Penetration in bimodal, polydisperse granular material

We investigate the impact penetration of spheres into granular media which are compositions of two discrete size ranges, thus creating a polydisperse bimodal material. We examine the penetration depth as a function of the composition (volume fractions of the respective sizes) and impact speed. Penetration depths were found to vary between delta = 0.5D(0) and delta = 7D(0), which, for mono-modal media only, could be correlated in terms of the total drop height, H = h + delta, as in previous studies, by incorporating correction factors for the packing fraction. Bimodal data can only be collapsed by deriving a critical packing fraction for each mass fraction. The data for the mixed grains exhibit a surprising lubricating effect, which was most significant when the finest grains [d(s) similar to O(30) mu m] were added to the larger particles [d(l) similar to O(200 - 500) mu m], with a size ratio, epsilon = d(l)/d(s), larger than 3 and mass fractions over 25%, despite the increased packing fraction. We postulate that the small grains get between the large grains and reduce their intergrain friction, only when their mass fraction is sufficiently large to prevent them from simply rattling in the voids between the large particles. This is supported by our experimental observations of the largest lubrication effect produced by adding small glass beads to a bed of large sand particles with rough surfaces.