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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
449
DOI: 10.4408/IJEGE.2011-03.B-050
MOVEMENT PATTERN OF DEBRIS FLOW
aZ. C. KANG
(*)
, K.T. LAW
(**)
, C.F. LEE
(***)
& X.Q. CHEN
(*)
,
(****)
(*)
Dongchuan Debris Flow Observation and Research Station, Chinese Academic of Sciences
(**)
Department of Civil and Environmental Engineering, Carleton University, Canada and visiting the University of Hong Kong
(***)
Department of Civil Engineering, the University of Hong Kong
(****)
Institute of Mountain Hazards and Environment, CAS, Chengdu, China
A gravitative debris flow is initiated by an increase
in water content in the loose soils and rocks at high
elevations, which reduces the material strength that in
turn causes a landslide to occur. As the mass slides
down the valley, it experiences strong disturbance that
leads to softening and liquefaction of the material. The
sliding down of this softened or liquefied debris along
the slope is called a debris flow. While a lot of studies
have been conducted on the first type of debris flow
(I
nveRson
, 1997, t
akaHasHi
1978, w
u
et alii, 1990,
among others), less emphasis has been placed on the
study of the second type (i
veRson
et alii, 1997). This
paper presents the development of a model for de-
scribing the movement pattern involved in the second
type of debris flow. The applicability of the model is
examined based on two well-documented case records
of gravitative debris flow. The first one occurred in
Japan while the second one in Hong Kong.
CHARATERISTICS OF MOVEMENT PAT-
TERNS
The first kind of debris flow is known as the hy-
draulic debris The first kind of debris flow is known as
the hydraulic debris flow. Q
ian
(1989) shows schemati-
cally the processes of initiation to full development of
a hydraulic debris flow. The sediments in the channel
bed, known as the static bed, go through several stages
to reach the final flowing state (Q
ian
, 1989). Initiation
of the sediment movement begins when the heavy run-
off starts to impart energy to the sediments. The sedi-
ABSTRACT
A kinematic model is developed to estimate the
velocity and runout distance of a gravitative debris
flow. The characteristics and the different stages of de-
velopment of a gravitative flow are first described. The
equations governing the motion during the flow are
then derived based on the Newtonian translation mo-
tion with some simplified assumptions on the erosion
process along the flow path. After the motion is initi-
ated, the debris is considered to behave as a frictional
material with the friction angle during motion being a
function of the distance travelled measured from the
initiation point. The equations derived are applied to
two well-documented case records to assess their ap-
plicability. The application shows that the computed
runout distances are slightly higher than the measured
values. This slight error on the safe side is consistent
with the simplified assumptions used in deriving the
equations. The small error is acceptable for engineer-
ing designs in areas vulnerable to debris flows.
K
ey
word
: debris flow, movement pattern, kinetic mode, case
record
INTRODUCTION
Two main types of debris flow are possible in na-
ture: hydraulic debris flow and gravitative debris flow.
A hydraulic debris flow is caused by a strong surface
runoff eroding large quantity of solid materials and
bringing them down a ravine to become a debris flow.
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
pressure and decreasing the shear strength of the slope
mass. When the decrease of strength reaches a critical
value, the slope mass starts to move. A landslide or
slump will follow if the situation remains critical. As
the sliding mass accelerates down the slope, the bottom
part of the loose mass near the sliding surface is subject
to disturbance leading to softening and liquefaction.
When this softened mass travels down the more gen-
tle part of the slope, two possibilities may occur. The
first is when additional water is present. The continuing
motion with the addition of water will turn the debris
into a semi-liquid flowing through the passing chan-
nel. The second possibility is no more additional water
being present. The debris flow will then experience an
increase in internal friction against the flow. In either
case, the flow will eventually reach the final stage of
deposition and complete termination of motion.
The first type of motion pattern above has already
been well described. In this paper, a model describing
the motion of the gravitative debris flow is proposed
based on many years of field observations of the first
author (k
anG
, 1989, 1991, 1997,1999). The applicabil-
ity of the model to actual case records is also illustrated.
THE PROPOSED MODEL
For ease of discussion, the four different zones
of a gravitative debris flow are shown in Figure 2: 1)
source zone, 2) acceleration zone, 3) passing chan-
nel, and 4) deposition zone.
