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Rainfall thresholds of shallow landslides in Wuyuan County of Jiangxi Province, China

  • Xiaochao Li , Handong Liu , Jishun Pan , Dongdong Li EMAIL logo and Jin Wang
Published/Copyright: October 3, 2020
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Abstract

Rainfall is a critical factor inducing landslides, and thus the study of rainfall thresholds is of great significance for the prediction and prevention of landslides. In June 2017, infrastructures such as electric power pylons and roads were threatened by group-occurring landslides due to continuous heavy rainfall in Wuyuan County, Jiangxi Province of China. Based on the analysis of the rainfall data from March to September in this region, the lower (92.4 mm/d) and the upper (217.1 mm/d) empirical rainfall thresholds were determined. The soil water characteristic parameters of a typical landslide were determined by laboratory tests and back-analysis. Then, the factor of safety (FOS) versus time and the mechanical response of failure process with rainfall infiltration were examined. The results showed that during rainfall infiltration, the pore-water pressure increased, while the matrix suction and the stability decreased gradually. After the rain, the FOS increased slowly to a constant value, which was smaller than the initial. The physical rainfall threshold (200 mm/d), determined using 18 numerical simulation tests considering different rainfall intensities and amounts, was consistent with the empirical rainfall threshold. The methods developed in this work provide a useful tool for the prediction of landslides under extreme rainfall conditions.

1 Introduction

Landslides induced by rainfall, posing a great threat to lives and infrastructures in mountain areas, have received increased attention in recent decades [1,2,3,4,5,6,7,8]. Thus, quantifying the triggering rainfall thresholds in a region will be of great importance in risk assessments and early warning of landslide hazards.

The relationship between rainfall and landslides is affected by several factors, such as rainfall intensity, rainfall duration, accumulated rainfall, antecedent accumulated rainfall, and geomorphologic and geological characteristics of a slope [9,10,11,12,13,14,15]. Thus, an effective method to study this dependence is essential. The widely used methods of threshold definition are the basic concept method [13,16,17] and the statistical method [17,18,19,20,21,22]. For the basic concept method, the thresholds were drawn manually by delimiting the lower bound of the point cloud representing the triggering rainfall conditions or by searching the best fit of the lower part of the cloud [13]. While the statistical method was conducted by establishing the relationship between rainfall conditions and rainfall thresholds based on the principles of statistics. Many triggering rainfall thresholds have been established for early warning of rainfall-induced landslides in different regions, depending on the statistical analysis of historical landslide records and the corresponding rainfall conditions [18,23,24,25,26,27,28,29,30,31,32,33,34,35]. The previous studies on triggering rainfall thresholds focused on the statistical analysis of rainfall events and landslides, and little attention was paid to the failure mechanism of rainfall-induced landslides [36,37,38]. In recent years, a synthetic approach has been adopted in many studies, combining the physical failure mechanism with empirical approaches [26,37,39,40].

Jiangxi Province is a region with high susceptibility to landslides in Southeast China. The number of landslides has reached 6,634 according to the Geological Hazard Survey of 35 counties in Jiangxi, among which the rainfall-induced landslides account for 79.7% [41]. However, few studies on triggering rainfall thresholds of shallow landslides are found for this region. Due to the lack of early warning, many infrastructures were threatened by rainfall-induced landslides, as shown in Figure 1, when a heavy rainfall storm hit Wuyuan on June 23–24, 2017, a county town in northeast Jiangxi. The aim of this study is to determine a regional rainfall threshold for Wuyuan County, Jiangxi Province, China, to enhance the capacity for early warning of landslide hazards. First, the empirical rainfall thresholds were determined by statistical analysis of rainfall data from March to September, 2017, in this area. After that, characteristics of rainfall infiltration and variation of unsaturated soil shear strength under rainfall were analyzed. Finally, the physical rainfall threshold was determined by analyzing the mechanisms of rainfall infiltration and slope failure processes, considering the regional geotechnical and hydrological conditions. The lower and upper empirical rainfall thresholds were proposed for the first time in Wuyuan County using synthetic methods.

