Experimental properties of a new form of creep dynamics are reported, as manifest in a variety of sandstones, limestone, and concrete. The creep is a recovery behavior, following the sharp drop in elastic modulus induced either by nonlinear acoustic straining or rapid temperature change. The extent of modulus recovery is universally proportional to the logarithm of the time after source discontinuation in all samples studied, over a scaling regime covering at least 10(3) s. Comparison of acoustically and thermally induced creep suggests a single origin based on internal strain, which breaks the symmetry of the inducing source.

[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.

In 1996 JOHNSON et al. were the first to identify peculiar rate effects in resonant bar experiments on various earth materials. The effects were evident on time scales of minutes to hours. They were also seen in both sedimentary and crystalline rocks, and have since been seen in geomaterials like concrete. Although these effects resemble some aspects of creep and creep recovery, they can be induced by a sinusoidal acoustic drive at strains three orders of magnitude below typical creep experiments. These strains are only a few tenths of a microstrain. Moreover, unlike most creep behavior, the effects have been shown to be macroscopically reversible and repeatable, over hundreds of experiments spanning nearly a year. The unique excitation and character of these rate effects cause them to be called slow dynamics. A review and discussion of slow dynamics is presented, pointing out similarities and differences with ordinary creep and focusing on laboratory experiments. A brief description of some possible mechanisms is included, and a new experiment on a sample of Berea sandstone in ultra high vacuum is shown to point out new research that hopes to help ascertain the role of water as a potential mechanism.

Quasistatic elasticity measurements on rocks show them to be strikingly nonlinear and to have elastic hysteresis with end point memory. When the model for this quasistatic elasticity is extended to the description of nonlinear dynamic elasticity the elastic elements responsible for the hysteresis dominate the behavior. Consequently, in a resonant bar, driven to nonlinearity, the frequency shift and the attenuation are predicted to be nonanalytic functions of the strain field. A resonant bar experiment yielding results in substantial qualitative and quantitative accord with these predictions is reported. [S0031-9007(99)08968-1] PACS numbers: 62.40. + i, 62.65. + k, Rocks have extreme dynamic elasticity; their velocity of sound changes by a factor of 2 under modest pressure change [1,2] and unusual quasistatic elasticity; their quasistatic stress-strain equation of state has hysteresis with end point memory [3]. These properties make rocks interesting as members in the sequence of elastic systems with increasing cohesiveness (sand, soil, rock, grain) and interesting as members of the class of hysteretic systems that possess memory [4].Quasistatic stress-strain measurements on rocks involve large strains (e ഠ 10 23 ) and low frequencies ͑ f ഠ 10 22 Hz͒ [5]. Dynamic nonlinear elasticity measurements involve very small strains (e ഠ 10 28 ) and high frequencies ͑ f ഠ 10 4 Hz͒ [1]. A mean field theory, using a Preisach description of hysteretic elastic elements [6,7], gives a sensible picture of the observed quasistatic behavior [8,9]. When this theory is extended to describe dynamic elasticity a number of unusual predictions result [10,11]. The purpose of this paper is to report measurements of dynamic elasticity on a Berea sandstone. These measurements confirm the predictions of the theory and establish its usefulness in describing the quasistatic and dynamic elasticity of consolidated materials over a large strain/time scale range, 10 28 , e , 10 23 and 10 22 , f , 10 4 Hz.Quasistatic stress-strain measurements on rock, e.g., a Berea sandstone, show striking nonlinearity and hysteresis with end point memory [5]. These observations have a theoretical explanation in terms of a new model for finding the equation of state of consolidated materials [8,9,12]. The new model has been extended to describe nonlinear elastic wave propagation [10] and the case at hand, resonant bar measurements [11,13]. A series of predictions results.(i) The resonant frequency should have a frequency shift that is linear in the magnitude of the strain field, U, i.e.,Df(ii) 1͞Q, a measure of the attenuation, should depart from 1͞Q 0 linearly in the magnitude of the strain field, i.e.,with C Q ͞C f 3p͞8 ഠ 1 and C f a. (The constant a, which characterizes the hysteretic elastic elements in the rock, is found from the analysis of quasistatic data, a ഠ 10 3 for a Berea sandstone [14].) The sample was a long, thin, cylindrical rod of Berea sandstone, 6 cm 3 30 cm, that had a low amplitude resonance at f 0 ഠ 2880 Hz with a Q, denoted Q 0 , of approxim...

The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a simple macroscopic dynamical model. At even higher strains, effects due to a driven nonequilibrium state, and relaxation from it, complicate the characterization of the nonlinear behavior. PACS numbers: 62.40.+i, 62.65.+k, 91.60.Lj Rocks possess a variety of remarkable nonlinear elastic properties including hysterisis with end-point memory [1], variation of attenuation and sound velocity with strain [2], strong dependence of elastic and loss constants on pressure, humidity, and pore fluids [3], long-time relaxation phenomena ('slow dynamics') [4], and nontrivial variation of resonance frequency with strain [5,6]. Significantly, materials as diverse as sintered ceramics and damaged steels are now known to display similar effects [6]. Thus rocks may be viewed as representative members of a class of fascinating, but poorly understood, nonlinear elastic materials: Fundamental questions still to be resolved relate not only to the underlying causes of the nonlinear phenomena but also to the conditions under which they occur.In this Letter, we focus on delineating two strain thresholds, one below which the rocks behave effectively as linear elastic materials, ǫ L , the other beyond which memory and conditioning effects occur, ǫ M , and the dynamic elastic behavior straddling the region of these thresholds. While in Ref. [2] it was argued that ǫ L ∼ 10 −6 (albeit with some uncertainty), more recent data [5,6,7] have been used to support an extension of the nonlinear region to substantially lower strains; doubt has been cast even on the very existence of a threshold [8]. In addition, results from resonant bar experiments [5,7] have been interpreted to exhibit a 'nonclassical' frequency and loss dependence on the drive amplitude, i.e., frequency and Q softening linearly with drive amplitude rather than quadratically as predicted by Landau theory [9], even at strains as small as 10 −8 . (The importance of ǫ M in interpreting resonant bar data is emphasized below.)We have carried out a new set of well-characterized experiments, over a wide dynamic range, to unambiguously settle these questions: While longitudinal resonant excitation of bars is a classic measurement technique [10], rock samples require substantial care in terms of controlling the temperature and humidity and characterizing possible systematic effects, especially those due to conditioning of the sample by the external drive [4].Our major conclusions are as follows. For Berea and Fontainebleau sandstone samples, below a threshold strain ǫ L ∼ 10 −8 −10 −7 (lower end for ...