Hardness-based resistance model for predicting penetration depths by rigid projectiles on various cement-based materials

With the development of advanced cement-based composites, conventional penetration models based primarily on uniaxial compressive strength have become increasingly inadequate. Although many empirical or semi-empirical models have been refined for specific concrete types, their accuracy levels are mostly limited to narrow material classes. This study introduces a novel penetration resistance model that uses the macroscopic effective hardness as the key parameter input. The use of hardness is motivated by the mechanical similarity between the static resistance component encountered during projectile penetration and the force response in indentation hardness tests. Drawing on this analogy, the effective hardness serves as a unified index that implicitly reflects the combined contributions of mortar, aggregates, and steel fibers within the cement-based matrix. The model integrates both previously published data and new experimental results for deep penetration, spanning a wide range of cement-based materials, including normal-strength concrete (NSC), fiber-reinforced cement paste (FRCP), fiber-reinforced mortar (FRM), engineered cementitious composites (ECC), fiber-reinforced concrete (FRC), fiber-reinforced high-strength mortar and concrete (FRHSM and FRHSC), as well as ultra-high-performance fiber-reinforced concrete (UHPFRC), with aggregate volume fractions up to 52% and compressive strengths from 37.9 to 238.5 MPa. Validation was performed using penetration depth data from ogive-, conical-, and spherical-nosed projectiles impacting at 372.0 to 833.1 m/s, with higher velocities excluded due to potential projectile failure, and prediction errors generally within 15%, demonstrating both accuracy and robustness. Compared to existing empirical formulas, the proposed model shows significantly improved generalizability and offers a practical, non-destructive approach for assessing and designing impact-resistant cement-based materials.