Key Points:• We perform a systematic classification of nonlinear elastic behavior in rocks • Two physical mechanisms can describe the nonlinear elasticity of these rocks Abstract Dynamic acoustoelastic testing is performed on a set of six rock samples (four sandstones, one soapstone, and one granite). From these studies at 20 strain levels 10 −7 < <10 −5 , four measures characterizing the nonlinear elastic response of each sample are found. Additionally, each sample is tested with nonlinear resonant ultrasonic spectroscopy and a fifth measure of nonlinear elastic response is found. These five measures of the nonlinear elastic response of the samples (approximately 3 × 6 × 20 × 5 numbers as each measurement is repeated 3 times) are subjected to careful analysis using model-independent statistical methods, principal component analysis, and fuzzy clustering. This analysis reveals differences among the samples and differences among the nonlinear measures. Four of the nonlinear measures are sensing much the same physical mechanism in the samples. The fifth is seeing something different. This is the case for all samples. Although the same physical mechanisms (two) are operating in all samples, there are distinctive features in the way the physical mechanisms present themselves from sample to sample. This suggests classification of the samples into two groups. The numbers in this study and the classification of the measures/samples constitute an empirical characterization of rock nonlinear elastic properties that can serve as a valuable testing ground for physically based theories that relate rock nonlinear elastic properties to microscopic elastic features.
Dynamic acousto-elastic testing, a pump-probe scheme, is employed to investigate the recovery of consolidated granular media systems from the non-equilibrium steady state established by a pump strain field. This measurement scheme makes it possible to follow the recovery from the nonequilibrium steady state over many orders of magnitude in time. The recovery is described with a relaxation time spectrum that is found to be independent of the amplitude of the non-equilibrium steady state (pump amplitude) and of the environment in which samples reside. The nonequilibrium steady state and its slow recovery are the laboratory realization of phenomena that are found in many physical systems of practical importance.
Acoustoelasticity measurements in a sample of room dry Berea sandstone are conducted at various loading frequencies to explore the transition between the quasi‐static (
f→0) and dynamic (few kilohertz) nonlinear elastic response. We carry out these measurements at multiple confining pressures and perform a multivariate regression analysis to quantify the dependence of the harmonic content on strain amplitude, frequency, and pressure. The modulus softening (equivalent to the harmonic at 0f) increases by a factor 2–3 over 3 orders of magnitude increase in frequency. Harmonics at 2f, 4f, and 6f exhibit similar behaviors. In contrast, the harmonic at 1f appears frequency independent. This result corroborates previous studies showing that the nonlinear elasticity of rocks can be described with a minimum of two physical mechanisms. This study provides quantitative data that describes the rate dependency of nonlinear elasticity. These findings can be used to improve theories relating the macroscopic elastic response to microstructural features.
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