A practical formula for penetration depth of rigid projectiles into rock and concrete considering the non-scaling effect

The non-scaling effect on the penetration depth of rigid projectiles is an important issue that must be considered when extending the results of scaled experiments to prototype scenes. In this study, the evolution of the stress and strain of the target under penetration was analyzed. Expressions for the penetration resistance and penetration depth were obtained based on the conservation equation and continuity condition of the target. The penetration coefficients that characterize the nose shape, target resistance, and non-scaling effect were defined. Simplified calculation methods for the coefficients within the range of rigid projectile penetration were developed. Two methods for estimating the target parameters are proposed. The results show that the non-scaling effect is related to the failure process of the target and depends on the ratio of cavity radius to comminuted region radius. The nose shape coefficient can be approximated as a linear function of the length-to-diameter ratio of the nose. The nose-shape coefficient of a flat-nosed projectile is 0.57. The caliber coefficient is related to the projectile diameter and reflects the non-scaling effect, which increases with the projectile diameter. A practical formula for calculating the penetration depth of rigid projectiles considering the non-scaling effect is also proposed. This formula is in good agreement with penetration experiments on rock and concrete.