Imaging sand deformation at the grain scale

Abstract

Shear banding, the localization of deformation into thin zones of intense shearing, is a phenomenon commonly observed in sand and other granular materials. The most valuable experimental contributions to the understanding of shear banding are those measuring, in one way or another, the full field of deformation in the specimen – which is the only means by which test results can be appropriately interpreted [1]. Full-field analysis of strain localization in sand possibly started in the late 1960s in Cambridge and was continued over the last decades in the work of a number of groups, including Grenoble. Most of these works were performed using specifically designed plane strain devices, and used a range of full-field methods, the more advanced of which allowed observation of the specimen throughout loading by optical methods, thereby permitting measurement of the evolving strain field. In the 1960s, x-ray radiography was first used to measure 2D strain fields in sand. From the early 1980s, x-ray tomography was used by a few groups working in geomechanics, including Desrues and coworkers (see [2] for a review). These studies provided valuable 3D information on localization patterning in sand, and also demonstrated the potential of x-ray tomography as a quantitative tool, e.g., for measuring the evolution of void ratio inside a shear band and its relation to critical state. The recent advent of x-ray micro tomography, originally with synchrotron sources and now with laboratory scanners, has provided much finer spatial resolution, which opens up new possibilities for understanding the mechanics of granular media (in 3D) at the scale of the grain. For example, Oda and coworkers [3] presented micro tomography images of sand grains inside a shear band, showing organized structures that would not have been seen in standard x-ray tomography images (because of insufficient resolution) and that had only previously been observed in 2D thin sections. It should be noted that the images by Oda were obtained post-mortem, i.e., after testing. However, a full understanding of the mechanisms of (localized) deformation can only be achieved if the entire deformation process is followed throughout a test while the specimen deforms. This is possible by using in-situ x-ray tomography (in-situ meaning x-ray scanning at the same time as loading). A number of such in-situ studies for triaxial tests on sand were performed over the last ten years or so, mostly using medical or industrial tomography systems, and in a few cases synchrotron micro tomography, which allows identifying individual sand grains and tracking their displacements throughout a test. The aim of the present study is both to observe the material evolution under loading with grainscale resolution and to image the deformation processes. In recent work [4], we applied 3D Volumetric Digital Image Correlation (V-DIC) to a sequence of x-ray tomography images taken during a triaxial test on a clay-rock specimen. In the present paper, we show results of a similar DICbased analysis of deformation for sand specimens under triaxial compression. Two different granular materials were tested: Hostun sand, a fine-grained, angular siliceous sand with a mean grain size (D50) of about 300 m, and Caicos ooid, a material characterized by spheroidal grains with D50 of about 420 m. In addition, we have developed a grain-scale V-DIC method that permits the characterization of the full kinematics (i.e., 3D displacements and rotations) of all the individual © Owned by the authors, published by EDP Sciences, 2010 DOI:10.1051/epjconf/20100622021 EPJ Web of Conferences 6, 22021 (2010)