Advertisement

Natural Hazards

, Volume 50, Issue 3, pp 623–650 | Cite as

Numerical simulations of flow motion and deposition characteristics of granular debris flows

  • Der-Guey Lin
  • Sen-Yen Hsu
  • Kuang-Tsung Chang
Original Paper

Abstract

Flow motion and deposition characteristics of debris flows are of concern regarding land use planning and management. A simple model for the prediction of mentioned characteristics has been developed, incorporating a friction–collision rheological model. It demonstrated to be able to satisfactorily simulate the two-dimensional behavior of laboratory results and the one-dimensional behavior of two real debris-flow events. The numerical results show that the topography of the channel bed, the yield stress level of the debris flows, and the inflow pattern have significant influence on the simulated flow motion and deposition characteristics of debris flows. In addition, the predicted run-out distance has been compared with analytical solutions and field observations. The model could be employed for the preliminary evaluation of one-dimensional run-out distance of granular debris flows provided that the volume of the debris involved in the initial mobilization is assumed.

Keywords

Granular debris flows Flow motion Deposition characteristics Routing model 

List of Symbols

ai

Frictional coefficient

b = b(x, y)

Elevation function of channel bed

B

Width of gully

βx and βy

Momentum correction factors of flow velocities in x- and y-direction

Cmax

Maximum sediment volumetric concentration of debris flow

Cd

Sediment volumetric concentration of debris flow

C*

Equilibrium sediment volumetric concentration of debris flow

CB

Volumetric concentration of deposition sediment at alluvial fan

d

Average diameter of deposition material at alluvial fan

Ds

Particle diameter of sediment

d50

Mean grain diameter of sediment particle

δ

Collision angle of inter-particle of sediment

δd

Dynamic friction angle

Δx and Δy

Dimension of finite difference grid in x- and y-direction

Δt

Time increment of computation scheme

ϕ

Internal friction angle of sediment

g

Gravity acceleration

h = h(x, y)

Elevation function of free surface of debris flow

hi

Initial flow depth at upstream

h0

Plug thickness (the minimum flow depth to cause flow motion)

\( \hat{h} \)

Flow depth

H

Depth perpendicular to the channel bed upward to the point in the debris flow, where the shear stress is equivalent to the yield stress

H0

Flow depth above deposition at alluvial fan

Hd

Elevation difference between upstream and downstream of gully channel

i

Erosion or deposition rate of channel bed

kx and ky

Coefficient of lateral earth pressure of sediment in x- and y-direction

Ka

Coefficient of active earth pressure

L

Length of gully channel

N

Number of grid point along channel bed in 1-D routing model

Lc

Maximum deposition length of alluvial fan

Qd

Flow rate of debris flow

γ

Intersection angle between deposition surface and channel bed

α

Parameter determined by the friction angle, concentration, and particle size of sediment

σ

Density of sediment solid

σij

Stress tensor

θ

Slope angle of channel bed

θ1 and θ2

Slope angles of channel bed at transportation zone and deposition zone

τb

Channel bed shear stress

τxb and τyb

x and y components of the channel bed shear stress

τy

Yield stress of debris flow

ρ

Density of clean water

ρf

Density of viscous fluid

ρd

Dry density of granular sediment

ρm

Density of debris-flow mixture

Uv

Resultant velocity of each finite difference grid

U*

Friction velocity

Vt

Total volume of outflow sediment

\( \bar{u}\;{\text{and}}\;\bar{v} \)

