Catena 183 (2019) 104238

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Rainfall-triggered mass movements on steep 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 and Dryland Farming on the Loess Plateau, Northwest A&F University, Yangling, 712100, Shaanxi, China b 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

ARTICLE INFO ABSTRACT

Keywords: Mass movements are predominant geomorphic processes on steep hillslopes. However, the mechanisms gov- Mass movement erning 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 Entrainment Liudaogou Catchment on the Loess Plateau of China. A novel topography meter was used to observe random Rainfall simulation experiments mass movements. A total of 499 mass movements in 42 rainfall events and an average of 11 mass movements for Loess Plateau each rainfall event were observed. Three mass movement types were detected: (67%) > mudflows (21%) > (12%). The volume of landslides dramatically increased through the entrainment of a wet gully bed material, and the volume of 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 et al. (2015a) suggested a systematic classification of mass movements, including landslides, mudflows, and avalanches. Mudflows have ob- Mass movement, also referred as gravity erosion or mass wasting, is vious flow performance and high compared with land- a slope failure on hillslopes. Mass movement is not only a natural ha- slides and avalanches (Guo et al., 2019). During erosion, the failure zard but also an important means of conveying sediments from slopes to block of an completely separates from the slope surface, channels in mountainous territories, thus severely affecting the struc- whereas that of a landslide slips down as a whole along a weak belt (Xu ture and function of ecosystems and societies (Keefer and Larsen, 2007; et al., 2015a). Zhang et al. (2012) found a close relationship between Qiu, 2014; Fuller et al., 2016; Xu et al., 2017). Therefore, under- the topographic attributes of post-landslide local surface and mass standing this phenomenon is necessary to implement hazard mitigation movement types. However, the responses of different movement types and control erosion. to rainfall characteristics and the distribution of mass movements have Rainfall is the most important triggering factor of mass movements received little attention despite their importance. on the Loess Plateau of China (Xu et al., 2017). Dry loess can sustain Previous studies have shown that the entrainment of initially static near-vertical slopes; however, loess can rapidly disaggregate when lo- materials can increase the mobility of avalanches (Mangeney et al., cally saturated by rainfall (Dai and Lee, 2002). Rainfall-triggered mass 2007). Accordingly, Breien et al. (2008) suggested that entrainment movements frequently occur on soil-mantled landforms (Minder et al., usually causes the debris flow to become increasingly erosive. Debris 2009). A field investigation shows that rainfall-triggered mass move- flow can markedly increase in size and speed when materials are en- ments only occur at a depth of < 2 m, corresponding to a surface layer trained from their beds. In addition, flow deposits from the underlying of completely saturated loess (Wang et al., 2015). erodible layer are difficult to distinguish when they are composed of the Mass movements include various types, each of which has specific same materials (Mangeney, 2011). Therefore, the quantitative mea- mechanisms and conditioning factors (Cruden and Varnes, 1996). Xu surement 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 0341-8162/ © 2019 Elsevier B.V. All rights reserved. W. Guo, et al. Catena 183 (2019) 104238

(a)

(b) (c)

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 Table 2 Experimental summary of the initial slope landform and rainfall. Error between design rainfall intensity and experiment rainfall intensity in experiment F1. Test Lower slope configuration Rainfall − number Rainfall events Rainfall intensity (mm h 1) Error Height (m) Gradient (°) Intensity Duration Runs −1 (mm h ) (min) Experiment Design

F1 1.0 70 50 60 6 1 47.4 50 5.2% F2 1.0 80 50 60 6 2 46.8 50 6.4% F3 1.0 60 50 60 6 3 48.8 50 2.4% F4 1.5 70 50 60 6 4 49.2 50 1.6% F5 1.5 80 50 60 6 5 50.4 50 −0.8% F6 1.5 60 50 60 6 6 47.4 50 5.2% F7 1.5 70 100 30 6 Average 48.3 50 3.3%

complicated. Furthermore, the mechanisms that govern the growth of Table 3 landslides remain unclear, hampering efforts to assess natural hazards Soil physical properties.

