A multi-scale approach is proposed as an attempt to assess internal erosion induced effects on the mechanical properties of a granular medium. In this first analysis, the degradation of a granular assembly is simulated through the progressive removal of its smallest particles for both isotropic and anisotropic stress states. A discrete element model as well as a micromechanical constitutive relation is used to compare induced deformations and mechanical properties changes along the extraction process. The shear strength and flow properties appear to be strongly modified by this degradation: both models highlight the occurrence of failure during degradation process for stress states beyond the characteristic state; and, for unfailed samples, a change from a typical dilatant to a typical contractant behavior after degradation.