Average velocities of the debris flow in x- and y-direction

tc

Flow concentration time

Zave

Average deposition height

Z0

Maximum deposition thickness of alluvial fan

References

  1. Bagnold RA (1954) Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc R Soc Lond 225:49–63CrossRefGoogle Scholar
  2. Chang TC, Shieh CL (1997) Field investigation and analysis of debris flow in central of Taiwan. J Chin Agric Eng 43(3):31–46 (in Chinese)Google Scholar
  3. Chen H, Lee CF (1999) Three-dimensional numerical modeling debris flows. In: Proceeding of the international symposium on slope stability engineering. Slope stability engineering, vol 2, pp 1397–1402Google Scholar
  4. Chen H, Su DI, Chen KM (2001) Some case studies on the engineering geological characteristics of debris flows in Taiwan, Western Pacific. Earth Sci 1(3):265–296Google Scholar
  5. Coussot P, Laigle K, Arattano M, Deganutti A, Marchi L (1998) Direct determination of rheological characteristics of debris-flow. J Hydraul Eng 124(8):865–868. doi: 10.1061/(ASCE)0733-9429(1998)124:8(865) CrossRefGoogle Scholar
  6. D’Ambrosio D, Iovine G, Spataro W, Miyamoto H (2007) A macroscopic collisional model for debrid-flows simulation. Environ Model Softw 22:1417–1436. doi: 10.1016/j.envsoft.2006.09.009 CrossRefGoogle Scholar
  7. Dorta D, Toyos G, Oppenheimer C, Pareschi MT, Sulpizio R, Zanchetta G (2006) Empirical modelling of the May 1998 small debris flows in Sarno (Italy) using LAHARZ. Nat Hazards 40:381–396CrossRefGoogle Scholar
  8. Frenette R, Eyheramendy D, Zimmermann T (1997) Numerical modeling of dam-break type problems for Navier–Stokes and granular flows. In: Proceeding, first international conference on debris-flow hazards mitigation: mechanics, prediction, and assessment. ASCE, New York, pp 568–595Google Scholar
  9. Honda N, Egashira S (1997) Prediction of debris flow characteristics in mountain torrents. In: Proceeding, first international conference on debris-flow hazards mitigation: mechanics, prediction, and assessment, ASCE, New York, pp 707–716Google Scholar
  10. Huang HB, Xu MX, Chang CR (2002) Simulation of debris flow and damage evaluation caused by debris flow hazard. Bureau of Soil and Water Conservation, Taiwan (in Chinese)Google Scholar
  11. Hungr O (1995) A model for the runout analysis of rapid flow slides, debris flows, and avalanches. Can Geotech J 32:610–623. doi: 10.1139/t95-063 CrossRefGoogle Scholar
  12. Hunt B (1994) Newtonian fluid mechanics treatment of debris flows and avalanches. J Hydraul Eng 120(12):1350–1363. doi: 10.1061/(ASCE)0733-9429(1994)120:12(1350) CrossRefGoogle Scholar
  13. Iovine G, Di Gregorio S, Lupiano V (2003) Assessing debris-flow susceptibility through cellular automata modelling: an example from the May 1998 disaster at Pizzo d’Alvano (Campania-Southern Italy). In: Rickenmann D, Chen CL (eds) Proceedings of the third international conference on debris-flow hazards mitigation: mechanics, prediction, and assessment, Davos, Switzerland, vol 1. Millpress, Rotterdam, pp 623–634Google Scholar
  14. Jan CD (1997) A study on the numerical modeling of debris flows. In: Proceeding, first international conference on debris-flow hazards mitigation: mechanics, prediction, and assessment. ASCE, New York, pp 717–726Google Scholar
  15. Johnson PC, Jackson R (1987) Frictional–collisional constitutive relations for granular materials with application to plane shearing. J Fluid Mech 176:67–93. doi: 10.1017/S0022112087000570 CrossRefGoogle Scholar
  16. Keefer DK, Wilson RC, Mark RK, Brabb EE, Brown WMIII, Ellen SD, Harp EL, Wieczorek GF, Alger CS, Zatkin RS (1987) Real-time landslide warning during heavy rainfall. Science 228:921–925. doi: 10.1126/science.238.4829.921 CrossRefGoogle Scholar
