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Stability analysis of loose accumulation slopes under rainfall: case study of a high-speed railway in Southwest China

Stability analysis of loose accumulation slopes under rainfall: case study of a high-speed... The high and steep slopes along a high-speed railway in the mountainous area of Southwest China are mostly composed of loose accumulations of debris with large internal pores and poor stability, which can easily induce adverse geological disasters under rainfall conditions. To ensure the smooth construction of the high-speed railway and the subsequent safe operation, it is necessary to master the stability evolution process of the loose accumulation slope under rainfall. This article simulates rainfall using the finite element analysis software’s hydromechanical coupling module. The slope stability under various rainfall situations is calculated and analysed based on the strength reduction method. To validate the simulation results, a field monitoring system is established to study the deformation characteristics of the slope under rainfall. The results show that rainfall duration is the key factor affecting slope stability. Given a constant amount of rainfall, the stability of the slope decreases with increasing duration of rainfall. Moreover, when the amount and duration of rainfall are constant, continuous rainfall has a greater impact on slope stability than intermittent rainfall. The setting of the field retaining structures has a significant role in improving slope stability. The field monitoring data show that the slope is in the initial deformation stage and has good stability, which verifies the rationality of the numerical simulation method. The research results can provide some references for understanding the influence of rainfall on the stability of loose accumulation slopes along high-speed railways and establishing a monitoring system. Keywords High-speed railway · Loose accumulation slope · Slope stability analysis · Rainfall effect · Strength reduction 1 Introduction rainfall on slope stability, much work has been reported. For instance, Springman et al. [3] proposed a hydraulic analysis The mountainous areas in Southwest China are character- system for slope instability and failure based on field meas- ized by unfavourable geological conditions, such as high urements and local meteorological data. Then, Bordoni et al. ground stress and high ground temperature, which can lead [4] supplemented the hydraulic analysis system for slope to geological disasters including debris flows and landslides, instability and failure and conducted in-depth research on posing risks and challenges to the construction and operation the influence of various physical and mechanical parameters. of local railways [1]. Using the basic theory of unsaturated soil water movement, Rainfall is an important factor affecting the stability of Li et al. [5] proposed a calculation model for the transient railway subgrades and slopes [2]. Regarding the impact of water content in rainfall infiltration analysis of an unsatu- rated soil slope and obtained the slope safety coefficient calculation formula. Lin et al. [6] conducted multiple sets * Qian Su of model tests on rainfall-induced slope instability and pro- tmsq@home.swjtu.edu.cn posed using the rainfall intensity and cumulative rainfall as School of Civil Engineering, Southwest Jiaotong University, two indicators for slope rainfall warning. Chengdu 610031, China Currently, the main methods for slope stability analysis Key Laboratory of High-Speed Railway Engineering include empirical analysis, limit equilibrium analysis, and Ministry of Education, School of Civil Engineering, numerical analysis. Hoek et al. [7] classified slope failure Southwest Jiaotong University, Chengdu 610031, China forms into planar failure, wedge failure, circular failure, CCCC Second Highway Consultants Co., Ltd., and toppling failure and obtained the failure mechanism Wuhan 430056, China Vol.:(0123456789) 1 3 X. Wang et al. and stability coefficient calculation methods for different However, research on high and steep loose accumulation forms. Douglas et al. [8] classified slope failure types into slopes has been relatively limited, and the understanding of landslides and toppling based on the motion characteristics their structure and stability is insufficient. Therefore, this before the critical failure of the slope. Sun [9] divided unsta- paper takes the slopes of the adverse geological section ble slope failures into 9 categories according to the failure along a high-speed railway in the southwest mountainous reasons. The above studies assumed the presence of weak area of China as the research object, uses numerical simula- zones in slopes to determine their failure modes. If a slope tion software to study the impact of rainfall on slope stabil- does not have significant weak zones, then the applicability ity, and evaluates the reinforcement effect of field retaining of the traditional empirical analysis and limit equilibrium structures. Additionally, an automated monitoring system is analysis will significantly decrease. established to evaluate the slope status based on monitoring With the development of numerical simulation tech- indicators. The study reveals the evolutionary process of the niques, new methods for analysing slope stability, such as the stability of loose accumulation slopes along the high-speed finite element method, finite difference method, and hybrid railway in the southwest mountainous area of China under methods based on finite element and new limit analysis or rainfall, which can provide a reference for the establishment new strength reduction methods, have emerged. Li et al. [10] of monitoring systems for such slopes and effective preven- carried out relevant research on slope stability using a new tion of geological disasters. limit analysis method based on the Hoek‒Brown criterion to obtain the slope stability coeci ffi ent and safety coeci ffi ent. Taking the disturbance effect into account, Qian et al. [11] carried out a new limit analysis of slope stability and sum- 2 Numerical model development marized the results in the form of design drawings. Aim- ing at the problem of soil slope stability, Tschuchnigg et al. In this section, the deformation characteristics and stability [12] systematically compared the difference between the of the loose accumulation slope under rainfall are inves- new limit analysis method and the new strength reduction tigated by setting various types of rainfall conditions in method. Wu et al. [13] used SEEP/W numerical simulation numerical simulation software. Furthermore, the effective- software to study the influencing parameters of unsaturated ness of retaining structures is evaluated through a compara- soil stability under rainfall and analysed the influence of tive analysis between natural slopes and reinforced slopes. rainfall intensity and other parameters on slope stability. In addition, Buscarnera et al. [14] studied the seepage defor- mation characteristics of shallow soil under the condition of 2.1 Project overview rainwater infiltration using the finite element method. Kim et al. [15] established the equivalent relationship between The study area is located in the southwestern mountainous region of China, with a natural slope of 30°–35° and an pore water pressure and load and evaluated the slope stabil- ity using the finite-element upper-bound analysis method. absolute elevation range of 3191–3760 m. The surface layer in the area is mainly composed of a Quaternary Holocene Zienkiewicz et al. [16] first combined traditional strength col reduction theory with the finite element method and pro- colluvial layer (Q4 ) such as coarse breccia soil, gravel soil, and rocky soil, while the underlying bedrock is com- posed a new strength reduction method based on the finite element method, which makes the analysis of slope stabil- posed of Neogene (ηγ N ) coarse-grained biotite monzo- granite. According to meteorological statistics, the average ity more intuitive and convenient. Zheng et al. [17] wrote a theoretical analysis program based on the new strength 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 reduction method and achieved good application results in several slope cases. Duncan et al. [18] studied the stability of July. The extreme lowest and highest temperatures in a year are −17.2 °C and 23.4 °C, respectively. The average annual soil slopes based on the new strength reduction method and obtained the slope stability coefficient, an important index rainfall is 947.5  mm, and the maximum daily rainfall is 63.14 mm. The maximum annual snow depth is 15.53 cm, to measure slope safety. The new strength reduction method has been increasingly used in slope stability analysis due to and the relative humidity is 64%. The sunshine duration is 2525.9 h, and the frost-free period lasts for 95 d. its clear computational logic, ease of programming imple- mentation, and high reliability of results. The slope stability To ensure slope stability during railway construction, reinforcement measures are planned for the field slope. Spe- analysis in this paper is also based on this method. In summary, scholars worldwide have made significant cific measures include installing anchor cable piles near the foot of the slope, arranging multilevel anchor cable frame progress in the study of slope stability, forming a series of theories and methods. In particular, the impact of rainfall beams in the middle and upper parts of the slope, and setting up flexible protective nets in areas where rockfall may occur. infiltration on slope stability has been studied in depth. Railway Engineering Science 1 3 Stability analysis of loose accumulation slopes under rainfall: case study of a high‑speed… 2.2 Principles of stability analysis (a) 100 168 150 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 Coarse breccia soil initial reduction coefficient and then perform numerical sim- ulation