**5. Summary and Conclusions**

In this study, ground motion amplification of the slope topography was analyzed using dynamic FEMs. The wave patterns, materials and slope sizes were discussed based on varying angles of incidence. A viscous-spring artificial boundary was borrowed, and an equivalent nodal force method was proposed to implement oblique incident waves in the FEM. Two numerical examples were adopted to verify the validity of the input method and the accuracy of the artificial boundary. Subsequently, the ground motions in slope topography were investigated with arbitrary directions of incidence, considering the main impact factors of site effects (wave patterns, materials and sizes of slope topography).

The main conclusions and findings are as follows: (1) the amplification effects are underestimated by the vertical incident waves, and the maximum ground motions are closely related to the scattered waves, which depend on the ridge inclinations and the incident directions. (2) Owing to the intense amplification effects under SV waves, the ground motions of slope topography are preferred for analysis using SV waves rather than P waves. (3) With an increase in the angles of incidence, the amplification effects are more complicated at the crest of the slope topography, and the amplification regions are focused on the ridges away from the epicenter. (4) The ground motion amplification effects are aggravated in soft materials owing to the much more scattered waves produced. The directions of the incident waves are a key factor in the analysis of ground motions in slope topography. The amplification effects of slope topography should be discussed separately owing to the complex transmission paths induced by oblique incident waves.

The results obtained here can be considered in the analysis of the ground motion amplification effects of slope topography subjected to earthquakes. The above findings were discussed in terms of three influencing factors that impact the topographic effects: the patterns of the incident waves, the materials of the slope and the slope sizes. The wave patterns that included P waves and SV waves were sufficient for the analysis of topographic effects. Even though the surface waves (e.g., Rayleigh and Love waves) have not been directly analyzed, they were still considered in this study because the conclusions were based on the incident body waves, that is, P waves or SV waves, and were actually a comprehensive result of body waves and surface waves. That is, the proposed input method can also express the impacts of Rayleigh waves (in two dimensions). Thus, the topographic effects calculated using P waves and SV waves in this study are meaningful and necessary. Even though the samples in the analysis of slope materials and slope sizes were relatively few, the conclusions could interpret several regularity phenomena, achieving the purpose of this study. Furthermore, the lack of experimental evidence for the comparison and calibration of the findings in the numerical studies is a serious obstacle [36,61]. Hence, a specific model should be established according to the study area while considering real materials based on the specific earthquake record for a specific study area. Data from field measurements should be collected simultaneously to support numerical modeling results.

**Author Contributions:** Conceptualization, C.Y.; methodology, C.Y. and W.-H.L.; software, C.Y.; validation, C.Y. and W.W.; formal analysis, C.Y. and W.-H.L.; writing—original draft preparation, C.Y. writing—review and editing, C.Y.; funding acquisition, C.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the Postdoctoral Science Foundation of China (2021M692242); the National Natural Science Foundation of Hebei Province (E2021210072, E2021210036); and the Central Leading Local Science and Technology Development Foundation of Hebei Province (216Z5403G). The support is gratefully acknowledged.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
