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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
211
DOI: 10.4408/IJEGE.2011-03.B-025
CHARACTERISTICS AND MECHANISM OF DEBRIS-FLOW
SURGES AT JIANGJIA RAVINE
k
aiHenG
HU
(*,**)
, C
HaolanG
HU
(***)
, y
onG
LI
(*,**)
& P
enG
CUI
(*,**)
(*)
Key Laboratory of Mountain Hazards and Earth Surface Processes, Chinese Academy of Sciences, Chengdu, 610041, China
(**)
Institute of Mountain Hazards and Environment, Chinese Academy of Sciences, Chengdu, 610041, China
(***)
Department of Mathematics, Sichuan University, Chengdu, 610064, China
Corresponding author: Kaiheng Hu, Email: khhu@imde.ac.cn
hydrograph of flood. Descriptions on the surges have
been given by many literatures, such as P
ieRson
(1980)
for Mt Thomas in New Zealand who called it stand-
ing wave, o
kuda
et alii (1980) for Mt Yakedake in Ja-
pan, and m
aRCHi
et alii (2002) for Moscardo torrent in
Italy. Especially, the long-term observations on debris
flows started from 1960s at Jiangjia Ravine in South-
west China have provided plentiful information on the
characteristics of debris-flow surges (l
i
et alii, 1983;
z
HanG
, 1991; d
avies
, 1997). Some of them concluded
that debris-flow surge is the main flow pattern of vis-
cous debris flow moving downstream in a channel, and
suggested the surge may be due to intermittent debris
supplies, discontinuous initiation of debris flows at the
upstream or complex topography of debris-flow basin.
However, these factors can not convincingly ex-
plain why the surge flow only appears with respect to
viscous debris flow. Pore-fluid pressure in debris flow
was considered to play a key role on the motion of its
surges (i
veRson
, 1997; s
avaGe
& i
veRson
, 2003). Not-
ing similarities between the surge and roll wave that
spontaneously develops on a shallow water layer in
a long open channel such as zigzag profile, many re-
searchers attempted to illuminate this phenomenon in
term of intrinsic instability of shallow water equations
that govern two-dimensional movement of some non-
Newtonian fluids including hyper-concentration flow
and debris flow (e
nGelund
& w
an
, 1984; w
anG
et
alii, 1990; n
G
& m
ei
, 1994; l
iu
& m
ei
, 1994; d
avies
,
1997; z
anuttiGH
& l
ambeRti
, 2007).
ABSTRACT
Debris Flows in nature, for example at Jiangjia
Ravine, were often observed moving in the form of in-
termittent surges which is considered as a kind of wave
that is termed as roll wave in this paper. Spatial and
temporal characteristics of the roll waves at Jiangjia,
as well as their separation and superposition were de-
scribed in details. First-arrived waves were observed
to smooth rough bed at the gentle middle reach and
produce a residual layer on which a sequent wave can
move with steady profile and high velocity. The data
measured by the Dongchuan Debris Flow Observation
and Research Station shows the waves are not periodic
and a kind of supercritical flow which only propagates
downstream. Furthermore, it is observed that there are
two kinds of wave profile, linear and non-linear, for the
same debris-flow surge in Lagrange and Euler refer-
ence frames. A power relationship between the depth-
averaged velocity and flow-depth of the surges is in-
ferred from the different profile functions in the two
frames. Finally, it was proposed that mass exchange
between the residual layer and moving wave reduces
frictional resistance and keeps the wave high-speed.
K
ey
words
: Debris flows; Roll wave; Velocity profile; Flow
depth; Residual layer
INTRODUCTION
Debris flows in nature have been often observed
as a succession of surges differing from a continuous
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k. HU, C. HU, Y. LI & P. CUI
212
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
September when most of debris-flow events hap-
pen. The Ravine is an ideal site for observing de-
bris flows as long-duration debris-flow event can
appear every year and various debris flow regimes
can be seen even in one event. There were 15 de-
bris flow events per year on average, and the maxi-
mum was 28 events according to the record data of
Dongchuan Debris Flow Observation and Research
Station (DDFORS) which was set up in 1960s, a
facility of the Institute of Mountain Hazards and
Environment, Chinese Academy of Science. In or-
der to study dynamic and static properties of debris
flows DDFORS have installed some equipments
such as debris-flow sampler, radar velometer, ul-
trasonic sensor for measuring debris-flow quanti-
ties such as velocity, flow depth. The debris-flow
events lasted from several hours to some dozens of
hours, each of which consisted of scores or hun-
dreds of waves. The maximum discharge of debris
flows is 2820 m
3
/s, five times of the peak discharge
of Xiaojiang River. The velocity of debris flows
is up to 15 m/s, and the mass density is as high as
2370 kg/m
3
(w
u
et alii 1990).
