Effects of debris-flow magnitude-frequency distribution on avulsions and fan development
T. de Haas 1,2* , A. Kruijt 2 , A. L. Densmore 1
1) Department of Geography, Durham University, Durham, UK; 2) Faculty of Geosciences, Universiteit Utrecht, Utrecht, The Netherlands; *) Presenting author: tjalling.de-haas@durham.ac.uk, t.dehaas@uu.nl
Fan evolution
Methods
Fan 01
Conclusions Introduction
Shifts in the active channel on a debris-flow fan, termed avulsions, pose a large threat because new
channels can bypass mitigation measures and cause damage to settlements and infrastructure. Recent, but limited, field evidence suggests that avulsion processes and tendency may depend on the flow-size distribution ans associated flow-size sequences, which are difficult to constrain in the field.
Objectives
Here, we investigate how flow magnitude-frequency distribution and associated flow sequences affect the spatio-temporal patterns of debris-flow-fan development. To do so, we study and compare the evo- lution and avulsion mechanisms of three experimentally-created debris-flow fans formed by different flow-magnitude distributions.
Overall, the three fans formed by similar patterns of development: alternating channelized and unchan- nelized phases governed by backstepping deposition and avulsion. Volume variations, however, lead
to contrasting avulsion mechanisms: (1) Large flows can overtop the channel and carve new flow paths, initiating avulsion within a single event. (2) Series of small-medium flows can block the active channel, leading to avulsion in the next large flow. We infer that there may be an optimal magnitude-frequency distribution that maximizes the avulsion frequency, reflected by the balance of small versus large flows.
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1.20 m
2.0 m
0.5 m
0.3 m
outflow plain
channel PLAN VIEW
CROSS-SECTIONAL VIEW
mixing tank hatch
hatch
mixing tank
0.3 m
debris-flow fan
0 0.20 0.100.15 0.05 0.25
Elevation (m)
3D FAN CAPTURING
x (m)
0 0.2
0.4 0.6
0.8 1.0
1.2
0.5
-0.5 0y (m)
100 0
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Fraction of flows
a Fan 01; uniform distribution
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Fraction of flows
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n = 85
Fig. 2: Magnitude-frequency distributions of the experimental debris-flow fans. The lines denote the double-Pareto distributions from which the debris-flow magnitudes were randomly extracted. The bars denote the actual number of events in each experiment, divided into 0.5 kg bins. The mean debris-flow mass is ~6.5 kg for all experiments. (a) Fan 01 with a uniform distribution; (b) fan 02 with a steep-tailed double-Pareto distribution; (c) fan 03 with a shallow-tailed double-Pareto distribution.
Fig. 1: Experimental flume setup. The 3D fan image shows the final mor- phology of fan 01. The flume setup is similar to that used in De Haas et al.
(2016).
0 5 10 15 20 25 30 35 40 45 50 55
Debris-flow event
0 10 20 30 40 50 60 70
Debris-flow event
-50 0 50
Flow angle (°) 0
10 20 30 40 50 60 70 80
Debris-flow event
0 0.5 1 1.5
Maximum runout (m)
0 0.5
Deposit width (m)
0 0.5 1
Deposit width/depth
0 0.01 0.02 Channel depth (m)
5 10
Flow size (kg)
0 0.65 1.30
Runout (m)
0
-45 -90 45 90
a b c d e f
g h i j k l
m n o p q r
Fan 01
Fan 02
Fan 03
0.2 m
Flow 19, 6.5 kg
Flow 24, 6.5 kg
Flow 29, 6.5 kg
Flow 34, 6.5 kg
Channelized phase
Backstepping
Channel overtopping
Searching phase
Enlarging channel
Channeliz
ed phase
Backstepping secondary
channel
Gradual backstepping, avulsion and channelization
a
b
d c
0 0.10
-0.10 0.20
Net deposition (m)
Time
0.2 m
0 0.10
-0.10 0.20
Net deposition (m)
a
b
d c
e
f
g
h
i
j
k
l
Flow 25, 6.8 kg
Flow 26, 6.6 kg
Flow 29, 5.2 kg
Flow 31, 7.5 kg
Flow 33, 7.2 kg
Flow 35, 5.9 kg
Flow 36, 5.5 kg
Flow 40, 6.0 kg
Flow 58, 6.2 kg
Flow 59, 11.6 kg
Flow 60, 6.8 kg
Flow 61, 6.0 kg
Backst
epping
DF 27
DF 28
Channel plug
Flow deflected by plug
Further backstepping and plug enlargement
Channel plug
Flow deflected by plug Further backstepping
