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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
237
DOI: 10.4408/IJEGE.2011-03.B-028
THE EXPERIMENTAL STUDY ON THE GEOMETRIC SIMILARITY
OF DEBRIS FLOW DEPOSITION
J
infenG
LIU, G
uoQianG
OU & y
onG
YOU
(*)
Key Laboratory of Mountain Surface Process and Hazards, Chinese Academy of Sciences,Chengdu 610041, China; 2. Institute of
Mountain Hazards and Environment, Chinese Academy of Sciences, Chengdu 610041, China.
(*)
Email: Liujf@imde.ac.cn
for, mountainous areas. Many of these projects have
been or will be built on debris fans and thus will be
threatened by debris flows. Therefore, the study of the
geometric parameters of debris fan deposition is es-
sential for organizing and implementing debris flow
disaster prevention and mitigation plans.
To date, debris fan deposition prediction studies
have mainly involved predicting debris flow volume
(e.g., i
keya
, 1980; t
anG
, 1993; f
Ranzi
, 2001; l
iu
,
2002), deposition length (e.g., P
eRla
et alii, 1980;
C
annon
, 1989; b
enda
& C
undy
, 1990; z
immeRmann
,
1991; w
HiPPle
, 1992; P
ieRson
, 1995; b
atHuRst
,
1997; i
veRson
, 1998; v
illaR
, 2000; f
annin
& w
ise
,
2001; l
anCasteR
, 2003; t
oyos
, 2006), and alluvial
area (b
ull
, 1964; C
HRistine
& R
obeRt
, 2003; b
eRti
and s
imoni
, 2007). These studies have focused on
making two dimensional predictions of debris flow
deposition and lack a prediction of deposition depth.
In order to make predictions in three dimensions, we
must first consider the geometric parameters of de-
bris flow deposition (x
ie
& C
ai
, 1998). x
ie
and C
ai
(1998) analyzed 72 debris deposition fans formed un-
der different conditions and concluded that the non-
dimensional longitudinal and cross-sectional profiles
of debris flow fans can be described with Gaussian
functions. In contrast, the non-dimensional plan form
of debris flow fans can be described with a circular
arc. However, the experimental fluid types employed
were representative of stony and low viscosity debris
flows. The geometric parameters of the viscous debris
ABSTRACT
With the rapid development of the Chinese econ-
omy, many important building projects are planned on
debris fans. Because of their location, these new con-
structions will be threatened by debris flows. Thus, it
is important to study debris flow deposition in different
conditions. Twenty debris fans under different experi-
mental conditions are considered in order to examine
the geometric similarity of debris flow deposition. The
experimental results show that the cross-section, pro-
file, and plane configuration of debris fans all have par-
abolic distributions. The quadratic term coefficients (a
1
,
a
2
) of the debris fan cross-section and profile define the
average deposition slope in the longitudinal and trans-
verse directions. For the plane configuration, -b
3
/2a
3
is
the degree of deviation of the maximum downstream
deposition width and c
3
is the ratio of the deposition
width at the outlet to the maximum deposition width.
K
ey
words
: geometric similarity, debris flow, deposition, la-
boratory experiments
INTRODUCTION
Debris flow is a sudden natural phenomenon,
common in mountainous areas. Debris flows prima-
rily cause erosion and deposition, particularly in the
area of the debris fan. With the rapid development of
the Chinese economy, many important transportation
routes, water conservation and hydropower plants,
towns, and factories have been built in, or are planned
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y. yoNG, l. JiNfeNG & c. XiNGZhANG
238
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
The experimental materials come from a sample
of the original debris flow collected from the Jiangjia
Gully, Dongchuan debris flow observation research
station in Yunnan Province, China. The maximum
grain size is 10 mm, the median grain size is 1.0 mm,
and the average grain size is 3.25 mm (Figure 2).
SETTING
Twenty experiments in three groups, varying the
scale and bulk density of the debris flow, and the slope
of the accumulation area are conducted (Table 1).
PARAMETERS
The parameters of the debris flow are defined
based on the results of experiment No.A
3
in Table 1
(Figures 3 and 5).