calculations on the slope stability. If the calculated Completely Strongly weathered granite weathered slope is still in a stable state, then increase the reduction granite 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 (b) 2.75 considered to be the stability coefficient of the slope [19]. Anchor cable frame beam The calculation formulas are shown in Eqs. (1) and (2): c = c∕F , (1) m r Coarse breccia soil = arc tan(tan∕F ), Anchor cable pile (2) m r Completely weathered Strongly weathered granite where c is the reduced cohesion of soil, c is the cohesion granite of soil, φ is the reduced internal friction angle of soil, φ is the internal friction angle of soil, and F is the reduction coefficient. Fig. 1 Model diagram: a natural slope and b reinforced slope (unit: m) 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 The natural slope soil is modelled using solid ele- ments, and the physical and mechanical parameters are method, the strength reduction method has the following advantages [20–23]: shown in Table  1. To describe the unsaturated seepage behaviour, the soil‒water characteristic curve of the soil (1) It can perform numerical analysis on slopes with com- is determined using a built-in model in the simulation software. Although there is some difference from reality, plex terrain and geological structures. (2) It can simulate multiphysics coupled engineering considering the important impact of rainfall on slope sta- bility, this approach is feasible [25]. The adopted model problems, such as earthquakes, rainfall, and changes in water levels. is shown in Fig.  2. The types of elements used in the retaining structure for the reinforced slope, as well as (3) It can consider the combined effects of soil and retain- ing structures. their corresponding material parameters, are shown in Table 2. (4) It does not require assuming sliding surfaces or divid- ing the soil into strips. In the model, the boundary condition of infiltration is set as follows: the bottom boundary is set as imperme- able, while the other boundaries are permeable. When the rainfall intensity is less than the saturated permeability 2.3 Model establishment and material parameters coefficient of the soil, it is assumed that all rainwater infil- trates into the soil. When the rainfall intensity exceeds the This paper uses PLAXIS 3D for numerical simula- tion. A numerical analysis model is established through saturated permeability coefficient of the soil, the rainwater infiltrates into the soil according to the magnitude of the proper cross-sectional simplification and size amplifi- cation [24] based on the field slope within the range of saturated permeability coefficient, and the excess part is discharged as slope runoff. D3K278 + 824 – D3K278 + 884. The cross section of the model is shown in Fig. 1. The dimensions, soil layer distri- The displacement boundary condition is set as follows: the free surface of the slope model selects the free bound- bution, and groundwater level of the reinforced slope model are the same as those of the natural slope, and the retaining ary, the side is constrained by horizontal displacement, and the bottom is fixed. structures are consistent with those in the field. Railway Engineering Science 1 3 1 1.85 68 20 154 26 X. Wang et al. Table 1 Soil material parameters Parameters Unit Saturated unit Cohe- Internal Elastic Poisson’s Porosity ratio Permeability weight weight sion friction modulus ratio coefficient 3 3 (kN/m ) (kN/m ) (kPa) angle (°) (MPa) (m/d) Coarse breccia soil 20 22 25 38 35 0.25 0.35 0.26 Completely weathered granite 21 23.5 20 20 50 0.3 0.5 0.7 Strongly weathered granite 23 24 0 45 200 0.25 0.4 0.36 (a) (b) -2.5 -2.5 -2.0 -2.0 -1.5 -1.5 -1.0 -1.0 -0.5 -0.5 0.0 0.0 -5 -4 -3 -2 -1 0 0.0 0.2 0.4 0.6 0.8 1.0 10 10 10 10 10 10 K S r r Fig. 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. K is the relative permeability coefficient, and S is the effective saturation, both of which are dimensionless quantities, and r r ψ is the matrix suction head Table 2 Material parameters of the retaining structures Parameters Simulation element Unit weight (kN/m ) Elastic modulus (MPa) Stabilizing pile Solid element 25 3.15 × 10 Free segment of the anchor cable Node to node anchor element – – Anchorage segment of the anchor cable Embedded beam element 24 3.90 × 10 Frame beam Plate element 25 3.15 × 10 groundwater level is above the model bottom boundary, 2.4 Numerical analysis methods so the "ignore suction" option is unchecked during the calculation. The specific steps of the numerical simulation analysis are as follows: (3) Rainfall in China is generally classified into seven grades, as shown in Table 3 [26]. By using the hydro- (1) The initial stress equilibrium of the natural slope is mechanical coupling module, the natural slope is simu- lated under rainfall conditions. Referring to local mete- calculated using the gravity loading method under the initial condition. orological and hydrological data, the total simulated rainfall is determined to be 300 mm, and four working (2) The stability of the natural slope is calculated using the safety calculation module. As shown in Fig. 1, the conditions are set as follows: Railway Engineering Science 1 3 (m) (m) Stability analysis of loose accumulation slopes under rainfall: case study of a high‑speed… Table 3 Rainfall grades 350 Rainfall grades 24-h rainfall (mm) Condition 1 Trace rain < 0.1 Condition 2 Light rain 0.1–10 Condition 3 Condition 4 Moderate rain 10–25 Heavy rain 25–50 Storm 50–100 Heavy storm 100–250 Super heavy storm ≥ 250 1) Condition 1: Super heavy storm with rainfall inten- 0246 810 sity of 300 mm/d and rainfall duration of 1 d. Rainfall duration (d) 2) Condition 2: Heavy storm with rainfall intensity of 100 mm/d and rainfall duration of 3 d. Fig. 3 Working conditions of rainfall 3) Condition 3: Heavy rain with a rainfall intensity of 30 mm/d and a rainfall duration of 10 d. 4) Condition 4: Intermittent Storm with rainfall inten- When the slope stability coefficient is greater than this value, sity of 60 mm/d and rainfall duration of 10 d. the slope is considered stable. Through calculation, the sta- bility coefficients of the natural slope and the reinforced In the remainder of the paper, Conditions 1, 2, 3, and slope in the initial state were found to be 1.453 and 1.692, 4 are abbreviated as C1, C2, C3, and C4, respectively. respectively. The relationship between rainfall intensity and duration Figure 4a and b shows that the stability coefficients of the for each condition is shown in Fig. 3. natural slope and the reinforced slope follow a similar pat- tern under the first two working conditions. Under C1, the stability coefficients almost linearly decrease with the dura - (4) After the simulation of rainfall on the natural slope is tion of rainfall. After rainfall, the stability coefficients of the completed, the safety calculation module is used again natural slope and the reinforced slope are 1.417 and 1.662, to analyse the impact of rainfall on the stability of the respectively, which decrease by 0.036 and 0.030 from their natural slope. initial states. The decrease in stability is small and similar (5) After step (1), the plastic calculation module is set for both slopes, indicating that rainfall conditions with short up, and the anchor cable piles and anchor cable frame duration and large amount of rainfall have a very limited beams are activated to simulate the construction pro- impact on the slope stability. cess of the slope support structure. The prestress of Under C2, the stability coefficients decrease approxi- the free segment of the anchor cable in the anchor mately linearly with rainfall duration and then accelerate cable piles and anchor cable frame beams is set as after 1.5 d. After rainfall ends, the stability coefficients 156 and 52 kN, respectively, based on the field design of the two slopes are 1.377 and 1.643, respectively, which data. decrease by 0.076 and 0.049 from their initial states. The (6) The stability of the reinforced slope is calculated using decrease in stability coefficients is greater than that under the safety calculation module. C1. This indicates that under a constant rainfall amount, (7) The rainfall condition of the reinforced slope is simu- a longer rainfall duration leads to a greater decrease in lated using the hydromechanical coupling module, with slope stability coefficients. This is because the infiltra- the same boundary and working conditions as the natu- tion volume and depth under C2 are larger than those ral slope. under C1. (8) The impact of rainfall on the stability of the rein- Under C1 and C2, the reduction in the two types of slope forced slope is analysed using the safety calculation stability coefficients is not significant. Under C1, due to the module. rainfall intensity being greater than the saturated permeabil- ity coefficient of the surface soil, not all of the rainwater 2.5 Analysis of the simulated results infiltrates into the soil, and some of it is discharged as sur - face runoff. Therefore, although rainfall increases the slid- According to the relevant regulations for slope classifica - ing force and reduces the anti-sliding force of the slope, its tion in Ref. [27], the research object belongs to a first-class impact on the stability of the slope is limited. After rainfall, slope, with a corresponding slope safety coefficient of 1.35. Railway Engineering Science 1 3 Rainfall intensity (mm/d) X. Wang et al. (a) (b) 1.46 300 1.70 300 1.69 250 1.44 1.68 200 1.42 1.67 150 1.66 100 1.40 100 1.65 50 1.38 1.64 0 0.00.5 1.01.5 2.02.5 3.0 0.00.5 1.01.5 2.02.5 3.0 Rainfall duration (d) Rainfall duration (d) Stability coefficients in condition 1 Rainfall in condition 1 Stability coefficients in condition 1 Rainfall in condition 1 Stability coefficients in condition 2 Rainfall in condition 2 Stability coefficients in condition 2 Rainfall in condition 2 (c) (d) 1.5 300 1.70 300 1.68 250 250 1.4 1.66 200 200 1.3 1.64 150 150 1.62 1.2 1.60 1.1 1.58 1.56 0 1.0 0 024 68 10 02 46 810 Rainfall duration (d) Rainfall duration (d) Stability coefficients in condition 3 Rainfall in condition 3 Stability coefficients in condition 3 Rainfall in condition 3 Stability coefficients in condition 4 Rainfall in condition 4 Stability coefficients in condition 4 Rainfall in condition 4 Fig. 