Probabilistic stability analysis of Bazimen landslide with monitored rainfall data and water level fluctuations in Three Gorges Reservoir, China

Abstract

Landslide is a common geological hazard in reservoir areas and may cause great damage to local residents’ life and property. It is widely accepted that rainfall and periodic variation of water level are the two main factors triggering reservoir landslides. In this study, the Bazimen landslide located in the Three Gorges Reservoir (TGR) was back-analyzed as a case study. Based on the statistical features of the last 3-year monitored data and field instrumentations, the landslide susceptibility in an annual cycle and four representative periods was investigated via the deterministic and probabilistic analysis, respectively. The results indicate that the fluctuation of the reservoir water level plays a pivotal role in inducing slope failures, for the minimum stability coefficient occurs at the rapid decline period of water level. The probabilistic analysis results reveal that the initial sliding surface is the most important area influencing the occurrence of landslide, compared with other parts in the landslide. The seepage calculations from probabilistic analysis imply that rainfall is a relatively inferior factor affecting slope stability. This study aims to provide preliminary guidance on risk management and early warning in the TGR area.

Keywords

reliability analysis / Bazimen landslide / rainfall / reservoir water level / slope stability

Introduction

The stability of reservoir high slopes is one of the main concerns in geotechnical engineering design and practice. China has the largest volume of hydroelectric power station in the world, known as the Three Gorges Dam. It has been reported that there has been a great number of landslides since its first impoundment in June 2003 [¹,²]. Slope failures may cause catastrophic damage to local people’s life and property. Slope safety evaluation is a significant prerequisite for landslide disaster prevention and control in geological practice. It is urgent and essential to reveal the failure mechanism underlying landslides and to further provide preliminary guidance on geological disaster migration of landslides in the Three Gorge Reservoir (TGR).

It has been widely accepted that rainfall and fluctuation of water level are the two main triggering factors for reservoir landslides [³–⁷]. For example, the catastrophic Qianjiangping landslide occurred on 13, July 2003, was considered to be induced by the combined effect of heavy rainfall and impoundment in the Yangtze River [⁸]. As reported by Li et al. [⁹], the Baishuihe landslide located in the TGR, was found to deform excessively when the fluctuation of reservoir water level and rainfall were coupled. Furthermore, the Baijiabao landslide located in Xiangxi River, which is a main tributary of the Yangtze River, was also observed that the deformation is jointly affected by the dual effects [¹⁰].

The existing dormant landslides might be reactivated and start to deform more noticeably owing to the heavy rainfall and fluctuation of reservoir water level [¹¹,¹²]. The combined effect of the two factors can change the pore water pressure and hydrogeological conditions in the slopes, which may subsequently lead to catastrophic landslides [⁷]. Although the evaluation of the independent influence of rainfall or water level fluctuation on the stability of reservoir landslides has been widely studied by numerous researchers, the combined effects of such two influence factors on slope stability has been rarely discussed [⁹]. Therefore, the relative importance of rainfall and reservoir water level fluctuation in triggering landslide is an essential issue to be revealed, since it is of great help to investigate the progressive failure process and provide early warning.

To systematically examine the triggering mechanism of rainfall and reservoir water level fluctuation, as well as the relative role of the dual factors in activating landslide, the Bazimen landslide was back analyzed as a case study. A statistical analysis of the past 3 years monitored data of displacement and records of hydrogeological conditions is carried out in this study. The analysis shows that there are four representative periods in the TGR, considering the climate change and normal operation conditions. The deterministic slope stability analysis is performed via SLOPE/W module contained in GeoStudio software, and the corresponding factor of safety is calculated by using the Morgenstern-Price method. The probabilistic stability analysis of slope considering four representative periods is carried out based on Monte Carlo simulation, due to its wide applicability [¹³].

