EVALUATING HYSTERESIS IN EARTH MATERIALS UNDER DYNAMIC RESONANCE

A lumped parameter model is derived for studying hysteretic effects in resonant bar experiments on rock. The model uses equations of state o btained by approximating closed hysteresis loops in the stress-strain plane by parallelograms. The associated approximate nonlinear state re lations have a sound speed (modulus) that takes two values. Assuming h ysteresis and discrete memory to be the primary nonlinear mechanisms, periodic solutions corresponding to these equations of state are obtai ned analytically for single-frequency continuous wave drivers, and the ir frequency spectral densities are analyzed. In this simple approxima tion, if hysteretic contributions to the signal speed are a correction to the linear elastic signal speed (i.e., the parallelogram is narrow ), the model predicts that the spectral density at even multiples of t he source frequency is zero, and an approximate ''pairing'' of amplitu des is predicted for odd harmonic multiples. Comparison of the model s pectrum with experimental data shows the model to be qualitatively cor rect. We conclude that hysteresis is an important mechanism in rocks. We consider the model to be a prototype.