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 the safety coefficients of the slopes are both greater than Under C4, the final stability coefficients of the two slopes 1.35, indicating that the slopes are still in a stable state. are 1.265 and 1.586, respectively, decreasing by 0.188 and According to Fig.  4c and d, the variation pattern of the 0.106 compared to their initial states. The decrease in stabil- stability coefficient differs between the natural slope and the ity coefficients is smaller than that under C3. By comparing reinforced slope. Under C3, after rainfall, the stability coeffi- C3 and C4, it can be concluded that under a constant rain- cients of the two slopes are 1.021 and 1.573, respectively, which fall duration and rainfall amount, continuous rainfall has a decrease by 0.432 and 0.119 from their initial states. The degree greater impact on slope stability than intermittent rainfall. of decrease is further increased compared to C2. Rainfall infil- Additionally, under C3 and C4, the stability coefficient tration has a significant impact on the stability of the natural curves of the two slopes are very close in the early stage slope, which is on the verge of failure after rainfall. This further and begin to separate after approximately 3 d. The stability illustrates that under a constant rainfall intensity, the longer the coefficient under C3 decreases faster than that under C4, and duration of rainfall is, the greater the decrease in the stability the difference between them becomes larger over time. This coefficient. Moreover, after a certain number of days, the stabil- suggests that the impact of continuous rainfall and intermit- ity coec ffi ient may decrease rapidly, and the slope will be on the tent rainfall on slope stability is almost the same in the early verge of failure. The reinforced slope has not experienced any stage, but the difference becomes more evident in the later failure under reasonable retaining structures. stage, especially after 8 d in the natural slope. Railway Engineering Science 1 3 Stability coefficients Stability coefficients Rainfall (mm) Rainfall (mm) Stability coefficients Stability coefficients Rainfall (mm) Rainfall (mm) Stability analysis of loose accumulation slopes under rainfall: case study of a high‑speed… Table 4 shows the stability status of the slopes after rainfall Finally, through the comparison between the field monitoring under different working conditions. There are significant dif- data, previous research results, and typical failure cases, the ferences in the final stability of natural slopes under different deformation and stability status of the field slope are scientifi- working conditions. The stability coefficients of the natural cally evaluated, providing reliable support for the numerical slope are greater than 1.35 under C1 and C2, indicating that simulation results presented in Sect. 2. 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 3.1 Monitoring overview state and on the verge of failure. Under C4, the stability coef- ficient of the slope is greater than 1 but less than 1.35, indicat - Automated monitoring of the slope using a rain gauge, a ing that the slope has an insufficient safety margin. global navigation satellite system (GNSS), and a deep dis- The stability coefficient of the reinforced slope decreases placement meter was carried out from January 11th to March to some extent under four working conditions. However, 31st, 2022. The monitoring contents and equipment can be compared with the natural slope, the difference in the sta- found in Table 5. bility coefficient is not significant under each condition, and As shown in Fig. 5, four monitoring sections (#1, #2, #3, the final value is still greater than 1.35, indicating that the and #4) were established in the area. A rain gauge was set slope is in a stable state. up in the area to monitor rainfall. A GNSS reference station Based on the above analysis, it can be concluded that was established in a relatively stable location to serve as the the establishment of slope retaining structures can not only benchmark, while GNSS monitoring stations were set up on improve the stability coefficient of the slope in its initial state the slope surface to monitor vertical and horizontal displace- but also effectively reduce the loss of the stability coefficient ments. Deep displacement meters were installed at different during the development of rainfall, ensuring slope stability. depths inside the slope through drilling to monitor internal Under the condition of a constant rainfall amount, this ee ff ct horizontal displacement. becomes more apparent as the rainfall duration increases. 3.2 Analysis of monitoring results 3 Field monitoring3.2.1 Rainfall intensity In this section, an automated monitoring system is established Figure 6 shows that the cumulative rainfall and daily rain- to monitor key indicators such as rainfall and slope displace- fall in the monitoring area gradually increased with time, ment for the stability analysis of a loose accumulation slope. and the rainfall frequency in March increased compared to By analysing the monitored data, the deformation characteris- before. The longest rainfall during the monitoring period tics of the slope under rainfall are revealed. The rationality of lasted from March 23rd to March 31st. The monitoring the numerical simulation model and the accuracy of the field data show that the rainfall intensity on site during the monitoring data are verified through a comparison between monitoring period is not very high compared to the his- the numerical simulation results and the field monitoring data. torical rainfall in this area. Table 4 Comparison of slope stability under different working conditions Slope types Initial state C1 C2 C3 C4 Natural slope Stable Stable Stable Limit equilibrium Insufficient safety margin (1.453) (1.417) (1.377) (1.021) (1.265) Reinforced slope Stable Stable Stable Stable Stable (1.692) (1.662) (1.643) (1.573) (1.586) The number in parentheses stands for the value of the stability coefficient in the corresponding working conditions Table 5 Monitoring content and equipment Equipment type Monitoring content Location of installation Rain gauge Rainfall Slope surface GNSS The vertical and horizontal displacement Deep displacement metre The horizontal displacement Inside of the slope Railway Engineering Science 1 3 X. Wang et al. 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 displace- ment, a horizontal composite displacement index (L) was G1 G4 established: G7 S1-S3 S10-S12 G10 S19-S20 2 2 (3) L = X + Y . G8 G5 G2 As shown in Table  6, the maximum vertical displace- S22-S24 S13-S15 G11 ment of all monitoring points is within 9 mm, with over 80% S4-S6 G9 S27-S29 of them within 7 mm. The maximum horizontal composite G3 S25-S26 displacement of each monitoring point is within 6 mm, with G6 S7-S9 approximately 73% of them within 4 mm. Overall, the sur- S16-S18 face 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 hori- zontal displacement of the slope in section #1. In the same Legend borehole, the larger the monitoring point number is, the Deep displacement meter GNSS reference station deeper it is buried. Among the upper part monitoring points S1–S3 of the slope, the displacement increase in S1 is much GNSS monitoring station Rain gauge larger than that in S2 and S3. The displacement variation curve of S1 is approximately linear, while the displacement Fig. 5 Monitoring area. G1–G11 stand for the monitoring points of variation of the other two monitoring points is relatively the internal horizontal displacement of the slope. S1–S29 represent small. At the middle part of the slope, the curves of S4–S6 the monitoring points of the slope surface displacement almost overlap with each other. The curves of S7 and S8 at 6 40 the lower part of the slope change similarly, while there is a Single-day rainfall slight change in the curve of monitoring point S9. Cumulative rainfall It can be observed from Fig. 7b that among the moni- toring 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 monitor- ing points in this monitoring section. Figure 7c shows that among the monitoring points at the 0 0 upper part of the slope in section #3, the displacement of Date 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 Fig. 6 Monitoring results of the rainfall intensity the curves. The displacement of S25 at the lower part of the slope increases significantly with time, while the displace- 3.2.2 Horizontal and vertical displacements on the slope ment of S26 develops slowly. surface As shown in Fig. 7d, the horizontal displacement of the deep monitoring points in #4 is generally small. Among In the GNSS monitoring results (Table 6), X and Y represent them, S29 at the deepest point is relatively stable with horizontal displacements, with their positive values indicat- almost no displacement. The displacements of S27 and S28 ing that the distances moved northward and eastward rela- develop slowly over time. tive to the initial time at the monitoring point, respectively, Railway Engineering Science 1 3 1/11 1/26 2/10 2/25 3/12 3/27 Single-day rainfall (mm) Cumulative rainfall (mm) Stability analysis of loose accumulation slopes under rainfall: case study of a high‑speed… Table 6 Monitoring results of the slope surface displacement Numbering and location of monitoring points Maximum vertical displacement Maximum horizontal (mm) composite displacement (mm) Slope in #1 Upper part G1 6.20 3.19 Middle part G2 6.40 4.90 Lower part G3 8.80 5.60 Slope in #2 Upper part G4 7.60 3.50 Middle part G5 7.00 3.70 Lower part G6 1.60 3.30 Slope in #3 Upper part G7 1.90 3.50 Middle part G8 6.50 3.30 Lower part G9 4.20 