4.3.3. Influence of Slope Inclination I

The inclination of the slope, which is defined as the width-depth ratio, varied from 0.5, 0.7, 1.0 and 1.5 to 2.0, whereas the other geometrical parameters (slope heights and slope widths) remained the same. The acceleration amplification ratios along the slope surface are illustrated in Figure 24 with varying angles of incidence.

**Figure 24.** 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 inclinations. (**a**) slope inclination of 0.5, (**b**) slope inclination of 0.7, (**c**) slope inclination of 1.0 (**d**) slope inclination of 1.5 (**e**) slope inclination of 2.0.

In Figure 24, the acceleration amplification ratios moved from the left slope crest to the right slope crest when the slope model became gentle. The amplification ratios moved away from the wave source with an increase in the angles of incidence, especially in the gentle slope model. These evolutions are indicated by the scattered waves induced by slope inclinations. The ground motions reached a maximum when the incident angles fluctuated between 5◦ and 10◦ in the steep slope model (*i* < 1.0). However, the ground motions reached a maximum when the incident angles were between 15◦ and 20◦ in the gentle slope model (*i* > 1.0). Thus, the greater the slope inclinations, the closer the maximum acceleration amplification ratios were to the greater inclinations of the incident waves. In summary, the ground motions were mainly concentrated on the slope ridges. The oblique incident waves and slope inclinations changed the propagation of the seismic wave paths, and the scattered waves easily concentrated as the slope became gentle. The maximum acceleration amplification ratios were obtained in the oblique direction of the incident waves.

Similar to the analyses of the slope height and slope widths, the slope toe and slope crest are also presented with horizontal amplification ratios and vertical amplification ratios in Figures 25 and 26, respectively. The comprehensive relations between the incident angles and slope inclinations are discussed.

**Figure 25.** 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 inclinations.

**Figure 26.** 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 inclinations.

The horizontal amplification ratios of the slope toe monotonously decreased with an increase in the angle of incidence, whereas the horizontal ratios increased as the slope inclination increased. That is, the ground motions at the slope toe increased as the slope became gentle. However, the vertical amplification ratios of the slope toe increased monotonously with an increase in the angle of incidence, and the ratios gradually decreased when the slope became gentle.

The variations in the amplification ratios at the slope crest were complicated at varying incident angles. The horizontal amplification ratios at the left crest decreased with an increase in the angle of incidence, and the reduced amplitude intensified as the slope became steeper (*i* < 1.0). The horizontal amplification ratios at the right crest remained the same with an increase in the angle of incidence, and the maximum ratios fell between 1.0

and 1.5 of *i*. The vertical amplification ratios at the left crest and right crest decreased with an increase in slope inclination. The ratios were intensified at the left crest whereas they were alleviated at a slope inclination of 1.0, at an incident angle of 15◦on the right crest.

In summary, the variations in the amplification ratios were concentrated on the slope crests at varying angles of incidence because the varying inclinations of slope ridges changed the propagation of wave paths in the topography.
