International audienceThe objective of this work was to observe and quantify the onset and evolution of localised deformation processes in sand with grain-scale resolution. The key element of the proposed approach is combining state-of-the-art X-ray micro tomography imaging with three-dimensional volumetric digital image correlation techniques. This allows not only the grain-scale details of a deforming sand specimen to be viewed, but also, and more importantly, the evolving three-dimensional displacement and strain fields throughout loading to be assessed. X-ray imaging and digital image correlation have been in the past applied individually to study sand deformation, but the combination of these two methods to study the kinematics of shear band formation at the grain scale is the first novel aspect of this work. Moreover, the authors have developed a completely original grain-scale volumetric digital image correlation method that permits the characterisation of the full kinematics (i.e. three-dimensional displacements and rotations) of all the individual sand grains in a specimen. The results obtained using the discrete volumetric digital image correlation confirm the importance of grain rotations associated with strain localisation

A set of triaxial compression tests on specimens of argillaceous rock were performed under tomographic monitoring at the European Synchrotron Radiation Facility in Grenoble, France, using an original experimental set-up developed at Laboratoire 3S, Grenoble. Complete 3D images of the specimens were recorded throughout each test using X-ray microtomography. Such images were subsequently analysed using a Volumetric Digital Image Correlation software developed at the Laboratoire de Mécanique des Solides in Palaiseau, France. Full-field incremental strain measurements were obtained, which allow to detect the onset of shear strain localisation and to characterise its development in a 3D complex pattern. Volumetric Digital Image Correlation revealed patterns which could not be directly observed from the original tomographic images, because the deformation process in the zones of localised deformation was essentially isochoric (i.e. without volumetric strain), hence not associated to density changes.

Recent developments in the application of x-ray micro-tomography in laboratory geomechanics have allowed all the individual grains of sand in a test sample to be seen and identified uniquely in 3D. Combining such imaging capabilities with experiments carried out "in-situ" within an imaging setup has lead to the possibility of directly observing the mechanisms of deformation as they happen. The challenge has thus become extracting pertinent, quantified information from these rich time-lapse 3D images to elucidate the mechanics at play. This paper presents a new approach (ID-Track) for the quantification of individual grain kinematics (displacements and rotations) of large quantities of sand grains (tens of thousands) in a test sample undergoing loading. With ID-Track, grains are tracked between images based on some geometrical feature(s) that allow their unique identification and matching between images. This differs from Digital Image Correlation (DIC), which makes measurements by recognising patterns between images. Since ID-Track does not use the image of a grain for tracking, it is significantly faster than DIC. The technique is detailed in the paper, and is shown to be fast and simple, giving good measurements of displacements, but suffering in the measurement of rotations when compared to Discrete DIC. Subsequently, results are presented from successful applications of ID-track to triaxial tests on two quite different sands: the angular Hostun sand and the rounded Caicos Ooids. This reveals details on the performance of the technique for different grain shapes and insight into the differences in the grain-scale mechanisms occurring in these two sands as they exhibit strain localisation under triaxial loading.

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The failure of rocks in the brittle regime is generally associated with the appearance of strain localization bands. For very porous rocks, three types of strain localization can be distinguished: extension bands, shear bands, and compaction bands. The first is associated with an extensional normal strain concentration inside the band; the second, with a shear strain concentration; and the third, with a compressive normal strain concentration. This paper shows the continuous transition between pure extension bands and pure compaction bands, via shear bands that evolve from dilating shear bands to compacting shear bands. By an extension to the analysis of Rudnicki and Rice [1975] (RR) on strain localization in pressure sensitive rocks, the prediction of the strain type inside bands at the onset of localization shows that inside shear bands, the shear strain can be associated with a volumetric dilatancy or compaction depending on the constitutive parameters of the material. The theoretical determination of the strain type is in accordance with recent observations of dilating and compacting shear bands in laboratory tests on porous sandstone specimens. A limit for the existence of a localized reduction of porosity within the band is expressed. A physical limit to the RR model is also proposed to insure continuity of the strain mechanism of localization with respect to the constitutive parameters.

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International audienceStrain localisation plays a key role in the deformation of granular materials. Such localisation involves bands of just a few grains wide, which dominate the material's macroscopic response. This grain-scale phenomenon presents challenges for continuum modelling, which is the rationale behind models that explicitly take micro-scales into account. These in turn require micro-scale experimental analysis. In this work, X-ray tomography is used to image a small sample of oolitic sand while it deforms under triaxial compression. Grains are followed with a technique combining recent developments in image correlation and particle tracking. From these rich data, the evolution of the material in a subvolume of a thousand grains inside the sample (which contains 53 000 grains) is presented. The subvolume is chosen to lie inside the shear band that appears at the sample scale. Three-dimensional (3D) grain kinematics are analysed in three increments: the beginning of the test, the peak of the sample's macroscopic axial stress response and the residual stress state. When the sample's deformation is homogeneous (increment one) or fully localised (increment three), the kinematics of the grains in the subvolume appear to be representative of the kinematics occurring at the sample scale, allowing micro-mechanical observations to be made. In the transition from homogeneous to localised deformation (increment two), however, the scale of observation requires a zoom out of the subvolume to the sample scale in order to capture the complex mechanisms at play