Elastic Pulsed Wave Propagation in Media with Second or Higher Order Nonlinearity. Part II: Simulation of Experimental Measurements on Berea Sandstone

Koen E-A Van Den Abeele

Post-Doctoral Research Fellow, EES-4, MS D443, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.
also Post-Doctoral Fellow of the Belgian Foundation for Scientific Research, K.U.Leuven Campus Kortrijk, Interdisciplinary Research Center, E. Sabbelaan 53, B-8500 Kortrijk, Belgium.


Abstract

We apply the theoretical 1D wave propagation model described in Part I to laboratory data from dynamic propagating wave experiments on a 2 meter long cylindrical rod of Berea sandstone as previously reported by Meegan et al.1 Using the iterative procedure, good agreement is obtained limiting model parameters up to cubic anharmonicity (i.e. 2 nonlinear terms proportional to ß and 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, non-compliant) materials. We discuss the values obtained for the dynamic nonlinearity parameters in relation to commonly obtained static and resonance results which suggest the need to include more complicated phenomena such as hysteresis in the theory.

[1] G.D. Meegan, P.A. Johnson, R.A. Guyer and K.R. McCall, "Observations of nonlinear elastic wave behavior in sandstone", J. Acoust. Soc. Am. 94 (6), 3387-3391, Dec. 1993.