The discrete numerical method is recognised today as a powerful method to describe the constitutive behaviour of granular media at both the scale of particles and the scale of the representative elementary volume. This method is also more and more used to address boundary value problems in particular when large deformations may occur or when fluid-solid interactions are involved as, for instance, for internal soil erosion problems. Such discrete numerical models are often calibrated and validated with respect to direct shear tests or drained triaxial compressions. However, even if the models provide satisfying results for these loading paths compared to experimental measurements, their validation with respect to more complex loading paths as the isochoric compression or the path at constant stress deviator still present difficulties, in particular for initially loose granular assemblies. This article investigates the importance of the description of the anisotropy of the initial fabric and of the inter-particle friction law in the simulated responses of loose granular assembly to different kinds of loading paths. It shows how the combination of both can modify importantly the simulated responses to some kinds of loading paths. This investigation is carried out for a numerical discrete model made of spheres by comparison with experimental results on sand. The real shape of particles is considered by introducing rolling resistance at contacts into the model, in order to keep a relatively light model and the possibility to tackle further boundary value problems with a limited computational cost.