Abstract
Debris flow deposits in natural channels typically have a wide grain size distribution (GSD). The effects of bed sediment GSD on the basal entrainment rate are neglected in current debris flow erosion models. Field investigations have detected three different vertical graded bedding structures: normal, inverse, and mixed-gradation, characterized by discontinuous gradation sediment and almost without intermediate-sized particles. This study conducted small-scale flume experiments to investigate the debris flow resistance forces and entrainment characteristics by incorporating the effects of discontinuous grading bed sediments. Discontinuous graded bed sediments with varying fine particle content, volumetric water content (VWC), and roundness were designed for comparison. Debris flow resistance in erodible beds generally increased in the group with gravel of larger-sized coarse particle, lower roundness, and higher bed sediment VWC. For discontinuous grading bed sediment, the entrained depths increased in the group with gravel of smaller coarse particle sizes, larger amounts of fine particles, and higher sediment roundness, and decreased with larger VWCs. This abnormality may be attributed to the disproportionately large effects of viscous flow resistance in our small-scale flume tests. The maximum erosion rates of the continuous bed sediment were higher than those of the corresponding discontinuous bed sediment with the same maximum coarse gravel size. This is because, for discontinuous grading bed sediments, localized failure of intermediate-sized sediment grains may cause a large-scale collapse of the solid grain skeleton and enhance basal entrainment rates. A revised formula for calculating the debris flow entrainment rate is proposed by incorporating the kurtosis coefficient, which describes the distribution of discontinuous bed sediments and fine particle content. Our revised formula could facilitate an elaborate estimation of basin erosion and sediment runoff and reveal the development and recession of debris flow fans.
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Abbreviations
- α :
-
Transition angle
- θ :
-
Slope of the erodible bed
- h :
-
Flow depth
- g:
-
Gravity acceleration
- v :
-
Debris flow velocity
- v r :
-
Debris flow velocity in rigid beds
- v e :
-
Debris flow velocity in erodible beds
- ρ :
-
Bulk density of debris flows before entrainment
- ρ′ :
-
Bulk density of debris flows after entrainment
- B * :
-
Kurtosis coefficient
- d max :
-
The maximum diameter of bed sediment
- d 50 :
-
The median diameter of bed sediment
- d′50 :
-
The median diameter of the debris material
- d c :
-
The coarse gravel size of discontinuous grading bed sediment
- d * c :
-
The coarse gravel size of continuous grading bed sediment
- d lack :
-
The size range of the lacking intermediate particles
- D c :
-
The median particle size of the gravel group
- D f :
-
The median particle size of the fine particle group
- P :
-
Fine particle contents
- Z ij :
-
Entrainment depth at each grid point
- V :
-
Total entrained volume of bed sediment
- V * t :
-
Normalized total entrained volume
- E :
-
Average entrainment rate
- E m :
-
Maximum erosion rates at the convex sites
- E k :
-
Size-specific entrainment flux
- E c m :
-
Average entrainment rate calculated based on Wu’s entrainment model
- d k :
-
The diameter of kth of the sediments
- ω k :
-
The settling velocity of the kth particle size
- v μf :
-
Kinematic viscosity of debris slurry
- C ek :
-
The size-specific sediment concentration at capacity
- R :
-
The hydraulic radius
- A k :
-
The areal exposure fraction of the kth particle on bed surface
- f ak :
-
The fraction of the kth size sediment in the active layer
- f :
-
The Darcy-Weisbach resistance coefficient
- f r :
-
The Darcy-Weisbach resistance coefficient in rigid beds
- f e :
-
The Darcy-Weisbach resistance coefficient in erodible beds
- n′ :
-
Manning roughness corresponding to grain resistance in debris flow.
- τ b :
-
Basal shear stress
- C z :
-
Chezy coefficient
- φ′ :
-
Internal friction angle of the debris mixture used in the Voellmy model
- n :
-
The internal Manning roughness within the debris mixture
- τ ck :
-
The critical shear stress for incipient motion of the kth bed sediment
- ψ k :
-
The correction coefficient for the bed slope
- η k :
-
The correction factor representing the hidden and exposure effects in multi-particle sizes of bed sediments
- P hk :
-
The total hidden probabilities of particles dk
- P ek :
-
The total exposed probabilities of particles dk
- a, b :
-
Dimensionless coefficients
- χ :
-
Dimensionless parameters
- Fr :
-
The Froude number
- N B :
-
The Bagnold number
- N S :
-
The Savage number
- N F :
-
The friction number
- N m :
-
The mass number
- ρ s :
-
Bulk density of sediment particle
- μ :
-
Interstitial fluid viscosity
- ν s :
-
Volumetric solid fraction
- ν f :
-
Volumetric fluid fraction
- δ :
-
Characteristic grain size
- ρ f :
-
Interstitial fluid density
- \(\dot \gamma\) :
-
Shear Rate
- ϕ k :
-
The repose angle of the bed material
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Acknowledgments
The study was funded by the National Natural Science Foundation of China (Grant No. 41801002), the National Key Foundation for Exploring Scientific Instrument Program (Grant No. 42027806), the Natural Science Foundation of Shanxi Province (Grant No. 2021JQ-452), the Second Tibetan Plateau Scientific Expedition and Research Program (STEP) (Grant No. 2019QZKK0902) and the National Key Research and Development Plan (Grant No. 2018YFC1504703). The authors are grateful for the support of the debris flow simulation test platform of the Department of Geology, Northwest University, China. Flume experiments were benefited from the participation of many people, especially WANG Fei, LI Shuai, XIONG Youbo, REN Wang, LI Chenglin, JIAO Shaotong and WEI Yao.
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Li, P., Wang, Jd., Hu, Kh. et al. Experimental investigation on debris flow resistance and entrainment characteristics: effects of the erodible bed with discontinuous grading. J. Mt. Sci. 19, 2397–2419 (2022). https://doi.org/10.1007/s11629-022-7365-y
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DOI: https://doi.org/10.1007/s11629-022-7365-y