Review of the Bazimen landslide

Location and hydrogeological conditions

The Bazimen landslide is located in Zigui county, Hubei province, in the middle part of China, at a longitude 110°45′30″ E and latitude 30°58′16″ N, on the right side of Xiangxi River, a major tributary of the Yangtze River. It is 0.8 km from the Xiangxi River estuary and 38 km away from the Three Gorges Dam. The slope is in a shape of dustpan at the foot of the bank, with a main slip direction 110°NE, facing the Xiangxi River. The potential landslide is of about 380 m in length, 100–500 m in width, with a slope angel varying from 10° to 30°. It is estimated that the landslide covers an area of 13.5 ha, with a volume of 2 million m³ (Fig. 1). The elevation of the landslide toe and crown is 139 and 280 m, respectively. The altitude difference of the landslide is approximately 140 m (Chinese National Field Scientific Observation Station of Landslide in the Yangtze Three Gorges).

The landslide boundary is defined by bedrock and soil. According to the borehole data, there are two main sliding surfaces found in the landslide (Fig. 2). The lower one is at the interface between the deposit and bedrock, which is the initial sliding surface. It is steep in the rear part, with an inclination angle from 20° to 30°. The approximate depth of the surface is 27–33 m, with a non-uniform thickness varying from 0.9 to 3.6 m. The upper one is the subordinate sliding surface at a depth of 8–20 m, with a thickness distribution of 2.5–3.2 m. The sliding material is similar in the two sliding zones, mostly composed by the quaternary deposits, consisting of gravel soil and silty clay. The upper and lower part of the sliding mass is thin, while the middle part is relatively thick.

The hydraulic condition of the Bazimen landslide is less complex. The groundwater recharge in the slope is mainly controlled by the atmospheric precipitation and the periodical variation of the reservoir water level. Considering the needs of flood control and power generation, the reservoir water level changed periodically between 145 m and 175 m, since the completion of the TGR in 2009. Therefore, half of the slope body is beneath the reservoir water level (Fig. 2). Besides, it is notable that the Bazimen landslide is located in an area of a humid climate, with an average annual precipitation over 1000 mm from year 2016 to 2018. According to the last 3-year record, the maximum daily precipitation reached 128 mm on 28th, June 2016 and the maximum monthly precipitation amounted to 229.4 mm in August 2017.

Deformation characteristics of Bazimen landslide

Since the first impoundment of the Yangtze River in June 2003, there are many instrumentations installed in the Bazimen landslide for early warning and risk management. The monitored data mainly comprises of the ground displacement, atmospheric precipitation, periodical variation of reservoir water level and underground water table. There are now ten GPS monitoring points used in Bazimen landslide. Two of these monitoring points, numbered as ZG110 and ZG111, are selected for deformation characteristic analysis. ZG110 is in the middle part of the landslide and ZG111 is in the rear part, at elevations of 191 m and 215 m (Fig. 1–2), respectively, based on the Huanghai Elevation System (1956, China). The last 3-year (2016–2018) monitored data are taken into consideration, as shown in Fig. 3. Based on the monitored data, the main features of the relationship curve can be observed as follows.

1) The accumulated displacement curves of the two GPS monitoring points, ZG110 and ZG111, show an increasing trend with time, in a step-wise shape. It indicates that the landslide is still developing, in a period of intermittent creep deformation.

2) The displacement monitoring curves show a synchronous change under the combined effects of rainfall and reservoir water level fluctuation. They got a rapid increase from April to August yearly, while changed within a narrow range in the remaining time of the year. This means that the deformation of Bazimen landslide mainly occurred during summer, the very time where combined effects of flood charge and monthly rainfall are greater than those of other seasons in the year. It suggests the occurrence of seasonal deformation feature reported by previous research [¹⁴], in which slope stability was closely related to rainfall and reservoir water level fluctuation.

3) The relationship between the reservoir water level and monthly displacement shows the significant role of water level fluctuation in controlling landslide deformation, especially during the period of water level drawdown. The monitored displacement curves show that the rise and stable operation stage of reservoir water level did not cause great displacement, while they get rapid increase after every drawdown period of the TGR. As shown in Fig. 3, there are three drawdown phases of reservoir water level from 2016 to 2018, and the displacement curves also show three acceleration stages. This implies that the decline of reservoir water level is more adverse to slope stability, compared with the impoundment period. The similar observation has also been proposed by several researches [⁷,¹⁰,¹⁵].

