Influences of Hydrodynamic Force on Deep Relaxation Rockslide in Cold and Arid Areas of Langjia Reservoir in China

Landslides often happened in cold and arid relaxation rock slope area due to excavation or natural climate conditions, especially in the construction of water conservancy and hydropower projects. In the past, most scholars have been devoted to the study of relaxation rock engineering characteristics or relaxation mechanism [1–4], but detailed studies of relaxation rock mass slope failure mechanisms in cold and arid area are sparse, especially considering the hydrodynamic force. In the construction of water conservancy and hydropower station in Western China, the stability of relaxation rock slope was often encountered at dam foundation or bank slope of the reservoir area. Several studies showed that hydrodynamic force played an important role in the failure process of the landslide. De et al. discussed the influence of lift forces and water lubrication, caused by ambient water, on submarine landslide [5]. Cao et al. discussed the relation between the landslide dam failure and resulting floods [6]. Zhang et al. proposed that hydrodynamic pressure generated by rainfall was the main factor of Zheng-gang landslide in Gu-Shui hydropower station of China [7]. Wang and Qiao suggested that for the reservoir landslide, the landslide is more likely to occur in the water discharge period than in the water storage period [8]. Taking Qianjiangping landslide as an example, Wei et al. concluded that excess pore-water pressure, appeared at the bottom of the landslide, was the main factor leading to the failure [9]. Dal et al. investigated a gravel-bed reach in the middle valley of the Noce River in Basilicata (Italy); the results showed that study area suffered a progressive morphohydrodynamic change during different landslide stages [10]. Klimes et al. discussed the sensitivity of water saturation on moraine slope [11]. Dragomyretska et al. revealed that the failure process of the landslide along the coast was influenced by hydrodynamic force [12]. Huang et al. explored the influence of different permeability on hydrodynamic pressure landslide [13]. Chen et al. revealed that the triggering factor of Wulipo landslide occurred in China was the increment of hydrostatic and hydrodynamic pressure caused by heavy rainfall [14]. Sun et al. discussed the hydrodynamic pressure on sliding surface and analyzed the evolution of stability of reservoir slope under the influence of decreasing reservoir level [15]. Chen et al. revealed that hydrodynamics factors have different effects on landslide during different deformation stages of landslide [16]. Wang et al. succeed in using submarine landslide monitoring system to observe the submarine landslide process caused by storm [17]. Han et al. discussed the importance of constant head between groundwater level and reservoir water level on reservoir slope [18]. Osawa et al. discussed the influence of pore-water pressure on the stability of landslides in cold areas [19]. Hinds et al. discussed the impact of snowmelt infiltration on landslides [20]. Luo et al. found that when the water level of the reservoir was low, rainfall and the drop of groundwater level were both the reasons for the rapid movement of the landslide [21]. Li et al. discussed the influence of groundwater level variation on deformation of landslide [22]. Zhu et al. took 11 experiments to explore the failure mode and process of landslide dam, especially considering seepage effect on different textural properties [23]. Feng et al. discussed the influence of soil-water characteristic curve on different hydrodynamic condition landslide [24]. Based on artificial neural network, Zhang et al. proposed a modified transfer coefficient method to calculate the Shuping landslide; the results showed the hydrodynamic pressure was very important to the stability coefficient of bank slope [25]. Taking the Dahua landslide, located in southwest China, Li et al. analyzed the permeability characteristics and evolution in the unsaturated seepage process [26]. Wu et al. analyzed the influence of the runoff supply from upstream on a giant landslide occurred in Yanyuan, Southwest China, and emphasized that the supply was the main triggering factor of landslide [27]. Ge et al. proposed an improved limit equilibrium method considering hydrodynamic pressure; the results of example showed that compared with the traditional calculation method, the improved method was more in line with the reality [28]. Wang et al. summarized that hydrodynamic pressure was one of the most important factors affecting the landslide occurred in the Three Gorges Reservoir [29]. Due to the stress relaxation caused by the river incision process, a large amount of tension cracks would appear in the mountain on both banks of the river, which destroyed the integrity of rock mass and also accelerated the infiltration of rainfall [30]. For the failure of geological bodies, the influence of stress was important [31, 32], stress relaxation would increase the failure probability of landslide [33, 34], and relaxation tension cracks also played an important role in controlling the sliding of landslide [35, 36]. Hamel has proposed the slope excavation at foot removed lateral support, in turn initiating stress release and progressive failure that loosened or broke bedrock adjacent to the cut [37]. Shaller et al. discussed valley-dipping, and moderately to steeply inclined joint sets will reduce the stability of the steepened slope [38]; Dylan and Ward have found the function of slope stability with stratum spacing, dip angle, and incision rate [39]. However, former studies focus on the influence of the hydrodynamic pressure on landslide, and little attention has been paid to the change of sliding mode caused by hydrodynamic force, especially combined with relaxation tension cracks. The present paper attempted to take the Langjia landslide as an example to explore the influence of hydrodynamic force on the failure process and sliding mode change of the landslide with several relaxation cracks. Although the Langjia landslide had been studied before, the previous research mainly discussed partial field investigation result and did not discuss in detail the failure mode of the landslide combined with temperature difference and rainfall [40]. In this paper, we revealed the influence of temperature and rainfall on the weathering process of conglomerate rock mass under the condition of relaxation crack development, and we discussed the influence of gravel produced after weathering conglomerate rock mass on the change of the landslide sliding mode.