Figure 1 Infrastructures threatened by rainfall-induced landslides in Wuyuan County on June 23–24, 2017 ((a and b) landslides nearby electric power pylons; (c and d) landslides along roads, photos were taken by Xiaochao Li).
Figure 1

Infrastructures threatened by rainfall-induced landslides in Wuyuan County on June 23–24, 2017 ((a and b) landslides nearby electric power pylons; (c and d) landslides along roads, photos were taken by Xiaochao Li).

2 Materials and methods

2.1 Study area

Wuyuan County is located in the southeast of Jiangxi Province, China, with a total land area of about 2,950 km2 (Figure 2). The topography of Wuyuan comprises steep mountainous areas and dissected valleys. The highest point is Leigujian Shan (1629.8 m) in the northeast. Other prominent topographic features include Huangjing Peak (507 m) in the middle and Miaobaowu Peak (233 m) in the southwest (Figure 2). A mountainous terrain with steep slopes occupies about 83% of the land. The rivers in the study area are densely distributed, and the main flow direction is from the northwest to the southeast. The main strata in the study area can be grouped into two categories [42]. One is the pre-Sinian System Shuangqiaoshan Group AnZzsh2, which mainly contains phyllitic slate and phyllitic sediment-tuff. The other is the Cretaceous System Shixi Group K1-s, including mudstone, shale, and sandstone. An overview of the two strata units is presented in Figure 3. The older category covers most of the regions with a phyllitic structure or a stratified primary structural plane, which leads to the poor weathering ability of the bedrock and forms a weak structural surface. Simultaneously, shallow residual soil has a goodwater retention capability.

Figure 2 Topography of Wuyuan County (position of landslides from Dr. Xiaochao Li’s emergency response).
Figure 2

Topography of Wuyuan County (position of landslides from Dr. Xiaochao Li’s emergency response).

Figure 3 Regional geology map of the study area.
Figure 3

Regional geology map of the study area.

Wuyuan County has the humid monsoon climate of central Asia with the characteristics of the East Asian monsoon region. There are abundant rainfall and short frost periods in this region. The monthly rainfall increases from January to June and decreases from July to December every year. The average annual rainfall equals 1962.3 mm, 69% of which takes place in the first half-year. During the rainy season (from April to June), the average monthly rainfall reaches >300 mm. The cumulative rainfall in the rainy season accounts for 47.9% of the annual precipitation. The maximum monthly and daily precipitations occurred in July 1998 and reached 970.4 and 269.8 mm, respectively.

Large areas of Wuyuan County are prone to landslide processes, due to the geological setting and seasonal rainfall. In general, these rainfall-induced shallow landslides with a depth of 1–5 m, a length of 5–20 m and a material volume of 10–300 m3 were produced on steeply dipping slopes (30–50°). The material involved in mass movement processes consists of saprolite and colluvium.

2.2 Rainfall data and effective rainfall model

The daily precipitation from March to September in 2017 was measured from the Sandu hydrological station and meteorological bureau (Figure 4). Evidently, the maximum daily rainfall (115.2 mm/d) and landslide occurred on the same day (June 24).

Figure 4 Variation of daily precipitation from March to September in 2017 in Wuyuan County.
Figure 4

Variation of daily precipitation from March to September in 2017 in Wuyuan County.

As an extremely important parameter to determine rainfall threshold, the cumulative rainfall of each rainfall event was calculated (Table 1). One rainfall event began when the rainfall lasted for more than 1 day. However, the accumulated rainfall has a variable duration, so there is no uniform standard and the metric is not very convenient in practice. Converting the accumulated rainfall into effective daily rainfall is a recommended method to normalize the time factor of cumulative rainfall. Yin et al. proposed a model to calculate the effective rainfall, in which the rainfall coefficient (attenuation coefficient) played a key role [43]. The effective rainfall (Re) is calculated as follows:

(1)Re=R0+i=1nλiRi

where R0 is the rainfall on the day of landslides, n is the number of days of rainfall events, Ri is the daily rainfall before landslides, and λ is the rainfall coefficient.