4) The landslide displacement shows that rainfall is another potential factor influencing slope stability. Figure 3 shows that the acceleration phase of monitored displacements is during rainy season every year, where intensive monthly rainfall is rarely below 150 mm. While in dry season, the displacement keeps unchanged or grows slowly, under much lower monthly rainfall. It indicates that the variation pattern of the landslide displacement is also closely related to the tendency of annual rainfall, suggesting the importance of rainfall in inducing periodical slope deformation.

5) A comparison of the displacement data at different locations shows that the deformation varies spatially. For monitoring point ZG111, the 3-year cumulative displacement is about 600 mm and it grows much greater from April to September in 2017, with an increase over than 250 mm. While for monitoring point ZG110, the approximate accumulated displacement in three years is 400 mm, and the greatest increase is between April and August in 2016, up to 200 mm. The displacement in the rear part (ZG111) is greater than that of the middle area (ZG110). It shows that the landslide is of “advancing” type, where the sliding mass is activated from the rear part and develops downwards with growing displacements and cracks [¹¹,¹⁶,¹⁷]. The displacement difference between the two monitoring points is likely correlated with the different importance roles of the various parts in the landslide [¹⁶]. Guo et al. [¹⁸] and Anitescu et al. [¹⁹] have also done some research related to landslide susceptibility assessment by using deep learning methods.

From the above, it can be inferred that the stability analysis of the Bazimen landslide should concentrate on both internal and external factors, in particular, the soil properties, rainfall and reservoir water level fluctuation. When dealing with slope failures, the similar emphasis have been proposed by many previous works [⁹,²⁰,²¹].

Methodology and theoretical considerations

In this work, the widely used commercial software GeoStudio (Geo-slope International Ltd. 2012) was adopted for deterministic and probabilistic analysis of slope stability. The research method mainly comprises of two steps: 1) Seepage analysis implemented in the SEEP/W program and 2) Factor of safety (F_s) and probability of failure (P_f) calculated in the SLOPE/W, based on the seepage information obtained in step 1). The methodology and theoretical considerations are as follows:

Saturated-unsaturated theory

The seepage filed can be greatly influenced by rainfall infiltration and fluctuation in reservoir water level [²²]. And in SEEP/W, the governing equation for the two-dimensional transient seepage analysis is given as:

(1){\displaystyle \frac{\partial }{\partial x}}\left(k_x{\displaystyle \frac{\partial h}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left(k_y{\displaystyle \frac{\partial h}{\partial y}}\right)+Q=m_w{\rho }_{w}g{\displaystyle \frac{\partial h}{\partial t}},

where h is the total head; k_xandk_y represent the permeability coefficient in the x and y directions, respectively; m_wdenotes the slope of the soil-water characteristic curve (SWCC); {\rho }_w is the density of water; g is the local gravitational acceleration and t is time. The SWCC and hydraulic conductivity function (HCF) are two elementary soil properties used in the seepage analysis. In this paper, the SWCC model proposed by van Genuchten [²³] was adopted, as follows:

(2)S_e={\left[{\displaystyle \frac{\mathrm{1}}{\mathrm{1}+{(\alpha \psi )}^n}}\right]}^m,

where \alpha, n, and m are curve fitting parameters related to the reciprocal of air-entry value, pore size distribution of soil and overall symmetry of the SWCC, respectively; S_e is the effective degree of saturation and \psi means matric suction. Once the SWCC is defined in SEEP/W, the hydraulic conductivity function (HCF) curve can be estimated directly if the saturated permeability is given. The HCF is as follows [²³]:

(3)k_r=S_e^{\mathrm{1}/\mathrm{2}}{[\mathrm{1}-{(\mathrm{1}-S_e^{\mathrm{1}/m})}^m]}^{\mathrm{2}},

where k_r is the relative permeability coefficient of the unsaturated soil, which reflects the ratio between unsaturated permeability and saturated permeability; S_e is the effective degree of saturation; and m is a curve fitting parameter.

