Grain-scale experimental investigation of localised deformation in sand: a discrete particle tracking approach

Abstract

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.

Revisiting localized deformation in sand with complex systems

“…grain-scale (measurement points being around 0.4 mm apart), using DIC [15]. The spatial distributions of the maximum shear strain corresponding to those in figure 6a for the four selected strain intervals discussed earlier are shown in figure 6b.…”

“…the difference between axial stress and cell pressure) is applied by advancing a piston which compresses the sample axially, at a constant speed. Further details concerning the material and the experimental technique are given in Andò et al [15]. The response is typical of dense sand as shown in the electronic supplementary material: there is a peak stress deviator at around 5.5 per cent imposed axial strain, followed by a reduction in stress, tending towards a 'residual' value at the end of the test.…”

“…This displacement field is 'inclined' relative to the direction of loading (evident in the tilted gradation of the colour map) because the sample axis is initially tilted by 1.4 • . The key aspect to note is that the change in the displacement field is gradual in the initial stages of loading (01-02, 02-04); as loading proceeds, particularly from around the peak stress ratio, the displacement field portrays to an increasing extent a 'shear band' that is some seven to eight grains wide by the last interval [15][16]. Using the benefit of hindsight, a retrospective analysis of the displacement field from vertical and cross-sectional slices of the sample, starting from the last interval 15-16 back to 01-02, reveals a contrasting trend: relative to the shear band boundaries marked by the lines of distinct step change in gradient in 15-16, the displacement field in 01-02 and 02-04 changes smoothly at a near constant rate in the direction perpendicular to the shear band.…”

High-resolution X-ray computed tomography in geosciences: A review of the current technology and applications

“…Between two scans, the sample has often been removed from the scanner, creating the need for alignment . The second subcategory is non-rigid deformation, where a sample has deformed and deformation needs to be quantified (Ando et al, 2012;Hall et al, 2010).…”

Micro origins for macro behavior in granular media

“…Traditionally, many relevant studies have been carried out based on experiments or continuum modeling [39,40]. The trend in methodology on this topic has recently shifted to combined, multiple approaches including advanced experimental tools such as X-Ray CT [41] and discrete element methods or computational multiscale modeling approaches [26,42]. Hadda et al [43] employed the discrete element method to examine particle-level energy decomposition in relation with their signature contributions to macroscopic failure modes including shear banding and diffuse failure.…”