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J. Mt. Sci. (2017) 14(2): 237-248

e-mail: [email protected]

http://jms.imde.ac.cn DOI: 10.1007/s11629-016-3968-5

Comparison of the entrainment rate of debris flows in distinctive triggering conditions

MA Chao 1 *

http://orcid.org/0000-0001-8385-0825;

WANG Yu-Jie

1

DU Cui

2

e-mail: [email protected]

http://orcid.org/0000-0002-5060-3489; e-mail: [email protected]

http://orcid.org/0000-0003-2892-1517; e-mail: [email protected]

* Corresponding author 1 Key Laboratory of State Forestry Administration on Soil and Water Conservation, Beijing Forestry University, Beijing 100083, China 2 School of civil engineering, Henan University of Science and Technology, Luoyang 471023, China Citation: Ma C, Wang YJ, Du C (2017) Comparison of the entrainment rate of debris flows in distinctive triggering conditions. Journal of Mountain Science 14(2). DOI: 10.1007/s11629-016-3968-5

© Science Press and Institute of Mountain Hazards and Environment, CAS and Springer-Verlag Berlin Heidelberg 2017

Abstract: Debris flows can be extremely destructive because they can increase in magnitude via progressive entrainment. In this paper, a total of 18 landslide-type debris flows and 268 channelized debris flows in Wenchuan earthquake and Taiwan region, as well as other regions were collected to analyze the entrainment rate of debris flows in each triggering condition. Results show that there is a power relationship between volume of initial triggered mass and final deposited debris for landslide type debris flow. The debris flows during 2008 and 2013 in Wenchuan earthquake-region have smaller entrainment rate than that from 2001 t0 2009 in Taiwan. The entrainment rate of debris flow events from 2001 to 2009 in Taiwan shows a decaying tendency as elapsed time. Comparison of the entrainment rate in the two earthquake-hit regions with other regions proves that entrainment rate has a close relation with major sediment availability and secondary rainstorm conditions. Keywords: Debris flows; Landslide; Magnitude; Entrainment rate; Earthquake

Received: 29 March 2016 Revised: 18 June 2016 Accepted: 24 November 2016

Introduction Debris flows occur when solid and fluid mixtures surge down a slope or channel. They are driven by gravity, commonly begin as shallow landslides or initiate from runoff erosion (Rickenmann and Weber 2003; Hungr et al. 2005; Hu et al. 2011; Iverson et al. 2011). Debris flows can strongly erode and carry sediments when they move on fully-saturated deposits in a channel. (Cenderelli and Kite 1998; Jakob et al. 2000; Wang et al. 2003; Revellino et al. 2004). In a watershed with sufficient available sediments, debris flows always exhibit high entrainment rate. Strong entrainment plays an important role in risk assessment and mitigation measure design. Entrainment ability of debris flows or other mass movements on earth surface has received increasing attention in recent years (Armanini et al. 2009; Egashira et al. 2001; Iverson et al. 2012; Stancanelli et al. 2015). To estimate the peak discharge and magnitude, one needs to sum the combined lengths of channel in each category downstream of an estimated point of initiation zone, multiplied by the respective entrainment rate

237

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(e.g., yield rate). For channelized debris flows, such as the mobilization from channel bed failures (D'Agostino and Marchi 2001; Marchi et al. 2002) and runoff erosion (Cannon et al. 2001), entrainment rate can be defined as the volume of sediments eroded from the streambed during the debris flow passage. For landslide-type debris flows, entrainment rate equals to eroded volume per traveling path from original site to marginal point. Both of the two types of debris flows exhibit strong entrainment, which can be exemplified by the case of Wenjia watershed in the Wenchuan earthquakehit region (Tang et al. 2012), and the Tsing Shan slope debris flow in Hongkong (Hungr et al. 2005). Besides, a moraine lake with an area of 10,000 m2 in Western Norway breached (Breien et al. 2008), causing a large debris flow with magnitude about 240,000 m3. Additionally, debris flows in earthquake-hit region and some burned regions frequently occurred. Debris flows in these regions usually have large magnitude as a result of sufficient erodible sediments and susceptible conditions of sediment delivery (Cannon et al. 2008; Santi et al. 2008; Cui et al. 2011; Chang et al. 2011; Ma et al. 2013a). Entrainment ability of debris flows are worthy of being examined, which may further our knowledge about the erosion intensity corresponding to their triggering conditions. In