The X-axis is the cross-section direction, the Y
axis is the profile direction, and the Z axis expresses
deposition depth. Lc is the deposition length of the
medial axis direction. Since the experimental depo-
sition conditions are homogeneous and symmetrical,
flows that typically occur in southwestern China are
still unknown. For this paper, a laboratory experiment
is designed in order to analyze the geometric param-
eters of viscous debris flow deposition.
LABORATORY EXPERIMENT
EXPERIMENTAL APPARATUS AND MATERIAL
The experimental apparatus includes a hopper,
flume, accumulation plate, and material recycling
pool (Figure 1). The hopper measures 50 × 40 × 85
cm, with a capacity of 0.1 m
3
. The flume is a steel-
truss structure with inside measurements of 20 × 30
cm, a valid flow length of 300 cm, and glass-rein-
forced sides to facilitate observation. The adjustable
slope of the flume ranges from 0-20°. The accu-
mulation plate is a rectangular steel-truss structure
measuring 300 × 180 cm. A leveling board on the
surface of the structure serves as an accumulation
plane. The material recycling pool, a brick-molded
rectangular pool, is positioned at the end of the ac-
cumulation plate. The pool measures 200 × 80 × 15
cm. the materials are cleaned after each experiment
for reuse in the following experiment.
Fig. 1 - Experimental apparatus
Fig. 2 - Particle gradation for the material used in the
experiment
Tab. 1 - Experimental conditions
Fig. 3 - Cross-section parameters
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DISASTER CHARACTERISTICS AND OPTIMAL DESIGN OF DRAINAGE CANAL OF DEBRIS FLOW FOLLOWING WENCHUAN EAR-
THQUAKE IN WEIGOU GULLY IN BEICHUAN COUNTY, SICHUAN PROVINCE, CHINA
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
239
a unary quadratic curve symmetrical around the Z/Zc
axis. The vertex coordinate is (0,1).
Thus, b
1
= 0, c
1
= 1 in formula (1). The shape of
the cross-section can be expressed as:
Z / Zc = a
1
(X / B)
2
 + 1
Next, we considered the relationship between
quadratic coefficient a1 and debris fan deposition.
Here, experimental group C in Table 1 as an example
is used. The relationships between |a1|, the transversal
average deposition slope (λ), and the slope of the ac-
cumulation area (θ
d
) are shown in Figure 7.
Figure 7 shows that |a1| and λ have a negative, linear
correlation with θ
d
. As the accumulation slope increas-
es, the maximum deposition width and depth decrease.
Thus, the average crosssection deposition slope decreas-
es as a result. Therefore, the quadratic coefficient, a
1
,
reflects the change in the transverse average deposition
slope of the debris fan. The greater the absolute value, the
greater the transverse average deposition slope.
GEOMETRIC SIMILARITY OF THE PROFILE
The relationship between the dimensionless pa-
rameters Zc/Z
0
and Y/Lc is shown in Figure 8.
Figure 8 shows that the debris fan profile also has
a parabolic distribution. This can be expressed as:
Z
c
/ Z
0
= a
2
(Y / Lc)
2
+ b
2
(Y / Lc) + c
2
Lc is the maximum deposition length. B is the width
of arbitrary cross section, Bmax is the maximum
deposition width. Zc is the deposition depth of the
center line of the cross section, Z
0
is the deposition
depth of the midpoint of the flume outlet. In order to
analyze the average deposition slope of the debris fan
in the cross section and profile, λ is the transversal
average deposition slope in the direction of the maxi-
mum deposition width (cross-section average deposi-
tion slope for short), γ is the average profile deposi-
tion slope in the direction of the maximum deposition
length (average profile deposition slope for short),
and θ
d
is the slope of the accumulation area.
RESULTS AND DISCUSSION
GEOMETRIC SIMILARITY OF THE CROSS-SECTION
The relation between the dimensionless param-
eters Z/Zc and /B are shown in Figure 6.
Figure 6 shows that the cross-section of the debris
fan under different conditions has a geometric simi-
larity according to parabolic distribution. This can be
expressed as follows:
Z / Zc = a
1
(X / B)
2
+ b
1
(X / B) + c
1
Since the debris fans in terms of a level and sym-
metrical deposition area are only considered in the ex-
periments, Figure 6 indicates that the cross-section is
Fig. 4 - Profile parameters
Fig. 5. Plane configuration parameters
Fig. 6 - Relationship between dimensionless parameters
Z/Zc and X/B
Fig. 7 - Relationship between |a
1
|, λ and θ
(1)
(2)
(3)
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y. yoNG, l. JiNfeNG & c. XiNGZhANG
240
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
can be expressed as:
B / B
max
= a
3
(Y / Lc)
2
+ b
3
(Y / Lc) + c
3
In the above formulas, -b
3
/2a
3
is the axis symme-
try and c
3
is the intercept of the curve. The relationship
between -b
3
/2a
3
, c
3
and θ
d
is shown in Figure 11.