  17. Liu X, Zhang D (2004) Comparison of two empirical models for gully-specific debris flow hazard assessment in Xiaojiang valley of Southwestern China. Nat Hazards 31:157–175. doi: 10.1023/B:NHAZ.0000020274.54664.a0 CrossRefGoogle Scholar
  18. MacCormack RW (1978) An efficient explicit–implicit characteristic method for solving the compressible Navier–Stokes equations. In: SIAM-AMS Proc, vol 11, pp 130–155Google Scholar
  19. Mambretti S, Larcan E, De Wrachien D (2008) 1D modelling of dam-break surges with floating debris. Biosyst Eng 100:297–308 (online)Google Scholar
  20. Medina V, Hürlimann M, Bateman A (2008) Application of FLATModel, a 2D finite volume code, to debris flows in the northeastern part of the Iberian Peninsula. Landslides 5:127–142. doi: 10.1007/s10346-007-0102-3 CrossRefGoogle Scholar
  21. O’Brien JS, Julien PY (1997) On the importance of mudflow routing. In: Proceeding of the first international conference on debris-flow hazards mitigation: mechanics, prediction, and assessment. ASCE, New York, pp 677–686Google Scholar
  22. O’Brien JS, Julien PY, Fullerton WT (1993) Two-dimensional water flood and mudflow simulation. J Hydraul Eng ASCE 119(2):244–259CrossRefGoogle Scholar
  23. Reid ME, Lahusen RG, Iverson RM (1997) Debris-flow initiation experiments using diverse hydrologic triggers. In: Proceedings, first international conference on debris-flow hazards mitigation: mechanics, prediction, and assessment. ASCE, New York, pp 32–43Google Scholar
  24. Rickenmann D (1999) Empirical relationships for debris flows. Nat Hazards 19:47–77CrossRefGoogle Scholar
  25. Savage SB, Hutter K (1989) The motion of a finite mass of granular material down a rough incline. J Fluid Mech 199:177–215CrossRefGoogle Scholar
  26. Sepúlveda SA, Padilla C (2008) Rain-induced debris and mudflow triggering factors assessment in the Santiago cordilleran foothills, Central Chile. Nat Hazards 47:207–215 (online)Google Scholar
  27. Shieh CL, Jiang JH, Chen LJ (1992) Field investigation of debris flow in Hualien and Taitung counties. J Chin Soil Water Conserv 23(2):109–122 (in Chinese)Google Scholar
  28. Shieh CL, Jan CD, Tsai YF (1996) A numerical simulation of debris flow and its application. Nat Hazards 13:39–54CrossRefGoogle Scholar
  29. Sitar N, Anderson SA, Johnson KA (1992) Conditions for initiation of rainfall-induced debris flows, instability and performance of slopes and embankments II. In: Seed RB, Boulanger RW (eds) ASCE, Geotechnical special publication no. 31, vol 1, pp 834–849Google Scholar
  30. Smith GD (1985) Numerical solution of partial differential equations—finite difference method, 3rd edn. Clarendon Press, OxfordGoogle Scholar
  31. Takahashi T (1991) Debris flow. IAHR monograph. Balkema Publication, RotterdamGoogle Scholar
  32. Tognacca C, Bezzola GR (1997) Debris-flow initiation by channel-bed failure. In: Proceedings, first international conference on debris-flow hazards mitigation: mechanics, prediction, and assessment. ASCE, New York, pp 44–53Google Scholar
  33. Tsao JW (1993) Development and application of the erosion and deposition model of debris flow. MS thesis, National Cheng Kung University (in Chinese)Google Scholar
  34. Wieczorek GF (1987) Effect of rainfall intensity and during on debris flows in central Santa Cruz Mountains, California. In: Costa JE, Wieczorek GF (eds) Debris flows/avalanches: process, recognition and mitigation. Geological Society of America, Reviews in Engineering Geology, vol 7, pp 93–104Google Scholar
  35. Yu FC, Chen CK (1987) A study on the debris flow disasters at Feng-Chiou. J Chin Soil Water Conserv 18(1):76–92 (in Chinese)Google Scholar
  36. Yu FC, Chen CG (1990) Fundamental study on the debris flow: preliminary study on the flow velocity of debris flow. J Soil Water Conserv 21–22:115–142 (in Chinese)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Soil and Water ConservationNational Chung Hsing UniversityTaichungTaiwan

Personalised recommendations