a finite element solution of non-linear creep problem in rocks

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