4.3.1. Influence of Slope Height H

In this subsection, the slope height varied from 20 m, 50 m, 100 m, to 200 m, whereas the other geometrical parameters (slope widths and slope inclinations) remained the same. The acceleration amplification ratios along the slope surface are illustrated in Figure 18 with varying angles of incident waves.

**Figure 18.** Variations of the seismic responses along the slope ridges and the slope crests of the real amplification ratio (*r*) of PGA with varied angles of wave incidence at different slope heights. (**a**) slope height of 20 m, (**b**) slope height of 50 m, (**c**) slope height of 100 m, (**d**) slope height of 200 m.

In Figure 18, different distributions of ground motions are presented with varying slope heights under SV incident waves. The acceleration amplification ratios rose signifi-

cantly with an increase in the slope height from 0.2*λ* to 2.0*λ*. The area of the maximum acceleration amplification ratios at each height moved to the center of the slope topography with an increase in slope height. In addition, the maximum acceleration amplification ratios could be obtained when the incident angles fell between 25◦ and 30◦ under a slope height of 0.2*λ*, whereas the maximum acceleration amplification ratios could be obtained when the incident angles fluctuated between 5◦ and 10◦ under a slope height of 2.0*λ*. Thus, the higher the slope heights, the closer the maximum acceleration amplification ratios were to the smaller inclinations of wave incidence. In summary, different slope heights influenced the wave aggregation at the crest; the higher the model, the larger the acceleration amplification ratios. The maximum ground motions were obtained in the oblique direction of the incident waves.

Moreover, the observation points (slope toe and slope crest) are presented with horizontal and vertical components in Figures 19 and 20, respectively, to analyze the comprehensive relations between the incident directions and slope heights.

**Figure 19.** Variations of the horizontal amplification ratios (*r*h) of PGA at the observation points ((**a**) left toe, (**b**) left crest, (**c**) right toe and (**d**) right crest) with varied angles of wave incidence at different slope heights.

**Figure 20.** Variations of the vertical amplification ratios (*r*v) of PGA at the observation points ((**a**) left toe, (**b**) left crest, (**c**) right toe and (**d**) right crest) with varied angles of wave incidence at different slope heights.

As shown in Figures 19 and 20, the variations in the amplification ratios at the slope toe were gentle. The horizontal amplification ratios at the left toe decreased with an increase in the angle of incidence and increased with an increase in slope height. However, the vertical amplification ratios at the left toe increased with an increase in the angle of incidence, whereas their variations remained almost unchanged with varying slope heights. The horizontal amplification ratios at the right toe increased with an increase in the angle of wave incidence (at a slope height of 0.2), whereas they first increased and then decreased as the incident angle increased (at slope heights of 0.5, 1.0 and 2.0). The vertical amplification ratios of the right toe grew with an increase in the angle of incidence. Nevertheless, these ratios increased significantly at angles of 10◦ and 20◦ (at a slope height of 1.0). The variations above were in good agreement with the seismic responses of the ground motions in Figure 18 (at a slope height of 1.0), which indicated that the variations in the horizontal and vertical amplification ratios were non-monotonous at the slope toe.

The variations in the horizontal and vertical amplification ratios at the slope crest are complicated. The horizontal amplification ratios at the left crest monotonously rose or decreased with an increase in the angle of incidence (at slope heights of 0.2, 0.5 and 1.0). However, the horizontal ratios first increased and then decreased with an increase in the angles of incidence (at a slope height of 2.0). The maximum horizontal amplification ratios fell between 5◦ and 15◦ (at a slope height of 2.0). The horizontal amplification ratios at the right crest first increased and then decreased as the incident angle increased, and the maximum horizontal amplification ratios moved from the an incident angle of 30◦ to those at 15◦ as the slope height increased. The vertical amplification ratios of the left crest increased with an increase in the angle of incidence, and the maximum vertical amplification ratios of the left crest were obtained at a slope height of 1.0. The vertical amplification ratios of the right crest increased with an increase in the angle of incidence (at slope heights of 0.2 and 0.5). The variations in the vertical amplification ratios of the right crest were intensely complicated (at slope heights of 1.0 and 2.0), and the maximum ratios were obtained when the incident angles fell between 10◦ and 20◦.

In summary, the variations in the amplification ratios at the slope toe were monotonous, that is, the ground motions changed regularly with varying incident angles and heights. Nonetheless, the variations in ground motions at the slope crest were complicated owing to the interactions between the input waves and the reflected waves in the topography.
