Displacement evolution of reverse-dip rock slope considering the change of the reservoir level

The fluctuation and periodic change of reservoir level are the important incentives that affect the stability of the reverse-dip rock slope. Based on the field monitoring data, this paper investigates the topping deformation evolution characteristics of a typical reverse-dip slope containing different geological partitions considering the fluctuation of reservoir level. A typical reverse-dip rock slope was taken as an engineering case, whose geological factors including elevation, slope angle, and aspect were first obtained by a field survey. Subsequently, the factors were superimposed through ArcGIS to obtain the geological partitions. Afterwards, a spatiotemporal evolution nephogram of the topping displacement was obtained by discrete monitoring data of surface displacement of the slope. Finally, the deformation characteristic of the prone zone was analyzed by superposing the nephogram of the displacement and the geometrical partition, considering the change of the reservoir level. The results show that the largest geological and geometric characteristic zone is at the bottom elevation, medium slope, and north aspect. The zone with significant horizontal displacement is distributed in the front and middle edges of the slope, which increases with the increase of the reservoir level and vice versa. The vertical displacement mainly occurs in the trailing of the slope. The area of superimposed displacement in strong deformation zones increases as either the reservoir level rises or falls. After the superposition, zones with strong deformation increase with the variation of the reservoir level, and the area with the largest displacement is distributed at the medium gradient, low elevation, and north aspect zones.


Introduction
Reverse-dip slope (Dong et al. 2020) indicates the dip direction of the strata is against the dip direction of the slope. The reverse dip is often considered as the favorable scenario in engineering practice, as the potential sliding surface should pass through several bedding layers. Therefore, the geotechnical profession pays little attention to the reverse-dip slope, and thus, the corresponding studies are limited. However, a number of hazardous natural events have occurred in recent years in relation to the reverse-dip slope (Aydan and Kawamoto 1992;Huang 2007;Martino et al. 2020). Many researchers have made attempts to investigate the failure mechanism of topping deformation of the reverse-dip slope (Fazelabdolabadi and Golestan 2020;Eberhardt, 2008;Gschwind et al. 2019;Huang et al. 2021;Lian et al. 2017;Xie et al. 2018;Ye et al. 2021). Terzaghi and Peck (1957) described the toppling deformation and failure characteristics of reverse-dip slopes from the perspective of engineering geology. Amini et al. (2008) considered the rock mass an inclined superimposed cantilever beam, and analyzed the bending and toppling failure modes of the layered slope, where the factors of safety between the layered rock masses were considered. Alzo'ubi et al. (2010) reported that the tensile strength mainly induces the bending and toppling deformations. Goodman (2013) defined three failure modes for reverse-dip slopes, including bending, block, and bending-block failures. Other researchers (Adhikary et al. 1997;Bhasin et al. 2004;Chen et al. 2015;Zheng et al. 2019) conducted a series of model centrifugal tests to study the mechanism of bending and toppling failures of jointed 1 3 717 Page 2 of 20 rock slopes. Alejano et al. (2010) and Li et al. (2015) used the discrete element method to investigate the failure mechanism of the open-pit mine, where the failure of the reversedip slope was defined as a complex combination of dumping failures. Dong et al. (2020) investigated the influences of lithology, dip angle, and rock thickness on the anti-dipping deformation, by simulating the excavation process of the anti-dipping slope. Xie et al. (2020) analyzed the evolutionary characteristics of toppling deformation in view of the energy field. Kassou et al. (2020) analyzed the slope stability of embankments on soft soil improved with vertical drains. Wang and Xiong (2020) investigated the influence of bolt set on the shear resistance of jointed rock masses.
In engineering practice, there are many influential factors to the toppling deformation and failure of the reversedip slope, where the influence of the reservoir level is particularly significant (Gu et al. 2020). Xu et al. (2005) used FLAC 3D to investigate the deformation and failure mechanisms of the Jiefanggou reverse-dip rock slope, considering the fluctuation of the reservoir level. Huang and Gu (2017) reported that the periodic fluctuation of reservoir level and long-term immersion are the significant triggers of landslides. Dong et al. (2020) believes that the lithology of reverse-dip rock slopes significantly influence the failure mode of toppling deformation. From the perspective of engineering geology, lithology is crucial to the stability of slopes. The front part of the bank slope is mainly dolomitic limestone, and the back part is mainly argillaceous limestone.
At present, most researchers mainly use methods of numerical simulation, centrifugal model tests, and theoretical analysis to study the deformation mechanism of the reverse-dip rock slope. The research on the mechanical behavior is generally applicable to the analysis of bank slope deformation, when there is no monitoring data or the monitoring data is scarce. Mechanics' analysis must establish an accurate engineering geological model and appropriate constitutive relations or limit equilibrium theory to achieve ideal results. In addition, the mechanism of external factors such as reservoir level and rainfall are also not well resolved by the current mechanical models. It is also one of the reasons why it is difficult to analyze the deformation and evolution of many slopes accurately. Actual deformation data is the most objective evaluation basis for testing various mechanical models. In this work, it is found that the toppling deformation characteristics of the anti-dip slope vary a lot in different portions considering the change of the reservoir level. Therefore, by considering the influence of reservoir water fluctuation on the toppling deformation of the reversedip rock slope, taking the typical reverse-dip slope as the research object, and a geological survey, with the elevation, slope, and aspect were taken as the geological factors and analyze the spatial distribution characteristics. The geological and geometric partitions were obtained by overlaying the raster layers. Discrete displacement monitoring data were selected, which were the most real deformation data, considering reservoir level and bank slope mechanics. Using inverse distance weighting (IDW), the spatiotemporal evolution nephogram of topping displacement under the change of reservoir level was obtained. By combining different geological partitions, the real deformation and evolution laws of each zone were analyzed. This paper discusses the topping deformation evolution characteristics of different geological partitions of the reverse-dip slope under the fluctuation of reservoir level. The research flowchart is shown in Fig. 1.