this paper, a total of 18 landslide type debris flows and 268 channelized debris flows in Wenchuan earthquake-hit and Taiwan regions, as well as other regions were collected to analyze the entrainment rate of debris flows in each triggering condition. Data of landslide-type debris flows are used to examine the relationship between initial volume and final volume. Debris flows in the Wenchuan earthquake-hit region and Chi-Chi earthquake-hit region are selected as the benchmark tests to analyze the relationship between the entrainment rate and triggering conditions after earthquake. Additionally, debris flows in other regions were used to compare the entrainment rate with those two earthquake-hit regions.

1

Material and Methods

The volume of initial mass and final deposited mass of landslide-type debris flows were collected. Other debris flow data are from Hungr et al. (1984), Garcia-Marinez and Lopez (2004), Gartner et al. (2008), Chang et al. (2011) and Ma et al. (2012). 18 landslide-type debris flow data were collected, which have tenfold and hundredfold volume of initial masses (Table 1). Table 2 shows the data resources of other debris flows. Debris flows in Wenchuan were

Table 1 Data of the initially triggered mass and the final deposited mass for landslide type debris flow

1 2 3 4 5 6 7

VI (104m3) 0.75 0.36 0.54 0.23 0.95 0.75 5.00

VF (104m3) 1.50 0.49 0.81 0.27 7.00 6.00 35.00

8

2.50

24.00

9 10

0.04 9.00

0.20 14.00

MagnifiType/Origination cation 2.00 1.36 Slope debris flow/Begin in steep hillslope hollows 1.50 1.17 7.37 Landslide-type debris flows 8.00 7.00 Debris flow/ From moraine 9.60 dam failures 5.00 Slope debris flow 1.56 Rock slide–debris flow

11

2.50

9.20

3.68

Debris avalanche

12 13 14 15 16 17

30.00 12.00 0.48 0.55 0.47 0.025 0.4 0.3

36.00 23.50 1.06 0.92 1.97 0.05 1.4 1.7

1.20 1.96 2.21 1.67 4.24 20.00 3.5 5.7

Rock avalanches Landslide-type debris flow

No

18

238

Region

References

North Fork Mountain, eastern West Virginia, USA

Cenderelli and Kite (1998)

Barcelonnette Basin, South East France

Maquaire et al. (2003)

Fjærland, Western Norway Hongkong British Columbia, Canada Hummingbird Creek, Mara Lake, British Columbia British Columbia, Canada

Slope debris flow

Wenchuan earthquake-hit region

Landslide-type debris flow Slope failure Slope failure

Kameyama area, Japan Barcelonnette Basin in South French Alps

Breien et al (2008) Hungr et al. (2005) McDougall et al. (2006) Jakob et al. (2000) HungrandEvans(2004) Ma et al.(2012) Wang et al. (2003) Remaître et al. (2011)

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affected by strong earthquake. In Taiwan, debris flows after the Chi-Chi earthquake were triggered by Typhoon except the case on 9 June 2006. The first hazardous debris flow event occurred in 2001. After this event, the Soil and Water Conservation Bureau, Council of Agriculture and the Geological Survey carried out investigations about damage, vulnerability factors and risk assessment of debris flows. In detail, Lin and Jeng (2001), Jan and Chen (2005) and Chang et al. (2011) published debris flow data before and after the Chi-Chi earthquake respectively. Most debris flow events were triggered by Typhoon such as Herb, Toraji, Mindulle, Haitang, Kalmaegi and Morakot. After Wenchuan earthquake, several clustering debris flow events occurred in the neighbouring regions such as Beichuan, Qingping, Dujiangyan and Yingxiu. These regions are located beside the Beichuan-Yingxiu fault. Aiming to assess the risk, field measurements, high resolution aerial photographs of 2 m, estimations of planimetric

deposited area and depth, and 1:2000 scale topographic maps were used to calculate the sediment volume and debris flow volume. Some empirical relationships between landslide area and sliding depth were also developed to calculate the seismic volume in a watershed (Table 3). These hazardous events resulted in serious damage beyond imagination. Debris flows in this region commonly occurred during 2008 and 2013, and few events during 2014 and 2016 occurred. Debris flows in burned regions of USA (Cannon et al. 2001; Gartner et al. 2008) had smaller magnitude and the volume were measured using 10-m resolution DEM, digital line graph and aerial photographs. Specifically, debris flow event in December 1999 in North - central Venezuela coast was the worst in Latin America. This event resulted in 15,000 deaths and 23,000 houses damage (GarcíaMartínez and López 2005). Besides, some volcanic debris flows (e.g., lahars) at Mount St. Helens were collected (Major et al. 2005).

