Flow Resistance of Inertial Debris Flows

Berzi, Diego; Larcan, E.

doi:10.1061/(asce)hy.1943-7900.0000664

Cited by 12 publications

(8 citation statements)

References 41 publications

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“…As related to the bed shear stresses, in the CM model, the Manning roughness n is calibrated based on the measured data from Run EB 1. In the BM closure model, the values of the coefficients

\overset{μ}{true}

, χ , and μ w are obtained from Berzi and Larcan (). Table lists the modeling values used in different closure models.…”

Section: Model Applications – Usgs Debris Flow Experimentsmentioning

confidence: 97%

“…Inevitably, empiricism is introduced regarding the bed shear stress estimation, which is common to all models for debris flows. The conventional practice in two‐phase flow modeling, which divides the total bed shear stresses for the fluid–solid mixture into the respective bed shear stress exerted on the fluid and solid phases, is followed in the present study (Iverson, ; Egashira, ; Pudasaini, ; Berzi and Larcan, ):

τ_{b} = τ_{fb} + \sum ((), τ_{s_{k} b})

To estimate the bed shear stresses, two closure models are used and evaluated, noted as ‘CM’ and ‘BM’ respectively. Specifically, in the CM model, the solid phase resistance is determined by the Coulomb friction law (Savage and Hutter, ; Egashira, ), which expresses the collinearity of shear stress and normal stress through a friction coefficient tan δ .…”

Section: Model Closuresmentioning

confidence: 99%

“…In the BM closure model, the solid phase resistance formula derived analytically under steady and uniform conditions by Berzi and Larcan () is employed

τ_{s_{k} b} = ρ_{s} g' h_{sk} j_{s}

where the friction slope j s of solid phase is determined as

j_{s} = \overset{μ}{true} \frac{((), σ - 1) C_{T}}{((), σ - 1) C_{T} + 1} + \frac{5 χ}{2} \frac{{[σ (σ - 1)]}^{1 / 2} C_{T}}{([], ((), σ - 1) C_{T} + 1) cos θ^{1 / 2}} ([], \frac{\overset{truê}{u}}{{\overset{h}{true}}^{3 / 2}} + \frac{2}{7} \frac{1}{χ} \frac{{(σ - 1)}^{1 / 2} cos θ^{1 / 2}}{σ^{1 / 2}} \frac{μ_{w}}{\overset{truê}{W}} \overset{h}{true})

where

\overset{μ}{true}

is the tangent of the angle of repose of the dry granular material in absence of lateral confinement; the ratio of solid to fluid density σ = ρ s / ρ f ; χ is a material coefficient of order unity; μ w is the coefficient of sliding friction; the normalized depth‐averaged solid velocity

\overset{u}{true} = {\overset{true¯}{U}}_{s} / \sqrt{{italicgd}_{m}}

, where

{\overset{true¯}{U}}_{s} = \sum ((), U_{sk} C_{k}) / C_{T}

; the normalized flow thickness

\overset{h}{true}

and channel width

\overset{...}{true}

…”

Section: Model Closuresmentioning

confidence: 99%

“…Consequently, the CM features wide applicability, which essentially is similar to the resistance estimation by the Manning equation widely used in open channel hydraulics. In the BM, the solid phase shear stress formula was built on the theoretical analysis under steady and uniform flow condition due to Berzi and Larcan () without considering the smooth/rough characteristics of the bed. Also, it remains unclear if the parameters in Equation for the fluid phase resistance (Berzi and Jenkins, ) could be properly tuned to gain flexibility as those in the Manning equation.…”

Section: Model Closuresmentioning

confidence: 99%

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A depth‐averaged two‐phase model for debris flows over erodible beds

