Dilatancy hysteresis in rocks: a generalized ramberg-osgood approach

Abstract

A review and interpretation of representative experimental data is given on the cyclic properties of rocks. Emphasis is placed on data concerning the development of hysteresis of volumetric strain. Volumetric strain occuring during stress cycles well below the peak stress value exhibits a remarkable hysteresis. The strain is either compactive or dilative. The hysteresis varies both in form and in width depending on the state of prior rock damage. Specifically, the volumetric compliance may either be higher in loading than in reloading or vice-versa, depending on the state of rock damage prior to the cyclic loading. Finally, the hysteresis form significantly varies with the number of cycles. A model is developed, which is a generalization to three dimensional cyclic loading of the well known Ramberg-Osgood equation for amplitudes. The model is based on an earlier idea of discretized kinematic hardening plasticity with a piecewise path independent stress - difference/strain - difference law. A particular anisotropic form of such a law is discussed in the light of the collected phenomenological data. The law is valid by pieces and is expressed through a non-linear hyperelastic relationship for amplitudes. The pieces are defined by characteristic points of the stress trajectory, like stress rate reversals or turns. To ensure the incremental continuity of such a law at reversals in non-radial cycles, the constitutive tensor of initial hysteresis moduli is assumed as a function of the reversal intensity. All irreversible strain effects of the material behaviour are lumped in the discrete points of the stress rate reversals, where material property parameters are adjusted. A special form of the constitutive functions is presented in the companion paper [12].