Foreword 1. Introduction 2. Interactions at the grain level 3. The granular solid: statics and elasticity 4. The granular solid: plasticity 5. Granular gases 6. The granular liquid 7. Immersed granular media 8. Erosion and sediment transport 9. Geomorphology References Index.

Granular Media: Between Fluid and Solid

[1] This paper presents a new, generalized two-phase debris flow model that includes many essential physical phenomena. The model employs the Mohr-Coulomb plasticity for the solid stress, and the fluid stress is modeled as a solid-volume-fraction-gradient-enhanced non-Newtonian viscous stress. The generalized interfacial momentum transfer includes viscous drag, buoyancy, and virtual mass. A new, generalized drag force is proposed that covers both solid-like and fluid-like contributions, and can be applied to drag ranging from linear to quadratic. Strong coupling between the solid- and the fluid-momentum transfer leads to simultaneous deformation, mixing, and separation of the phases. Inclusion of the non-Newtonian viscous stresses is important in several aspects. The evolution, advection, and diffusion of the solid-volume fraction plays an important role. The model, which includes three innovative, fundamentally new, and dominant physical aspects (enhanced viscous stress, virtual mass, generalized drag) constitutes the most generalized two-phase flow model to date, and can reproduce results from most previous simple models that consider single- and two-phase avalanches and debris flows as special cases. Numerical results indicate that the model can adequately describe the complex dynamics of subaerial two-phase debris flows, particle-laden and dispersive flows, sediment transport, and submarine debris flows and associated phenomena.

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A general two-phase debris flow model

Suspensions are composed of mixtures of particles and fluid and are omnipresent in natural phenomena and in industrial processes. The present paper addresses the rheology of concentrated suspensions of non-colloidal particles. While hydrodynamic interactions or lubrication forces between the particles are important in the dilute regime, they become of lesser significance when the concentration is increased, and direct particle contacts become dominant in the rheological response of concentrated suspensions, particularly those close to the maximum volume fraction where the suspension ceases to flow. The rheology of these dense suspensions can be approached via a diversity of approaches that the paper introduces successively. The mixture of particles and fluid can be seen as a fluid with effective rheological properties but also as a two-phase system wherein the fluid and particles can experience relative motion. Rheometry can be undertaken at an imposed volume fraction but also at imposed values of particle normal stress, which is particularly suited to yield examination of the rheology close to the jamming transition. The response of suspensions to unsteady or transient flows provides access to different features of the suspension rheology. Finally, beyond the problem of suspension of rigid, non-colloidal spheres in a Newtonian fluid, there are a great variety of complex mixtures of particles and fluid that remain relatively unexplored.

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Rheology of dense granular suspensions

To simulate debris-flow behaviour from initiation to deposition, we derive a depth-averaged, two-phase model that combines concepts of critical-state soil mechanics, grain-flow mechanics and fluid ...

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2013.0819

A depth-averaged debris-flow model that includes the effects of evolving dilatancy. I. Physical basis

[1] Analyses of mass and momentum exchange between a debris flow or avalanche and an underlying sediment layer aid interpretations and predictions of bed-sediment entrainment rates. A preliminary analysis assesses the behavior of a Coulomb slide block that entrains bed material as it descends a uniform slope. The analysis demonstrates that the block's momentum can grow unstably, even in the presence of limited entrainment efficiency. A more-detailed, depth-integrated continuum analysis of interacting, deformable bodies identifies mechanical controls on entrainment efficiency, and shows that entrainment rates satisfy a jump condition that involves shear-traction and velocity discontinuities at the flow-bed boundary. Explicit predictions of the entrainment rateEresult from making reasonable assumptions about flow velocity profiles and boundary shear tractions. For Coulomb-friction tractions, predicted entrainment rates are sensitive to pore fluid pressures that develop in bed sediment as it is overridden. In the simplest scenario the bed sediment liquefies completely, and the entrainment-rate equation reduces toE = 2μ1gh1 cos θ(1 − λ1)/ v¯1, where θ is the slope angle, μ1 is the flow's Coulomb friction coefficient, h1 is its thickness, λ1 is its degree of liquefaction, and v¯1is its depth-averaged velocity. For values ofλ1ranging from 0.5 to 0.8, this equation predicts entrainment rates consistent with rates of 0.05 to 0.1 m/s measured in large-scale debris-flow experiments in which wet sediment beds liquefied almost completely. The propensity for bed liquefaction depends on several factors, including sediment porosity, permeability, and thickness, and rates of compression and shear deformation that occur when beds are overridden.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2011JF002189

Elementary theory of bed-sediment entrainment by debris flows and avalanches

Geophysical mass flows—debris flows, avalanches, landslides—can contain O (10 6 –10 10 )m 3 or more of material, often a mixture of soil and rocks with a significant quantity of interstitial fluid. These flows can be tens of meters in depth and hundreds of meters in length. The range of scales and the rheology of this mixture presents significant modelling and computational challenges. This paper describes a depth-averaged ‘thin layer’ model of geophysical mass flows containing a mixture of solid material and fluid. The model is derived from a ‘two-phase’ or ‘two-fluid’ system of equations commonly used in engineering research. Phenomenological modelling and depth averaging combine to yield a tractable set of equations, a hyperbolic system that describes the motion of the two constituent phases. If the fluid inertia is small, a reduced model system that is easier to solve may be derived.

A two-fluid model for avalanche and debris flows

Geophysical mass flows, such as debris flows, volcanic avalanches, and landslides, can be initiated consequent to volcanic activities. These flows can be tens of meters in depth and hundreds of meters in length and contain $O(10^6$–$10^8)\,\mathrm{m}^3$ or more of material. The bulk flow can easily erode the volcanic rocks and soil on the slopes of mountains, thereby increasing their size several fold. The range of scales and the rheology of these flows, especially with erosion, present significant modeling and computational challenges. This paper describes an approach to incorporate the interaction between a mass flow, an erodible bed, and the topography of that bed. The kinetic theory for rapid granular flow is employed to model a “mixing” layer, the interface between the flowing material and the basal surface and the area where erosion occurs. A tractable set of equations is derived, a hyperbolic system that describes the motion of a granular flow and the elevation of erodible bed.

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Long Le

Papers

A two-fluid model for avalanche and debris flows

A Model for Granular Flows over an Erodible Surface