Calculation theory for unsaturated soil

Based on the pore-water pressure calculated in SEEP/W, both factor of safety (F_S) and probability of failure (P_f) can be calculated in SLOPE/W. The stability analysis was carried out by considering the shear strength theory of unsaturated soil, which was proposed by Fredlund and Rahardjo [²⁴]. The empirical equation incorporated the contribution of matric suction in unsaturated soil and was obtained according to Mohr-Coulomb, as follows:

(4)\tau =c\text{'}+({\sigma }_n-u_a)\tan \phi \text{'}+(u_a-u_w)\tan {\phi }^{\mathrm{b}},

where \tau is the shear strength of the unsaturated soil; c\text{'} and \phi \text{'} are the parameters of shear strength that denotes effective cohesion and effective internal friction angle, respectively; {\sigma }_n is the total normal stress; u_a is the pore air pressure; u_w is the pore water pressure; {\phi }^b is the angle expressing the increase rate in shear strength induced by matric suction; {\sigma }_n-u_a is net normal stress; and u_a-u_w is the matric suction.

In this study, limit equilibrium methods (LEM_S) were used for slope stability analysis. The main LEM_S used in geotechnical project and design are built in SLOPE/W, such as Bishop’s simplified method, Spencer method, Janbu method and Morgenstern-Price (MP) method. Compared with the first three methods, MP method can reflect the actual stress conditions between soil sections and determine the F_S with any potential sliding surface [⁷,²²]. Therefore, the MP method was chosen for landslide stability analysis in this study considering its robustness and ability in calculating F_S and P_f with accuracy.

Monte Carlo simulation

The probabilistic method used in SLOPE/W is Monte Carlo simulation. The main idea of this method is generating random datum of assumed variables (c,\phi ,\lambda...), with given statistical distribution and value range. Then, the set of random datum can be used in the performance function, F_s(c,\phi ,\lambda ,\mathrm{...}), to calculate every independent F_s under given working conditions. If there are N trials in calculating F_s, and M times where F_s is less than 1, the probability of failure (P_f) can be defined as follows:

(5)

Generally, the MC method necessitates extensive computational efforts for ensuring its result with the desired accuracy. To strike the balance between computational efforts and efficiency, the number of trials, N, is set as 2000 in this study.

Design of working conditions

Based on the engineering characteristics and geological features of Bazimen landslide, the \mathrm{1}-\mathrm{1}\text{'} section was selected to calculate the stability coefficient,F_s, and failure probability, P_f (Fig. 2). The model was divided into 3846 nodes and 3715 elements. To reveal the relative role of different areas in the landslide, the model is divided into five parts: part 1 is the upper layer of silty clay; part 2 is the lower layer of rubble soil; part 3 is the secondary sliding surface; part 4 is the initial sliding surface and part 5 is the bedrock. The model of bedrock is regarded as empty in SEEP/W and impenetrable in SLOPE/W. Considering the computational cost, deterministic method is adopted for annual slope stability analysis, and probabilistic stability analysis is used under the four representative working conditions. In overall stability analysis, the initial hydraulic condition was set as stable seepage when the reservoir water level is 175 m, with an inclination of 14°, revealed by borehole data. The boundary conditions for the model are: the interface of deposit and bedrock is impervious boundary, also known as the zero flow boundary. Slope surface between 145m and 175m was influenced by the fluctuation in reservoir water level, as the variable water head condition. The landslide above 175 m is subjected to the rainfall infiltration boundary. In failure probability analysis, the elementary boundary conditions are similar but the initial reservoir water level fluctuates at different periods.

Geotechnical parameters

The hydraulic and mechanical parameters of the Bazimen landslide used in this work are obtained by the method of engineering geological analogy and the statistical features of landslides in the TGR. According to the site location, hydrogeological conditions and composition of sliding materials, the main parameters of soils are designed and selected. The reference data used in this paper are obtained from Refs. [¹⁰,¹⁵,²⁵].

