## 1 Introduction  
The fluctuation of reservoir water level, which is caused by heavy rainfall, water storage, and flood discharge, may result in the instability of slopes in hydraulic engineering. In 1959, a large-area landslide occurred upstream of the Zhexi reservoir in Hunan province, which was mainly triggered by the rapid rise of the water level [1]. In October 1963, a major landslide occurred on the left bank of the Vajont reservoir in Italy, with a total volume of 240 million cubic meters, and 2600 people were killed [2]. Since 2008, the water level of the Three Gorges Reservoir area in China has been tentatively impounded by 175 m. The reservoir experiences nearly 30 m of water level fluctuation, which has caused nearly 500 ancient landslides to be revived, and the deformation and instability have led to the occurrence of new landslides [3]. Scholars and engineers have studied the causes, mechanisms, and characteristics of landslides, such as the Woshavi, Qianjiangping, Shuping, and Quchi landslides, in the Three Gorges Reservoir area [4, 5, 6, 7, 8]. It is widely considered that hydraulic factors such as atmospheric precipitation, fluctuation, and the change rate of the water level of the reservoir, as well as river wave erosion, etc., could reduce the stability of bank slopes, even leading to landslide disasters. Landslides often occur after long rainy periods due to the increase in the positive pore pressure on a potential sliding surface and the decrease in the stability of deeper slopes [9, 10, 11]. If intense rainfall occurs or the water level of the reservoir fluctuates rapidly, shallow landslides can occur as the moisture content in the soil becomes close to saturation, resulting in a considerable reduction in soil strength [12, 13]. According to the scale model based on the Liangshuijing landslide, slope failure mainly occurs in the drainage stage, and the stability of the reservoir bank slope would gradually deteriorate during the long-term cyclic operation of the Three Gorges Reservoir [14]. Rainfall before an earthquake will increase the water content on the surface of the slope and reduce the strength of loess, causing a large displacement and deep cracks in the slope [15]. In general, an earthquake causes permanent damage to the slope and secondary damage results from rainstorms after the earthquake [16]. The rock slopes formed by the bedding structures of fractured rocks disturbed by human activities and subjected to heavy rainfall are liable to a loss of stability [17]. The damage of high bedding rock slopes by flood discharge of atomized rain was studied based on the slope in the Baihetan Hydropower Station. The results showed that the failure modes of the bedding rock slope were of two types: sliding-fracturing (the first slip block) and fracturing-sliding (other blocks) [18]. The long-term effects of rainfall recharge and the fluctuation of groundwater weaken the rock and soil, causing creep deformation and even landslides [19]. [PERSON] and [PERSON] [20] studied the failure mode of soil slopes caused by drawdowns through transparent soil testing, dividing the process of the destabilization of coast slopes into two stages: surface sliding and overall sliding. Not only hydrological factors but other factors, such as the properties of the slope itself (e.g., the inclination of the slope, the density, and cohesion of slope soil, etc. ), also affect the stability of a slope [21]. The key variables for slope stability and the thresholds of water can be determined by sensitivity analysis, which can help engineers to identify the key variables triggering landslides. Sensitivity analysis involves studying the influence of factor changes on the outputs by changing the values of related factors. The purpose is to identify the sensitive factors that have an important influence on the outputs from many uncertain factors and to obtain the degree of influence of different factors on the outputs.