4.3.2. Influence of the Width of Slope Crest W

The width of the slope crest varied from 50 m, 100 m and 200 m to 400 m, whereas the other geometrical parameters (slope heights and slope inclinations) remained the same. The acceleration amplification ratios along the slope surface are illustrated in Figure 21 with varying incident angles.

**Figure 21.** Variations of the seismic responses along the slope ridges and slope crests of the real amplification ratios (*r*) of PGA with varied angles of wave incidence at different slope widths, (**a**) slope width of 50 m, (**b**) slope width of 100 m, (**c**) slope width of 200 m (**d**) slope width of 400 m.

As illustrated in Figure 21, the acceleration amplification ratios at a slope width of 1.0 H were the greatest. This phenomenon can be indicated by the resonance of the model sizes and wavelengths. The ground motions were concentrated on the slope crest, especially when the slope width was 4.0 H. In addition, the maximum acceleration amplification ratios were obtained when the incident angles were between 5◦ and 10◦ at a width of 0.5 H, whereas the ratios reached a maximum when the incident angles fluctuated between 25◦ and 30◦ at a slope width of 4.0 H. Thus, the wider the slope crests, the closer the maximum acceleration amplification ratios were to the greater inclinations of incident waves. In summary, the energies of earthquake waves were mainly concentrated at the crest of the slope topography. The maximum ground motions occurred as the width of the slope model was nearly one wavelength, especially in certain directions of seismic incident waves.

Moreover, the observation points (slope toe and slope crest) are analyzed in Figures 22 and 23, respectively. All the observation points are illustrated based on the horizontal and vertical amplification ratios, to analyze the comprehensive relations between the incident angles and slope widths.

**Figure 22.** 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 widths.

**Figure 23.** 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 widths.

The horizontal amplification ratios at the slope toe decreased monotonously with an increase in the incident angle, whereas they increased as the slope width increased. The vertical amplification ratios at the left toe increased with an increase in the incident angle.

The vertical amplification ratios at the right toe reached a maximum when the slope widths were between 1.0 and 2.0. With an increase in the incident angle, the vertical amplification ratios were almost the same for each slope width.

Nonetheless, variations in the acceleration amplification ratios at the slope crest were complicated. The horizontal amplification ratios at the left crest first decreased and then increased with an increase in the incident angle (at slope widths of 2.0 and 4.0). The horizontal ratios first increased and then decreased as the incident angle increased (at slope widths of 0.5 and 1.0). In addition, the ratios increased from an incident angle of 5◦ to an incident angle of 20◦ at a slope width of 0.5, which could be interpreted by the superposition of the scattered waves in the narrow models. The vertical amplification ratios at the left crest first decreased and then increased with an increase in the angle of incidence. Furthermore, the horizontal amplification ratios at the right crest first increased and then decreased with an increase in the angle of incidence. The maximum horizontal ratios were obtained between 15◦ and 25◦ of the incident angle (at a slope width of 1.0). The vertical amplification ratios at the right crest were almost the same for various incident angles. The vertical ratios reached a maximum between 15◦ and 25◦ of the incident angles (at a slope width of 1.0). The above variations were in good agreement with the seismic responses of ground motions of PGA in Figure 21b, and these evolutions could be interpreted by the correlations between the wavelength and the slope widths.

In summary, the variations in the amplification ratios were mainly concentrated on the slope crest with varying angles of incidence, and these complexities were aggravated when the width was almost one wavelength.