Table 2 Data resources for analyzing entrainment rate Numbers of Debris flows

Region

1

93

Wenchuan earthquake-hit region

24 September 2008 13-14 August 2010 13 June 2013

Ma et al. (2013a, 2013b); Qu et al. (2015); Fang et al. (2016);Ding (2016)

2

9

Taiwan-Before Chi-Chi earth quake

24 July 1996

Lin and Jeng (2001)

Taiwan-after Chi-Chi earth quake

30 July 2001 3 July 2004 20 July 2005 9 June 2006 17 July 2008 14 September 2008 8 August 2009

Chang et al. (2011)

16 December 1999

García-Martínez and López (2005)

18 May 1980

Major et al. (2005)

1982

Hungr et al. (1984)

No

3

77

4

12

5

11

6

5

North-central Venezuela coast Mount St. Helens Southern coast ranges in British Columbia

Date/Year

References

7

5

King Mountain, Colorado

1 September 1994

Cannon et al. (2001)

8

56

San Gabriel Mountain, California

2002-2005

Gartner et al. (2008)

Lithology/geology Sinian shale, sandstone and siltstone, limestone, slate and phyllite, Quaternary deposits Most areas have highly deformed sediments and metasediments of Palaeogene and Neogene age. The eastern part of the range is underlain by a Permian metamorphic belt. Gneisses and schists, Marbles Volcanic ash(tephra), Eruption-related deposits Crystalline and volcanic rocks Older landslide deposits; Maroon formation residuum; Younger colluvium and sheet wash deposits Tertiary and Quaternary marine sedimentary; highly fractured, weathered and faulted coarsely crystalline igneous and metamorphic rocks; crystalline plutonic rocks

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Table 3 Data of entrainment rate, watershed area and channel gradient of 93 debris flow events in the Wenchuan earthquake region No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

240

Watershed area (km2) 0.69 0.53 0.60 0.55 0.53 0.56 0.56 0.64 0.94 0.98 0.51 0.51 0.62 0.45 0.53 0.84 0.10 0.18 0.27 0.80 0.05 0.45 0.26 0.35 0.56 0.32 0.37 0.31 0.41 0.49 0.39 0.33 0.39 0.45 0.44 0.36 0.47 0.35 0.35 0.32 0.42 0.35 0.34 1.36 1.00 1.00 1.71

Channel gradient 0.85 0.86 0.84 1.70 1.70 0.31 0.60 0.63 0.54 0.57 0.48 1.04 0.48 0.80 0.61 1.09 0.47 0.80 0.51 0.46 1.02 1.13 0.44 0.45 0.55 0.36 0.51 0.53 0.63 0.62 0.48 0.58 0.31 0.37 0.74 0.44 0.95 0.55 0.48 0.42 0.51 0.58 0.81 0.16 0.39 0.55 1.48

Entrainment rate (m3/m) 43.68 50.61 47.37 6.15 3.85 1.67 3.37 1.36 2.33 3.69 1.67 74.82 13.51 16.00 17.78 8.14 47.69 14.17 23.41 55.25 190.48 202.02 78.46 122.29 111.69 19.14 22.19 57.39 14.43 8.20 12.32 200.84 21.20 99.08 6.61 91.13 9.45 21.52 1.62 19.25 4.69 28.12 27.39 96.53 70.00 4.92 17.62

No 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93

Watershed area (km2) 1.54 1.21 1.00 1.45 1.12 1.40 1.76 1.31 1.03 1.31 1.23 1.73 2.73 2.02 2.88 2.81 2.43 2.42 2.78 2.80 5.70 2.28 2.50 3.10 3.99 3.43 3.57 3.79 5.79 5.35 5.32 5.80 7.18 7.59 7.16 7.40 7.81 7.78 14.30 16.49 50.86 33.00 10.70 10.39 54.20 23.70

