Modelling shallow debris flows of the Coulomb-mixture type over temporally varying topography

Tai, Yih-Chin; Kuo, Chih‐Yu

doi:10.5194/nhess-12-269-2012

Cited by 12 publications

(6 citation statements)

References 33 publications

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“…There is significant potential to apply the friction law (3.10)-(3.12) to geophysical flows such as snow slab avalanches, where there is a clearly defined layer of erodible material on top of the underlying topography. Incorporation of new snow into such flows is a long standing problem and most models (Bouchaud et al 1994;Douady, Andreotti & Daerr 1999;Gray 2001;Doyle et al 2007;Bouchut et al 2008;Tai & Kuo 2008;Gray & Ancey 2009;Iverson 2012;Tai & Kuo 2012;Capart, Hung & Stark 2015) assume that this happens by basal entrainment. In our approach the material is either static or flowing through its entire depth, and there are evolving regions of flow and no flow, which are governed by the effective basal friction law (3.10)-(3.12).…”

Section: Discussionmentioning

confidence: 99%

“…2007; Bouchut et al. 2008; Tai & Kuo 2008; Gray & Ancey 2009; Iverson 2012; Tai & Kuo 2012; Capart, Hung & Stark 2015) assume that this happens by basal entrainment. In our approach the material is either static or flowing through its entire depth, and there are evolving regions of flow and no flow, which are governed by the effective basal friction law (3.10)–(3.12).…”

Section: Discussionmentioning

confidence: 99%

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Frictional hysteresis and particle deposition in granular free-surface flows

et al. 2019

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Shallow granular avalanches on slopes close to repose exhibit hysteretic behaviour. For instance, when a steady-uniform granular flow is brought to rest it leaves a deposit of thickness $h_{stop}(\unicode[STIX]{x1D701})$ on a rough slope inclined at an angle $\unicode[STIX]{x1D701}$ to the horizontal. However, this layer will not spontaneously start to flow again until it is inclined to a higher angle $\unicode[STIX]{x1D701}_{start}$, or the thickness is increased to $h_{start}(\unicode[STIX]{x1D701})>h_{stop}(\unicode[STIX]{x1D701})$. This simple phenomenology leads to a rich variety of flows with co-existing regions of solid-like and fluid-like granular behaviour that evolve in space and time. In particular, frictional hysteresis is directly responsible for the spontaneous formation of self-channelized flows with static levees, retrogressive failures as well as erosion–deposition waves that travel through the material. This paper is motivated by the experimental observation that a travelling-wave develops, when a steady uniform flow of carborundum particles on a bed of larger glass beads, runs out to leave a deposit that is approximately equal to $h_{stop}$. Numerical simulations using the friction law originally proposed by Edwards et al. (J. Fluid Mech., vol. 823, 2017, pp. 278–315) and modified here, demonstrate that there are in fact two travelling waves. One that marks the trailing edge of the steady-uniform flow and another that rapidly deposits the particles, directly connecting the point of minimum dynamic friction (at thickness $h_{\ast }$) with the deposited layer. The first wave moves slightly faster than the second wave, and so there is a slowly expanding region between them in which the flow thins and the particles slow down. An exact inviscid solution for the second travelling wave is derived and it is shown that for a steady-uniform flow of thickness $h_{\ast }$ it produces a deposit close to $h_{stop}$ for all inclination angles. Numerical simulations show that the two-wave structure deposits layers that are approximately equal to $h_{stop}$ for all initial thicknesses. This insensitivity to the initial conditions implies that $h_{stop}$ is a universal quantity, at least for carborundum particles on a bed of larger glass beads. Numerical simulations are therefore able to capture the complete experimental staircase procedure, which is commonly used to determine the $h_{stop}$ and $h_{start}$ curves by progressively increasing the inclination of the chute. In general, however, the deposit thickness may depend on the depth of the flowing layer that generated it, so the most robust way to determine $h_{stop}$ is to measure the deposit thickness from a flow that was moving at the minimum steady-uniform velocity. Finally, some of the pathologies in earlier non-monotonic friction laws are discussed and it is explicitly shown that with these models either steadily travelling deposition waves do not form or they do not leave the correct deposit depth $h_{stop}$.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Frictional hysteresis and particle deposition in granular free-surface flows

