An improved transfer coefficient method considering the combined effect of reservoir level variation and rainfall and its application in the stability evaluation of multistage sliding ancient landslides

With the water storage operation in the Three Gorges, Xiaowan, Baihetan, and other hydropower projects, affected by climate change and reservoir water level periodic fluctuation, the runoff will increase, and the erosion of ancient landslides will revive. The ancient landslide often shows the form of multistage sliding (Xu & Ma 1979; Shahid et al. 2018; Wang et al. 2020; Wen et al. 2022; Xu 2022). Multistage landslides usually refer to the same sliding pattern, repeated shows many times. The common instability process of multistage sliding is as follows: leading edge unloading induces the trailing edge to produce tractive multistage tension (Ren 2020; Guo et al. 2021; Jiang et al. 2022). In the reservoir area of a hydropower station, it is difficult to make a rapid and accurate evaluation of the ancient landslides' multistage sliding mechanism and stability due to the combined influence of reservoir water level variation, bank slope erosion, and rainfall (Haeri et al. 2021; Tong et al. 2021; Yang et al. 2022). Therefore, it is of great practical engineering significance to accurately evaluate the stability of multistage sliding ancient landslides under the combined effect of reservoir level variation and rainfall. An improved transfer coefficient method is necessary by considering the dynamic water pressure and particle migration effect caused by reservoir level variation, the weakening effect of slip zone soil influenced by rainfall infiltration, and the interaction force between multistage sliding bodies.

The main stability analysis methods of multistage sliding ancient landslides are as follows: (1) using numerical simulation software combined with strength reduction method to search the potential sliding surface of multistage landslides, respectively, and using the limit equilibrium method to calculate the stability (Xiao et al. 2013; Song et al. 2019). (2) Based on nonlinear theory, the Monte Carlo method and other statistical and probability theory methods were used to analyze the reliability of multistage landslides (He et al. 2011). (3) The limit equilibrium analysis method, based on the principle of static equilibrium, analyzes the stress state of a multistage landslide under different failure modes and determines the multistage landslide stability by analyzing the ratio relationship between landslide anti-sliding force and sliding force. Among them, the transfer coefficient method is a widely used limit equilibrium analysis method, which has the advantages of simple calculation principles and intuitive calculation processes (Tan et al. 2015; Pacheco et al. 2023; Zhao et al. 2023).

However, the current research shows that when the traditional transfer coefficient method is used to calculate the stability of ancient landslide under the multistage sliding mode, the influence of factors such as the combined effect of reservoir level variation and rainfall, complex sliding mode, and the difference of sliding zone soil parameters is not taken into account, the stability coefficient calculated results is often too large, resulting in insufficient design safety reserve of the retaining project (Wang et al. 2022; Xue et al. 2023; Yang et al. 2023). Many scholars have conducted improved studies on the transfer coefficient method, mainly focusing on (1) improving the transfer coefficient method based on the migration effect of slipping soil particles caused by seepage under dynamic water conditions (Ren 2020). (2) Improving the transfer coefficient method by considering the interaction force of sliding bodies and the different sliding surface dip angles at the bottom of sliding bodies (He & Zhao 2010). (3) Improving the landslide sliding force calculation formula by considering the interaction force of sliding bodies under the multistage sliding mode (Tan et al. 2016; Sarada & Tariq 2020). In summary, although many scholars have explored the transfer coefficient method for calculating the stability of ancient landslides and have achieved good results, most of them only consider the influence of single factors such as rainfall, earthquake, or reservoir water level change. It is still rare to study the transfer coefficient method of multistage sliding ancient landslide stability under the combined action of multiple factors such as rainfall and reservoir water level (Xu & Wang 1980; Chen et al. 2020; Li et al. 2022; Wu et al. 2022).