(Iverson et al., 2011; Mangeney, 2011). − Initial water content/ Dry density/g cm 3 Primary particle size (%) Recently, numerous scholars have conducted laboratory experi- % ments on mass movements to understand their processes and mechan- /mm /mm /mm isms. For instance, Terajima et al. (2014) conducted a flume experiment < 0.002 0.002–0.05 > 0.05 to examine slope subsurface and found that seepage forces 9.3–13.6 1.44–1.66 2 30 68 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. landslides. Kharismalatri et al. (2019) conducted a flume experiment to Yuliza et al. (2016) prepared a small-scale landslide experiments to evaluate factors for controlling sediment connectivity of landslide ma- determine the soil characteristics and water content that induce terials. However, these laboratory experiments used remolded soil,

2 W. Guo, et al. Catena 183 (2019) 104238

(a) (c)

(b) (d)

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 Number of mass movements Amount of mass movements/103 cm3

Avalanche Landslide Mudflow Total Avalanche Landslide Mudflow Total

F1 12 41 5 58 11.0 53.3 4.2 68.6 F2 7 14 1 22 3.7 8.4 0.4 12.5 F3 1 3 3 7 0.3 9.5 1.5 11.4 F4 7 126 45 178 5.3 173.4 40.9 219.6 F5 10 89 18 117 5.6 92.2 13.2 111.0 F6 9 56 32 97 6.8 56.1 20.6 83.6 F7 16 4 0 20 49.4 3.1 0.0 52.5 Summation 62 333 104 499 82.2 396.1 80.7 559.0 Percentage 12% 67% 21% 100% 15% 71% 14% 100% destroyed the mechanical structure of the original soil, and could not contribution of avalanches, landslides, and mudflows to the amounts of truly reflect the changes of the stress field on natural slopes. Further- mass movements. In addition, the distribution of mass movements in more, few experiments have focused on the distribution of mass terms of failure volume and rainfall was explored. Different from la- movements in terms of failure volume and rainfall. boratory experiments, the experiment on the segment of unscaled rea- Therefore, this study conducted a series of mass movement experi- lity on natural loess slopes retains the loess scale and natural char- ments on segments of unscaled reality on natural loess slopes on the acteristics (such as the internal structure and vertical joints) while Loess Plateau of China. The objective of this study was to investigate controlling for the location and timing of mass movement occurrence the characteristics and distribution of mass movements and the (Guo et al., 2019). This characteristic in our study is an important

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80% Number landslides, mudflows, and avalanches that contribute large amounts of 71% Volume 67% sediment yield by conveying soil into valleys. 70%

