# IJEGE-11_BS-Ou-et-alii

*Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza*

*DOI: 10.4408/IJEGE.2011-03.B-028*

**THE EXPERIMENTAL STUDY ON THE GEOMETRIC SIMILARITY**

**OF DEBRIS FLOW DEPOSITION**

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.

(e.g., i

*et alii*, 1980;

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

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**

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

verse directions. For the plane configuration, -b

deposition width and c

**K**

**ey**

**words***: geometric similarity, debris flow, deposition, la-*

*boratory experiments*

**INTRODUCTION**

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

*y. yoNG, l. JiNfeNG & c. XiNGZhANG*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

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*

of the accumulation area are conducted (Table 1).

*PARAMETERS*

deposition depth. Lc is the deposition length of the

medial axis direction. Since the experimental depo-

sition conditions are homogeneous and symmetrical,

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*

pool (Figure 1). The hopper measures 50 × 40 × 85

cm, with a capacity of 0.1 m

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*

**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*

axis. The vertex coordinate is (0,1).

*Z*/

*Zc*=

*a*

*X*/

*B*)

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

Thus, the average crosssection deposition slope decreas-

es as a result. Therefore, the quadratic coefficient, a

slope of the debris fan. The greater the absolute value, the

greater the transverse average deposition slope.

*GEOMETRIC SIMILARITY OF THE PROFILE*

*Z*

*c*

*Z*

*a*

*Y*/

*Lc*)

*b*

*Y*/

*Lc*) +

*c*

of arbitrary cross section, Bmax is the maximum

deposition width. Zc is the deposition depth of the

center line of the cross section, Z

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

**RESULTS AND DISCUSSION**

*GEOMETRIC SIMILARITY OF THE CROSS-SECTION*

larity according to parabolic distribution. This can be

expressed as follows:

*Z / Zc*=

*a*

*(X / B)*

*+*

* b*

*(X / B)*+

* c*

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*

*d·*

*y. yoNG, l. JiNfeNG & c. XiNGZhANG*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

*B*/

*B*

*a*

*Y*/

*Lc*)

*b*

*Y*/

*Lc*) +

*c*

further from the outlet. In summary, -b

width. The greater the value, the greater the deviation.

c

value, the more similar is the deposition width at the

outlet of the gully to the maximum width.

**CONCLUSIONS**

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.

8 shows that the profile is a unary quadratic curve on

the right side symmetrical around the Zc/Z

*Z*

*c*

*Z*

*a*

*Y*/

*Lc*)

mulation area (θ

deposition slope of the profile decreases. Therefore, the

quadratic coefficient, a

the greater the longitudinal average deposition slope.

*GEOMETRIC SIMILARITY OF THE PLANE*

CONFIGURATION

CONFIGURATION

*Fig. 8 - Relationship between dimensionless parameters*

*Zc/Z*

*0*

*and Y/Lc*

*Fig. 9 - Relationship between |a*

*2*

*|, γ and θ*

*d*

*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*

**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*

**ACKNOWLEDGEMENTS**

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).

of the debris fan in the longitudinal and transverse direc-

tions. The greater the value, the smaller the slope. For the

plane configuration, -b

the greater the deviation. c

greater the value is, the more similar is the maximum

deposition width and the deposition width at the outlet.

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