SUMMARYExperimental results are presented from the extensive program of drained plane strain compression tests on sand carried out in Grenoble over the last two decades. Systematic analysis of photographs of the deforming specimen allowed for measuring deformations and determining strain fields throughout the test, that is: prior to, at, and after the onset of strain localization. The principles, details and accuracy of the procedure are described, as well as its suitability to properly depict the patterns of deformation. Findings concerning the occurrence and progression of strain localization are discussed. The issues of shear band orientation and thickness are addressed, as well as temporary and persistent complex localization patterns, and the volumetric behaviour inside a band after its formation. The influence of such variables as initial state of the sand (effective stress and relative density), specimen size and slenderness, as well as grain size, is discussed.

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.

Experimental results are presented which characterize the behaviour of a loose, fine-grained, water-saturated sand tested under globally undrained and drained conditions in a plane strain apparatus. The objective of this investigation is to provide insight into the phenomenon of shear banding in loose sand. Together with local measurements of boundary forces and deformations, stereophotogrammetry is used to investigate the progression of strain localization in plane strain compression. Typical results and findings concerning the evolution of non-homogeneous deformation are presented in detail. Shear banding occurred in both undrained and drained experiments on loose masonry sand. In general, temporary modes of strain localization, observed during macroscopically ‘uniform’ deformations of a specimen, gave way to a single, persistent shear band. A clear pattern of onset of the formation of the persistent shear band, mobilization of the maximum effective friction and complete formation of the band was observed in all tests. The stress state when the localization begins is very close to, yet precedes that corresponding to the maximum mobilized friction. The persistent shear bands evolve with changing width and orientation. L'exposé présente les résultats d'essais de compression plane visant à caractériser le comportement de sable meuble, à grains fins et saturé d'ean dans des conditions générales non drainées et drainées. L'objectif de cette étude est de mieux faire comprendre la formation de bandes de cisaillement dans le sable meuble. En plus de mesurer les forces limites et les déformations, on a eu recours à la stéréophotogrammétrie pour étudier la progression de la localisation des tensions sous l'effect d'une compression plane. L'exposé présente en détail les résultats et constatations types concernant l'évolution de déformations non homogénes. Lors d'essais non drainés et drainés, des bandes de cisaillement se sont formées dans du sable de construction meuble. En règlegénérale, la formation d'une seule bande de cisaillement persistante s'est substituée aux modes temporaires de localisation des contraintes, observés pendant des déformations macroscopiquement «uniformes« d'une éprouvette. Dans tous les essais, le début de la formation d'une bande de cisaillement persistante, la mobillsation du frottement efficace maximal et la formation complète de la bande ont suivi un schéma bien défini. L'état de contrainte où commence la localisation est très proche de celui qui correspond au frottement mobilisé maximal, mais le précède. Les bandes de cisaillement persistantes évoluent en fonction de la largeur et de l'orientation

Particle breakage is of fundamental importance for understanding the mechanical behaviour of sands and is relevant to many geotechnical engineering problems. In order to gain new insights into the mechanism of breakage of individual sand particles under single-particle compression, this study combines mechanical tests with three-dimensional X-ray micro-computed tomography (μCT) performed 'in situ', that is, during loading. A novel mini-loading apparatus was developed to perform in-situ compression tests within a laboratory nanofocus X-ray CT. The tests were performed on eight particles, four Leighton Buzzard sand (LBS) particles and four highly decomposed granite (HDG) particles, to study their different fracture mechanisms. A series of image processing and analysing techniques was utilised to obtain both qualitative and quantitative results. The most important factors in determining the fracture patterns of the LBS and HDG particles were found to be particle morphology and initial microstructure, respectively. Versatile fracture patterns deviating from simple vertical splitting were observed, particularly in HDG particles. The change of morphology parameters during loading was found to depend on the fracture mechanisms and material properties, independently of their initial values. The fragments of both the LBS and HDG particles satisfy the fractal distribution, which indicates that the fragmentation is scale invariant. Different energy dissipation mechanisms were found. The energy dissipation by friction gradually prevails against the energy dissipated in generating new surfaces.

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This paper presents discrete element method (DEM) simulations with experimental comparisons at multiple length scales-underscoring the crucial role of particle shape. The simulations build on technological advances in the DEM furnished by level sets (LS-DEM), which enable the mathematical representation of the surface of arbitrarily-shaped particles such as sands. We show that this ability to model shape enables unprecedented capture of the mechanics of granular materials across scales ranging from macroscopic behavior to local behavior to particle behavior. Specifically, the model is able to predict the onset and evolution of shear banding in sands, replicating the most advanced high-fidelity experiments in triaxial compression equipped with sequential X-ray tomography imaging. We present comparisons of the model and experiment at an unprecedented level of quantitative agreement-building a one-to-one model where every particle in the more than 53,000-particle array has its own avatar or numerical twin. Furthermore, the boundary conditions of the experiment are faithfully captured by modeling the membrane effect, as well as the platen displacement and tilting. The results show a computational tool that can give insight into the physics and mechanics of granular materials undergoing shear deformation and failure, with computational times comparable to those of the experiment. One quantitative measure that is extracted from the LS-DEM simulations that is currently not available experimentally is the evolution of three dimensional force chains inside and outside of the shear band. We show that the rotations on the force chains are correlated to the rotations in stress principal directions.