Rainfall-triggered mass movements on steep loess slopes and their entrainment and distribution

Catena 183 (2019) 104238

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Rainfall-triggered mass movements on steep loess slopes and their entrainment and distribution

T

⁎

Wenzhao Guoa,b, Xiangzhou Xuc, Wenlong Wanga,b, , Yakun Liuc, Mingming Guoa, Zhiqiang Cuib a

State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Northwest A&F University, Yangling, 712100, Shaanxi, China Institute of Soil and Water Conservation, Chinese Academy of Sciences and Ministry of Water Resources, Yangling, 712100, Shaanxi, China c School of Hydraulic Engineering, Dalian University of Technology, Dalian 116024, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Mass movement Soil erosion Entrainment Rainfall simulation experiments Loess Plateau

Mass movements are predominant geomorphic processes on steep hillslopes. However, the mechanisms governing the erosion and entrainment of mass movements remain poorly understood. In this study, experiments on natural loess slopes were conducted to induce a series of mass movements under simulated rainfalls in the Liudaogou Catchment on the Loess Plateau of China. A novel topography meter was used to observe random mass movements. A total of 499 mass movements in 42 rainfall events and an average of 11 mass movements for each rainfall event were observed. Three mass movement types were detected: landslides (67%) > mudflows (21%) > avalanches (12%). The volume of landslides dramatically increased through the entrainment of a wet gully bed material, and the volume of landslide mass was magnified by 29% on average through material entrainment. Based on the observed data, the probability of mass movement occurrences decreased with the increasing mass movement volume in a power-law relationship. The critical rainfall amount for mass movement failure was approximately 25.6 mm at a rainfall intensity of 50 mm h−1. These results can serve as guides to mitigate geological hazards and assess erosion processes on steep loess slopes of the Loess Plateau.

1. Introduction Mass movement, also referred as gravity erosion or mass wasting, is a slope failure on hillslopes. Mass movement is not only a natural hazard but also an important means of conveying sediments from slopes to channels in mountainous territories, thus severely affecting the structure and function of ecosystems and societies (Keefer and Larsen, 2007; Qiu, 2014; Fuller et al., 2016; Xu et al., 2017). Therefore, understanding this phenomenon is necessary to implement hazard mitigation and control erosion. Rainfall is the most important triggering factor of mass movements on the Loess Plateau of China (Xu et al., 2017). Dry loess can sustain near-vertical slopes; however, loess can rapidly disaggregate when locally saturated by rainfall (Dai and Lee, 2002). Rainfall-triggered mass movements frequently occur on soil-mantled landforms (Minder et al., 2009). A field investigation shows that rainfall-triggered mass movements only occur at a depth of < 2 m, corresponding to a surface layer of completely saturated loess (Wang et al., 2015). Mass movements include various types, each of which has specific mechanisms and conditioning factors (Cruden and Varnes, 1996). Xu

et al. (2015a) suggested a systematic classification of mass movements, including landslides, mudflows, and avalanches. Mudflows have obvious flow performance and high water content compared with landslides and avalanches (Guo et al., 2019). During erosion, the failure block of an avalanche completely separates from the slope surface, whereas that of a landslide slips down as a whole along a weak belt (Xu et al., 2015a). Zhang et al. (2012) found a close relationship between the topographic attributes of post-landslide local surface and mass movement types. However, the responses of different movement types to rainfall characteristics and the distribution of mass movements have received little attention despite their importance. Previous studies have shown that the entrainment of initially static materials can increase the mobility of avalanches (Mangeney et al., 2007). Accordingly, Breien et al. (2008) suggested that entrainment usually causes the debris flow to become increasingly erosive. Debris flow can markedly increase in size and speed when materials are entrained from their beds. In addition, flow deposits from the underlying erodible layer are difficult to distinguish when they are composed of the same materials (Mangeney, 2011). Therefore, the quantitative measurement of entrainment volumes under field conditions becomes

⁎ Corresponding author at: State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Northwest Agriculture and Forestry University, Yangling, 712100, Shaanxi, China. E-mail addresses: [email protected] (W. Guo), [email protected] (W. Wang).

https://doi.org/10.1016/j.catena.2019.104238 Received 25 October 2018; Received in revised form 19 August 2019; Accepted 23 August 2019 Available online 30 August 2019 0341-8162/ © 2019 Elsevier B.V. All rights reserved.

