6.1 Modeling repacking in a granular medium from a continuum
perspective
The loading curves for Hoyos et al. (2022), in some cases,
display sharp discontinuities. These discontinuities were termed “load
drops” by Hoyos et al. (2022) and were attributed to the
disruption or failure of force chains. Force chains - collections of
jammed particles prevented from freely rotating and translating
(Bergantz et al. , 2017, Philpotts et al. , 1998, Qin &
Suckale, 2020, Schleicher & Bergantz, 2017) - build up over the
duration of the experiment. The formation of force chains acts to jam
the granular medium and is a highly stochastic process, as illustrated
from the variable evolution of \(\Sigma\) for repeated experiments using
the same particle shape, size, and distribution. Hoyos et al.(2022) demonstrated that the buildup of force chains may be attributed
to the fact that the ability of particles to freely rotate is impinged
by the apparatus walls, with larger particles experiencing locking more
frequently.
The development of coupled modeling-experimental studies that validate
models for compaction is rare as of now but necessary. The results of
the optimizations and the load curves of the experiments of Hoyoset al. (2022) and the porosity profiles of the olivine centrifuge
experiments are in good agreement (Fig. 5 , Fig. 6 , andFig. 9 ). It is an important result because compaction models
have been applied to model phase separation in magma reservoirs with
limited experimental validation. We find that across all particle types
tested by Hoyos et al. (2022) – both in the case of pure and mixture
endmembers – the model fits the data well, even for the experiments
with load curves that exhibit sharp discontinuities. The fact that the
continuum-scale model fits the data well and within reasonable bounds
for the inverted parameters is promising.