1 Introduction

The mountainous areas in Southwest China are characterized by unfavourable geological conditions, such as high ground stress and high ground temperature, which can lead to geological disasters including debris flows and landslides, posing risks and challenges to the construction and operation of local railways [1].

Rainfall is an important factor affecting the stability of railway subgrades and slopes [2]. Regarding the impact of rainfall on slope stability, much work has been reported. For instance, Springman et al. [3] proposed a hydraulic analysis system for slope instability and failure based on field measurements and local meteorological data. Then, Bordoni et al. [4] supplemented the hydraulic analysis system for slope instability and failure and conducted in-depth research on the influence of various physical and mechanical parameters. Using the basic theory of unsaturated soil water movement, Li et al. [5] proposed a calculation model for the transient water content in rainfall infiltration analysis of an unsaturated soil slope and obtained the slope safety coefficient calculation formula. Lin et al. [6] conducted multiple sets of model tests on rainfall-induced slope instability and proposed using the rainfall intensity and cumulative rainfall as two indicators for slope rainfall warning.

Currently, the main methods for slope stability analysis include empirical analysis, limit equilibrium analysis, and numerical analysis. Hoek et al. [7] classified slope failure forms into planar failure, wedge failure, circular failure, and toppling failure and obtained the failure mechanism and stability coefficient calculation methods for different forms. Douglas et al. [8] classified slope failure types into landslides and toppling based on the motion characteristics before the critical failure of the slope. Sun [9] divided unstable slope failures into 9 categories according to the failure reasons. The above studies assumed the presence of weak zones in slopes to determine their failure modes. If a slope does not have significant weak zones, then the applicability of the traditional empirical analysis and limit equilibrium analysis will significantly decrease.

With the development of numerical simulation techniques, new methods for analysing slope stability, such as the finite element method, finite difference method, and hybrid methods based on finite element and new limit analysis or new strength reduction methods, have emerged. Li et al. [10] carried out relevant research on slope stability using a new limit analysis method based on the Hoek‒Brown criterion to obtain the slope stability coefficient and safety coefficient. Taking the disturbance effect into account, Qian et al. [11] carried out a new limit analysis of slope stability and summarized the results in the form of design drawings. Aiming at the problem of soil slope stability, Tschuchnigg et al. [12] systematically compared the difference between the new limit analysis method and the new strength reduction method. Wu et al. [13] used SEEP/W numerical simulation software to study the influencing parameters of unsaturated soil stability under rainfall and analysed the influence of rainfall intensity and other parameters on slope stability. In addition, Buscarnera et al. [14] studied the seepage deformation characteristics of shallow soil under the condition of rainwater infiltration using the finite element method. Kim et al. [15] established the equivalent relationship between pore water pressure and load and evaluated the slope stability using the finite-element upper-bound analysis method. Zienkiewicz et al. [16] first combined traditional strength reduction theory with the finite element method and proposed a new strength reduction method based on the finite element method, which makes the analysis of slope stability more intuitive and convenient. Zheng et al. [17] wrote a theoretical analysis program based on the new strength reduction method and achieved good application results in several slope cases. Duncan et al. [18] studied the stability of soil slopes based on the new strength reduction method and obtained the slope stability coefficient, an important index to measure slope safety. The new strength reduction method has been increasingly used in slope stability analysis due to its clear computational logic, ease of programming implementation, and high reliability of results. The slope stability analysis in this paper is also based on this method.

In summary, scholars worldwide have made significant progress in the study of slope stability, forming a series of theories and methods. In particular, the impact of rainfall infiltration on slope stability has been studied in depth. However, research on high and steep loose accumulation slopes has been relatively limited, and the understanding of their structure and stability is insufficient. Therefore, this paper takes the slopes of the adverse geological section along a high-speed railway in the southwest mountainous area of China as the research object, uses numerical simulation software to study the impact of rainfall on slope stability, and evaluates the reinforcement effect of field retaining structures. Additionally, an automated monitoring system is established to evaluate the slope status based on monitoring indicators. The study reveals the evolutionary process of the stability of loose accumulation slopes along the high-speed railway in the southwest mountainous area of China under rainfall, which can provide a reference for the establishment of monitoring systems for such slopes and effective prevention of geological disasters.