Roll waves are denoted as intermittent waves
that are sandwiched between long stretches of gentle
profiles increasing monotonically in depth from rear
to front (n
G
& m
ei
, 1994). With reference to them,
we term the surges in debris flows as roll waves. This
paper does not focus on theoretical analyses of the
shallow water equations, but on the descriptions of
debris-flow roll wave characteristics from the field
investigations and measurements at Jiangjia Ravine.
Based on the descriptions, the profiles of roll-wave
flow depth and velocity are discussed.
STUDY AREA
Jiangjia Ravine with 48.6 km
2
watershed and
13.9 km main stream, a branch of Xiaojiang Riv-
er in the upper reaches of Yangtze River, lies in
Dongchuan, Kunming, Yunnan Province in south-
west China (figure 1). It becomes a high frequent
debris-flow Ravine because of 2227 m relative el-
evation, complex geological structure and fragile
rocks, numerous landslides, and rich rainfall. Mean
annual rainfall is 700 ~ 1200mm from the foot to
top of the mountain and more than 80% rainfall
concentrates in the rainy season between June and
Fig. 1 - The location of Jiangjia Ravine (the elevation unit of the open triangle points is meter)
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CHARACTERISTICS AND MECHANISM OF DEBRIS-FLOW SURGES AT JIANGJIA RAVINE
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
213
us observe the paving process more clearly. As a roll
wave moved into the observed section that not covered
by the residual layer, the wave decelerated and debris-
flow material was continuously left on the coarse and
dry channel. The wave’s head became thinner and thin-
ner, and at last it stopped. Each of roll waves extend-
ed the layer 50-100m longer. The residual layer was
0.5~0.6 m and its edge 0.1~0.2m high. Compared with
the height at the wave head, from 1m to 4m, the layer
is rather shallow. After the successive waves travelled
upon the layer, the layer’s depth varied slightly. This
implied that a kind of dynamic mass balance exists be-
tween the layer and the moving wave.
The formation of residual layer is crucial for roll
waves to keep moving. If no residual layer, it is im-
possible for viscous debris flows to move quickly and
constantly in the gentle channel whose slope is less
than 6%. First of all, the existence of the layer makes
the bed smooth, and so reduces bed roughness for de-
bris flows. Secondly, the residual layer increases flow
depth of debris-flow surges. Thirdly, the fluid compo-
nent in the layer has a lubricant effect.
SPATIAL AND TEMPORAL CHARACTERISTICS
n
G
& m
ei
(1994) presented that there are distinc-
tive parts within one wave profile. Actually, we ob-
served that a roll wave exhibits several flow patterns
at the different parts. In general, a roll wave is 10m
to 200m long and can be divided into three distinc-
tive parts: the head, turbulent flow; the body, laminar
flow; the tail, laminar flow (Fig.3).
The head with semi-parabolic plan shape is the high-
est and widest one among the three parts. It was found
that the surface of the residual layer before the head keeps
stationary (Fig.3), which indicates roll wave propagation
CHARACTERISTICS OF ROLL WAVES
RESIDUAL LAYER
When first-arrived wave passes by rough bed at the
gentle middle reach of Jiangjia, its debris material will
deposit upon the channel bed and result in a temporary
bottom which is called as residual layer (figure 2). The
layer smoothes the bed, and allows subsequent waves
to move farther towards downstream. Every roll wave
makes the layer longer than its predecessor. Gradually,
the layer will extend from the middle stream to down-
stream. This process is termed as ‘pavement’ and would
not be interrupted until a roll wave reaches into Xiao-
jiang River if the debris-flow magnitude is adequate for
the layer formation on the whole downstream reach.
One typical event occurred at 15:30 on July 24
th
,
1999 when there was no rainfall in the middle and
down streams. So the residual layer’s surface was not
destroyed by the raining water washing, which helps
Fig. 2 - The residual layer (a. the residual layer smooth-
ing the channel; b. the channel was re-emerged
after the residual layer was scoured by hyper-
concentration flow. The channel is about 80m
wide. The first photo was taken on Jul l
st
, 2001,
the second on Jun 27
th
, 2004.)