Channel gradient 0.41 0.85 0.37 0.50 1.04 0.35 0.23 0.15 0.04 0.27 0.17 0.37 0.92 0.99 1.02 0.62 0.63 0.49 0.51 0.46 0.34 0.45 0.87 0.18 0.46 0.39 0.31 0.64 0.75 0.38 0.50 0.36 0.60 0.42 0.50 0.47 0.29 0.19 0.22 0.42 0.20 0.32 0.36 0.37 0.20 0.11

Entrainment rate (m3/m) 7.07 79.14 61.55 12.73 24.22 6.41 3.33 4.00 5.94 93.37 57.38 82.22 7.78 8.49 4.58 2.19 6.51 10.68 8.97 2.24 85.71 4.21 75.21 10.00 1.85 11.17 1.75 131.23 5.00 83.33 43.29 11.75 23.90 3.64 4.63 86.98 865.38 13.48 3.87 20.81 9.86 19.77 7.41 88.91 51.79 81.31

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2

Results

2.1 Volume increment of landslide-type debris flow Generally, landslide-type debris flows can enlarge their magnitude by sediment entrainment. Displaced landslides from source area can deposit a volume several or more than 10 times as great as initial volume. In Table 1, 18 mass movement events commonly have a final volume greater than the initial triggered mass including slope failures, rocks slides, debris avalanches and moraine dam. A large rock avalanche at British Columbia, Canada has an initial volume of 300,000m3 and entrains sediments to 360,000m3. The Kameyama landslide-type debris flow has a final deposited volume of 5000m3, which is 20 times of original triggered volume (Wang et al. 2003). Data of the 18 debris flows show that the final deposited volume is far larger than the initial triggered volume (Figure 1). The data spots can be fitted by a power-law expression:

V F = 3.35 × V I 0.87

Figure 1 Relationship between initial triggered volume and final deposited volume

(1)

where VI is volume of initial mass failures m3), 4 3 VF is volume of final deposited debris (10 m ). The coefficient determination is 0.77. Except the data of large rock avalanche, coefficient and power exponent of fitted power function are 3.29 and 0.88. Corresponding coefficient of determination is 0.77. (104

2.2 Entrainment rate of debris flows in the Wenchuan earthquake-hit region Debris flows after Wenchuan earthquake mainly occurred during 2008 and 2013. The postquake debris flows seriously eroded the channel bed as a result of sufficient available sediments produced by strong earthquake. Figure 2a reveals the frequency number of entrainment rate in Wenchuan region. About 38% debris flows have an entrainment rate < 10 m3/m. About 55% debris flows have an entrainment rate > 20 m3/m. Among the 93 debris flow cases, debris flows in small watershed have a largest mean entrainment rate. Debris flows in watershed with area 800 m3/m. The mean entrainment rate of debris flows in watershed with area over 6 km2 is 32 m3/m if Wenjia watershed is not included. Watersheds with small area have limited capacities that are not suited to stock large quantity of erodible sediments. The volume of post-quake debris flows is largest because few debris flows occurred before Wenchuan earthquake. After the largest event, volume of subsequent debris flows become smaller, which can be exemplified by the case of Wenjia watershed and those along Longxi River (Yu et al. 2011; Tang et al. 2012). Besides, a total of 21 debris flows have entrainment rate < 20 m3/m among the 46 cases with watershed area of 1 km2. The reason why the mean entrainment rate is larger lies in that some landslides in source area act the main sediment supplement. After the first debris flow event, subsequent debris flows are small scale. Therefore, entrainment rate in small watersheds is relatively larger than others during the short time after strong earthquake. Then, a relationship between the percentage number of debris flows (P) and entrainment rate (E) can be fitted by a logarithmic function: (2) P = 0.1273 × ln ( E ) + 0.206 The coefficient of determination is close to 0.90. This empirical function reveals that most debris flows in the 5 years after Wenchuan earthquake have smaller entrainment rate. However, these debris flows are still hazardous because they can delivery tremendous sediments to rivers. Specifically, debris flows with entrainment rate > 40 m3/m have been reported to block river or resulted in great economic loss and human deaths. These debris flows with higher entrainment rate possibly exhibit higher frequency in subsequent years because great mount of debris remained after the last debris flow event. 2.3 Entrainment rate decay in Chi-Chi earthquake-hit region In Taiwan, the relationship between the percentage number of debris flows and entrainment rate from 2001 to 2009 after Chi-Chi earthquake can also be fitted as:

