Abstract
Rapid shallow granular flows over inclined planes are often seen in nature in the form of avalanches, landslides and pyroclastic flows. In these situations the flow develops an inversely graded (large at the top) particle-size distribution perpendicular to the plane. As the surface velocity of such flows is larger than the mean velocity, the larger material is transported to the flow front. This causes size segregation in the downstream direction, resulting in a flow front composed of large particles. Since the large particles are often more frictional than the small, the mobility of the flow front is reduced, resulting in a so-called bulbous head. This study focuses on the formation and evolution of this bulbous head, which we show to emerge in both a depth-averaged continuum framework and discrete particle simulations. Furthermore, our numerical solutions of the continuum model converge to a travelling wave solution, which allows for a very efficient computation of the long-time behaviour of the flow. We use small-scale periodic discrete particle simulations to calibrate (close) our continuum framework, and validate the simple one-dimensional (1-D) model with full-scale 3-D discrete particle simulations. The comparison shows that there are conditions under which the model works surprisingly well given the strong approximations made; for example, instantaneous vertical segregation.
Highlights
For accurate zonation and risk assessment, it is important to accurately predict the distance to which hazardous particulate natural flows such as debris flows, pyroclastic flows or snow slab avalanches might travel (Dalbey et al 2008)
We demonstrate that the bulbous head develops in three-dimensional discrete particle simulations, with reasonable agreement between the simple one-dimensional continuum model and the fully three-dimensional discrete particle simulations
This is exactly the shock speed that we see, which is significantly lower than the outflow speed. This difference in uf and uout leads to a net transport of large particles to the front, causing the bulbous head to grow in volume
Summary
For accurate zonation and risk assessment, it is important to accurately predict the distance to which hazardous particulate natural flows such as debris flows, pyroclastic flows or snow slab avalanches might travel (Dalbey et al 2008). We focus on bidisperse granular materials, i.e. materials consisting of just two constituents of different sizes This greatly simplifies the problem, while maintaining the leading-order segregation behaviour (Pouliquen & Vallance 1999; Goujon, Dalloz-Dubrujeaud & Thomas 2007; Gray & Ancey 2009). This depth-averaged model can be coupled to single-phase shallow layer models to investigate the mobility feedback that segregation provides (Woodhouse et al 2012) This simple model represents the leading-order behaviour of the flow, as demonstrated by the fact that Woodhouse et al (2012) successfully showed it can reproduce the fingering instability of bidisperse granular flow fronts.
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