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The loading of a granular material induces anisotropies 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 discrete element 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 …