# Analysis of the Dynamic Behavior of Multi-Layered Soil Grounds
## 3 Results and Discussion
### Spectral Acceleration  
Spectral Acceleration (SA) refers to the acceleration response spectrum at various frequencies experienced during seismic events when seismic waves pass through layers of different soil properties. The SA values at each frequency are influenced by the impedance contrast between soil layers, as well as the resonance frequencies and damping characteristics of individual layers. In multi-layered soil profiles, the SA distribution can vary spatially due to the complex interactions of seismic waves with the soil layers, resulting in the amplification or attenuation of ground motion at different frequencies across the site. Understanding the SA characteristics in multi-layered soil profiles is essential for seismic hazard assessment and site-specific ground motion prediction. Figures 13-16 show the Spectral Acceleration (SA) of the artificial seismic waves in Case 1, 2, 3, and 4.  
Figure 13: Spectral Acceleration of the artificial seismic wave in Case 1. (**a**) DEEPSOIL results; (**b**) experimental results; (**c**) ABAQUS results; (**d**) DEEPSOIL, experimental, and ABAQUS results (ACC 3).  
Figure 14: Spectral Acceleration of the artificial seismic wave in Case 2. (**a**) DEEPSOIL results; (**b**) experimental results; (**c**) ABAQUS results; (**d**) DEEPSOIL, experimental, and ABAQUS results (ACC 3).  
Figure 15: Spectral Acceleration of the artificial seismic wave in Case 3. (**a**) DEEPSOIL results; (**b**) experimental results; (**c**) ABAQUS results; (**d**) DEEPSOIL, experimental, and ABAQUS results (ACC 4).  
In Figure 13, the DEEPSOIL and ABAQUS results show comparable Spectral Accelerations (SAs), with DEEPSOIL closely matching the SA at ACC 2 and ACC 3, attributed to the inherent frequency of the silica sand layer. Post earthquake, significant settlement in the DEEPSOIL model's nonlinear constitutive and computational modes led to an amplified position SA. For ACC 1, the experimental and numerical results align well. By comparing the results in Figure 14, DEEPSOIL yields slightly higher results than the ABAQUS and experimental results. Moreover, the natural frequencies of the soil layers in the numerical analysis are generally consistent, with the experimental soil layer frequencies slightly exceeding those of the numerical analysis. This is attributed to the inclusion of the laminar shear box's mass in the experiment, adjusted through calculations to approximately 12.5 Hz, closely matching the numerical analysis. In the weathered soil case, comparing Figure 15a-c, DEEPSOIL and ABAQUS exhibit highly similar Spectral Accelerations, slightly higher than the experimental SA. Comparing Figure 15d, the numerical analysis closely matches the experimental SA. In the weathered soil layer, comparing Figure 16a-c, DEEPSOIL closely matches the experimental Spectral Accelerations, slightly exceeding ABAQUS. Comparing Figure 16d, the numerical analysis closely matches the experimental Spectral Accelerations.  
The Spectral Acceleration (SA) during earthquakes varies due to soil types and properties. In silica sand layers, seismic waves' energy is more easily absorbed and amplified due to the lower soil density and shear wave velocity, resulting in higher SA within a certain frequency range. In contrast, in weathered soil layers, the higher soil density and shear wave velocity lead to less damping and the amplification of seismic wave propagation, resulting in relatively lower SA within the same frequency range. Therefore, silica sand layers may experience greater seismic responses, while weathered soil layers may experience relatively smaller seismic responses.  
Figure 16: Spectral Acceleration of the artificial seismic wave in Case 4. (**a**) DEEPSOIL results; (**b**) experimental results; (**c**) ABAQUS results; (**d**) DEEPSOIL, experimental, and ABAQUS results (ACC 6).