A laboratory-numerical approach for modelling scale effects in dry granular slides

Granular slides are omnipresent in both natural and industrial contexts. Scale effects are changes in physical behaviour of a phenomenon at different geometric scales, such as between a laboratory experiment and a corresponding larger event observed in nature. These scale effects can be significant and can render models of small size inaccurate by underpredicting key characteristics such as ow velocity or runout distance. Although scale effects are highly relevant to granular slides due to the multiplicity of length and time scales in the flow, they are currently not well understood. A laboratory setup under Froude similarity has been developed, allowing dry granular slides to be investigated at a variety of scales, with a channel width configurable between 0.25-1.00 m. Maximum estimated grain Reynolds numbers, which quantify whether the drag force between a particle and the surrounding air act in a turbulent or viscous manner, are found in the range 102-103. A discrete element method (DEM) simulation has also been developed, validated against an axisymmetric column collapse and a granular slide experiment of Hutter and Koch (1995), before being used to model the present laboratory experiments and to examine a granular slide of significantly larger scale. This article discusses the details of this laboratory-numerical approach, with the main aim of examining scale effects related to the grain Reynolds number. Increasing dust formation with increasing scale may also exert influence on laboratory experiments. Overall, significant scale effects have been identified for characteristics such as ow velocity and runout distance in the physical experiments. While the numerical modelling shows good general agreement at the medium scale, it does not capture differences in behaviour seen at the smaller scale, highlighting the importance of physical models in capturing these scale effects

Stress, stress-asymmetry and contact moments in granular matter

The physical nature of contact moments within granular assemblies is reviewed and a new approach is developed for the homogenisation of stress within these materials. This approach revolves around capturing the effects of contact moments through the concept of contact eccentricity. By this method it is possible to calculate an expression for bulk stress that is both symmetric for material in equilibrium and fully consistent with the usual definition of bulk stress as an ensemble average of material stress over a representative volume element. The technique is demonstrated in a simple two dimensional example, as well as a larger scale discrete element modelling simulation of a steady state direct shear experiment

The prediction of permeability with the aid of computer simulations

The particular area of focus for this study is the use of theory to predict the permeability of a material through the use of the Ergun equation and the Kozeny-Carman equation along with computer simulations. The Ergun equation is well known for estimating permeability, and the Kozeny-Carman equation has also beet used to a lesser extent. Existing literature extensively covers the use of these equations with homogeneous materials containing mono-size particles. In this study, ate alternative way is sought to characterize mixtures that is based on the structure of the porosity, or void size, rather than the traditional method of using mean particle diameter. In doing so, this allows the Ergun and Kozeny-Carman equations to be rewritten to provide for an expansion in the type of mixtures that they can be applied to. Results are presented in this article on the application of these equations to mixtures including mono-size particles, then modified to include binary and distributed mixtures

The effects of particle dynamics on the calculation of bulk stress in granular media

Expressions for bulk stress within a granular material in a dynamic setting are reviewed and explicitly derived for assemblies of three dimensional arbitrary shaped particles. By employing classical continuum and rigid body mechanics, the mean stress tensor for a single particle is separated into three distinct components; the familiar Love-Webber formula describing the direct effect of contacts, a component due to the net unbalanced moment arising from contact and a symmetric term due to the centripetal acceleration of material within the particle. A case is made that the latter term be ignored without exception when determining bulk stress within an assembly of particles. In the absence of this centripetal term an important observation is made regarding the nature of the symmetry in the stress tensor for certain types of particles; in the case of particles with cubic symmetry, the effects of dynamics on the bulk stress in an assembly is captured by an entirely skew-symmetric tensor. In this situation, it is recognised that the symmetric part of the Love-Webber formula is all that is required for defining the mean stress tensor within an assembly - regardless of the dynamics of the system