  The impact of single passive intruders into granular particles has been
studied in detail. However, the impact force produced by multiple intruders
separated at a distance from one another, and hence the effect of their
presence in close proximity to one another, is largely unexplored. Here, we use
numerical simulations and laboratory experiments to study the force response of
two parallel rods intruding vertically into granular media while varying the
gap spacing between them. We also explored the effect of variations in
friction, intruder size, and particle size on the force response. The net work
($W$) of the two rods over the depth of intrusion was measured, and the
instantaneous velocities of particles over the duration of intrusion were
calculated by simulations. We found that the work done by the intruders changes
with distance between them. We observed a peak in $W$ at a gap spacing of
$\sim$3 particle diameters, which was up to 25% greater than $W$ at large
separation (\textgreater 11 particle diameters), beyond which the net work
plateaued. This peak was likely due to less particle flow between intruders as
we found a larger number of strong forces---identified as force chains---in the
particle domain at gaps surrounding the peak force. Although higher friction
caused greater force generation during intrusion, the gap spacing between the
intruders at which the peak work was generated remained unchanged. Larger
intruder sizes resulted in greater net work with the peak in $W$ occurring at
slightly larger intruder separations. Taken together, our results show that
peak work done by two parallel intruders remained within a narrow range,
remaining robust to most other tested parameters.