Table 1

Rainfall values exceeding 10 mm recorded from March to September in 2017 in Wuyuan County

Event no.StartEndDuration (d)Cumulative (mm)Event no.StartEndDuration (d)Cumulative (mm)
1Mar. 12thMar. 13th240.011May 10thMay 10th130.0
2Mar. 17thMar. 22nd6127.012Jun. 4thJun. 6th333.0
3Mar. 24thMar. 24th128.513Jun. 9thJun. 15th7110.2
4Mar. 27thMar. 30th433.014Jun. 18thJun. 29th12338.2
5Apr. 5thApr. 5th154.515Jul. 10thJul. 10th132.0
6Apr. 7thApr. 9th3134.016Jul. 30thAug. 4th683.0
7Apr. 18thApr. 18th152.517Aug. 11thAug. 17th7102.0
8Apr. 24thApr. 25th235.018Sep. 10thSep. 11th232.6
9May 2ndMay 3rd242.619Sep. 19thSep. 20th225.5
10May 6thMay 7th263.020Sep. 27thSep. 28th229.0

Note: The daily rainfall of Apr. 7th is 84.5 mm.

The physical significance of λ is clear. It indicates that the effect of rainfall on the disaster gradually diminishes with time and eventually disappears. Shan [44] studied 115 rainfall-induced landslides from 1970 to 1999 in Jiangxi Province and determined the rainfall coefficient (λ) to be 0.75. Chen et al. [41] took λ to be 0.82 by studying 1,158 rainfall-induced landslides from 1973 to 2002 in Jiangxi Province. The smaller λ of 0.75 was chosen in this study.

2.3 Numerical equations of unsaturated soil

For the shallow landslides caused by rainfall, the sliding surface is mostly along the bedrock surface. Studies on the failure mechanism of rainfall-induced landslides mainly target the process of rainfall infiltration and the strength of unsaturated soil. In general, rainfall infiltration leads to an increase of pore-water pressure and a decrease of matrix suction in an unsaturated slope, which further results in a reduction in the shear strength of the soil [11,38,45,46]. The following shows the equations of rainfall infiltration in unsaturated soil and the corresponding constitutive model.

2.3.1 Partial differential equation of seepage in unsaturated soil

For unsaturated soil, the coefficient of permeability is not always a constant. The permeability coefficient decreases with the decrease of water content in unsaturated soil. When water flows through two-dimensional unsaturated soil, the governing equation is adopted as follows [47,53]:

(2)xkxhwx+ykyhwy+q=mw2γwhwt

where mw2 is the slope of the soil water characteristic curve (SWCC), hw is the total hydraulic head, kx is the water permeability relevant to matrix suction in the x-direction, ky is the water permeability relevant to matrix suction in the y-direction, γw is the unit weight of water, q is the applied flux at the boundary, and t is the flow time.

2.3.2 Stress–strain relationship of unsaturated soil

Fredlund and Rahardjo [47] studied the stress–strain relation of unsaturated soil and proposed its incremental form as:

(3)Δσ=DΔεDmHσauw+Δua.

Suppose that the atmosphere is a constant, equation (3) can be simplified as:

(4)Δσ=DΔε+DmHuw.

The stress–strain finite element equation can be obtained based on the virtual work principle,

(5)BTDBΔδ+BTDBmHNuw=F.

Equation (5) can be written in another form:

(6-1)KΔδ+LdΔuw=ΔF
(6-2)mHT=1H1H1H0,

where K=BTDB is the stiffness matrix, B is the strain matrix, D is the drainage constitutive matrix, Ld=BTDBmHN is the coupled matrix, Δδ is the incremental displacement vector, and Δuw is the incremental pore-water pressure vector.

