Density dependent macro-micro behavior of granular materials in general triaxial loading for varying intermediate principal stress using DEM

Abstract

This study presents the density dependent behavior of granular materials for varying intermediate principal stress $(\sigma _{{{2}}})$ in general triaxial loading using the discrete element method (DEM). The variation of intermediate principal stress is represented by a non-dimensional parameter $b[={(\sigma _{{{2}}}-\sigma _{{{3}}})}/{(\sigma _{{{1}}} -\sigma _{{{3}}})}]$, where $\sigma _{{{1}}}$ and $\sigma _{{{3}}}$ are the major and minor principal stresses, respectively. Isotropically compressed dense and loose samples were prepared numerically using the periodic boundaries. The numerical dense and loose samples were subjected to shear deformation under strain controlled condition for different $b$ values ranging from 0 to 1. The simulated macro results depict that the friction angle increases with $b$ until it reaches a peak value and beyond the peak, the friction angle decreases with $b$ regardless of the density of sample. A unique relationship between dilatancy index and equivalent deviatoric strain exists at small strain level for different $b$ values when dense sample is considered. By contrast, the same relationship for loose sample does not show uniqueness. The relationships among the major, intermediate and minor principal strains depict non-linear behavior. The non-linearity is dominant for loose sample. The fluctuation in the evolution of strain increment vector direction is dominant in loose sample than dense sample. The evolution of different micro results is presented as well. It is noted that a unique relationship exists between the stress ratio and the fabric measure regardless of $b$ and the density of sample when strong contacts are considered.