242

P = 0.1531 × ln ( E ) − 0.0237

(3)

The coefficient of determination is 0.97. The coefficient in Eq. (3) is larger than that in Eq. (2), indicating that the debris flow entrainment rate in Taiwan region is higher. The Wenchuan and Chi-Chi earthquake produced tremendous sediments for subsequent debris flows. Higher entrainment rate in the Taiwan region possibly relate to the higher rainfall amount and prolonged duration from Typhoon, and higher mean rainfall intensity and duration than the several triggering rainstorms in Wenchuan region. Among the triggering rainstorms in Table 4, typhoon Toraji produced a minimum rainfall amount of 497 mm in 18 hours, corresponding mean entrainment rate is highest. Though the rainfall intensity of some rainstorms in Wenchuan earthquake-hit region are higher than that of Typhoon (Table 5), the mean entrainment rate is smaller (Table 6). In Wenchuan region, the clustering debris flow event on 24 September 2008 was the first catastrophic one, following extensive shallow landslides, debris avalanches. This rainstorm produced a total of 272.7 mm in effective duration of 23 hours (Tang et al. 2009; Ma et al. 2013a). Rainstorm from 13 to 14 August 2010 triggered clustering debris flows in Qingping, Dujiangyan and Yingxiu (Xu et al. 2012). Mean entrainment rate of these rainfall-induced debris flows are < 15 m3/m (Table 6). Besides, the rainfall intensity (I) and duration (D) of several rainstorms in Wenchuan earthquake region is smaller than that in Chi-Chi earthquake region. For example, Guo et al. (2016) found that the debris flows in 2008 were triggered by the rainfall threshold of I=5.25D-0.75, while debris flows in 2009, 2010 and 2013 were triggered by I=9.97 D-0.75, I=11.35D-0.75, and I=17.14D-0.75 respectively. The coefficient of I-D formula in each year is increasing while is < 20. Besides, Ma et al. (2013) proposed a rainfall threshold expressed as I=34.4D-0.56 for clustering debris flows. Zhou and Tang (2014) proposed the rainfall threshold of I=66.36D-0.79 based on four catastrophic debris flow events. However, the I-D rainfall threshold for Typhoon events is far higher than the triggering rainstorms in Wenchuan region (Figure 3). Debris flows in the year of 2001, 2004 and 2009 were triggered by a higher rainfall intensity-duration. The rainfall intensity-duration of the three typhoon

J. Mt. Sci. (2017) 14(2): 237-248

events can be expressed as I=76.4D-0.35, I=98.4D-0.21, and I=72.3D-0.05 respectively. The coefficients in I-D expressions for the 3 typhoon events are higher than that mentioned in Wenchuan region. Nevertheless, absolute exponent number is smaller, indicating that high rainfall amount was produced throughout the typhoon events. 2.3.1 Entrainment rate in 2001 In 1996, Typhoon Herb produced heavy rainfall and triggered a lot of debris flows in Chenyoulan watershed. The maximum 10-minnute, 1-hour, 12-hour, and 24-hour rainfall in headwaters were 25 mm, 113 mm, 1158 mm, and 1794 mm respectively. However, maximum and mean entrainment rate are merely 1.02 m3/m and 0.423 m3/m (Table 5). Most debris flows have an entrainment rate < 1 m3/m owing to few available sediments (Figure 4). During 1999 to 2000, few debris flows were reported in the Chi-Chi earthquake-hit region. The debris flow event triggered by Typhoon Toraji in 2001 (two years after Chi-Chi earthquake) was the first catastrophic one. The entrainment rate increased a lot In 2001, debris flows commonly exhibit larger magnitude and higher entrainment rate (Figure 2b). Debris flows from 2004 to 2009 have a smaller entrainment rate than that in 2001 (Figure 2c), while is still larger than that in 1996 (Figure 3). It was noted that typhoon Toraji produced a total rainfall amount of 497 mm in 18 hours, which is the smallest and

Table 4 Accumulative rainfall, effective duration of mean rainfall intensity of triggering rainstorms in Chinese Taipei and Venezuela Rainstorm events 1996-Typhoon Herb 2001-Typhoon Toraji 2004-Typhoon Mindulle 2005-Typhoon Haitang 2006-Rainstom in Nantou 2008-Typhoon Kalmaegi 2009-Typhoon Morakot 1999-11-14-Venezuela

