## 3 Seismic Response of the Slope Based on the Time-Domain Analysis
### Analysis of Acceleration Magnification Effect of the Slope  
To investigate the seismic response characteristics of the slope, taking the _WE_ wave (0.1 g) when input in _x_-direction as an example, the acceleration-time history of the points is shown in Figures 8 and 9. According to Figure 8, the PGA (peak ground acceleration) of the slope surface shows an increasing trend with the elevation. Figure 9 also shows that the PGA increases with the elevation inside the slope. This phenomenon suggests that the elevation is positively correlated with the PGA. To further investigate the seismic response of the slope, M\({}_{\text{PGA}}\) is introduced to define the ratio of PGA at any point in the slope and PGA at the slope toe (point A1) as M\({}_{\text{PGA}}\), which represents acceleration magnification at certain a point of the slope. The change rules of M\({}_{\text{PGA}}\) with the slope relative elevation (\(h/H\)) are shown in Figure 10. The \(h\) and \(H\) refer to the total height and the height of a point in the slope; respectively, Figure 10a shows that, under horizontal seismic force, the M\({}_{\text{PGA}}\) near the slope surface increases with the \(h/H\), and the M\({}_{\text{PGAmax}}\) is about 1.41 at the slope crest, while the M\({}_{\text{PGA}}\) inside the slope increases with the elevation, reaching a maximum of about 1.26 at the point A10.  
The dynamic acceleration magnification effect of the slope has an increased effect with the elevation, indicating that the slope has an elevation amplification effect. However, the M\({}_{\text{PGA}}\) shows an obvious nonlinear variation characteristic, which is caused by the discontinuity of the rock mass, and wave refraction and reflection effects appear near the  
Figure 8: Acceleration time history of measuring points at the slope surface: (a) A1, (b) A3, (c) A5, (d) A7, (e) A9.  
Figure 7: Wave propagation characteristics through the slope when input wave is in _z_-direction.  
structural planes, resulting in nonlinear variation characteristics of the amplification effect. By comparing the \(\mathrm{M_{PGA}}\) of the internal slope with that of the slope surface, it can be found that the \(\mathrm{M_{PGA}}\) of the slope surface is significantly larger than that of the internal slope. For example, when the elevation is about 0.6 m, \(\mathrm{M_{PGA}}\) of the points A5 and A6 are 1.27 and 1.02, respectively, which indicates that the slope has an obvious slope surface amplification effect. The slope surface is the free surface, which results in a great amplification effect on the seismic energy and indicates that the surface slope amplification effect is much larger and damage is more severe near the slope surface. Figure 10b shows that the \(\mathrm{M_{PGA}}\) variation rule of the bedded slope under vertical seismic force is similar to Figure 10a, and the \(\mathrm{M_{PGA}}\) reaches the maximum at the slope crest (point A9), approximately 1.19. Moreover, the direction of ground motion has an impact on the dynamic magnification effect of the slope. Figure 10 shows that \(\mathrm{M_{PGAx}}\) under horizontal seismic loading is about 1.10-1.20 times larger than \(\mathrm{M_{PGAz}}\) under vertical seismic loading. For example, the \(\mathrm{M_{PGAx}}\) and \(\mathrm{M_{PGAz}}\) of A4 are 1.36 and 1.12, respectively. The horizontal seismic force has a greater effect on the dynamic amplification and deformation of the slope. When waves propagate through joints, refraction and reflection phenomena occur on the joint surfaces, which impacts the seismic energy propagation within the slope.  
Figure 10: \(\mathrm{M_{PGA}}\) change rule of the slope when inputting WE wave: (**a**) when input in \(x\) direction, (**b**) when input in \(z\) direction.  
Figure 9: Acceleration time history of measuring points inside the slope: (**a**) A2, (**b**) A4, (**c**) A6, (**d**) A8, (**e**) A10.