Calculation of explosion-produced craters-high-explosive sources

Abstract

A simple two-dimensional model is developed of cratering physics for high-explosive sources in alluvium during the surface gas-acceleration phase of excavation. The required initial conditions for the model are knowledge of the earth's free-surface topography and motion at the time the surface gas acceleration begins (tG) and knowledge of the cavity pressure and volume. At tG the overburden material—that material between the cavity and the earth's free surface—is assumed to be homogeneous, incompressible fluid. At this time the cavity is approximated as follows: (a) the radius of the lower hemisphere is calculated by a one-dimensional hydrodynamic plastic-elastic model of the response of a geologic medium to an explosive source, and (b) the cavity configuration above the shot horizon is calculated from mass conservation of the overburden material and the calculated free-surface topography at the time tG. In the model, the upper cavity surface is subdivided into elemental surface areas, and mass zones are defined which subtend these elemental surface areas. Newton's second law of motion with a simple phenomenological frictional force (calibrated on the Scooter event) is applied to each mass element. The cavity gas is assumed to behave adiabatically. The physical laws, assumptions, and initial conditions cited above provide a basis for the numerical simulation of the cavity evolution, mound development, and formation of the lip through up-thrust during the surface gas-acceleration phase of excavation. With the development of a calibrated numerical simulation model of excavation processes during the surface gas-acceleration phase, it is appropriate to explore the use of the model for estimating the apparent crater radii and depth for 0.5-kt high-explosive sources at various emplacement depths. Assuming a reasonable angle of repose for alluvium (45°), we have prepared estimates of the apparent crater radii for scaled depth of burst from about 10 to 65 m/kt1/3.4. These estimated crater radii compare very favorably with the observed (scaled) crater radii for high explosives in alluvium. The apparent (scaled) crater depths, for certain types of craters, are also calculated. Perhaps the most significant contribution of the study is the development of a physical model for calculating the time history of the mound, the lip formation, and the cavity geometry during the surface gas-acceleration phase of cratering.