Natural Hazards

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

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

Original Paper


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.


Granular debris flows Flow motion Deposition characteristics Routing model 

List of Symbols


Frictional coefficient

b = b(x, y)

Elevation function of channel bed


Width of gully

βx and βy

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


Maximum sediment volumetric concentration of debris flow


Sediment volumetric concentration of debris flow


Equilibrium sediment volumetric concentration of debris flow


Volumetric concentration of deposition sediment at alluvial fan


Average diameter of deposition material at alluvial fan


Particle diameter of sediment


Mean grain diameter of sediment particle


Collision angle of inter-particle of sediment


Dynamic friction angle

Δx and Δy

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


Time increment of computation scheme


Internal friction angle of sediment


Gravity acceleration

h = h(x, y)

Elevation function of free surface of debris flow


Initial flow depth at upstream


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

\( \hat{h} \)

Flow depth


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


Flow depth above deposition at alluvial fan


Elevation difference between upstream and downstream of gully channel


Erosion or deposition rate of channel bed

kx and ky

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


Coefficient of active earth pressure


Length of gully channel


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


Maximum deposition length of alluvial fan


Flow rate of debris flow


Intersection angle between deposition surface and channel bed


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


Density of sediment solid


Stress tensor


Slope angle of channel bed

θ1 and θ2

Slope angles of channel bed at transportation zone and deposition zone


Channel bed shear stress

τxb and τyb

x and y components of the channel bed shear stress


Yield stress of debris flow


Density of clean water


Density of viscous fluid


Dry density of granular sediment


Density of debris-flow mixture


Resultant velocity of each finite difference grid


Friction velocity


Total volume of outflow sediment

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

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


Flow concentration time


Average deposition height


Maximum deposition thickness of alluvial fan


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

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

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