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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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.

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.

Combining x-ray tomography and three-dimensional (3D) image analysis has finally opened the way for experimental micro-(geo)mechanics, allowing access to different scales of interest. When these correspond to a scale that has been imaged at high spatial resolution, high-quality measurements can be obtained (e.g. 3D displacements and rotations of individual grains of sand sample under load). However, there are issues when the scale of interest is smaller, for example the characterisation of grain-to-grain contacts (their orientations and evolution) or production of fines by grain breakage. This paper presents a short selection of new grain-scale measurements obtained using existing techniques. The challenges associated with smaller scale measurements on the same images are also discussed through a few examples from ongoing work.

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Complex systems techniques are used to analyse X-ray micro-CT measurements of grain kinematics in Hostun sand under triaxial compression. Network nodes with the least mean shortest path length to all other nodes, or highest relative closeness centrality, reside in the region where the persistent shear band ultimately develops. This trend, whereby a group of grains distinguishes themselves from the rest in the sample, remarkably manifests from the onset of loading. The shear band's boundaries and thickness, evident from the network communities' borders and essentially constant mean size, provide corroborating evidence of early detection of strain localization. Our findings raise the possibility that the formation and the location of the persistent shear band may be decided in the nascent stages of loading, well before peak shear stress. Grain-scale digital image correlation strain measurements and statistical tests confirm the results are robust. Moreover, the trends are unambiguously reproduced in a discrete element simulation of plane strain compression.

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