Theory and experiments on centrifuge cratering

Abstract

Centrifuge experimental techniques provide possibilities for laboratory simulation of ground motion and cratering effects due to explosive loadings. The results of a similarity analysis for the thermomechanical response of a continuum show that increased gravity is a necessary condition for subscale testing when identical materials for both model and prototype are being used. The general similarity requirements for this type of subscale testing are examined both theoretically and experimentally. The similarity analysis is used to derive the necessary and sufficient requirements due to the general balance and jump equations and gives relations among all the scale factors for size, density, stress, body forces, internal energy, heat supply, heat conduction, heat of detonation, and time. Additional constraints due to specific choices of material constitutive equations are evaluated separately. The class of constitutive equations that add no further requirements is identified. For this class of materials, direct simulation of large‐scale cratering events at small scale on the centrifuge is possible and independent of the actual constitutive equations. For a rate‐independent soil it is shown that a small experiment at gravity g and energy E is similar to a large event at 1 G but with energy equal to g3E. Consequently, experiments at 500 G with 8 grams of explosives can be used to simulate a kiloton in the field. A series of centrifuge experiments was performed to validate the derived similarity requirements and to determine the practicality of applying the technique to dry granular soils having little or no cohesion. Ten shots using Ottawa sand at various gravities confirmed reproducibility of results in the centrifuge environment, provided information on particle size effects, and demonstrated the applicability of the derived similitude requirements. These experiments used 0.5–4 grams of pentaerythritol‐tetranitrate (PETN) and 1.7 grams of lead‐azide explosives. They were placed at zero depth of burial and were detonated at gravities up to 450 G. These results provide rules for scaling crater dimensions in Ottawa sand over a range of more than 10 orders of magnitude in total energy release.

A simply constructed but efficacious shock tester for high-g level shock simulation

“…Current high-g level testing methods commonly used on lightweight components include the rail gun, air gun, free fall drop test, live fire test, Hopkinson Bar, pendulum striker, hammer below, piezo-actuators, and half-sine shock machines. [5][6][7][8][9][10][11][12][13] With the uses of a Mass Shock Amplifier, such as the Model MSA-89 × 89 developed by L.A.B. Equipment Inc., 14 such shock machines can generate accelerations as high as 100 000 g.…”

Experimental ejection angles for oblique impacts: Implications for the subsurface flow‐field

“…A point-source model is often used to approximate the effects of momentum and energy deposition from projectile to target material during an impact (e.g., Holsapple and Schmidt 1987), similar to the deposition from a chemical or nuclear source to the target during an explosion. It is possible to produce explosion craters that generally resemble impact craters in shape and morphology from laboratory to planetary scales (i.e., Roddy 1968;Oberbeck 1971;Roddy 1976;Schmidt and Holsapple 1980). Since planetary-scale impact craters are impossible to create experimentally, largescale chemical and nuclear explosion craters provide a useful reference for understanding planetary impact craters.…”

“…The point-source approximation is based on experimental and computational data for near-surface explosions (e.g., Oberbeck 1971;Roddy 1976;Piekutowski 1977Piekutowski , 1980Schmidt and Holsapple 1980) and vertical impacts (e.g., Oberbeck 1971;Stöffler et al 1975;Gault and Wedekind 1977). Various aspects of vertical impacts (such as ejecta curtain shape, crater shape and volume, and subsurface deformation) can be matched reasonably well by the optimum burial of an explosive source (e.g., Oberbeck 1971;Cooper 1977;Oberbeck 1977;Holsapple 1980).…”

Ejecta scaling laws for craters in dry alluvial sites

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The existing factor-of-20 scatter in the ejecta thickness data, for surface bursts (chemical and nuclear) in dry alluvium, is reduced to a scatter a factor of --•4 by a simple yield correction. Centrifuge experiments and dimensional analyses [Gault and Wedekind, 1977;Schmidt and Holsapple, 1980;Housen et al, 1983] offer another way to study large-yield explosions.For basic cratering mechanisms, small-scale (gram-sized charges) laboratory experiments [Piekutowski, 1977] can be very useful. Craters from surface bursts obey strength scaling, in which linear crater dimensions scale as cube root of the yield.

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