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(a)

(c)

(b)

Rainfall simulators Gully Steep slope Mass movement Gully Mass movement

T1

Fig. 1. Study area and sampling sites. (a) Location of the Liudaogou Catchment on the Loess Plateau of China; (b) Topography of typical mass movement; (c) Mass movement experiment in the Liudaogou Catchment. T1: Topography meter. Table 1 Experimental summary of the initial slope landform and rainfall. Test number

F1 F2 F3 F4 F5 F6 F7

Lower slope configuration

Rainfall

Height (m)

Intensity (mm h−1)

Table 2 Error between design rainfall intensity and experiment rainfall intensity in experiment F1. Rainfall intensity (mm h−1)

Rainfall events

1.0 1.0 1.0 1.5 1.5 1.5 1.5

Gradient (°)

70 80 60 70 80 60 70

50 50 50 50 50 50 100

Duration (min) 60 60 60 60 60 60 30

Error

Runs Experiment 6 6 6 6 6 6 6

1 2 3 4 5 6 Average

complicated. Furthermore, the mechanisms that govern the growth of landslides remain unclear, hampering efforts to assess natural hazards (Iverson et al., 2011; Mangeney, 2011). Recently, numerous scholars have conducted laboratory experiments on mass movements to understand their processes and mechanisms. For instance, Terajima et al. (2014) conducted a flume experiment to examine slope subsurface hydrology and found that seepage forces affect the promotion of shallow landslide initiation. Xu et al. (2015b) tested the stability of different slope geometries and rainfalls to explore the triggering mechanisms of mass movements on a remolding slope. Yuliza et al. (2016) prepared a small-scale landslide experiments to determine the soil characteristics and water content that induce

Design

47.4 46.8 48.8 49.2 50.4 47.4 48.3

50 50 50 50 50 50 50

5.2% 6.4% 2.4% 1.6% −0.8% 5.2% 3.3%

Dry density/g cm−3

Primary particle size (%)

Table 3 Soil physical properties. Initial water content/ %

9.3–13.6

1.44–1.66

Clay/mm < 0.002

Silt/mm 0.002–0.05

Sand/mm > 0.05

2

30

68

landslides. Kharismalatri et al. (2019) conducted a flume experiment to evaluate factors for controlling sediment connectivity of landslide materials. However, these laboratory experiments used remolded soil, 2

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(a)

(c)

(d)

(b)

Fig. 2. Comparison of a mass movement and the three-dimensional vector model. (a) Crevice was created and expanded, which indicated that a mass movement was occurring. (b) Failure block was fragmentized and stacked in the main channel. (c) and (d) are 3D surface models reconstructed with ArcGIS corresponding to (a) and (b), respectively. Table 4 Summary information on mass movement in experiments F1–F7. Test number

F1 F2 F3 F4 F5 F6 F7 Summation Percentage

Amount of mass movements/103 cm3

Number of mass movements Avalanche

Landslide

Mudflow

Total

Avalanche

Landslide

Mudflow

Total

12 7 1 7 10 9 16 62 12%

41 14 3 126 89 56 4 333 67%

5 1 3 45 18 32 0 104 21%

58 22 7 178 117 97 20 499 100%

11.0 3.7 0.3 5.3 5.6 6.8 49.4 82.2 15%

53.3 8.4 9.5 173.4 92.2 56.1 3.1 396.1 71%

4.2 0.4 1.5 40.9 13.2 20.6 0.0 80.7 14%

68.6 12.5 11.4 219.6 111.0 83.6 52.5 559.0 100%

contribution of avalanches, landslides, and mudflows to the amounts of mass movements. In addition, the distribution of mass movements in terms of failure volume and rainfall was explored. Different from laboratory experiments, the experiment on the segment of unscaled reality on natural loess slopes retains the loess scale and natural characteristics (such as the internal structure and vertical joints) while controlling for the location and timing of mass movement occurrence (Guo et al., 2019). This characteristic in our study is an important

destroyed the mechanical structure of the original soil, and could not truly reflect the changes of the stress field on natural slopes. Furthermore, few experiments have focused on the distribution of mass movements in terms of failure volume and rainfall. Therefore, this study conducted a series of mass movement experiments on segments of unscaled reality on natural loess slopes on the Loess Plateau of China. The objective of this study was to investigate the characteristics and distribution of mass movements and the

3

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80% 70%

Number Volume

67%

landslides, mudflows, and avalanches that contribute large amounts of sediment yield by conveying soil into valleys.