In general, loose soil and fractured rock accumu-
lated at high concave slopes mainly come from land-
sliding at higher elevations of the mountain. Having
subject to long-term physio-chemical weathering, the
body of loose soil and rock often contains a definite
amount of finer particles exhibiting some cohesive
ments then go into the second stage know as bed load
motion. The term “bed load” is used here in the usual
sense that the sediments are supported by the dispersive
force stemmed from particle collisions. Relative motion
exists between these sediments and the flowing water,
both in the vertical direction and along the general flow
direction. To sustain such relative motion, some poten-
tial energy of the flow is dissipated. In the third stage,
parts of the sediments are suspended in the flow. The
suspension of these particles is maintained by the turbu-
lence in the flowing water, thus some turbulence energy
is consumed. From this point on, this type of debris flow
can be subdivided into two groups. In the first group, the
sediments contain clayey particles exceeding a certain
limit. The flow process then goes into the fourth stage
in which the fine clayey particles remain in suspension
to form slurry. Under this condition, there exists no rela-
tive motion between the flowing water and the clayey
particles and the flow can no longer be described by the
Newtonian fluid. Instead, the Bingham model should be
used. As the flow continues, the turbulence energy will
decrease until the flow slows down to a laminar flow.
This first group is known as a viscous debris flow. For
the second group, the clay content is less than the limit-
ing value and the flow directly becomes laminar without
forming slurry. This group is called a water-stone flow.
The second kind of debris flow is known as the
gravitative debris flow. A schematic representation
of this kind of flow is given in Figure 1. This type of
debris flow normally takes place on high slopes with
loose soils and fractured rocks. During rainfalls, water
infiltrates into the loose soil mass, increasing the pore
Fig. 1 - Schematic diagram showing the different stages of
movement pattern in gravitative debris flow
Fig. 2 - Typical flow path and cross section of a gravitati-
ve debris flow
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MOVEMENT PATTERN OF DEBRIS FLOW
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
451
decrease with increases in water content due to infil-
trating rainwater. Based on this observation, the fol-
lowing is developed.
There are three stages for the increase of water
content leading to the initiation of a landslide (Figure
3-a, b, and c).
The following notations are used in establishing
the proposed model:
Where ρm and dcp = density and average diam-
eter of the solid particles, respectively;
g = gravitational acceleration; and Φ = static fric-
tion angle of the soil and rock.
Stage 1 (Figure 3-a) At this stage, the loose soil
and rock in the source zone is under a stable condition
without rainwater infiltration. Consideration of the
stress condition leads to:
Where τ and τ
c
are the shear stress and the shear
strength, respectively.
For stable equilibrium, τ < τ
c
, hence:
The second term on the right hand side of Eq.(3)
is negligibly small since
dcp << z cos q
1
at any significant depth z. Hence
Eq. (3) isreduced to:
strength, C. Under normal water content, the slope
is in stable condition. During rainfall, rainwater infil-
trates into the slope causing the pore water pressure
to rise with the consequence that the material strength
decreases. If the strength decreases to a certain point,
the slope will lose its stability and start moving down-
wards. For some given conditions, the slide will turn
into a debris flow and go through the path as shown in
Figure 2. The governing equations for equilibrium or
motion for each zone are discussed in the following.
INITIATION OF DEBRIS
There are two main approaches for considering
the initiation of debris motion. The first is based on
conventional soil mechanics for stability of slopes
composed of unsaturated soils. Infiltration of rain-
water into the soil reduces the soil suction that leads
to a lowering of the apparent cohesion (f
Redlund
&
R
aHaRdJo
, 1993). When the suction is completely
removed, positive pore pressure will build up that
reduces the effective stress and lowers the frictional
resistance. When the overall strength is reduced to a
critical point, a failure will occur and the slope mass
will start to move. Analysis of such a process can be
carried out by many existing methods. One conven-
ient and popular method is the method of slices based
on the limit equilibrium concept (e.g., b
isHoP
, 1955;
m
oRGensteRn
& P
RiCe
, 1965).
A slightly different approach is adopted here for
analysing debris motion initiation in the study of de-
bris flow. Based on large direct shear box tests on soil
samples recovered from a debris flow, z
HanG
(1992)
demonstrated that, the strength parameters of the de-
bris, both the cohesion (C) and the friction angle (Φ),
Fig. 3 - Schematic diagrams
for stress distribution
involved in the ini-
tiation of debris move-
ment(1- wetting line;
2- water saturation
line; 3- Over-satura-
tion line)
(1)
(2)
(3)
(4)
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
where a = acceleration, and θ
2
= slope angle of this
zone. With the initial velocity v
o
= 0, the velocity vt at
any time t is given by:
PASSING CHANNEL
After going through the acceleration stage, the de-
bris mass now enters into a gentler sloping channel as
a semi-solid and semi-liquid material. The motion of
the debris mass depends on the presence of additional
water. If additional water is available, the motion of
the debris will advance to the viscous liquefied flow
state. Many equations exist for computing the veloc-
ity of the flow for this condition. One well established
equation is given below:
where V
c
is the velocity of the debris flow, θ
3
the slope
angle of the channel, h the thickness of the debris, and
mc the resistance coefficient. The value of mc depends
on the properties of the fluid. Based on observations
between 1960s and 1990s (k
anG
, 1999), on Jiangjia-
gou Ravine, Dongchuan, Yunnan, m
c
=1/10~1/7, and
from Huoshao Gully in Wudu, Gansum, mc varies
from 1/5 to 1/7.
