Two different DEM models are proposed for quantitatively simulating Toyoura sand macroscopic response along various monotonous loading paths and for a wide range of initial densities. The first model adopts spherical particles and compensates for the irregular shapes of Toyoura sand grains by adding an additional rolling resistance stiffness to the classical linear contact model. The second model follows a different strategy whereby rolling stiffness is abandoned in favour of more complex shapes in the form of a few different 3D polyhedrons defined from a 2D micrograph of Toyoura particles. After a preliminary analysis of the number of particles for optimal REV simulations, the two different modelling approaches are calibrated using triaxial compression in so-called drained conditions, adopting a common contact friction angle for the two models. Similar predictive abilities are then obtained along so-called undrained (constant volume) triaxial compression and extension paths. Although it leads to 9-times longer simulations, the polyhedral approach is easier to calibrate regarding the contact parameters. It also enables a more precise description of the microstructure in terms of particle shapes and initial fabric anisotropy, whose crucial role is evidenced in a parametric analysis.