The Langjia landslide was located in cold and arid area of Qinghai Tibet Plateau, China. In this area, the speed of crustal uplift and river undercutting is fast, the relaxation of river bank slope rock mass is severe, the temperature difference between day and night is great, and the physical weathering is strong. According to the investigation of the sliding characteristics and the soil test of the landslide mass, the failure mechanism of the deep relaxation rock slope under the action of hydrodynamic force and particles rolling force in sliding surface were discussed in this paper.

The main objectives of the present research are as follows: (i) to reveal the mechanism of the hydrodynamics influence on deep relaxation slope stability in cold and arid region; (ii) to improve the stability analysis method of argillaceous conglomerate relaxation rock slope; and (iii) to explore the slope failure mechanism under weathering, intense infiltration along well-developed relaxation tension cracks, and shear stress along sliding surface. This study contributes to a more comprehensive understanding of the deep relaxation slope failure mechanism in cold and arid areas.

Langjia landslide was located in Tongren County, Huangnan State, Qinghai Province, China, about 20 km away from Tongren County (Figure 1). The landslide has occurred during Langjia reservoir project construction. The relative height difference of Langjia reservoir basin is 400-700 m. The rivers and main mountains extend northwest, with steep terrain and crisscross gullies. The mountains on both sides of the river valley are steep with a slope angle of about 50°. The highest elevation of both sides is 2750-2800 m, and the bottom elevation of the river is 2590 m-2610 m, which is caused by tectonic erosion and accumulation.

The main buildings of the reservoir include retaining dam, spillway, and diversion tunnel. The maximum dam height is 52.4 m, the average water level is 2644.3 m, and the corresponding total storage capacity is $458.27×104$ m³. On December 20, 2016, the construction of the Langjia reservoir project was officially started. In April 2019, the second stage of cofferdam foundation excavation work started. According to the excavation requirements of the dam foundation of Langjia reservoir, No. 2 slope and No. 3 slope on the left bank were excavated vertically 5 m high without any support below the elevation of 2600 m. On May 12, 2019, during the excavation of the dam foundation of Langjia reservoir, large-scale landslides occurred on the left bank 100 meters away from the dam axis. The landslide is at 102° 09$′$ 12$″$ E, 35° 34$′$ 53$″$ N, and overall sliding direction is about NE20°. It started at 5 : 00 p.m. and lasted for 15 minutes. The highest trailing edge of the landslide was 2799 m, the sliding vertical displacement was about 20 m, the front shear outlet was about 2.0 m~3.0 m below the excavation foundation pit of the riverbed diversion cofferdam, and the maximum height of the front uplift was 38 m. The height difference between the front and the back edge of the landslide was about 180 m; the volume of the landslide was about $320×104$ m³. It buried the construction machinery at the foot of the slope. The landslide accumulation filled the whole foundation pit of the dam, which leads to the suspension of most engineering construction and seriously affects the normal construction of the whole project. The landslide mass damaged two transmission lines of 35 kV and 10 kV. One communication line was interrupted.