2 Numerical model development

In this section, the deformation characteristics and stability of the loose accumulation slope under rainfall are investigated by setting various types of rainfall conditions in numerical simulation software. Furthermore, the effectiveness of retaining structures is evaluated through a comparative analysis between natural slopes and reinforced slopes.

2.1 Project overview

The study area is located in the southwestern mountainous region of China, with a natural slope of 30°–35° and an absolute elevation range of 3191–3760 m. The surface layer in the area is mainly composed of a Quaternary Holocene colluvial layer (Q4col) such as coarse breccia soil, gravel soil, and rocky soil, while the underlying bedrock is composed of Neogene (ηγ1N1) coarse-grained biotite monzogranite. According to meteorological statistics, the average annual temperature in the study area is 3.11 °C, with an average temperature of −5.3 °C in January and 10.3 °C in July. The extreme lowest and highest temperatures in a year are −17.2 °C and 23.4 °C, respectively. The average annual rainfall is 947.5 mm, and the maximum daily rainfall is 63.14 mm. The maximum annual snow depth is 15.53 cm, and the relative humidity is 64%. The sunshine duration is 2525.9 h, and the frost-free period lasts for 95 d.

To ensure slope stability during railway construction, reinforcement measures are planned for the field slope. Specific measures include installing anchor cable piles near the foot of the slope, arranging multilevel anchor cable frame beams in the middle and upper parts of the slope, and setting up flexible protective nets in areas where rockfall may occur.

2.2 Principles of stability analysis

In this study, the strength reduction method is employed to analyse the stability of slopes. The basic principle is to reduce the shear strength index of slope soil with a small initial reduction coefficient and then perform numerical simulation calculations on the slope stability. If the calculated slope is still in a stable state, then increase the reduction coefficient; otherwise, decrease the reduction coefficient. Then, the shear strength index of the slope soil is reduced again. This process is repeated until the slope reaches the critical failure state, at which the reduction coefficient is considered to be the stability coefficient of the slope [19]. The calculation formulas are shown in Eqs. (1) and (2):

$$c_{\text{m}} = c/F_\text{r},$$
(1)
$$\varphi_{\text{m}} = {\rm{arc}}\;{\rm{tan(tan}}\varphi /F_{\text{r}} {\rm{)}},$$
(2)

where cm is the reduced cohesion of soil, c is the cohesion of soil, φm is the reduced internal friction angle of soil, φ is the internal friction angle of soil, and Fr is the reduction coefficient.

From the perspective of soil strength reserve, the physical meaning of the strength reduction method is consistent with that of the limit equilibrium method in calculating the slope stability coefficient. Compared with the limit equilibrium method, the strength reduction method has the following advantages [20,21,22,23]:

  1. (1)

    It can perform numerical analysis on slopes with complex terrain and geological structures.

  2. (2)

    It can simulate multiphysics coupled engineering problems, such as earthquakes, rainfall, and changes in water levels.

  3. (3)

    It can consider the combined effects of soil and retaining structures.

  4. (4)

    It does not require assuming sliding surfaces or dividing the soil into strips.

2.3 Model establishment and material parameters

This paper uses PLAXIS 3D for numerical simulation. A numerical analysis model is established through proper cross-sectional simplification and size amplification [24] based on the field slope within the range of D3K278 + 824 – D3K278 + 884. The cross section of the model is shown in Fig. 1. The dimensions, soil layer distribution, and groundwater level of the reinforced slope model are the same as those of the natural slope, and the retaining structures are consistent with those in the field.

Fig. 1
figure 1

Model diagram: a natural slope and b reinforced slope (unit: m)

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The natural slope soil is modelled using solid elements, and the physical and mechanical parameters are shown in Table 1. To describe the unsaturated seepage behaviour, the soil‒water characteristic curve of the soil is determined using a built-in model in the simulation software. Although there is some difference from reality, considering the important impact of rainfall on slope stability, this approach is feasible [25]. The adopted model is shown in Fig. 2. The types of elements used in the retaining structure for the reinforced slope, as well as their corresponding material parameters, are shown in Table 2.

