The Transition from Elastic Linear to Classically Nonlinear Behavior in Rock at Low Strains

Donatella Pasqualini
Geophysics Group, LANL, Los Alamos, New Mexico 87545, USA

In this work we investigate the nonlinear elastic properties of rocks at amplitudes lower than have ever been explored in order to understand the onset of elastic nonlinearity. We studied two sandstones, Berea and Fontainebleau, to characterize their behavior applying resonant-bar experiments under carefully controlled thermal and humidity conditions. This study establishes the existence of two strain regimes: the first where the material shows classical nonlinearity (this has never before been characterized), and the second where the behavior becomes truly nonequilibrium - as demonstrated by the existence of relaxation (slow dynamics) - and where the theory of classical nonlinearity no longer applies. The separate effects of nonlinearity and relaxation in this regime cannot be disentangled.

This transition from classical nonlinearity to nonlinear nonequilibrium dynamics elasticity in rocks is of considerable interest in understanding the basic dynamical processes in consolidated granular materials. The new experimental evidence and the theoretical interpretation present a breakthrough for the investigation of the nonlinear elastic behavior of geomaterials underscoring the need for new experiments and a new theoretical framework.

Preliminary results were described in a previous paper: TenCate, J., D. Pasqualini, S. Habib, K. Heitmann, D. Higdon, and P. Johnson, Nonlinear and nonequilibrium dynamics in geomaterials, Physical Review Letters, 93, 06551-06555 (2004).

Figure A - The polarized thin section of Fontainebleau, one of the two rocks studied in this paper. Click on thumbnail to display a larger image.


Figure B - The resonance frequency (linked to the elastic modulus) shift versus strain. For strains below 5*10-7, the material displays only an intrinsic reversible nonlinearity, for strains above 5*10-7 nonlinear and nonequilibrium effects are combined. Click on a thumbnail to display a larger image.

See Pasqualini, Donatella, Katrin Heitmann, James TenCate, Salman Habib, David Higdon, and Paul A. Johnson, "Nonequilibrium and nonlinear dynamics in Berea and Fontainebleau sandstones: Low-strain regime", J. Geophys. Res., Vol.112, No.B1, B01204 10.1029/2006JB004264 (2007). (PDF File - 684 KB)