**1. Introduction**

Earthquake-induced landslides are among the most hazardous secondary effects of strong seismicity in mountainous regions. Several historical cases highlight the potentially devastating consequences in the last 30 years [1–6] because nearly one-third of deaths are caused by earthquake-induced landslides among all disasters [7–10]. Many researchers have indicated that topographic effects have possible interactions between landslide mechanisms and triggering conditions [11–16]. Thus, the topographic effects, represented by the ground motions on the slope model, should be better understood.

Generally, convex topographies such as mountains, slopes and individual ridges lead to intense aggravation of the seismic responses irregularly along the ground surface [17]. Many acceleration-time histories recorded by the seismometers near the epicenter all proved that the peak acceleration at the slope crest showed intense amplification based on instrumental data from strong earthquakes such as the 1987 California earthquake, the 1994 Northridge earthquake, the 1995 Egion earthquake and the 2008 Wenchuan earthquake [12,18–20]. In addition, statistical analysis of the seismological stations in Iran and Israel showed that the acceleration amplification ratios with respect to the slope crest and ground could reach as much as four times [21,22]. These measured records confirmed that the slope topography modified the seismic ground motions.

**Citation:** Yin, C.; Li, W.-H.; Wang, W. Evaluation of Ground Motion Amplification Effects in Slope Topography Induced by the Arbitrary Directions of Seismic Waves. *Energies* **2021**, *14*, 6744. https://doi.org/ 10.3390/en14206744

Academic Editor: Manoj Khandelwal

Received: 20 August 2021 Accepted: 13 October 2021 Published: 16 October 2021

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In the analysis of topographic effects, both analytical and numerical methods were utilized [23–34]. Nevertheless, the analytical method (e.g., Newmark's method) can neither quantify the plastic strains of the non-shearing models nor consider the interaction between the models and the seismic waves in terms of ground motion amplification or de-amplification owing to irregular topographic patterns [17]. Conversely, the complicated stress-strain relationships can be described clearly based on the numerical method, and the expected plastic strain effects of the model can be quantified owing to seismic events [35]. Thus, for convex topographies (mountains, slopes and individual ridges), the most common method is a numerical simulation, such as finite difference methods [13,36–39], finite element methods [40–45], boundary element methods [37,46,47], generalized consistent transmitting boundary methods [29,30] and distinct element methods [48].

Many researchers have analyzed the ground motions in slope topography [13,36,37,40–45,49,50]; however, they preferred the vertical directions of incident waves rather than considering the influences of the incident angles. According to the regression analysis of numerous seismological records in America and Japan, the incident angles near the ground are usually oblique [51,52]. Undoubtedly, the oblique incident directions change the seismic wave paths in the slope model, and the different seismic responses lead to the irregularly intense amplification of the ground motions and aggravation of the slope instability [11,30]. Thus, the varied angles of incident waves definitely influence the amplification of the slope topography, and overlooking the wave inclination oversimplifies the analyses of the seismic responses on the ground motions. Even though this problem has been discussed by some researchers [30,35], there has been little systematic analysis of the influences of the incident directions on the ground motions in slope topography, such as the impacts of slope materials and sizes under oblique angles of incident waves.

Based on the analyses above, this study aimed to investigate the impact of the incident directions of seismic waves on the ground motions in slope topography. The remainder of this paper is organized as follows. The problem is proposed and the slope model is established in Section 2. The derivation of the input method in the numerical simulation with arbitrary directions of incident waves is presented in Section 3. In Section 4, the influencing factors (wave patterns, slope materials and slope geometries) are discussed separately under a double-faced slope topography with varying angles of incident waves. Finally, the conclusions and future prospects are presented in Section 5.
