  We study the drag force experienced by an object slowly moving at constant
velocity through a 2D granular material consisting of bidisperse disks. The
drag force is dominated by force chain structures in the bulk of the system,
thus showing strong fluctuations. We consider the effect of three important
control parameters for the system: the packing fraction, the drag velocity and
the size of the tracer particle. We find that the mean drag force increases as
a power-law (exponent of 1.5) in the reduced packing fraction, $(\gamma -
\gamma_c)/\gamma_c$, as $\gamma$ passes through a critical packing fraction,
$\gamma_c$. By comparison, the mean drag grows slowly (basically logarithmic)
with the drag velocity, showing a weak rate-dependence. However, the system
nevertheless exhibits strong statistical invariance in the sense that many
physical quantities collapse onto a single curve under appropriate scaling. We
also show that the system can be understood using simple failure models, which
reproduce many experimental observations. These experimental data and
simulations indicate that fluctuations in the drag force seem to be associated
with the force chain formation and breaking in the system. Moreover, our
simulations suggest that the logarithmic increase of the mean drag force with
rate can be accounted for if slow relaxation of the force chain networks is
included.