To reveal the importance of each part, the uncertainty of soils is considered in some research works [²⁶,²⁷]. Yang et al. [⁷] reexamined the Maliulin landslide in the TGR via statistical analysis, and suggested that parameters c and \phi follow normal distribution. In addition, the statistical features of shear strength parameters show that the dispersion degree can vary greatly for different soils. In view of this, three types of coefficient of variation (COV) were taken into consideration in this work, applicable for all the four materials. For simplicity, the potential relationship between cohesion and frictional angle was not thought in this work. In the probabilistic analysis, the variability of each part in the landslide is taken into account respectively, under a common COV. Then the calculated P_f of each part is compared with the overall failure probability, where the landslide is considered as an entirety varied under the same COV. Therefore, it can be inferred that smaller difference between one part and the entirety, the more important of the part in controlling slope stability.

The physical and mechanical parameters of soils are listed in Table 1. The hydraulic parameters of soils for Van Genuchten model are listed in Table 2, based on the field testing and recommendation of Vogel et al. [²⁸].

Determination of reservoir water level

Deterministic analysis

For consideration of flood control and power generation, the reservoir water level in the TGR varies periodically in one year. Figure 4 shows the annual variation of reservoir water level in the past three years. It is observed that the variation of reservoir water level is staged and almost changes linearly between adjacent periods. More precisely, the annual variation can be divided into four representative periods: P₁ (175–165 m) October to early April of next year, P₂ (165–145m) the middle April to the end of May, P₃ (145–150m) June to August and P₄ (150–175m) September to the middle of October. Based on the analysis above, the average reservoir water level from year 2016 to 2018 can be estimated by using the method of piecewise linear fitting (Fig. 4). The fitted curve is selected as the fluctuation schedule in annual stability analysis (Fig.7).

Probabilistic analysis

In view of the computational cost, the four representative running operations are used in the probabilistic analysis. Some researchers investigated four soil slopes in Singapore about the seepage filed distribution after rainfall, and suggested that 5 days antecedent precipitation has great impact on the slope stability [²⁹–³¹]. In view of this, a 10-day research cycle is selected in the probability analysis, where the combined effects of rainfall and reservoir water level fluctuation last 5 days.

Li et al. [⁹] analyzed the Qianjiangping landslide in the TGR and found that the fluctuation rate of reservoir water level is an important role in inducing slope failures. Based on the statistical analysis of the reservoir water level (Fig. 5), it is found that the fluctuation velocity is almost within 1.0 m/d. Thus, the working conditions are designed as follows.

Condition 2-1 (slow descending stage) the water level drops from 175 to 172.5 m at a descending speed of 0.5m/d,

Condition 2-2 (rapid descending stage) the water level declines from 165 to 160 m at a falling velocity of 1.0m/d,

Condition 2-3 (slow ascending stage) the water level rises from 145 to 147.5 m at an increasing rate of 0.5m/d and

Condition 2-4 (rapid ascending stage) the water level increases from 150 to 155 m at a rising speed of 1.0 m/d (shown in Table 3).

Determination of rainfall

Deterministic slope stability analysis

The Zigui county is located in central China with plentiful rainfall, which belongs to the humid monsoon climate zone. The latest 3-year atmospheric precipitation in the Bazimen layer area is shown in Fig. 6. The recording data of daily rainfall shows that rainfall mainly concentrated between April and September, with a proportion more than 70% of the annual precipitation. According to the classification of the China Meteorological Administration (CMA), the 24-h rainfall can be divided into light rain, moderate rain, heavy rain and rainstorm, at rainfall intensity threshold of 10, 25, 50, and 250 mm/d. It is seen that most of the rainfall are of light to moderate intensity. The average annual precipitation from year 2016 to 2018 is used as the rainfall condition in the annual stability analysis (Fig. 7).

