Clay anisotropy: bridging the gap between micro and macro scales

Constitutive models for anisotropic clays incorporate a tensor-valued quantity named the ‘fabric tensor’ to describe the direction-dependent mechanical response of the material. Although the term ‘fabric’ reflects the directional properties at the microscale, this tensor is not actually measured or observed at the microscale but formulated as a mathematical entity and calibrated by best-fitting experimental observations at the macro-scale. This paper presents a first attempt to bridge the gap between micro and macro scales by using direct measurements of the fabric tensor at the microscale to inform a continuum-based constitutive model. Owing to the scarcity of experimental measurements of the fabric in clayey geomaterials, this paper turns to virtual experiments using the discrete-element method (DEM) to quantify the microstructural arrangement and its evolution in response to imposed stress or strain history. The virtual experimental programme was performed in a simplified two-dimensional numerical framework and consisted of a set of virgin radial paths to generate different macroscopic anisotropic responses, quantified by way of the elastic stiffness in the horizontal and vertical direction. An existing constitutive model developed within the framework of thermodynamics with internal variables (TIV) was then used to describe the macroscopic behaviour of the DEM specimens, once the fabric-related parameters had been inferred from particle orientations. The DEM-based TIV model was proven to simulate satisfactorily the numerical compressibility curves for radial compression paths at different stress ratios and, most importantly, to reproduce well the macroscopic anisotropic elastic stiffness and its evolution.