4.90 Slope in #4 Upper part G10 6.50 3.00 Lower part G11 6.50 2.90 (a) (b) S10 S1 S11 S2 S12 S3 S13 8 S4 S14 S5 S15 S6 S16 S7 S17 S8 4 S18 S9 -2 Date Date (c) (d) 3.5 9.0 S19 S27 S20 3.0 S28 S21 7.5 S29 S22 2.5 S23 6.0 S24 2.0 S25 4.5 S26 1.5 3.0 1.0 1.5 0.5 0.0 0.0 Date Date Fig. 7 Monitoring results of the internal horizontal displacement of the slope in monitoring sections a #1, b #2, c #3, and d #4 Railway Engineering Science 1 3 1/11 1/26 1/11 2/10 1/26 2/25 2/10 3/12 2/25 3/27 3/12 3/27 1/11 1/26 2/10 2/25 3/12 3/27 1/11 1/26 2/10 2/25 3/12 3/27 Displacement (mm) Displacement (mm) Displacement (mm) Displacement (mm) X. Wang et al. deformation rates of the other monitoring points are within (a) 0.5 mm/d. 3 S1 S2 S3 S4 3.3 Validation and analysis/discussion S5 S6 -1 3.3.1 Data verification S7 -2 S8 -3 S9 Considering the accuracy of the sensors and the influence of 1/12 1/26 2/92/233/9 3/23 the data collection environment, deep displacement gauges Date were selected for analysis. Rainfall data obtained from moni- (b) toring were imported into the simulation model for hydrome- S10 1.5 chanical coupling calculation. As shown in Fig. 9, the selec- S11 1.0 tion of deep displacement monitoring points in the model was S12 S13 consistent with field monitoring. Displacement simulation 0.5 S14 results were extracted at positions M1 to M8, resulting in 0.0 S15 Fig. 10. Overall, the simulation data and the actual monitor- S16 -0.5 ing data match well in the curves, indicating that the relevant S17 -1.0 parameters and boundary conditions set in the simulation S18 model are reasonable, and the modelling is simplified prop- 1/12 1/26 2/92/233/9 3/23 Date erly, which can reflect the actual state of the slope. It also (c) verifies the accuracy of the field monitoring data to some extent. 1.0 S19 S20 0.5 S21 S22 3.3.2 Data analysis 0.0 S26 S24 -0.5 In terms of the surface displacement of the slope, the GNSS S25 S26 monitoring data show fluctuations, especially in the verti- -1.0 cal displacement, and the maximum vertical displacement 1/12 1/26 2/92/233/9 3/23 of points is within 9 mm. The fluctuation amplitude of the Date (d) horizontal displacement is much smaller than that of the vertical displacement, while the horizontal displacement of 1.2 each point is within 6 mm. 0.9 In terms of the internal horizontal displacement of the S27 0.6 slope, the displacement of each point generally increases S28 0.3 over time, and the maximum displacement of most points is S29 within 6 mm. The deformation rate of each point has obvious 0.0 oscillations, with a maximum value of 2.7 mm/d, and during -0.3 most of the time, it does not exceed 1 mm/d. 1/12 1/26 2/92/233/9 3/23 Combining the monitoring results and Table 7, one can Date see that the displacement and deformation rate of the slope are currently very small, indicating that the slope is cur- Fig. 8 The horizontal displacement change rate inside the slope in rently undergoing slow deformation in its initial deforma- monitoring sections a #1, b #2, c #3, and d #4 tion stage and has good stability. From Fig.  8, the deformation rates of various monitor- 4 Conclusions ing points in sections #1 to #3 are generally within 1 mm/d, except for a few moments with larger values. Overall, the This paper investigates the evolution of the stability of a slope deformation rate is relatively small, and the curve shows loose accumulation slope along a high-speed railway in obvious oscillations. In section #4, except for the larger defor- the southwest mountainous area of China under rainfall mation rate of point S27 in the early monitoring period, the Railway Engineering Science 1 3 Deformation rate (mm/d) Deformation rate (mm/d) Deformation rate (mm/d) Deformation rate (mm/d) Stability analysis of loose accumulation slopes under rainfall: case study of a high‑speed… Anchor cable frame beam (a) M3 Deep displacement 4 M1 monitoring points S19 S20 S21 M6 M2 M7 M4 M1 M2 M3 Anchor cable pile M8 M5 3 Coarse breccia soil Completely Strongly weathered granite weathered granite Fig. 9 Locations of the monitoring points in the numerical simulation model Date conditions. By establishing a hydromechanical coupling finite element calculation model of the slope, the stability (b) of the loose accumulation slope under different rainfall con- ditions was analysed, and the validity of the finite element S22 S23 S24 model was verified by field monitoring data. The main con- M4 M5 M6 clusions are summarized as follows: (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 1 rainfall has a more significant impact on the stability of the slope than intermittent rainfall. -1 (2) The setting of retaining structures in the reinforced loose accumulation slope improves the initial stability Date of the slope and significantly alleviates the deteriora- (c) tion of the slope stability coefficient. Under all work - ing conditions, the stability coefficient of the reinforced S25 S26 slope is greater than 1.35, indicating good slope stabil- M7 M8 ity. This shows that field retaining structures can effec- tively reinforce the loose accumulation slope. (3) The deep displacement data of the slope in the numeri- cal 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 moni- toring 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) In this paper, the types of monitoring equipment and Date analysis indicators are relatively simple. In follow-up work, the stability analysis and monitoring of the loose Fig. 10 Comparison between the simulation results and the monitor- ing results of the horizontal displacement inside the slope: a between deposit slope can be studied from other angles by add- S19–S21 and M1–M3, b between S22–S24 and M4–M6, and c ing soil pressure sensors and soil moisture sensors. between S25–S26 and M7–M8 Railway Engineering Science 1 3 1/11 1/26 2/10 2/25 3/12 3/27 1/11 1/26 2/10 2/25 3/12 3/27 1/11 1/26 2/10 2/25 3/12 3/27 Displacement (mm) Displacement (mm) Displacement (mm) X. Wang et al. Table 7 Typical deformation conditions before slope failure Typical slope failure cases Prefailure state Xintan River landslide One month before failure, the deformation rate was between 85.9 and 399 mm/d Vajont landslide The deformation rate increased to 400 mm/d just before failure Jiming Temple landslide Ten days before failure, the deformation rate was above 50 mm/d, and one day before failure, it was above 100 mm/d Zipingpu Hydropower Station landslide Ten days before failure, the maximum horizontal displacement of the slope was 150.1 mm, and the maximum vertical displacement was 97.6 mm Huanglongxi Village landslide Seven days before failure, the deformation rate was 8.2 mm/d, and it increased to 300 mm/d near failure Acknowledgements This work was supported by the National Natural 12. Tschuchnigg F, Schweiger HF, Sloan SW (2015) Slope stability a Science Foundation of China (No. 51978588). nalysis by means of finite element limit analysis and finite element strength reduction techniques. Part I: numerical studies consider- Open Access This article is licensed under a Creative Commons Attri- ing non-associated plasticity. Comput Geotech 70:169–177 bution 4.0 International License, which permits use, sharing, adapta- 13. Wu H, Chen S, Pang Y (1999) Parametric study of effects of tion, distribution and reproduction in any medium or format, as long rain infiltration on unsaturated slopes. Rock Soil Mech 1:2–15 (in as you give appropriate credit to the original author(s) and the source, Chinese) provide a link to the Creative Commons licence, and indicate if changes 14. Buscarnera G, Di Prisco C (2013) Soil stability and flow slides in were made. The images or other third party material in this article are unsaturated shallow slopes: can saturation events trigger liquefac- included in the article’s Creative Commons licence, unless indicated tion processes? Géotechnique 63(10):801–817 otherwise in a credit line to the material. If material is not included in 15. Kim J, Salgado R, Yu HS (1999) Limit analysis of soil slopes the article’s Creative Commons licence and your intended use is not subjected to pore-water pressures. J Geotech Geoenviron Eng permitted by statutory regulation or exceeds the permitted use, you will 125(1):49–58 need to obtain permission directly from the copyright holder. To view a 16. Zienkiewicz OC, Humpheson C, Lewis RW (1975) Associated copy of this licence, visit http://cr eativ ecommons. or g/licen ses/ b y/4.0/ . and non-associated visco-plasticity and plasticity in soil mechan- ics. Geotechnique 25(4):671–689 17. Zheng Y, Zhao S, Zhang L (2002) Stability analysis by strength reduction FEM. Eng Sci 4(10):57–61 (in Chinese) References 18. Duncan JM (1996) State of the art: limit equilibrium and finite- element analysis of slopes. J Geotech Eng 122(7):577–596 1. Song Z, Zhang G, Jiang L et al (2016) Analysis of the character- 19. Han J, Chen A, Chuai X (2017) Mechanism of mountain typi- istics of major geological disasters and geological alignment of cal geological disaster and corresponding strategies: the case of Sichuan-Tibet railway. Railw Stand Des 60(1):14–19 (in Chinese) Lishui landslide and Wencheng debris flow. Henan Sci Technol 2. Wan Z, Li S, Bian X et al (2022) Mud pumping in high-speed 19:147–151 (in Chinese) railway: in-situ soil core test and full-scale model testing. Railw 20. Chen Y, Xu D (2013) FLAC/FLAC3D foundation and engineering Eng Sci 30(3):289–303 example, 2nd edn. China Water Resources and Hydropower Press, 3. Springman SM, Thielen A, Kienzler P et al (2013) A long-term Beijing, pp 265–276 (in Chinese) field study for the investigation of rainfall-induced landslides. 