Heterogeneous and scale-dependent behaviour of an initially dense sand specimen in triaxial compression

Abstract

The heterogeneity of a dense sand specimen in triaxial compression has been revealed in many different studies using tools such as x-ray computed tomography. It has been shown that a significant variation of the soil variables already exists at the initial state and that, if shear banding occurs, all variables localise inside the specimen. To resolve the discrepancy between such observations and the assumption of a homogeneous specimen, which is commonly made in the interpretation of triaxial tests, one could either extract the local soil behaviour rather than the global one or use the initial distribution of the variables as the initial state of a boundary value problem. For both purposes, the size of a representative elementary volume (REV) is determined regarding the void ratio, two contact fabric descriptors, the volumetric and deviatoric strain. The size of the REV is either determined for individual loading states or by considering the evolution of deforming elements throughout the triaxial test. At the final loading state, a REV size of 3.6 \(d_{50}\) is identified, which is also the size where the statistical distribution of the variables becomes independent of the element size. The same size is determined for the deforming elements and is therefore used to extract the soil behaviour from the evolving shear band. The local soil behaviour is found to be much simpler than the global one, which suggests that the complexity of the global behaviour mainly results from homogenising the highly different zones inside the specimen.

Graphical Abstract

Extraction of the soil behaviour inside the evolving shear band with the help of deforming representativeelementary volumes. The volumetric behaviour is represented by the evolution of the void ratio and the evolution ofthe contact fabric anisotropy is closely connected to the stress-strain behaviour. The soil behaviour on the REVscale might form the basis for an alternative approach for the development and calibration of constitutive modelsconsidering the heterogeneity of a soil specimen.