Effects of Rapid Water-Level Fluctuations on the Stability of an Unsaturated Reservoir Bank Slope

Changjiang Survey, Planning, Design and Research Co., Ltd. (CSPDR), Changjiang, Hubei 430015, China Department of Civil Engineering and Mechanics, Faculty of Engineering, China University of Geosciences, Wuhan, Hubei 430074, China Department of Ocean Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China State Key Laboratory of Water Resources and Hydropower Engineering Science, Institute of Engineering Risk and Disaster Prevention, Wuhan University, 299 Bayi Road, Wuhan 430072, China


Introduction
e instability of reservoir slope is likely to cause some natural hazards such as surge and barrier lake when the reservoir water-level fluctuates rapidly (see, e.g., [1][2][3]). e danger derives from unsaturated residual soil due to rapid water-level fluctuations of a reservoir bank slope. A key influence factor is the matrix suction which varies according to the changes in water seepage and water infiltration line. As reported by Ng et al. [4], the rainfall infiltration would reduce the matrix suction, resulting in an increase in moisture content and soil permeability in unsaturated soil. e failure criterion of strength of unsaturated soil differs from that of saturated soil, which increases the difficulty of studying the stability of unsaturated soil slope [5]. Fredlund et al. [6] developed a Mohr-Coulomb shear strength theory for extensional unsaturated soil. Furthermore, Fredlund et al. [7] proposed a slope stability evaluation method (GLE method) which accounts for the matric suction.
To investigate the stability of unsaturated soil slope, the theory of limit equilibrium with respect to unsaturated soil is commonly used. For example, Qi and Vanapalli [8] reported the formulation for calculating slope safety factor based on the strength theory of unsaturated soil and the limit equilibrium method and discussed the stability of unsaturated soil slope under rainfall infiltration. Liu et al. [9,10] simulated the undrained shear strength as a random field to reflect the spatial variability of slope soil properties and combined the Monte Carlo method to determine the factor of safety. Hiroyuki et al. [11] reported that the influence factors for landslide stability in reservoir areas include the immersion of the reservoir water, the sharp decline of the reservoir water-level, and the rainstorm. Fredlund and Rahardjo [12] proposed a method for calculating the critical height of vertical or nearly vertical slopes based on the theory of earth pressure in unsaturated soil. Fredlund et al. [13] put forth a nonlinear law for the variation of shear strength of unsaturated soil with matric suction based on the soil-water characteristic curve equation of unsaturated soil. Zhang et al. [14] and Luo and Ye [15] noticed that when the water-level fluctuates dramatically, the infiltration line and the matric suction field on the slope will change significantly and subsequently affect the stability of the bank slope. However, the slope reliability analysis as well as the changes in seepage field and the unsaturated zone of a reservoir bank slope subjected to rapid water-level fluctuations has not been discussed in these studies. e effects of rapid water-level fluctuations on the stability of the reservoir slope in unsaturated soil still remain unclear. Unlike saturated soil, the interaction between pore air pressure and pore water pressure in unsaturated soil is more complicated. Firstly, the pore pressure in unsaturated soil may become negative, thereby reducing the effective soil stress [16]. Secondly, the water content and the permeability coefficient in unsaturated soil vary spatially which may cause soil-water content and permeability coefficient exhibiting spatial variability [17][18][19]. irdly, the failure criterion of strength of saturated soil differs from that of unsaturated soil. All these lead to the difficulty of studying the slope stability in unsaturated soil.
In this study, a genuine engineering case of reservoir landslide at Nuozhadu Reservoir area in Yunnan Province is examined using the finite element method. e hydraulic effect of water-level fluctuations on the interior of unsaturated soil slope is considered. e suction matrix is used to calculate the influence of a changing rate of water-level on the unsaturated soil of the typical landslide deposit H 12 of an engineering example of bank slope investigation in Nuozhadu Reservoir area. In the stability analysis of the slope, the coupling effects of matrix suction in the unsaturated area, pore water seepage in the saturated area, and gravity stress field of rock and soil are taken into account. e results can serve as a reference for stability evaluation of reservoir bank and river side slopes and other related engineering areas (see, e.g., Chen et al. [20]).