DEPOSITION AND TERMINATION
The flowing mass eventually enters its last stage
characterized by deposition and termination of mo-
This states that a stable condition exists if the
slope angle is smaller than the static friction angle of
the material.
Stage 2 (Figure 3-b)
At this stage the debris body is moistened but has
not yet reached the saturation state with the infiltrat-
ing rainwater from a moderate rainfall. The moistened
zone is demarcated with a moist front. The debris
body is still stable as the increase in the water content
has not reduced sufficiently the strength of the mate-
rial to trigger a landslide. The governing condition is
similar to Eq. (4).
Where Φ
1
is the friction angle of the moist debris,
which islower than that in Stage 1.
Stage 3 (Figure 3-c)
As rainfall increases, the water content of the de-
bris body reaches the saturation point. Hence the fric-
tion angle, now corresponding to the saturated condi-
tion, will drop further to Φ
2
. Initiation of the motion
will occur if ττ
c.
Hence
ACCELERATION OF DEBRIS
After movement is initiated, the soil and rock
mass is now turned into debris that starts to accelerate
down the slope. As a result of the motion, there will be
a change in the physical properties in the entire body
of the debris. Near the sliding surface, the debris there
is fully saturated and subjected to severe mechanical
disturbance. A layer of softened or liquefied soil is
formed. Consequently the apparent friction angle will
be reduced. As the distance of travel increases, the de-
gree of disturbance and liquefaction increases, which
in turn further reduces the apparent angle of friction.
The rest of the debris will be undergoing a transition
from visco-elastic solid into a visco-elastic liquid.
The apparent angle of friction (Φm) at this state cor-
responds to the transition state. This apparent friction
angle is smaller than the static friction angle.
The equations governing the motion for this state
of the debris flow can be derived with the aid of Figure
4. At this state, the cohesion, C, can be considered neg-
ligible, i.e., C=0. Therefore, consideration of the New-
tonian motion equation along the X-direction yields:
(5)
(6)
Fig. 4 - Force equilibrium of soil in X-direction
(7)
(8)
(9)
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MOVEMENT PATTERN OF DEBRIS FLOW
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
453
CASE RECORDS STUDY
The applicability of the above principles is illus-
trated with two well-documented case records: the
Ontake debris avalanche in Japan and the Tsing Shan
debris flow in Hong Kong.
THE ONTAkE DEBRIS AVALANCHE
The Ontake debris avalanche occurred on the
southeast slope of Ontake Volcano in Japan in 1984.
A saturated mass of soil and rock of 3.6×107 m3, slid
down the mountain at high speed along a gully and
travelled over 9 km before coming to a stop at the
gently sloping foothill. s
assa
(1987) conducted an
analysis of the debris flow using a sled model based
on consideration of conservation of energy. The en-
ergy dissipated by the debris sliding over the slope is
related to the apparent angle of friction (Φ
m
) that is
related to the degree of saturation of the debris and the
excess pore pressure generated. The parameters for
estimating Φm can be obtained from high-speed ring
shear tests on debris samples taken from the site. For
this debris flow, the apparent angle of friction (Φm)
and the slope angle of the different sections of the flow
path are shown in Figure 5. By equating the change in
kinetic energy and the energy dissipated by friction
during the travel of the debris, s
assa
(1987) estimated
an average velocity of flow of 22 m/s. This velocity
however cannot be verified, as there were no measure-
ments on the actual velocity or total travel time of the
debris avalanche.