In 2015, the reservoir engineering geological survey was carried out, and the engineering geological conditions of the reservoir bank slope are revealed. The field investigation area of the Langjia landslide covered a total area of 150000 m², and a 1 : 1000 scale geological map was drawn in the study area. The field investigation contained two stages: one stage was the field investigation before occurrence of the landslide, and the other stage was the field investigation after occurrence of the landslide. The two stages adopted the total station, handheld GPS and range finder, and drilling holes. The field investigation before landslide focused on the distribution of relaxation cracks and the lithology of the landslide. The field investigation after the landslide focused on the trace of the sliding surface, the depth of the sliding bed, and the development of surface cracks. The results of field investigation after occurrence of the landslide showed that the sliding soil was rich in high moisture, and the mirror image of shear friction and gravel rolling phenomenon were found along the sliding surface. The typical physical and mechanical tests related to sliding soil and sliding body shall be sent to the indoor laboratory for testing by means of on-site sampling.

Before the landslide, the riverbed elevation is about 2600 m, the mountain top elevation is 2750-2800 m, and the height difference is about 200 m. The natural slope is gentle on the top and steep on the bottom. The upper slope is about 20°, and the lower slope is about 50°~70°. The front edge is nearly vertical locally, which provides favourable topographic conditions for slope deformation. The dam construction changed the terrain conditions in front of the slope (Figure 2).

The bedrock strata in the slope area are mainly the thick layer conglomerates of Cretaceous Hekou Formation (k₁^hk) in purplish-red and the loose deposits of the quaternary system.

• (1)

  Cretaceous Hekou Formation (k₁^hk). It is mainly purplish-red, dark purplish-red thick layered conglomerate, pebbly sandstone with argillaceous siltstone, argillaceous interlayer, and thin mudstone. The conglomerate is mainly argillaceous cementation with ferromanganese cementation characteristics, which is a set of inland lacustrine sedimentary strata. The joint of the rock mass is well developed, and it is easy to be weathered and softened and disintegrated in case of water. The slightly weathered conglomerate has low saturated compressive strength, belongs to soft rock and low softening coefficient.

• (2)

  Loose Deposits of the Upper Pleistocene. The deposits of the upper Pleistocene include aeolian loess (Q₃^eol) and alluvial proluvial pebble layer (Q₃^alp),; the former is mainly distributed in strips and flakes on the top of the lower ridge on both sides, and the thickness of the left bank is generally 1-3 m.

• (3)

  Quaternary Holocene Loose Deposits. There are many types of deposits in Holocene in the area, mainly including alluvial proluvial gravel (Q₄^alp), proluvial gravel (gravel) soil (Q₄^pl), colluvial gravel soil (Q4col+dl), and landslide accumulation (Q₄^del).

The argillaceous interlayer is found on the surface and in the core of the borehole. It is distributed along with the layer. The shale interlayer and thin mudstone developed in the rock layer are also the control boundary of the upper and middle part of the upstream boundary of the landslide. The rock mass slides along the interface between the conglomerate and thin mudstone or the shale interlayer.

The relaxation fractures were well developed in the slope (Figure 3), and the strike mainly extends along with NW and NE directions, mostly with steep dip angle, functional connectivity, distinct opening form, and broad width, and it is filled with rock debris or debris. According to statistics, the development width of the relaxation tension cracks was generally 0.1-1.5 m (Figure 3(a)), the maximum visible depth was generally 0.25-20 m, and the extension length was 0.9-50 m. The relaxation shear joint generally distributed at the bank slope surface (Figure 3(b)). According to the drilling hole ZK15-7 before dam construction, relaxation cracks of rock mass were found at the positions of 18.2-19.6 m and 40.0-44.5 m depth, of which 18.2-19.6 m section has a substantial development width and a long extension. Besides, a substantial relaxation fracture was found in the mountain. The maximum width of the tension crack was about 1.5 m (Figure 3(c)), the opening was 30-40 cm, the extension was more significant than 10 m, and the relaxation depth was tens of meters, which was developed in a steep angle. The relaxation fractures were found about 350 m horizontally from the Langjia river bank.

Groundwater in the landslide area is divided into bedrock fissure water and pore water of Quaternary overburden. The atmospheric precipitation supplies the bedrock fissure water and mainly exists in the bedrock fissure and weathered layer. The pore water in the Quaternary overburden mainly exists in the gravel pebble layer of the river valley floodplain and terrace.

