Nonlinear viscoelastic behavior of sedimentary rocks, Part I: Effect of frequency and strain amplitude

Abstract

Sedimentary rocks display nonlinear elastic behavior. This nonlinearity is a strong function of frequency, strain amplitude, and the properties of the saturating fluid. Experimental observations and potential mechanisms that cause these nonlinearities are presented in this and a companion paper. Young’s moduli and Poisson’s ratios obtained from ultrasonic laboratory measurements (50 kHz, 100 kHz, 180kHz and 1 MHz), low‐frequency measurements (1–2000 Hz) and static measurements (0.001–0.05 Hz) show significant differences under identical stress conditions. A comparison of the laboratory‐measured quantities with log‐derived moduli measured at 20 kHz indicates that [Formula: see text]. This shows clearly that a wide variety of sandstones demonstrate frequency‐dependent elastic behavior (viscoelastic behavior) over a range of frequencies. Differences between static (low‐frequency, high‐strain amplitude) velocities and ultrasonic velocities can be explained partially by differences in frequency as predicted by grain contact models. Such models, however, do not explain the strain amplitude dependence observed in our data. A series of uniaxial stress cycling measurements were carried out to investigate the influence of strain amplitude on elastic moduli. These low‐frequency measurements (0.01 Hz) clearly show that the Young’s modulus decreases with strain amplitude for a wide variety of sandstones. Attenuation increases with strain amplitude. The strain amplitude dependence does not change when the rocks are saturated with brine although the rocks soften measureably.