Resonance and elastic nonlinear phenomena in rock

Abstract

In a great variety of laboratory experiments over large intervals in stress, strain, and frequency, rocks display pronounced nonlinear elastic behavior. Here we describe nonlinear response in rock from resonance experiments. Two important features of nonlinear resonant behavior are a shift in resonant frequency away from the linear resonant frequency as the amplitude of the disturbance is increased and the harmonics in the time signal that accompany this shift. We have conducted Young's mode resonance experiments using bars of a variety of rock types (limestone, sandstone, marble, chalk) and of varying diameters and lengths. Typically, samples with resonant frequencies of approximately 0.5–1.5 kHz display resonant frequency shifts of 10% or more, over strain intervals of 10−7 to 10−6 and under a variety of saturation conditions and ambient pressure conditions. Correspondingly rich harmonic spectra measured from the time signal progressively develop with increasing drive level. In our experiments to date, the resonant peak is observed to always shift downward (if indeed the peak shifts), indicating a net softening of the modulus with drive level. This observation is in agreement with our pulse mode and static test observations, and those of other researchers. Resonant peak shift is not always observed, even at large drive levels; however, harmonics are always observed even in the absence of peak shift when detected strain levels exceed 10−7 or so. This is an unexpected result. Important implications for the classical perturbation model approach to resonance results from this work. Observations imply that stress‐strain hysteresis and discrete memory may play an important role in dynamic measurements and should be included in modeling. This work also illustrates that measurement of linear modulus and Q must be undertaken with great caution when using resonance.