A continuum description of granular flows would be of considerable help in predicting natural geophysical hazards or in designing industrial processes. However, the constitutive equations for dry granular flows, which govern how the material moves under shear, are still a matter of debate. One difficulty is that grains can behave like a solid (in a sand pile), a liquid (when poured from a silo) or a gas (when strongly agitated). For the two extreme regimes, constitutive equations have been proposed based on kinetic theory for collisional rapid flows, and soil mechanics for slow plastic flows. However, the intermediate dense regime, where the granular material flows like a liquid, still lacks a unified view and has motivated many studies over the past decade. The main characteristics of granular liquids are: a yield criterion (a critical shear stress below which flow is not possible) and a complex dependence on shear rate when flowing. In this sense, granular matter shares similarities with classical visco-plastic fluids such as Bingham fluids. Here we propose a new constitutive relation for dense granular flows, inspired by this analogy and recent numerical and experimental work. We then test our three-dimensional (3D) model through experiments on granular flows on a pile between rough sidewalls, in which a complex 3D flow pattern develops. We show that, without any fitting parameter, the model gives quantitative predictions for the flow shape and velocity profiles. Our results support the idea that a simple visco-plastic approach can quantitatively capture granular flow properties, and could serve as a basic tool for modelling more complex flows in geophysical or industrial applications.

https://hal.archives-ouvertes.fr/hal-00118375/document

A constitutive law for dense granular flows

[1] Field observations of mature crustal faults suggest that slip in individual events occurs primarily within a thin shear zone, <1–5 mm, within a finely granulated, ultracataclastic fault core. Relevant weakening processes in large crustal events are therefore suggested to be thermal, and to involve the following: (1) thermal pressurization of pore fluid within and adjacent to the deforming fault core, which reduces the effective normal stress and hence also the shear strength for a given friction coefficient and (2) flash heating at highly stressed frictional microcontacts during rapid slip, which reduces the friction coefficient. (Macroscopic melting, or possibly gel formation in silica-rich lithologies, may become important too at large enough slip.) Theoretical modeling of mechanisms 1 and 2 is constrained with lab-determined hydrologic and poroelastic properties of fault core materials and lab friction studies at high slip rates. Predictions are that strength drop should often be nearly complete at large slip and that the onset of melting should be precluded over much (and, for small enough slip, all) of the seismogenic zone. A testable prediction is of the shear fracture energies that would be implied if actual earthquake ruptures were controlled by those thermal mechanisms. Seismic data have been compiled on the fracture energy of crustal events, including its variation with slip in an event. It is plausibly described by theoretical predictions based on the above mechanisms, within a considerable range of uncertainty of parameter choices, thus allowing the possibility that such thermal weakening prevails in the Earth.

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Heating and weakening of faults during earthquake slip

We review flows of dense cohesionless granular materials, with a special focus on the question of constitutive equations. We first discuss the existence of a dense flow regime characterized by enduring contacts. We then emphasize that dimensional analysis strongly constrains the relation between stresses and shear rates, and show that results from experiments and simulations in different configurations support a description in terms of a frictional visco-plastic constitutive law. We then discuss the successes and limitations of this empirical rheology in light of recent alternative theoretical approaches. Finally, we briefly present depth-averaged methods developed for free surface granular flows.

Flows of Dense Granular Media

Using an original pressure-imposed shear cell, we study the rheology of dense suspensions. We show that they exhibit a viscoplastic behavior similarly to granular media successfully described by a frictional rheology and fully characterized by the evolution of the friction coefficient μ and the volume fraction ϕ with a dimensionless viscous number I(v). Dense suspension and granular media are thus unified under a common framework. These results are shown to be compatible with classical empirical models of suspension rheology and provide a clear determination of constitutive laws close to the jamming transition.

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Unifying suspension and granular rheology.

Statics and kinematics of granular materials

We study the plane shear flow of a dense assembly of dissipative disks using discrete simulation and prescribing the pressure and the shear rate. Those shear states are steady and uniform, and become intermittent in the quasistatic regime. In the limit of rigid grains, the shear state is determined by a single dimensionless number, called the inertial number I , which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasistatic critical state of soil mechanics, while large values of I correspond to the fully collisional regime of kinetic theory. When I increases in the intermediate dense flow regime, we measure an approximately linear decrease of the solid fraction from the maximum packing value, and an approximately linear increase of the effective friction coefficient from the static internal friction value. From those dilatancy and friction laws, we deduce the constitutive law for dense granular flows, with a plastic Coulomb term and a viscous Bagnold term. The mechanical characteristics of the grains (restitution, friction, and elasticity) have a small influence in the dense flow regime. Finally, we show that the evolution of the relative velocity fluctuations and of the contact force anisotropy as a function of I provides a simple explanation of the friction law.

Rheophysics of dense granular materials: Discrete simulation of plane shear flows

Impact of particle shape on breakage of recycled construction and demolition aggregates

In recent years, civil engineers have started to use discrete-element modelling to simulate large-scale soil volumes thanks to technological improvements in both hardware and software. However, exi...

/pdf/numerical-techniques-for-fast-generation-of-large-discrete-dqn3s720pw.pdf

Numerical techniques for fast generation of large discrete-element models

A Three-Dimensional Model For Rock Slopes Based On Micromechanics

In geotechnical applications the success of the discrete element method (DEM) in simulating fundamental aspects of soil behaviour has increased the interest in applications for direct simulation of engineering scale boundary value problems (BVP’s). The main problem is that the method remains relatively expensive in terms of computational cost. A non-negligible part of that cost is related to specimen creation and initialization. As the response of soil is strongly dependant on its initial state (stress and porosity), attaining a specified initial state is a crucial part of a DEM model. Different procedures for controlled sample generation are available. However, applying the existing REV-oriented initialization procedures to such models is inefficient in terms of computational cost and challenging in terms of sample homogeneity. In this work a simple but efficient procedure to initialize large-scale DEM models is presented. Periodic cells are first generated with a sufficient number of particles matching a desired particle size distribution (PSD). The cells are then equilibrated at low-level isotropic stress at target porosity. Once the cell is in equilibrium, it is replicated in space in order to fill the model domain. After the domain is thus filled a few mechanical cycles are needed to re-equilibrate the large domain. The result is a large, homogeneous sample, equilibrated under prescribed stress at the desired porosity. The method is applicable to both isotropic and anisotropic initial stress states, with stress magnitude varying in space.

/pdf/periodic-cells-for-large-scale-problem-initialization-4aput7uybd.pdf

Sacha Emam

Papers

Rheophysics of dense granular materials: Discrete simulation of plane shear flows

Impact of particle shape on breakage of recycled construction and demolition aggregates

Numerical techniques for fast generation of large discrete-element models

A Three-Dimensional Model For Rock Slopes Based On Micromechanics

Periodic cells for large-scale problem initialization