Nonlinear elasticity in rocks: impact of saturation, stress, and
wave-amplitude on harmonics in sedimentary rocks
Abstract
Higher-order harmonics of elastic waves have emerged as valuable for
detecting nonlinearities associated with material damage, such as
cracks, and those related to partial saturation with free gas. In this
study, we conducted low-frequency forced oscillation measurements on
Bentheimer and Berea sandstone samples under varying saturation levels,
including dry, partially saturated, and fully water-saturated
conditions. We also performed tests at different strain amplitudes
controlling the production of higher-order harmonics. With increasing
effective static stresses, cracks progressively close, resulting in a
decrease in the harmonic content. At dry conditions, nonlinearities are
attributed to grain contacts and microcrack deformation. Partially
saturated samples exhibit nonlinearities produced by liquid bridges. In
particular, the second harmonic increased for saturation levels above
79% but decreased again for nearly fully saturated samples. In
contrast, the third harmonic showed no consistent trend with saturation.
The theory devised by Rozhko 2021 matches the experimental observations.
In particular, only the second harmonic shows an amplitude dependence on
fluid saturation. We also observed a correlation between the attenuation
of seismic waves and the amplitude of the second harmonic, as both
depend on the saturation level. However, for the third harmonic, no
correlation with attenuation exists.