Representative elementary volume analysis of sands using X-ray computed tomography

The concept of a representative elementary volume (REV) provides an effective means of developing macroscopic measures in the description of granular materials. However, due to the difficulties associated with the measurement and characterization of granular microstructure the existence and size of an REV has remained largely conjectural. This study presents a systematic method to examine the characteristics of the REV using X-ray computed tomography images. The 3-D images of spherical glass beads., Silica sand, and Ottawa sand have been characterized using advanced image processing techniques. An interactive computer program is developed to study porosity variation within a sphere with increasing radius from the images of these materials. The porosity variation of Silica sand and Ottawa sand showed three characteristic regions: an initial fluctuation region due to microscopic variations, a constant plateau region, and a region with a monotonic increase/decrease due to heterogeneity. The homogenous medium of glass beads did not show the last region. The results show that for a random packing of spherical glass beads the REV is about two to three times of the identical average diameter. The radius for Silica sand composed mainly of elongated particles is between 5 to 11 times of d(50), and for Ottawa sand composed mainly of subrounded particles is between 9 to 16 times of d(50).