After the landslide occurred, the engineering geological survey of landslide mass was further carried out. Six boreholes were arranged on the landslide body after sliding, and the material composition and structural characteristics of the landslide mass were determined by in situ investigation. The landslide was in the form of “long strip” on the plane, which was narrow in the upper part and wide at the lower part. The shear outlet of the landslide is located at the excavation position of the foundation pit of the modern Langjia riverbed, with an elevation of about 2597 m. Figure 4 shows the overall view of the landslide. It is a large-scale relaxation rockslide. The low elevation part of the upstream boundary was developed along the upstream gully channel, then passed through the No. 3 slope obliquely upward, and extended to the elevation of 2800 m at the back edge. There are geese shaped shear cracks and sliding scratches along the boundary (Figure 4(a)). Tension cracks were well developed at trailing edge. There are long pull-out grooves at the back edge of the main landslide (Figures 4(b) and 4(c)). The shear outlet at the front edge of the landslide is located at the excavation foundation pit of the river channel, with an elevation of about 2600 m. The foundation pit has been buried by landslide deposits, with an accumulative thickness of about 20 meters (Figures 4(d) and 4(e)). The overall sliding direction is about NE20°. There are many relaxation cracks distributed in the middle and upper part of the downstream area, making the landslide mass disintegration (Figures 4(f) and 4(g)).

The material composition of the landslide mass is composed of gravelly soil or original rock blocks with different degrees of disintegration. A small amount of aeolian loess was found at the rear edge of the landslide. The thickness of the accumulated landslide mass at the original riverbed foundation pit of the shear outlet is more than 20 m. The original No. 3 slope at the upstream of the landslide is relatively seriously disintegrated after sliding. The overall thickness of the sliding body is between 20 m and 35 m. The landslide bed is mainly Cretaceous Hekou Formation (k₁^hk) conglomerate. The exploration shows that the conglomerate in the lower part of the sliding bed, especially the front of the landslide near the river valley, is relatively broken, with poor integrity. The muddy intercalation in the conglomerate relatively developed with 3 cm~10 cm thickness. The material composition of the sliding zone is composed of mud mixed with debris, which is uneven in thickness, thin in a mud film shape, and 5 cm~10 cm in thickness. The sliding surface is smooth and scratched. The soil in the sliding zone has high water content and plastic state. Based on the comprehensive drilling and geophysical exploration, the characteristics of the landslide profiles are shown in Figure 5.

The surface of the landslide is subject to tension, shear cracks, and collapse zones. The surface of the landslide body was broken in the sliding process. The local tension and collapse depth of the middle and rear parts is about 2 m-5 m, and the deepest part is up to 15 m-20 m. The extension length of some tension cracks is about 80 m, and the visible depth of tension cracks is more than 20 m.

According to the topography, landslide boundary, disintegration during sliding, and distribution of deformation tension cracks, the landslides can be divided into main sliding area and traction area. The main sliding area is located in the middle and lower part of the landslide, with the main sliding direction of 20° including the No. 2 slope position at the downstream side of the main sliding area, with a plane area of about 0.047 km², and the No. 3 slope area on the upper side of the main sliding area, with 0.025 km². The overall disintegration of the landslide mass is severe, and the surface is broken. The traction area was located at the back edge of the landslide, with an elevation of 2730-2800 m and a “Crescent” shape on the plane. The “saddle” terrain between the No. 2 slope and the No. 3 slope top is controlled by the sliding traction of the front edge and the free terrain of the two ridges, which makes the slopes on both sides of the “saddle” between the upper and lower ridges of the rear edge slid.

In order to study the sliding mechanism of the landslide mass, the improved Sarma’s method of slope stability analysis named limit analysis energy method was carried out for the external load during sliding and sliding starting. The program developed by authors obtains the critical slip surface and the corresponding strip inclination through optimization calculation. According to the geological structural conditions of the slope rock mass, the dip angle of the slice side simulates a group of steep dip relaxation fissures. The interface of the inclined slices represents the relaxation joints. The multiblock failure mechanism is adopted for the treatment of the sliding surface. A slip surface of any shape can be composed of straight lines or smooth curves connecting a series of points. The two adjacent points can be connected by a curve or a straight line to form a slip surface of any shape. In the calculation, the program will automatically subdivide the soil (rock) body (or block) between two adjacent nodes into several pieces. Meanwhile, the pore-water pressure, hydrodynamic pressure, and hydrostatic pressure in relaxation tension cracks were considered in the program.

During the calculation, the stability was considered firstly before and after foundation pit excavation and then considered the hydrostatic pressure in the relaxation tension cracks at the rear edge; the shear stress at the bottom of turbulent flow and rolling friction force were taken into account in the process of groundwater seepage after foundation pit excavation of dam cofferdam.

