ABSTRACT
Creep behavior is prominent in soft rocks such as salt rock and potash, and has even been observed in hard rocks, highlighting the importance of designing for such behaviour. In this paper we present a family of time-dependent constitutive models which take into account both the secondary and tertiary stages of creep deformation. Three stages of creep are typically observed in laboratory creep tests: a primary stage considered to be viscoelastic, a secondary stage considered to be viscoplastic and a tertiary stage considered to be caused by material damage through the formation of cracks. Thus here we develop viscoplastic-damage constitutive models.These models are novel as they are derived using the hyperplastic framework of Houlsby and Puzrin (2000) and therefore obey the laws of thermodynamics. In this approach the entire constitutive behaviour can be derived from two scalar potentials; a free energy potential which provides the elasticity law, and a dissipation potential which provides the yield function, the direction of plastic flow and the evolution of a damage variable. No additional assumptions are required. In these models, we assume that the viscoplasticity and damage are coupled, therefore they occur simultaneously. The classical sign convention in soil mechanics is considered here where compressive stresses are taken to be positive.