Probabilistic slope stability analysis

Similar to the reservoir water level fluctuation, the monthly rainfall in the TGR is also periodical and seasonal. The spatial distribution of rainfall is not considered in this part, i.e., the rainfall pattern is normal and the daily rainfall intensity is consistent. Miao et al. [²⁵] counted the 54 years rainfall data at Zigui County from 1960 to 2013, and found that the maximum of five days cumulative rainfall among the 54 years is 134 mm. Based on the finding and the statistical features of rainfall from year 2016 to 2018, the typical daily rainfall intensity for the four representative periods is as follows: Condition 2-1 (slow descent stage) the rainfall intensity is 10 mm/d, Condition 2-2 (rapid descent stage) the rainfall intensity is 15 mm/d, Condition 2-3 (slow ascent stage) the rainfall intensity is 30 mm/d and Condition 2-4 (rapid ascent stage) the rainfall intensity is 10 mm/d (shown in Table 3).

Results and discussion

Calculation of annual stability

The calculation of overall stability coefficient of Bazimen landslide in a complete annual cycle was implemented in SLOPE/W, under Condition 1. Select one day as a time step. The computed stability coefficient is shown in Fig. 7. The results show that the stability coefficient varies between 1.0 and 1.3 throughout the year. It is observed that the stability coefficient decreases during the period of water level drawdown and increases again in the impoundment period. It can be deduced that the declination of water level is unfavorable to slope stability while the increase of water level is conducive. Moreover, the periodical and staged variation of F_S coincides well with the annual fluctuation in reservoir water level. However, due to the effect of rainfall, the variation curve of F_S is not as smooth as the fluctuation schedule. The temporary effect of rainfall does not cause great change to F_S, indicating that rainfall is a relatively inferior factor to long-term slope stability, compared with reservoir water level fluctuation.

Figure 8 shows the relationship between annual displacement and annual precipitation, in a longer period from 2003 to 2018. The curve shows that the annual precipitation has less effect on the landslide stability. Yang et al. [⁷] also found in a case study of Maliulin landslide in the TGR that the annual variation of landslide stability is mainly controlled by reservoir water level, while intensive rainfall has greater impact on slope safety in short-period below 4 days. The minimum F_S occurs in May, several days after the stop of reservoir water level decrease. It shows that the fluctuation in reservoir water level has a lagging effect on slope stability.

Similarly, the 3-year average cumulative displacement of the two GPS monitoring points, ZG110 and ZG111, shows a good coincidence trend with the landslide stability coefficient. The deformation curve increases greatly when the stability coefficient declines and changes into stable development when it is rising to a safe situation. The differences of displacement range and duration between the two GPS monitoring points show that the displacement is spatially variable. This fact emphasized the importance of considering the variability and uncertainty involved in the soil properties and different parts in the landslide.

Calculation of failure probability

As mentioned above, there are four representative working operations for probabilistic analysis of slope stability, based on the statistical features of the latest 3-year (2016-2018) monitored data. The calculation processes of stability coefficient and failure probability under conditions 2-1 to 2-4 are also implemented in SLOPE/W, based on the combined effort of Morgenstern-Price method and Monte Carlo simulation. Choose one day as a time step. The calculated results are shown in Figs. 9–12.

Condition 2-1

Condition 2-1 denotes the period of a high reservoir water level (175 m) declines at a slow falling rate of 0.5m/d, combined with 5-day low-intensity rainfall (10 mm/d). The scenario is common to see in October to next year March. Figures 9(a), 9(b), 9(c) and 9(d) show the variation of safety factor and failure probability of COV 0.05, 0.1 and 0.2 in the 10-day research cycle, respectively, under Condition 2-1. The variation of F_S with time shows that the slope stability is in consistent with the fluctuation of reservoir water level. The stability coefficient decreases gradually when the landslide is subjected to rainfall and water level declination, and it tends to be stable when the combined effect ceases.

