Qualifying mass failures on loess gully sidewalls using laboratory experimentation

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Qualifying mass failures on loess gully sidewalls using laboratory experimentation Xiangzhou Xua,1,⁎, Yulei Maa,1, Wenjun Yangb, Hongwu Zhangc, Paolo Tarollid, Yunzhong Jiange, Qiao Yana a

School of Hydraulic Engineering, Dalian University of Technology, Dalian 116024, China Key Laboratory of River Regulation and Flood Control of MWR, Yangtze River Scientific Research Institute, Wuhan 430010, China c State Key Laboratory of Hydro Science and Engineering, Tsinghua University, Beijing 100084, China d Department of Land, Environment, Agriculture and Forestry, University of Padova, Padova 35122, Italy e Institute of Water Resources, China Institute of Water Resources and Hydropower Research, Beijing 100038, China b

ARTICLE INFO

ABSTRACT

Keywords: Loess Plateau Gravity erosion Failure scar Rainfall Topography

The morphology of the failure scar has been a long-debated issue concerning the Loess Plateau of China, and the lack of normative data has hampered vital research in this area. In this study, a series of laboratory experiments were conducted to observe failure geometries and volumes under rainfall simulations. The following six failurescar types occurred: The sequence of the types described here may be same to that of the following text, namely Tf, Cd, Cu, Ia, Ps, and Co. The number of failure masses in the experiment for scar types Tf, Cd, Cu, Ia, Ps, and Co amounted to 45, 26, 23, 3, 2, and 1% of the total, and the corresponding volumes were 58, 16, 20, 2, 3, and 1% of the total, respectively. This implies that Tf, Cd, and Cu were the three major types of failure scars during the process of gravity erosion on a steep loess slope, and the scar Tf was the most significant. The sensitivity coefficient – the degree of variation in the target value caused by a change in a crucial factor when other conditions remain unchanged – of the slope gradient and rainfall intensity for the total volume of the Tf scar were 4.5 and 3.7, respectively. In other words, a relatively dangerous failure scar (Tf) might appear if the slope became steeper, or if the rainfall became more intensive. In addition, the sensitivity coefficients of the rainfall duration for the total volume of the Cu scar was significant, being 12.4. This shows that a long-duration storm could easily induce a large-volume failure with a Cu scar. The experimental results obtained here provide a morphogenic insight into the gravity-erosion control on a loess gully sidewall.

1. Introduction A failure scar is a crucial morphological characteristic in that it can be regarded as a fingerprint that indicates the stability of a slope, the failure trigger, and the frequency and size of the gravity erosion. Scar size might reflect the scale of the gravity erosion to some extent, although these are not really equivalent. Several studies (e.g., Guzzetti et al., 2009; Zhang et al., 1997) have estimated the amount of gravity erosion based on the size of the scar. Moreover, different scar morphologies correspond to diverse failure mechanisms (Millar and Quick, 1997; Tarolli et al., 2012). Consequently, determining the scar morphology is a key to conserving soil and water, and assessing the efficacy of gravity erosion treatments.

Mass movement – also called gravity erosion, mass wasting, slope movement, and slope failure (Blaschke et al., 2000) – is prone to occur on steep slopes (Basharat et al., 2014; Krohn et al., 2014; Xu et al., 2015a, 2015b). The mass movement is the outward or downward gravitational movement of earth materials without the aid of running water as a transportation agent (Crozier, 1986). Numerous studies have suggested that the mass failure is the principal cause of long-term agricultural productivity losses (Dregne, 1995; Luckman et al., 1999). In fact, mass failure processes essentially feature the catastrophic removal or displacement of a body of soil from a slope through gravity, which frequently causes serious on-site and proximal damage. Local hazards, such as serious soil degradation, result from mass failure because the entire soil profile can be removed in one event. Even if mass

Abbreviations: Tf, translational face; Co, convex; Cu, concave upward; Cd, concave downward; Ps, polygonal-sided; Ia, irregular in appearance ⁎ Corresponding author. E-mail address: [email protected] (X. Xu). 1 These authors contributed equally to this work. https://doi.org/10.1016/j.catena.2019.104252 Received 20 December 2018; Received in revised form 3 July 2019; Accepted 9 September 2019 0341-8162/ © 2019 Elsevier B.V. All rights reserved.

Please cite this article as: Xiangzhou Xu, et al., Catena, https://doi.org/10.1016/j.catena.2019.104252

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failure removes only part of the soil profile, that part almost always includes the organic matter and nutrient-rich A and upper B horizons (Blaschke et al., 2000). The mass failure also brings about related damages by the transported sediment, such as transport route damage (Penna et al. 2014; Zieliński et al., 2016), building damage (Hungr et al., 2016), fluvial sediment deposition (West et al., 2014), reservoir sedimentation (Tsai et al., 2013), channel silting (Sayed and González, 2014), and even casualties (Zhuang and Peng, 2014). The above-mentioned types of damage correlate to the pattern of the scar because the failure scar (i.e., the fingerprint) mirrors the size of the gravity erosion (Lucas et al., 2011). The physics of fingerprinting has been embraced in studies of mass failure. For example, Convertino et al. (2013) argued that landslide size distribution is a fingerprint of the geomorphic effectiveness of rainfall as a function of climate change; Densmore and Hovius (2000) used the topographic fingerprints of bedrock landslides to distinguish the triggers of earthquake and rainfall processes; and Tseng et al. (2015) found that the characteristic topographic signature of a valley was affected by large-scale landslide processes, e.g., deep-seated landslides or large scars associated with evident debris-flow phenomena. Indeed, the scar type is the best way to explore the triggering mechanisms of mass failure, since previous studies have indicated that mass failures occurring in natural slopes produce distinctly different scar morphologies (i.e., fingerprints) during the process of mass failure. Skempton and Hutchinson (1969) showed that the ratio between the depth and length of a failure scar was generally between 0.15 and 0.33 when the mass moved along a concave upward scar. Meanwhile, the ratio was less than 0.1 when the mass slid along a translational face (Lu and Godt, 2013). In addition, different scar morphologies have been applied to the analysis of the stability of hill-slopes, including planar, concave, convex, and terraced surfaces (Highland and Bobrowsky, 2008; Leshchinski et al., 1985; Yin et al., 2009). However, the lack of normative data for the morphology of massive failure has hampered vital research in this area. Varying failure surfaces have been applied to slope movement models, but all of them have suffered from a significant lack of experimental validation, thus possibly leading to inaccurate predictions (Lu and Godt, 2013). A physical model of a selected geomorphological feature, produced under closely-monitored and -controlled experimental conditions, would be an effective way to probe the mechanisms behind mass movements on gully sidewalls. Chorley (1964) identified three broad classes of physical models –segments of unscaled reality, scale models, and analog models – with the former being the most widespread in the field of soil and water conservation. Several studies (e.g., Jeong et al., 2003; Lee et al., 1995), based on simplified scars, have revealed the mechanisms of mass failure; however, applying a conceptual scar (i.e., a simplified scar shape) to the study of triggering mechanisms in gravity erosion might have limitations and flaws. Osman and Thorne (1988) assumed that steep slopes failed along an almost planar failure surface. The major limitation of this is that the failure plane was constrained to pass through the toe of the slope, which was unrealistic (Darby and Thorne, 1996). Simon et al. (1991) determined that the scar might, in fact, intersect the slope profile at other points. In addition, the classical methods of slope-stability analysis in the mass failure, based on a conceptual arc-shaped scar, such as the Swedish slice and Bishop methods, present some limitations (Lu and Godt, 2013; Zhu et al., 2013). As addressed by Xu and Low (2006), analysis based solely upon circular slip surfaces may significantly overestimate the safety of the slope. In many cases, the failure scar can deviate significantly from a circle or a plane (Morgenstern and Price, 1965). Therefore, the limitations associated with simplifying the landform have hampered attempts to apply classical methods to forecasting mass failures (Deng et al., 2011). In fact, natural slip scars encompass a wide variety of surfaces that can satisfy any failure mechanism, such as scars with differing shear-strength properties or with complex pore-pressure distributions. Hence, to improve the accuracy and practicability of model predictions, future

