  As a granular material is compressed, the particles and forces within the
system arrange to form complex heterogeneous structures. Force chains are a
prime example and are thought to constrain bulk properties such as mechanical
stability and acoustic transmission. However, characterizing the dynamic nature
of mesoscale architectures in granular systems can be challenging. A growing
body of work has shown that graph theoretic approaches may provide a useful
foundation for tackling these problems. Here, we extend current approaches by
utilizing multilayer networks as a framework for directly quantifying the
evolution of mesoscale architecture in a compressed granular system. We examine
a quasi-two-dimensional aggregate of photoelastic disks, subject to biaxial
compression through a series of small, quasistatic steps. Treating particles as
network nodes and inter-particle forces as network edges, we construct a
multilayer network by linking together the series of static force networks that
exist at each strain step. We then extract the inherent mesoscale structure
from the system by using a generalization of community detection methods, and
we define quantitative measures to characterize the reconfiguration and
evolution of this structure throughout compression. By separately considering
the network of normal and tangential forces, we find that they display
different structural evolution. To test the sensitivity of the network model to
particle properties, we examine whether the method can distinguish a subsystem
of low-friction particles within a bath of higher-friction particles. We find
that this can be done by considering the network of tangential forces. The
results discussed throughout this study suggest that these novel network
science techniques may provide a direct way to compare and classify data from
systems under different external conditions or with different physical makeup.