60% 3. Materials and methods 50% To analyze the failure mechanism of mass movements, a series of 40% experiments (F1–F7) were conducted on natural loess slopes in the Liudaogou Catchment of Shenmu County in the summer of 2014 Percentage 30% (Fig. 1). A mobile laboratory was built in the test plot to avoid wind and 21% sunlight. Experimental slopes with 3 m length and 2.8 m width were 15% 20% 12% 14% isolated from their surroundings by inserting steel plates approximately 0.5 m deep into the soil in the mobile lab. The experimental slopes were 10% “” without disturbing the slope underground to maintain the original 0% texture and density of the experimental soil (Guo et al., 2016). Ac- Avalanche landslide cording to the typical topography of the Liudaogou Catchment, ex- perimental slopes F1–F7 had a height of 1–1.5 m, a gentle upper slope Fig. 3. Percentages of the type of mass movement. A total of 499 mass move- of 3°, and a steep lower slope of 60°–80° (Table 1). – ments occurred in 42 rainfall events in experiments F1 F7. 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 − advantage over the traditional methods mainly undertaken via the la- rainfall intensity of 2.0 mm min 1 and a duration of 30 min, which boratory test of remodeling soil. cause severe gravity erosion (Xu et al., 2015b). To guarantee equal precipitation, rainfall events in the experiment slopes F1–F6 and F7 − 2. Study area 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 The Loess Plateau of China is a region that suffers from severe soil applied to each experimental slope. A 12-hour interval was maintained erosion. It is mainly distributed in the middle reaches of the Yellow after each rainfall to ensure an approximation of the initial water River basin (Liang et al., 2015) and covers a total area of 624,000 km2 content. Table 2 shows that the error between the design and experi- (Fig. 1). The study site, Liudaogou Catchment (110°21′–110°23′E, ment rainfall intensities was < 7%. Table 3 shows the loess properties 38°46′–38°51′N), is located in the Loess Plateau, which is distinguished as determined from the experiments. by several gullies and undulating loess slopes. The elevation ranges The erosion and entrainment processes were monitored, and the from 1094.0 m to 1273.9 m above sea level. The watershed has an volumes of mass movements were measured. A novel topography meter average annual precipitation of 437 mm, of which approximately 77% based on a structural laser was used to observe random mass move- occurs as intense rainstorms from June to September (Wu et al., 2016). ments (Guo et al., 2016). Based on the contour map obtained from the Rainstorm-induced mass movements frequently occur in steep gully topography meter, a three-dimensional can be digitally re- banks with slope gradients higher than 70° (Xu et al., 2015a) due to the constructed with ArcGIS (Esri) (Fig. 2c and d). Consequently, the vo- crisscrossing gullies of the undulating terrain, sparse vegetation, and lume of mass movements on steep slope was calculated. The topo- numerous vertical joints. In this area, headwall retreat, gully bank graphy meter results were relatively accurate (< ± 10% of the volume erosion, and downcut during gully processes are often accompanied by error) (Xu et al., 2015c). Mass movements on the Loess Plateau were

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.

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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 (cm3) 849.3 5171.8 1024.0 4116.9 728.5 714.5 Entrainment volume (cm3) 598.9 373.7 732.3 628.0 300.8 549.1 Post-entrainment collapse volume (cm3) 1448.3 5545.6 1756.4 4744.9 1029.4 1263.6 Rate of increment (%) 41% 7% 42% 13% 29% 43%