projections should avoid overly simplified conceptual scars and rather be based on a suitably complete mass-failure theory. Sensitivity analysis plays an important role in exploring the triggering mechanisms that cause gravity erosion. The method can help in identifying the most influential factors, including the geology, geomorphology, and climate. The eigenvalues of erosive precipitation, such as rainfall amount, intensity, and duration, are the primary driving forces behind gravity erosion on loess sidewalls (Tarolli et al., 2008; Zhou et al., 2016; Zhou and Wang, 1992), and the soil water content, infiltration depth, specific weight, cohesiveness, and friction angle change with time during the rainfall infiltration period (Chang et al., 2013; Lanni et al., 2012; Penna et al. 2014; Stark et al., 2005). Meanwhile, slope failure is generally located along the slope where the stress is concentrated, while the geometry of the slope, including the slope shape, height, and gradient, is a critical factor affecting stress distribution in the slope (Lu and Godt, 2013; Zhang and Fan, 2015). Continued global warming is expected to cause a more vigorous hydrological cycle, including increased total rainfall and more frequent high-intensity rainfall events (Nearing et al., 2004). Hence, identifying the most influential factors corresponding to scar patterns may improve the accuracy and feasibility of the prediction models. Recently, an increase-rate-analysis method was proposed for recognizing the effect of each causal factor, and combination of factors, on the susceptibility to the gravity erosion (Xu et al., 2015b). An advantage of this method is that the influences caused by the randomness of the gravity erosion can be readily overcome. Nevertheless, the average number of mass failures per rainfall event is not a suitable factor with which to analyze the sensitivity of the number of gravity erosion events. In this work, we have improved the method of Xu et al. (2015b) by using a total value (i.e., the total volume and number of mass failures in an experiment) to evaluate the variations in scar morphologies associated with gravity erosion with respect to changes in various causal factors. A quantitative exploration of the triggering mechanisms of mass failure from a morphogenic perspective of the failure scar is necessary. Based on the movement processes, gravity erosion can be divided into three types – landslide, avalanche, and mudslide (Xu et al., 2015c); however, the failure scars left on slopes after mass failure events remain challenging features to explore. Scars are the most direct visual proof of gravity erosion. In addition, although rainfall simulation experiments allow a complete observation of the processes of gravity erosion and an accurate determination of the type of gravity erosion, such as landslide, avalanche or mudslide, in a real catchment, with natural rainfall, the failure scars left on the slope can only be investigated and observed after the rainfall event. In this study, the movement styles and scar morphologies caused by gravity erosion were used to explore the triggering mechanisms of mass failure from different perspectives. Scar morphologies can reflect not only the triggering mechanism, but also the size of the gravity erosion. Hence, in this study, the scars were classified into six types – translational face (Tf), polygonal-sided (Ps), convex (Co), concave upward (Cu), concave downward (Cd), and irregular in appearance (Ia), as discussed in Section 3.1. The Loess Plateau of China suffers from some of the highest soil erosion rates in the world, which are about 5000–10,000 Mg/km2 per year in most areas (Fu et al., 2005). Loess gully sidewall is particularly prone to the mass failures induced by the rainfall on the Loess Plateau (Wang et al., 2014; Xu et al., 2015a) because the area is characterized for the steep slope, low vegetation cover and highly erodible loess soil, and it is significantly impacted by frequent heavy rainfall events during summer (Qiu et al., 2017; Zhang et al., 2005). As a result, the contribution of mass failure to soil loss on the Loess Plateau is remarkable (Chen et al., 2007). Usually, most of the soil loss is caused by a few events of infrequent intense rainfall events in the area (Wang et al., 2016). The volume of the erosion caused by a short-burst rainfall event can account for as much as 40–90% of the total annual soil erosion for a given location (Wang et al., 2016). Short-burst rainfall events are characterized by rainfall intensities of >0.5 mm/min and rainfall 2

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(a)

Fig. 1. Landscape simulator in which the rainfall simulation experiments were conducted (all units in mm). (a) Blueprint of the topography meter measurement system. (b) Images of the experimental site. 1 – rainfall simulator, 2 – topography meter (i – camera with collimator, ii – laser source), 3 – positioning marks, 4 – model slope, 5 –equidistant horizontal projections, and 6 – receiving pool.