et al. 2019

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“…Most current avalanche models try to incorporate erosion and deposition by introducing mass and momentum source terms into the depth-averaged mass and momentum balances (e.g. Bouchaud et al 1994;Douady, Andreotti & Daerr 1999;Gray 2001;Doyle et al 2007;Tai & Kuo 2008;Gray & Ancey 2009;Iverson 2012;Tai & Kuo 2012) and sometimes to augment them with an energy balance equation (e.g. Bouchut et al 2008;Capart, Hung & Stark 2015).…”

Section: Introductionmentioning

confidence: 99%

Formation of levees, troughs and elevated channels by avalanches on erodible slopes

et al. 2017

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Snow avalanches are typically initiated on marginally stable slopes with a surface layer of fresh snow that may easily be incorporated into them. The erosion of snow at the front is fundamental to the dynamics and growth of snow avalanches and they may rapidly bulk up, making them much more destructive than the initial release. Snow may also deposit at the rear, base and sides of the flow and the net balance of erosion and deposition determines whether an avalanche grows or decays. In this paper, small-scale analogue experiments are performed on a rough inclined plane with a static erodible layer of carborundum grains. The static layer is prepared by slowly closing down a flow from a hopper at the top of the slope. This leaves behind a uniform-depth layer of thickness $h_{stop}$ at a given slope inclination. Due to the hysteresis of the rough bed friction law, this layer can then be inclined to higher angles provided that the thickness does not exceed $h_{start}$, which is the maximum depth that can be held static on a rough bed. An avalanche is then initiated on top of the static layer by releasing a fixed volume of carborundum grains. Dependent on the slope inclination and the depth of the static layer three different behaviours are observed. For initial deposit depths above $h_{stop}$, the avalanche rapidly grows in size by progressively entraining more and more grains at the front and sides, and depositing relatively few particles at the base and tail. This leaves behind a trough eroded to a depth below the initial deposit surface and whose maximal areal extent has a triangular shape. Conversely, a release on a shallower slope, with a deposit of thickness $h_{stop}$, leads to net deposition. This time the avalanche leaves behind a levee-flanked channel, the floor of which lies above the level of the initial deposit and narrows downstream. It is also possible to generate avalanches that have a perfect balance between net erosion and deposition. These avalanches propagate perfectly steadily downslope, leaving a constant-width trail with levees flanking a shallow trough cut slightly lower than the initial deposit surface. The cross-section of the trail therefore represents an exact redistribution of the mass reworked from the initial static layer. Granular flow problems involving erosion and deposition are notoriously difficult, because there is no accepted method of modelling the phase transition between static and moving particles. Remarkably, it is shown in this paper that by combining Pouliquen & Forterre’s (J. Fluid Mech., vol. 453, 2002, pp. 133–151) extended friction law with the depth-averaged $\unicode[STIX]{x1D707}(I)$-rheology of Gray & Edwards (J. Fluid Mech., vol. 755, 2014, pp. 503–544) it is possible to develop a two-dimensional shallow-water-like avalanche model that qualitatively captures all of the experimentally observed behaviour. Furthermore, the computed wavespeed, wave peak height and stationary layer thickness, as well as the distance travelled by decaying avalanches, are all in good quantitative agreement with the experiments. This model is therefore likely to have important practical implications for modelling the initiation, growth and decay of snow avalanches for hazard assessment and risk mitigation.

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“…1994; Douady, Andreotti & Daerr 1999; Gray 2001; Doyle et al. 2007; Tai & Kuo 2008; Gray & Ancey 2009; Iverson 2012; Tai & Kuo 2012), which are also sometimes augmented with an energy balance equation (e.g. Bouchut et al.…”

Section: Introductionmentioning

confidence: 99%