Résumé
Nonlinear elasticity is studied at the laboratory scale with the goal of understanding observations at earth scales, for instance during strong ground motion, tidal forcing and earthquake slip processes. Here we report frequency and pressure dependences on elasticity when applying dynamic acousto-elasticity (DAE) of rock samples, 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 a sample of Berea sandstone subject to 0.5 MPa uniaxial load, with sinusoidal oscillating strain amplitudes ranging from 10-6 to 10-5 and at frequencies from 0.1 to 260 Hz. In addition, the confining pressure is increased stepwise from 0 to 30 MPa. We compare results to previous measurements made at lower (mHz) and higher (kHz) frequencies. Nonlinear elastic parameters corresponding to conditioning effects, third order elastic constants and fourth order elastic constants are quantitatively compared over the pressure and frequency ranges. We observe that the decrease in modulus due to conditioning increases with frequency, suggesting a frequency and/or strain-rate dependence that should be included in nonlinear elastic models of rocks. In agreement with previous measurements, nonlinear elastic effects also decrease with confining pressure, suggesting that nonlinear elastic sources such as micro-cracks, soft bonds and dislocations are turned off as the pressure increases.