(b) 2(i)

1

Rainfall

3000

000

3

4

3 2(ii)

5 6

durations ranging from 30 to 120 min (Jiao et al., 2001; Wang et al., 1996). The aim of this study was to evaluate the factors affecting the distribution of different scar morphologies on an experimental gully sidewall. To that end, we conducted a series of modeling experiments on slope collapses, using a topography meter designed by us to observe the patterns of failure scars during the process of mass failure. In addition, the increase rate analysis method was used to analyze the association of the gravity erosion to different scar morphologies.

the vertical profiles on the slope surface, were created as a result of a block of soil separating from a sloped face. Herein, we used the intersection line that ran through a longitudinal section of the scar center to define the morphology of the failure scar. A MX-2010-G topography meter, consisting of a camera with a collimator and laser source, was designed and manufactured to observe the process of mass failure under the rainfall simulations (Xu et al., 2015c). The slope-deforming process was recorded by computer video technology. With the help of laser marking, plane figures were vectorially transformed into 3D graphs, so that the shape of the target surface was accurately computed. By comparing the slope geometries in the moments before and after the erosion incident on the snapshot images for a particular time, the volume of the gravity erosion and several other erosion-related data could be obtained, including the volume of the slide mass and the amount of soil loss. The relative error of the volume observed by the MX-2010-G topography meter was within 10% (Xu et al., 2015c). To ensure the accuracy of the scar pattern morphologies obtained from direct observation during the experiments, videos from the topography meter were used as a check. For each gravity erosion event, the volume of the failure mass was calculated and the form of the scar was classified. Then, we obtained the total number of mass failures (gn) and the sum amount of the mass failures (gv) corresponding to all types of scars. Only the failure masses with volumes >500 cm3 were considered in the study because the sum of the failure masses with volumes <500 cm3 accounted for only 1% or less of the total volume of the failure masses in each experiment. To evaluate the independent effects of slope gradient and height and rainfall intensity and duration on the mass volume of each scar pattern, 10 sets of experiments were divided into the following seven experimental groups: Ga (experiments L1, 2, 5, and 6), Gb (experiments L3, 4, 7, and 8), Gc (experiments L1, 3, 5, and 7), Gd (experiments L2, 4, 6, and 8), Ge (experiments L5, 6), Gf (experiments L9, 10), and Gh (experiments L1, 2). As shown in Figs. 4 and 5, the experimental groups Ga vs Gb, Gc vs Gd, Gh vs Gf, and Ge vs Gf were used to reveal the independent effects of the slope height, slope gradient, rainfall intensity, and rainfall duration on the mass volume of each scar morphology, respectively. A sensitivity coefficient, which represents the extent of change in the target value triggered by variation in a crucial factor when other conditions are fixed, is the ratio of the percentage change in the target value to the percentage change in the parameter. The larger the

2. Methods and materials The experiments of gully-sidewall collapses conducted under closely-controlled conditions in the Joint Laboratory for Soil Erosion of Dalian University of Technology and Tsinghua University (Beijing, China). The landscape simulator consisted of a rainfall simulator and a conceptual landform covering an area of 3.0 m × 3.0 m (Fig. 1). The rainfall simulator, comprising an array of spray nozzles, was used to generate rainfall. The simulated rainfall covered the experimental landform over an area of 3.5 m × 3.5 m. The uniformity coefficients of the rainfall intensities for the simulator exceeded 80%. The conceptual landform had a gentle upper slope of 3° and steep lower slopes of 70 and 80°. More details of the experiments, including slope height gradients and rainfall intensity durations, are provided in Table 1. Five runs of rainfall were applied, in turns, to the landform, and the rainfall interval was approximately 12 h. The conceptual slope was made by hand with loess from Ligezhuang, Beijing. The physical properties of the model soil were similar to those of the Loess Plateau, with the grain size distribution and bulk density being close to those of the soils from Shanxi, Gansu, and Shannxi (Xu et al., 2009, 2015c). The 50% diameter of the soil particles (D50) and the bulk density of the test soil were 0.05 mm and 2.56, respectively. The RR-1008 – an automatic moisture measuring and monitoring system – was employed to collect the water content during rainfall. The five sensor probes of the monitor were equidistantly buried inside the landform. The RR-1008 recorded data at 30-s intervals, and the relative error of the monitoring system was ±1%. Before starting each rainfall event experiment, a small intensity of rainfall was applied to the landform, with the experiment proper beginning after the upper layer of soil (∼2–3 cm from the surface) was saturated. The forms of the failure scars, i.e., the geometry of the slip surfaces and the shape of 3

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Table 1 Volume and number of mass failures with different scar patterns for an initial landform after five rainfalls. Test number

Total volume of mass failures (103 cm3/m)

Number of mass failures Tf

Co

Cu

Cd

Ps

Ia

Tf

Co

Cu

Cd

Ps

Ia

L1(S30-1-70d) L2(S30-1-80d) L3(S30-1.5-70d) L4(S30-1.5-80d) L5(G60-1-70d) L6(G60-1-80d) L7(G60-1.5-70d) L8(G60-1.5-80d) L9(G30-1-70d) L10(G30-1-80d) Total

18 11 30 11 10 12 20 15 4 3 134

0 0 0 1 0 0 1 0 1 0 3

5 6 25 11 2 8 2 5 1 4 69

16 8 11 6 8 5 12 1 3 6 76

2 1 1 0 0 1 1 0 1 0 7

6 0 1 0 0 1 1 0 0 0 9

31.9 213.8 107.7 191.1 123.2 41.3 112.3 171.4 30.1 7.5 1030.3

0.0 0.0 0.0 1.2 0.0 0.0 7.9 0.0 1.7 0.0 10.8

3.3 50.8 82.5 79.7 15.3 105.6 3.8 13.5 0.1 8.9 363.4

18.1 64.9 7.2 19.1 11.2 24.7 82.1 13.4 9.8 36.5 287.0

7.3 1.8 2.4 0.0 0.0 20.1 0.7 0.0 20.4 0.0 52.7

17.2 0.0 2.3 0.0 0.0 7.6 0.5 0.0 0.0 0.0 27.6

Percentage

45%

1%

23%

26%

2%

3%

58%

1%

20%

16%

3%

2%

Note: The following figure explains the meaning of each symbol next to the test number:

sensitivity coefficient, the more susceptible the target value to the change in the parameter. The increase-rate-analysis method (Xu et al., 2015b) was used to assess variations in the gravity erosion with respect to changes in causal factors, such as rainfall intensity and duration, and slope gradient and height. The increase rate of the gravity erosion, Rg (%), was obtained as follows:

Rg = (g2

g1)/ g1,

(1) Translational face (Tf). This comprises an inclined plane with an intersection line consisting of a straight line (Fig. 2a) in which the soil block fails along an almost planar failure surface; (2) Polygonal-sided (Ps). In this type, the intersection line is broken, giving the appearance of a stepped shape (Fig. 2b). This kind of scar has at least two intersecting planes, one of which is a low-angled inclined plane, and another of which is a relatively steep surface. (3) Convex (Co). This is where the intersection line approximates the shape of an arc, and its corresponding center is in the inner slope. Such scars are characterized by a gentle upper slope and steep lower slope (Fig. 2c); (4) Concave upward (Cu). Here, the intersection line is concave-upward in shape, where the scar has an upward-arced surface with a reverse foreside, gentle middle, and steep tail. This scar is similar to a crescent-shaped bed form, as shown in Fig. 2d; (5) Concave downward (Cd). This a downward-arced surface, where the center of the arc is located in the downside of the scar. Generally, Cd scars have lower stability than Cu scars. Fig. 2j shows a Cd scar, which looks like a spoon-shaped concavity or parabolic concavity on the slope; and (6) Irregular in appearance (Ia). These are a combination of at least two kinds of the scars described above.

(1)

where g1 is the total volume of all failures (in cm3), or total number of mass failures in an experiment before the triggering element was changed, and g2 is that after the triggering element was changed. An increased ratio of the above output (in %) was calculated with the growth rate of a parameter, while the other parameters were fixed in an experiment: (2)

S = Rg / Rt

Rt = (t2

t1)/t1

(3)

where S is the sensitivity coefficient for analyzing the sensitivity of the triggering elements on the failure number and volume of each scar morphology,t is one of the triggering elements (e.g., slope height, slope gradient, rainfall duration, rainfall intensity), Rt is the increased ratio of the triggering element (in %), t1 is the value before being changed in an experimental group, and t2 is that after being changed. The approach allows for a quantitative analysis of the effects of the conditioning factors.

As shown in Table 1, 10 sets of gully sidewall collapse experiments were conducted at slope heights of 1.0 and 1.5 m and slope gradients of 70 or 80°, under rainfall intensities of 0.8 and 2.0 mm/min, respectively. The results show that the number of mass failures of scar types Tf, Cd, Cu, Ia, Ps, and Co were 134, 76, 69, 9, 7, and 3, respectively. That is, the number of mass failures in the experiments corresponding to scar types Tf, Cd, Cu, Ia, Ps, and Co amounted to 45, 26, 23, 3, 2, and 1% of the total, respectively. Meanwhile, the total volumes of the failures of scar types Tf, Cu, Cd, Ps, Ia, and Co were 1030.3, 363.4, 287.0, 52.7, 27.6, and 10.8 × 103 cm3/m, and their volumes accounted for 58, 20, 16, 3, 2, and 1% of the total, respectively. This implies that the scars Tf, Cu, and Cd were the three main types of scars occurring in the gravity erosion processes on the steep loess slope, with the scar Tf being the most crucial. Large-scale and frequent mass failures may harm both local

3. Results 3.1. Characteristics of failure scars The classification of failure-scar morphologies can reflect the stability of their slope scars, the triggering method of the mass failure, and the frequency and size of the gravity erosion. We observed the scar morphologies associated with all gravity erosion events in 10 sets of rainfall experiments (Table 1). Then, we classified the scars into the following six types, based on the shapes of the intersection lines: 4

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(a)

3.2. Impact factors of failure scars

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

To assess the effects of topography and rainfall on scar pattern type, the frequency and volume of the gravity erosion events associated with each scar pattern in each group experiment were compared, as shown in Figs. 4 and 5. The histogram in Fig. 4a illustrates the variation in number and volume of mass failures corresponding to the different scar types caused by a rainfall event as slope height was increased. While the other factors were fixed, and the slope height was increased from 1.0 to 1.5 m, the total number and volume of failures producing a Tf scar increased by 49% and 42%, respectively. Meanwhile, the total number of Cu scars was increased by 105%, while that of the mass failures with Cd scars was decreased by 19%, although their volumes did not change significantly. In addition, the total events and volumes of the mass failures corresponding to scars Ps and Ia were decreased by more than 50%; however, for slope with a height of 1.0 or 1.5 m, the occurrence probability of scar Co was low in the two-group comparisons. Slope gradient also had a significant influence on the distribution of scar morphologies. As shown in Fig. 4b, when other parameters were fixed, but the slope gradient was increased by 14% (i.e., the slope gradient was increased from 70 to 80°), the total numbers of mass failures for the six different scar types were decreased, whereas their volumes were increased, with the exception of scars Co and Ia, which were reduced. The finding is likely due to two reasons. First, the increased slope gradient may have caused poor rainfall infiltration on the slope face, resulting in a lower frequency of mass failures for the scars. Table 1 provides strong evidence that the mass failure frequency decreased as the slope gradient increased. For the gully sidewalls with a slope of 70° (i.e., experiments L1, 3, 5, 7, and 9), the total number of mass failures was 182, while for those with a slope of 80° (i.e., experiments L2, 4, 6, 8, and 10), the total number was 116. Second, slope stability decreased with increased slope gradient. As shown in Table 2, in the experimental groups with slopes of 70° (i.e., experiments L1, 3, 5, 7, and 9), the total volume of all peak individual mass failures was 606.22 × 103 cm3. Nevertheless, the total volume of all peak events for the experiments with slopes of 80° was 914.95 × 103 cm3. That is to say, the total volume of peak volumes increased by 51% with an initial slope increase from 70 to 80°. The effects of rainfall duration were also investigated by varying the rainfall duration from 30 to 60 min, while the rainfall intensity was kept constant at 0.8 mm/min. Fig. 5a portrays the changes in the failure scars with increased rainfall duration. The number of failure masses corresponding to types Tf, Cu, and Cd were increased, with Tf being significantly increased (by 400%), while the gravity-erosion events with scar types Co and Ps were reduced by more than 50%. Meanwhile, the volumes of the gravity erosion events corresponding to scar types Tf, Cu, and Co were increased by 338, 1236, and 376%, respectively, while no substantial changes occurred in the failures producing scar types Cd and Ps. In other words, the change in volume associated with different scar types was tremendous, and the volumes of Cu-type failures saw a significant increase. Rainfall intensity also has a direct impact on gravity erosion. An inspection of Fig. 5b reveals that there was a substantial increase in the total numbers or volumes of gravity erosion events corresponding to three types of scars – Tf, Cu, and Cd – when rainfall duration was kept constant at 30 min, but rainfall intensity was increased from 0.8 to 2.0 mm/min. In particular, the volume of the gravity erosion for scar type Tf was increased by 553%. These increases indicate that the rainfall intensity significantly influenced the size and frequency of the gravity erosion associated with certain scar types. In contrast, the changes in the gravity erosion events corresponding to scar types Co, Ps, and Ia were not statistically significant. In addition, soil content plays an important role in triggering gravity erosion. As shown in Fig. 6a, although the soil moisture content at a

