## 4 Conclusions and Discussions  
The laboratory test study has been carried out on the failure characteristics of fly ash dam slope under rainfall. The conclusions are as follows:  
(1) Based on the tests, three failure mechanisms of the fly ash dam slope under rainfall are revealed: sliding failure, runoff erosion, and flow-slide failure. Due to the low density of fly ash, runoff erosion is more likely to occur under rainfall. Runoff erosion causes looseness of nearby fly ash, which is easily liquefied under rainfall, causing flow-slide damage. This is different from the general clay slope, where the nearby clay after runoff erosion is more prone to collapse. In the tests, flow slide was an important failure mechanism of the fly ash slope, and played a key role in the failure process of the fly ash slope in tests S1 and S2.  
(2) Local erosion damages caused by runoff erosion and flow slide are the important triggering factors of the fly ash dam-slope failure under rainfall. For the fly ash dam slope, in the early stage of rainfall, the local erosion damage was often caused by runoff erosionand flow slide. With the progress of rainfall, the local erosion will trigger a series of failures, including overall sliding failures, retrogressive landslides, and further erosion.  
(3) According to the test, three different failure modes of fly ash dam slopes under rainfall are proposed: overall sliding failure, the retrogressive landslide caused by multi-stage local sliding, and progressive erosion failure (caused by the combined action of runoff erosion and flow slide). The overall sliding failure is sudden, but the latter two failure modes occur gradually.  
(4) The slope ratio has an important influence on the failure mode. With the decrease in slope ratio, the failure mode evolves from sliding failure to flow-slide failure and runoff erosion failure. The greater the slope ratio, the more obvious the sliding failure characteristics; the lower the slope ratio, the greater the runoff erosion damage.  
(5) The failure mode is related to the initial seepage field in the dam slope, and the existence of an internal seepage field in the slope intensifies the occurrence of flow slide. When there is a seepage field before rainfall, the flow-slide failure easily occurs in the erosion process of the slope under rainfall. On the contrary, runoff erosion mainly occurs in the erosion process of the slope under rainfall.  
It can be seen from the above conclusions that local erosion damages are the important triggering factors of the fly ash dam-slope failure under rainfall. Therefore, the protection of the fly-ash dam slope should be strengthened, and the smaller dam slope ratio and the lower buried depth of the phreatic line should be controlled in order to prevent rain erosion. Considering that there are many factors affecting the failure law of fly ash dam slopes under rainfall, and the three failure mechanisms may play different roles in the failure processes of fly ash dam slopes under different conditions, which may have an impact on the failure process. It is suggested that in future research, the erosion of fly-ash dam slopes under the action of rainfall should be further studied. The impact of erosion laws and shallow failure laws of fly-ash dam slopes under different rainfall intensity, different dam density, and greater slope ratios should be considered. The next step is to further study the relationship between the potential failure mode and the above influencing factors under rainfall conditions by combining experiment and theory, as a way to provide a basis for the stability analysis of fly ash dam slopes under rainfall.  
Not applicable.  
The authors declare no conflict of interest.