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Effects of bed longitudinal inflexion and sediment porosity on basal entrainment mechanism: insights from laboratory debris flows

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Abstract

Channel morphology and bed sediment erodibility are two crucial factors that significantly affect debris flow entrainment processes. Current debris flow entrainment models mostly hypothesize the erodible beds are infinite with uniform slopes. In this study, a series of small-scale flume experiments were conducted to investigate the effects of bed longitudinal inflexion and sediment porosity on basal entrainment characteristics. Experimental observations revealed that sediment entrainment is negligible at early stages and accelerates rapidly as several erosion points appear. Continual evolution of flow-bed interfaces changes interactions between debris flows and bed sediments, rendering the interfacial shear action involved into a mixed shear and frontal collisional action. Lower bed sediment porosity will change the spatial arrangement and orientation of particle mixture, strengthen the interlocking and anti-slide forces of adjacent sediment particles, and promote the formation of particle clusters, all of which will increase bed sediment resistance to erosion. By examining the post-experimental bed morphology, the slope-cutting amounts and topographic reliefs are determined to positively correlate with longitudinal transition angles. These high topographic reliefs may indicate the propensity of triangular slab erosion, rather than strip-shaped slab erosion, in non-uniform channels with relatively steep erodible beds. Empirical formulas are obtained that denote the relationships among bed sediment strength, channel curvature radius, and sediment porosity through a multi-parameter regression analysis. This study may aid in clarifying the complex coupling effects of spatial variations in debris flow dynamics as well as sediment erodibility and bed morphology in non-uniform channels with abundant seismic loose material.

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Abbreviations

α :

Transition angle

θ 0 :

Slope of the flume baseboard

θ :

Slope of the erodible bed

h:

Flow depth

g :

Gravity acceleration

v:

Debris flow velocity

Fr :

The Froude number

N B :

The Bagnold number

N S :

The Savage number

N F :

The friction number

ρ s :

Bulk density of sediment particle

μ :

Interstitial fluid viscosity

v s :

Volumetric solid fraction

δ :

Characteristic grain size

ρ f :

Interstitial fluid density

\( \dot{\gamma} \) :

Shear rate

ϕ :

Internal friction angle of bed sediment

dmax,d50 :

The maximum and median diameter of bed sediment

η :

Bed sediment porosity

Δh:

Compression height

ρ b :

Bulk density of bed sediment

ρ,ρ 1,ρ 2 :

Bulk density of debris flow

Z :

Total bed entrained depth

V ∗ :

Normalized total entrained volume

\( {Z}_m^{\ast } \) :

Normalized maximum entrained depth

dθ :

Slope cutting amount

Δθ :

Bed relief

E :

Erosion rate

τ b :

Basal shear stress

τ c :

Bed resistance

C g :

Empirical coefficient

τ b _ cvex, τ b _ cave :

Basal shear stress at the convex and concave sites

τ c _ cvex, τ c _ cave :

Back-calculated bed resistance at the convex and concave sites

\( {\tau}_{\mathrm{c}\_\mathrm{cvex}}^{MC},{\tau}_{\mathrm{c}\_\mathrm{cave}}^{MC} \) :

Bed resistance at the convex and concave site based on the Mohr–Coulomb criterion

R cvex, R cave :

Bed curvature radius at the convex and concave sites

E cvex, E cave :

Average erosion rate at the convex and concave sites

a,b,c,d,e,f:

Dimensionless coefficients

χ,ψ :

Dimensionless parameters

K d :

Coefficient of erodibility

Φ:

Granular concentrations in the Kelvin-Helmholtz instabilities

λ :

Erosion wave wavelength

ρ w :

Water density

ω :

Coarse particle content of the debris flow mixture

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Acknowledgements

The authors are grateful for the support of the debris flow simulation test platform of the Department of Geology, Northwest University, China.

Funding

The study is funded by the National Natural Science Foundation of China (Grant No. 41801002), the National Key Research and Development Plan (Grant No. 2018YFC1504703), the National Natural Science Foundation of China (Nos. 41630639), and the National Natural Science Foundation of China (Grant No. 41371039).

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Authors and Affiliations

  1. State Key Laboratory of Continental Dynamics/Department of Geology, Northwest University, Xi’an, 710069, Shaanxi, China

    Pu Li & Jiading Wang

  2. Key Laboratory of Mountain Hazards and Earth Surface Processes, Chinese Academy of Sciences, Chengdu, 610041, Sichuan, China

    Kaiheng Hu

  3. Institute of Mountain Hazards and Environment, Chinese Academy of Sciences & Ministry of Water Conservancy, Chengdu, 610041, Sichuan, China

    Kaiheng Hu

  4. Sichuan Tianshengyuan Environmental Services Co., Ltd, Chengdu, 610032, China

    Fei Shen

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Li, P., Wang, J., Hu, K. et al. Effects of bed longitudinal inflexion and sediment porosity on basal entrainment mechanism: insights from laboratory debris flows. Landslides 18, 3041–3062 (2021). https://doi.org/10.1007/s10346-020-01618-w

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