Experimental determination of the linear and nonlinear dynamic moduli of rock from quasistatic measurements

The central construct of a new theory of the elastic behavior of consolidated materials is the density in Preisach–Mayergoyz (PM) space. PM space is an abstract space in which the response of the mechanical units in the material to changes in stress state can be tracked. The theory provides a recipe for using quasistatic data to determine ρPM, the density of mechanical units in PM space. This recipe has been applied to quasistatic stress/strain data on three sandstones samples: (a) Berea I, (b) Berea II, and (c) Castlegate. The density of mechanical units ρPM was found for each sample. From ρPM the dynamic behavior of the samples can be predicted. Using the experimentally determined ρPM for each of the three samples the strain response to complicated stress protocols is predicted and the linear and nonlinear dynamic moduli of the samples are found as a function of pressure. The predictions agree well with experiments that test them.