Manifestation of nonlinear elasticity in rock: Convincing evidence over large frequency and strain intervals from laboratory studies

Abstract

Nonlinear elastic response in rock is established as a robust and representative characteristic of rock rather than a curiosity. This behavior is illustrated from a variety of experiments conducted over many orders of magnitude in strain and frequency. The evidence leads to a pattern of unifying behavior in rock: (1) Nonlinear response in rock is enormous; (2) the response takes place over a large frequency interval (dc–106 Hz at least); (3) the response not only occurs, as is commonly appreciated, at large strains but also at small strains where nonlinear response and the manifestations of this behavior are commonly disregarded. Nonlinear response may manifest itself in a variety of manners, including a nonlinear stress−strain relation (hysteretic/discrete memory), nonlinear dissipation, harmonic generation, and resonant peak shift, all of which are related. The experiments described include: quasistatic stress−strain tests (strains of 10-4–10-1 at frequencies near dc-1Hz); torsional oscillator experiments (strains of 10−4–10−7, frequencies between 0.1 and 100Hz); resonant bar experiments (strains of 10−4–10−8, frequencies between 103 and 104 Hz); and dynamic, propagating wave experiments (strains of 10−6–10−9, frequencies between 103 and 106 Hz). [Work supported by OBES/DOE through the University of California and the Institut Français du Pétrole.]