Resistance force scaling and the solution for penetration depth of impacting wet granular materials

In-depth understanding and mastery of the dynamic characteristics of objects during impact and penetration into granular materials are of great significance for studying natural phenomena and applications in industrial fields. Existing studies mainly focus on the impact of dry and non-cohesive granular materials, while the presence of liquid leads to differences in penetration depth. There are relatively few studies on the wet granular materials, especially regarding the effect of interstitial liquids in wet particle packings on the resistance force experienced by projectiles, which has not yet been quantitatively described. To clarify the effect of interstitial liquid on the resistance force borne by the projectile and the final penetration depth, this study conducted laboratory tests of the spherical projectile impacting wet particle packings and monitored the dynamic characteristics of the projectile during the impact process. Based on the motion equations of the projectile, the relationship between the inertial resistance term, the frictional resistance term, and the water content of the granular material was investigated, and an empirical parametric scale for the impact resistance force in wet granular materials was proposed. Additionally, with the help of the Lambert W function in mathematics, the analytical solution for the final penetration depth is given, and its reasonableness and accuracy were verified through experimental data.