The Ontake debris avalanche is reanalyzed here
based on the proposed model using the same apparent
friction angle as used by s
assa
(1987). With reference
to Figure 5, Point A is the centre of the debris mass
where motion was initiated. From A to C is the ac-
celeration zone, and from C to D is the deceleration
tion. Some debris mass may gothrough the accelera-
tion stage and the passing channel stages before ar-
riving at this stage while others may arrive directly
from the acceleration stage. In any case, the debris
mass enters this final stage without the presence of
additional water. There it will encounter two kinds
of resistance. Firstly the inclination of the slope (θ
4
)
usually drops from 30°–25° to 10°–4°. This severely
limits the energy development of the moving debris
and results in a reduction of its speed. Secondly, the
surface of this zone is normally rugged and dry. The
travelling viscous debris will lose some of its water
into the dry ground, gradually increasing the apparent
friction angle. Together, these two types of resistance
will turn the visco-elastic liquid into a visco-elastic
solid, eventually causing the debris to come to a halt.
For this stage, the apparent friction angle Φm is larger
than the slope angle θ
4
. The equation of motion can
be given by:
Since θ
4
is less than Φm, a is a deceleration for the
debris in this stage.
With the initial velocity = v
o
at this stage of mo-
tion, the velocity, vt, at time t can be obtained in the
same manner as in the acceleration stage. They can be
expressed as:
Since the velocity at the end of this stage is zero,
the duration for this stage is given by:
The distance of travel, S, in this stage can be es-
timated from:
Substituting Eq.(12) into Eq.(13) yields:
(10)
(11)
(12)
(13)
(14)
Fig. 5 - Flow path of the Ontake debris avalanche (S
ASSA
, 1987)
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454
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
zone. Point D is the motion termination point to be
estimated in the proposed model
For the acceleration zone, there is a change in the
slope angle breaking up the zone into two sections. The
acceleration in each of the sections is therefore differ-
ent. Based on Eq (7), the acceleration of the upper sec-
tion with a slope angle (θ ) of 16° is estimated to be
0.346 m/s
2
. The corresponding velocity at B is found
to be 23.52 m/s and the duration for the debris to move
through this section is calculated to be 68 s. For section
BC, the acceleration is approximately zero as the slope
angle is equal to the apparent friction angle. Using a
similar approach, the velocity at C is 23.52 m and the
duration through this section is 287 s. For the decelera-
tion zone C to D, application of Eq. (10) and Eq. (12)
leads to a deceleration of 0.137 m/s
2
, duration of 172 s
and the average velocity of 11.74 m/s.
Based on this model, the total time for the com-
plete travel of the debris avalanche is estimated to be
527s with an average speed of 18.26 m/s. Hence the
estimated distance of travel is about 9.5 km. This dis-
tance is remarkably close to the observed value of 9
km, giving support to the validity of the model.
THE TSING SHAN DEBRIS FLOw
The Tsing Shan debris flow took place in the new
Territories, Hong Kong in September 1990. This debris
flow is the largest recorded landslide in natural terrain
in the recent history of Hong Kong. Approximately
19,000 m
3
of soil and rock was involved in the land-
slide and the debris trail reached about 1035 m. As the
landslide occurred in an undeveloped area, there was no
injury and damage to facilities was negligible. Details
of the debris flow were described by k
inG
(1996).
The debris flow occurred during a heavy rain-
storm on a thick deposit of granite colluvium overly-
ing completely decomposed granite. The rainfall trig-
gered a small landslide, which in turn initiated a larger
parent landslide with a volume exceeding 2000 m
3
on
the steep upper slopes of Tsing Shan. It was this par-
ent landslide that instigated the debris flow. The parent
sliding mass started to accelerate downslope, eroding
and sweeping away the bouldery colluvium for about
300 m. It then reached the more gentle part of the
slope where the process of deposition began. The
larger pieces of boulders were first deposited form-
ing a bouldery lateral ridge. Here, a concrete water
intake was badly damaged by the boudery debris. The
finer part of the debris, mainly of gravel and sand not
exceeding 20 mm in diameter, continued to move on
in the form of a slurry for another 500 m. The slurry
moved slowly and non-erosively around obstacles. Its
potential hazard to existing structures was low.
The observed movement pattern of the Tsing Shan
debris flow closely conforms to a classic example of
the gravitative debris flow in which a sliding mass
transforms into a debris flow. The three zones can
be clearly identified: the source zone, the accelera-
tion zone and the deposition zone. In this case record,
the acceleration zone and the passing channel were
merged into one. The method of analysis proposed
herein is again applied to this case to test its validity.
The parameters and results used in the method are
summarized in Table 1. For each zone, the material
type and the geometric parameters have been obtained
by k
inG
(1996) and listed in the upper part of Table 1.
Based on this information, the model is applied.