Fig. 2. Schematic representations (left) and sample images of observed examples (right) of scar morphologies. Intersection lines shown in red on the representations (left). (a), (b) Tf; (c), (d) Ps; (e), (f) Co; (g), (h) Cu; and (i), (j) Cd. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

buildings and lives. In the results shown in Fig. 3a and b, the peak volumes of individual mass failures producing scar types Tf, Cu, and Cd accounted for 78, 17, and 5% of the total volume of all the peak events. Meanwhile, the frequencies of mass failure occurrences corresponding to types Tf, Cu, and Cd respectively amounted to 60, 30, and 10% of the total number in all of the maximum-mass failures. Consequently, on steep slopes and under intense rain, the hazards caused by translational-shaped failures may be much more serious and hazardous than those caused by other-shaped failures. Although peak volumes of individual mass failures were not observed in scar types Co, Ps, and Ia, those types of mass failures did also occur in the experiments. As shown in Fig. 3c and d, the volumes and frequencies of mass failures resulting in Co, Ps, and Ia scar types accounted for 6% of the total volumes and frequencies of all types of gravity erosion events.

5

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Fig. 3. Distribution of scar morphologies by the maximum individual failure masses in 10 sets of experiments. (a) Frequency of mass failures where the scars were Tf, or Cu, Cd, Co, Ps, or Ia in all of the maximum mass failures. (b) Proportion of the largest volumes of individual mass failures with scar types Tf, Cu, Cd, Co, Ps, and Ia in all peak events. (c) Frequencies of mass failures with scar types of the scars Tf, Cu, Cd, Co, Ps, and Ia in all mass failures. (d) Proportion of the volumes of mass failures with scar types Tf, Cu, Cd, Co, Ps, and Ia in all events. Although the peak volume of individual mass failures was not observed in association with Co, Ps and Ia scars, those types of mass failure did also occur in the experiments.

depth of 10 cm was significantly increased after the first rainfall event in experiment L6, the moisture content showed only a slight increase at a depth of 30 cm, and the corresponding volume of the gravity erosion was small. Comparatively, after the fourth rainfall event (Fig. 6b), the soil moisture content at depths of 10, 30, and 50 cm reached 25%, and the corresponding gravity erosion occurred frequently, with the occurrence of a peak event. Commonly, peak events occurred in the third or fourth rainfall events in each experiment, as the soil moisture content rose.

20%

-19% -50%

20

-71%

-100%

0 800

60% 42%

20%

2% 3%

400

-20%

200

-60% -89%

0

Volume (103 cm3/m)

600

-40%

Tf

Co

Cu

Cd

Ps

-89% Ia

-100%

60 40

0% -12%

-25% -57%

-37%

-50%

20

-88%

0 800 600

-50%

Rg

80%

0%

-75% -100% 140%

138% 111%

65%

80%

400

20%

Rg

40

Events of gravity erosions

105%

49%

Rg

60

80

140%

80

Gc(L1,L3,L5,L7) Gd(L2,L4,L6,L8) An increase of 10° in slope gradient

(b)

Rg

Events of gravity erosions

A sensitivity analysis was implemented to evaluate the influences of topography and rainfall on the size and frequency of the mass failures associated with the six scar types. As shown in Fig. 7a, the sensitivity parameters of the number of mass failures on slope height, slope gradient, rainfall duration, and rainfall intensity for scar types Tf, Cd, Cu, Ia, Ps, and Co ranged from −6.1 to 4.0. In particular, rainfall duration had a significant effect on the number of failures associated with scar type Tf (SNTf = 4.0). The frequency of mass failures associated with scar

Ga(L1,L2,L5,L6) Gb(L3,L4,L7,L8) An increase of 0.5 m in slope height

(a)

Volume (103 cm3/m)

3.3. Sensitivity coefficients

3% 200

-62%

-40%

-85% 0

Tf

Co

Cu

Cd

Ps

Ia

-100%

Fig. 4. Increments of gravity erosion with increase in slope height and gradient. (a) Slope height increased from 1.0 to 1.5 m. (b) Slope gradient increased from 70 to 80°. 6

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150% 44% 0% 0%

-50%

-100%

-150%

0

700% 338%

50

-22%

376%

0

Tf

Co

300% -1%

Cu

Cd

Ps

167%

0% 0% -300% 700%

553%

210

500%

498%

300%

140 79%

70 0

-100%

Ia

300%

200%

280

1100%

100

120%

-100%

0

Volumes (103 cm3/m)

1236%

150

314%

10

1500%

200 Volumes (103 cm3/m)

20

Rg

100%

Ge(L9,L10) Gh(L1,L2) An increase of 1.2 mm/min in rainfall intensity 30 600%

Co

100% -55%

-100% Tf

Rg

300%

20 10

450%

Events of gravity erosions

400%

30

(b)

Rg

Events of gravity erosions

40

Gf(L9,L10) Ge(L5,L6) An increase of 30 min in rainfall duration

Rg

(a)

Cu

Cd

Ps

Ia

-100%

Fig. 5. Increment of gravity erosion with increase in rainfall duration and intensity. (a) Rainfall duration increased from 30 to 60 min. (b) Rainfall intensity increased from 0.8 to 2 mm/min.

types Cd, Ps, and Ia were greatly influenced by change in slope gradient, with sensitivity coefficients of −4.0, −3.5, and −6.1, respectively. In other words, the number of mass failures associated with scar type Cu was highly susceptible to slope height for SNCu = 2.1. Meanwhile, in terms of gravity erosion volume, the results of the sensitivity analysis (Fig. 7b) revealed that the sensitivity coefficients on the slope height, slope gradient, rainfall duration, and rainfall intensity for the scar types Tf, Cd, Cu, Ia, Ps, and Co varied dramatically, with values ranging from −5.9 to 12.4. It is worth mentioning that rainfall duration was the most influential element on the size of the mass failures, with the sensitivity coefficient for the effect of rainfall duration on total volume for scar type Cu being up to 12.4. This is discussed further in Section 4.2. Slope gradient was the second most prominent trigger factor for size in Cu-shaped failures, with the value of the sensitivity coefficient being 9.7. Additionally, the sensitivity coefficients for the slope gradient effect on total volume of failures with scar types Tf, Co, Ps, and Ia were comparable, at 4.5, −5.9, 7.8, and −5.0, respectively. Also, the sensitivity coefficients for the total volume and number of gravity erosions based on slope gradient were −2.8 and 4.1, respectively.

