Geometrical scaling effect for penetration depth of hard projectiles into concrete targets

Since penetration tests of concrete targets against rigid projectiles are commonly conducted in reduced geometrical scale, whether the replica scaling law holds or not is very important for extending the knowledge based on the small-scale experiments to the large-scale or prototype penetration scenarios. In this paper, based on the available experimental data for depth of penetration (DOP) and discussions on the empirical formulae, it is verified that the replica scaling law is satisfied for DOP in rigid projectile penetrations, as long as the scaling is done strictly for both projectiles and concrete targets including the coarse aggregates. And the coarse aggregates with invariant size (not replica-scaled) could account for the non-scaling effect in DOP found in tests and empirical formulae. To explore the non-scaling effect in DOP caused by aggregates, a 3D mesoscopic finite element model for concrete target is developed. Based on the parametric analyses, it indicates that, the magnitude of the non-scaling effect decreases with the increasing of the cement strength when the aggregate strength is fixed. While the influence of the aggregate strength on the non-scaling effect is not so obvious comparing with the influence of cement strength. Besides, the magnitude increases with the increasing of the volume fraction of aggregates. These conclusions imply that, the non-scaling effect in DOP for different concrete targets with the same magnitude implied by the empirical formulae, and the always held scaling law in the (semi-)analytical models, may be unreasonable. Finally, based on the numerical results, a semi-analytical model for predicting DOP is proposed, which improved our previous model by further considering the non-scaling effect.