71%

Percentage

60%

3. Materials and methods

50%

To analyze the failure mechanism of mass movements, a series of experiments (F1–F7) were conducted on natural loess slopes in the Liudaogou Catchment of Shenmu County in the summer of 2014 (Fig. 1). A mobile laboratory was built in the test plot to avoid wind and sunlight. Experimental slopes with 3 m length and 2.8 m width were isolated from their surroundings by inserting steel plates approximately 0.5 m deep into the soil in the mobile lab. The experimental slopes were “cut” without disturbing the slope underground to maintain the original texture and density of the experimental soil (Guo et al., 2016). According to the typical topography of the Liudaogou Catchment, experimental slopes F1–F7 had a height of 1–1.5 m, a gentle upper slope of 3°, and a steep lower slope of 60°–80° (Table 1). The Loess Plateau typically receives short and intense downpours with a rainfall intensity of 0.8 mm min−1 and a duration of 60 min or a rainfall intensity of 2.0 mm min−1 and a duration of 30 min, which cause severe gravity erosion (Xu et al., 2015b). To guarantee equal precipitation, rainfall events in the experiment slopes F1–F6 and F7 were set to have intensities of 50 and 100 mm h−1 and durations of 60 and 30 min, respectively (Table 1). In turn, six rainfall events were applied to each experimental slope. A 12-hour interval was maintained after each rainfall to ensure an approximation of the initial water content. Table 2 shows that the error between the design and experiment rainfall intensities was < 7%. Table 3 shows the loess properties as determined from the experiments. The erosion and entrainment processes were monitored, and the volumes of mass movements were measured. A novel topography meter based on a structural laser was used to observe random mass movements (Guo et al., 2016). Based on the contour map obtained from the topography meter, a three-dimensional terrain can be digitally reconstructed with ArcGIS (Esri) (Fig. 2c and d). Consequently, the volume of mass movements on steep slope was calculated. The topography meter results were relatively accurate (< ± 10% of the volume error) (Xu et al., 2015c). Mass movements on the Loess Plateau were

40% 30% 20%

21% 12%

15%

14%

10% 0% Avalanche

landslide

Mudflow

Fig. 3. Percentages of the type of mass movement. A total of 499 mass movements occurred in 42 rainfall events in experiments F1–F7.

advantage over the traditional methods mainly undertaken via the laboratory test of remodeling soil. 2. Study area The Loess Plateau of China is a region that suffers from severe soil erosion. It is mainly distributed in the middle reaches of the Yellow River basin (Liang et al., 2015) and covers a total area of 624,000 km2 (Fig. 1). The study site, Liudaogou Catchment (110°21′–110°23′E, 38°46′–38°51′N), is located in the Loess Plateau, which is distinguished by several gullies and undulating loess slopes. The elevation ranges from 1094.0 m to 1273.9 m above sea level. The watershed has an average annual precipitation of 437 mm, of which approximately 77% occurs as intense rainstorms from June to September (Wu et al., 2016). Rainstorm-induced mass movements frequently occur in steep gully banks with slope gradients higher than 70° (Xu et al., 2015a) due to the crisscrossing gullies of the undulating terrain, sparse vegetation, and numerous vertical joints. In this area, headwall retreat, gully bank erosion, and downcut during gully processes are often accompanied by

Fig. 4. Bed material entrainment for mass movements in the moving processes: (a) local terrain before the failure; (b) local terrain after the failure. In steep gullies, the entrainment of wet bed material can dramatically increase the volume of a landslide. 4

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Table 5 Statistical results of slide entrainment in the moving processes. Volume

Mass movement events 1-1515

2-4320

3-4915

4-5844

5-5110

6-3001

Pre-entrainment collapse volume (cm ) Entrainment volume (cm3) Post-entrainment collapse volume (cm3) Rate of increment (%)

849.3 598.9 1448.3 41%

5171.8 373.7 5545.6 7%

1024.0 732.3 1756.4 42%

4116.9 628.0 4744.9 13%

728.5 300.8 1029.4 29%

714.5 549.1 1263.6 43%

– Pre-entrainment collapse volume (cm3) Entrainment volume (cm3) Post-entrainment collapse volume (cm3) Rate of increment (%)