The maximum volume of individual failure events (103 cm3) Tf

Cu

Cd

Co

Ps

Ia

L1(S30-1-70d) L2(S30-1-80d) L3(S30-1.5-70d) L4(S30-1.5-80d) L5(G60-1-70d) L6(G60-1-80d) L7(G60-1.5-70d) L8(G60-1.5-80d) L9(G30-1-70d) L10(G30-1-80d) Total

– 168.41 – 369.91 177.6 – 224.06 183.71 66.27 – 1189.96

41.13 – 97.16 – – 117.7 – – – – 255.99

– – – – – – – – – 75.22 75.22

– – – – – – – – – – –

– – – – – – – – – – –

– – – – – – – – – – –

Percentage

78%

17%

5%

–

–

–

(a)

10cm

30cm

50cm

Gravity erosion

(b)

Moisture content (%)

48

25

36

20

24

15 10

12 0

10

20 30 40 50 Rain duration (min)

60

Moisture content (%)

60

30

Volume (103 cm3)

Test number

30

10cm

30cm

50cm

Gravity erosion

120 100

28

80

26

60

24

40

22

0

20

Volume (103 cm3)

Table 2 The maximum volumes of individual failure masses with different scar patterns that formed in the experiments.

20 0

10

20 30 40 Rain duration (min)

50

60

0

Fig. 6. Temporal variation in soil moisture content and gravity erosion for rain duration of 60 min for different rainfall simulations in experiment L6. (a) Soil moisture content at depths of 10, 30 and 50 cm during the first rainfall event. (b) Soil moisture content at depths of 10, 30 and 50 cm in the fourth rainfall event. 7

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Height Duration

(a) 4

13

4.0

S

10

2.1

2

7

-1.4

0 -2 -4

4

Gradient Intesity 7.8

9.7 4.5

4.1

3.7

1 -2.6

-4.0

-6 -8

Height Duration 12.4

(b)

S

6

Gradient Intensity

-2.8

-3.5

-2 -5

-6.1 Tf

Co

Cu

Cd

Ps

Ia

-8

Total

-5.0

-5.9 Tf

Co

Cu

Cd

Ps

Ia

Total

Fig. 7. Sensitivity analysis of the impact factors. (a) Total number, and (b) Total volume.

internal friction and the existence of any cohesive strength along the slip surfaces, both of which are impossible to further quantify at this level of investigation (Dortch et al., 2009). In addition, the slope instability can also be influenced by other factors. For instance, human activities that denude hill slopes may increase slope instability after vegetation is cleared, with root decay leading to a critical loss of soil cohesion (Ziemer, 1981).

4. Discussion 4.1. Formation mechanisms for scar morphologies Loess is a special type of geological material that has soil structure homogeneity and peculiar mechanical properties that lead to failure scars characterized by obvious geometrical morphologies (Gan et al., 1999). In this study, the scar patterns were seen to also have a distinct geometric appearance, which could be divided into six types –Tf, Cu, Cd, Ps, Co, and Ia. Generally, mass failure occurs along an inclined plane when the shear strength is primarily provided by interparticle frictional resistance (Wang and Li, 2009). Although loess is sticky, its cohesion rapidly decreases to zero, while the internal friction angle normally reaches a stable state, if the moisture content exceeds its plastic limit (Derbyshire et al., 1994). Thus, loess often fails along scar type Tf. As we know, mass failure strongly depends on the shear strength of the slope material, which not only relates to the internal friction angle, but also the cohesion. Changes in the apparent cohesion due to variations in soil water content result in a redistribution of the shear strength during the process of rainwater infiltration. Owing to the phenomenon whereby the strength diminishes as the shear stress increases, the mass failure process is characterized by a nonuniform distribution of the shear strength along the potential slip surface (Chen et al., 2016). Consequently, rainfall-induced failures also bring about different types of scars. For instance, failure will produce an arc-shaped scar (Cu, Cd, and Co) when cohesion plays an important role in the shear strength of the soil (Wang and Li, 2009); however, the proportion of cohesion in the shear strength was dynamic in this study. As a result, other scar morphologies (Tf, Ps, and Ia) occurred. There is significant evidence that mass failure critically depends on the shear strength, tensile strength, and effective stress of the slope material (Goulding, 2006). Furthermore, although the initial slope gradients were 70 or 80° in the experiments, the instantaneous slope gradients of the individual mass failures were different, as failures frequently occurred. Hence, dynamic slope gradients might affect the shear strength of the slope surface (Meng, 1996); however, rainwater infiltration triggers variations in soil water content, leading to increased pore water pressure, in turn causing a redistribution of the macroscopic stress and strength of the potential scar, together with the dynamic changes in instantaneous slopes and cohesion, ultimately resulting in different scar morphologies. Gravity erosion – also termed mass failure – events are shallow shear failures that take place on gully sidewalls when there is an imbalance between frictional, cohesive, and gravitational forces (Sidle and Ochiai, 2006; Stark and Guzzetti, 2009). In rainfall-induced failures, changes in pore water pressure due to variations in soil water content lead to a redistribution of shear strength during the process of rainwater infiltration. The likelihood that increased pore water pressure to alone trigger any of the mass failures would depend on the actual angle of the

