# IJEGE-11_BS-Paik-&-Park

*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-054*

**NUMERICAL SIMULATION OF FLOOD AND DEBRIS FLOWS THROUGH**

**DRAINAGE CULVERT**

gineering tool for practical simulations of such flows.

We elucidate the transient features of flood and debris

flows through culverts, based on numerical solutions

of such flows in the open channel with culvert at vari-

ous configurations of different bottom slopes between

the channel and the culvert.

**K**

**ey**

**words**

**:**debris flow, culvert, numerical simulation**INTRODUCTION**

behavior of the debris flows. Due to the huge diffi-

culty of the real-time field measurements, the major-

ity of debris flow researches have been carried out by

laboratory experiments and numerical simulations

with the parameters back-calculated or calibrated to

match previous field events. The physical modeling

has provided much of what we know about the rheol-

ogy of the debris flow, but their results suffer from

spatial scale effects and are approximately applica-

ble to large-scale events. The numerical simulation

has become an ideal approach for reproducing the

debris flow propagation.

made structures. Debris flow is generally considered

to contain more than 50% particles larger than sand

size (v

**ABSTRACT**

derneath road or embankment. Flood and debris flows

typically undergo a sudden change of the flow depth

in the open channel with culvert due to the discontinu-

ity of the bottom slope and the cross-sectional area

near the culvert inlet, which can result in culvert fail-

ure due to blockage. In this study, we seek to improve

our understanding of the culvert flow and its transition

in such open channel. A second-order-accurate finite

volume method using a shock-capturing scheme with

TVD limiters has been developed for solving one-

dimensional shallow water equations with debris flow

resistance terms to predict the time-dependent behav-

ior of non-Newtonian debris flow through culverts. To

evaluate the numerical model, we first apply it to cal-

culate a saturated debris flow in a large scale experi-

mental channel. The comparison of the numerical re-

sults with experimental measurements shows that the

present model can reasonably well reproduce labora-

tory but fairly large scale debris flows. To investigate

the behaviour of the common flood flow, an immature

debris flow and debris flow in our laboratory flume

with a square culvert and an abrupt change of bed

slope, we conducted these flows using corresponding

flow resistance relations. The numerical results appear

to be in good agreement with our experimental meas-

urements which provide useful information on the

debris flow transient through culverts. The numerical

*J. PAIk & S.-D. PARk*

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

flow rate condition. Recently, these flows had been also

investigated in our laboratory channel with rectangular

cross section and an abrupt slope change of the slope.

Finally, conclusions about behaviour of these flows

with same flow rate but different sediment concentra-

tions in the culvert-like experimental flume are drawn

**NUMERICAL MODEL**

*GOVERNING EQUATIONS*

debris flows with an appropriate flow resistance term

(J

*et alii*, 2000; n

*et alii*,

written in the conservative form as follows:

*t*= time;

*x*= the distance along

*h*= the flow depth

normal to the local bed surface;

*u*is the depth-aver-

aged velocity;

*q*

*g*= the

*S*

*θ*

*z*(

*x*,

*t*) = the bed level respect to an arbitrary

horizontal reference. In this study, various flow re-

sistance relations for the flow resistance term S f

available for mud/debris flows are implemented in

the model.

ing on the turbulenceand viscosity.

Distinct physical processes differentiate these type of

flows based on the rheology of the water-sediment

mixture. According to J

and the dispersive stress is dominant in debris flows.

The sediment concentration also can be used to dis-

tinguish between stony debris flow, immature debris

flow (less than about 0.2), and turbulent flow (less

than about 0.02) (t

practical problems are to determine representative

parameters, such as bulk viscosity and yield stress,

characterizing the solid-fluid mixture and to select

the appropriate flow resistance relations (n

*et alii,*

flow compared to those of common flood flow, in this

study, we solved the governing equations with con-

sidering three resistance formula available for differ-

ent flow regimes: 1) the turbulent flow relation for the

bed load/suspended load flow; 2) the immature debris

flow model (t

the finite volume context with an approximate Riemann

solver, to simulate fluid mixture (mud/debris) flows.