– 7-2711 8-3949 9-4320 10-2547 11-5025 12-4432 Pre-entrainment collapse volume (cm3) 721.4 1947.2 1547.3 686.1 972.5 1008.1 Entrainment volume (cm3) 127.9 394.5 280.5 787.7 705.7 396.0 Post-entrainment collapse volume (cm3) 849.4 2341.7 1827.8 1473.8 1678.2 1404.1 Rate of increment (%) 15% 17% 15% 53% 42% 28% classified into three types: landslides, mudflows, and avalanches (Xu most frequently observed failures. This finding is consistent with that of et al., 2015a). During the experiments, occurrence time, locations, and previous research on the Loess Plateau (e.g., Zhang et al., 2012). As types of mass movements were recorded through direct observations shown in Fig. 3 and Tables 4, 333 landslides accounted for 67% of the and a video camera. Mass movements with volume over 300 cm3 were total 499 mass movements and contributed 71% (396.1 × 103 cm3)of considered in this study. Soil loss caused by mass movements was cal- the total volume of mass movements. In particular, the amount of culated using the following formula: landslides for F1, F4, and F5 accounted for 78%, 79%, and 83%, re- spectively. gvij =−1(ij , ) v 2( ij , ) (1) Mudflows were particularly frequent in areas of steep slopes. In where i represents the sequence number of failure incidents during total, 104 mudflows accounted for approximately 21% of the total mass 3 3 rainfall; j represents the sequence number of rainfall events for a certain movements and contributed 14% (80.7 × 10 cm ) to the total volume landform; gi,j is the volume of an individual failure mass; and v1(i, j) and of mass movements (Fig. 3 and Table 4). In addition, 62 avalanches, v2(i, j) are the slope volumes within the incident scope before and after approximately 12% of the total mass movements, occurred in the ex- 3 3 the failure, respectively. periments and contributed 15% (82.2 × 10 cm ) to the total volume of Landslides that occurred in a steep gully induced material entrain- mass movements. The frequency of mudflows was higher than that of ment. The entrainment volumes were obtained by measuring gully bed avalanches, whereas the proportion of mudflows was smaller than that material volumes before and after the passage of mass movements. of avalanches in the total amount of mass movements. This result was 3 With a volume interval of 100 cm3, the mass movement volume attributed to the mean avalanche volumes (1325.8 cm ), which were 3 fl 3 (cm ) v = [300, 17,000] was graded into 167 subintervals Ii larger than the mean mud ow volumes (776.0 cm ). (I1 = [300–400], I2 = [400–500], I3 = [500–600], …, The frequency of avalanche occurrence was the smallest, re- I167 = [169000–17,000]). The number (ni) of mass movements was presenting < 12% of the whole mass movement. In particular, for F4, counted for each Ii subinterval. The occurrence frequency (Pi) of mass 178 mass movements occurred, whereas avalanches only accounted for movements for the Ii subinterval was obtained by dividing the number 4%. An avalanche occurs only when the tensile torque on the ruptured (ni) of mass movements in each subinterval by the total number of loess surface is less than the gravitational torque generated by the soil landslides (N). A power-law regression model was used to fit the re- gravity. lationship between mass movement frequency (P) and mass movement volume (v). 4.3. Gully bed material entrainment for mass movements

4. Results Material entrainment can play an important role in landslide movements. Experiments suggest that the entrainment of gully bed 4.1. Group characteristics of mass movements material magnifies the volume of landslides in a steep gully (Fig. 4). The above entrainment phenomenon was observed in approximately 12 Rainfall-induced mass movements (e.g., avalanches, landslides, and landslides in the experiments. Table 5 shows the statistical results of the mudflows) frequently occur in steep slopes. As shown in Table 4, the slide entrainment in the movements. For instance, for the landslide mass movements in the experiments in the Liudaogou Catchment ex- event 12-4432 in the upper part of the slope, the initial volume was hibit a group characteristic. A total of 499 shallow mass movements 1008.1 cm3. Material entrainment in the gully was induced by land- were observed in 42 rainfall events for F1–F7, an average of 11 mass slides and caused debris mass to grow by 28% (entrainment volume was movements occurred on steep slope in each rainfall event, and a max- 396 cm3) before deposition began on the flatter main channel. The post- imum of 43 mass movements occurred in each rainfall event. The de- entrainment landslide volume was 1404.1 cm3. As shown in Table 5, velopment of a typical mass movement is given in Fig. 2a and b with the volumes of the landslide mass increased in the range of reference to the images from the video camera. The mass movement 127.9–787.7 cm3 and were magnified by 29% on average through frequency was approximately 1.5 mass movements per m2 in each material entrainment for 12 landslide events. rainfall event. The minimum, mean, and maximum mass movement 3 volumes were 300.3, 1120.2, and 16,883.6 cm , respectively. Further- 4.4. Distribution of mass movements on failure volume more, frequent small mass movements produced irregular slopes. In this study, the volume distribution of mass movements was ex- 4.2. Contribution of avalanches, landslides, and mudflows in mass plored based on the data of 499 mass movements from experiments movements F1–F7. Fig. 5a shows a histogram of volume distribution on mass movements. The volumes of rainfall-induced mass movements ranged The mass movements were classified as follows: landslides (67%), from 300.3 cm3 to 16,883.6 cm3, with the majority of failures in the mudflows (21%), and avalanches (12%) (Fig. 3). Landslides were the range of 300–2600 cm3. Most mass movements were triggered in the

