Modeling the elasto-acoustic hysteretic nonlinearity of dry Berea sandstone

By means of the dynamic acousto-elastic technique the instantaneous state of a material is probed by a high-frequency pulse while an external, low-frequency dynamic source modulates it in time. When it is applied to rocks, a remarkable variety of responses in the form of hysteresis of the material’s modulus defect is obtained. Among them, the response by Berea sandstone is perhaps the most investigated. Hysteresis of the modulus defect in dry Berea sandstone shows intriguing features which have not yet been interpreted in terms of specific mechanisms occurring at atomic or meso-scale. In the present communication, three rheological models providing simplified representations of realistic mechanisms are considered. They involve dislocations interacting with point defects, and microcracks with finite stiffness in compression. Constitutive relations linking macroscopic anelastic strain and stress are derived from them together with the modulus defect associated to each model. These relationships are employed to construct a composite model capable of reproducing several of the main features observed in the experimental data. The limitations of the present approach, the validity of its physical interpretation, and, possibly, of the current implementation of the dynamic acousto-elastic technique are also discussed.