7-2711 721.4 127.9 849.4 15%

8-3949 1947.2 394.5 2341.7 17%

9-4320 1547.3 280.5 1827.8 15%

10-2547 686.1 787.7 1473.8 53%

11-5025 972.5 705.7 1678.2 42%

12-4432 1008.1 396.0 1404.1 28%

3

most frequently observed failures. This finding is consistent with that of previous research on the Loess Plateau (e.g., Zhang et al., 2012). As shown in Fig. 3 and Tables 4, 333 landslides accounted for 67% of the total 499 mass movements and contributed 71% (396.1 × 103 cm3) of the total volume of mass movements. In particular, the amount of landslides for F1, F4, and F5 accounted for 78%, 79%, and 83%, respectively. Mudflows were particularly frequent in areas of steep slopes. In total, 104 mudflows accounted for approximately 21% of the total mass movements and contributed 14% (80.7 × 103 cm3) to the total volume of mass movements (Fig. 3 and Table 4). In addition, 62 avalanches, approximately 12% of the total mass movements, occurred in the experiments and contributed 15% (82.2 × 103 cm3) to the total volume of mass movements. The frequency of mudflows was higher than that of avalanches, whereas the proportion of mudflows was smaller than that of avalanches in the total amount of mass movements. This result was attributed to the mean avalanche volumes (1325.8 cm3), which were larger than the mean mudflow volumes (776.0 cm3). The frequency of avalanche occurrence was the smallest, representing < 12% of the whole mass movement. In particular, for F4, 178 mass movements occurred, whereas avalanches only accounted for 4%. An avalanche occurs only when the tensile torque on the ruptured loess surface is less than the gravitational torque generated by the soil gravity.

classified into three types: landslides, mudflows, and avalanches (Xu et al., 2015a). During the experiments, occurrence time, locations, and types of mass movements were recorded through direct observations and a video camera. Mass movements with volume over 300 cm3 were considered in this study. Soil loss caused by mass movements was calculated using the following formula:

gij = v1(i, j) − v2(i, j)

(1)

where i represents the sequence number of failure incidents during rainfall; j represents the sequence number of rainfall events for a certain landform; gi,j is the volume of an individual failure mass; and v1(i, j) and v2(i, j) are the slope volumes within the incident scope before and after the failure, respectively. Landslides that occurred in a steep gully induced material entrainment. The entrainment volumes were obtained by measuring gully bed material volumes before and after the passage of mass movements. With a volume interval of 100 cm3, the mass movement volume (cm3) v = [300, 17,000] was graded into 167 subintervals Ii (I1 = [300–400], I2 = [400–500], I3 = [500–600], …, I167 = [169000–17,000]). The number (ni) of mass movements was counted for each Ii subinterval. The occurrence frequency (Pi) of mass movements for the Ii subinterval was obtained by dividing the number (ni) of mass movements in each subinterval by the total number of landslides (N). A power-law regression model was used to fit the relationship between mass movement frequency (P) and mass movement volume (v).

4.3. Gully bed material entrainment for mass movements Material entrainment can play an important role in landslide movements. Experiments suggest that the entrainment of gully bed material magnifies the volume of landslides in a steep gully (Fig. 4). The above entrainment phenomenon was observed in approximately 12 landslides in the experiments. Table 5 shows the statistical results of the slide entrainment in the movements. For instance, for the landslide event 12-4432 in the upper part of the slope, the initial volume was 1008.1 cm3. Material entrainment in the gully was induced by landslides and caused debris mass to grow by 28% (entrainment volume was 396 cm3) before deposition began on the flatter main channel. The postentrainment landslide volume was 1404.1 cm3. As shown in Table 5, the volumes of the landslide mass increased in the range of 127.9–787.7 cm3 and were magnified by 29% on average through material entrainment for 12 landslide events.

4. Results 4.1. Group characteristics of mass movements Rainfall-induced mass movements (e.g., avalanches, landslides, and mudflows) frequently occur in steep slopes. As shown in Table 4, the mass movements in the experiments in the Liudaogou Catchment exhibit a group characteristic. A total of 499 shallow mass movements were observed in 42 rainfall events for F1–F7, an average of 11 mass movements occurred on steep slope in each rainfall event, and a maximum of 43 mass movements occurred in each rainfall event. The development of a typical mass movement is given in Fig. 2a and b with reference to the images from the video camera. The mass movement frequency was approximately 1.5 mass movements per m2 in each rainfall event. The minimum, mean, and maximum mass movement volumes were 300.3, 1120.2, and 16,883.6 cm3, respectively. Furthermore, frequent small mass movements produced irregular slopes.

