Publications Details
Using power series expansions of moduli to interpolate between release curves from dynamic tests: Technique and application
Recently an appreciable number of continuous release profiles have been measured from dynamic experiments with geological materials. For each material an empirical generalization of the available release curves may be constructed to allow easy application of the experimental data to problems in much the same way as a linear shock velocity -- particle velocity fit allows easy application of Hugoniot data. This generalization is made in two steps. The first is to compute the Eulerian axial modulus at the Hugoniot pressure and its first three pressure derivatives along the release for each test. This corresponds to a partial Taylor series of the axial modulus, which integrates to give a very close match to the original release. An alternative formulation, which takes volume as the independent variable, fails because that Taylor series does not converge with the rapidity needed for these calculations. The second step is to plot each of these quantities against the Hugoniot pressure for the suite of tests, and fit these data. A release from an arbitrary pressure within the general range of the experimental data may be computed by using the interpolated modulus and its interpolated derivatives. This generalization, which allows volume to be computed as a function of pressure, reproduces the experimental curves fairly well. We present the results of applying this technique to release data for Mini Jade 2 grout, and briefly compare these results with those from several Nevada Test Site tuffs, saturated and dry Indiana Limestone, and aluminum. Finally, we use the generalized Mini Jade 2 data to solve a sample problem, that of estimating the error produced by making the release = Hugoniot'' assumption in the analysis of ground motion gauges in an underground test. 12 refs., 14 figs., 5 tabs.