4.2. Effects of parameters on scar types Failure scars can reflect failure triggers and the frequency and size of gravity erosion (Millar and Quick, 1997; Zhang et al., 1997). In this study, scar types Tf, Cu, and Cd were found to be the three major types of failure surfaces that occurred as a result of the processes of gravity erosion on steep loess slopes, among which type Tf was the most crucial. This finding is similar to those of studies on the Loess Plateau, including Shi et al. (2016), who also found that arc-shaped and translational scars were the two major types in the northern bank of the Weihe River on the Loess Plateau. In fact, most well-preserved arcshaped scars on natural slopes are type Cu scars because the stability of scar type Cd is weak, tending to induce subsequent mass failures. Meanwhile, obvious disparities were seen among the mass failures associated with different scar types in the experiments. Indeed, changing the scar geometry while keeping the upper surface of the released mass constant induces a change in the released volume (Lucas et al., 2011). Our study revealed that the total volume of the failure masses with scar types Tf, Cu, and Cd accounted for a large percentage of the total volume of the mass failures, with Tf being the most decisive. Different triggering methods can explain why the failure volumes associated with scar Tf were larger than those associated with scars Cu and Cd. In this study, there were three ways of triggering mass failure, including crack propagation (Fig. 8), the deformation of partially-saturated soil (Fig. 9), and the combined effects of these (Fig. 10). The latter was prone to form scar Tf resulting in maximum-volume mass failures in the experiments. A failure scar is not only a fingerprint of a slide trace, or a vertical profile formed by a soil block separating from a sloped face, but also a measure of the geomorphological effectiveness of rainfall as a function of climate change (Convertino et al., 2013; Waldmann et al., 2011). In turn, mass failure is affected and constrained by rainfall parameters, particularly rainfall intensity and duration (Guzzetti et al., 2008). Our results show that rainfall duration significantly influences the size and frequency of mass failures, with the failures producing scars Tf or Cu (Fig. 5a). In addition, the results of this study reveal that, with an increase in rainfall intensity, both the number and volume of mass failures of the three main scar types (i.e., Tf, Cu, and Cd were increased (Fig. 5b). Previous studies have shown that, with an increase in the volume of a mass failure, the most significant rainfall variable might be rainfall duration (Dai and Lee, 2001). As rainfall intensity increases, the frequency of mass failures also increases, likely 8

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Fig. 8. Triggering of crack propagation. (a) and (b) Tension cracks formed and expanded, indicating a landslide was coming. (c) Tf and (d) Cd scars. This is a failure scar caused by the propagation of cracks.

because intensive rainfall leads to high initial and steady infiltration rates, as well as a rapid increment in the water infiltration depth and accumulated infiltration (Li et al., 2006). Topography parameters, such as slope height and gradient, also have significant influences on the distribution of scar morphologies. In this study, as slope height increased, the events and volumes of the three major types of failures increased. In particular, the number of Cushaped mass failures, and the number and volume of Tf-shaped mass failures, were significantly increased (Fig. 4a and b). An increase in slope height – which encourages shear stress concentrations to arise at the toe and tension stresses to arise at the top – will result in a significantly increased probability of mass failure. In addition, the slope height has a striking effect on mass failure size and frequency (Qiu et al., 2017). As slope gradient grew, the total volumes of the mass failures associated with type Tf, Cd, and Cu scars were increased

(Fig. 4b). These results agree with the simulation of Katz et al. (2014), which revealed that large-scale mass failures are associated with a higher slope gradient. In comparison, the frequency and size of mass failures associated with different scar patterns were more susceptible to changes in slope gradient than slope height (Fig. 7a and b). Zhu and Hong (2011) also discovered that slope gradient is more sensitive to slope stability than to slope height. The slope gradient determines the state and distribution of the stresses in the slope mass, and controls the stability and mode of instability of the slope (Dai et al., 2017; Zhang and Liu, 2010). For the rainfall characteristics, rainfall intensity and duration were herein found to be equally important in influencing the frequency of mass failures with scar type Cu, while rainfall duration significantly affected the size of the failure mass (Fig. 7a and b). This could explain why small-scale mass failures are typically induced by intense rainfall, while

Fig. 9. Triggering method of partially-saturated soil deformation. (a) and (b): Partially-saturated soil becomes more saturated, leading to deformation of the saturated soil at the bottom, followed by slope failure. (c) and (d): Scars Cd and Tf, respectively. This is a failure scar caused by the deformation of partially-saturated soil. 9

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Fig. 10. Triggering mode driven by the combined effects of tension cracks and saturated soil. A scar Tf was formed here.

In addition to the damage mentioned above, mass failure can also cause channels to widen because mass failure is a frequent and successive process of geomorphological evolution. It has been established that the main cause of gully sidewall retreat is mass movement, and not the tractive force of flowing water (Lohnes, 1991). Very little attention, however, has been focused on the widening processes of gully channels caused by gravitational cantilever failures. If mass failures on gully sidewalls are not controlled, gully expansion can reach its maximum size, forcing farmers to retreat from, and reduce the cultivated area around, such gullies (Yitbarek et al., 2012). From this perspective, gravity erosion is an important natural geomorphological hazard that affects livelihoods in a catchment, especially on the Loess Plateau of China. Hence, determining the effects of mass failure on gully sidewall retreat may improve the effectiveness and sustainability of its management and reduce land loss in ravine regions on the Loess Plateau.

large-scale mass failures require rainfall with a longer duration (Zhang et al., 2016). Increased rainfall duration increases water content and pore water pressure, thus reducing the soil shear strength, and eventually resulting in mass failure (Xu et al., 2013). Meanwhile, rainfall intensity affects rainfall kinetic energy, which shortens the pathway for water to infiltrate deeper soil strata, thus increasing the possibility of mass failure (Lin and Chen, 2012). 4.3. Hazards mirrored by the scars The damage caused by a mass failure largely depends on its velocity and volume, but the velocity is very difficult to evaluate systematically. Hence, some researchers have assessed the hazard of mass failure using the type, volume, and scar of the mass failure (e.g., Jaiswal et al., 2011). In this paper, the mass volume and scar morphology were applied to assess the damage caused by the gravity erosion. The results show that the damage caused by Tf-type failures may be much more serious than those caused by the other types. In particular, the largescale, rapid mass failures corresponding to scar type Tf were often accompanied by a crack at the top of the slope (Fig. 10). Due to this crack, the mass failure associated with a Tf-type scars will widen the channel. In other words, once gullies develop, they increase connectivity in the landscape, increasing the risk of flooding and reservoir sedimentation in a catchment (Ionita et al., 2015; Poesen et al., 2003). Derbyshire et al. (2001) also pointed out that the mass failures associated with the scar Tf had the characteristics of rapid disintegration and high sliding velocities, and this kind of failure is abundant in the loess region of North China. As we know, rapid mass movements pose a lethal threat, whereas slow movements damage property, but seldom cause fatalities (Iverson et al., 2000). Thus, the mass failures associated with scar type Tf, which move quite rapidly downhill, are the most violent gravity erosion events, with the potential for causing great harm to buildings and lives. Although the slope gradients of the initial landform were 70 or 80° in the experiments, multiple mass failures occurred in one region, resulting in a decrease in the slope gradient. Therefore, arc-shaped scars, including Cu, Cd, and Co, also occurred in the experiments. In experiments L1, L3, and L6, the scar morphology associated with the maximum volume of individual mass failures was Cu, although in experiment L10 it was Cd (Table 2). Generally, the above-mentioned individual mass failures occurred during the third or fourth rainfall events for each model. This implies that multiple mass failures, after two or three rainfall events, may decrease the initial slope gradient and lead to the occurrence of mass failures with scar types Cu and Cd. Indeed, the mass failures resulting in Cd and Cu scars always occurred on relatively gentle slopes rather than nearly vertical slopes. Lohnes (1991) also found that mass failures producing scar type Tf always occurred on steep gully sidewalls, and that arc-shaped scars (Cu or Cd) generally formed at low slope angles. Moreover, a Cd scar with low stability tends to cause subsequent mass failures. For example, concave failures generally form a spoon-shaped cavity on a slope, as shown in Fig. 2j, and so the soil block on top of the cavity surface can fall due to its own gravity.

