An exercise on slope stability and perfect elastoplasticity

In this paper the stability of an infinitely long granular slope is addressed in the framework of small-strain perfect elastoplasticity. The problem is approached by discussing the condition of strain localisation and, through a reinterpretation of the concept of ‘angle of natural repose', a modified strategy for evaluating the slope safety factor is introduced. The angle of natural repose is demonstrated to differ substantially from the material internal friction angle (as this can be determined from standard triaxial tests). The role of non-associativeness is critically discussed and simple shear stress paths are numerically simulated: pseudo-hardening and pseudo-softening regimes are described. The influence of the loading history on the overall ductility/brittleness of the system mechanical response is analysed. To stress the dependency of the angle of natural repose on the material ductility/brittleness, additional simple shear numerical results are illustrated for the case of a strain-softening constitutive relationship. Finally, the stability of the stratum under undrained conditions is critically tackled with reference to the phenomenon of static liquefaction of loose sands.