Fig. 3 - Three parts of one roll wave on Aug 5
th
, 2007 (The
head was about 2m high and 40m wide. The mud
surface ahead of the wave head is stationary)
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
higher wave catches up with its former at last if the
stream channel is long enough (Fig.6). But unlike other
kinds of wave such as ripple, the combined wave does
not separate longitudinally again. The ripples can keep
their shapes unchanged before and after superposition,
but the roll waves of debris flows do not so. That is one
of reasons why the discharge of intermittent flow is far
more than that of continuous flow. Figure 6 taken on
July 8
th
, 2001 shows five roll waves in the about 800 m
channel. The distance between the first and the second
was increasing while decreasing between the third and
the fourth. At the wider section the first was extending
more widely and separated into two waves. The third
caught up with the second wave after a few moments.
speed is less than debris-flow particle speed. Based on
the measured data (unpublished) on July 25
th
, 1999 from
DDFORS, when the head’s height is 2 m the velocity is
9.5m/s. The propagation speed is estimated roughly to be
4.43 m/s by virtue of
for long wave of water,
where c is wave speed, g gravity acceleration, h the head
height. The particle velocity (9.5 m/s) is greater than the
wave velocity (4.43 m/s). Then the roll waves are a kind
of supercritical flow. Unlike at the head, the flow surface
at the body is smooth and regular, and can be generally
considered as a laminar flow. Nevertheless, it is still not
clear whether there are some inner flow structures, e.g.
vortices, in the body. The unimportant part is the tail
which in fact is a wake left by the wave body.
The time interval between two successive waves
that passed across the same section in the event on July
8
th
, 2001 is ranged from 29s to 478s (Fig.4). The aver-
aged frequency is equal to 1/144.2 s
-1
, approximately
one wave per two minutes. Smaller interval is permit-
ted if the wave head is higher. It is obvious that the roll
waves are not quite periodic in one event. Although
d
avies
(1997) mentioned debris-flow surges in one
event often occur at quite regular intervals, H
u
& l
i
(2001) analysed the time interval data, and didn’t find
any predominant frequency in the roll waves by using
Fourier Transform. Based on the average frequency
and the wave speed of 4.43 m/s, the average wave-
length, namely average distance between two waves,
is 638.81 m, 3-60 times of the surge’s length itself.
SEPARATION AND SUPERPOSITION
Another interesting phenomenon is the separation
and superposition of the roll waves. A roll wave would
extend more widely and becomes thinner at the wider
open channel, and when there are some topographic
changes along the transverse direction the wave will
be separated into two waves, each alone moving down-
stream (Fig.5a). On the other hand, along the longitu-
dinal direction two or more waves can superpose to-
gether to a higher wave (Fig.5b). Generally speaking,
the higher the wave head is, the faster it moves. So a
Fig. 4 - Time interval of roll wave’s series
on July 8
th
, 2001
Fig. 5 - Schematic diagram of the separation and super-
position (a. separation due to topographic change
across transverse section; b. superposition due to
different longitudinal velocities.)
Fig. 6 - Separation and superposition of surges (the first
wave in the picture is dividing into two waves and
the third will catch up with the second.)
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CHARACTERISTICS AND MECHANISM OF DEBRIS-FLOW SURGES AT JIANGJIA RAVINE
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
215
PROFILES OF FLOw DEPTH OF ROLL wAVES
Flow-depth profiles of roll waves show distinc-
tive shapes in Euler and Langrange observing systems.
z
HanG
& C
Hen
(2003) measured longitudinal and trans-
verse profiles of roll waves by image analysis based
on the principle of close-range photogrammetry (Fig.
7a). The longitudinal profile is triangular and close to
the shape by eyewitness. But, the roll waves recorded
by ultrasonic sensor exhibits a distinctive longitudinal
profile with abruptly decreasing front and gen-
tle rear, resembling a power curve. The observ-
ing system in the image analysis measurement
belongs to Lagrange reference frame in which
the time point is fixed. On the contrary, the sys-
tem in figure 7b is a kind of Euler reference
frame because the observing point is fixed in
space. Debris-flow longitudinal velocity within
one wave must vary with flow depth. Other-
wise, the shapes of the longitudinal profiles in
the two observing systems would be same.