Geological condition of the slope
Xiaodongcao slope is located on the right bank of the upper reaches of the Xixi River in the Zhonglian township, Wuxi county, Chongqing city (Fig. 2). It is 1.2 km away from Zhongliang reservoir. The elevation of the slope is in the range 540-1183 m, and the width of the slope is around 700 m. The topography of the slope is steep, with an averaged aspect of around 345°. Herein, the middle portion of the slope is particularly steep, with the slope angle being in 45°-68°. The back edge of the slope is relatively stable, with the slope angle being in 11°-18° (some areas of the back part can exhibit 37° slope angle). Topographic features of the bank slope are mainly controlled by the lithology and geological structure, The profile of the slope is mainly composed of Quaternary residual and slope sediments      medium-thick layered dolomitic limestone, which is mainly distributed in the middle and front of the bank slope. And, it is mainly affected by the shear stress. Rock mass structure is relatively complete, but the local weathering is strong. Daye Formation (T1d) is a thin, medium, and thick layered argillaceous limestone, which is mainly distributed in the middle and rear of the bank slope. Due to the obvious tensile stress in the process of bending toppling deformation, the rock structure is broken and the rock bending toppling deformation is obvious. According to the calculation principle of G-B method (Goodman and Bray 1976), the stability, sliding, and toppling criteria of single rock mass of anti-dip rock slope is established (Fig. 3). The bank slope is divided into shear deformation and toppling deformation zones by the stress characteristics of rock mass. The dolomitic limestone is mainly located in the shear deformation zone, and argillaceous limestone is located in the toppling deformation zone. After the completion of the reservoir, the water level on the slope is nearly 100 m higher than the original one. Slope deformations in the front and trailing edges of the slope have become more pronounced. Furthermore, tensile cracks can be observed in the trailing edge of the slope, indicating the slope may be under a dangerous condition.
Monitoring system of the slope 22 monitoring points were set to detect the shallow displacement of the slope, which are uniformly distributed. Herein, 17 monitoring points are deployed on the main slope body, and the other monitoring points were deployed outside the slope boundary. The monitoring period is from December 2011 to April 2020, and the slope is divided into five crosssections and three longitudinal planes, as shown in Fig. 4. Figure 5 shows that the slope is divided into seven portions, and the deformation and failure characteristics of each partition are, respectively, analyzed according to the deformation magnitudes obtained from the monitoring results. Herein, the deformation of the front part of the slope is significantly different from that of the back part. The deformation at the front part of the slope is the larger, and the shear deformation is mainly dominated, associated with the local collapses. Bending fracture mainly occurs in the central part of the slope. In addition, the trailing edge of the slope is generally flat, with some obvious tension cracks. The field investigation indicates that the investigated slope displays the dip direction of the strata being against the dip direction of the slope (i.e., reverse-dip slope) ( Table 1).
The seven deformation portions can only represent the deformation and failure characteristics of each portion of the bank slope simply, and so are more applicable for engineering practice. Therefore, we try to select the three most common geometric characteristics including elevation, slope, and aspect, and obtain different combinations of geological partitioning through factor superposition. This partitioning can be applied to all reverse-dip rock slopes, and the study of deformation evolution of geological and geometric partition under the effect of reservoir water can be more conveniently referred for other similar cases.