Therefore, the uniqueness of this manuscript compared with other literature is that the traditional transfer coefficient method is improved under the condition of reservoir level variation, the particle migration effect of the sliding body, the action of dynamic water pressure, the sliding zone soil parameter value obtained in the multistage sliding body progressive failure during rainfall infiltration, and the influence of the interaction between multistage sliding bodies. The research results are expected to provide a new reference for the stability accurate evaluation of multistage sliding ancient landslides under the combined action of reservoir level variation and rainfall in hydropower stations. The structure of this manuscript is arranged as follows: (1) the effect of particle migration caused by reservoir water level variation on landslide stability; the influence of dynamic water pressure caused by reservoir water level fluctuation on landslide stability; (2) an improved transfer coefficient method considering the combined effect of reservoir water level variation and rainfall is proposed; (3) calculation cases; the improved transfer coefficient method is compared with the traditional method.

Stability coefficient is calculated by the traditional transfer coefficient method.

With the study result of Zhang (2019), which considers the influence of hydrodynamic pressure on the calculation of the bank slope stability coefficient, the calculation of the ancient landslide stability coefficient under reservoir level variation is analyzed as follows. The dynamic water pressure is caused by the small infiltration coefficient of the sliding body and the dissipation of pore water pressure in the sliding body inner behind the decrease of osmotic force under the reservoir water level variation conditions. When the water level in the sliding body inner decreases simultaneously with the reservoir water level, the sliding body is affected by the stable osmotic force (Figure 2(b)). At the time t, when the reservoir water level rises and drops rapidly, after the pore water pressure dissipation in the sliding body inner, the seepage pressure is ⁠.

When the reservoir water level drops rapidly, compared with the water level in the i strip when the reservoir water level is synchronized, a water level difference will be formed, and resulting in a dynamic water pressure ⁠. The dynamic water pressure is the vector difference between the osmotic force when the reservoir water level drops and the stable osmotic force when the strip water level and the reservoir water level decrease synchronously, that is: ⁠.

The transfer coefficient formula is the same as that of Equation (8). By substituting Equations (16)–(18) into the inter-strip force Equation (8), the stability coefficient calculation formula of the ancient landslide saturated part under the condition of dynamic water pressure effects can be derived by making ⁠.

By substituting the improved sliding force and anti-sliding force into Equation (9), the stability coefficient of ancient landslides affected by particle migration can be obtained.

Under the combined action of reservoir level variation and rainfall, the erosion effect of the ancient landslide front caused by the reservoir water level repeated rise and fall. And a multistage sliding phenomenon occurs (Song et al. 2019; Dolojan et al. 2023). Multistage tension cracks appear on the surface of the ancient landslide, which provide a preferential migration passage for rainwater to accelerate the landslide infiltration (Yi et al. 2023). At the same time, with the tension crack as the dividing line, the original landslide body is divided into multistage slide bodies, forming an obviously step placement (Sepe et al. 2023).

When the rainfall intensity exceeds the infiltration capacity of the slope soil, the landslide soil surface will generate surface runoff. And the surface of the ancient landslide will reach a saturated state soon. Under the action of surface runoff, the cracks on the landslide surface develop rapidly and cause rainwater to quickly enter into the landslide inner. Due to the erosion effect of surface runoff, the landslide shape and structure will change, and the influence of reservoir water level rising and falling repeatedly will eventually cause the landslide body to produce multistage instability failure.

Along with the rainfall infiltration and the repeated rise and fall of reservoir water level, the region passed by the infiltration front and infiltration surface will reach the saturation state quickly. The mechanical parameters of the landslide body decrease rapidly and the stability coefficient decreases continuously. One of the key factors determining the multistage sliding ancient landslides instability is the sliding zone soil mechanical parameters (Liao et al. 2023). When the infiltration front and the infiltration surface reach the slip surface, the slip zone soil's physical and mechanical parameters will plummet in a short time. In this paper, it is considered that multistage sliding failure occurs when the infiltration front and the infiltration surface reach the sliding surface, and the parameters of the landslide are all saturated.

Under the combined influence of reservoir level fluctuations and rainfall, the progressive failure process of ancient landslides in multiple stages is observed, with the soil mechanical properties within the slip zone gradually deteriorating (Liu et al. 2023). The soil strength parameters of the slip zone undergo a sequence of stages, including pre-peak stress, softening stress, and residual stress (Dou et al. 2023; Zhang et al. 2023a). In this study, when a tensile failure occurs at the upper portion of the multistage sliding body and shear failure transpires at the base of the slope, it is considered that the soil strength parameters within the sliding zone represent residual strength. Conversely, if the sliding surface of the ancient landslide is not connected and no apparent damage is observed in the middle section, the soil strength parameters within the sliding zone can be interpreted as peak stress. Throughout the multistage sliding process of ancient landslides, the downward extension of tensile failure from the slope's top synchronously develops with the upward extension of shear failure from the foot of the slope (Wang et al. 2023; Zhang et al. 2023b).