4.4. Distribution of mass movements on failure volume In this study, the volume distribution of mass movements was explored based on the data of 499 mass movements from experiments F1–F7. Fig. 5a shows a histogram of volume distribution on mass movements. The volumes of rainfall-induced mass movements ranged from 300.3 cm3 to 16,883.6 cm3, with the majority of failures in the range of 300–2600 cm3. Most mass movements were triggered in the

4.2. Contribution of avalanches, landslides, and mudflows in mass movements The mass movements were classified as follows: landslides (67%), mudflows (21%), and avalanches (12%) (Fig. 3). Landslides were the 5

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500

50

400

40

300

30

200

20

100

10 0

vicinity of the interface of the two sloping sections. As shown in Fig. 5a and b, the mass movement frequency decreased as the volume size increased. Fig. 5b indicates that the frequency of mass movements in the range of 300 cm3 ≤ volume ≤ 1000 cm3 was 63.9% (319 failures), where the frequency was the highest. When the volume was in the range of 1000–2000 cm3, the proportion of mass movements was approximately 27.3% (136 failures). Approximately 41 mass movements (8.2%) occurred when the volume was in the range of 2000–8000 cm3. The frequency of mass movements was lowest at 0.6% (3 failures) when 8000 cm3 was exceeded. As shown in Fig. 5b and c, 2,000 cm3 was a key demarcation point for mass movements in the experiments. Fig. 5b shows that 90% of the 499 mass movement events had a volume < 2000 cm3, whereas only 10% had a volume > 2000 cm3. However, these large mass movements (44 failures) accounted for 33% of the total mass movement volume (Fig. 5c). The frequency of mass movements with a volume > 6000 cm3 was only 1.4% (7 failures), but they accounted for 12.7% of the total amount of mass movements. The frequency and volume of the mass movements were fit with a power-law distribution. The relationship was established based on the 499 mass movement data from the experiments:

Cumulative number

60

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000 17000

Number of mass movement

Number of mass movement Cumulative number 600

(a)

70

0

Mass movement volume (cm3) Probability Cumulave probability Probability funcon

(b) 15%

100%

Probability (%)

12%

(2000 cm , 90%)

9%

60%

6%

40% P = 1256.4v-1.525 R² = 0.82

3% 0%

100% Cumulativ failure volume (%)

80%

3

20%

Cumulave probability (%)

P = 1256.4v−1.525

where v is the mass movement volume and P is the occurrence probability of mass movement. The R2 value was 0.82. 4.5. Distributions of mass movements on rainfall Each rainfall event (per hour) in experiments F1–F6 had an intensity of 50 mm h−1 and a duration of 60 min, whereas that in experiment F7 had an intensity of 100 mm h−1 and a duration of 30 min. Therefore, the distribution of mass movements on rainfall time (per hour) was explored based on the data of 479 mass movements from experiments F1–F6. Fig. 6 shows these distributions from the six slopes (F1–F6) at different slope heights (1 and 1.5 m) and slope gradients (60°, 70°, and 80°). The probability of mass movement failure dramatically increased with the increases in rainfall duration in experiments F1–F6. The highest failure frequency (28.0%; 134 failures) was 50–60 min, which was 16.5 times higher than the lowest failure frequency (1.7%; 8 failures) of 0–10 min rainfall event. In experiment F4, approximately 54 mass movements occurred at 50–60 min, where the amount of failure was the highest in all experiments (Fig. 6a). As shown in Fig. 6b, the probability of mass movement failure was only 8.6% at the initial stage of rainfall (0–20 min), then increased to 39.8% at the middle stage (20–40 min), and reached as high as 51.6% at the later stage (40–60 min). This result demonstrates that mass movements mainly occurred at the middle and later stages of rainfall. The distribution of mass movements with rainfall events on experiments F1–F6 is shown in Fig. 7. The probability of mass movement failure initially increased and then decreased with rainfall events. The frequency of mass movement occurrence in the second rainfall event was highest at 28.8% (138 failures), which was 5.8 times higher than the lowest failure frequency (5.0%) in the sixth rainfall event. For experiment F4, approximately 43 mass movements occurred in the second rainfall event, where the number of failures was the highest in all experiments (Fig. 7a). Moreover, about two-thirds (65%) of the total mass movements occurred in the second, third, and fourth rainfall events. The failure frequency (Fig. 7b) decreased in the fifth and sixth rainfall events, indicating that excessive rainfall does not necessarily result in excessive failures. The cumulative failure volume through rainfall time and rainfall amount in experiments F1–F6 is shown in Fig. 8. The relationship between the cumulative failure volume and cumulative rainfall shows an S-shape curve. Fig. 8 shows that the maximum increases in failure volume occurred during the rainfall of approximately 50–200 mm (rainfall time of 60–240 min) and not during the highest rainfall

