# Seismic Response of Aeolian Sand High Embankment Slopes in Shaking Table Tests
## 3 Horizontal Acceleration Response Results and Discussion  
Horizontal acceleration magnification (HAM) is widely used to study the seismic response of embankment slopes [44]. In this research, acceleration magnification is defined as the ratio of peak acceleration of each test point in slopes to the peak acceleration of the test points on the shaking table (AC1 and AC3)  
The distribution of the HAM of four accelerators of the slope surface and that of three accelerators inside the slope were summarized and shown in Figure 10. The results show that the HAM of three models always exceeds 1.0, showing an increasing trend with height. The amplification effects due to the dynamic response of the embankment triggered by both incident and reflected waves are the main reasons for these phenomena. When considering the actual tests, these phenomena can also be explained by the reflection of earthquake waves between sand particles, and the superposition of incident waves and reflected waves along the slope surface. In addition, The HAM of model 1 increases with increasing input peak acceleration. The HAM of model 2 and model 3 shows attenuation when the input peak acceleration reaches a specific value (300 gal in this test). These phenomena can be explained by the failure mechanism of sand under horizontal accelerations. As shown in Figure 11, the destruction of aeolian sand high embankments under earthquakes follows three stages: the reflected wave emergence (RWE) stage, the reflected wave strengthening (RWS) stage, and the acceleration magnification attenuation (AMA) stage. At the RWE stage, the shear trituration of sand particles is not present because the seismic load is sufficiently small; however, the reflection of earthquake waves among sand particles results in the amplification of the input peak acceleration. At the RWS stage, with increasing seismic load, shear trituration of sand particles appeared. These micro-particles, generated by shear trituration, can strengthen the reflection of seismic waves, and this area is named the RWS zone in this paper. At the same time, microcracks appeared as well. Although these microcracks cause slight movement of sand particles, which result in the release of earthquake force and attenuate the HAM to a certain extent, the RWS zone expands rapidly and predominates the change of HAM. Therefore, the HAM increases during this stage. At the AWA stage, with the expansion of the RWS zone, the microcracks connect, and cracks that extend to the slope surface form. Then, the sand near the cracks will shift and permanent deformation will appear at the slope surface, which will lead to a large degree of seismic force release. Although the RWS zone still exists, the cracks predominate the change of HAM. Therefore, the HAM shows attenuation at this stage. According to the distribution of HAM, it can be seen that 300 gal(cm/s\({}^{2}\)) is the critical acceleration of model 2 and model 3 for the transformation from the RWS stage to the AMA stage. Model 1 only experienced the RWE and RWS stages during the test. These results are highly consistent regardless of whether tests are conducted under El-Centro motions or under Lanzhou motions. Generally, the critical acceleration of embankments during their transformation from the RWS stage to the AMA stage is a reference for the  
Figure 9: Fourier spectrum of excitations. quantitative estimation of the anti-seismic ability of aeolian sand high embankments. With the increase of this critical acceleration, the anti-seismic ability of aeolian sand high embankments will improve. Figure 10: _Cont._  
Figure 10: Distribution of HAM (1 gal = 1 cm/s\({}^{2}\)): (**a**) slope surface (**b**) inside the slope.