RESONANCE AND ELASTIC NONLINEAR PHENOMENA IN ROCK

In a great variety of laboratory experiments over large intervals in s tress, strain, and frequency, rocks display pronounced nonlinear elast ic behavior. Here we describe nonlinear response in rock from resonanc e experiments. Two important features of nonlinear resonant behavior a re a shift in resonant frequency away from the linear resonant frequen cy 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 (li mestone, sandstone, marble, chalk) and of varying diameters and length s. Typically, samples with resonant frequencies of approximately 0.5-1 .5 kHz display resonant frequency shifts of 10% or more, over strain i ntervals of 10(-7) to 10(-6) and under a variety of saturation conditi ons and ambient pressure conditions. Correspondingly rich harmonic spe ctra measured from the time signal progressively develop with increasi ng drive level. In our experiments to date, the resonant peak is obser ved 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, eve n at large drive levels; however, harmonics are always observed even i n the absence of peak shift when detected strain levels exceed 10(-7) or so. This is an unexpected result. Important implications for the cl assical perturbation model approach to resonance results from this wor k. Observations imply that stress-strain hysteresis and discrete memor y may play an important role in dynamic measurements and should be inc luded in modeling. This work also illustrates that measurement of line ar modulus and Q must be undertaken with great caution when using reso nance.