2.3.3 Failure criteria of unsaturated soil

Fredlund and Rahardjo [47] proposed an extended Mohr–Coulomb failure criterion, in which the matrix suction of unsaturated soil was considered. Slope stability analysis was carried out using this equation after solving transient seepage. The equation is as follows:

(7)τ=c+(σnua)tanφ+(σauw)tanφb,

where τ is the shear strength of unsaturated soil, c is the effective cohesion, (σnua) is the net normal stress, σn is the total normal stress, ua is the pore-air pressure, φ is the effective angle of internal friction, (σauw) is the matrix suction, uw is the pore-water pressure, and φb is the angle indicating the rate of change in shear strength associated with matrix suction.

2.4 Numerical model and soil properties

Numerical simulation is an effective tool to reveal the mechanical response of slope under rainfall infiltration [48,49,50,51,52]. The landslide near the 83# iron tower of the Ziyang II 220 kV overhead transmission line is a typical case in Wuyuan County. Based on the geotechnical investigation report and reinforcement scheme, a numerical model and boundary conditions were built in SEEP/W, SIGMA/W, and SLOPE/W to simulate the mechanism of deformation and failure process under rainfall. The slope model is shown in Figure 5, which consisted of two types of materials. The upper one was overburden soil of about 2.5 m thickness and the lower one was bedrock (intensely weathered phyllitic slate). The model had a length of 32 m and an altitude of 20.85 m. The maximum elevation difference of the slope was 15.85 m and the angle of the slope was about 46°.

Figure 5 Slope geometry and boundary conditions; units: m (A–A, B–B, and C–C represent different sections along the slope).
Figure 5

Slope geometry and boundary conditions; units: m (A–A, B–B, and C–C represent different sections along the slope).

These simulations were conducted as follows. (1) The transient seepage analysis was performed by applying rainfall boundary on the slope surface in the SEEP/W program. (2) The time-dependent pore-water pressure determined from SEEP/W was coupled with SIGMA/W to obtain the stress–strain field. (3) The transient seepage and stress–strain analysis were used in SLOPE/W as a parent analysis to study the variation of the factor of safety (FOS) and slope deformation with time. In this process, the slip surface was fully specified according to the field survey, and the general limit equilibrium was used for slope stability analysis based on the finite element method.

The SWCC is an essential element in the transient seepage and stability analysis of unsaturated soil. In order to obtain the SWCC of the overburden soil, the technique of back-analysis was used on the basis of rainfall Event 14. Fredlund and Xing [53] proposed a general equation for the SWCC, which provided a good fit for sand, silt, and clay soils over the entire suction range from 0 to 106 kPa. A series of initial values were applied to the numerical model in terms of the general equation of the SWCC, and the numerical failure moment was compared with the real one. Then the unsaturated soil parameters were adjusted until the failure moments became consistent. The simulation started from the beginning of Event 14. The back-analysis results are presented in Figure 6. The FOS decreased with the daily rainfall intensity. On the seventh day, the slope was almost saturated and its FOS was below 1.0. The properties and the physical–mechanical indexes of soil or rock are listed in Table 2.

Figure 6 The seepage field at the moment of failure and the FOS versus time.
Figure 6

The seepage field at the moment of failure and the FOS versus time.

Table 2

Parameters of soil and rock

LayerParameters
γ (kN/m3)c (kPa)φ (degrees)φb (degrees)ksat (cm/s)μ
Overburden soil19.51020Vol. WC fn.8.68 × 10−50.3
Intensely weathered phyllitic slate20.235301.16 × 10−70.25
Soil water characteristic valuesOverburden soil: a= 40 kPa, n = 1, m = 0.8, Sat. WC = 0.4; bedrock: a = 4.5 kPa, n = 1, m = 0.9, Sat. WC = 0.25

