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Granular materials segregate by size when sheared, which increases the destructive power in avalanches and causes demixing in industrial flows. Here we present a concise theory to describe this phenomenon for systems that for the first time include particles of arbitrary size. The evolution of the grainsize distribution during flow is described based on mass and momentum conservation. The theory is derived in a five-dimensional space, which besides position and time, includes a grainsize coordinate. By coupling the theory with a simple constitutive law we predict the kinematics of the flow, which depends on the grainsize dynamics. We show that the underpinning mechanism controlling segregation is a stress variation with grainsize. The theory, solved by a finite difference scheme, is found to predict the dynamics of segregation consistent with results obtained from discrete element simulations of polydisperse granular flow down inclined planes. Moreover, when applied to bimixtures, the general polydisperse theory reveals the role of grainsize contrast.

SUMMARYThe problem of penetration resistance involves a continuously moving zone of plastic distortion in the soil medium. This has been explored for cone penetration and pile installation, where additional volume is intruded into the soil, using the strain path method with the flow field derived from classical fluid mechanics. This paper focuses on a new generation of penetrometers, which have a much greater projected area than the cone shaft, and introduces a version of the strain path method based on classical upper bound solutions for the penetrometers. The new approach is used to explore the effects of high strain rates, and gradual strength degradation, on the penetration resistance of cylindrical and spherical penetrometers.

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The shapes of standing jumps formed in shallow granular flows down an inclined smooth-based chute are analysed in detail, by varying both the slope and mass discharge. Laboratory tests and analytic jump solutions highlight two important transitions. First, for dense flows at high mass discharge, we observe a transition between steep jumps and more diffuse jumps. The traditional shallow-water equation offers a valid prediction for the thickness of the steep water-like jumps. Diffuse frictional jumps require a more general equation accounting for the forces acting inside the jump volume. Second, moving from dense to dilute flows produces another transition between incompressible and compressible jumps. The observed jump height decrease may be reproduced for a more dilute incoming flow by including experimentally measured density variation in the jump equation. Finally, we briefly discuss the likely relevance to avalanche protection dam design that currently utilises traditional shock equations for incompressible frictionless fluids.