Progressive Failure in Viscoplastic Materials

Abstract

In the assessment of rainfall induced landslide hazard, both the comprehension and the theoretical interpretation of the inception phase of unexpected collapses are crucial. In this paper, the case of an infinite long slope is theoretically discussed by assuming the mechanical behaviour of the materials involved to be strain softening elastic-viscoplastic. Rainfall is assumed to induce variations, taking place with time, in the water table level and, consequently, in the effective state of stress. Consequently, accelerations in both strains and displacements, due to the temporal evolution of the perturbation, are not necessarily associated with a system instability or vice versa decelerations are not the signature of a stable system response. In this paper, from a theoretical point of view, the authors apply the controllability theory conceived for a representative elementary volume to a boundary value problem and demonstrate that (i) irreversible strains accumulate, due to the structural hardening, even outside of the shear band, whose thickness is a function of the imposed perturbation, (ii) local instability anticipates the global one, (iii) once assigned the temporal evolution of the perturbation, its frequency does not affect the system response.