Finite Element Model
2.1. Model Setup. By collecting of relevant data and field geological investigation in Nuozhadu Reservoir area, it is found that H 12 is an ancient landslide accumulation body, which is located in the branch of Lancang River. Figure 1 shows the overall picture of the landslide accumulation body, with obvious landslide morphology. Figure 2 is a section sketch of H 12 . e elevation of the front edge of the landslide is 660 m, the elevation of the back edge is 827 m, the height difference is about 207 m, and the volume of the landslide accumulation is 6 million cubic meters. e main sliding direction of the landslide is about 5°and the length of the main sliding direction is about 1000 m. e boundary of the landslide is basically clear. e boundary of both sides of the landslide is gully. e bedrock in the gully is exposed. e occurrence of the bedrock surface is 5°, which is less than 17°as shown in Figure 2. e landslide body slides along the bedrock surface. e shape of the landslide accumulation body is as follows: the back edge of the accumulation body is steep, the slope in the middle part is gentle, and the slope at the shear outlet of the front edge is steep, which has typical landslide characteristics. e reservoir bank slope is subjected to the water-level fluctuations at different rates. Figure 3 shows the schematic of a typical vertical cross section of a H 12 landslide deposit which is obtained based on the basic geological survey and 1 : 10000 topographic map. e typical sections are intercepted reasonably. e orientation of the sections is consistent with the main sliding direction. e strata are divided into three layers. From top to bottom, the landslide deposits (gravelbearing silty clay), the sliding zones are mainly strong weathered argillaceous sandstone and the magenta siltyargillaceous siltstone.
ere is a horizontal displacement of the side walls and the vertical and horizontal ones. Regarding the boundary conditions, horizontal constraints are imposed on both sides of the model, and all nodes on the ground are added with horizontal and vertical constraints. ere is water pressure on the slope, and the pressure value is determined by the reservoir water-level. According to the material composition of the landslide and the mechanical parameters of the adjacent rock and soil, the comprehensive calculation determines the calculation parameters as shown in Table 1. e normal storage water-level is 812 m and the initial water-level is 625 m, which is lower than the toe of the landslide mass, i.e., the elevation of the landslide body. When the initial water-level is achieved, the river bed in the section is free of water. e reservoir is impounded in three stages: the first stage from the current water-level to 672.5 m, the second stage from 672.5 m to the dead water-level of 765 m, and the third stage from the dead water-level of 765 m to the normal water-level of 812 m. e cases modelled in the analysis of the landslide are shown in Table 2.

Computation Conditions.
e finite element model is implemented using the SIGMA/W module of the commercial finite element software GeoStudio. is module is able to correctly model the stability behavior of an unsaturated slope which involves the coupling of seepage and stress-strain behavior of soil. e study that the slope stability analysis under unsaturated soil is calculated using the linear elasticity model implemented in GeoStudio 2007 is proposed by Oh et al. [21]. e soil and the bed rock of the landslide are modelled using an elastoplastic constitutive model and linear elastic constitutive model, respectively. Figure 4 shows the meshes of the landslide soil and bedrock domains. Based on the working conditions of Nuozhadu Reservoir in the periods of impoundment and operation, two scenarios are considered in this study. e parameters used in the analysis are displayed in Table 1.

