Constraining damage size and crater depth: A physical model of transient crater formation in rocky targets

• It is derived how crater and damage depth depend on impact velocity, projectile mass, and strength and porosity of rock.
• The derived formulae could be seen as specific forms of Holsapple–Housen model in strength regime.
• Higher porosity yields a deeper crater depth but a shallower damage depth.

This paper derives mathematically how crater depth and crater damage depend on impact velocity, mass of projectiles, and strength and porosity properties of rocky targets. In this impact model, stage I is based on an one-dimensional impact assumption and Rankine–Hugoniot jump conditions. Stage II is based on cavity expansion process in target materials considering Mohr–Coulomb criterion and porosity. The derived formulae could be seen as specific forms of Holsapple–Housen model in strength regime, and the model quantitatively predicts 1) the crater depth in tuff, dry sandstone, quartzit, gabbro and ice targets, and 2) the damage depth in dry sandstone and gabbro targets. The porosity effects on crater depth and damage depth are also discussed and compared with existing results from numerical calculations, and it shows that a higher porosity yields a deeper crater depth but a shallower damage depth.