Figures 9(b), 9(c) and 9(d) show a similar pattern of failure probability. It is observed that no matter how the COV changes, the variation pattern of P_f presents an opposite tendency compared with F_S, increasing at first and falling slowly after 6th day. This implies that the 5-day combined effect of rainfall and reservoir water level drawdown is unfavorable to slope stability. Besides, a comparison of the probabilistic results in Figs. 9(b), 9(c) and 9(d) among the same landslide area but different degree of variability shows that the larger COV the higher failure probability. Besides, the probabilistic results reveal the relative importance of different parts of the Bazimen landslide in inducing slope failures. The differences of the maximum failure probability among the landslide areas show that part 4 is the most significant area and part 2 follows. While for the other two parts, they are relatively unimportant under Condition 2-1.

Condition 2-2

Condition 2-2 represents the rapid decline period of the reservoir water level (165 m) at a high rate of descent (1.0 m/d), with high-intensity rainfall. The scenario is a common phase during April to May, where the reservoir water level declines to meet the needs of flood control. Figure 10(a) shows the variation of F_S versus time, t, subjected to the 5-day combined effect of rainfall (15 mm/d) and reservoir water level fluctuation (165-160 m). Figures 10(b), 10(c) and 10(d) show the variation of failure probability of COV 0.05, 0.1 and 0.2, respectively, under Condition 2-2. It is observed that the general tendencies and rules of both deterministic and probabilistic results under Condition 2-2 are similar to findings revealed in Fig. 10.

However, with the increases of rainfall intensity and water level drawdown velocity, the variation of P_f is greater and faster. The maximum P_f of Condition 2-2 occurs approximate to 3rd day, while under Condition 2-1, it occurs near 5th day, the very time where rainfall and reservoir water level fluctuation ceases. This indicates that the combined effect of higher intensity rainfall and faster drawdown velocity of reservoir water level is more unfavorable to slope stability. Nevertheless, the sequence of relative importance of different parts in the Bazimen landslide is unaltered, the part four (the initial sliding surface) is still the pivotal area to slope stability under Condition 2-2.

Condition 2-3

Condition 2-3 denotes the most rainy season in the TGR, from June to August, where the reservoir water level is at a relatively low elevation (145 m). The selection of the increasing speed in reservoir water level (0.5 m/d) and the rainfall intensity (30 mm/d) is based on the statistical analysis and historical records. Figures 11(a), 11(b), 11(c) and 11(d) show the deterministic analysis result and probabilistic analysis results under COV 0.05, 0.1 and 0.2, respectively. It is easily observed that slope stability improves greatly under Condition 2-3. Figure 11(a) shows that the 10-day variation of the stability coefficient is almost consistent with the change of reservoir water level. However, with the infiltration of rainwater, the landslide stability falls back to a relatively lower situation. This implies that the impoundment of reservoir is conducive to slope stability, while rainfall is adverse and has a lagging influence on the landslide.

The risk level of the probabilistic results also indicates the improvement of landslide stability. With the augment of COV, the maximum failure probability increase synchronously. However, the maximum P_f of the most dangerous scenario is well below 12%. It proves again that the landslide is relatively stable under Condition 2-3, where the TGR rises from a low elevation to a high water level. The importance role of different parts in the slope stay the same order with Condition 2-1 and 2-2.

Condition 2-4

Condition 2-4 denotes the rapid filling period of the TGR, where the reservoir water level rises at a low elevation (150 m) to meet the needs of impoundment. This phase always exists during September and early days of October, where the light and moderate rain is common. Figures 12(a), 12(b), 12(c) and 12(d) show the deterministic analysis result and probabilistic analysis results under COV 0.05, 0.1 and 0.2, respectively. It is noted that the variation tendency of the landslide stability is in accord with the change of reservoir water level. The factor of safety increases with the rise in reservoir water level and keeps changing at a steady-state when the combined effect of rainfall and reservoir water level ceases. Compared with Condition 2-3, there is not an early reduction of F_S in the first 5 days, indicating that the low-intensity rainfall has a lagging and less important impact on landslide stability.