The first parameter to be obtained is the static fric-
tion angle, Φ, for the debris material. This material
is largely composed of granite colluvium. Based on
its particle size (ignoring the boulders), the colluvium
is a gravelly, silty sand. Although there are no triax-
ial test results on this material, a lot of test results on
materials similar to this are available in Hong Kong.
Based on such information (e.g., Geoguide I 1993), a
value of 38° is chosen for Φ for this material.
The next parameter to be obtained is the appar-
ent friction angle Φ
m
for the material. To be rigorous,
highly specialized experimental equipment, such as
the high speed ring shear device, is required for its
determination. At present no such data exist for this
case record. However one can use the relationship es-
tablished for the Ontake debris avalanche as a first ap-
proximation. This relationship can be written as:
where km is a factor dependent on the distance of
travel of the debris and can be derived from Figure
5. The Φ
m
values thus computed are listed in Table 1
Based on calculations similar to those in the pre-
vious case, the velocities of the debris mass at differ-
ent points and stages of the flow path are summarized
in Table 1. The estimated stopping point of the debris
flow or the leading edge of the debris is marked by
point D on Figure 6, while the corresponding meas-
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MOVEMENT PATTERN OF DEBRIS FLOW
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
455
The discrepancy between the measured and the
actual runout distance based on the proposed model
is small. The discrepancies for the Ontake debris
avalanche and for the Tsing Shan debris flow are 5%
and 9%, respectively. This discrepancy errs on the
safe side. Recognizing the many uncertain factors
involved in a debris flow, this discrepancy is accept-
able for design consideration.
A reliable method for estimating the runout dis-
tance has great value in construction and develop-
ment in areas vulnerable to debris flow. The present
method erring on the safe side by about 10% pro-
vides a useful tool for locating facilities in areas vul-
nerable to debris flow occurrence. Hence this method
will help reduce hazards and risks for developments
in debris flow zones.
SUMMARY AND CONCLUSIONS
Based on past observations, a general movement
pattern is described for the gravitative debris flow
in which a landslip or slump is transformed into a
debris flow. A simple kinematic model is proposed
for characterizing the different stages of a gravitative
ured point is marked as M in the same figure. The dis-
tances from A to D and to M are 505 m and 555 m, re-
spectively. Comparing these two points, it is obvious
that the estimated stopping point is slightly ahead of
the actual one. The agreement between the estimated
and the measurement is quite acceptable recognizing
the approximation used in establishing Φ
m
.
DISCUSSION
The runout distance of a debris flow is equal to
the distance between the initiation point to the final
point of stoppage. The application of the proposed
model has shown that the proposed model yields a
runout distance slightly larger than the measured val-
ues. There is one major reason for this discrepancy.
The model assumes that once initiated the debris
continues its journey down the slope with no addi-
tion of materials. In reality in the acceleration zone,
erosion of in-situ materials is quite likely. This will
add mass to the debris and will consume part of the
original kinetic energy in the flowing mass. Hence
the actual runout distance will be shorter than that is
obtained from the model.
Tab. 1 - Movement characteris-
tics at different stages
of the Tsing Shan debris
flow
Fig. 6 - Flow path of the Tsing
Shan debris flow
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456
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
also gives a result slightly on the safe side. Hence
this approach has a good potential for design applica-
tions in areas vulnerable to debris flows.
ACKNOWLEDGEMENTS
The research is supported by National Basic Re-
search Program of China (Grant No. 2011CB409903),
and the Hong Kong Jockey Club Charities Trust. The
authors express deep appreciation to Mr. Y.C. Chan
and Dr. D. Lo, both of the Geotechcnical Engineer-
ing Office, Hong Kong SAR Government, for their
conscientious efforts in taking the authors for a tour
of the Tsing Shan debris flow site and for provid-
ing valuable information on the failure. This paper
is published with the financial support of the Jockey
Club Charities Trust and the Research Grant Council
of Hong Kong.
debris flow. From the model, the runout distance of
the debris flow can be determined. The model has
been applied to two well-documented records. The
first one is the Ontake Volcano debris flow in Japan
and the other is the Tsing Shan debris flow in Hong
Kong. Comparison has been made between the es-
timated and the observed runout distances for these
two debris flows. The estimated values are within
10% higher than the observed values. The reason
for the estimated value being higher is due to the
simplified assumption of ignoring the added mass to
the debris due to erosion along the path of the de-
bris flow. Recognizing the highly complex nature of
debris flows, one may conclude that the proposed
model gives excellent estimates of the actual runout
distances of debris flows. Furthermore the simplified
assumption leads not only ease of calculation, but it
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