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(a) Number of mass movement vicinity of the interface of the two sloping sections. As shown in Fig. 5a 70 Cumulative number 600 and b, the mass movement frequency decreased as the volume size increased. Fig. 5b indicates that the frequency of mass movements in 60 500 the range of 300 cm3 ≤ volume ≤ 1000 cm3 was 63.9% (319 failures), 50 where the frequency was the highest. When the volume was in the 400 range of 1000–2000 cm3, the proportion of mass movements was ap- 40 proximately 27.3% (136 failures). Approximately 41 mass movements 300 (8.2%) occurred when the volume was in the range of 2000–8000 cm3. 30 The frequency of mass movements was lowest at 0.6% (3 failures) when 200 8000 cm3 was exceeded.

20 Cumulative number As shown in Fig. 5b and c, 2,000 cm3 was a key demarcation point 10 100 for mass movements in the experiments. Fig. 5b shows that 90% of the Number of mass movement Number 499 mass movement events had a volume < 2000 cm3, whereas only 0 0 10% had a volume > 2000 cm3. However, these large mass movements 0 (44 failures) accounted for 33% of the total mass movement volume 3 1000 9000 4000 5000 3000 6000 7000 2000 8000 13000 10000 11000 12000 16000 14000 15000 17000 (Fig. 5c). The frequency of mass movements with a volume > 6000 cm Mass movement volume (cm3) was only 1.4% (7 failures), but they accounted for 12.7% of the total amount of mass movements. Probability The frequency and volume of the mass movements were fit with a (b) Cumulave probability power-law distribution. The relationship was established based on the 15% Probability funcon 100% 499 mass movement data from the experiments: P = 1256.4v−1.525 (2) 12% (2000 cm3, 90%) 80% where v is the mass movement volume and P is the occurrence prob- ability of mass movement. The R2 value was 0.82. 9% 60% 4.5. Distributions of mass movements on rainfall 6% 40% Each rainfall event (per hour) in experiments F1–F6 had an intensity − Probability (%) of 50 mm h 1 and a duration of 60 min, whereas that in experiment F7 P v-1.525 −1 3% = 1256.4 20% had an intensity of 100 mm h and a duration of 30 min. Therefore, R² = 0.82 the distribution of mass movements on rainfall time (per hour) was Cumulave probability (%) explored based on the data of 479 mass movements from experiments 0% 0% F1–F6. Fig. 6 shows these distributions from the six slopes (F1–F6) at 0 3000 6000 9000 12000 15000 18000 different slope heights (1 and 1.5 m) and slope gradients (60°, 70°, and 3 Mass movement volume (cm ) 80°). The probability of mass movement failure dramatically increased with the increases in rainfall duration in experiments F1–F6. The – 100% (c) highest failure frequency (28.0%; 134 failures) was 50 60 min, which 2000cm3 was 16.5 times higher than the lowest failure frequency (1.7%; 8 fail- ures) of 0–10 min rainfall event. In experiment F4, approximately 54 3 80% 300 ~ 2000 cm mass movements occurred at 50–60 min, where the amount of failure 2000 ~ 17000 cm3 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 60% 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 40% 10% of mass movement occurred at the middle and later stages of rainfall. accounts for 33% of the The distribution of mass movements with rainfall events on ex- total volume of gravity – 20% erosion. periments F1 F6 is shown in Fig. 7. The probability of mass movement