Cao

et al. 2017

Earth Surf Processes Landf

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Mass exchange between debris flow and the bed plays a vital role in debris flow dynamics. Here a depth‐averaged two‐phase model is proposed for debris flows over erodible beds. Compared to previous depth‐averaged two‐phase models, the present model features a physical step forward by explicitly incorporating the mass exchange between the flow and the bed. A widely used closure model in fluvial hydraulics is employed to estimate the mass exchange between the debris flow and the bed, and an existing relationship for bed entrainment rate is introduced for comparison. Also, two distinct closure models for the bed shear stresses are evaluated. One uses the Coulomb friction law and Manning's equation to determine the solid and fluid resistances respectively, while the other employs an analytically derived formula for the solid phase and the mixing length approach for the fluid phase. A well‐balanced numerical algorithm is applied to solve the governing equations of the model. The present model is first shown to reproduce average sediment concentrations in steady and uniform debris flows over saturated bed as compared to an existing formula underpinned by experimental datasets. Then, it is demonstrated to perform rather well as compared to the full set of USGS large‐scale experimental debris flows over erodible beds, in producing debris flow depth, front location and bed deformation. The effects of initial conditions on debris flow mass and momentum gain are resolved by the present model, which explicitly demonstrates the roles of the wetness, porosity and volume of bed sediments in affecting the flow. By virtue of extended modeling cases, the present model produces debris flow efficiency that, as revealed by existing observations and empirical relations, increases with initial volume, which is enhanced by mass gain from the bed. Copyright © 2017 John Wiley & Sons, Ltd.

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“…As related to the bed shear stresses, in the CM model, the Manning roughness n is calibrated based on the measured data from Run EB 1. In the BM closure model, the values of the coefficients

\overset{μ}{true}

, χ , and μ w are obtained from Berzi and Larcan (). Table lists the modeling values used in different closure models.…”

Section: Model Applications – Usgs Debris Flow Experimentsmentioning

confidence: 97%

τ_{b} = τ_{fb} + \sum ((), τ_{s_{k} b})

Section: Model Closuresmentioning

confidence: 99%

“…In the BM closure model, the solid phase resistance formula derived analytically under steady and uniform conditions by Berzi and Larcan () is employed

τ_{s_{k} b} = ρ_{s} g' h_{sk} j_{s}

where the friction slope j s of solid phase is determined as

j_{s} = \overset{μ}{true} \frac{((), σ - 1) C_{T}}{((), σ - 1) C_{T} + 1} + \frac{5 χ}{2} \frac{{[σ (σ - 1)]}^{1 / 2} C_{T}}{([], ((), σ - 1) C_{T} + 1) cos θ^{1 / 2}} ([], \frac{\overset{truê}{u}}{{\overset{h}{true}}^{3 / 2}} + \frac{2}{7} \frac{1}{χ} \frac{{(σ - 1)}^{1 / 2} cos θ^{1 / 2}}{σ^{1 / 2}} \frac{μ_{w}}{\overset{truê}{W}} \overset{h}{true})

where

\overset{μ}{true}

\overset{u}{true} = {\overset{true¯}{U}}_{s} / \sqrt{{italicgd}_{m}}

, where

{\overset{true¯}{U}}_{s} = \sum ((), U_{sk} C_{k}) / C_{T}

; the normalized flow thickness

\overset{h}{true}

and channel width

\overset{...}{true}

…”

Section: Model Closuresmentioning

confidence: 99%

Section: Model Closuresmentioning

confidence: 99%

See 2 more Smart Citations

A depth‐averaged two‐phase model for debris flows over erodible beds

Cao

et al. 2017

Earth Surf Processes Landf

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show abstract

“…In short, two distinct mechanisms are generally involved in mass exchange with the bed: upward bed sediment entrainment due to interphase and inter-grain size interactions and downward sediment deposition as the result of primarily gravitational action. Following the conventional practice in two-phase flow modelling, the total bed shear stresses for the water-sediment mixture in the lower flow layer are divided into the bed shear stress components exerted respectively on the water and sediment phases [61][62][63]. The solid resistance is determined by the Coulomb friction law [64], which expresses the collinearity of shear stress and normal stress through a 14).…”

Section: Governing Equationsmentioning

confidence: 99%

Barrier lake formation due to landslide impacting a river: A numerical study using a double layer-averaged two-phase flow model

Cao

Cui

et al. 2020

Applied Mathematical Modelling

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 A new double layer-averaged two-phase flow model is proposed for barrier lake formation due to landslide impacting a river  Grains play a key role in driving water movement during subaqueous landslide motion and a two-phase theory is warranted  Grain size effects are revealed, i.e., coarse grains and grain-size uniformity favour barrier lake formation  A new threshold for barrier lake formation is proposed, based on landslide-to-river momentum ratio and grain size 2

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