Modeling Granular Mechanics on Low-Gravity Planetary Surfaces

Abstract

This dissertation details a series of modeling studies under the topic of granular dynamicsoperating on the regolith surfaces of low-gravity planetary bodies, with a specific focus on rubble- pile asteroids. Primarily, we investigate the influence of packing structure, particle shape, and bulk stiffness in regolith media on global strains, resurfacing, and induced seismicity in close planetary encounters and wave speeds in regolith as compared to laboratory experiments. For these investigations, we make use of the parallel, N-body gravity tree code with soft-sphere discrete element method, PKDGRAV, to model the discrete interactions between particles in regolith systems. We present herein our work improving the efficiency and physical accuracy of PKDGRAV’s implementation of non-spherical particles, with the aim of moving past the spherical particle ap- proximation. Decades of work in granular physics and geomechanics indicate that grain inter- locking due to irregular particle shapes plays a significant role in increasing the shear strength of granular systems. We apply this improved irregular particle model to small proof-of-concept studies of the Brazil-nut effect in low gravity, rubble-pile spin-up, and close planetary tidal en- counters, and find new behavior in all cases. The subject of the bulk of our investigations is the upcoming close planetary encounter between suspected rubble-pile asteroid (99942) Apophis and Earth, to take place on April 13, 2029. The natural experiment presented by the non-catastrophic tidal encounter between Apophis and Earth makes Apophis a prime target for space missions like OSIRIS-APEx and RAMSES that are motivated by planetary defense and the investigation of rubble pile dynamics and interior structure. We use PKDGRAV to model the full Apophis close encounter, assuming a rubble- pile Apophis, and investigate the global shape change on the body, estimate the measurability, depth, and frequency of the long- and short-period seismic signals, and predict localized areas with high likelihoods of resurfacing, all induced by the Earth’s tidal forcing in the encounter. Our main findings indicate relatively little global shape change at the nominal encounter distance, likely changes to the spin state of the body, little resurfacing outside of particularly susceptible surface patches, and seismic signals that are measurable by current-generation seismometers. These results, particularly regarding the induced seismicity, may help with inferring the interior structure of Apophis. We conclude with brief reviews of work from several ongoing studies matching simulated experiments to Earth-based laboratory experiments measuring pressure and shear wave speeds in regolith. Waves in regolith move along the chains of the strongest contact forces between particles in the medium. These complex systems of force chains are unique to the individual packing history and structure of a given regolith medium. We compare against low-speed impact experiments of ball bearings into sand, high-speed impact experiments of bullets into gravel, and bender element experiments measuring shear wave speeds in glass bead systems. In all cases, we find that the initial DEM parameters need to be carefully calibrated to match the physical materials and that large grain-size distributions and low packing densities can weaken force chains and decrease wave speeds. We also investigate the role that reduced gravity and confining pressure play in the wave speeds measured in these studies, finding slower wave speeds and weaker force chains in preliminary models of systems with lower gravity and confining pressure.