Determination of Calculation Method.
e fluid-soil interaction is explicitly considered as the finite element modelling. e soil is assumed to be a continuous medium. e seepage is characterized by the static pore pressure and the hydrodynamic force, which is manifested by the osmotic pressure P applied to a certain action surface and the seepage volume force f distributed in the seepage region. e former is the surface force, and the latter is physical strength; the expression is illustrated in  Normal storage water level

Advances in Civil Engineering
On the other hand, the permeability coefficient k will change with the volumetric strain ε v and porosity n, which in turn affects the seepage field. e expressions are given by e coupled fluid-soil interaction is implemented using nonlinear finite element method for slope stability analysis. e main steps include solving the seepage field through the initial permeability coefficient k 0 , and obtaining the head distribution so that the hydrostatic pressure and the permeation volume force can be calculated. e above results are then brought into the stress field, and the boundary conditions are combined to resolve the stress field. e volume strain is obtained, and the volume strain is substituted into (2) to solve the permeability coefficient k 1 . e above steps are repeated continuously until equilibrium is arrived to obtain the stress-strain distribution.

Results and Analysis
3.1. Cases 1 to 2. When analyzing the stability of the slope due to the sudden rise and fall of the water-level, consider the coupling effect of the seepage force and the stress field; that is, the seepage force is added to the landslide micro-unit, and the variation rate of 2 m/day is selected and analyzed. As shown in Figure 5, the reservoir water-level is reduced from 812 m to 765 m. Considering the finite element method stability calculation results of the unsaturated landslide deposits after the coupling of the seepage field and the stress field, the results show the overall sliding. e stability factor is 1.123, which is generally stable. When the reservoir water-level rises from 672.5 m to 765 m, the hydromechanical coupling effect is examined. During the analysis, the matric suction is reckoned. As shown in Figure 6, the factor of safety of the slope is 1.255.
In order to study the influence of the matric suction of unsaturated soil on the stability of unsaturated landslide deposits, the suction force is not considered; that is, the strength of the soil due to suction is removed in the software, and other parameters are unchanged, considering the effect of seepage force. e potential sliding conditions are shown in Figure 7. e factor of safety decreases from 1.255 to 1.138, which indicates that the matric suction has a positive effect on the slope stability when the water-level rises rapidly.
Compared with the rising condition of the reservoir water-level, the stability of the deposit body is superior to that of the sudden drop. e favorable factors for the antisliding of the reservoir water-level rising are schematically shown in Figure 8. Firstly, the reservoir water-level is suddenly raised, and the landslide body is subjected to the seepage force F(K) addressed to the slope, which is beneficial to enhance the antisliding force. Secondly, during the abrupt rise of the water-level, the water will be pressed by a selfweight in a short period of time, which is perpendicular to the slope F′(N). e slope foot increases the antislip force of the leading edge, which increases the stability of the entire slope.
e unfavorable factors of water storage on slope stability also exist. After a period of water storage, the front edge of the slope is saturated, and the leading edge rock and soil itself will decrease due to water immersion strength, reducing the resistance. e sliding force causes a landslide. Because the leading edge of the slope is saturated by the upward pressure F(N) of the water after the leading edge is saturated, the water seeps into the sliding surface to play a lubricating role, so that the anterior edge antisliding force  Advances in Civil Engineering reduces. However, under the condition of water-level dropping at a rate of 2 m/day, the stability coefficient of the slope is broad and safe, indicating that the favorable factors are greater than the unfavorable factors. e slope stability under the influence of the matrix suction in the unsaturated zone is also considered. It is found that when the matrix suction is calculated, the stability of the slope is likely to be improved, and the increase is mainly dominated by the range of the unsaturated zone. e larger the range, the greater the increase in stability. Under the condition of the reservoir water-level falling, the range of the unsaturated zone is not as large as that of the rising condition, so the unsaturated zone has less impact on the stability of the slope under the precipitation condition. e above results suggest that the landslide accumulation body is stable under all the above-mentioned reservoir water-level fluctuation conditions. e calculation results are more accurate when the hydromechanical coupling effect is reckoned under unsaturated conditions. Figure 9 shows the seepage velocity field in landslide deposit H 12 for Case 3 with water-level dropping from 812 m to 765 m at a rate of 2 m/day. As can be seen, the maximum seepage velocity occurs near the slope surface at water elevation of 765 m, i.e., a velocity of 2 m/day, which is Advances in Civil Engineering probably due to the relatively low soil permeability coefficient. e seepage velocity is a key influence factor on the stability of slopes [22]. is can be reflected from pore water pressure and saturation change. is effect would become more significant when the direction of flow velocity is the same as the sliding direction and the flow velocity is greater than the sliding velocity of the landslide. Figure 10 shows the contours of the displacement, shear stress, and strain of the landslide for Case 3 with water-level dropping from 812 m to 765 m at a rate of 2 m/day. e displacement, shear stress, and strain distribution calculated by considering the coupling effect of the seepage field and the stress field are displayed in the displacement contour map along the horizontal and vertical directions. ere is x-zero displacement at the 475 m of the landslide body. Due to the water pressure acting on the slope after water storage, the soil is consolidated and displaced along the positive direction of x-axis. e maximum displacement value is 0.31 m at x-axis of 200 m. At the trailing edge of the landslide body, due to the combined action of the sliding force and the seepage force, the trailing edge has a displacement along the negative x-axis direction, and the maximum value of 0.29 m is located at the trailing edge of the landslide. e displacement along y-axis is predominantly negative. e maximum settlement is 0.78 m, which is mainly due to soil consolidation caused by water pressure. e above results indicate that the potential failure mode is a typical thrust load-caused landslide. e consequences of stress-strain calculation show that the shear stress is concentrated in the linear elastic model of the sliding bed; the maximum value reaches 2500 kPa. e landslide body is elastoplastic model, the shear stress is small, but the shear strain is large, and the shear strain at the landslide front and slip surface is great. Figure 11 shows the displacement, shear stress, and shear strain contours when the reservoir water-level rises from 672.5 m to 765 m at a rate of 2 m/day. From the dip displacement and stress-strain distribution contours, the following findings can be observed. Firstly, when the reservoir water-level rises, the displacement of the landslide body is lower than the reservoir water-level from 812 m to 765 m. e shear strain is much smaller. Because the reservoir water-level rises sharply, the projection of the seepage force direction and the sliding direction is negative, which offsets the effect of a part of the sliding force. erefore, when the water-level rises, the displacement of the landslide body tends to be small. Secondly, at the elevation of 765 m, the seepage force exists along the opposite direction of the sliding direction, and the trailing edge receives the glide force caused by gravity; as a result, two zero displacement lines appear in the sliding body along x-axis displacement contour. In the shear strain contour map, two zero shear strain lines also appear in the sliding body. irdly, the shear stress distribution in the sliding body is the same as that    under the precipitous drop condition, and the shear stress is large in the sliding bed. e shear strain distribution is great in the sliding body and small in the sliding bed.