Cumulativ failure volume (%) Cumulativ failure volume failure initially increased and then decreased with rainfall events. The frequency of mass movement occurrence in the second rainfall event 0% was highest at 28.8% (138 failures), which was 5.8 times higher than 0% 20% 40% 60% 80% 100% the lowest failure frequency (5.0%) in the sixth rainfall event. For ex- Cumulative mass movement number (%) periment F4, approximately 43 mass movements occurred in the second rainfall event, where the number of failures was the highest in all ex- Fig. 5. Frequency distribution and probability function of mass movement (499 periments (Fig. 7a). Moreover, about two-thirds (65%) of the total mass – mass movement events in experiments F1 F7). (a) histogram of frequency movements occurred in the second, third, and fourth rainfall events. 3 distribution on mass movement, with the highest volume ranging from 300 cm The failure frequency (Fig. 7b) decreased in the fifth and sixth rainfall to 2600 cm3; (b) probability function of mass movement (approximately 90% of events, indicating that excessive rainfall does not necessarily result in 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 excessive failures. movements. The 44 largest mass movements (10% of total number) accounted The cumulative failure volume through rainfall time and rainfall for 33% of the total mass movement volume. amount in experiments F1–F6 is shown in Fig. 8. The relationship be- tween the cumulative failure volume and cumulative rainfall shows an S-shape curve. Fig. 8 shows that the maximum increases in failure vo- lume occurred during the rainfall of approximately 50–200 mm (rain- fall time of 60–240 min) and not during the highest rainfall

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(a) (b) 60 F1 F2 F3 30.0% 28.0% F4 F5 F6 24.0% 50 25.0% 23.6%

40 20.0% 15.8% 30 15.0%

20 10.0% 6.9% Probability (%)

10 5.0% 1.7% Number of mass movement Number 0 0.0% 0 102030405060 0-10 10-20 20-30 30-40 40-50 50-60 Rainfall time (min) Rainfall time (min)

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) 50 35.0% F1 F2 F3 F4 F5 F6 28.8% 30.0% 40 25.0% 30 18.0% 17.7% 20.0% 16.5% 14.0% 20 15.0%

Probability (%) 10.0% 10 5.0% 5.0% Number of mass movement Number 0 0.0% 123456 123456 Rainfall events Rainfall events

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).

(250–300 mm). This result indicates that the largest erosion rates and maximum of 178 mass movements occurred in F4 (Table 4). Landslides sediment production result from these rainfall times and quantity. Fig. 7 that occur due to heavy rainstorms may be distributed over regions that shows that approximately 45.3% of the 479 mass movements in ex- extend from a few to tens of thousands of square kilometers (Lu and periments F1–F6 occurred when the cumulative rainfall was < 100 Godt, 2013). The largest of these landslide events may comprise thou- mm, 35.7% of the total mass movements occurred when the cumulative of landslides and dominate sediment production from hillslopes rainfall was 100–200 mm, and only 19% occurred when rainfall ex- (Parker et al., 2011; Lin and Chen, 2012). For example, Yan'an, which is ceeded 200 mm. A great amount of the potential mass movements oc- located on the Loess Plateau and has an area of approximately curred when rainfall exceeded the critical rainfall level to trigger 37,000 km2, experienced heavy rainfall (577 mm) in July 2013, which landslides (Li et al., 2011). Therefore, the subsequent amount of rainfall resulted in 8135 slope failures (Wang et al., 2015). (250–300 mm) can merely result in a few mass movements (Fig. 7). Mass movements induced material entrainment in gullies. In our

