A numerical campaign by means of the Discrete Element Method (DEM) was carried out in order to investigate the accuracy of the assumption of quasi-static (QS) conditions in DEM experiments. The dimensionless inertial number, , was considered in order to assess the inertia of the system at both the peak and critical states of the material. DEM triaxial tests were run in a 3D periodic cell at increasing inertial number (e.g. loading rate). The classical Hert-Mindlin no-slip solution was employed at the contact level and grains were assigned with realistic properties of silica sands. Furthermore, a realistic wide particles size distribution was adopted.
Macroscopic observations show that the QS limit is not approached even for very small inertial numbers, i.e. I≈10−5, in contrast with the threshold identified by Roux and Combe (2010), i.e. I≤10−3. Nevertheless, the rate dependency of the mechanical response should be interpreted as a result of local dynamic effects (micro-inertial effects) rather than an indication of a time-dependent behaviour. Interestingly, such behaviour was only visible at very small strains, i.e. less than 3%, suggesting that different mechanisms may dominate at the particulate level at different stages of shearing.
The combined influence of inertia and confining stress was then studied in detail at the critical state. Results show that the influence of the applied pressure is non-negligible on the critical void ratio. Nevertheless, the opposite and counterintuitive behaviour is exhibited (i.e. higher void ratios for higher pressures) when a constant inertial number I≤10−3 is adopted. A modified definition of limiting inertial number, proportional to the speed of sound, is proposed which appears to produce results in agreement with the principles of critical state theory.