21. Yuan W (2014) Research on strength reduction method. Disserta- Géotechnique 63(14):1177–1193 tion, University of Chinese Academy of Sciences (in Chinese) 4. Bordoni M, Meisina C, Valentino R et al (2015) Hydrological factors 22. Zhou H, Cao P, Zhang K (2012) Analysis of slope reliability based affecting rainfall-induced shallow landslides: from the field monitor - on response surface method and strength reduction method. China ing to a simplified slope stability analysis. Eng Geol 193:19–37 Saf Sci J 22(5):79–84 5. Li Z, Zhang N (2001) Effects of rain infiltration on transient safety 23. Ye H, Zheng Y, Huang R et al (2010) Application of dynamic of unsaturated soil slope. Chin Civil Eng J 34(5):57–61 (in Chinese) analysis of strength reduction in the slope engineering under 6. Lin H, Yu Y, Li G et al (2009) Influence of rainfall characteristics earthquake. Eng Sci 8(3):41–48 on soil slope failure. Chin J Rock Mech Eng 28(1):198–204 (in 24. Zhang L, Zheng Y, Zhao S et al (2003) The feasibility study of Chinese) strength-reduction method with FEM for calculating safety factors 7. Hoek E, Bray JD (1981) Rock slope engineering. CRC Press, Boca of soil slope stability. J Hydraul Eng 34(1):21–26 (in Chinese) Raton, pp 12–86 25. Liu Z, Zhang H (2014) PLAXIS 3D basics tutorial. China 8. Stead D, Eberhardt E (1997) Developments in the analysis of foot- Machine Press, Beijing (in Chinese) wall slopes in surface coal mining. Eng Geol 46(1):41–61 26. General Administration of Quality Supervision, Inspection and 9. Sun G (1993) On the theory of structure-controlled rockmass. J Quarantine of the People’s Republic of China, China National Eng Geol 1(1):14–18 (in Chinese) Standardization Administration (2012) GB/T 28592–2012 Grade 10. Li AJ, Merifield RS, Lyamin AV (2008) Stability charts for rock of Precipitation. Meteorological Publishing House, Beijing (in slopes based on the Hoek-Brown failure criterion. Int J Rock Mech Chinese) Min Sci 45(5):689–700 27. Wu Y, Lan H, Gao X et al (2014) Rainfall threshold of storm- 11. Qian ZG, Li AJ, Lyamin AV et al (2017) Parametric studies of induced landslides in typhoon areas: a case study of Fujian prov- disturbed rock slope stability based on finite element limit analysis ince. J Eng Geol 22(2):255–262 (in Chinese) methods. Comput Geotech 81:155–166 Railway Engineering Science 1 3 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Railway Engineering Science Springer Journals

Stability analysis of loose accumulation slopes under rainfall: case study of a high-speed railway in Southwest China

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2662-4745
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10.1007/s40534-023-00317-1
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Abstract

The high and steep slopes along a high-speed railway in the mountainous area of Southwest China are mostly composed of loose accumulations of debris with large internal pores and poor stability, which can easily induce adverse geological disasters under rainfall conditions. To ensure the smooth construction of the high-speed railway and the subsequent safe operation, it is necessary to master the stability evolution process of the loose accumulation slope under rainfall. This article simulates rainfall using the finite element analysis software’s hydromechanical coupling module. The slope stability under various rainfall situations is calculated and analysed based on the strength reduction method. To validate the simulation results, a field monitoring system is established to study the deformation characteristics of the slope under rainfall. The results show that rainfall duration is the key factor affecting slope stability. Given a constant amount of rainfall, the stability of the slope decreases with increasing duration of rainfall. Moreover, when the amount and duration of rainfall are constant, continuous rainfall has a greater impact on slope stability than intermittent rainfall. The setting of the field retaining structures has a significant role in improving slope stability. The field monitoring data show that the slope is in the initial deformation stage and has good stability, which verifies the rationality of the numerical simulation method. The research results can provide some references for understanding the influence of rainfall on the stability of loose accumulation slopes along high-speed railways and establishing a monitoring system. Keywords High-speed railway · Loose accumulation slope · Slope stability analysis · Rainfall effect · Strength reduction 1 Introduction rainfall on slope stability, much work has been reported. For instance, Springman et al. [3] proposed a hydraulic analysis The mountainous areas in Southwest China are character- system for slope instability and failure based on field meas- ized by unfavourable geological conditions, such as high urements and local meteorological data. Then, Bordoni et al. ground stress and high ground temperature, which can lead [4] supplemented the hydraulic analysis system for slope to geological disasters including debris flows and landslides, instability and failure and conducted in-depth research on posing risks and challenges to the construction and operation the influence of various physical and mechanical parameters. of local railways [1]. Using the basic theory of unsaturated soil water movement, Rainfall is an important factor affecting the stability of Li et al. [5] proposed a calculation model for the transient railway subgrades and slopes [2]. Regarding the impact of water content in rainfall infiltration analysis of an unsatu- rated soil slope and obtained the slope safety coefficient calculation formula. Lin et al. [6] conducted multiple sets * Qian Su of model tests on rainfall-induced slope instability and pro- tmsq@home.swjtu.edu.cn posed using the rainfall intensity and cumulative rainfall as School of Civil Engineering, Southwest Jiaotong University, two indicators for slope rainfall warning. Chengdu 610031, China Currently, the main methods for slope stability analysis Key Laboratory of High-Speed Railway Engineering include empirical analysis, limit equilibrium analysis, and Ministry of Education, School of Civil Engineering, numerical analysis. Hoek et al. [7] classified slope failure Southwest Jiaotong University, Chengdu 610031, China forms into planar failure, wedge failure, circular failure, CCCC Second Highway Consultants Co., Ltd., and toppling failure and obtained the failure mechanism Wuhan 430056, China Vol.:(0123456789) 1 3 X. Wang et al. and stability coefficient calculation methods for different However, research on high and steep loose accumulation forms. Douglas et al. [8] classified slope failure types into slopes has been relatively limited, and the understanding of landslides and toppling based on the motion characteristics their structure and stability is insufficient. Therefore, this before the critical failure of the slope. Sun [9] divided unsta- paper takes the slopes of the adverse geological section ble slope failures into 9 categories according to the failure along a high-speed railway in the southwest mountainous reasons. The above studies assumed the presence of weak area of China as the research object, uses numerical simula- zones in slopes to determine their failure modes. If a slope tion software to study the impact of rainfall on slope stabil- does not have significant weak zones, then the applicability ity, and evaluates the reinforcement effect of field retaining of the traditional empirical analysis and limit equilibrium structures. Additionally, an automated monitoring system is analysis will significantly decrease. established to evaluate the slope status based on monitoring With the development of numerical simulation tech- indicators. The study reveals the evolutionary process of the niques, new methods for analysing slope stability, such as the stability of loose accumulation slopes along the high-speed finite element method, finite difference method, and hybrid railway in the southwest mountainous area of China under methods based on finite element and new limit analysis or rainfall, which can provide a reference for the establishment new strength reduction methods, have emerged. Li et al. [10] of monitoring systems for such slopes and effective preven- carried out relevant research on slope stability using a new tion of geological disasters. limit analysis method based on the Hoek‒Brown criterion to obtain the slope stability coeci ffi ent and safety coeci ffi ent. Taking the disturbance effect into account, Qian et al. [11] carried out a new limit analysis of slope stability and sum- 2 Numerical model development marized the results in the form of design drawings. Aim- ing at the problem of soil slope stability, Tschuchnigg et al. In this section, the deformation characteristics and stability [12] systematically compared the difference between the of the loose accumulation slope under rainfall are inves- new limit analysis method and the new strength reduction tigated by setting various types of rainfall conditions in method. Wu et al. [13] used SEEP/W numerical simulation numerical simulation software. Furthermore, the effective- software to study the influencing parameters of unsaturated ness of retaining structures is evaluated through a compara- soil stability under rainfall and analysed the influence of tive analysis between natural slopes and reinforced slopes. rainfall intensity and other parameters on slope stability. In addition, Buscarnera et al. [14] studied the seepage defor- mation characteristics of shallow soil under the condition of 2.1 Project overview rainwater infiltration using the finite element method. Kim et al. [15] established the equivalent relationship between The study area is located in the southwestern mountainous region of China, with a natural slope of 30°–35° and an pore water pressure and load and evaluated the slope stabil- ity using the finite-element upper-bound analysis method. absolute elevation range of 3191–3760 m. The surface layer in the area is mainly composed of a Quaternary Holocene Zienkiewicz et al. [16] first combined traditional strength col reduction theory with the finite element method and pro- colluvial layer (Q4 ) such as coarse breccia soil, gravel soil, and rocky soil, while the underlying bedrock is com- posed a new strength reduction method based on the finite element method, which makes