and plug formation
1. Backstepping and avulsion 2. Plug formation and avulsion 3. Large event causing avulsion
Channel plugged
Large event forming 2 new channels
New channel established
Time
0.2 m
0 0.10
-0.10 0.20
Net deposition (m)
a
b
d c
e
f
g
h
Flow 24; 7.6 kg
Flow 25; 4.1 kg
Flow 26; 3.2 kg
Flow 27; 9.6 kg
Flow 55; 7.6 kg
Flow 57; 6.3 kg
Flow 61; 6.0 kg
Flow 64; 9.2 kg
1. Channel persistence 2. Large event opening new channels
Backstepping
Backstepping
Large event unaffected by backstepping
Backstepping
Backstepping
New pathways to topographically
favorable side
Time
Spatio-temporal patterns
Fig. 3: Typical avulsion sequence on fan 01. Evolution from a well-defined channel (a) through gradual backstepping of deposition toward the fan apex, followed by a searching phase (b), avulsion to a new channel pathway and enlarge- ment (c), and channelization (d).
Fig. 4: Common debris-flow-magnitude sequences leading to avulsion on fan 02. (a-d) Backstepping and avulsion sequence during debris flows 25-31. A sequence of small- to moderately-sized flows induced a sequence of backstepping deposition (b and c), which was followed by avulsion during the large flow 31 (panel d). (e-h) Channel plug formation by two small debris flows that blocked the main channel (f and g), followed by avulsion during a moderate- ly-sized flow (h). (i-l) A very large debris flow created two new channels (j), one of which became blocked by a flow snout in the next, smaller flow (k). Avul- sion then proceeded into the topographically-favored right-hand channel (l).
Fig. 5: Common spatio-temporal patterns of debris-flow activity on fan 03. (a-d) Persistent channel position during debris flows 24-27. The direction of the large debris flow 27 (d) was unaffected by the backstepping plug deposits from the small flows 25 and 26 (b-c). Overbank surges were abundant. (e-h) After a partial backstepping sequence from debris flow 55 to 62 (e-g), large flows 63 and 64 opened up three new channel pathways on the left side of the fan (h, shown by arrows) that allowed subsequent avulsion towards the left.
Fan 02 Fan 03
Fig. 6: Summary of the spatio-temporal patterns of debris-flow activity. Solid line segments join successive flows in the same channel. (b) Maximum runout distance during each debris flow on fan 01. (c) Deposit width during each event on fan 01. (d) Deposit width/depth ratio for each debris flow on fan 01, defined as deposit width divided by maximum runout distance. (e) Channel depth after each debris-flow event on fan 01, measured 10 cm downstream of the fan apex. (f) Debris-flow mass in kg. (g-l) As above for fan 02. (m-r) As above for fan 03.
100 m
0.2 m
a b
d
c
e f
Debris flow 20 Debris flow 23 Debris flow 27
2005-2006 2006-2009 2012-2013
Channelized phase
Channel plug
Multiple channels active
Searching phase:
main activity to right
Channelized phase
Searching phase:
Multiple channels active
Backstepping
Main activity from right to left
Time
Fig. 7: Cross-profiles through the experimental debris-flow fans at distances of 0.2 m (left-hand column) and 0.8 m (right-hand column) down- stream of the fan apex. Colors show progressive flow sequence from cool to warm. (a-b) Fan 01.
(c-d) Fan 02. (e-f) Fan 03. Note how overbank deposition became increasingly important for fan construction and how large lateral shifts became less pronounced with increasing flow-magnitude variability from fan 01 to 03.
Fig. 8: Examples of the transition from channelized to searching phases on (a-c) the Ohya debris-flow fan in Japan (images modified from Imaizumi et al., 2016; De Haas et al., 2018) and (d-f) experimental debris-flow fan 01. Flow in all panels was from top to bottom. On both the natural and experimental fans, activity during the searching phase was spread over multiple channels on the proximal fan, and the locus of activity shifted laterally across the fan over multi- ple debris flows. Warm colors indicate deposition and cool colors indicate erosion, although absolute scales differ.
