Penetration Law in Loose Granular Medium for the Chang’E 5 and Chang’E 6 Footpad

Abstract This study investigates the penetration behavior of the footpads used in the Chang’e-5 (CE-5) and Chang’e-6 (CE-6) lunar probes when interacting with granular materials. Through a series of controlled impact experiments conducted using a full-scale footpad model, the influence of the impact height, impactor mass, landing velocity, and the properties of the granular medium on the penetration depth is investigated. The results yield an empirical formula for predicting the penetration depth of the CE-5/-6 footpad from the impactor mass, landing velocity, footpad area, and the internal friction angle of the granular material under impact. A validation experiment conducted on lunar regolith simulant verified that the empirical formula can accurately predict the internal friction angle of granular material. The maximum deviation between the predicted values of the lunar soil simulant and those measured by conventional consolidated drained triaxial tests is 3 . ° 3 (6.8%). Additional experiment results show that the impact depth of the medium, to which the impact energy attenuates to a negligible level, is about 15.2 times the penetration depth of the footpad. These findings offer an approach for in-situ measurement of the friction angles of the lunar soils at the landing sites of the CE-5/-6 probes and probes of future missions.