the analysis of slope stabil- posed of Neogene (ηγ N ) coarse-grained biotite monzo- granite. According to meteorological statistics, the average ity more intuitive and convenient. Zheng et al. [17] wrote a theoretical analysis program based on the new strength 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 reduction method and achieved good application results in several slope cases. Duncan et al. [18] studied the stability of July. The extreme lowest and highest temperatures in a year are −17.2 °C and 23.4 °C, respectively. The average annual soil slopes based on the new strength reduction method and obtained the slope stability coefficient, an important index rainfall is 947.5  mm, and the maximum daily rainfall is 63.14 mm. The maximum annual snow depth is 15.53 cm, to measure slope safety. The new strength reduction method has been increasingly used in slope stability analysis due to and the relative humidity is 64%. The sunshine duration is 2525.9 h, and the frost-free period lasts for 95 d. its clear computational logic, ease of programming imple- mentation, and high reliability of results. The slope stability To ensure slope stability during railway construction, reinforcement measures are planned for the field slope. Spe- analysis in this paper is also based on this method. In summary, scholars worldwide have made significant cific measures include installing anchor cable piles near the foot of the slope, arranging multilevel anchor cable frame progress in the study of slope stability, forming a series of theories and methods. In particular, the impact of rainfall beams in the middle and upper parts of the slope, and setting up flexible protective nets in areas where rockfall may occur. infiltration on slope stability has been studied in depth. Railway Engineering Science 1 3 Stability analysis of loose accumulation slopes under rainfall: case study of a high‑speed… 2.2 Principles of stability analysis (a) 100 168 150 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 Coarse breccia soil initial reduction coefficient and then perform numerical sim- ulation calculations on the slope stability. If the calculated Completely Strongly weathered granite weathered slope is still in a stable state, then increase the reduction granite 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 (b) 2.75 considered to be the stability coefficient of the slope [19]. Anchor cable frame beam The calculation formulas are shown in Eqs. (1) and (2): c = c∕F , (1) m r Coarse breccia soil = arc tan(tan∕F ), Anchor cable pile (2) m r Completely weathered Strongly weathered granite where c is the reduced cohesion of soil, c is the cohesion granite of soil, φ is the reduced internal friction angle of soil, φ is the internal friction angle of soil, and F is the reduction coefficient. Fig. 1 Model diagram: a natural slope and b reinforced slope (unit: m) 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 The natural slope soil is modelled using solid ele- ments, and the physical and mechanical parameters are method, the strength reduction method has the following advantages [20–23]: shown in Table  1. To describe the unsaturated seepage behaviour, the soil‒water characteristic curve of the soil (1) It can perform numerical analysis on slopes with com- is determined using a built-in model in the simulation software. Although there is some difference from reality, plex terrain and geological structures. (2) It can simulate multiphysics coupled engineering considering the important impact of rainfall on slope sta- bility, this approach is feasible [25]. The adopted model problems, such as earthquakes, rainfall, and changes in water levels. is shown in Fig.  2. The types of elements used in the retaining structure for the reinforced slope, as well as (3) It can consider the combined effects of soil and retain- ing structures. their corresponding material parameters, are shown in Table 2. (4) It does not require assuming sliding surfaces or divid- ing the soil into strips. In the model, the boundary condition of infiltration is set as follows: the bottom boundary is set as imperme- able, while the other boundaries are permeable. When the rainfall intensity is less than the saturated permeability 2.3 Model establishment and material parameters coefficient of the soil, it is assumed that all rainwater infil- trates into the soil. When the rainfall intensity exceeds the This paper uses PLAXIS 3D for numerical simula- tion. A numerical analysis model is established through saturated permeability coefficient of the soil, the rainwater infiltrates into the soil according to the magnitude of the proper cross-sectional simplification and size amplifi- cation [24] based on the field slope within the range of saturated permeability coefficient, and the excess part is discharged as slope runoff. D3K278 + 824 – D3K278 + 884. The cross section of the model is shown in Fig. 1. The dimensions, soil layer distri- The displacement boundary condition is set as follows: the free surface of the slope model selects the free bound- bution, and groundwater level of the reinforced slope model are the same as those of the natural slope, and the retaining ary, the side is constrained by horizontal displacement, and the bottom is fixed. structures are consistent with those in the field. Railway Engineering Science 1 3 1 1.85 68 20 154 26 X. Wang et al. Table 1 Soil material parameters Parameters Unit Saturated unit Cohe- Internal Elastic Poisson’s Porosity ratio Permeability weight weight sion friction modulus ratio coefficient 3 3 (kN/m ) (kN/m ) (kPa) angle (°) (MPa) (m/d) Coarse breccia soil 20 22 25 38 35 0.25 0.35 0.26 Completely weathered granite 21 23.5 20 20 50 0.3 0.5 0.7 Strongly weathered granite 23 24 0 45 200 0.25 0.4 0.36 (a) (b) -2.5 -2.5 -2.0 -2.0 -1.5 -1.5 -1.0 -1.0 -0.5 -0.5 0.0 0.0 -5 -4 -3 -2 -1 0 0.0 0.2 0.4 0.6 0.8 1.0 10 10 10 10 10 10 K S r r Fig. 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. K is the relative permeability coefficient, and S is the effective saturation, both of which are dimensionless quantities, and r r ψ is the matrix suction head Table 2 Material parameters of the retaining structures Parameters Simulation element Unit weight (kN/m ) Elastic modulus (MPa) Stabilizing pile Solid element 25 3.15 × 10 Free segment of the anchor cable Node to node anchor element – – Anchorage segment of the anchor cable Embedded beam element 24 3.90 × 10 Frame beam Plate element 25 3.15 × 10 groundwater level is above the model bottom boundary, 2.4 Numerical analysis methods so the "ignore suction" option is unchecked during the calculation. The specific steps of the numerical simulation analysis are as follows: (3) Rainfall in China is generally classified into seven grades, as shown in Table 3 [26]. By using the hydro- (1) The initial stress equilibrium of the natural slope is mechanical coupling module, the natural slope is simu- lated under rainfall conditions. Referring to local mete- calculated using the gravity loading method under the initial condition. orological and hydrological data, the total simulated rainfall is determined to be 300 mm, and four working (2) The stability of the natural slope is calculated using the safety calculation module. As shown in Fig. 1, the conditions are set as follows: Railway Engineering Science 1 3 (m) (m) Stability analysis of loose accumulation slopes under rainfall: case study of a high‑speed… Table 3 Rainfall grades 350 Rainfall grades 24-h rainfall (mm) Condition 1 Trace rain < 0.1 Condition 2 Light rain 0.1–10 Condition 3 Condition 4 Moderate rain 10–25 Heavy rain 25–50 Storm 50–100 Heavy storm 100–250 Super heavy storm ≥ 250 1) Condition 1: Super heavy storm with rainfall inten- 0246 810 sity of 300 mm/d and rainfall duration of 1 d. Rainfall duration (d) 2) Condition 2: Heavy storm with rainfall intensity of 100 mm/d and rainfall duration of 3 d. Fig. 3 Working conditions of rainfall 3) Condition 3: Heavy rain with a rainfall intensity of 30 mm/d and a rainfall duration of 10 d. 4) Condition 4: Intermittent Storm with rainfall inten- When the slope stability coefficient is greater than this value, sity of 60 mm/d and rainfall duration of 10 d. the slope is considered stable. Through calculation, the sta- bility coefficients of the natural slope and the reinforced In the remainder of the paper, Conditions 1, 2, 3, and slope in the initial state were found to be 1.453 and 1.692, 4 are abbreviated as C1, C2, C3, and C4, respectively. respectively. The relationship between rainfall intensity and duration Figure 4a and b shows that the stability coefficients of the for each condition is shown in Fig. 3. natural slope and the reinforced slope follow a similar pat- tern under the first two working conditions. Under C1, the stability coefficients almost linearly decrease with the dura - (4) After the simulation of rainfall on the natural slope is tion of rainfall. After rainfall, the stability coefficients of the completed, the safety calculation module is used again natural slope and the reinforced slope are 1.417 and 1.662, to analyse the impact of rainfall on the stability of the respectively, which decrease by 0.036 and 0.030 from their natural slope. initial states. The decrease in stability is small and similar (5) After step (1), the plastic calculation module is set for both slopes, indicating that rainfall conditions with short up, and the anchor cable piles and anchor cable frame duration and large amount of rainfall have a very limited beams are activated to simulate the construction pro- impact on the slope stability. cess of the slope support structure. The prestress of Under C2, the stability coefficients decrease approxi- the free segment of the anchor cable in the anchor mately linearly with rainfall duration and then accelerate cable piles and anchor cable frame beams is set as after 1.5 d. After rainfall ends, the stability coefficients 156 and 52 kN, respectively, based on the field design of the two slopes are 1.377 and 1.643, respectively, which