The relationship between the cumulative failure volume (Gc) and experiments, material entrainment magnified the volumes of landslides the rainfall amount (Rc) in the first rainfall event in experiments F1–F6 by 29% on average (Table 5). Material entrainment frequently occurred are shown in Fig. 9. The relationship was fit in an equation to obtain the in steep gullies. Valley widening was frequently achieved through critical rainfall amount (Rv) for a mass movement failure. As shown in landslide development (Mather et al., 2002). Field evidence of material Table 6, Rv values in experiments F1, F2, F4, F5, and F6 were 27.2, entrainment has been often observed, involving avalanches and debris 32.1, 24.8, 19.2, and 24.7 mm, respectively, with an average of flows (Mangeney et al., 2010). Several studies have shown that en- 25.6 mm. Therefore, in our experiments, the rainfall amount of ap- trainment can arise from collapses and cause debris flow mass to ex- proximately 25.6 mm can be considered critical for mass movement pand (Breien et al., 2008; Iverson et al., 2011). Iverson et al. (2011) − failure at a rainfall intensity of 50 mm h 1. Furthermore, Table 6 shows found that the entrainment is accompanied by increased flow mo- that the critical rainfall amount had a negative correlation with slope mentum and speed only if large positive pore pressures develop in wet height. On average, Rv was 29.7 mm at a slope height of 1.0 m but was bed sediments. Furthermore, high bed water content increases mass only 22.9 mm at a slope height of 1.5 m. entrainment in landslides (Mangeney, 2011). Mass movement probability-volume distribution exhibited a power- law relationship with a = −1.525 and b = 1256.4 for mass entrain- 5. Discussion ment data in our experiments (Fig. 5b). The frequency distribution of mass movements decreased with the increasing mass movement vo- Mass movements generally occur under heavy and prolonged rain- lume. The probability distribution is consistent with that determined by – fall. In experiments F1 F7, an average of 64 mass movements occurred Densmore et al. (1997) and Chen et al. (2014). The relative frequency on steep loess slopes at a cumulative rainfall of 300 mm, and a

7 W. Guo, et al. Catena 183 (2019) 104238

Failure volume Failure volume F1 F2 Cumulative rainfall (mm) Cumulative rainfall (mm) 0 50 100 150 200 250 300 0 50 100 150 200 250 300 80000 14000 ) 4500 ) 1600 -1- -2- -3- -4- -5- -6- 3 -1- -2- -3- -4- -5- -6- 3

) 4000 70000 ) 3 3 1400 12000 3500 60000 1200 10000 3000 50000 1000 2500 8000 40000 800 2000 6000 30000 600 1500 Failure volume (cm Failure volume (cm 4000 20000 1000 400 10000 2000 500 Cumulativ failure volume (cm 200 Cumulativ failure volume (cm 0 0 0 0 0 60 120 180 240 300 360 0 60 120 180 240 300 360 Rainfall time (min) Rainfall time (min)

Failure volume Failure volume F3 F4 Cumulative rainfall (mm) Cumulative rainfall (mm) 0 50 100 150 200 250 300 0 50 100 150 200 250 300 14000 250000 9000 ) 14000 ) -1- -2- -3- -4- -5- -6- 3 -1- -2- -3- -4- -5- -6- 3

) 8000 ) 3 12000 3 12000 200000 7000 10000 10000 6000 150000 5000 8000 8000 4000 6000 6000 100000 3000 Failure volume (cm Failure volume 4000 (cm Failure volume 4000 2000 50000 2000 2000 Cumulativ failure volume (cm Cumulativ failure volume 1000 (cm Cumulativ failure volume 0 0 0 0 0 60 120 180 240 300 360 0 60 120 180 240 300 360 Rainfall time (min) Rainfall time (min)

Failure volume Failure volume F5 F6 Cumulative rainfall (mm) Cumulative rainfall (mm) 0 50 100 150 200 250 300 0 50 100 150 200 250 300 120000 100000 ) 5000 ) 3500 3 -1- -2- -3- -4- -5- -6- 3 -1- -2- -3- -4- -5- -6-

) 4500 ) 3 100000 3 3000 4000 80000 3500 80000 2500 60000 3000 2000 2500 60000 2000 1500 40000 40000 Failure volume (cm Failure volume 1500 (cm Failure volume 1000 1000 20000 20000 500 Cumulativ failure volume (cm

500 Cumulative failure volume (cm 0 0 0 0 0 60 120 180 240 300 360 0 60 120 180 240 300 360 Rainfall time (min) Rainfall time (min)