Geological and geometrical factors
The difference between the overall rock and soil mass of the bank slope is insignificant. The reason that the bank slope deforms into seven deformation zones, as reported in previous work (Xie et al. 2018(Xie et al. , 2020, is mainly because of the elevation, slope, aspect and other factors related. In the context of the traditional slope theory, the bottom of the slope is subjected to shear stress, and the top is subjected to  tensile stress, which indicates that the selection of elevation can reflect the stress state of rock and soil mass to a certain extent. In addition, the steepness of the slope can directly affect the local stability of the bank slope, and the different slope directions will form different joint combination cutting. Therefore, the elevation, slope and slope direction are commonly and easily obtained, and they are important factors that can affect the stability of the slope. Therefore, the geological partition of this paper is the further refinement and extension of the seven portions. According to the geological survey and monitoring results, the elevation, slope angle, and aspect were selected as the geometrical factors, by analyzing the geometrical characteristics of the slope using ArcGIS (Fig. 6). The elevation, slope angle, and aspect were classified into 10, 6, and 8 categories, respectively, using the Jenks natural break method (Chen et al. 2013). Table 1 presents the area for the each category. As can be indicated from Fig. 6 and Table 2, the slope is relatively steep (slope angle is generally larger than 41°) except for the trailing edge (the slope angle is in 0°-26°). The portion with angle in 63°-71° accounts for the largest area of the slope (2,8685 m 2 ). The gullies in the slope are developed, and the shape of the valley is V-shaped. The topography of the study area fluctuates. The area of the north aspect is the largest (4,0187 m 2 ), and the area of the north-west aspect is 2,0052 m 2 . In general, the north and north-west aspects dominate the study area.

Superposed characteristics
The elevation, slope, and aspect were reclassified and superimposed to obtain the partition map, based on the standards presented in Table 3. Consequently, the slope is divided into 118 zones by ArcGIS, with a total area of 9,6140 m 2 (Fig. 7). The portion with an area larger than 1500 m 2 in Fig. 8 accounts for 56% of the total area of the slope. From Fig. 7, it can be seen that the zone with the largest area is 312 (6202 m 2 ) (i.e., medium slope angle, low elevation, and north aspect zones).

Spatiotemporal nephogram of the displacement
Since the impoundment of Zhongliang Reservoir began in 2011, the reservoir level has risen by around 100 m (Fig. 2b). There were a number of tension cracks along the road, and a large collapsed area in the valley (Fig. 2c-f). The reservoir is in the stage of trial operation. Local deformation and failure occurred on the bank slope, and cracks can be observed on the rear edge. The reservoir was forced to stop water storage until the end of 2014. Monitoring data from 2014 to 2017 are considered. In the current work, the reservoir is numbered (Table 4). Considering the monitoring data of the superficial displacement, the inverse distance weighting (IDW) method was used to generate the spatiotemporal nephogram of the total displacement and that in the horizontal direction. The spatiotemporal evolution nephogram of the water level was also generated. Figure 9 shows the spatiotemporal nephogram of the horizontal displacement, which is divide into ten zones, using the natural breaks (Jenks) method (Chen et al. 2013). The zone with the horizontal displacement > 145 mm is defined as the zone with strong deformation. Figure 10 shows that the area with strong horizontal deformation decreases with the decrease of water level and vice versa. In the drawdown stage of the reservoir level, from 622 to 592 m, the topping deformation of the horizontal displacement moves to the front of the bank slope, and the area with strong deformation decreases gradually. When the reservoir level drops to 592 m, the area with strong deformation reaches a minimum of 1,8799 m 2 . When the reservoir water level rises, from 592 to 623 m, the topping deformation gradually extends from the front of the bank slope to the middle and from the point to the strip. Herein, the middle deformation is obvious, and the right side is larger than the left side. The maximum horizontal displacement occurs at the central axis of the front of the bank slope, and the area of strong deformation partition increases gradually. When the reservoir water level rises to 620 m, it reaches a maximum of 3,6480 m 2 . Figure 11 shows the spatiotemporal evolution of the vertical displacement, which is divide into ten zones, using the natural breaks (Jenks) method (Chen et al. 2013). The portion with the vertical displacement deformation > 85 mm is defined as the zone with strong deformation, which is mainly distributed in the front and rear edges of the slope. These zones gradually extend from the front and rear edges of the slope to the middle portion, and large tensile cracks can be observed on the rear edge. That indicates the rear edge mainly exhibits the vertical deformation. As shown in Fig. 12, in general, the area of strong deformation zone in vertical direction increases when the reservoir level changes. When the reservoir level is around 617 m, the zone with pronounced vertical displacement is the minimum (3,5059 m 2 ), and when the reservoir level rises to around 623 m, it reaches the maximum value (5,5684 m 2 ). Figure 13 shows the spatiotemporal evolution of the total displacement. The portion with the total displacement deformation > 171 mm is defined as the zone with strong deformation, which is mainly distributed in the front and middle parts of the slope. As shown in Fig. 14, the area with strong horizontal deformation total displacement decreases with the decrease of the reservoir level and vice versa. When the reservoir level is around 610 m, the zone with pronounced total displacement is the minimum (1,7492 m 2 ). On the other hand, when the reservoir water level rises to around 620 m, it reaches the maximum value (3,4481 m 2 ). It can be seen that the horizontal displacement deformation is larger than the vertical displacement, and the spatiotemporal evolution of the total displacement is similar to the horizontal one, which indicates that the slope deformation is mainly in the horizontal orientation.