In the progressive failure process, the single sliding body is divided into three regions: Region 1, located at the upper left of the sliding body, is the tension failure zone, where the development of tension cracks causes the sliding body to break, and shear slide occurs along the fracture plane. Due to the occurrence of macroscopic fracture, the strength parameter of the sliding body in this region is considered to be zero. Region 2: located in the middle of the sliding body, is the critical undamaged region, and it is considered that the cohesion and internal friction angle of the sliding body in this region are both peak values. Region 3: located at the lower right, is the shear failure zone. Obvious shear failure occurs in the sliding body in this region. It is considered that the cohesive force and internal friction angle values of the sliding body in this region are residual values.

Where, the tensile crack depth ⁠, ⁠. Here, c and are the corresponding residual strength values.

According to the calculation of the multistage sliding body residual sliding force, it can be known that when the sliding body is in a critical state, the anti-sliding force of the strip is equal to the sliding force, and ⁠. When the sliding force of the strip is greater than the anti-sliding force, the sliding body is in an unstable state, and ⁠. When the sliding force of the strip is less than the anti-sliding force, the sliding body is in a stable state, and ⁠. For slope bodies in different states, the stability coefficient can be characterized by a linear equation, but the interaction force between multistage slide bodies cannot be ignored.

The multistage landslide sliding surface is formed from the beginning to the end. Therefore, the last stage is the -stage sliding body, and it moves forward to the first-stage sliding body in turn.

The T22 multistage sliding ancient landslide of Xiaowan Hydropower Station is located in the Xiaowan Hydropower Station region in Lancang River. The main composition of landslide deposits is loessial powder soil and clay. The gravel content is 10%. The block diameter is 3–8 cm and the block diameter larger than 10 cm is rare. The bedrock is mainly the upper Jurassic purplish red mudstone and sandy mudstone with siltstone.

The T22 multistage sliding ancient landslide is located in the Heihuijiang reservoir area of Xiaowan Hydropower Station in Lancang River. The geological structure is loose, and the stratigraphic lithology is Jurassic purplish red mudstone and sandy mudstone, which is easy to soften and has slipped before the water storage of Xiaowan Hydropower Station. With the impounded water of Xiaowan Hydropower Station, due to the influence of periodic reservoir water level rise and fall, its front suffers the influence of erosion, which leads to the loss of a key strip of the ancient landslide in front.

The phenomenon of multistage pulling cracks is shown. And the ancient landslide reactivation. In addition, under the influence of continuous heavy rainfall, rainwater develops infiltration from the loose quaternary deposits and vertical cracks at the top of the ancient landslide. Due to the sliding zone region being a relatively closed environment, after rainwater infiltration, the sliding zone soil is saturated. The mechanical strength is significantly reduced, and the saturated gravity of the slide body is increased, resulting in the sliding force increasing. Combined with the reservoir water erosion of the front, the anti-sliding force decreases, which intensifies the ancient landslide deformation, and the sliding surfaces are gradually connected forming a multistage sliding body.

The topographic features of the T22 ancient landslide reflect the spatial position relationship of each sliding body. The multistage sliding body occurs shear slip at the slope foot of the front primary sliding body, which is from the front to the back edge along the same main sliding direction and from the high-steep air face. The key slide strip at the slope foot is eroded by the reservoir water level variation. The sliding body strength decreases sharply. The front slope body preferentially forms tension cracks and becomes unstable, which provides a favorable slip space for the rear slide body downward sliding. Then the ancient landslide gradually failed and formed a multistage sliding body.

The slip zone soil saturated bulk density of the T22 multistage sliding ancient landslide in Xiaowan Hydropower Station is 21.2 kN/m³. The partial strength parameters of the sliding zone soil obtained through laboratory tests are shown in Table 1.