3 Results and discussion

3.1 Empirical rainfall thresholds

Many field inspections are performed each year by the State Grid of Jiangxi and other infrastructure departments (i.e., highway related and hydraulic related) in Wuyuan County. The inspection results show that there have not been group-occurring landslides in recent years except for the disaster on June 24, 2017. As shown in Table 1, a rainfall intensity of 84.5 mm/d and an accumulated rainfall of 134.0 mm cannot trigger group-occurring landslides, but a rainfall intensity of 115.2 mm/d and a total rainfall of 277.8 mm (June 18–24) could undoubtedly trigger group-occurring landslides. According to Chen et al. [41], when the accumulated rainfall is <63 mm, landslides rarely occur in the Jiangxi Province. Therefore, 7 of the 24 events with rainfall exceeding 63 mm were selected for further analysis. For Event No. 14, the time of failure was June 24, R0 was 115.2 mm/d, n was 6, and Ri was daily rainfall from 18 to 23 June. Therefore, the result of effective rainfall was 217.1 mm/d. Similarly, the effective rainfall was calculated for Event No. 2, 6, 10, 13, 16, and 17, as shown in Table 3. Although the accumulated rainfall of these events was large, the effective rainfall was not large enough to trigger landslides.

Table 3

The effective rainfall of some important events from March to September in 2017 in Wuyuan County

Event no.Cumulative rainfall (mm)Effective rainfall (mm/d)Event no.Cumulative rainfall (mm)Effective rainfall (mm/d)
2127.068.96134.092.4
1063.059.013110.247.3
14277.8217.1168343.8
17102.037.7Apr. 7th84.584.5

Note: The rainfall intensity of Apr. 7th was 84.5 mm/d, which was higher than 63 mm. So it was selected for analysis.

According to the above analysis, a lower effective rainfall threshold of 92.4 mm/d was determined, below which group-occurring landslides would not occur. Meanwhile, an upper effective rainfall threshold of 217.1 mm/d was determined, above which landslides always occurred. If the effective rainfall was in the range of 92.4 to 217.1 mm/d, the change of matrix suction and geological conditions should be considered to decide whether a landslide would occur or not.

3.2 Mechanical response of failure process with rainfall infiltration

Eighteen tests in three groups were designed to study the effects of total rainfall and intensity on slope stability, as shown in Table 4. According to the analyses above, the upper and lower empirical rainfall thresholds were 217.1 and 92.4 mm/d, respectively. Therefore, the total rainfall range from 140 to 240 mm with an interval of 20 mm was considered in this study. Furthermore, to assess the impact of rainfall intensity, the total rainfall was assumed to end within 24, 16, and 8 h of one day. In order to fully consider the influence of rainfall infiltration on slope stability, the calculation time was set to 10 days in the analysis process. The variations of pore-water pressure over time at different depths of Section-A, B, and C (Figure 5) are shown in Figure 7.

Table 4

The minimum FOS of different numerical tests

GroupDuration (h)Total rainfall (mm)
IIIIIIIVVVI
140160180200220240
A241.1071.0681.0541.0351.0120.935
B161.0591.0631.0260.9890.9800.929
C81.0651.0561.0510.9670.9380.914
Figure 7 The variation of pore-water pressure over time: (a) Section-A, (b) Section-B, and (c) Section-C (Figure 5). Test A-IV is taken for example.
Figure 7

The variation of pore-water pressure over time: (a) Section-A, (b) Section-B, and (c) Section-C (Figure 5). Test A-IV is taken for example.

For Section-A, located at the upper part of the landslide, the pore-water pressure increased rapidly from an initial value of −50 kPa to nearly −5 kPa in 30 h. On the tenth day, the pore-water pressure gradually recovered to the initial value within 1.2 m depth, while it was slightly larger than the initial value under 1.2 m depth. For Section-B, the pore-water pressure increased rapidly from −50 kPa to nearly −10 kPa in 30 h within 1.0 m depth, and then decreased quickly to a relatively stable value in a short time. However, the bottom part of Section-B reached a maximum value of −10 kPa in 60 h, and then declined slowly to −15 kPa. For Section C, the pore-water pressure increased to a maximum value at different depths in 30 h and then stayed at this level. The pore-water pressure increased continuously during the rainfall, which was consistent with the law of rainfall infiltration. The variation of pore-water pressure indicated that water permeated from the surface to the deep part, and from the top to the bottom of the slope.