Table 1 Soil material parameters
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Fig. 2
figure 2

The soil permeability function and soil‒water characteristic curve of soil in the model: a soil permeability function and b soil‒water characteristics curve. Kr is the relative permeability coefficient, and Sr is the effective saturation, both of which are dimensionless quantities, and ψ is the matrix suction head

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Table 2 Material parameters of the retaining structures
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In the model, the boundary condition of infiltration is set as follows: the bottom boundary is set as impermeable, while the other boundaries are permeable. When the rainfall intensity is less than the saturated permeability coefficient of the soil, it is assumed that all rainwater infiltrates into the soil. When the rainfall intensity exceeds the saturated permeability coefficient of the soil, the rainwater infiltrates into the soil according to the magnitude of the saturated permeability coefficient, and the excess part is discharged as slope runoff.

The displacement boundary condition is set as follows: the free surface of the slope model selects the free boundary, the side is constrained by horizontal displacement, and the bottom is fixed.

2.4 Numerical analysis methods

The specific steps of the numerical simulation analysis are as follows:

  1. (1)

    The initial stress equilibrium of the natural slope is calculated using the gravity loading method under the initial condition.

  2. (2)

    The stability of the natural slope is calculated using the safety calculation module. As shown in Fig. 1, the groundwater level is above the model bottom boundary, so the "ignore suction" option is unchecked during the calculation.

  3. (3)

    Rainfall in China is generally classified into seven grades, as shown in Table 3 [26]. By using the hydromechanical coupling module, the natural slope is simulated under rainfall conditions. Referring to local meteorological and hydrological data, the total simulated rainfall is determined to be 300 mm, and four working conditions are set as follows:

    1. 1)

      Condition 1: Super heavy storm with rainfall intensity of 300 mm/d and rainfall duration of 1 d.

    2. 2)

      Condition 2: Heavy storm with rainfall intensity of 100 mm/d and rainfall duration of 3 d.

    3. 3)

      Condition 3: Heavy rain with a rainfall intensity of 30 mm/d and a rainfall duration of 10 d.

    4. 4)

      Condition 4: Intermittent Storm with rainfall intensity of 60 mm/d and rainfall duration of 10 d.

    In the remainder of the paper, Conditions 1, 2, 3, and 4 are abbreviated as C1, C2, C3, and C4, respectively. The relationship between rainfall intensity and duration for each condition is shown in Fig. 3.

Table 3 Rainfall grades
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  1. (4)

    After the simulation of rainfall on the natural slope is completed, the safety calculation module is used again to analyse the impact of rainfall on the stability of the natural slope.

  2. (5)

    After step (1), the plastic calculation module is set up, and the anchor cable piles and anchor cable frame beams are activated to simulate the construction process of the slope support structure. The prestress of the free segment of the anchor cable in the anchor cable piles and anchor cable frame beams is set as 156 and 52 kN, respectively, based on the field design data.

  3. (6)

    The stability of the reinforced slope is calculated using the safety calculation module.

  4. (7)

    The rainfall condition of the reinforced slope is simulated using the hydromechanical coupling module, with the same boundary and working conditions as the natural slope.

  5. (8)

    The impact of rainfall on the stability of the reinforced slope is analysed using the safety calculation module.

Fig. 3
figure 3

Working conditions of rainfall

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2.5 Analysis of the simulated results

According to the relevant regulations for slope classification in Ref. [27], the research object belongs to a first-class slope, with a corresponding slope safety coefficient of 1.35. When the slope stability coefficient is greater than this value, the slope is considered stable. Through calculation, the stability coefficients of the natural slope and the reinforced slope in the initial state were found to be 1.453 and 1.692, respectively.

Figure 4a and b shows that the stability coefficients of the natural slope and the reinforced slope follow a similar pattern under the first two working conditions. Under C1, the stability coefficients almost linearly decrease with the duration of rainfall. After rainfall, the stability coefficients of the natural slope and the reinforced slope are 1.417 and 1.662, respectively, which decrease by 0.036 and 0.030 from their initial states. The decrease in stability is small and similar for both slopes, indicating that rainfall conditions with short duration and large amount of rainfall have a very limited impact on the slope stability.