The present model solves the time-dependent non-

linear one dimensional shallow water equations with

complex source terms by the Weighted Averaged Flux

(WAF) method using the HLL approximate Riemann

solver, with total variation diminishing (TVD) limiters

incorporated with various flow resistance relations to

determine the basal and/or internal friction slope and

the numerical methods. In P

*et alii*(2010), the nu-

dam break problem with analytical solutions account-

ing for a Coulomb-type behavior with constant fric-

tion angle on constant slope bottom and to a mudflow

which was experimentally investigated in a small scale

rectangular channel of a constant slope. In this study,

we apply the present model to a debris flow experimen-

tally reproduced in a large scale USGS flume to further

evaluate its computational performance. Subsequently,

we present and discuss numerical results of a flood

(water) flow, an immature debris flow with relatively

**NUMERICAL SIMULATION OF FLOOD AND DEBRIS FLOWS THROUGH DRAINAGE CULVERT**

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

*C*

*S*

*t*/Δ

*x*Courant number related to the

*S*

ther minmod or superbee limiter (t

**F**

*k*:

order-accurate solution elsewhere. To determine the

wave speeds and flux jumps, we employ the HLL

approximate Riemann solver which is based on the

estimates of the smallest and the largest wave speeds

arising in the Riemann solution:

*q*

*h*in the star region

*n*= pseudo Manning’s roughness coefficient

which accounts for both turbulent boundary friction

and internal collisional stresses.

*h*

*A/P*= the hydraulic radius,

*P*= the wetted

*d*

friction losses and a basal friction term to describe the

stopping mechanism, and presents the good behav-

iour regarding both the debris flow behavior and the

deposit characteristics (b

*et alii,*2006; m

*et alii*, 2008).

*θ*is internal friction angle of the flowing mass

and

*C*

*NUMERICAL METHODS*

solver. Using the explicit conservative formulation of

the governing equations, the upwind scheme can be

applied in the form

*t*= the time interval; Δ

*x*= the spatial step; n

= the time interval index;

*i*= the spatial node index;

and

**F**

*x=x*

*i*+1/2

method (t

spurious oscillations in the vicinity of discontinui-

ties. The resulting TVD version of the secondorder

WAF flux is

*J. PAIk & S.-D. PARk*

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

**RESULTS AND DISCUSSION**

*wATER-SATURATED DEBRIS FLOwS*

merical methods for reproducing the debris flow in a

large scale USGS experimental flume which was ex-

perimentally and numerically investigated by d

the USGS debris flow flume which is a rectangular

concrete chute 95 m long and 2 m wide that slopes

31° throughout most of its length and flattens at its

base to adjoin a runout surface that slopes 2.5°. The

solid-water mixture was initially placed as a triangular

wedge against a vertical gate of 2m height, and sud-

denly released by the gate opening. In the experiment,

the flow was confined by concrete panels which effec-

tively extended the flow length 7.4m across the runout

surface. Details of the flume facility and experimental

methods have been reported in i

debris properties of

*ρ*= 2000 kg /m

*θ*

*Φ*= 7°. The computational domain is dis-

cretized using 841 grid points and the computational

time-step is set with a CLF number of 0.9.

with experimental measurements and previously

simulated results of d

Iverson, the most significant simulation errors occur

at the location 2m downstream of the gate. As already

pointed out by d

tion forces exerted by the static bed in response to the

slope-normal acceleration, and it consequently pre-

dicts too much thinning just downstream of the gate.

can reasonably well reproduce the flow.

*COMPARISON OF FLOOD AND DEBRIS FLOwS*

for the development of the design criteria of culverts

in the debris flow potential regions. Laboratory experi-

ments are presented that model the debris flows with

mination of the wet/dry frontvelocities (t

speeds as follows:

volves a two-step solution procedure. In the first step,

only the homogeneous part of the system is solved

with the HLL approximate Riemann solver. In the

second step, the source term is taken into account by

solving the ordinary differential equation using the

first-order accurate, splitting method.

**U**

The friction term has been discretized by a full im-

plicit method (l

*D*=1-

*ΔΔ*n (∂S

*f*

comparing the numerical solutions computed on suc-

cessively refined grids with analytical solutions ac-

counting for a Coulomb-type friction law on the dry

bottom of the constant slope which is higher than the

internal friction slope and some experimental measure-

ments of debris flows. Numerical tests confirm that the

numerical model yields solutions in very good agree-

ment with the analytical solutions even near the discon-

tinuities at appropriately refined grid resolution. For a

detailed description of the numerical method and its

performance the reader is referred to P

*et alii*(2010).