In this paper, the above calculation formula was substituted into the improved Sarma’s method.

FLAC3D is widely used in the study of wading landslide because of its convenient calculation and corresponding seepage module [41, 42]. In this paper, three-dimensional finite difference numerical simulation method was used to analyze the deformation of unloaded rock slope under hydrodynamic action. The FLAC3D software was used to calculate the three-dimensional numerical model of landslide based on flu-solid coupling model. Using the measured geological map data, taking the NE direction as the $x$-axis, the NW direction as the $y$-axis, and the vertical direction as the $z$-axis, two three-dimensional calculation models of slope 2 and slope 3 were established. The vertical coordinates adopted the actual elevation coordinates. The bottom boundary of the model was fixed in all three directions (⁠$x$⁠, $y$⁠, and $z$ directions). The two side boundaries in directions of the $y$-axis were fixed with the displacement in the $y$ direction, and the two side boundaries in directions of the $x$-axis were fixed with the displacement in the $y$ direction. In the fluid-solid coupling analysis, rock and soil were regarded as porous media, and the fluid flow in porous media met both the Fourier–Biot equation and Darcy’s law. During the analysis, the seepage field generated by the seepage module and the initial stress field generated by the stress module were combined for flu-solid coupling analysis.

Two groups of relaxation cracks were developed on the slope; one group is the relaxation shear joints with a slow angle, which is close to the bottom of the slope, and this group of cracks generally formed the sliding surface (Figure 4) of the landslide mass. The other group is relaxation tension cracks with a steep angle, which formed the cutting surface (Figure 4) of the back edge of the landslide mass. In the No. 2 and No. 3 slopes of the landslide area, there are a large number of dense relaxation cracks with different extension length and tensile crack depth. The relaxation fracture, which the trend is nearly perpendicular to the bank slope dip direction, has a development frequency of about 3-5 m. These relaxation fractures not only destroy the integrity of the rock mass but also provide the conditions for the rainfall to infiltrate into the slope directly and supply the groundwater.

Langjia landslide is located in the Qinghai Tibet Plateau. It belongs to the alpine region, the temperature of Tongren County was below zero for 5 months in a year (Figure 7), the coldest month’s average temperature is -7.3°C, the extreme minimum temperature is -23.0°C on December 14, 1975, and the extreme maximum temperature over the years is 35.0°C on July 24 and 25, 2000. Due to the difference of permeability, the under groundwater accumulated between the conglomerate and mudstone/shale interlayer during the slow seepage process, and the groundwater cannot drain into the river valley natural. Furthermore, the freeze–thaw effect of the landslide area was powerful; the water in the slope mass could form ice deeper in winter. With the groundwater goes deep often freezing in winter and the melting of ice in spring, the volume expansion during the freezing process, it loosened the rock mass structure of the slope. From April 2019, the ice in the rock mass began to melt. The disintegration of the rock mass further weakened its strength, lubricated the conglomerate cement, and leads to the slope failure occurred. The freeze–thaw cycle of the water filled in the cracks would have reduced the shear strength near the cracks further.

According to the rainfall data of Tongren Meteorological Bureau in 2018 and 2019, the cumulative rainfall from July to September in 2018 is 459.5 mm, which is much larger than the average annual rainfall in the region over the years. Meanwhile, the rainfall in the region has increased since April 2019, including 20.5 mm in April and 30.7 mm in the first ten days of May, which is also significantly higher than that of previous years (Figure 8). The landslide sliding does not occur at the end of September 2018 in the winter immediately, but it slides after 7 months in the spring season.

By the end of April, a large amount of ice enriched in the relaxation rock mass of the slope began to melt. Due to the relaxation of the conglomerate rock mass, wind, temperature, precipitation, and other factors acted on the upper slope along the deep relaxation fracture, accelerating the weathering of argillaceous cement in the rock mass and accumulating a certain amount of water pressure at the bottom of the fracture. After the excavation of the foundation pit at the foot of the slope revealed the seepage channel, seepage occurred. Because the gravel after the weathering and disintegration of the conglomerate produced turbulence in the seepage process, the bottom boundary layer of the contact surface between the conglomerate and the mudstone formed bottom shear stress [3], which increased the sliding force and induced the sliding failure of the slope.