0% 3000 6000 9000 12000 15000 18000 Mass movement volume (cm3)

0

(c) 2000cm3 300 ~ 2000 cm3

80%

2000 ~ 17000 cm3

60% 40%

10% of mass movement accounts for 33% of the total volume of gravity erosion.

20% 0% 0%

20% 40% 60% 80% Cumulative mass movement number (%)

(2)

100%

Fig. 5. Frequency distribution and probability function of mass movement (499 mass movement events in experiments F1–F7). (a) histogram of frequency distribution on mass movement, with the highest volume ranging from 300 cm3 to 2600 cm3; (b) probability function of mass movement (approximately 90% of the 499 mass movements occurred when the volume was < 2000 cm3); (c) cumulative mass movement volume as a function of the total number of mass movements. The 44 largest mass movements (10% of total number) accounted for 33% of the total mass movement volume.

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(b) F1 F4

50

F2 F5

28.0%

30.0%

F3 F6

24.0% 23.6%

25.0%

40

20.0%

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Number of mass movement

60

30

15.8%

15.0%

20

10.0%

10

5.0%

0

6.9% 1.7%

0.0% 0

10

20 30 40 Rainfall time (min)

50

60

0-10

10-20 20-30 30-40 Rainfall time (min)

40-50

50-60

Fig. 6. Distribution of mass movements as a function of time in every rainfall (per hour). (a) Number of mass movement; (b) Probability of mass movement (the experiments F1–F6).

(a)

(b) F1

F2

F3

F4

F5

35.0%

F6

28.8%

30.0%

40 Probability (%)

Number of mass movement

50

30 20 10

25.0% 20.0%

16.5%

18.0% 17.7% 14.0%

15.0% 10.0%

5.0%

5.0%

0

0.0% 1

2

3 4 Rainfall events

5

6

1

2 3 4 Rainfall events

5

6

Fig. 7. Distribution of mass movements as a function of rainfall events. (a) Number of mass movements; (b) Probability of mass movements (the experiments F1–F6).

maximum of 178 mass movements occurred in F4 (Table 4). Landslides that occur due to heavy rainstorms may be distributed over regions that extend from a few to tens of thousands of square kilometers (Lu and Godt, 2013). The largest of these landslide events may comprise thousands of landslides and dominate sediment production from hillslopes (Parker et al., 2011; Lin and Chen, 2012). For example, Yan'an, which is located on the Loess Plateau and has an area of approximately 37,000 km2, experienced heavy rainfall (577 mm) in July 2013, which resulted in 8135 slope failures (Wang et al., 2015). Mass movements induced material entrainment in gullies. In our experiments, material entrainment magnified the volumes of landslides by 29% on average (Table 5). Material entrainment frequently occurred in steep gullies. Valley widening was frequently achieved through landslide development (Mather et al., 2002). Field evidence of material entrainment has been often observed, involving avalanches and debris flows (Mangeney et al., 2010). Several studies have shown that entrainment can arise from collapses and cause debris flow mass to expand (Breien et al., 2008; Iverson et al., 2011). Iverson et al. (2011) found that the entrainment is accompanied by increased flow momentum and speed only if large positive pore pressures develop in wet bed sediments. Furthermore, high bed water content increases mass entrainment in landslides (Mangeney, 2011). Mass movement probability-volume distribution exhibited a powerlaw relationship with a = −1.525 and b = 1256.4 for mass entrainment data in our experiments (Fig. 5b). The frequency distribution of mass movements decreased with the increasing mass movement volume. The probability distribution is consistent with that determined by Densmore et al. (1997) and Chen et al. (2014). The relative frequency