Due to the erosion effect caused by the variation of reservoir water level, the stage I sliding body strip 5 weight loss. Here, this paper regards strip 5 losing weight as the starting sliding force (572.31 kN/m). The residual sliding force calculation results of different strips and each sliding body are shown in Table 2.

Table 2

The T22 multistage sliding ancient landslide residual sliding force calculation results

Sliding body number .	Strip number .	.	α (°) .	.	.	.	.	.
Stage I sliding body	1	2,756.10	58	–	–	452.17	2,893.41	–
	2	3,982.14	24	34	0.67	1,265.41	1,231.57	2,269.74
	3	4,513.23	24	0	1.00	1,324.58	1,208.14	1,327.45
	4	4,257.58	21	3	0.97	1,107.21	1,154.63	887.41
	5	5,251.09	21	0	1.00	507.34	503.29	569.33
	6	6,217.33	18	3	1.00	632.74	585.11	742.56
Stage Ⅱ sliding body	7	2,617.43	62	–	–	498.14	3,345.88	–
	8	4,327.55	47	15	0.82	1,352.29	2,473.19	2,852.16
	9	3,897.14	35	12	0.85	1,467.81	1,653.24	2,734.31
Stage Ⅲ sliding body	10	2,634.59	42	–	–	789.31	587.14	–
	11	3,124.54	17	25	0.89	1,038.41	2,120.45	2,387.12
	12	2,706.28	17	0	1.00	821.03	774.58	952.13
Stage Ⅳ sliding body	13	2,434.12	54	–	–	358.12	1,853.26	–
	14	3,617.52	35	19	0.79	877.24	1,765.58	1,598.37
	15	3,858.43	35	0	1.00	1,045.31	1,533.71	1,675.14
	16	3,345.21	18	17	0.81	1,124.35	884.32	276.14
	17	2,321.47	18	0	1.00	705.21	573.13	1,731.25

Sliding body number .	Strip number .	.	α (°) .	.	.	.	.	.
Stage I sliding body	1	2,756.10	58	–	–	452.17	2,893.41	–
	2	3,982.14	24	34	0.67	1,265.41	1,231.57	2,269.74
	3	4,513.23	24	0	1.00	1,324.58	1,208.14	1,327.45
	4	4,257.58	21	3	0.97	1,107.21	1,154.63	887.41
	5	5,251.09	21	0	1.00	507.34	503.29	569.33
	6	6,217.33	18	3	1.00	632.74	585.11	742.56
Stage Ⅱ sliding body	7	2,617.43	62	–	–	498.14	3,345.88	–
	8	4,327.55	47	15	0.82	1,352.29	2,473.19	2,852.16
	9	3,897.14	35	12	0.85	1,467.81	1,653.24	2,734.31
Stage Ⅲ sliding body	10	2,634.59	42	–	–	789.31	587.14	–
	11	3,124.54	17	25	0.89	1,038.41	2,120.45	2,387.12
	12	2,706.28	17	0	1.00	821.03	774.58	952.13
Stage Ⅳ sliding body	13	2,434.12	54	–	–	358.12	1,853.26	–
	14	3,617.52	35	19	0.79	877.24	1,765.58	1,598.37
	15	3,858.43	35	0	1.00	1,045.31	1,533.71	1,675.14
	16	3,345.21	18	17	0.81	1,124.35	884.32	276.14
	17	2,321.47	18	0	1.00	705.21	573.13	1,731.25

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Contrastive analysis of the improved transfer coefficient method and the traditional transfer coefficient method. For the T22 multistage sliding ancient landslide in Xiaowan Hydropower Station, the stability coefficient calculated by the improved transfer coefficient method is compared with the stability calculated by considering some factors’ influence and considering none of the factors (Zhao et al. 2023). Considering the influence of some factors means that (1) the particle migration effect is not considered, that is, the stage I sliding body front edge exists in the multistage sliding body, and there is a key strip anti-sliding effect. (2) The differences of sliding zone soil parameters values are not considered, that is, the multistage sliding body strength parameters do not weaken gradually, and there is no difference in different sliding zone regions. (3) The interaction force between sliding bodies is not considered, that is, the multistage sliding body is regarded as a single independent sliding body, and there is no interaction influence between sliding bodies. At the same time, to compare the difference in landslide stability under the influence of different factors, this paper also calculates the stability coefficient when the whole landslide is unstable (Pacheco et al. 2023).