A (mm) 1987 497 1359 1055 1054 999 2660 911

D(hours) 43 18 69 55 59 52 97 48

RI(mm/h) 46.2 27.6 19.7 19.2 17.9 19.2 27.4 19.0

Notes: A is accumulative rainfall; D is effective rainstorm duration and RI is mean rainfall intensity. Table 5 Accumulative rainfall, effective duration of mean rainfall intensity of triggering rainstorms in Wenchuan earthquake-hit region Rainstorm events

A (mm)

2008-09-24-Beichuan 2010-08-13-Qingping 2010-08-13-Dujiangyan 2010-08-18-Dujiangyan 2012-08-18-Yingxiu 2010-08-14-Yingxiu 2013-07-10-Yingxiu

272.7 161.3 150 251 245 221.9 395

D(hours) 23 8 3 12 8 40 74

RI(mm/h) 11.9 20.2 50.0 20.9 30.65 5.5 5.3

Table 6 Minimum, maximum and mean entrainment rate of debris flows in Wenchuan earthquake-hit region and Taiwan region Entrainment rate (m3/m) Regions Year-Region Min Max Mean 2008-Beichuan 1.17 19.05 7.79 2010-Minjiang 0.14 2.39 0.64 Wenchuan earthquake-hit 2013-Minjiang 0.31 13.12 4.78 region 2010-Qingping 0.42 86.54 10.62 2010-Dujiuangyan 0.16 20.08 4.03 1996 0.00625 1.02 0.423 2001 61.76 1054.10 355.00 2004 0.97 95.40 26.74 Taiwan 2005 4.90 58.70 22.40 2006 2.10 46.30 24.20 2008 1.34 130.80 23.80 2009 2.26 60.10 20.50

Figure 3 Comparison of the “I-D” relationship for debris flow in Wenchuan (from 2008 to 2013) and Taiwan region (from 2001 to 2009).

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shortest among the several Typhoon events. Typhoon Morakot in 2009 produced a total rainfall amount of 2660 mm in 97 hours (Table 4). Entrainment rate of debris flows in 2009 is smaller (Table 5). In detail, most entrainment rate in 2001 are > 60 m3/m when the first catastrophic debris flow events were triggered by the Typhoon Toraji. About 30% entrainment rate ranges from 60 to 100 m3/m. More than half ranges from 200 to 600 m3/m. The first debris flow event in 2001 exhibits a far larger entrainment rate than that in subsequent 5 years after the Chi-Chi earthquake. Therefore, the entrainment rate of debris flows is closely related to the volume of available sediments, which can be exemplified by the debris flow cases in 2001 and 2009, respectively. For post-quake debris flows in Taiwan, the entrainment rate of debris flows is mainly controlled by the volume of available erodible sediments. Similarly, some researchers found that the debris flow volume was strongly related to loose materials volume in Wenchuan region (Ma et al. 2013b). However the entrainment rate of debris flows in Wenchuan region appears to be smaller than that in Taiwan region (Figure 4). Therefore, rainfall conditions act the secondary role in controlling the entrainment rate. Debris flow in Wenchuan earthquake region may last longer as a relatively smaller entrainment rate.

a result of increasing frequency. Therefore, the entrainment rate of debris flows in subsequent years will be smaller than that of last event. Table 6 reveals the variation of entrainment rate of individual typhoon event with elapsed time to earthquake. The decaying tendency can be fitted by a power function:

E = 828.4e−1.77T

(4)

where E is the mean entrainment rate, T is the elapsed year to earthquake in 1999, and e is natural logarithm. The coefficient of determination is 0.85. Besides, some watersheds in Wenchuan region have an extremely steep channel with gradient exceeding 1000‰, and maximum gradient of 1732‰ (Figure 5). They can be termed as small watersheds with smaller area and n0 any debris

2.3.2 Entrainment rate decay after 2001

Figure 4 Channel gradient and entrainment rate in Wenchuan (from 2008 to 2013) and Taiwan region (from 1996 to 2009).

