On the influence of strain rate in acousto-elasticity : experimental results for Berea sandstone

Elastic nonlinear effects are pervasive in the Earth, including during strong ground motion, tidal forcing and earthquake slip processes. We study elastic nonlinear effects in the laboratory with the goal of developing new methods to probe elastic changes in the Earth, and to characterize and understand their origins. Here we report on nonlinear, frequency dispersion effects by applying a method termed dynamic acousto-elasticity (DAE), analogous to quasi-static acousto-elasticity. DAE allows one to obtain the elastic behavior over the entire dynamic cycle, detailing the full nonlinear behavior under tension and compression, including hysteresis and memory effects. We perform DAE on samples of Berea sandstone subject to 0.5 MPa uniaxial and biaxial loading conditions with oscillating loads at frequencies from 0.001 to 10 Hz and amplitudes of a few 100 kPa. We compare results to DAE measurements made in the kHz range. We observe that the average decrease in modulus due to nonlinear material softening increases with frequency, suggesting a frequency and/or a strain rate dependence. Previous quasi-static measurements (Claytor et al., GRL 2009) show that stress-strain nonlinear hysteretic behavior disappears when the experiment is performed at a very low strain-rate, implying that a rate dependent nonlinear elastic model would be useful (Gusev et al., PRB 2004). Our results also suggest that when elastic nonlinear Earth processes are studied, stress forcing frequency is an important consideration, and may lead to unexpected behaviors.