# IJEGE-11_BS-Fan-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-046*

**SIMULATION BASED ON FINITE VOLUME METHOD**

**OF THE ENTRAIMENT OF DEBRIS FLOW**

offered. Therefore, the dynamic simulation of debris

flow is significant and valuable.

ure and slide with debris flow during the motion proc-

ess so that the entrainment is formed which increase

the volume of debris flow and change the composition

of motion material. For this reason, the surface mate-

rial is an important factor in the development of debris

flow and should be considered in its dynamic simula-

tion. At the moment, many scholars have begun their

studies on the entrainment problems during the mo-

tion of debris flow and some progress has been made.

entrainment on dynamic simulation, the back analy-

sis is made to study a typical historical debris flow,

Nomash River in Canada, by combining entrainment

dynamic model theory which considers the entrain-

ment effects and the method of finite volume discre-

tization based on the approximate Riemann solver of

HLL Scheme. The calculation also takes the variation

of terrain slope caused by entrainment into account.

The calculation results which are identical to actual

disaster-caused area confirm the effectivity of the dy-

namic model theory and the numerical solution. Com-

pared with the results which have no consideration of

entrainment, the influence of entrainment action on

dynamic process of debris flow is analysed.

**ABSTRACT**

structive power which seriously threaten human lives

and belongings. Therefore, it is necessary to study

more about the happenings and developments of these

disasters. Among the important and common features

of the debris flow, the entrainment is the one that can

increase the volume of debris flow and affects signifi-

cantly the flow motion. These influences usually re-

sult in a more harmful and stronger destructive power.

With the method of finite volume discretization, the

numerical simulation of the entrainment process of

debris flow is achieved in this paper. The influences

of entrainment capabilities on the motion and deposi-

tion of debris flow are mainly studied. The typical en-

gineering examples show and prove the stability and

effectivity of numerical methods.

**K**

**ey**

**words***: debris flow, entrainment, finite volume, dynamic,*

*simulation*

**INTRODUCTION**

characteristics of disasters by inversing and reappear-

ing the development law of debris flow disasters, but

also predict the disaster-caused area and intensity of

debris flow, and consequently, scientific references

of industry planning and construction, and the meas-

*y. FAN, S. wANG, e. wANG & Z. LIU*

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

*u*,

*v*) is velocity vector.

If there exists water during the motion process of

ered, in this case, Voellmy resistance is usually used as

the resistance model (H

*a*) is sign function which can be described as:

friction resistance which has the same form with eq.

(4),

*f*corresponds to tan

*δ*, and the second item repre-

sents other resistances, which are experientially used

to express the items relative to velocity in the analysis.

*ENTRAINMENT VELOCITY*

*E*

*E*

*s*

*is as follows:*

*E*

*s*

feasible method is to use the average rate of increase

*Ē*

*s*

*V*

*V*

*f*

*d*is the approximate average

**FINITE VOLUME NUMERICAL METHOD**

*FINITE VOLUME DISCRETIZATION*

angular meshes and Cell Center which have a great

adaptability.

**DYNAMIC MODEL THEORY**

*BASIC EQUATION*

tion of physical variable in the direction of flow depth,

the dynamic model equation is as follows:

*U*is conservation variable,

*F*=(

*E*,

*H*) is

*S*is source item, these items can be

expressed as follows:

*H*is the depth of flow,

*u*and

*v*are respectively the velocities in

*x*direction and

*y*

direction,

*g*is acceleration of gravity,

*E*

*t*

*z*

*b*

*S*

*f*

ent conditions,

*k*

*act/pass*

*is the coefficient of lateral stress*

*et alii*, 2007):

with different cofficients of lateral stress. When

∂

*u/*∂

*x+*∂

*v/*∂

*y>0*, the motion is in active state, how-

ever when ∂

*u/*∂

*x+*∂

*v/*∂

*y<0*, the motion is in passive

state (s

*et alii*, 2007).

*RESISTANCE MODEL*

the dynamic simulation of debris flow. In this paper,

analysis is achieved by use of friction resistance and

Voellmy resistance.

During the process of debris flow, the resistance

resistance can be considered as (s

*et alii*, 2007; H

**SIMULATION BASED ON FINITE VOLUME METHOD OF THE ENTRAIMENT OF DEBRIS FLOW**

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

*s*

*L*

*s*

*R*

*SPATIAL SECOND-ORDER LINEAR RECON-*

STRUCTION

STRUCTION

volume of spatial second-order accuracy should be

distributed linearly. With the MUSCL method (o

interpolating variables, the linear reconstruction on

unstructured mesh is as described in Fig.1.

