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Comprehensive modelling of runoff-generated debris flow from formation to propagation in a catchment

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Abstract

This study aimed to develop an integrated model of the runoff-generated debris flow that considers the initial conditions, movement mechanisms, and entrainment effect. The study focused on the formation and propagation processes of debris flow within a catchment, and the process is divided into three stages: rainfall infiltration, runoff, and debris flow routing. Soil saturation, rainfall, and entrainment are the main factors that influence the debris flow formation and propagation processes. Existing models for each stage, including Richards’s equations, shallow water equations, and two-phase debris flow equations, were coupled. The tridiagonal matrix algorithm and finite volume method were applied to solve these equations. Finally, several experimental cases and the 2010 debris flow event in the Hongchun catchment in China were simulated by using the proposed model. The results showed that the proposed model could effectively describe the behaviours of each stage during the debris flow formation and propagation processes. Although several aspects of the model require further improvement, the physical-parameter-based prediction of runoff-generated debris flows from formation to propagation is effectively performed by the model.

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Abbreviations

A :

coefficient related to the mobility of the fluid at the interface (-)

c :

volumetric sediment concentration (-)

C a :

near-bed volumetric sediment concentration (-)

C D :

drag coefficient of debris flow (-)

co :

cohesion of the bed material (Pa)

d :

grain diameter of bed sediment (m)

D :

hydraulic diffusivity tensor (cm2/min)

D r :

deposition flux (m/s)

E f :

fluid flux per unit area between debris flow and bed (ms−1)

E r :

entrainment flux (m/s)

E s :

solid flux per unit area between debris flow and bed (ms−1)

F :

fluid-like contribution in generalized drag (-)

g :

(gx, gy, gz) gravitational acceleration (m/s2)

G :

solid-like contribution in generalized drag (-)

h :

runoff depth (m)

H :

typical height of flow (m)

I :

infiltration rate (cm/min)

J :

exponent for linear or quadratic drag (-)

k :

(kx, ky), earth pressure coefficient of debris flow (-)

K :

hydraulic conductivity tensor (cm/min)

L :

typical extent of flow (m)

M e :

a parameter depending on Reynolds number (-)

n b :

Manning friction coefficient (-)

(NR, NRA):

dimensionless parameter (-)

(pbs, pbf):

pressure coefficient of debris flow (-)

P :

a parameter which combines the solid-like and fluid-like drag contributions to flow resistance (-)

R :

rainfall intensity (cm/min)

R ep :

particle Reynolds number (-)

(Rm, α, αc, s, m, Vm, U∞):

coefficient related to entrainment of non-cohesive sediment (-)

(Sfx, Sfy):

friction slope (-)

t :

time (s)

(u, v):

runoff depth-averaged velocity (m/s)

u * :

(u*, v*), phase-averaged velocity of debris flow (ms−1)

u f :

(uf, vf), velocity for the fluid phase (ms−1)

u f b :

(ufb, vfb), erosion velocity for the fluid phase at the bottom boundary (ms−1)

u s :

(us, vs), velocity for the solid phase (ms−1)

u s b :

(usb, vsb), erosion velocity for the solid phase at the bottom boundary (ms−1)

V T :

terminal velocity of a particle falling in a fluid (ms−1)

x, y, z :

coordinate lines/flow directions (-)

z b :

basal topography elevation (m)

α f :

volumetric fraction for the fluid phase of debris flow (-)

α s :

volumetric fraction for the solid phase of debris flow (-)

βxs, βxf, βys, βyf :

combined parameter(-)

γ :

density ratio (-)

ε :

aspect ratio of debris flow (-)

(ζ, uc, δ):

coefficient related to entrainment of cohesive sediment (-)

η :

pore pressure ratio of the bed material (-)

θ :

soil moisture content (-)

θ m :

initial soil moisture content (-)

θ s :

maximum soil moisture content (-)

μc :

pure fluid viscosity (Pa s)

μf :

viscosity of the fluid phase of debris flow (Pa s)

ρ :

water–sediment mixture density (kg/m3)

ρ f :

water density (kg/m3)

ρ s :

solid density (kg/m3)

ρ * :

mixture density of debris flow (kg m−3)

τ b :

total basal shear traction (N)

τ bf :

basal shear stress for the fluid phase (N)

τ bs :

basal shear stress for the solid phase (N)

τ r :

sediment shear resistance from the erodible bed (N)

υ :

the water kinematic viscosity (m2/s)

φ bed :

Coulomb friction angle of the basal surface (°)

φ bin :

internal friction angle of the bed material (°)

χ :

velocity shape factor in vertical direction (-)

ω:

particle settling velocity (m/s)

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Funding

This work was supported by the Original Innovation Program-CAS (grant no. ZDBS-LY-DQC039), National Natural Science Foundation of China (grant nos. 41907241, 41790433), NSFCICIMOD (grant no. 41661144041), and CAS “Light of West China” Program.

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Authors and Affiliations

  1. Key Laboratory of Mountain Hazards and Surface Process, Institute of Mountain Hazards and Environment, Chinese Academy of Sciences, Chengdu, 610041, China

    Wei Liu & Siming He

  2. University of Chinese Academy of Sciences, Beijing, 100049, China

    Wei Liu & Siming He

  3. Center for Excellence in Tibetan Plateau Earth Sciences, Chinese Academy of Sciences, Beijing, 100101, China

    Siming He

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  1. Wei Liu
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Key Points

• An integrated model, which couples initial conditions, movement mechanisms, and entrainment effects, of debris flow formation and propagation processes is presented.

• Experimental and case applications support the model’s reliability in simulating infiltration, runoff, entrainment, and debris flow propagation.

• The model facilitates hazard and risk assessment applications.

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Liu, W., He, S. Comprehensive modelling of runoff-generated debris flow from formation to propagation in a catchment. Landslides 17, 1529–1544 (2020). https://doi.org/10.1007/s10346-020-01383-w

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