Discrete element method analysis of non-linear stiffness for granular media

This contribution considers the nonlinearity of stiffness in granular materials using 3D DEM simulations, with a primary focus being placed on three issues. First, it assesses stress-dependent stiffness and density-dependent stiffness based on DEM simulations of monotonic triaxial tests. The modified formulation of hyperbolic relation based on the DEM data is generated to capture stiffness degradation, which can take the various types of an S-shaped curve due to the initial mean effective stress and the sample density. The use of various void ratio correction functions is made to remove the effect of density on the stiffness curve. DEM results reveal that inclusion of the coordination number in both forms of the void ratio function serve a better role in unifying the stiffness dataset from samples with different densities. Second, the framework of kinematic modified yielding points proposed by Jardine (1992) that identifies three main zones (i.e. linear elastic behaviour, non-linear elastic behaviour and elasto-plastic behaviour) provides a benchmark for the gap between the dynamic stiffness and the static stiffness to be studied in an effective manner. A key observation is that the dynamic shear stiffness tends to increase to a peak value before experiencing of a decrease in magnitude. Third, the investigation into the nature of energy dissipation during triaxial shearing tests is made. Several DEM simulations were performed to assess effects of the coefficient of uniformity (C-u) on the non-linear behaviour of granular materials, arriving at some key observations that: (i) a higher amount of work should be input for samples with coarse particles to attain a particular strain level; and (ii) more energy dissipation is observed for samples with a lower C-u value.