Fig. 4
figure 4

Stability coefficient variation of the slopes under four working conditions: a natural slope under C1 and C2; b reinforced slope under C1 and C2; c natural slope under C3 and C4; and d reinforced slope under C3 and C4

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Under C2, the stability coefficients decrease approximately linearly with rainfall duration and then accelerate after 1.5 d. After rainfall ends, the stability coefficients of the two slopes are 1.377 and 1.643, respectively, which decrease by 0.076 and 0.049 from their initial states. The decrease in stability coefficients is greater than that under C1. This indicates that under a constant rainfall amount, a longer rainfall duration leads to a greater decrease in slope stability coefficients. This is because the infiltration volume and depth under C2 are larger than those under C1.

Under C1 and C2, the reduction in the two types of slope stability coefficients is not significant. Under C1, due to the rainfall intensity being greater than the saturated permeability coefficient of the surface soil, not all of the rainwater infiltrates into the soil, and some of it is discharged as surface runoff. Therefore, although rainfall increases the sliding force and reduces the anti-sliding force of the slope, its impact on the stability of the slope is limited. After rainfall, the safety coefficients of the slopes are both greater than 1.35, indicating that the slopes are still in a stable state.

According to Fig. 4c and d, the variation pattern of the stability coefficient differs between the natural slope and the reinforced slope. Under C3, after rainfall, the stability coefficients of the two slopes are 1.021 and 1.573, respectively, which decrease by 0.432 and 0.119 from their initial states. The degree of decrease is further increased compared to C2. Rainfall infiltration has a significant impact on the stability of the natural slope, which is on the verge of failure after rainfall. This further illustrates that under a constant rainfall intensity, the longer the duration of rainfall is, the greater the decrease in the stability coefficient. Moreover, after a certain number of days, the stability coefficient may decrease rapidly, and the slope will be on the verge of failure. The reinforced slope has not experienced any failure under reasonable retaining structures.

Under C4, the final stability coefficients of the two slopes are 1.265 and 1.586, respectively, decreasing by 0.188 and 0.106 compared to their initial states. The decrease in stability coefficients is smaller than that under C3. By comparing C3 and C4, it can be concluded that under a constant rainfall duration and rainfall amount, continuous rainfall has a greater impact on slope stability than intermittent rainfall.

Additionally, under C3 and C4, the stability coefficient curves of the two slopes are very close in the early stage and begin to separate after approximately 3 d. The stability coefficient under C3 decreases faster than that under C4, and the difference between them becomes larger over time. This suggests that the impact of continuous rainfall and intermittent rainfall on slope stability is almost the same in the early stage, but the difference becomes more evident in the later stage, especially after 8 d in the natural slope.

Table 4 shows the stability status of the slopes after rainfall under different working conditions. There are significant differences in the final stability of natural slopes under different working conditions. The stability coefficients of the natural slope are greater than 1.35 under C1 and C2, indicating that the slope is in a stable state. Under C3, the stability coefficient is close to 1, indicating that the slope is in a limit equilibrium state and on the verge of failure. Under C4, the stability coefficient of the slope is greater than 1 but less than 1.35, indicating that the slope has an insufficient safety margin.

Table 4 Comparison of slope stability under different working conditions
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The stability coefficient of the reinforced slope decreases to some extent under four working conditions. However, compared with the natural slope, the difference in the stability coefficient is not significant under each condition, and the final value is still greater than 1.35, indicating that the slope is in a stable state.

Based on the above analysis, it can be concluded that the establishment of slope retaining structures can not only improve the stability coefficient of the slope in its initial state but also effectively reduce the loss of the stability coefficient during the development of rainfall, ensuring slope stability. Under the condition of a constant rainfall amount, this effect becomes more apparent as the rainfall duration increases.

