Characterisation of the heterogeneity of a sand specimen in triaxial compression using x-ray CT and representative elementary volumes

Abstract

Standard laboratory tests, such as the triaxial test, are often considered to be element tests. But, when observing such a test, it becomes obvious that this assumption of homogeneity is far from accurate. The localisation of strain is often visible to the naked eye and becomes even more obvious when observed on the grain scale. Other variables, such as those describing the soil fabric, are expected to localise as well. In this work, two sand samples are analysed at different loading states regarding the heterogeneity of three soil variables: void ratio, coordination number and contact orientation anisotropy. For this purpose, the size of a Representative Elementary Volume (REV) is determined using three criteria: the convergence of the mean and variance of the variables with increasing element size as well as a χ2-test. The size of the REV is varying depending on the chosen variable but almost the same for the two specimens when related to the mean grain diameter d50. The REV is placed in a regular grid throughout the specimen and the three variables are determined for each REV. The stochastic as well as spatial heterogeneity is identified for each specimen. As one of the samples is analysed for different loading states throughout a triaxial test, the evolution of the soil heterogeneity is identified. A localisation of all three variables can be observed at the end of the triaxial test as well as a strong initial heterogeneity for both sand samples.