data. decrease by 0.076 and 0.049 from their initial states. The (6) The stability of the reinforced slope is calculated using decrease in stability coefficients is greater than that under the safety calculation module. C1. This indicates that under a constant rainfall amount, (7) The rainfall condition of the reinforced slope is simu- a longer rainfall duration leads to a greater decrease in lated using the hydromechanical coupling module, with slope stability coefficients. This is because the infiltra- the same boundary and working conditions as the natu- tion volume and depth under C2 are larger than those ral slope. under C1. (8) The impact of rainfall on the stability of the rein- Under C1 and C2, the reduction in the two types of slope forced slope is analysed using the safety calculation stability coefficients is not significant. Under C1, due to the module. rainfall intensity being greater than the saturated permeabil- ity coefficient of the surface soil, not all of the rainwater 2.5 Analysis of the simulated results infiltrates into the soil, and some of it is discharged as sur - face runoff. Therefore, although rainfall increases the slid- According to the relevant regulations for slope classifica - ing force and reduces the anti-sliding force of the slope, its tion in Ref. [27], the research object belongs to a first-class impact on the stability of the slope is limited. After rainfall, slope, with a corresponding slope safety coefficient of 1.35. Railway Engineering Science 1 3 Rainfall intensity (mm/d) X. Wang et al. (a) (b) 1.46 300 1.70 300 1.69 250 1.44 1.68 200 1.42 1.67 150 1.66 100 1.40 100 1.65 50 1.38 1.64 0 0.00.5 1.01.5 2.02.5 3.0 0.00.5 1.01.5 2.02.5 3.0 Rainfall duration (d) Rainfall duration (d) Stability coefficients in condition 1 Rainfall in condition 1 Stability coefficients in condition 1 Rainfall in condition 1 Stability coefficients in condition 2 Rainfall in condition 2 Stability coefficients in condition 2 Rainfall in condition 2 (c) (d) 1.5 300 1.70 300 1.68 250 250 1.4 1.66 200 200 1.3 1.64 150 150 1.62 1.2 1.60 1.1 1.58 1.56 0 1.0 0 024 68 10 02 46 810 Rainfall duration (d) Rainfall duration (d) Stability coefficients in condition 3 Rainfall in condition 3 Stability coefficients in condition 3 Rainfall in condition 3 Stability coefficients in condition 4 Rainfall in condition 4 Stability coefficients in condition 4 Rainfall in condition 4 Fig. 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 the safety coefficients of the slopes are both greater than Under C4, the final stability coefficients of the two slopes 1.35, indicating that the slopes are still in a stable state. are 1.265 and 1.586, respectively, decreasing by 0.188 and According to Fig.  4c and d, the variation pattern of the 0.106 compared to their initial states. The decrease in stabil- stability coefficient differs between the natural slope and the ity coefficients is smaller than that under C3. By comparing reinforced slope. Under C3, after rainfall, the stability coeffi- C3 and C4, it can be concluded that under a constant rain- cients of the two slopes are 1.021 and 1.573, respectively, which fall duration and rainfall amount, continuous rainfall has a decrease by 0.432 and 0.119 from their initial states. The degree greater impact on slope stability than intermittent rainfall. of decrease is further increased compared to C2. Rainfall infil- Additionally, under C3 and C4, the stability coefficient tration has a significant impact on the stability of the natural curves of the two slopes are very close in the early stage slope, which is on the verge of failure after rainfall. This further and begin to separate after approximately 3 d. The stability illustrates that under a constant rainfall intensity, the longer the coefficient under C3 decreases faster than that under C4, and duration of rainfall is, the greater the decrease in the stability the difference between them becomes larger over time. This coefficient. Moreover, after a certain number of days, the stabil- suggests that the impact of continuous rainfall and intermit- ity coec ffi ient may decrease rapidly, and the slope will be on the tent rainfall on slope stability is almost the same in the early verge of failure. The reinforced slope has not experienced any stage, but the difference becomes more evident in the later failure under reasonable retaining structures. stage, especially after 8 d in the natural slope. Railway Engineering Science 1 3 Stability coefficients Stability coefficients Rainfall (mm) Rainfall (mm) Stability coefficients Stability coefficients Rainfall (mm) Rainfall (mm) Stability analysis of loose accumulation slopes under rainfall: case study of a high‑speed… Table 4 shows the stability status of the slopes after rainfall Finally, through the comparison between the field monitoring under different working conditions. There are significant dif- data, previous research results, and typical failure cases, the ferences in the final stability of natural slopes under different deformation and stability status of the field slope are scientifi- working conditions. The stability coefficients of the natural cally evaluated, providing reliable support for the numerical slope are greater than 1.35 under C1 and C2, indicating that simulation results presented in Sect. 2. 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 3.1 Monitoring overview state and on the verge of failure. Under C4, the stability coef- ficient of the slope is greater than 1 but less than 1.35, indicat - Automated monitoring of the slope using a rain gauge, a ing that the slope has an insufficient safety margin. global navigation satellite system (GNSS), and a deep dis- The stability coefficient of the reinforced slope decreases placement meter was carried out from January 11th to March to some extent under four working conditions. However, 31st, 2022. The monitoring contents and equipment can be compared with the natural slope, the difference in the sta- found in Table 5. bility coefficient is not significant under each condition, and As shown in Fig. 5, four monitoring sections (#1, #2, #3, the final value is still greater than 1.35, indicating that the and #4) were established in the area. A rain gauge was set slope is in a stable state. up in the area to monitor rainfall. A GNSS reference station Based on the above analysis, it can be concluded that was established in a relatively stable location to serve as the the establishment of slope retaining structures can not only benchmark, while GNSS monitoring stations were set up on improve the stability coefficient of the slope in its initial state the slope surface to monitor vertical and horizontal displace- but also effectively reduce the loss of the stability coefficient ments. Deep displacement meters were installed at different during the development of rainfall, ensuring slope stability. depths inside the slope through drilling to monitor internal Under the condition of a constant rainfall amount, this ee ff ct horizontal displacement. becomes more apparent as the rainfall duration increases. 3.2 Analysis of monitoring results 3 Field monitoring3.2.1 Rainfall intensity In this section, an automated monitoring system is established Figure 6 shows that the cumulative rainfall and daily rain- to monitor key indicators such as rainfall and slope displace- fall in the monitoring area gradually increased with time, ment for the stability analysis of a loose accumulation slope. and the rainfall frequency in March increased compared to By analysing the monitored data, the deformation characteris- before. The longest rainfall during the monitoring period tics of the slope under rainfall are revealed. The rationality of lasted from March 23rd to March 31st. The monitoring the numerical simulation model and the accuracy of the field data show that the rainfall intensity on site during the monitoring data are verified through a comparison between monitoring period is not very high compared to the his- the numerical simulation results and the field monitoring data. torical rainfall in this area. Table 4 Comparison of slope stability under different working conditions Slope types Initial state C1 C2 C3 C4 Natural slope Stable Stable Stable Limit equilibrium Insufficient safety margin (1.453) (1.417) (1.377) (1.021) (1.265) Reinforced slope Stable Stable Stable Stable Stable (1.692) (1.662) (1.643) (1.573) (1.586) The number in parentheses stands for the value of the stability coefficient in the corresponding working conditions Table 5 Monitoring content and equipment Equipment type Monitoring content Location of installation Rain gauge Rainfall Slope surface GNSS The vertical and horizontal displacement Deep displacement metre The horizontal displacement Inside of the slope Railway Engineering Science 1 3 X. Wang et al. 