Elastic pulsed wave propagation in media with second- or higher-order nonlinearity. Part II. Simulation of experimental measurements on Berea sandstone

The theoretical 1-D wave propagation model described in Part I is applied to laboratory data from dynamic propagating wave experiments on a 2-m-long cylindrical rod of Berea sandstone as previously reported by Meegan et al. [J. Acoust. Soc. Am. 94, 3387–3391 (1993)]. Using the iterative procedure, good agreement is obtained limiting model parameters up to cubic anharmonicity (i.e., two nonlinear terms proportional to β and δ in the stress-strain polynomial expansion). Both the data and simulations illustrate that nonlinear response is likely to occur even at extremely small strains (order 10−7). As generally expected for disordered materials, the resulting values for the nonlinear parameters are several orders of magnitude larger than those for intact (uncracked, noncompliant) materials. The values obtained for the dynamic nonlinearity parameters are discussed in relation to commonly obtained static and resonance results which suggest the need to include more complicated phenomena such as hysteresis in the theory.