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. of landslide size also increases with the decreasing landslide area in an landslides accounted for 10% of the total landslide volume in Umbria, inverse power-law relationship up to a limit of a few hundred square central Italy. Therefore, a large-scale mass movement increases the meters (Lu and Godt, 2013). In addition, the cumulative landslide fre- sensitivity to the total amount of mass movements, but the probability quency correlates with rainfall (Li et al., 2011) and magni- of this occurrence is very low. Moreover, the critical rainfall amount tude (Reid and Page, 2003). De Rose (2013) observed a linear increase has important practical significance to forecast and prevent the occur- in scar areal density with slope angle on steep slopes. The spatial dis- rence of landslides. In our experiments, rainfall amount of approxi- tribution of landslides can be affected by the spatial variation of soil mately 25.6 mm is a critical value for mass movement failure. This properties (Fan et al., 2016). finding is consistent with that of Chen and Wang (2014), who found The frequency of mass movements was only 0.6% (3 failures) when that a rainfall threshold amount of 23 mm initiates loess landslides 8000 cm3 was exceeded. This result confirms the importance of large based on 175 rainfall records in Yan'an from 2001 to 2003. mass movements in determining the total volume in a region (Guzzetti Shallow mass movements are a predominant erosion process in et al., 2008, 2009). Guzzetti et al. (2009) found that the seven largest several catchments of the Loess Plateau (Guo et al., 2016; Xu et al.,

8 W. Guo, et al. Catena 183 (2019) 104238

16000 4000 F1 F2 ) 3 m ) c(emuloverul 12000 3 3000 y = 208.14x - 6682.6 y = 666.57x - 18108.0 R² = 0.96 R² = 0.91

8000 2000 iafevitalumuC

4000 1000 Cumulative failure volume (cm 0 0 0 1020304050 01020304050 Rainfall amount (mm) Rainfall amount (mm)

50000 1000 F3 F4 ) 3

) 800 40000 3 mc(emuloveruliafevi y = 1558.30x - 38617.0 600 30000 R² = 0.98

400 20000 talumuC 200 10000 Cumulative failure volume (cm

0 0 0 1020304050 01020304050 Rainfall amount (mm) Rainfall amount (mm)

25000 15000 F5 F6 ) 3 ) 3

mc(emuloveruliafevi 20000 12000

y = 482.65x - 11910.0 15000 y = 520.81x - 9998.8 9000 R² = 0.96 R² = 0.83 10000 6000 t alu

muC 5000 3000 Cumulative failure volume (cm

0 0 0 1020304050 01020304050 Rainfall amount (mm) Rainfall amount (mm)

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.

2017), and an accurate measurement of failure frequency provides a occurrences. useful spatial layer for predicting erosion rates and sediment yields in small watersheds subject to mass movements (De Rose, 2013). Identi- fying the number and volume of landslides is important to determine 6. Conclusion landslide susceptibility and evaluate the evolution and erosion of landscapes dominated by mass movements (Korup, 2005; Guzzetti Our experiments in the Liudaogou Catchment reveal that mass et al., 2009). In our experiments, the size of mass movements is rela- movements have group characteristics. A total of 499 mass movements tively small compared with that in actual fields, but the characteristics, were recorded in 42 rainfall events, and an average of 11 mass move- types, and distributions of mass movements are consistent with actual ments occurred on steep slope in each rainfall event. The results show that landslides (67%) are the most frequent mass movement, followed

9 W. Guo, et al. Catena 183 (2019) 104238

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 ap- proximately equal to Rv.

2 Test number Slope height (m) Equation Number of mass movements Determination coefficient R Rv (mm)

F1 1 Gc = 666.57 Rc – 18,108.0 11 0.91 27.2

F2 1 Gc = 208.14 Rc – 6682.6 5 0.96 32.1 F3 1 – 1 ––

F4 1.5 Gc = 1558.30 Rc – 38,617.0 18 0.98 24.8

F5 1.5 Gc = 520.81 Rc - 9998.8 20 0.83 19.2

F6 1.5 Gc = 482.65 Rc − 11,910.0 15 0.96 24.7 Average 1.25 – 12 0.93 25.6

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