The mechanical behavior of granular materials is characterized by strong nonlinearity

which is known to be directly linked to the details of the underlying microstructure of contacts

or fabric. The incremental behavior in different loading directions can be obtained by performing a series of axisymmetric stress probing on the specimens. Since the macro- and micro-scale response in different loading directions cannot be obtained experimentally on the very same specimen

discrete element method is employed in the present study

and the stress probing tests on the Rendulic plane are carried out on the specimens of different stress histories

stress states and particle size distributions (PSD). Simulation results indicate that the classic plasticity theories are unable to describe all the observed features when the specimens have different stress histories. However

a linear correlation between the deviatoric strain and the deviatoric part of the contact-normal-based fabric can be obtained. For the specimens with the same relative density

only confining pressure is found to have a significant effect on the linear factor while the linear factor seems to be insensitive to the variation of the stress ratio

stress history and PSD. Since the anisotropy of sand and therefore the impact of stress histories can be characterized by the deviatoric part of the fabric tensor

these observations would provide the necessary micro-scale physical basis for the development of elasto-plastic incremental constitutive relations of granular soils.