**NUMERICAL SIMULATION OF FLOOD AND DEBRIS FLOWS THROUGH DRAINAGE CULVERT**

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

be 0.8mm based on the particle size analysis. The total

simulation time is 120 s and the time step is specified

at every time with a CFL number of 0.6.

pared in Fig. 2 where the flow depth is doubled for

visualization. As shown in the figure, the fresh water

flow, computed flow depth is appeared to increase

by 40% at the downstream channel. Note the overall

longitudinal depth profile of flood flow shown in Fig.

2(a) is in very good agreement with the experimental

measurement. Interestingly, the numerical result of

an immature debris flow reveals the emergence of the

debris flow surge as shown in Fig. 2(b). This kind of

debris flow surges were experimentally investigated

by d

deposition of sediments in the downstream channel

was not observed in the numerical results. In contrast,

which consists of two channel of different slope angles:

the upstream channel of 5 m length and 25° slope and

the downstream channel of the length of 3 m and a bed

slope of 6° including a culvert at various angles. The

measurement methods include six ultrasonic sensors

to measure flow depth and record stage hydrographs

and video cameras to assess the surface velocity and

interpret the flow processes of debris flows. The ex-

perimental measurements show that the flow depth of

debris flows dramatically increase as compared with

that of the clear water flow, and depends on the angle

of culvert slope as well as the sediment concentration.

We calculate a flood flow, a immature debris flow and

a debris flow in the experimental flume using flow re-

sistance relations of Eq. (3), Eq( 4) and Eq. (5), respec-

tively. Based on the calibration and the test of material

properties, the manning coefficient n in Eq. (3) is set

to be 0.01 s m

*Fig .2 - Computed depth profiles of (upper) flood flow,*

*(centre) immature debris flow, and (lower) debris*

*flow at t = 120s*

*Fig.1 - Comparison of [upper] measurement and predic-*

*tion of D*

*eNliNGer*

*& i*

*verSoN*

*(2001) with [lower]*

*present prediction*

*J. PAIk & S.-D. PARk*

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

relations shows that the typical debris flow results in

the significant deposition of sediments in the down-

stream culvert of low bed slope. The computed debris

flow deposition is in good agreement with our flow

visualization shown in inset, as shown in Fig. 2(c).

with experimental measurements obtained by ultra-

sonic sensors in Fig. 3. As shown in the figure, the

patterns of sediment deposition in the computed flow

field are different from those of the measurements.

It is because of the assumption of a complete single

phase flow for the debris flow in the computation.

It should be note, however, that the final deposition

depth computed based on the single phase flow is

comparable to the experimental measurements. This

result provide useful information on the debris flow

transient through culverts.

**CONCLUSIONS**

veloped to simulate 1D non- Newtonian debris flows.

Three flow resistance relations for the flood flow, im-

mature debris flow and debris flows are incorporated

into the model to investigate the time-dependent be-

haviours of such flows in the culvert-like channel of

low bed angle. The governing equations are solved

by a second-order-accurate finite volume method em-

ploying Godunov-type schemes with spatially discre-

tized flux functions and TVD-limiters for high-resolu-

tion monotone solutions.

experimental channel. The comparison of the numeri-

cal results with experimental measurements shows

laboratory but fairly large scale debris flows. To in-

vestigate the behaviour of the common flood flow, an

immature debris flow and debris flow in our labora-

tory flume with a square culvert and an abrupt change

of bed slope, we conducted these flows using cor-

responding flow resistance relations. The numerical

results appear to be in good agreement with our ex-

perimental measurements which provide useful infor-

mation on the debris flow transient through culverts.

The numerical results show that the present model is

a promising engineering tool for practical simulations

of such flows. We elucidate the transient features of

flood and debris flows through culverts, based on nu-

merical solutions of such flows in the open channel

with culvert at various configurations of different bot-

tom slopes between the channel and the culvert

**ACKNOWLEDGEMENTS**

gional Technology Innovation Program funded by the

Ministry of Land, Transport and Maritime Affairs of

Korean Government..

*Fig. 3 - Experimental measurements (solid lines) and*

*numerical predictions (dashed lines) at four dif-*

*ferent sections (see Fig. 2 for section numbers,*

*S1- S6)*

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**NUMERICAL SIMULATION OF FLOOD AND DEBRIS FLOWS THROUGH DRAINAGE CULVERT**

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