Conclusions
Based on the study of rapid water-level fluctuations on the stability and hydromechanical behavior of an unsaturated reservoir bank slope, the following conclusions can be obtained.
(1) e matrix suction should be considered when calculating the stability of unsaturated soil, which is beneficial for slope stability in unsaturated soil. (2) e stability of an unsaturated reservoir bank is weaker when the water-level drops dramatically and then rises sharply. e result is attributed to the orientation of seepage force being inclined to the outer edge of the slope when the water-level drops dramatically.
(3) e coupled seepage-soil stress field should be considered in calculating the stability of an unsaturated reservoir bank slope when the water-level changes rapidly. (4) e unsaturated area of the slope body is becoming smaller after the water-level rises abruptly, which can make the reservoir bank slope be unstable.
In the process of water storage, due to the rapid disappearance of the matrix suction, it is not difficult to cause some shallow surface landslides. It is found that the most dangerous working condition for the bank slope is under deliberate storage and quick release of water. Compared with the rising condition of the reservoir water-level, the deposit body is more stable than that of the sudden water-level drop condition. When the matrix suction is reckoned, the stability of the slope is likely to be improved. A larger unsaturated zone often benefits the slope stability. is study is based on 2D model, and a more complete assessment should consider a 3D model of slope. As a multiphase material, the soil along the sliding surface should be spatially variable (see [23,24]) which may also affect the failure mode and sliding velocity. ese form strands of future work.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.