*4.2. Effects of Materials*

In this section, materials are discussed based on the specific slope topography with varying directions of incident waves. Three models, wherein the slope is soft whereas the foundation is hard, the slope and foundation are both the same, and the slope is hard whereas the foundation is soft, were built to investigate the effects of the materials on the ground motion amplification of slope topography. The investigated model was 100 m high, 100 m wide and 1.0 (45◦) in inclination. The so-called softness and hardness of the materials in the slopes or foundations in Figure 15 is in contrast to that of the materials in the foundation (the foundation materials are fixed); that is, the materials of the slope changed from soft to hard (from left to right in Figure 15). The acceleration amplification ratios of the different materials at different incident angles are summarized in Figure 15.

**Figure 15.** 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 under different materials. (**a**) slope soft while foundation hard, (**b**) slope and foundation are same, (**c**) slope hard while foundation soft.

In Figure 15, the acceleration amplification ratios of the SV waves were larger than those of the P waves for each material. The ratios gradually decreased as the materials in the slope varied from soft to hard; that is, the soft materials intensified the amplification whereas the hard materials alleviated the amplification in the slope topography. In addition, the maximum acceleration amplification ratios were acquired when the incident angles fluctuated between 10◦ and 25◦ under SV waves incidence and fell between 0◦ and 10◦ under P waves incidence. Consequently, the slope topographies that covered soft materials were more harmful during earthquake events, and the maximum ground motions of slope topographies were usually in a certain direction of oblique incident seismic waves.

The synthetic accelerograms of the horizontal and vertical components of SV waves and P waves with incident angles of 0◦ and 30◦are presented in Figures 16 and 17, respectively. In the figures, "soft-hard" was the abbreviation of "the slope is soft and the foundation is hard," which corresponded to the situation of "a" in Figure 15; "same" referred to the situation of "b" in Figure 15, and "hard-soft" was marked as the situation of "c" in Figure 15.

As illustrated in the figures, the soft materials led to intense amplification of the ground motions, whereas the hard materials caused de-amplification. The scattered waves under the soft materials were abundant, whereas they were weakened in the hard materials. These evolutions were observed in the horizontal components of the SV waves and the vertical components of the P waves. In addition, compared with the scattered waves at 0◦ incidence and 30◦ incidence in Figures 16 and 17, the scattered waves were much more abundant at the oblique incident waves owing to the added refraction effects by the oblique directions of incident waves. In summary, the intense ground motions with soft materials in slope topography could be explained by the abundantly scattered waves, and this phenomenon would aggravate at oblique incident waves.

**Figure 16.** *Cont*.

**Figure 16.** Synthetic accelerogram (accelerations recorded along the ground with time) generated along the topographic profile, plotted from the horizontal or vertical components of P waves and SV waves arriving from the left of the model at an incident angle of 0, (**a**) horizontal P waves with vertical direction, (**b**) vertical P waves with vertical direction, (**c**) horizontal SV waves with vertical direction (**d**) vertical SV waves with vertical direction.

**Figure 17.** *Cont*.

**Figure 17.** Synthetic accelerogram (accelerations recorded along the ground with time) generated along the topographic profile, plotted from the horizontal or vertical components of P waves and SV waves arriving from the left of the model at incident angle of 30◦. (**a**) horizontal P waves with 30◦ directions, (**b**) vertical P waves with 30◦ directions, (**c**) horizontal SV waves with 30◦ directions (**d**) vertical SV waves with 30◦ directions.

#### *4.3. Effects of Slope Geometries*

According to the analysis of the impacts of wave patterns, the pattern of P waves was weak because of the amplification ratios of the ground motions, whereas that of SV waves was strong. Thus, the effects of the slope geometries were discussed only based on the SV waves rather than the P waves. In addition, the slope geometry changed the wave paths at various directions of wave incidence; thus, the materials of the slope topographies were assumed to be homogenous to eliminate the impacts of non-geometric factors. Consequently, this section, discusses the investigation of the effects of the slope geometries using homogeneous materials under SV incident waves.
