The second order work criterion appears as an interesting tool to analyse failure in geomaterials (Nicot & Darve 2007, Nicot & al. 2007, Darve & al. 2007), essentially because the non associative character of their plastic strains implies the non-symmetry of the elasto-plastic matrix. Consequently the second order work criterion coincides with neither a plastic limit condition nor a localisation criterion. After having studied this criterion for axisymmetric and plane strain conditions (Darve & al. 2004, Khoa & al. 2006), it is proposed here to consider general 3D conditions and to establish the equations of the boundary of the bifurcation domain and of the cones of unstable directions. In a second part direct numerical simulations with a discrete element method (Sibille et al. 2007) confirm the existence of this bifurcation domain and of these instability cones. Effective diffuse failure modes are simulated in the conditions predicted by the theory (i.e. stress states inside the bifurcation domain, loading directions inside the instability cones, proper control parameters for the loading). The features of diffuse failure (i.e. burst of kinetic energy, exponentially growing strains, decreasing stresses) are shown from the numerical results.