Based on different appearance of wave
profile in the two frames, an empirical rela-
tionship between depth-averaged longitudinal
velocity and flow depth can be derived from
the transformation of linear function to power
function. Given the wave profile in the La-
grange frame is represented by
h (x) ∞ x, 0 ≤ xX
and that in the Euler frame by
h (x) ∞ t
n
, 0 ≤ tT
where t is time, x is longitudinal spatial coor-
dinate, X is wave length, T is wave duration,
h is flow depth, and n is power exponent. The
origins in the two systems are the forefront of
the wave. Furthermore, the depth-averaged
longitudinal velocity can be represented as:
where u is the velocity, h
t
and h
x
denote re-
spectively spatial and temporal derivatives
of flow depth. Combined Eq.(1), (2) and (3),
it can be obtained:
Many velocity profiles with similar form
as Eq.(4) were proposed for one-dimensional
non-Newtonian debris flows such as dilatant
(t
akaHasHi
1978), b
inGHam
(m
ainali
& R
a
-
JaRatnam
1994), and power-law (n
G
& m
ei
1994) models. However, the point of Eq.(4) is
in that its velocity exponent is associated with the flow
depth exponent n in Eq.(2), and therefore can be cal-
culated from n. Non-linear regression analysis on the
profile data of Aug 2
nd
, 1985 gave the power exponent
an estimated value of -0.6417 with 95% confidence
bound [-0.6996, -0.5839] (Fig. 8), which indicates that
the longitudinal velocity is proportional to 2.56 power
of flow depth. Fitted curve has a better agreement with
measured data at the wave head and body than at the
Fig. 7 - Flow depth profiles of roll waves under Lagrange (a) and
Euler observing systems (b)
Fig. 8 - Fitted power curve between normalized flow depth and
time for five surges on Aug 2
nd
, 1985 (H is the maximum
flow depth of the surges.)
(2)
(1)
(3)
(4)
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k. HU, C. HU, Y. LI & P. CUI
216
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
Debris-flow roll waves display two kinds of
flow-depth profiles in Lagrange and Euler reference
frames. Under the assumption that the flow-depth pro-
file is linear in the Lagrange frame and power shape
in the Euler, a power relationship between the depth-
averaged longitudinal velocity and the flow depth is
inferred for one-dimensional steady movement of de-
bris-flow surge. The connection of the velocity profile
with the flow-depth shape in the Euler frame provides
a feasible method for estimating debris-flow veloc-
ity in protection engineering. The empirical value of
2.56 for the velocity exponent limits to the case of
viscous debris flows with high density. The theoreti-
cal value is 1.5 for dilatant fluid, and 2.0 for Bingham
fluid, which means this kind of debris flow at Jiangjia
cannot be described by the two models.
ACKNOWLEDGEMENTS
This research was financially supported by
the National Natural Science Foundation of China
(Grant No. 40701014), Project Group of Knowledge
Innovation Program of Chinese Academy Sciences
(Grant No. KZCX2-YW-Q03-5), and the National
Basic Research Program of China (973 Program)
(No. 2008CB425802). Special thanks are given to
Dongchuan Debris Flow Observation and Research
Station, Chinese Academy of Sciences for providing
the observation data.
tail as Fig. 8 shows. This implies Eq.(4) is not applica-
ble when the flow depth is lower than the tail height.
DISCUSSION AND CONCLUDING REMARKS
Based on the field observations in Jiangjia Ravine,
characteristics of debris-flow roll waves are described in
details. Some interesting phenomena such as the residu-
al layer, the separation and superposition are introduced.
The existence of residual layer is crucial for roll waves
to keep moving at the gentle channel. The roll wave
can be divided into three distinctive parts: head, body
and tail, each of them corresponding to a kind of flow
pattern. The time intervals between successive waves
in one event indicate the roll waves are not periodic,
at least not so regular, and their average wavelength is
much longer than the length of themselves. According
to these characteristics, a possible mechanism for the
roll waves moving with high velocity at gentle chan-
nel is proposed. That is, mass exchange between the
residual layer and moving wave makes less kinetic en-
ergy converse into thermal energy than direct frictional
contact. The head with the highest velocity incorporate
the depositional materials in the residual layer while the
body and tail leave almost same amount of materials for
the layer. Therefore, the frictional contact only limits in
the head part. Of course, the existence of the layer also
reduces bed roughness, increases flow depth of debris-
flow surges, and has a kind of lubricant effect.
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u
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i
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i
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ei
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G
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anG
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