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.