Experimental and Numerical Investigation on the Effect of Projectile Mass and Apex Angle on Penetration Depth into Sandy Soils

Projectile penetration in granular soils remains a critical concern in defense engineering and ballistics research. This study presents an experimental and numerical investigation of rigid cone-tip projectile penetration into very dense sand, examining the influence of apex angle and projectile weight on penetration depth. Laboratory experiments were conducted using metallic projectiles with apex angles of 10°, 30°, 60°, and 90° and weights of 2.445, 3.87, 5.33, and 6.81 kg, dropped from a height of 4.295 m into a 500×500×500 mm wooden tank filled with sand to 400 mm height at 95% relative density. Through systematic testing, two empirical correlation equations were initially developed: one relating penetration depth to apex angle and another linking depth to projectile weight. To enhance the accuracy of these correlations, Abaqus Explicit finite element simulations were employed using Coupled Eulerian-Lagrangian (CEL) methodology. The sand was modeled using the Mohr-Coulomb constitutive model with parameters derived from laboratory characterization. Validation was performed for 30° and 90° apex angle projectiles, achieving excellent convergence accuracy of 96.1%. Subsequently, four additional numerical models were developed for extended apex angles (105°, 75°, 45°, 20°) and four models for increased projectile weights (8.265, 9.72, 11.175, and 12.63 kg), significantly expanding the experimental database. The enhanced correlations demonstrated substantial improvement, with the apex angle relationship evolving from polynomial to power form (R² = 0.97) and the weight correlation maintaining polynomial characteristics with improved coefficients (R² = 0.9839). These findings provide robust empirical tools for predicting projectile penetration behavior in dense sandy soils.