The persistent reduction of failure probability in Figs. 12(b), 12(c) and 12(d) also indicate that Condition 2-4 is relatively conducive to slope stability, where the landslide is subjected to the rapid rise of the reservoir water level and low-intensity rainfall. The risk grade reveals again the importance of part 4 (the initial sliding surface) in inducing slope failures.

Figure 13 shows the convergence curves of the most dangerous scenarios shown in Figs. 9 to 12, where the landslide was considered as a whole under the condition of the maximum COV, 0.5. It can be observed from the figure that the number of simulations, 2000, is enough to obtain reliable results. Considering the computational and time cost, a performance function may be used in future works, using the multivariate adaptive regression method proposed by Refs. [³²,³³].

The above results and discussion indicate that the fluctuation of reservoir water level plays a dominate role in controlling landslide stability, the declination period is more unfavorable to the slope stability. Rainfall is a lagging and less important impact on the overall landslide stability. The initial sliding surface is the pivotal area of the Bazimen landslide in inducing slope failures. Based on the historical records and monitored data, this fact can reflect real situation of the Bazimen landslide region.

Seepage analysis

To investigate the different failure mechanisms of rainfall and reservoir water level fluctuation clearly, a series of vertical observation points are set at the contact position of 175 m reservoir water level and the landslide. The volumetric water content (VWC) and the saturation are chosen as research objects, for they are key factors in influencing the soil permeability and water infiltration. Figure 14 shows the saturation of the monitoring points at different depth, under the four conditions 2-1 to 2-4. The very time (6th day) when the joint action of rainfall and reservoir water level fluctuation stops is chosen as the testing time. When the reservoir water level is at a relatively high elevation, it is observed that the saturation of surface soil is lower than that of internal soil, and it increases with the increasing depth. While for the scenarios having relatively low water level, it is seen that the saturation of soil decrease at first and starts to increase gradually at the depth where the observation point is about 10 m from the phreatic line.

More details can be revealed by analyzing the cycle variation of the VWC with time. Taking Condition 2-4 as example, the VWC of the soils between 175 and 140 m is shown in Fig. 15. There is a total of 8 observation points selected for analysis, at a depth gradient of 5 m. It is observed that only the monitoring points at 175 m and 160 m are greatly influenced under the combined effect of rainfall and reservoir water level rising. The VWC of the surface observation point (175 m) progressively increases under rainfall and that of the internal observation point (160 m) continuously rises with the promotion of phreatic line. The observation points at other depth of the landslide keep changing within narrow range or unchanged. Therefore, it can be deduced that rainfall mainly affects the upper soil mass and the lower soil mass is controlled by the fluctuation of the reservoir water level. This is similar to the observation of Hamrouni et al. [³⁴], who found that rainfall infiltration mainly influences the superficial zone of slopes. To reveal more details, the phase field model (PFM) could be used in future research, because it will help to detect the gradually evolving failure surface and the influence of seepage on slope stability can be fully considered [³⁵–³⁸].

Summary and conclusions

Based on the last three-year monitored data of the displacement and hydrologic conditions, the Bazimen landslide in the TGR is studied under the combined effect of rainfall and reservoir water level fluctuation. With the aid of statistical analysis and engineering analogy method, the geotechnical model is used to calculate the annual variation of landslide stability and the failure probabilities of the four representative periods.

According to the monitored data and overall stability analysis, the annual variation of the stability coefficient is well consistent with the fluctuation of reservoir water level. Rainfall has temporary and secondary impact on the stability of Bazimen landslide. The minimum stability coefficient occurs during the rapid declination period of the reservoir water level and rainy season. Therefore, the time from March to April should be placed emphasis on for early warning and risk management.

The probabilistic stability analysis of the four representative periods shows that the initial sliding surface is the pivotal area in controlling the stability of Bazimen landslide. The maximum failure probability increases with the increasing variability degree of soil properties. The volumetric water content and saturation of the soils at different depth show that rainfall is more likely to induce shallow landslides. While the fluctuation of the reservoir water level has dominate influence on the critical sliding surface.

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