Elastic/viscoplastic constitutive equations for rock

Abstract The experimental data needed for the formulation of a constitutive equation to describe the creep of rocks in uniaxial or triaxial tests are reviewed and the influence of loading rate on dilatancy is pointed out. The assumptions which have to be made in obtaining a constitutive equation from these experimental data are specified. A general constitutive equation is then formulated for rocks, which can describe their elastic and viscoplastic properties for any triaxial compressive stress state. Dilatancy and volumetric compressibility of rocks are defined in mathematical terms and so are the concepts of the compressibility/ dilatancy boundary and that of damage. Various time-dependent effects which can be modelled with such a constitutive equation are illustrated. It is shown, for instance, how the loading rate influences the dilatancy and/or the compressibility as well as the various stress-strain curves and the ultimate failure. The peculiarities of the creep phenomenon as described by the model are discussed. Numerical examples are given for several rocks. Various mining engineering problems have already been solved with such constitutive equations.

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