(250–300 mm). This result indicates that the largest erosion rates and sediment production result from these rainfall times and quantity. Fig. 7 shows that approximately 45.3% of the 479 mass movements in experiments F1–F6 occurred when the cumulative rainfall was < 100 mm, 35.7% of the total mass movements occurred when the cumulative rainfall was 100–200 mm, and only 19% occurred when rainfall exceeded 200 mm. A great amount of the potential mass movements occurred when rainfall exceeded the critical rainfall level to trigger landslides (Li et al., 2011). Therefore, the subsequent amount of rainfall (250–300 mm) can merely result in a few mass movements (Fig. 7). The relationship between the cumulative failure volume (Gc) and the rainfall amount (Rc) in the first rainfall event in experiments F1–F6 are shown in Fig. 9. The relationship was fit in an equation to obtain the critical rainfall amount (Rv) for a mass movement failure. As shown in Table 6, Rv values in experiments F1, F2, F4, F5, and F6 were 27.2, 32.1, 24.8, 19.2, and 24.7 mm, respectively, with an average of 25.6 mm. Therefore, in our experiments, the rainfall amount of approximately 25.6 mm can be considered critical for mass movement failure at a rainfall intensity of 50 mm h−1. Furthermore, Table 6 shows that the critical rainfall amount had a negative correlation with slope height. On average, Rv was 29.7 mm at a slope height of 1.0 m but was only 22.9 mm at a slope height of 1.5 m.

5. Discussion Mass movements generally occur under heavy and prolonged rainfall. In experiments F1–F7, an average of 64 mass movements occurred on steep loess slopes at a cumulative rainfall of 300 mm, and a 7

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1000 20000

500

0

12000

6000

600

0

120000

14000

8000

800

F6 300

-5- -6-

10000

0

Failure volume (cm3)

0

Cumulative rainfall (mm) 50 100 150 200 250

-4-

1000

0

Failure volume

F5 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0

120

-3-

1200

F4 300

-2-

0

Failure volume (cm3)

9000

-1-

1400

0

Cumulativ failure volume (cm3)

Cumulative rainfall (mm) 50 100 150 200 250

0 Failure volume (cm3)

120

Failure volume

F3

Failure volume (cm3)

70000

Cumulativ failure volume (cm3)

-3-

300

Cumulativ failure volume (cm3)

-2-

1600 Failure volume (cm3)

-1-

4000

80000

Cumulative rainfall (mm) 50 100 150 200 250

0

Cumulativ failure volume (cm3)

Failure volume (cm3)

4500

300

Cumulativ failure volume (cm3)

Cumulative rainfall (mm) 50 100 150 200 250

0

Failure volume

F2

0 0

60

120 180 240 300 Rainfall time (min)

360

Cumulative failure volume (cm3)

Failure volume

F1

0

Fig. 8. Distribution of failure volume for the cumulative rainfall time in experiments F1–F6. Six events of rainfalls were applied to the slope in each experiment. Each simulated rainfall had an intensity of 50 mm h−1 and a duration of 60 min. Total rainfall time was 360 min, and cumulative rainfall was 300 mm.

landslides accounted for 10% of the total landslide volume in Umbria, central Italy. Therefore, a large-scale mass movement increases the sensitivity to the total amount of mass movements, but the probability of this occurrence is very low. Moreover, the critical rainfall amount has important practical significance to forecast and prevent the occurrence of landslides. In our experiments, rainfall amount of approximately 25.6 mm is a critical value for mass movement failure. This finding is consistent with that of Chen and Wang (2014), who found that a rainfall threshold amount of 23 mm initiates loess landslides based on 175 rainfall records in Yan'an from 2001 to 2003. Shallow mass movements are a predominant erosion process in several catchments of the Loess Plateau (Guo et al., 2016; Xu et al.,

of landslide size also increases with the decreasing landslide area in an inverse power-law relationship up to a limit of a few hundred square meters (Lu and Godt, 2013). In addition, the cumulative landslide frequency correlates well with rainfall (Li et al., 2011) and storm magnitude (Reid and Page, 2003). De Rose (2013) observed a linear increase in scar areal density with slope angle on steep slopes. The spatial distribution of landslides can be affected by the spatial variation of soil properties (Fan et al., 2016). The frequency of mass movements was only 0.6% (3 failures) when 8000 cm3 was exceeded. This result confirms the importance of large mass movements in determining the total volume in a region (Guzzetti et al., 2008, 2009). Guzzetti et al. (2009) found that the seven largest 8