*U*

*i*

*U*

*k*

*U*

*l*

*U*

*j*

*U*

*s*

*U*

*r*

*U*

*lk*

*U*

*lr*

*U*

*ij*

*U*

*ks*

*U*

*rs*

*U*

*L*

*ij*

*U*

*R*

*ij*

variables,

*U*

*C*

*ij*

pressed as:

*r*) employs the scheme of Van leer:

*et*

*alii*, 1999), the format of space-time second order ac-

curacy is obtained.

*U*

*i*

*S*

*i*

placing them in the centre of element, then:

*A*

*i*

*i*,

*n*=(

*n*

*s*

*n*

*y*

*θ*,sin

*θ*) is the direc-

*θ*is the angle between the

exterior normal and

*x*-axis.

*U*

*i*

*l*

*ij*

*F*

*ij*

*NUMERICAL FLUX CALCULATION*

as follows (H

*et alii*, 1983; a

er edge respectively; (

*U*

*L*

*i,j*

*U*

*R*

*i,j*

*U*value

ment, respectively;

*s*

*L*

*s*

*R*

*u*

***

*c*

***

*s*

*L*

*s*

*R*

*Fig. 1 - Schematic plan of numerical reconstruction*

*y. FAN, S. wANG, e. wANG & Z. LIU*

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

which is really alarming number. After the entrain-

ment, a 100~150 m-wide erosion area was left, the

vestige and trace of entrainment are visible in Fig. 3

*CALCULATION AND RESULT ANALYSIS*

*V*

*V*

*f*

*d*=350 m, and according

to eq. (8),

*Ē*

*s*

the internal friction angle

*φ*=35°, and the bottom friction

angle

*δ*=30°, when the entrainment happened, Voellmy

*CALCULATION OF TERRAIN SLOPE*

traited. On unstructured triangular meshes, through

the calculation with the coordinate values of the three

nodes of the triangle element, this derivative term can

be obtained as follows:

*x*

*k*

*y*

*k*

*k*th

*i*th triangle,

*z*

*bk*

*k*th node in the coordinate system.

mass, at this time, the elevation on bottom surface recon-

structs linearly in space like other variables above-men-

tioned, so the derivative term of the source items can be

calculated with the reconstructed values of the element:

*x*

*ij*

*y*

*ij*

*j*th edge of the

*i*th triangle ele-

ment,

*z*

*bLj*

*j*th edge which is obtained through the

spatial second-order linear reconstruction.

**CALCULATION AND ANALYSIS OF AN**

**EXAMPLE**

*NOMASH RIVER DEBRIS FLOw*

crystalline limestone.

as shown in Fig. 2. The source area located on a moun-

tain slope angled at 50° to the northeast of the U-shaped

river valley. At the beginning, a continuous shear plane

was formed after a series of crossed joints about 430

m above the river, then 300 000 m

25% bulking of the source failure, there was 375.000

m

*Fig. 2 - Nomash River debris flow*

*Fig. 3 - Entrainment area of Nomash River debris flow*

**SIMULATION BASED ON FINITE VOLUME METHOD OF THE ENTRAIMENT OF DEBRIS FLOW**

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

The final results in Fig.5 obtained at the 40

because of lacking forces which can push it to climb

the slope, as a result, the disaster-caused area is much

smaller than that is shown in Fig.4. Thus it is known

that entrainment plays a very important role during a dy-

namic process of debris flow. It makes debris flow more

powerful and harmful and should be considered as a key

factor in the formation of large-scale debris flows.

are

*ξ*=400

*m/s*

*f*=0.05. With the above method, the

the geography contours is 20m, and the flow depth con-

tour is 1m. It can be seen from the above calculation that

the back analysis shows the whole motion process of the

debris flow: at the 30

mountain slope, at the 60

formed. Certes, there still exists some differences between

the calculation results and actual situation, and the calcu-

lation results could be more exact if a more reasonable

modification of geography can be made and the calcu-

lation parameters of entrainment of path material which

can better conform to the actual situation are applicable.

Nevertheless, it is still satisfactory that the simulation re-

sults are relatively identical to actual disaster-caused area.

*Fig. 4 - Calculation results at different times*

*Fig. 5 - Calculation results without the consideration of*

*entrainment*

*y. FAN, S. wANG, e. wANG & Z. LIU*

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

**CONCLUSIONS**

bris flow, which should be considered in the dynamic

simulation of debris flows.

model theory and the method of finite volume discreti-

zation. The variation of terrain slope caused by entrain-

ment is also considered in the simulation. The back

analysis is made to study Nomash River debris flow,

a typical historical debris flow happened in Canada.

to actual disaster-caused area confirm the effectiv-

ity of the dynamic model theory and the numerical

solution. Compared with the results which have no

consideration of entrainment, it is can be seen that the

entrainment action can increase the motion volume of

entrainment, change the composition of motion mate-

rials and enhance the motility of debris flow, so that

the entrainment will be more destructive and harm-

ful. In fact, entrainment is a main cause of large-scale

debris flow, so it should be paid more attention in the

dynamic simulation of debris flow.

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