3 Field monitoring

In this section, an automated monitoring system is established to monitor key indicators such as rainfall and slope displacement for the stability analysis of a loose accumulation slope. By analysing the monitored data, the deformation characteristics of the slope under rainfall are revealed. The rationality of the numerical simulation model and the accuracy of the field monitoring data are verified through a comparison between the numerical simulation results and the field monitoring data. Finally, through the comparison between the field monitoring data, previous research results, and typical failure cases, the deformation and stability status of the field slope are scientifically evaluated, providing reliable support for the numerical simulation results presented in Sect. 2.

3.1 Monitoring overview

Automated monitoring of the slope using a rain gauge, a global navigation satellite system (GNSS), and a deep displacement meter was carried out from January 11th to March 31st, 2022. The monitoring contents and equipment can be found in Table 5.

Table 5 Monitoring content and equipment
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As shown in Fig. 5, four monitoring sections (#1, #2, #3, and #4) were established in the area. A rain gauge was set up in the area to monitor rainfall. A GNSS reference station was established in a relatively stable location to serve as the benchmark, while GNSS monitoring stations were set up on the slope surface to monitor vertical and horizontal displacements. Deep displacement meters were installed at different depths inside the slope through drilling to monitor internal horizontal displacement.

Fig. 5
figure 5

Monitoring area. G1–G11 stand for the monitoring points of the internal horizontal displacement of the slope. S1–S29 represent the monitoring points of the slope surface displacement

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3.2 Analysis of monitoring results

3.2.1 Rainfall intensity

Figure 6 shows that the cumulative rainfall and daily rainfall in the monitoring area gradually increased with time, and the rainfall frequency in March increased compared to before. The longest rainfall during the monitoring period lasted from March 23rd to March 31st. The monitoring data show that the rainfall intensity on site during the monitoring period is not very high compared to the historical rainfall in this area.

Fig. 6
figure 6

Monitoring results of the rainfall intensity

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3.2.2 Horizontal and vertical displacements on the slope surface

In the GNSS monitoring results (Table 6), X and Y represent horizontal displacements, with their positive values indicating that the distances moved northward and eastward relative to the initial time at the monitoring point, respectively, and Z represents the vertical displacement, with a positive value indicating that the distance moved upwards relative to the initial time at the monitoring point. To provide a more intuitive analysis of the slope surface horizontal displacement, a horizontal composite displacement index (L) was established:

Table 6 Monitoring results of the slope surface displacement
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$$L = \sqrt {X^2 + Y^2 }.$$
(3)

As shown in Table 6, the maximum vertical displacement of all monitoring points is within 9 mm, with over 80% of them within 7 mm. The maximum horizontal composite displacement of each monitoring point is within 6 mm, with approximately 73% of them within 4 mm. Overall, the surface displacement of the slope is relatively small.

3.2.3 Internal horizontal displacement of the slope

Figure 7a shows the monitoring results of the internal horizontal displacement of the slope in section #1. In the same borehole, the larger the monitoring point number is, the deeper it is buried. Among the upper part monitoring points S1–S3 of the slope, the displacement increase in S1 is much larger than that in S2 and S3. The displacement variation curve of S1 is approximately linear, while the displacement variation of the other two monitoring points is relatively small. At the middle part of the slope, the curves of S4–S6 almost overlap with each other. The curves of S7 and S8 at the lower part of the slope change similarly, while there is a slight change in the curve of monitoring point S9.

Fig. 7
figure 7

Monitoring results of the internal horizontal displacement of the slope in monitoring sections a #1, b #2, c #3, and d #4

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It can be observed from Fig. 7b that among the monitoring points of the slope in section #2, the displacement curves of S10–S12 at the upper part of the slope exhibit a step-like change. The curves of S13–S15 at the middle part of the slope show some fluctuations. Compared with S13, the displacements of S14 and S15 develop more slowly, with similar variation patterns. The displacement of S16–S18 at the lower part of the slope is the largest among all monitoring points in this monitoring section.

Figure 7c shows that among the monitoring points at the upper part of the slope in section #3, the displacement of S19 is significantly greater than that of S20 and S21. The displacement patterns of S22–S24 at the middle part of the slope are relatively similar, with obvious step-like changes in the curves. The displacement of S25 at the lower part of the slope increases significantly with time, while the displacement of S26 develops slowly.

