Reservoir level changes and rainfall are two critical triggers inducing landslide deformation (Gutiérrez et al., 2010; Segoni et al., 2018; Jaboyedoff et al., 2020; Miao et al., 2022). Rainfall significantly diminishes landslide stability and predominantly results in movement through two key mechanisms: 1) Rainfall infiltration causes an increase in pore pressure within the soil, consequently reducing the effective stress of the soil to a critical threshold (Marjanovi´c et al., 2018); 2) The ingress of rainfall increases landslide mass, thereby augmenting the sliding force acting upon it (Yang et al., 2023). Rising and falling reservoir levels induce landslide deformation through distinct mechanisms. Firstly, during reservoir water level drawdown, some landslides experience a lack of rapid dissipation of groundwater. This inadequate dissipation leads to an increase in dynamic pressure, resulting in decreased landslide stability (Zhou et al., 2022). Secondly, as the reservoir water level increases, it exerts buoyancy on some landslides, reducing the effective weight acting on the anti-sliding section in front of landslides (Huang et al., 2020). Additionally, the infiltration of reservoir water into the landslide can cause a reduction in soil strength. In analyzing and predicting landslide deformation, some candidate controlling factors, such as average reservoir level, monthly reservoir level change, and monthly rainfall, have often been considered (Yang et al., 2019; Liu et al., 2020).

The Three Gorges Reservoir impoundment and operation progressed through three phases, as shown in Figure 3 . In the initial phase, spanning between April 2003 and September 2006, the water level underwent a significant increase from 69 m to 139 m, followed by relatively minor fluctuations. Moving into the second phase, which extended from September 2006 to September 2008, the reservoir level experienced a rapid increase from 139 m to 156 m within a month and subsequently fluctuated annually between 145 m and 156 m. During the third phase, beginning in 2008, the reservoir level increased to 172 m and thereafter fluctuated between 145 m and 172 m from 2008 to 2010. Since then, the reservoir level fluctuated periodically between 145 m and 175 m. During the annual reservoir level schedule in 2016, one can distinguish six successive periods: slow drawdown (Stage I), rapid drawdown (Stage II), low reservoir conditions (Stage III), rapid rise (Stage IV), slower rise (Stage V) and high reservoir conditions (Stage VI).

At times of fluctuating water levels, varying rainfall also occurs. The Wanzhou District has the second-highest annual rainfall in the TGRA. Between 1960 and 2015, the largest monthly rainfall in the Wanzhou District is 683.2 mm, the largest daily rainfall is 243.3 mm, and the longest string is 16 continuous rainfall days (Yang et al., 2017).

GRA was first proposed by Deng (1989) and had been applied to identifying quantitatively the key factors influencing landslide deformation (Wu et al., 2019; Yang et al., 2019; Guo et al., 2020; Wang et al., 2023). The GRA method, a commonly utilized model within grey system theory, categorizes situations with no information as black and those with perfect information as white. However, in practical real-world problems, these ideal situations rarely exist. Instead, situations with partial information, lying between these extremes, are referred to as grey, hazy, or fuzzy.

The GRA method is adopted in this work to quantitatively pinpoint the primary causes of the Sanzhouxi landslide’s movement. The correlation between each variable is assessed using the grey relational grade (GRG). The process of triggers identification inducing landslide deformation includes the following four steps.

(1) Based on the available monitoring data, which comprises measurements of rainfall, reservoir water level, and surface displacement, an incidence matrix (X) is constructed. Monthly displacement is assigned as the primary sequence (X_displacement), while the two causal factors, monthly reservoir level change (X_{reservoir level}) and monthly rainfall (X_rainfall), are selected as sub-sequences. The matrix X is denoted as X = {X_displacement, X_{reservoir level}, X_rainfall}.

(2) Normalization of the data in matrix X is achieved from:

where i = 0 ,   1 ,   ⋯ ,   n ; k = 0 ,   1 ,   ⋯ ,   m ; n and m are the number of data points and influencing factors, respectively.

(3) The grey relational coefficient can be computed from:

where ρ is the resolution coefficient for adjusting the range of comparison environments, typically assigned a value of 0.5 (Lian et al, 2014; Yang et al., 2019; Guo et al., 2020).

