Nonequilibrium and nonlinear dynamics in Berea and Fontainebleau sandstones: Low‐strain regime

Abstract

[1] Members of a wide class of geomaterials are known to display complex and fascinating nonlinear and nonequilibrium dynamical behaviors over a wide range of bulk strains, down to surprisingly low values, e.g., 10À7 . In this paper we investigate two sandstones, Berea and Fontainebleau, and characterize their behavior under the influence of very small external forces via carefully controlled resonant bar experiments. By reducing environmental effects due to temperature and humidity variations, we are able to systematically and reproducibly study dynamical behavior at strains as low as 10 À9 . Our study establishes the existence of two strain regimes separated by M . At strains below M the material is nonlinear and quasi-equilibrium thermodynamics applies as evidenced by the success of Landau theory and a simple macroscopic description based on the Duffing oscillator. At strains above M the behavior becomes truly nonequilibrium, as demonstrated by the existence of material conditioning, and Landau theory no longer applies. The main focus of this paper is the study of the first region, but we also comment on how our work clarifies and resolves previous experimental conflicts, as well as suggest new directions of research.

Measurements of the Relationship Between Microstructure, pH, and the Streaming and Zeta Potentials of Sandstones

“…This approach can be automated and avoids setting a threshold gradient below which equilibrium is achieved, which needs to be considered carefully and altered according to the magnitude of the measurements. In practice, we applied the method conservatively, often waiting for many more pore volumes to pass Pasqualini et al (2007), and Worden and Morad (2009) than was strictly necessary. The black line in Fig.…”

Nonlinear acoustic resonances to probe a threaded interface

“…has to be considered, Landau theory 40 allows to describe "classical" materials, where nonlinearity arises from atomic scale ͑nanoscopic scale͒. In the case of more complex materials, either heterogeneous, cracked, or granular ͑mesoscopic scales͒, and for strain above roughly 10 −6 , 41, 42 Landau theory is no longer valid. 43,44 Indeed, some typical behaviors appear in this case: an hysteresis with cusps is present in the stressstrain response, odd harmonics are favored, resonance frequency exhibits a linear shift with level of excitation, 38 and a slow dynamic phenomenon appears.…”

Inherent acoustic nonlinearity of fiber reinforced composites

“…Guyer et al [22] performed a set of resonant bar experiments with geomaterials at low strains and reported a linear dependence of frequency even at very low strains (10 -8 ≤ ≤ 5x10 -7 ). But in some recent research by Pasqualini et al [23], it was reported that rocks and other geomaterials exhibit different frequency shift responses depending on the strain magnitude; (a) low strain linear zone, where the material behaves linear elastic and no frequency shift exists, (b) mid-range strain classical nonlinear zone where a quadratic decrease in frequency can be observed as shown by Landau [24], (c) high strain non-classical non-equilibrium zone where the response is controlled by slow and fast-dynamics and linear decrease in frequency can be observed. Pasqualini et al showed that the linear softening observed experimentally in the non-equilibrium zone is due to the material conditioning effects resulting from slow dynamics.…”

“…Pasqualini et al showed that the linear softening observed experimentally in the non-equilibrium zone is due to the material conditioning effects resulting from slow dynamics. P. A. Johnson (personal correspondence) later found out that damaged materials behave in a similar fashion and have three strain ranges as described [23]. (f/ f0) is the shift in the resonant frequency normalized to linear frequency.…”

“…from Los Alamos [9][10][11][12][20][21][22][23]. Van Den Abeele, Guyer and McCall [20] used a phenomenological model to show that for a nonlinear hysteretic material, linear softening (i.e.…”