Nonequilibrium and Nonlinear Dynamics in Geomaterials I : The Low Strain Regime

TL;DR

This study investigates the nonlinear and nonequilibrium behaviors of sandstones at extremely low strains, identifying thresholds that distinguish linear, nonlinear, and truly nonequilibrium regimes, with implications for understanding geomaterial dynamics.

Contribution

It provides the first systematic characterization of low-strain nonlinear behaviors in sandstones, establishing thresholds and validating macroscopic models like Landau theory and Duffing oscillator.

Findings

Existence of two strain thresholds, epsilon_L and epsilon_M.

Material behavior is linear below epsilon_L and nonlinear but quasi-equilibrium below epsilon_M.

Behavior becomes truly nonequilibrium above epsilon_M, with material conditioning evidence.

Abstract

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., 10^{-7}. 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^{-9}. Our study establishes the existence of two strain thresholds, the first, epsilon_L, below which the material is essentially linear, and the second, epsilon_M, below which the material is nonlinear but where quasiequilibrium thermodynamics still applies as evidenced by the success of Landau theory and a simple macroscopic description based on the Duffing oscillator. At strains above epsilon_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 region below the second threshold, but we also comment on how our work clarifies and resolves previous experimental conflicts, as well as suggest new directions of research.