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Impact dynamics during collisions of spheres with granular media reveal apronounced and non-trivial dependence on volume fraction \phi. Post impactcrater morphology identifies the critical packing state \phi_{cps}, wheresheared grains neither dilate nor consolidate, and indicates an associatedchange in spatial response. Current phenomenological models fail to capture theobserved impact force for most \phi; only near \phi_{cps} is force separableinto additive terms linear in depth and quadratic in velocity. At fixed depththe quadratic drag coefficient decreases (increases) with depth for \phi <\phi_{cps} (\phi > \phi_{cps}). At fixed low velocity, depth dependence offorce shows a Janssen-type exponential response with a length scale thatdecreases with increasing \phi; and is nearly constant for \phi > \phi_{cps}.

Granular impact and the critical packing state