The sliding zone soil sample tests show that the water content of the soil in the sliding zone was significantly higher than the water content in the shallow part of the landslide body. The particle composition test of the slip zone indicates the content of sand particles of 2~0.075 mm accounts for 31.87%~41.81%, and the content of gravel particles larger than 2 mm accounts for 10.65%. The content of particles larger than 2 mm accounts for 82.61-86.94% for landslide accumulation. Moreover, there are mirror and gravel rolling phenomena of shear friction distributed along the sliding surface. It means the water pressure acts on the slope rock mass and forms a mesocircular shear stress around the gravel. The field exploration indicated that the shear and rolling process occurs in the sliding zone; the gravel has a specific rotation effect. Due to the high content of gravel in the landslide mass (Figure 9), under the action of groundwater seepage, the rolling friction of gravel occurs in the sliding zone, which is combined with the sliding friction to accelerate the sliding of the slope mass.

The road construction and foundation pit excavation in the front of the slope exposed the sliding surface and unloaded the rock mass at the toe of the slope, and the free face was formed by the slope excavation. It also increased the way of groundwater flow, changed the balance state of the initial slope, and led to the deterioration of the slope stability and the occurrence of landslides.

The analysis of slope failure mechanism is an important aspect of evaluating landslide disaster and selecting treatment measures. In order to analyze the mechanism of the slope sliding and the factors affecting the occurrence of the landslide, the improved Sarma’s method and numerical simulation method were used. Physical and mechanical parameters of rock and soil mass of slope are listed in Table 1.

(1) Regardless of Relaxation Fissure Water Pressure. Two sections of No. 2 slope on the left bank were selected to calculate the stability, which in accordance with the maximum direction of sliding potential energy. The critical and most dangerous sliding surface is automatically searched out by improved Sarma’s method. The stability coefficient of each section under different working conditions is obtained by using corresponding calculation parameters (Table 2).

In the stability calculation of No. 2 slope, the hydraulic affection on relaxation fissures was not considered, but the pore-water pressure was adopted under different working conditions, which is shown in Table 2. The stability coefficient of the two sections of the slope is 1.164 for section 3-3 and 1.112 for section D-D, indicating that the stability of the slope cannot meet the safety requirements. The calculated minimum stability coefficient slip surface is shown in Figures 10(a) and 10(b).

Two sections of No. 3 slope were also selected to calculate the stability according to the maximum potential energy direction. The critical and most dangerous sliding surface is automatically searched out under different working conditions. In the stability calculation of No. 3 slope, the pore-water pressure coefficient adopted under different working conditions is shown in Table 2. The stability coefficient of two sections of the slope was 1.152 for section E-E and 1.203 for section F-F under rainstorm conditions. The calculated minimum stability coefficient slip surface is shown in Figures 10(c) and 10(d).

(2) Stability Analysis on considering Only the Relaxation Tension Crack when It Is Full Filled with Water. In order to analyze the stability of the slope on considering the tension fracture at the back edge filled with water, the typical section D-D of No. 2 slope was selected to calculate the stability by using limit equilibrium method. The depth of the tension fracture was considered to be 20 m downwards, and the calculation results are shown in Figures 11(a) and 11(b).

The stability factor of No. 2 slope is 1.567 without water filling, but the stability coefficient is only 1.078 when the fracture is considered fully filled with water. It can be seen that the range of potential landslide mass when considering relaxation tension crack water filling is much larger than that not considering water filling, which indicates that the cracks and hydrodynamic action have a significant impact on slope stability. It shows that the water filling of the tension crack is one of the main factors of the slope instability.

(3) Stability Analysis on considering Hydrodynamic Effects on the Slope. In order to analyze the hydrodynamic force and slope toe excavation effects on relaxation rock slope stability, the bottom shear stress and rolling friction along sliding surface on slope stability were considered in slope stability analysis. The calculation results are listed in Table 3. Before dam foundation excavation, considering the three forces of relaxation tension crack water pressure, bottom shear stress, and seepage force, the stability coefficients of No. 2 slope and No. 3 slope are 1.023~1.048, which are in limit equilibrium state. When only considered the relaxation cracks are fully filled with water and the pore-water pressure as calculation condition, the overall stability factors of No. 2 slope and No. 3 slope are only reduced 0.03 after the foundation pit at the slope toe is excavated for 5 m. When the rolling friction and bottom shear strength are further considered, the stability coefficient decreases to 0.958~0.976, indicating that the bottom shear strength and rolling friction have a significant impact on the stability of argillaceous conglomerate relaxation slope. After the excavation of the dam foundation at the front edge of the slope, considering the three forces of tension crack water pressure, bottom shear stress, and seepage force, the stability coefficient of No. 2 slope and No. 3 slope decreases to 0.947~0.963, which are in an unstable state. When the rolling friction is further considered, the stability coefficient is reduced to 0.90 and the slope is in failure state. The calculated results are in good agreement with the actual situation. Bottom shear stress and rolling friction are the key factors causing landslide of relaxation argillaceous conglomerate slope.