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 displace- ment, a horizontal composite displacement index (L) was G1 G4 established: G7 S1-S3 S10-S12 G10 S19-S20 2 2 (3) L = X + Y . G8 G5 G2 As shown in Table  6, the maximum vertical displace- S22-S24 S13-S15 G11 ment of all monitoring points is within 9 mm, with over 80% S4-S6 G9 S27-S29 of them within 7 mm. The maximum horizontal composite G3 S25-S26 displacement of each monitoring point is within 6 mm, with G6 S7-S9 approximately 73% of them within 4 mm. Overall, the sur- S16-S18 face 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 hori- zontal displacement of the slope in section #1. In the same Legend borehole, the larger the monitoring point number is, the Deep displacement meter GNSS reference station deeper it is buried. Among the upper part monitoring points S1–S3 of the slope, the displacement increase in S1 is much GNSS monitoring station Rain gauge larger than that in S2 and S3. The displacement variation curve of S1 is approximately linear, while the displacement Fig. 5 Monitoring area. G1–G11 stand for the monitoring points of variation of the other two monitoring points is relatively the internal horizontal displacement of the slope. S1–S29 represent small. At the middle part of the slope, the curves of S4–S6 the monitoring points of the slope surface displacement almost overlap with each other. The curves of S7 and S8 at 6 40 the lower part of the slope change similarly, while there is a Single-day rainfall slight change in the curve of monitoring point S9. Cumulative rainfall It can be observed from Fig. 7b that among the moni- toring 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 monitor- ing points in this monitoring section. Figure 7c shows that among the monitoring points at the 0 0 upper part of the slope in section #3, the displacement of Date 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 Fig. 6 Monitoring results of the rainfall intensity the curves. The displacement of S25 at the lower part of the slope increases significantly with time, while the displace- 3.2.2 Horizontal and vertical displacements on the slope ment of S26 develops slowly. surface As shown in Fig. 7d, the horizontal displacement of the deep monitoring points in #4 is generally small. Among In the GNSS monitoring results (Table 6), X and Y represent them, S29 at the deepest point is relatively stable with horizontal displacements, with their positive values indicat- almost no displacement. The displacements of S27 and S28 ing that the distances moved northward and eastward rela- develop slowly over time. tive to the initial time at the monitoring point, respectively, Railway Engineering Science 1 3 1/11 1/26 2/10 2/25 3/12 3/27 Single-day rainfall (mm) Cumulative rainfall (mm) Stability analysis of loose accumulation slopes under rainfall: case study of a high‑speed… Table 6 Monitoring results of the slope surface displacement Numbering and location of monitoring points Maximum vertical displacement Maximum horizontal (mm) composite displacement (mm) Slope in #1 Upper part G1 6.20 3.19 Middle part G2 6.40 4.90 Lower part G3 8.80 5.60 Slope in #2 Upper part G4 7.60 3.50 Middle part G5 7.00 3.70 Lower part G6 1.60 3.30 Slope in #3 Upper part G7 1.90 3.50 Middle part G8 6.50 3.30 Lower part G9 4.20 4.90 Slope in #4 Upper part G10 6.50 3.00 Lower part G11 6.50 2.90 (a) (b) S10 S1 S11 S2 S12 S3 S13 8 S4 S14 S5 S15 S6 S16 S7 S17 S8 4 S18 S9 -2 Date Date (c) (d) 3.5 9.0 S19 S27 S20 3.0 S28 S21 7.5 S29 S22 2.5 S23 6.0 S24 2.0 S25 4.5 S26 1.5 3.0 1.0 1.5 0.5 0.0 0.0 Date Date Fig. 7 Monitoring results of the internal horizontal displacement of the slope in monitoring sections a #1, b #2, c #3, and d #4 Railway Engineering Science 1 3 1/11 1/26 1/11 2/10 1/26 2/25 2/10 3/12 2/25 3/27 3/12 3/27 1/11 1/26 2/10 2/25 3/12 3/27 1/11 1/26 2/10 2/25 3/12 3/27 Displacement (mm) Displacement (mm) Displacement (mm) Displacement (mm) X. Wang et al. deformation rates of the other monitoring points are within (a) 0.5 mm/d. 3 S1 S2 S3 S4 3.3 Validation and analysis/discussion S5 S6 -1 3.3.1 Data verification S7 -2 S8 -3 S9 Considering the accuracy of the sensors and the influence of 1/12 1/26 2/92/233/9 3/23 the data collection environment, deep displacement gauges Date were selected for analysis. Rainfall data obtained from moni- (b) toring were imported into the simulation model for hydrome- S10 1.5 chanical coupling calculation. As shown in Fig. 9, the selec- S11 1.0 tion of deep displacement monitoring points in the model was S12 S13 consistent with field monitoring. Displacement simulation 0.5 S14 results were extracted at positions M1 to M8, resulting in 0.0 S15 Fig. 10. Overall, the simulation data and the actual monitor- S16 -0.5 ing data match well in the curves, indicating that the relevant S17 -1.0 parameters and boundary conditions set in the simulation S18 model are reasonable, and the modelling is simplified prop- 1/12 1/26 2/92/233/9 3/23 Date erly, which can reflect the actual state of the slope. It also (c) verifies the accuracy of the field monitoring data to some extent. 1.0 S19 S20 0.5 S21 S22 3.3.2 Data analysis 0.0 S26 S24 -0.5 In terms of the surface displacement of the slope, the GNSS S25 S26 monitoring data show fluctuations, especially in the verti- -1.0 cal displacement, and the maximum vertical displacement 1/12 1/26 2/92/233/9 3/23 of points is within 9 mm. The fluctuation amplitude of the Date (d) horizontal displacement is much smaller than that of the vertical displacement, while the horizontal displacement of 1.2 each point is within 6 mm. 0.9 In terms of the internal horizontal displacement of the S27 0.6 slope, the displacement of each point generally increases S28 0.3 over time, and the maximum displacement of most points is S29 within 6 mm. The deformation rate of each point has obvious 0.0 oscillations, with a maximum value of 2.7 mm/d, and during -0.3 most of the time, it does not exceed 1 mm/d. 1/12 1/26 2/92/233/9 3/23 Combining the monitoring results and Table 7, one can Date see that the displacement and deformation rate of the slope are currently very small, indicating that the slope is cur- Fig. 8 The horizontal displacement change rate inside the slope in rently undergoing slow deformation in its initial deforma- monitoring sections a #1, b #2, c #3, and d #4 tion stage and has good stability. From Fig.  8, the deformation rates of various monitor- 4 Conclusions ing points in sections #1 to #3 are generally within 1 mm/d, except for a few moments with larger values. Overall, the This paper investigates the evolution of the stability of a slope deformation rate is relatively small, and the curve shows loose accumulation slope along a high-speed railway in obvious oscillations. In section #4, except for the larger defor- the southwest mountainous area of China under rainfall mation rate of point S27 in the early monitoring period, the Railway Engineering Science 1 3 Deformation rate (mm/d) Deformation rate (mm/d) Deformation rate (mm/d) Deformation rate (mm/d) Stability analysis of loose accumulation slopes under rainfall: case study of a high‑speed… Anchor cable frame beam (a) M3 Deep displacement 4 M1 monitoring points S19 S20 S21 M6 M2 M7 M4 M1 M2 M3 Anchor cable pile M8 M5 3 Coarse breccia soil Completely Strongly weathered granite weathered granite Fig. 9 Locations of the monitoring points in the numerical simulation model Date conditions. By establishing a hydromechanical coupling finite element calculation model of the slope, the stability (b) of the loose accumulation slope under different rainfall con- ditions was analysed, and the validity of the finite element S22 S23 S24 model was verified by field monitoring data. The main con- M4 M5 M6 clusions are summarized as follows: (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 1 rainfall has a more significant impact on the stability of the slope than intermittent rainfall. -1 (2) The setting of retaining structures in the reinforced loose accumulation slope improves the initial stability Date of the slope and significantly alleviates the deteriora- (c) tion of the slope stability coefficient. Under all work - ing conditions, the stability coefficient of the reinforced S25 S26 slope is greater than 1.35, indicating good slope stabil- M7 M8 ity. This shows that field retaining structures can effec- tively reinforce the loose accumulation slope. (3) The deep displacement data of the slope in the numeri- cal 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 moni- toring 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) In this paper, the types of monitoring equipment and Date analysis indicators are relatively simple. In follow-up work, the stability analysis and monitoring of the loose Fig. 10 Comparison between the simulation results and the monitor- ing results of the horizontal displacement inside the slope: a between deposit slope can be studied from other angles by add- S19–S21 and M1–M3, b between S22–S24 and M4–M6, and c ing soil pressure sensors and soil moisture sensors. between S25–S26 and M7–M8 Railway Engineering Science 1 3 1/11 1/26 2/10 2/25 3/12 3/27 1/11 1/26 2/10 2/25 3/12 3/27 1/11 1/26 2/10 2/25 3/12 3/27 Displacement (mm) Displacement (mm) Displacement (mm) X. Wang et al. Table 7 Typical deformation conditions before slope failure Typical slope failure cases Prefailure state Xintan River landslide One month before failure, the deformation rate was between 85.9 and 399 mm/d Vajont landslide The deformation rate increased to 400 mm/d just before failure Jiming Temple landslide Ten days before failure, the deformation rate was above 50 mm/d, and one day before failure, it was above 100 mm/d Zipingpu Hydropower Station landslide Ten days before failure, the maximum horizontal displacement of the slope was 150.1 mm, and the maximum vertical displacement was 97.6 mm Huanglongxi Village landslide Seven days before failure, the deformation rate was 8.2 mm/d, and it increased to 300 mm/d near failure Acknowledgements This work was supported by the National Natural 12. Tschuchnigg F, Schweiger HF, Sloan SW (2015) Slope stability a Science Foundation of China (No. 51978588). nalysis by means of finite element limit analysis and finite element strength reduction techniques. Part I: numerical studies consider- Open Access This article is licensed under a Creative Commons Attri- ing non-associated plasticity. Comput Geotech 70:169–177 bution 4.0 International License, which permits use, sharing, adapta- 13. Wu H, Chen S, Pang Y (1999) Parametric study of effects of tion, distribution and reproduction in any medium or format, as long rain infiltration on unsaturated slopes. Rock Soil Mech 1:2–15 (in as you give appropriate credit to the original author(s) and the source, Chinese) provide a link to the Creative Commons licence, and indicate if changes 14. Buscarnera G, Di Prisco C (2013) Soil stability and flow slides in were made. 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Journal

Railway Engineering ScienceSpringer Journals

Published: Sep 12, 2023

Keywords: High-speed railway; Loose accumulation slope; Slope stability analysis; Rainfall effect; Strength reduction

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