Analysis of shock wave arrival time from underground explosions

Abstract

The arrival times of the shocks from underground explosions in the highly inelastic region were used to determine the energy of the explosions driving the shocks. The relation between arrival time and radial distance was obtained with the use of the equation U = a + bu relating shock velocity U to particle velocity u. Also used was the similarity assumption that the peak pressure at the spherical shock front was linearly related to the average energy within the sphere. Numerical coefficients in the derived formula were determined from experimental data on peak pressure and peak particle velocity from explosions in tuff and in granite. This anlaysis was used successfully for energy determination of nuclear explosions from about 1 kiloton to several megatons energy output. The stress range covered was from about 5×108 Pa up to more than 1011 Pa. The good agreement between experimental and computed results showed that the similarity assumption was reasonable. Computed arrival times in wet tuff were compared with those from an empirical formula from the Los Alamos National Laboratory with good agreement over a limited peak stress range. Similar comparison with results from a semiempirical formula of Kurtz did not give good agreement unless the constants in the Kurtz formula were adjusted.