A finite element solution of non-linear creep problems in rocks

Abstract A numerical procedure is presented, belonging to the class of ‘evolutive’ approaches, for the finite element solution of stress analysis problems involving non-linear creep of rocks. The approach proposed allows both for non-linear reversible behaviour (non-linear viscoelasticity) and for non-linear non-reversible behaviour (viscoplasticity); either associated or non-associated flow rules can be considered. Primary, secondary and tertiary creep can be accounted for by supplying suitable laws governing the variation of material parameters (such as viscosity) with stresses and strains. The numerical procedure is based on Newmark's time integration scheme; along each loading/ time step quadratic variation of the stress and strain fields and linear variation of the material parameters are assumed. As an example, a hollow cylinder test on a rock sample behaving according to a simple non-linear viscoplastic rheological model is simulated numerically.