4.4. Effects of slope morphology on slope stability After a series of mass movements, a slope can exhibit different morphologies, such as scar types Tf, Cu, Cd, Ps, Co, and Ia, even if the initial slope morphology was planar. Straight, convex, concave, and concavo-convex slope profiles are all common in natural hill slopes, resulting from diverse bedrock lithologies and structures, climates and vegetation, and geological histories (Carson and Kirkby, 1972; Reid et al., 1992). Slope morphology influences the role of rainfall in provoking slope instability. Stochastic statistics of 300 unstable slopes in China have shown that the stability of concave slopes is better than that of convex slopes (Lu and Zhu, 2014). Concave slopes include upward and downward concavities (Cu and Cd in this study). Herein, compared with Cu slopes, Cd slopes had lower stability because they tended to induce subsequent mass failures. When other parameters were fixed, but the slope morphology was different, the slope stabilities of the slopes producing the various morphologies were different. Indeed, the differences in slope stability were most significant when the radius of curvature was relatively small. The stability of the convex slopes decreased with the growth of the relative curvature radius (Farzaneh et al., 2008). The influence of slope morphology on slope stability was predominantly driven by the extent of concavity and convexity in the slope (i.e., curvature radii, soil properties, and slope gradient; Liu and Kong, 2013; Lu and Zhu, 2014). For concave slopes, the stability increases as the relative curvature radii decrease (Zhang, 1988). The check dam is one of the most effectively measures to control the gravity erosion on the Loess Plateau of China. Because of the gravity erosion, severe soil loss happens from the gullies on the Loess Plateau. The sediments yields from the gullies account for 60–70% and even 90% of the total amounts in the Loess Hill Ravine Region and Loess Mesa Ravine Region, respectively (Fang et al., 1998; Xu et al., 2004). However, as the check dams have been built, the thalwegs in the upper reaches of the gullies will rise by virtue of the siltation behind the check-dams. That’s to say, fewer mass failures will happen because the height of the side wall behind the check-dam will be shorten. On the other hand, the check-dam also has the function of reducing the gravity 10

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erosion in the lower reaches by reducing the flood peak for the sediments are retained and floodwater is impounded within the check-dam.

China (51879032), National Key R & D Project (2016YFC0402504), and Foundation of the Changjiang River Scientific Research Institute, Changjiang Water Resources Commission (CKWV2016388/KY).

4.5. The way forward

References

Gravity erosion is a natural or man-made hazard that results in an event of substantial extent, which can cause significant physical damage or destruction, loss of life, and/or drastic changes in the environment. Hence, there is an urgent need to control gravity erosion on steep slopes. Several studies (e.g., Norris et al., 2008; Stokes et al., 2007) have focused on improving slope stability using eco-technologies, such as eco- and bio-engineering methodologies. In addition, the use of surface drainage, anchor piles, prestressed anchor beams, and other engineering measures have been suggested for controlling and preventing slope instability (Xia et al., 2012). By combining structural and vegetative practices with managerial measures, slope erosion can be effectively controlled to minimize the risk of failure. Moreover, both public awareness of disaster prevention and early warning systems before hazards happen are considered to be important factors in fundamentally controlling loess mass movements (Xu et al., 2015c). Laboratory experiments have allowed us to systematically analyze soil deformation in much shorter times, and to deeply investigate interacting factors and their various influences on deformation processes. In this study, rainfall and topographic factors were considered in the collapse experiments; however, gravity erosion may be influenced and constrained by other factors, including vegetation cover and slope morphology. In these experiments, although the initial slope morphology was always planar, the slope presented different morphologies – Tf, Cu, Cd, Ps, Co, and Ia – after a series of mass movements. These straight, convex, concave, and concavo-convex slope profiles are all common in natural hill slopes, and result from diverse bedrock lithologies and structures, climate and vegetation, and geological histories (Carson and Kirkby, 1972; Reid et al., 1992). Slope morphology influences the role of rainfall in provoking slope instability. In addition, the internal friction angle and cohesion become dynamic during rainfall, and can also strongly influence slope stabilty. Hence, in future experiments, a more comprehensive set of circumstances, and the combined results of all such factors, should be taken into account for the mass movement on the loess-gully sidewall.

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5. Conclusions This paper provides a morphogenic insight into an analysis of the mechanisms behind gravity erosion on the loess gully sidewalls. The morphologies of the failure scars encountered were classified into six types based on the shapes of their intersection lines. In a rainfall event, different scar morphologies of mass failure might emerge in the same period. Tf, Cu, and Cd were the three major scar types that occurred as a result of the processes of gravity erosion on steep loess slopes, with Tf being the most crucial. In this study, three ways to trigger mass failures were found, including the crack propagation, deformation of partiallysaturated soil, and a combination of the two. Slope gradient and rainfall duration prominently influenced the distribution of the scar morphologies. In particular, steeper slope gradients resulted in significant increases in the number of mass failures having Tf scars, and longer rainfall duration led to remarkable increases in the total volume of mass failures with Cu scars. Sensitivity coefficients of the slope gradients on the number of mass failures with the Tf scars, and rainfall duration on the total volume of mass failures with the Uc scars were 4.0 and 12.4, respectively. Acknowledgements This study was supported by the Open Research Fund of State Key Laboratory of Simulation and Regulation of the Water Cycle in River Basins (IWHR-SKL-201707), National Natural Science Foundation of 11

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