Figure 11 indicates that as the accumulation slope
increases, the position of the maximum width deviates
further from the outlet. In summary, -b
3
/2a
3
is the maxi-
mum degree of deviation of the downstream deposition
width. The greater the value, the greater the deviation.
c
3
is the ratio of the deposition width at the outlet of the
gully to the maximum deposition width. The greater the
value, the more similar is the deposition width at the
outlet of the gully to the maximum width.
CONCLUSIONS
In this paper, twenty debris fans under different ex-
perimental conditions are examined in order to define the
geometric similarity of viscous debris flow deposition. The
results indicate that the crosssection, profile, and plane con-
figuration of debris fans all have parabolic distributions. In
addition, the physical meanings of the geometric similarity
coefficients related to the geometry of debris fan cross-
sections, profiles, and plane configurations are discussed.
Since the debris fans in terms of a level and sym-
metrical deposition area are only considered, Figure
8 shows that the profile is a unary quadratic curve on
the right side symmetrical around the Zc/Z
0
axis. The
vertex coordinate is (0, 1). Thus, b
2
= 0, c
2
= 1 in for-
mula (3). The shape of the profile can be expressed as:
Z
c
/ Z
0
= a
2
(Y / Lc)
2
+ 1
The relationship between |a
2
|, the longitudinal av-
erage deposition slope (γ), and the slope of the accu-
mulation area (θ
d
) is shown in Figure 9.
Figure 9 shows that |a
2
| and γ have a negative, linear
correlation with θ
d
. As the accumulation slope increases,
the maximum deposition length increases and the average
deposition slope of the profile decreases. Therefore, the
quadratic coefficient, a
2
, reflects the change in the slope of
the debris fan deposition. The greater the absolute value,
the greater the longitudinal average deposition slope.
GEOMETRIC SIMILARITY OF THE PLANE
CONFIGURATION
The relationship between the dimensionless pa-
rameters B/B
max
and Y/Lc is shown in Figure 10.
Figure 10 shows that the plane configuration of
the debris fan also has a parabolic distribution. This
Fig. 8 - Relationship between dimensionless parameters
Zc/Z
0
and Y/Lc
(4)
Fig. 9 - Relationship between |a
2
|, γ and θ
d
(5)
Fig. 10 - Relationship between dimensionless parameters
B/B
max
and Y/Lc
Fig. 11. Relationship between -b
3
/2a
3
, c
3
and θ
d
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DISASTER CHARACTERISTICS AND OPTIMAL DESIGN OF DRAINAGE CANAL OF DEBRIS FLOW FOLLOWING WENCHUAN EAR-
THQUAKE IN WEIGOU GULLY IN BEICHUAN COUNTY, SICHUAN PROVINCE, CHINA
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
241
ACKNOWLEDGEMENTS
We are grateful for the technical support of Prof.
Chjeng-Lun Shieh (Department of Hydraulic and
Ocean Engineering, National Cheng Kung University,
Taiwan, China) and Prof. Yuan-Fan Tsai (Social Stud-
ies Education, National Taipei University of Education,
Taipei, Taiwan, China). This research was financially
supported by the National Natural Science Founda-
tion of China (40901008) and the Project group of the
Knowledge Innovation Program (Kzcx2-Yw-Q03-5-2).
The quadratic term coefficients (a
1
,a
2
) of the cross-
section and profile define the average deposition slope
of the debris fan in the longitudinal and transverse direc-
tions. The greater the value, the smaller the slope. For the
plane configuration, -b
3
/2a
3
is the degree of deviation of
the maximum deposition width. The greater the value,
the greater the deviation. c
3
is the ratio of the deposition
width at the outlet to the maximum deposition width. The
greater the value is, the more similar is the maximum
deposition width and the deposition width at the outlet.
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