Evolution of the superposed displacement in the horizontal direction
Considering the change of the reservoir level, the magnitude of the horizontal displacement is divided into three levels by the Jenks natural breaks method (Chen et al. 2013). Herein, the zone with displacement of 0-112 mm is the small deformation zone, which is represented by 1. The zone with displacement of 112-145 mm is the medium deformation zone, which is represented by 2. The zone with the displacement larger than 145 mm is the large deformation zone, which is represented by 3. Based on the geological and geometrical characteristic partitions (Fig. 7), the evolution of the superposed displacement in the horizontal direction was obtained by adding the value to the thousandth, as shown in Fig. 15.
Based on the results in Fig. 15, ignoring the impact of small areas on the results, the large deformation zone with an area greater than 1500 m 2 is defined as the zone with strong deformation of displacement superposition in the horizontal direction. The area with strong deformation and its proportion is obtained, as shown in Fig. 16. It can be seen that with the change of the reservoir level, the area of the zone with strong deformation of superposed displacement in the horizontal direction increases. When the reservoir level drops to around 622 m, the area of the strong deformation zone in the horizontal direction reaches the minimum (1,2146 m 2 ) and its proportion to the total area is 45%. On the other hand, when the reservoir level rises to 620 m, it reaches the maximum value of 2,5573 m 2 and the percentage is 57%.
The characteristic zone with the significant change of the superposed displacement in the horizontal direction greater than 15% was selected (Fig. 17). With the variation of the reservoir level, the characteristic zone with the largest area is the zone 312 (i.e., medium slope angle, low elevation, and north aspect zones). In general, the characteristic zone in the horizontal direction shows an increasing trend with the change of reservoir level. The characteristic zone with the largest area changing under different reservoir levels is defined as the prone zone of the superposed displacement, as shown in Fig. 18. When the reservoir level drops from around 617-610 m, the most prone characteristic zone with significant superposed displacement in the horizontal direction is 321 (the maximum area is 1084 m 2 ) (i.e., the middle-low slope angle, middle elevation, and north aspect zones).

Evolution of the superposed displacement in the vertical direction
Considering the change of the reservoir level, the magnitude of the vertical displacement is divided into three levels by the Jenks natural breaks method (Chen et al. 2013). Herein, the zone with displacement of -63 to 5 mm is the small deformation zone, which is represented by 1. The zone with displacement of −89 to − 63 mm is the medium deformation zone, which is represented by 2. The zone with the displacement of -141 to − 89 is the large deformation zone, which is represented by 3. Based on the geological and geometrical characteristic partitions (Fig. 7), the evolution of strong superposed displacement in the vertical direction was obtained by adding the value to the thousandth, as shown in Fig. 19.
Based on the results in Fig. 19, ignoring the impact of small areas on the results, the large deformation zone with an area greater than 1500 m 2 is defined as the strong deformation zone of displacement superposition in the vertical direction. The area of the zone with strong deformation and its proportion is obtained, as shown in Fig. 20. It can be seen that with the change of the reservoir water level, the area with significant superposed displacement in the vertical direction increases. When the reservoir level rises to around 620 m, the area with significant superposed displacement in the vertical direction reaches the maximum value (2,8720 m 2 ) and its proportion to the total area is 45%.
The characteristic zone with the significant change of the superposed displacement in the vertical direction greater than 15% was selected (Fig. 21). With the variation of reservoir level, the characteristic zone with the largest area is the zone 312 (i.e., medium slope angle, low elevation, and north aspect zones). In general, the characteristic zone in the vertical direction shows an increasing trend with the change of reservoir level. The zone with the largest area changing under different reservoir levels is defined as the prone zone of the superposed displacement, as shown in Fig. 22. When the reservoir level rises from 609 to 620 m, the most prone zone with significant superposed displacement in the vertical direction is 322 (the maximum area is 1497 m 2 ) (i.e., low slope angle, medium elevation, and north aspect zones).