Finite difference method (FLAC3D5.0 software) is used for numerical simulation, and two calculation conditions of natural and rainstorm state are considered. Under the condition of rainstorm condition, the effects of seepage along cracks and pore-water pressure on slope stress, strain, and plastic zone are considered. Calculation parameters are listed in Table 1.

(1) No. 2 Slope Numerical Simulation Results. The model takes the NW direction as the $z$-axis, the NE direction as the $x$-axis, and the vertical direction as the $y$-axis. The vertical coordinate adopts the actual elevation coordinate to establish the Cartesian coordinate system. The bottom elevation of the model is 2525 m, and the top elevation is 2721 m. The length of the slope along the strike direction is 96 m, and the length along the dip direction is 196 m. The model is divided into four layers from bottom to top, which are slightly weathered rock mass, moderately weathered rock mass, highly weathered rock mass, and residual deluvial deposits on the slope surface. There are 19098 units and 4114 nodes in the No. 2 slope model.

The results show that the maximum principal stress and the minimum principal stress of No. 2 slope are distributed in layers under the natural condition and rainstorm condition, and the stress concentration occurs at the toe of the slope. The maximum principal stress value of the slope is 4.0 MPa natural condition and 4.3 MPa at rainstorm condition (Figure 12(a)). The direction points to the toe of the slope. The plastic area is mainly concentrated in the shallow surface layer, with the depth range of 10 m-15 m (Figure 12(b)). Under the rainstorm condition, the whole stability coefficient $FS$ of No. 2 slope is 1.15. According to the shear strain distribution map (Figure 12(c)), the slope is unstable from 2604 m to 2680 m. As can be seen in Figure 13(d), at the $x=35$ m section, the plastic through area is located in the middle of the slope, with the possibility of sliding.

(2) No. 3 Slope Numerical Simulation Results. The model takes the NW direction as the $z$-axis, the NE direction as the $x$-axis, and the vertical direction as the $y$-axis. The vertical coordinate adopts the actual elevation coordinate to establish the Cartesian coordinate system. The bottom elevation of the model is 2500 m, and the top elevation is 2735 m. The length of the slope along the strike direction is 135 m, and the length along the dip slope is 258 m. The model is divided into four groups from bottom to top, which are slightly weathered rock mass, moderately weathered rock mass, highly weathered rock mass, and residual deluvial deposits on the slope surface. There are 19254 units and 4194 nodes in model slope No. 3.

Under the natural state, the maximum and minimum principal stresses of No. 3 slope are distributed in layers. The maximum principal stress value of the slope is 5.5 MPa. The plastic areas are mainly concentrated in the shallow surface, with a depth range of 15 m-20 m. Under the rainstorm condition, the maximum principal stress value of the slope is 5.6 MPa. The plastic area is mainly concentrated in the depth range of 15 m-25 m (Figure 13(a)).

By using the strength reduction method, the whole stability coefficient $FS$ of No. 3 slope under natural state is 1.19. According to the shear strain distribution under the rainstorm condition (Figure 13(b)), the area from 2604 m to 2685 m, which the relaxation cracks well developed, is in danger of instability. It shows that the plastic area at model section $x=40$ m is distributed from 2604 m to 2685 m, i.e., between the slope toe and the back edge tension crack of the landslide, and the sliding surface is located in the strong weathering zone. The whole stability coefficient $FS$ of No.3 slope is 1.13 at the rainstorm condition. At the $x=40$ m section, the plastic area is located in the middle of the slope, mainly concentrated between the toe of the slope and the tension crack at the back edge. The vertical displacement at the steep area is large, and the maximum displacement is 8 m (Figure 13(c)).

Based on field investigation and calculation results, the deformation and failure process of relaxation rock slope in the cold and arid area can be described as the next three stages.

The first stage: with the river undercutting, the stress in front of the slope is released, resulting in local tension and relaxation cracks. During the river undercutting process, the front edge of the slope was partially removed, forming a steep front slope; furthermore, tension and relaxation cracks formed in the upper part of the slope (Figures 14(a) and 14(b)).

