## 3 Results and Discussion
### Characteristics of the Seismic Signals of the Slope Failure (Baseline Case)  
Wave erosion leads to changes in the slope profile, and these changes in profile can affect the hydraulic conditions of the waves, which in turn can lead to changes in the scenarios of slope failure. In the Baseline Case, we observed three types of failure scenarios during Stage 3:  
1. Slope sliding induced by cyclic wave backwash: This occurs when the water retreating back into the'sea' (backwash) pulls material from the slope with it, leading to sliding. The cyclic nature of the waves can cause repeated sliding events. 2. Re-sliding of the previously slid soil mass induced by wave swash: Swash refers to the water rushing up the slope after breaking. This scenario involves the reactivation and further movement of soil masses that had previously slid down but not completely detached or been washed away. 3. Slope collapse induced by wave impact: This refers to the failure and sudden movement of a portion of the slope due to the force of the waves impacting the slope, often accompanied by breaking and splashing. To understand the characteristics of the seismic signals of slope failure under these three scenarios, we selected seismic signals from three periods for analysis, specifically 3835 s-3900 s, 3800 s-4680 s, and 4500 s-4600 s, and we discuss them in detail as follows. Figure 8 presents the pore pressure PP1, seismic signal Acc 2, time-frequency spectrum, and spectral magnitude profile from 3835 s to 3900 s. The PP1 piezometer, being close to the slope surface, can measure changes in the water level above it. In Stage 3, wave generation starts at 3840 s, and the amplitude of both the PP1 pore pressure (Figure 8a) and the seismic signal Acc 2 (Figure 8b) begin to increase after this time. During 3850 s-3858 s, the slope experienced five slides. The yellow and red energy traces in the time-frequency spectrum (Figure 8c) are caused by the slope sliding. Since the energy traces are approximately concentrated around 311 Hz, we plotted the spectral magnitude profile of 311 Hz, as shown in Figure 8d. The 311 Hz is auxiliary, determined by using Fourier Transform to convert the signal from the time domain to the frequency domain, and then the frequency centroid is calculated to determine the frequency where the energy is concentrated. Figure 8d marks the times (t\(\gamma\)-t\({}_{\rm 11}\)) when the spectral values rise, which also represent the moments of slope sliding. Comparing Figure 8a with Figure 8d, we observe that the peaks in spectral values (t\(\gamma\)-t\({}_{\rm 11}\)) correspond to decreases in PP1 pore pressure, indicating that slope sliding occurs during backwash when the water level on the slope face drops. Therefore, as the waves cyclically backwash, rapid drawdown might also be one of the causes of slope sliding. Figure 9 is a set of snapshots during 3840 s-3858 s, with the red dashed line representing the area of slope sliding. The processes of t\(\gamma\)-t\({}_{\rm 11}\) sliding and timing can be viewed from Video S2. Figure 10 presents the seismic signal, time-frequency graph, spectral magnitude profile of Acc 2, and retreat from 3800 s to 4680 s. Since the energy traces were also concentrated around 311 Hz during 3835 s-3900 s, we plotted the spectral magnitude profile at 311 Hz. The 311 Hz is auxiliary, selected by using Fourier Transform to convert the signal from the time domain to the frequency domain, and then calculate the frequency centroid where the energy is concentrated. Figure 10c shows spectral peaks at t\({}_{12}\)-t\({}_{16}\), which are due to slope sliding (t\({}_{12}\)-t\({}_{15}\)) and collapse (t\({}_{16}\)). Because collapse causes the slope to retreat, the retreat distance increases at t\({}_{16}\) (Figure 10d). Figure 11a presents photos of the landslide (t\({}_{12}\)-t\({}_{15}\)) and collapse (t\({}_{16}\)) during 4025 s-4388 s. During the test, the upper part of the slope gradually formed a cliff (Figure 11a) due to wave erosion.