Equation of state hysteresis and resonant bar measurements on rock

The frequencies of the fundamental resonances of a suite of rock samples have been measured as a function of drive amplitude. Representative results from a measurement on Fountainbleu sandstone are reported. The resonant frequency shifts downward with increased drive amplitude exhibiting a softening nonlinearity. The traditional theory of the nonlinear elastic response of rock is reviewed. When applied to resonant bar measurements this theory predicts qualitative and quantitative features that are markedly unlike experiment. The new paradigm introduced by McCall and Guyer (1994) to describe the nonlinear behavior of consolidated materials is reviewed. This paradigm is applied, using extant stress-strain data on Berea sandstone, to describe resonant bar measurements. Good qualitative and quantitative agreement with the experimental observations is found.