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4000

F1

12000

Cumulative failure volume (cm3)

Cumulative failure volume (cm3)

16000

y = 666.57x - 18108.0 R² = 0.91

8000

4000

0

1000

10 20 30 Rainfall amount (mm)

40

2000

1000

50

0

50000

F3 Cumulative failure volume (cm3)

Cumulative failure volume (cm3)

y = 208.14x - 6682.6 R² = 0.96

3000

0 0

800

600

400

200

10

20 30 40 Rainfall amount (mm)

50

F4

40000

y = 1558.30x - 38617.0 R² = 0.98

30000

20000

10000

0

0 0

25000

10

20 30 40 Rainfall amount (mm)

0

50

15000

F5 Cumulative failure volume (cm3)

Cumulative failure volume (cm3)

F2

20000

15000

y = 520.81x - 9998.8 R² = 0.83

10000

5000

0

10

20 30 40 Rainfall amount (mm)

50

F6

12000

y = 482.65x - 11910.0 R² = 0.96

9000

6000

3000

0 0

10

20 30 40 Rainfall amount (mm)

50

0

10

20 30 40 Rainfall amount (mm)

50

Fig. 9. The relationship between the cumulative failure volume (Gc) and the rainfall amount (Rc) in the first rainfall event (0 mm < Rc < 50 mm) in experiments F1–F6. Fitting equation between Gc and Rc could not be applied because only one mass movement occurred in the first rainfall event in experiment F3.

occurrences.

2017), and an accurate measurement of failure frequency provides a useful spatial layer for predicting erosion rates and sediment yields in small watersheds subject to mass movements (De Rose, 2013). Identifying the number and volume of landslides is important to determine landslide susceptibility and evaluate the evolution and erosion of landscapes dominated by mass movements (Korup, 2005; Guzzetti et al., 2009). In our experiments, the size of mass movements is relatively small compared with that in actual fields, but the characteristics, types, and distributions of mass movements are consistent with actual

6. Conclusion Our experiments in the Liudaogou Catchment reveal that mass movements have group characteristics. A total of 499 mass movements were recorded in 42 rainfall events, and an average of 11 mass movements occurred on steep slope in each rainfall event. The results show that landslides (67%) are the most frequent mass movement, followed 9

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Table 6 Summary of the critical rainfall amount for mass movement failure in experiments F1–F6 (as shown in Fig. 9). Gc is the cumulative volume of mass movements, Rc is the rainfall amount (0 mm < Rc < 50 mm), and Rv is the critical rainfall amount for mass movement failure. When Gc is equal to zero in Equation, Rc is approximately equal to Rv. Test number

Slope height (m)

Equation

Number of mass movements

Determination coefficient R2

Rv (mm)

F1 F2 F3 F4 F5 F6 Average

1 1 1 1.5 1.5 1.5 1.25

Gc = 666.57 Rc – 18,108.0 Gc = 208.14 Rc – 6682.6 – Gc = 1558.30 Rc – 38,617.0 Gc = 520.81 Rc - 9998.8 Gc = 482.65 Rc − 11,910.0 –

11 5 1 18 20 15 12

0.91 0.96 – 0.98 0.83 0.96 0.93

27.2 32.1 – 24.8 19.2 24.7 25.6

by mudflows (21%), and avalanches (12%). Material entrainment of wet bed material in steep gullies can dramatically increase the volume of landslides. In our experiments, material entrainment magnified the volume of landslides by 29% on average for 12 landslide events. The distribution of mass movements was explored based on the data of 499 mass movements from the experiments. The results show that 2000 cm3 is a key demarcation point for mass movements. Approximately 90% of the 499 mass movements occurred with a volume of < 2000 cm3, and only 10% occurred with > 2000 cm3. The frequency distribution (P) of mass movements decreased with increasing mass movement volume (v) in a power-law relationship: P = 1256.4v−1.525. Approximately 92% of the mass movements occurred at the middle and later stages of rainfall. The critical rainfall amount for mass movement failure was approximately 25.6 mm at a rainfall intensity of 50 mm h−1. These findings provide insights into the failure mechanism and erosion processes on steep slopes in small watersheds.

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