Granular impact and the critical packing state

Impact dynamics during collisions of spheres with granular media reveal a pronounced and non-trivial dependence on volume fraction ϕ. Post impact crater morphology identifies the critical packing state ϕ_{cps}, where sheared grains neither dilate nor consolidate, and indicates an associated change in spatial response. Current phenomenological models fail to capture the observed impact force for most ϕ; only near ϕ_{cps} is force separable into additive terms linear in depth and quadratic in velocity. At fixed depth the quadratic drag coefficient decreases (increases) with depth for ϕ< ϕ_{cps} (ϕ> ϕ_{cps}). At fixed low velocity, depth dependence of force shows a Janssen-type exponential response with a length scale that decreases with increasing ϕ; and is nearly constant for ϕ> ϕ_{cps}.

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