were subsequently employed in the dynamic equation calculations of the structural system. Furthermore, the stiffness and damping of the equivalent soil were incorporated into the structural system stiffness and damping matrices, thereby allowing for the consideration of the influence of soil properties on the structural system. In the ANSYS model, the soil was represented using an actual finite element model. Once the overall structural system model had been established, the soil was meshed to create numerous soil elements. Subsequently, the entire model was subjected to a seismic analysis. Secondly, the modeling methods employed for the pile differ between the two models. In the MATLAB model, the pile was simplified into a lumped-mass model based on soil stratification. In the ANSYS model, the pile was simulated using BEAM elements. Thirdly, the seismic wave input methods differed. In the MATLAB model, the seismic analysis of the structural system involved the calculation of seismic forces for all mass points, with consideration given  
Figure 4: The third story structure responses as spectrum of: (**a**) displacement, (**b**) velocity, (**c**) acceleration. Figure 3: The third story structure responses as time–history concerning: (**a**) displacement, (**b**) velocity, (**c**) acceleration. to the soil-structure interaction within the dynamic equations. In contrast, the ANSYS model input seismic acceleration from all nodes at the bottom bedrock surface, which may introduce filtering effects. Although discrepancies existed between the two models due to differences in soil modeling, pile modeling and seismic input methods, the nonlinear soil-structure interaction simplified calculation model was capable of rapidly and effectively reflecting the structure response under seismic loads, while considering soil-structure interaction. The simplified model has been sufficiently validated for both soil and superstructure nonlinearity. Consequently, it can be employed as a computational model for nonlinear systems in the field of soil-structure interaction research, offering effective guidance for design and optimization in practical engineering applications with the objective of ensuring structure safety and stability under seismic effects.