(4) The GRG is obtained from:

The GRG is a measure that ranges from 0 to 1, with a GRG-value of 0.6 or higher indicating a strong correlation. As the value of GRG approaches 1, it signifies a stronger association between the two series under consideration. Within this study, the correlation between landslide displacement and reservoir level fluctuation is represented by r(x _displacement, x _{reservoir level}), while the correlation between landslide displacement and rainfall is denoted by r(x _displacement, x _rainfall). If r(x _displacement, x _{reservoir level}) > r(x _displacement, x _rainfall), it suggests that the primary factor contributing to landslide deformation is the fluctuation of the reservoir water level. Conversely, if r(x _displacement, x _{reservoir level})< r(x _displacement, x _rainfall), it indicates that rainfall serves as the dominant trigger. By comparing the GRG values, the relative influence of each factor on landslide deformation can be determined.

The Sanzhouxi landslide located in the Wanzhou District of Chongqing, China, is situated on the eastern side of the Yangtze River (30°45′08.27″N, 108°25′32.08″E) ( Figure 4 ). The landslide is fan-shaped from a bird’s eye view and exhibits a sliding direction oriented at approximately 245°. The rear portion of the landslide displays a steeper inclination compared to the middle and front sections. The landslide surface is inclined at an angle of 10° to 30°. The frontal section of the landslide stretches towards the Yangtze River bed, with the elevation varying between 160 m and 175 m. The upper landslide boundary is marked by a bedrock cliff at the elevation of 230 m, while the left and right boundaries coincide with the interface between the bedrock and the soil ( Figure 5A ). The landslide measures 320 m in length and 360 m in width. The thickness of the sliding mass ranges from 5 m to 22 m, covering an area of 13.4 × 10⁴ m² and having an estimated volume of 135.6 × 10⁴ m³.

The sliding masses consisted mainly of quaternary deposits, including silty clay and fragmented rubble. The relative proportions of these two material types were between 8:2 and 7:3. The sliding zone occurs at the interface between bedrock and soil, and primarily consists of silty clay and fragmented sandstone rubble, with the presence of some montmorillonite. The subjacent bedrocks are sandstone and siltstone ( Figure 6 ).

The Sanzhouxi area, with the potential for landslides, posed a serious threat to both public and property, including residents, dwellings, roads and infrastructure, and agricultural fields. According to historical records, the residents living on the landslide in 2005, 2009, and 2010 were 123, 217, and 135, respectively. With the development of deformations, some residents were relocated, and only 13 residents lived there in the area of the Sanzhouxi landslide in 2013.

The Sanzhouxi landslide began to deform in 1990. Near the trailing edge of the landslide, an observed ground crack measures approximately 100 m in length, 2 cm to 10 cm in width, and has a depth of 10 cm. Intense rainfall occurred in May with a rainfall of 247.4 mm seeming to be mainly responsible for the beginning of the landslide deformation in 1990. In the following years, landslide deformations intensified, and the crack extended from the trailing edge of the landslide into the middle and front parts regions. In June 2003, the landslide deformation caused some resident houses to crack.

In 2007, numerous tension cracks along a road across the landslide were observed. The largest crack had about 4 cm to 6 cm in width and a depth of 60 cm. The road in the landslide area experienced vertical displacement. The majority of the resident houses on or close to the landslide began to deform. In June 2010, multiple tension cracks were observed on the frontal section, in which the subsidence and width of the largest crack were up to 33 cm and 26 cm, respectively.

In 2012, nine cracks on the ground were observed in the landslide area by field investigations. The majority of the cracks were concentrated in the frontal area of the landslide. The largest width of the crack was 12 cm, and the largest depth was 27 cm. Among these nine cracks, six cracks that had developed perpendicular to the sliding direction were monitored continuously since then ( Figure 5A ).

In 2014, deformations were observed across the entire landslide area, while the front part deformed more than the other parts of the landslide. Transverse cracks were observed in the front right section of the landslide ( Figure 5B ). A second sliding was induced due to excavation within the part below 180 m of the landslide ( Figure 5C ). Scratch traces were found on the sliding surface with a direction of 245° ( Figure 5D ). In addition, a failure on the riverbank extending 30 m occurred along the landslide ‘s toe ( Figure 5E ). During this time frame, the deformations in the front part were mainly transverse surface cracks, while on the back part of the landslide mainly cracks were observed ( Figures 5F, G ).

