Stress-induced anisotropy in granular materials: fabric, stiffness and permeability
Matthew Kuhn, WaiChing Sun, Qi Wong
The loading of a granular material induces an anisotropy of the particle arrangement (fabric) and of the material's strength, incremental stiffness, and permeability. Thirteen measures of fabric anisotropy are developed, which are arranged in four categories: as preferred orientations of the particle bodies, the particle surfaces, the contact normals, and the void space. Anisotropy of the voids is described through image analysis and with Minkowski tensors. The thirteen measures of anisotropy change during loading, as determined with three-dimensional (3D) discrete element (DEM) simulations of biaxial plane-strain compression with constant mean stress. Assemblies with four different particle shapes were simulated. The measures of contact orientation are the most responsive to loading, and they change greatly at small strains; whereas, the other measures lag the loading process and continue to change beyond the state of peak stress and even after the deviatoric stress has nearly reached a steady state. The paper implements a methodology for characterizing the incremental stiffness of a granular assembly during biaxial loading, with orthotropic loading increments that preserve the principal axes of the the fabric and stiffness tensors. The linear part of the hypoplastic tangential stiffness is monitored with oedometric loading increments. This stiffness increases in the direction of the initial compressive loading but decreases in the direction of extension. Anisotropy of this stiffness is closely correlated with a particular measure of the contact fabric. Permeabilities are measured in three directions with lattice Boltzmann methods at various stages of loading and for assemblies with four particle shapes. Permeability is negatively correlated with the directional mean free path and is positively correlated with pore width, indicating that the anisotropy of permeability that is induced by loading is produced by changes in the directional hydraulic radius.
News about Computational Poromechanics lab at Columbia University.