## 3 Results and Discussion
### Characteristics of the Seismic Signals of the Slope Failure (Baseline Case)
The soil accumulated on the cliff's surface, already loosened by previous sliding, was prone to re-sliding due to wave swash (Figure 11a-d). As the soil on the upper cliff was gradually carried away by backwash, the cliff lost its protection, making it susceptible to collapse due to wave erosion (Figure 11e). The processes of t\({}_{12}\)-t\({}_{15}\) sliding and t\({}_{16}\) collapsing can be viewed from Videos S3 and S4. These videos provide a visual representation of the slope's transformation and re-sliding events. Figure 8: Duration: 3835 s–3900 s in Stage 3. (**a**) Pore pressure, PP1; (**b**) acceleration, Acc 2; (**c**) time–frequency spectrum; (**d**) spectral magnitude profile of 311 Hz (The timing of t\({}_{7}\) to t\({}_{11}\) represents local slides of the slope model). Figure 9: Series front images of the slope model during 3840 s–3858 s (The red arrows indicate the sliding direction). Figure 12 presents the seismic signal Acc 2, time-frequency graph, and spectral magnitude profile from 4500 s to 4600 s. During this period, the force of the wave impact on the slope was substantial, and significant sounds of wave impact can be heard from the experimental video. Figure 12b shows faint blue vertical energy traces in the time-frequency spectrum, which are caused by wave impact on the slope. Figure 12c marks the times of slope collapse (t\({}_{17}\)-t\({}_{22}\)) that were observed from the test video, with spectral value peaks at t\({}_{18}\), t\({}_{20}\), and t\({}_{22}\). The collapses at t\({}_{17}\), t\({}_{19}\), and t\({}_{21}\) are hard to recognize from Figure 12c, which may due to the very small energy and the characteristic of the seismic frequency content of the collapses. Corresponding photos from the experiment (Figure 13c,e,g) show that the upper cliff of the slope had larger collapses at t\({}_{18}\) and t\({}_{20}\), resulting in greater vibrations. The collapse event at t\({}_{22}\) was recorded due to the falling soil mass being closer to the sensor Acc 2. There are no peaks in the spectral values at t\({}_{17}\), t\({}_{19}\), and t\({}_{21}\), possibly because the volume of the collapse was small, or the locations of the falling soils were too far from the sensor to be reflected in the seismic signal. During the rapid retreat of the slope, the force of the wave impact was stronger, creating many energy traces in the time-frequency spectrum (Figure 12b), making it more challenging to identify collapse events. However, during periods of wave swash, there are fewer energy traces from wave impact on the slope; therefore, the collapse event can be identified. The processes of t\({}_{17}\)-t\({}_{22}\) collapse can be viewed in Video S5. Figure 10: Duration: 3800 s-4700 s in Stage 3. (**a**) Acceleration, Acc 2; (**b**) time–frequency spectrum; (**c**) spectral magnitude profile of 311 Hz; (**d**) retreat (the timing from t\({}_{12}\) to t\({}_{15}\) and t\({}_{16}\) represents sliding and collapsing of the slope model). Figure 11: Series front images of the slope model during 3800 s–4680 s (The red dashed lines represent the sliding and collapse areas and the red arrows indicate the sliding direction). The above discussion provides a detailed account of how wave-induced changes in slope profiles lead to varied forms of slope failure, utilizing seismic signal analysis to understand the complex interactions between wave action and slope stability. We believe that the ultimate causes of slope failure due to wave erosion are cyclic processes, such as swash, backwash, rapid drawdown, and toe erosion. As the soil masses on the upper cliff of the slope are gradually carried away by backwash, the cliff becomes prone to collapse due to wave erosion. If a collapse occurs under the conditions of wave impact on the slope, the energy traces of the collapse on the time-frequency spectrum may be obscured or interfered with by the traces of wave impact energy.