Three-dimensional description of nonlinear elasticity in rocks: Modeling and experiments

We study theoretically and experimentally the mechanisms of nonlinear and nonequilibrium dynamics in geomaterials through dynamic acousto-elasticity testing. In the proposed theoretical formulation, the classical theory of nonlinear elasticity is extended to include the effects of conditioning. This formulation is adapted to the context of dynamic acousto-elasticity testing in which a low-frequency “pump”-wave induces a strain field in the sample and modulates the propagation of a high-frequency “probe”-wave. Experiments are conducted to validate the formulation in a long thin bar of Berea sandstone. Several configurations of the pump and probe are examined—the pump successively consists of the first longitudinal and first torsional mode of vibration of the sample while the probe is successively based on (pressure) P- and (shear) S-waves. The theoretical predictions reproduce many features of the elastic response observed experimentally, in particular, the coupling between nonlinear and nonequilibrium dyn...