After 2001, subsequent debris flows were triggered by typhoon Mindulle in 2004, Haitang in 2005, rainstorm on 9 June 2006, Typhoon Kalmaegi in 2008, and Morakot in 2009 respectively. The mean rate of debris flow in these events is < 30 m3/m (Figure 2c) and decays as elapsed time to earthquake (Table 5). Typhoon Morakot produced more intensive rainfall than other events, while the mean entrainment rate is smallest. As mentioned above, debris flows in 2001 have a highest entrainment rate as it was the first debris flow event after the Chi-Chi earthquake. Each debris flow event delivered tremendous sediments downstream and the volume in individual watershed will reduce as

Figure 5 Watershed area and entrainment rate in Wenchuan and Taiwan region.

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flow histories before quake. The seismic landslides in upstream of these small watersheds serve as the main sediments supplement. These debris flows exhibit higher entrainment rate, which is close to debris flows in 2001 of Taiwan. Furthermore, watershed area from 2001 to 2009 seems to be no change, while the channel gradient becomes softer. For example, channel gradient in 2001 ranges from 250‰ to 790‰, while in 2008 it decreases from 130‰ to 480‰. In 2009, channel gradient ranges from 70‰ to 360‰. Variation of channel gradient indicates that large watershed have enough capacity to stock sediments and a lot of sediments on slopes were transported into channel, which are waiting to be delivered by next debris flow event.

3

Table 7 Minimum, maximum and mean entrainment rate in other regions Year-Region 1994-Storm King Mountain Mount St. Helens 1999-Venezuela 1982-Southern coast ranges in British Columbia

Entrainment rate (m3/m) Min Max Mean 2.8

11.19

0.31

33.3 204.1

9333.3 1193.6

1797 615.7

5.50

18.4

10.2

Discussions

3.1 Comparison with Venezuela, burned regions of USA and other regions The debris flow event in 1999 of Venezuela was one of the most catastrophic natural hazards all around the world. The minimum and maximum entrainment rate are 204.1 m3/m and 9333.3 m3/m respectively (Table 7). In this event, 12 watersheds have a softer channel gradient < 200‰ (Figure 6) and area ranging from 4.6 to 42.9 km2 (Figure 7). Before this event, a continuous antecedent precipitation accumulated rainfall about 293 mm in last 13 days. Besides, a rainfall station at Maiquetia recorded rainfall of 911 mm from 14 to 16 December, which breaks the maximum record in last 270 years’ (Table 4). Besides, the lithology of the 12 watersheds in Avila Mountain are mainly composed of schists and gneiss. Prolonged antecedent precipitation and intensive hourly rainfall can fully saturate the debris avalanches which formed scars from top of ridges to slope toes. Some slide scars reach to top of basin divide, illustrating that these debris flows were triggered by a combination of large landslide failures. The entrainment rate in the burned regions, USA appears to be smaller though watershed area and debris flow volume were merely collected. About 40% debris flow volume (Gartner et al. 2005) are no less than 4000 m3. Debris flow volume > 100,000 m3 is no more than 10 of 56 samples. These debris flow were delivered from erosion of

Figure 6 Channel gradient and entrainment rate for debris flows in burned regions in King Mountain, USA, Venezuela and Southern coast ranges in British Columbia.

Figure 7 Watershed area and entrainment rate for debris flows in Venezuela in 1999 and Southern coast ranges in British Columbia in 1982.

overland flow by 5 or 10 years’ rainstorm. Sediments supplement were from fire ashes, of which the amount is far less than the seismic debris, such as landslides, rock avalanches and Quaternary sediments. The debris flows in British Columbia suffered no affection from earthquake and fire hazards. The entrainment rate ranges from 6.2 to 18.4 m3/m, which is smaller than those in Wenchuan and Taiwan region. However, entrainment rate in this region is close to those of 2005 to 2009 in Taiwan.

