The present contribution tackles the issue of incipient conditions for initiation of erosion by a fluid flow at the surface of cohesive materials. To this end, a typical assessment procedure consists in subjecting a soil sample to progressive hydrodynamic stresses induced by a submerged impinging jet flow whose injection velocity is gradually increased. This paper presents the results of an extensive use of this protocol both in experiments and numerical simulations, the latter being based on a coupled DEM and LBM approach. Here we consider the specific case of weakly cemented soils, either made experimentally of glass beads bonded by solid bridges or modelled numerically by a solid bond rheology with a parabolic yield condition involving the micromechanical traction, shearing and bending of the bonds. The results show that, as expected, the hydrodynamic stress for erosion onset substantially increases with solid cohesion as compared to cohesion-less cases but can, however, be satisfactorily predicted by a simple extension of the usual Shields criterion that only applies for cohesion-less granular sediments. This extension includes a cohesion number, the granular Bond number, with a simple definition based on tensile yield values.