The second stage: due to the atmospheric precipitation, the relaxation cracks along the top of the slope are seeping. At the same time, the water in slope was affected by freezing and thawing under temperature difference between day and night or seasons, the plateau illumination accelerates the physical weathering of the slope along the relaxation cracks, especially for the disintegrated rock mass, and the slope gradually weathered and partially disintegrated (Figure 14(c)).

The third stage: the stress at the slope toe released rapidly under excavation or downcutting of river valley, and the relaxation tension crack in the slope rock mass developed rapidly, which provides the conditions for rainfall infiltration. At the same time, the discharge port of the leakage channel in the slope body exposed, increased the way of groundwater flow, so that the bottom shear stress along the seepage path was formed in the slope body. In this bottom shear stress zone, the weathered and disintegrated gravel moves along the water seepage direction, and rolling friction and sliding friction had produced, which makes the slope slide (Figure 14(d)).

The stability of the landslide mass seriously affects the safe construction of the project. In order to select treatment methods, it is necessary to evaluate the stability of Langjia landslide. According to a large number of test results, combined with the physical and mechanical parameters of rock mass recommended by Qinghai Water Resources and Hydroelectric Investigation & Design Institute, the physical and mechanical parameters of rock mass and landslide body are shown in Table 4.

In view of the disintegration of most landslide accumulation, the sliding surface may be considered as circular arc shape, and the simplified Bishop method and Morgenstern Price method should be used for calculating the stability of the landslide accumulation. The stability analysis and calculation were carried out with the Slide 6.0 Software compiled by Rocscience Company of Canada. The calculation results of the current slope stability of No. 2 and No. 3 slopes are illustrated in Table 5 and Figure 15.

From the calculation results, no matter the specified sliding surface or the automatic search sliding surface calculation, the minimum safety factor does not meet the specification requirements under various application conditions, and the landslide body is in an unstable state, so engineering government methods should be taken to deal with it. Since the downstream boundary of the front edge of the landslide body is close to the dam axis at the downstream, once the landslide deposit is damaged, it will directly affect the safety of the pivotal project. The excavation load reduction measures, slope protection measures, random anchor piles, water interception, and drainage facilities should be considered for treatment the landslide.

The deep relaxation rock mass landslide in cold and arid areas is mainly due to the development of relaxation cracks, particularly hydrodynamic action in super precipitation on the slope, temperature difference, and excavation in front of the slope. The research results are as follows:

• (1)

  The deep relaxation cracks have the effect of accelerating the deep rock mass weathering in the cold and dry areas obviously, which leads to the increase of permeability of rock mass and forming the instability condition of the landslide

• (2)

  Under the influence of rainfall, snow melting infiltration, and atmospheric temperature difference in the deep relaxation cracks, the conglomerate cement disintegrates, the hydration film around the gravel thickens, and the mechanical strength of the rock mass decreases. The sliding surface lies at the interface between conglomerate and mudstone gradually formed. After rainfall and snowmelt infiltration, the bottom shear stress of the turbulent boundary layer and rolling friction formed in the contact zone to accelerate the slope failure

• (3)

  The failure process of deep relaxation slope can be divided into three stages: the first is relaxation cracks formed under rapid undercutting of river valley and stress released; the second is the slope rock mass gradually weathered and partially disintegrated through relaxation cracks under temperature difference affection; the third is the discharge port of the seepage path in the slope body exposed and lateral support removed under excavation or river undercutting. The calculation results of three-dimensional numerical simulation and improved Sarma’s method on considering the hydrodynamic action on relaxation slope stability are consistent with the actual situation

• (4)

  In order to determine the treatment scheme of landslide mass, the stability of landslide accumulation mass was analyzed by limit equilibrium theory. The calculation shows that the minimum safety factor does not meet the specification requirements under various application conditions, and the landslide body is in an unstable state. Corresponding treatment measures should be taken for reinforcement

The data used to support the findings of this study were supplied by Wansheng Ling under license and so cannot be made freely available. Requests for access to these data should be made to [Wansheng Ling, lws603@126.com].

The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

This work was supported by the National Natural Science Foundation of China (Grant No. 51909074 and 52104125), China Postdoctoral Science Foundation (Grant No. 2019M661713), the open fund of the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology (grant number LP2105), and Key Laboratory of Coastal Disaster and Defence of Ministry of Education, Hohai University (Grant No. 201912).