The variation of pore-water pressure at different depths with different rainfall intensities is shown in Figure 8. The variation trend of pore-water pressure is similar for different rainfall intensities. With the increase of rainfall intensity, the pore-water pressure at the same depth also increased. At the beginning of the rainfall (T = 8 h), the pore-water pressure of shallow soil changed more significantly than the deep part with the increasing rainfall intensity. When the rain stopped (T = 24 h), the pore-water pressure of the whole slope increased, while the change at the bottom was more remarkable. Nine days later (T = 240 h), the pore-water pressure of Section-A nearly recovered to the initial value, and Section-C still maintained at a high level. The process of rainfall infiltration was well revealed by the variation of pore-water pressure. When the rainfall intensity increased to a critical value, the shear strength became smaller than the shear stress on the slide surface and landslides would occur.

Figure 8 Pore-water pressure at different depths in the test of group-A (RI means the rainfall amount within 24 h).
Figure 8

Pore-water pressure at different depths in the test of group-A (RI means the rainfall amount within 24 h).

3.3 FOS and physical rainfall threshold

The FOS versus time for three groups of tests is shown in Figure 9 and the minimum FOS of each test is listed in Table 4. The slope stability decreased continuously with the increase of rainfall and reached the minimum within 8 h after the rain. After that, the pore-water pressure decreased as the water drained and the FOS increased slowly to a new constant, which was smaller than the initial one. When the total rainfall was smaller than 200 mm, the FOS values of each test of the three groups were all greater than 1.0. But, when the total rainfall reached 200 mm, the FOS of test B-IV was 0.989.

Figure 9 FOS versus time. (a) Rainfall duration = 8 h, (b) rainfall duration = 16 h, (c) rainfall duration = 24 h.
Figure 9

FOS versus time. (a) Rainfall duration = 8 h, (b) rainfall duration = 16 h, (c) rainfall duration = 24 h.

In this article, the slope was considered failed when the FOS was below 1.0, and the corresponding rainfall was determined as the physical rainfall threshold. Therefore, the physical rainfall threshold is proposed to be 200 mm/day in Wuyuan County.

4 Conclusions

In this study, the rainfall thresholds were analyzed based on empirical and physical methods in Wuyuan County, considering the group-occurring landslides induced by rainfall. The results showed that the lower and upper empirical rainfall thresholds were 92.4 and 217.1 mm/d, respectively. When the rainfall was less than 92.4 mm/d, group-occurring landslides were not observed. When the rainfall was greater than 217.1 mm/d, landslides always occurred. If the rainfall was in the window interval (92.4–217.1 mm/d), the change of matrix suction and geological conditions should be considered. Eighteen numerical simulation tests considering different rainfall intensities and rainfall amounts were conducted. The process of rainfall infiltration was well revealed by the variation of pore-water pressure. The FOS decreased rapidly with the rain. After the rain, the soil matrix suction and the FOS gradually recovered because the water discharged out of the slope. The numerical results also showed that the physical rainfall threshold of Wuyuan was 200 mm/d, similar to the empirical rainfall threshold (217.1 mm/d) determined by the empirical method. Therefore, an effective rainfall of 200 mm/d could be regarded as the threshold that would trigger group-occurring shallow landslides in this area. The results of this study can provide useful information in the framework of landslide risk management. However, parameters of the SWCC used to determine the physical rainfall threshold, which were obtained by back-analysis, need to be supplemented by more in situ and laboratory tests.


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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. U1704243).

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Received: 2019-09-01
Revised: 2020-04-08
Accepted: 2020-04-11
Published Online: 2020-10-03

© 2020 Xiaochao Li et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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