Evolution of the total superposed displacement
Considering the change of the reservoir level, the magnitude of the total displacement is divided into three levels by the Jenks natural breaks method (Chen et al. 2013). Herein, the zone with displacement < 121 mm is the small deformation zone, which is represented by 1. The zone with displacement of 121-171 mm is the medium deformation zone, which is represented by 2. The zone with the displacement > 171 mm is the large deformation zone, which is represented by 3. Based on the geological and geometrical characteristic partitions (Fig. 7), the evolution of the total superposed displacement was obtained by adding the value to the thousandth, as shown in Fig. 23. Based on the results in Fig. 23, ignoring the impact of small areas on the results, the zone with an area greater than 1500 m 2 is defined as the strong deformed zone. Also, the characteristic zone with the change of superposed total displacement greater than 15% was selected (Fig. 24). With the variation of the reservoir level, the characteristic zone with the largest area is the zone 312 (i.e., medium slope angle, low elevation, and north aspect zones). In general, the characteristic zone with total superposed displacement shows an increasing trend with the change of reservoir level. The zone with the largest area changing with different reservoir levels is defined as the prone zone of the total superposed displacement, as shown in Fig. 25. When the reservoir level drops from around 622-617 m, the most prone zone of the total superposed displacement is 312 (the maximum area is 3713 m 2 ) (i.e., low slope angle, low elevation, and north aspect zones).

Conclusion
This paper studies the deformation and failure processes of the reverse-dip slope using actual monitoring data. It focuses on the real deformation evolution law of different geological partitions under different reservoir levels, providing an effective method for monitoring, early warning, and disaster prevention and mitigation of reverse-dip slope in the future. The proposed study is of great practical significance and engineering application value, making it a good reference for similar engineering cases of the reverse-dip slope. The main conclusions are as follows: 1. The geological geometric zoning of bank slope is obtained by superposition of elevation, slope, and aspect. In the studied case, the bank slope is divided into 118 characteristic areas. The geological and geometric characteristics of the largest geological zoning are bottom elevation, medium slope, and north aspect. 2. Through the analysis of the spatiotemporal evolution characteristics of the toppling displacement, the horizontal displacement deformation mainly distributes in the front and the middle of the bank slope. It gradually moves from the front to the middle, and gradually expands from a point to a strip. The vertical displacement deformation distributes in the front and back of the bank slope, and large tensile cracks exist at the back edge, indicating the back edge is dominated by the vertical deformation. The total displacement and horizontal displacement are similar, proving that the horizontal displacement dominates the toppling deformation of the bank slope. 3. The area of strong horizontal deformation changes with the increase of reservoir level. When the reservoir is underwater to the lowest point of 592 m, the area reaches the minimum. In contrast, when the reservoir level rises to 620 m, it reaches the maximum. On the other hand, the area with significant vertical displacement increases gradually as the reservoir level changes. When the reservoir water level rises to the highest point of 623 m, the area reaches the maximum. 4. Under the effect of the reservoir level, the area with significant superposed displacement increases with the variation of the reservoir level, and it reaches the maximum value when the reservoir level rises to around 620 m. The geological partition with the largest area of superposed displacement is distributed at the medium gradient, low elevation and north aspect zones. When the reservoir level drops from around 617-610 m, the most prone characteristic zone with significant superposed displacement is in the horizontal direction (i.e., middle-low slope angle, middle elevation, and north aspect zones). When the reservoir level rises from 609 to 620 m, the most prone zone with significant superposed displacement is in the vertical direction (i.e., low slope angle, medium elevation, and north aspect zones). When the reservoir level drops from around 622-617 m, the most prone zone of the total superposed displacement is related to the low slope angle, low elevation, and north aspect zone.