According to the data analysis results in Table 3, when the three factors are not considered, the sliding bodies' stability coefficients from back to forward are increasing by 28.84, 18.13, 19.26, and 21.01%, respectively, than the improved transfer coefficient method calculating results. Compared with the improved transfer coefficient method calculating results are smaller than the stability coefficients calculating results when ancient landslide overall unstability. Therefore, we can think that the traditional transfer coefficient method may cause the deviation of ancient landslide stability evaluation, which does not reflect the actual landslide stability (Tong et al. 2021).

By comparing and analyzing the stability calculation results of the improved transfer coefficient method and considering the influence of some factors, we can see that the stability calculation results of the improved transfer coefficient method are the least. Because the improved transfer coefficient method takes into account the particle migration effect of the multistage sliding ancient landslide affected by reservoir water level variation, the interaction force between multistage sliding bodies, and the difference of sliding zone soil strength parameters, it can better reflect the progressive instability failure process of multistage sliding ancient landslide (Haeri et al. 2021; Wen et al. 2022).

Therefore, when evaluating the stability of multistage sliding ancient landslide under the combined action of reservoir level variation and rainfall, the stability calculation results of the improved transfer coefficient method should be adopted, which can ensure that the supporting structure can provide sufficient supporting force in the support design process and effectively complete the control of ancient landslide. In the improved transfer coefficient method, the sliding force is closely related to the cohesive force and internal friction Angle of the sliding body. The sliding force is only related to its gravity, which makes the settlement result of the stability coefficient small on the whole.

The accurate assessment of multistage sliding ancient landslides stability in hydropower station reservoir area still cannot ignore the impact of climate change. Further research will be needed in the evaluation of landslide stability within regional climate change, and suitable monitoring methods and machine learning methods (Shahid et al. 2018; Xu et al. 2019; Wang et al. 2020).

By improving the traditional transfer coefficient method, this manuscript accurately evaluates the stability of the multistage sliding ancient landslide in the reservoir area of Xiaowan Hydropower Station under the combined influence of reservoir level variation and rainfall and draws the following conclusions:

• (1)

  The improved transfer coefficient method can accurately evaluate the sliding body stability of multistage sliding ancient landslides under the combined action of reservoir water level variation and rainfall. The improved transfer coefficient method stability coefficient calculation results are less than that of the traditional transfer coefficient method. Based on the stability coefficient calculated by the improved transfer coefficient method, the supporting force of the multistage sliding ancient landslide retaining structure will be greater.

• (2)

  In the progressive failure process of a multistage sliding ancient landslide, the sliding body can be divided into a tensile failure zone, shear failure zone, and critical undamaged zone. The sliding body strength parameter in the tensile failure region is recommended to be zero. The sliding body strength parameters in the shear failure region are recommended to be residual strength. And the sliding body strength parameters in the critical unbroken region are recommended to be peak strength. The stability coefficient calculation result of multistage sliding ancient landslide by considering the sliding body region division will be more realistic. The interaction force between strips can also not be ignored.

• (3)

  The improved transfer coefficient method takes into account the dynamic water pressure caused by the repeated reservoir water level rise and fall, the ancient landslide front erosion phenomenon due to the effect of particle migration, and the effect of hydrostatic pressure generated during rainfall infiltration, which is more consistent with the multistage sliding ancient landslides mechanical characteristics. By using the improved transfer coefficient method to analyze the T22 ancient landslide stability in Xiaowan Hydropower Station, it can be seen that the stability coefficient of the multistage sliding body shows a gradually increasing trend, that is, the sliding surface is gradually connected from front to back, which conforms to the typical multistage sliding characteristics.

This research was financially supported by the Chengdu University of Technology Postgraduate Innovative Cultivation Program: Study on red-bed soft rock trans-dimensional damage mechanical properties and constitutive model in central Yunnan under long-term soak (CDUT2022BJCX007).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.