Six GPS monitoring stations (numbered WZ01 to WZ06) and two deep displacement monitoring points (QZK01 and QZK02) were installed on the Sanzhouxi landslide in 2007. Significant deformations developed in the following years. Six ground cracks monitoring points (DL01 to DL06) were installed in 2012, and two groundwater monitoring boreholes (STK01 and STK02) were installed in 2013 ( Figure 5A ). The monitoring data for groundwater level was collected from January 27^th, 2013, to July 26^th, 2014. GPS displacement was monitored continuously from March 2007 to July 2014, with measurements recorded on a monthly basis. The crack width was monitored between September 19^th, 2012 and July 17^th, 2014.

Qualitative analysis of monitoring data in the preceding sections has been conducted to examine the relationship between landslide deformation and hydrological factors, namely rainfall and reservoir level rise. A quantitative analysis using grey relational analysis (GRA) is performed here to identify the predominant triggers for inducing landslide deformation during various evolutionary periods. We will use WZ03, which shows the largest displacement among the six GPS monitoring stations, as an example. The calculation process of the GRA method can be found in the section “2.2 Identification of triggering factors using GRA”.

Seven periods of reservoir impoundment were present between 2007 and 2014 ( Figure 10 ). The correlation between monthly displacement and reservoir level rise was quantified as r(x _displacement, x_{reservoir level}), while the correlation between monthly displacement and rainfall was indicated as r(x _displacement, x _rainfall). GRG of the seven periods was displayed in Figure 13 . For all the reservoir raise periods, the calculated GRG was higher for the reservoir level fluctuations, i.e., r(x _displacement, x _{reservoir level})>r(x _displacement, x _rainfall), meaning that the movement was primarily induced by reservoir level rising, while rainfall played a subordinate role. This finding aligns with the qualitative analysis obtained in the previous sections.

Moreover, the GRG value of r(x _displacement, x _{reservoir level}) remained at approximately 0.8 in the preceding years but exhibited a decreasing trend starting from 2013, indicating a reduced impact of the reservoir level rising on landslide movement. This conclusion agreed with the research of Zhang et al. (2020) and Yang et al. (2023). Their findings suggest that reservoir-induced landslides generally display more pronounced responses to reservoir water during the initial phase of reservoir impoundment. However, over time, this impact gradually diminishes, eventually leading to a self-adjusted stable state.

The saturation line at each end of the reservoir stage for the Sanzhouxi landslide was shown in Figure 14B . The groundwater was discharged from the landslide without time lag when the reservoir level decreases (stages I and II). In the following low reservoir stage (stage III), the reservoir level frequently fluctuated at a small range due to the realimentation by the rainfall. The frequent change of reservoir level resulted in the infiltration line of the front part of the landslide being slightly convex, while the infiltration line of the remaining sections was kept the same. As the reservoir level increased (stages IV and V), the infiltration line of the front part rises higher than the middle and rear parts, resulting in the infiltration line within the slope being concave. After a high reservoir level has been kept for about 10 days (stage VI), the infiltration line at the middle part of the landslide gradually rises to the same level as the front edge.

Figure 15 displayed the factor of safety (FS), daily rainfall, and reservoir level. When rainfall and reservoir level changes were coupled, the two-dimensional (2D) FS computed by Slope/W ranged from 1.07 to 1.17 over one year. The computed FS suggested that the slope was stable, although an FS of 1.07 was not very robust, given that there were many uncertainties in the soil parameters and 2D LEM model. During stage I, the FS kept decreasing for 25 days and subsequently increased. In stage II, the FS was constant at about 1.10 for 20 days and then increased with the reservoir level rising rapidly. In stage III, the FS continued to rise, but the rate of increase slowed down. The reservoir level increased from 146.4 m to 161.1 m in stage IV, resulting in an FS of 1.15 without significant variation. The main reason was that the leading edge of the landslide covered within a range of 160 m to 175 m, and thus only a tiny part of the leading edge can be submerged in the reservoir water during this stage. The computed FS showed a slight increase during stage V and decreased from 1.15 to 1.11 during stage VI. In stage V, the rise of the reservoir water level led to an increase in hydrostatic pressure acting on the landslide, consequently augmenting the FS of the slope. After entering stage VI, the infiltration of reservoir water into the landslide caused a reduction in soil strength, which was evident in a pronounced downward trend of the FS of the landslide.

The FS under the sole influence of reservoir level changing was also calculated for comparison. The FS was slightly higher than the FS with the coupled effect of reservoir level fluctuations and rainfall. Among stages, I to IV, the smallest difference in the FS for the two conditions occurred in stage I, while the largest difference in the FS appeared in stage IV, although the differences in the FS were not significant.