Laboratory study of linear and nonlinear elastic pulse propagation in sandstone

Abstract

Linear and nonlinear elastic wave pulse propagation experiments were performed in sandstone rods, both at ambient conditions and in vacuum. The purpose of these experiments was to obtain a quantitative measure of the extremely large nonlinear response found in microcracked (i.e., micro-inhomogeneous) media like rock. Two rods were used, (1) a 2-m-long, 5-cm-diam rod of Berea sandstone (with embedded detectors) used in previously published experiments and (2) a somewhat smaller 1.8-m-long, 3.8-cm-diam rod. In the earlier experiments, wave scattering from the embedded detectors was a critical problem. In most of the experiments reported here, this problem was avoided by mounting accelerometers directly to the outside surface of the rod. Linear results show out of vacuum attenuations varied from 1.7 Np/m at 15 kHz (Q=10) for the large rod to 0.4 Np/m at 15 kHz (Q=55) for the small rod; attenuations for the small rod in vacuum were much less, typically about 0.15 Np/m at 15 kHz (Q=150). Wave velocities ranged from 1900 to 2600 m/s. The nonlinear results illustrate growth of the second and third harmonics and accompanying decay of the fundamental. These nonlinear results compare well with a numerical model. Although the results here were performed at peak strain amplitudes as low as 5×10−7, they still show the pronounced nonlinearity characteristic of rock, in agreement with static and resonance studies using the same rock type.