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Lahars can be triggered by volcano eruption, snow melting or rainfall that can erode the pyroclastic material with low density and large porosity. For example, solid particle density for lahar, pyroclastic flow and lava at the Volcano Shiveluch eastern Russia is less than 1.4 g/cm3 (Hu et al. 2015). Lahars commonly exhibit longer travel distance and huge magnitude, leading to more severe damage than debris flows that merely triggered by rainstorm. From 1980 to 1986, several lahars at Mount St. Helens traveled a long distance from 4 to 70 km, corresponding entrainment rate ranges from 200 to 9333 m3/m (Major et al. 2005). Additionally, Thouret et al. (2007) found that sediment yield does not decline drastically within the first post-eruption years after eruption of Mount Semeru, as a result of daily supply of pyroclastic debris shed over the summit cone. Continuous available sediments contribute to the higher sediment. In 2000, however, the catchment of the Curah Lengkong River on the ESE flank shows a denudation rate comparing with the values reported at other active composite cones in wet environment. This indicates that the entrainment rate is closely related to the volume of available sediments. Assuming that the total volume of available sediments is fixed, subsequent debris flow events will exhibit a decreasing entrainment rate as each case delivered sediments away. 3.2 Implications of entrainment rate decay Lots of mass movements on earth surface, such as debris flows, rock avalanches have a similarity in volume amplification. Eq. (1) by data in Table 1 represents the positive relationship between initial triggered volume and final deposited volume. For limited data resources, the relationship and volume magnification for varied initial volume are worthy of further study. The debris flow events in the Chi-Chi earthquake region prove that entrainment rate is closely related to debris flow frequency in a given watershed. After an earthquake, volcanic eruption, the amount of available sediments will increase substantially within the slopes and the channel. As increasing debris flows occur, the amount of available sediments will reduce, the entrainment rate will decay. Besides, a longer time prior to last event may lead to large debris flow with high

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entrainment rate. Such event is mainly controlled by the amount of sediments, which can be produced by weathering, logging and other factors. In Taiwan, debris flows after Chi-Chi earthquake occurred in a higher frequency, the amount of available sediments reduce as debris flow occurrence, thus the entrainment rate will decay. Comparison of the triggering conditions of debris flows in the Wenchuan and Chi-Chi earthquake-hit region illustrates that available sediments act a main role and rainfall is the secondary factor in controlling the entrainment rate. During the first 3 years after strong earthquake, debris flows triggered by Typhoon events in the Chi-Chi earthquake region have a larger entrainment rate than Wenchuan region. High rainfall amount, long duration and higher rainfall intensity-duration in triggering rainstorms may result in the difference of entrainment rate in two earthquake-hit regions. Among the attracting issues, the lasting time and potential magnitude are one of the major two concerns about postquake debris flows. In the Wenchuan earthquakehit region, most catastrophic debris flows occurred during 2008 and 2013. Few debris flows were reported in the year of 2014, 2015 and 2016. In a regional scale, most debris flows merely occurred 1 or 2 times, thus it is difficult to examine the relationship between entrainment rate and elapsed time. Eq. (4) proves a fact that entrainment rate decays as elapsed times. The decaying entrainment rate is closely related to the debris flow frequency. Each event can deliver tremendous sediments and the volume of erodible sediments in individual watershed will deduce. The triggering rainstorm in 1999 for Venezuela debris flows produced more rainfall than that in Wenchuan region, corresponding entrainment rate is approximately to those of 2001 in Taiwan. For varied materials supplement, debris flows in burned regions exhibit smaller entrainment rate while lahars have a largest one.

4

Conclusions

A total of 18 landslide type debris flows and 268 channelized debris flow events in Wenchuan earthquake and Chi-Chi earthquake region, as well as other regions were collected. Analyzing the

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volume of initial mass failures and final deposited debris for landslide-type debris flows, and the entrainment rate with triggering conditions for channelized debris flows reveals that: 1. There is a power relationship between volume of initial triggered mass and final deposited debris for landslide-type debris flow. 2. Debris flow events in the Wenchuan and Taiwan region illustrate that available sediments are the main controlling factor of entrainment rate while the rainfall acts as a secondary role. 3. Entrainment rate for debris flows in Taiwan after Chi-Chi earthquake shows a decaying tendency as elapsed time to earthquake. The mean entrainment rate after 2001 appears to remain at relatively constant, while the channel gradient for debris flow becomes softer, illustrating that materials resources were mainly from stream bed other than steep slopes. Comparison results with

other regions such as burned regions, Mount St. Helens, and Venezuela in 1999 illustrate that entrainment rate closely relates to storm and material conditions.

Acknowledgments This study was funded by CRSRI Open Research Program (CKWV2013203/KY), Fundamental Research Funds for the Central Universities of China (Grant No. BLX2014-12), and the National Natural Science Foundation (Grant No. 41601004). We are grateful to the contributions of authors listed in Table 1 and Table 2 who published their valuable data of debris flows all around the world. These data support this paper to examine the entrainment rate of debris flow and explore some findings.

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