**2. Problem Layout and Model Establishment**

Topography has an important influence on the amplification of ground motions. The convex topography, which includes slopes, individual hills and mountains, leads to irregular amplification of the topographic effects. In this study, the configurations of the slopes, hills and mountains were simplified as double-faced slope topographies, and the universality of the inclinations of seismic waves that enter the site was considered. The impacts of the topographic effects were analyzed based on the double-faced slope topographies and the site effects were investigated under arbitrary directions of incident waves with other factors (e.g., components of the seismic waves, slope materials and slope sizes).

A dynamic finite element method (FEM) was used to analyze the ground motion process. Even though a three-dimensional (3-D) model was required to fully describe the topographic effects, two-dimensional (2-D) topographic profiles adequately captured the essential geometry of mountain ridges and allowed exploration of key features of the observed landslide patterns [35]. Thus, a 2-D homogeneous double-faced slope with varying slope sizes was established, as illustrated in Figure 1. The height of the slope was assumed to be *H*, which varied according to the wavelength *λ*. That is, the height of the slope was considered to be the normalized height in this study [36]. The width of the slope crest, *W*, corresponded to the slope height. The inclination of slope *i* evolved from gentle to steep. Moreover, the widths of the ground surfaces were 200 m per side, and the depths of the foundation were 200 m. The seismic waves were input from the left bottom of the foundation with incident angles *θ* in the range of 0◦–30◦, with intervals of 5◦. To ensure the accurate representation of wave transmissions through a model in the FEM, the element size of the model had to be less than one-twelfth of the wavelength [53], and the time step of the dynamic analysis was determined to be one-tenth of the maximum frequency of the seismic waves [13].

**Figure 1.** Sketch of the calculated modeling.

The seismic waves were analyzed by two components of the seismic waves (considering only the body waves), that is, P waves and SV waves. The influence of the wave components was analyzed using the same model size. The materials of the slope were assumed to be isotropic, and the medium was linearly elastic. To investigate the influence of materials in the evaluation of the topographic effects, the material of the foundation was fixed, whereas the materials of the slope varied according to the variations in the materials in the foundations. The specific parameters of the materials are presented in Table 1.


**Table 1.** Parameters of soil medium implemented in FEM.
