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.

Subgrade fatigue life effects due to a pressurized void

“…Experimental research described by Chadwick et al (1963Chadwick et al ( --1964 showed that the void diameter D was between 1.15W 0.333 and 1.19W 0.333 m. Further experimental research by Waterways Experiment Station ( , 1961( ) Chadwick et al (1963( --1964, and Knox et al (1965) also suggested that the void vertical and horizontal diameters (D v and D h , respectively) were equal and lay between 0.754W 0.33 and 1.19W 0.33 m. Experimental research by Christopherson (1945) found that the void was nearly spherical, with a volume V between 2.738W and 3.3465W m 3 and a diameter D between 0.9918W 0.333 and 1.0711W 0.333 m. According to Zverev and Fetisov (1989) the range of diameters is due to the dissipation and absorption of the detonation gases into the voids behind the fracture surface. A void diameter of 6.246 m (1.048W 0.333 ) was chosen as satisfying the spread of experimental data.…”

“…A number of authors (Waterways Experiment Station 1960,1961, Knox and Terhune 1965, Bocharov et al 1989 have shown that the roof of the void, formed as described above, will eventually collapse in single or multiple stages in one of three ways, with the time to collapse varying between a few minutes and a number of years depending upon the type of subgrade. First, the whole of the cone of disturbance collapses into the void, with a settlement funnel being formed on the ground surface.…”

“…A void diameter of 6.246 m (1.048W 0.333 ) was chosen as satisfying the spread of experimental data. Research by Waterways Experiment Station (1960,1961) and Knox et al (1965) showed that the void is surrounded by a compacted spherical shell of subgrade, with an outer diameter some 20% larger than the diameter of the void. Thus a diameter of 7.496 m was chosen.…”

Fatigue life of subgrade in the cone of disturbance following an underground explosion

“…The repair team must ensure that this collapse does not occur during the 30-day runway operating period [6,7,15,18,19]. Dome collapse is complete when one of three conditions occurs.…”

Examination of cratering formulas and scaling methods

“…Several authors [Nuckolls, 1959;Maenchen and Sack, 1963;Knox and Terhune, 1965;Cherry, 1967] have developed computer codes to simulate the behavior of earth materials, and if the properties of the material being modeled are well known, results that accurately coincide with data from field experiments are obtained. Although computer calculations are time consuming and expensive, the investment is worth while for multimillon-dollar projects.…”