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In the mechanics of granular materials, interparticle contacts play a major role. These have been historically difficult to study experimentally, but the advent of x-ray micro tomography allows the identification of all the thousands of individual particles needed for representative mechanical testing. This paper studies the metrology of detecting interparticle contacts and measuring their orientation from such images. Using synthetic images of spheres, and high-resolution tomographies of two very different granular materials (spherical and very angular) as ground truths we find that these measurements are far from trivial. For example, if a physically-correct threshold is used to separate particles from pores there is a systematic over-detection of contacts. We propose a method of improvement that is effective for non-angular particles. When contact orientations are measured from the pixels that make up the contact area, standard watershed approaches make significant systematic errors. We confirm and build upon previous results showing the improvement in orientation measurement using a refined notion of particle separation. Building on this solid basis, future work should focus on a link between contact topology and measurement error, as well as evaluating the use of local surface normals for orientation measurement.

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The mechanical behaviour of geomaterials is complex and, as a consequence, material models form an important part of any numerical analysis in geotechnical engineering. There are so many constitutive models already available that an external observer might well question whether further constitutive models should be developed or, rather, existing models should somehow be compared and evaluated. There is no consensus within the geotechnical engineering community in addressing this question. Practising engineers are at the mercy of the model developers as they try to discover which model might be suitable for which purpose. The developers themselves are rarely impartial in their evaluation: they will typically extol the virtues of their own modelling framework while at the same time recommending further enhancement.However, there is, in our opinion, a logical way to respond to the question. The evaluation of constitutive models should be in the hands of researchers and practitioners who wish to make use of the models for solving practical problems; leaving the developers to respond to their objective conclusions and use them for further improvement of the models. Unfortunately, the current state of constitutive modelling does not permit this line of thinking to be followed. Users of constitutive models generally have neither the time nor the expertise to implement the models into finite element (FE) codes by themselves and therefore their choice of models remains confined to the few (often primitive) models that happen to be already available in commercial FE codes or, perhaps, they may have access only to particular models that are being developed at their own research institutions. *

SUMMARYThe paper is concerned with shear localization in the form of a spontaneous shear zone inside a granular material during a plane strain compression test. The in#uence of an initial void ratio, pressure and a mean grain diameter on the thickness of a shear zone is investigated. A plane strain compression test with dry sand is numerically modelled with a "nite element method taking into account a polar hypoplastic constitutive relation which was laid down within a polar (Cosserat) continuum. The relation was obtained through an extension of a non-polar hypoplastic constitutive law according to Gudehus and Bauer by polar quantities: rotations, curvatures, couple stresses and a characteristic length. It can reproduce the essential features of granular bodies during shear localization. The material constants can be easily calibrated. The FEcalculations demonstrate an increase in the thickness of the shear zone with increasing initial void ratio, pressure level and mean grain diameter. Polar e!ects manifested by the appearance of grain rotations and couple stresses are only signi"cant in the shear zone. A comparison between numerical calculations and experimental results shows a satisfying agreement.

Numerous studies have shown that the fabric of granular materials plays a fundamental role in its macroscopic behaviour. Due to technical limitations, this fabric remained inaccessible in real experiments until recently when x-ray tomography became accessible. However, determining the fabric from tomographic images is relatively challenging, due to various inherent imaging properties. Triaxial experiments on natural sands are chosen to investigate the contact fabric evolution. Two different observation windows in the specimen are chosen for the contact fabric analysis: one inside and another one outside a shear band. Individual contact orientations are measured using advanced image analysis approaches within these windows. The fabric is then statistically captured using a second order tensor and the evolution of its anisotropy is related to the macroscopic behaviour.

SUMMARYA new version of a hypoplastic constitutive equation is presented which is characterized by the introduction of a stress-like internal parameter called back stress. The back stress is a function of the void ratio and of the hydrostatic stress. Using a unique set of material constants, the new constitutive equation describes many aspects of the behaviour of cohesionless soils including the influence of density and stress level. This is demonstrated by a series of verification tests. The determination of the material constants from laboratory tests is described analytically.