As shown in Fig. 7d, the horizontal displacement of the deep monitoring points in #4 is generally small. Among them, S29 at the deepest point is relatively stable with almost no displacement. The displacements of S27 and S28 develop slowly over time.

From Fig. 8, the deformation rates of various monitoring points in sections #1 to #3 are generally within 1 mm/d, except for a few moments with larger values. Overall, the slope deformation rate is relatively small, and the curve shows obvious oscillations. In section #4, except for the larger deformation rate of point S27 in the early monitoring period, the deformation rates of the other monitoring points are within 0.5 mm/d.

Fig. 8
figure 8

The horizontal displacement change rate inside the slope in monitoring sections a #1, b #2, c #3, and d #4

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3.3 Validation and analysis/discussion

3.3.1 Data verification

Considering the accuracy of the sensors and the influence of the data collection environment, deep displacement gauges were selected for analysis. Rainfall data obtained from monitoring were imported into the simulation model for hydromechanical coupling calculation. As shown in Fig. 9, the selection of deep displacement monitoring points in the model was consistent with field monitoring. Displacement simulation results were extracted at positions M1 to M8, resulting in Fig. 10. Overall, the simulation data and the actual monitoring data match well in the curves, indicating that the relevant parameters and boundary conditions set in the simulation model are reasonable, and the modelling is simplified properly, which can reflect the actual state of the slope. It also verifies the accuracy of the field monitoring data to some extent.

Fig. 9
figure 9

Locations of the monitoring points in the numerical simulation model

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Fig. 10
figure 10

Comparison between the simulation results and the monitoring results of the horizontal displacement inside the slope: a between S19–S21 and M1–M3, b between S22–S24 and M4–M6, and c between S25–S26 and M7–M8

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3.3.2 Data analysis

In terms of the surface displacement of the slope, the GNSS monitoring data show fluctuations, especially in the vertical displacement, and the maximum vertical displacement of points is within 9 mm. The fluctuation amplitude of the horizontal displacement is much smaller than that of the vertical displacement, while the horizontal displacement of each point is within 6 mm.

In terms of the internal horizontal displacement of the slope, the displacement of each point generally increases over time, and the maximum displacement of most points is within 6 mm. The deformation rate of each point has obvious oscillations, with a maximum value of 2.7 mm/d, and during most of the time, it does not exceed 1 mm/d.

Combining the monitoring results and Table 7, one can see that the displacement and deformation rate of the slope are currently very small, indicating that the slope is currently undergoing slow deformation in its initial deformation stage and has good stability.

Table 7 Typical deformation conditions before slope failure
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4 Conclusions

This paper investigates the evolution of the stability of a loose accumulation slope along a high-speed railway in the southwest mountainous area of China under rainfall conditions. By establishing a hydromechanical coupling finite element calculation model of the slope, the stability of the loose accumulation slope under different rainfall conditions was analysed, and the validity of the finite element model was verified by field monitoring data. The main conclusions are summarized as follows:

  1. (1)

    Rainfall can lead to a decrease in the stability of loose accumulation slopes. When the cumulative rainfall is constant, the longer the duration of rainfall is, the lower the safety coefficient of the slope. When the cumulative rainfall and rainfall duration are constant, continuous rainfall has a more significant impact on the stability of the slope than intermittent rainfall.

  2. (2)

    The setting of retaining structures in the reinforced loose accumulation slope improves the initial stability of the slope and significantly alleviates the deterioration of the slope stability coefficient. Under all working conditions, the stability coefficient of the reinforced slope is greater than 1.35, indicating good slope stability. This shows that field retaining structures can effectively reinforce the loose accumulation slope.

  3. (3)

    The deep displacement data of the slope in the numerical simulation agree well with the field monitoring data, which verifies the rationality of the numerical simulation and the field automated monitoring system. By analysing the changes in monitoring data and comparing the monitoring data with related research and typical slope failure cases, we conclude that field slope deformation is slow in the initial deformation stage and has good stability.

  4. (4)

    In this paper, the types of monitoring equipment and analysis indicators are relatively simple. In follow-up work, the stability analysis and monitoring of the loose deposit slope can be studied from other angles by adding soil pressure sensors and soil moisture sensors.