Effect of two parallel intruders on net work during granular penetrations

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.