## 4 Dynamic Response of the Slope Based on the Frequency-Domain Analysis
### Dynamic Response of the Slope Using Fourier Spectrum Analysis  
To study the amplification effect of the slope, taking the horizontal seismic load (0.1 g) as examples, the Fourier spectra of the points are shown in Figures 13 and 14. There are four predominant frequencies (\(f_{1},f_{2},f_{3}\), and \(f_{4}\)) in Figures 13 and 14, including the \(f_{1}\) (2.50 Hz), the \(f_{2}\) (7.30 Hz), the \(f_{3}\) (10.50 Hz), and the \(f_{4}\) (17.30 Hz). The change of topographic and geological conditions directly leads to the change of the magnification effect of the slope [23; 24]. Figures 13 and 14 show that the Fourier spectrum amplitude of the first three natural frequencies is much larger, and the PFSA (peak Fourier spectrum amplitude) of the \(f_{1},f_{2}\), and \(f_{3}\) increases gradually with the slope elevation on the whole, which indicates that \(f_{1},f_{2}\), and \(f_{3}\) are closely related to the magnification effect of the bedded slope. In combination with the results of the modal analysis of the slope (Figure 12), the \(f_{1},f_{2}\), and \(f_{3}\) of the slope have an important impact on the modal characteristic of the slope. In particular, the PFSA of the \(f_{1}\) is the largest of all, and increases rapidly with the slope elevation, indicating that \(f_{1}\) has a controlling effect on the deformation of the bedded slope. Moreover,  
Figure 12: Results of modal analysis of the bedded rock slope. when the frequency is >20 Hz, the Fourier spectrum amplitude has no obvious change with the increasing elevation, suggesting that the amplification effect is not obvious in the frequency component range. Therefore, certain frequency components (\(f_{1},f_{2}\), and \(f_{3}\)) have magnification effects on the dynamic response of the slope, and their PFSA was selected to clarify the dynamic response of the slope during earthquakes. To investigate the dynamic response of the slope, taking the horizontal seismic load (0.1 g) as an example, the PFSA of \(f_{1},f_{2}\), and \(f_{3}\) is shown in Figure 15. The PFSA has an increase with the elevation of the slope, and reaches the maximum at the top slope, suggesting that the slope elevation has an impact on the seismic response of the slope. Figure 15a shows that the PFSA increases linearly overall firstly, but a rapid increase in the PFSA can be identified when the \(h/H\) is > 0.62 on the slope surface and the \(h/H\) is > 0.82 inside the slope, which suggests that an obvious amplification effect can be found in the surface slope that is above the topmost structural plane, and the difference of magnification effect between the surface slope and the lower rock mass, resulting in the different dynamic response of the slip mass and slip bed. The phenomenon indicates that the structural surface has a magnification effect on the dynamic response of the slope, due to the following reason: when the seismic waves pass through structural planes, the reflection and refraction of waves occur, which results in the wave superposition in some frequency bands, and a great difference of physical properties between structural surfaces and rock masses directly leads to the redistribution of energy [41], directly magnifying the dynamic response of slopes. Figure 15 also shows that the PFSA reaches the maximum at the slope crest, indicating that the dynamic amplification effect is mainly concentrated  
Figure 13: Acceleration time history of different measuring points at the slope surface. in the surface slope, where the mechanical properties are very unstable. Moreover, it can be seen that when the slope has multiple structural planes, the topmost structural plane has the most obvious magnification effect on the slope. When the surface slope begins to be damaged, the topmost structural plane is a potential sliding surface. With the increase in seismic load, after the formation of the primary slip mass (surface slope), the potential sliding surface continues to expand in the lower structural plane, leading to further promoting the formation of the larger-scale sliding body.