Extreme nonlinearity in rocks: An investigation using elastic pulse wave propagation
Because of the presence of structural defects such as microcracks and grain boundaries, the effective moduli in a highly disordered material change dramatically as a function of stress. Earth materials (rocks) are an important example of this type of disordered media and are of practical interest in geophysics and seismology. At the laboratory scale, static stress-strain theory and elastic resonance experiments on rocks suggest that the ratio of third order elastic constants to second-order elastic constants in such materials is several orders of magnitude higher than in the case of ordinary uncracked materials. In this paper we report a model for that describes the nonlinear interaction of frequency components in arbitrary pulsed elastic waves during one-dimensional propagation in an infinite medium. The model is based on the use of one dimensional Green`s Function theory in combination with a perturbation method. A polynomial expansion is used for the stress-strain relation in which we account for four orders of nonlinearity. The perturbation expression corresponds to a higher order equivalent of the Burgers` equation solution for velocity fields in solids. It has conceptual clarity and is easy to implement numerically, even with the inclusion of an arbitrary attenuation function. A comparison with experimental data on Berea sandstone is given to illustrate the model when used in an iterative procedure, and good agreement is obtained limiting model parameters up to cubic anharmonicity. The resulting values for the nonlinear parameters are several orders of magnitude larger than those for uncracked materials. Finally we discuss the values obtained for the dynamic nonlinearity parameters in comparison with static and resonance results.
- Research Organization:
- Los Alamos National Lab., NM (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 34441
- Report Number(s):
- LA-UR--95-511; CONF-9506141--1; ON: DE95007879
- Country of Publication:
- United States
- Language:
- English
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