We present a series of measurements examining the penetration force required to push a flat plate vertically through a dense granular medium, focusing in particular on the effects of the bottom boundary of the vessel containing the medium. Our data demonstrate that the penetration force near the bottom is strongly affected by the surface properties of the bottom boundary, even many grain diameters above the bottom. Furthermore, the data indicate an intrinsic length scale for the interaction of the penetrating plate with the vessel bottom via the medium. This length scale, which corresponds to the extent of local jamming induced by the penetrating plate, has a square root dependence both upon the plate radius and the ambient granular stress near the bottom boundary, but it is independent of penetration velocity and grain diameter.

Penetration by an object through a dense granular medium (for example, by a finger pushing slowly into the sand on a beach) presents an interesting physics problem that is closely related to issues of practical importance in soil science. Here we measure the penetration-resistance force for an object approaching the solid bottom boundary of a granular sample--analogous to the finger approaching a flat rock buried in the beach. We find that the penetration resistance near the boundary increases exponentially, which demonstrates the existence of an intrinsic length scale to the 'jamming' caused by a locally applied stress.

We have measured the flux of grains from a hole in the bottom of a shaken container of grains. We find that the peak velocity of the vibration, v max , controls the flux, i.e., the flux is nearly independent of the frequency and acceleration amplitude for a given value of v max .The flux decreases with increasing peak velocity and then becomes almost constant for the largest values of v max . The data at low peak velocity can be quantitatively described by a simple model, but the crossover to nearly constant flux at larger peak velocity suggests a regime in which the granular density near the container bottom is independent of the energy input to the system. † We study the flux of grains emerging though a small hole in the bottom of a container of a vibrating granular sample. This flux has analogs both in the familiar act of shaking salt from a salt shaker and also in the important statistical mechanics problem of fluid flow through a hole. While the flux has been studied extensively for unvibrated grains, 18, , , 19 20 21 for vibrated grains the flux has only been studied in the case of flow from a vibrated hopper (in which the boundaries all slope toward an open bottom). , 23Our measurements complement these studies by examining the simpler case of flux from a vibrated granular medium through a hole in a flat boundary over a broader range of parameters, and we demonstrate that this quantity can be largely understood within a simple model. were large enough so that the effects of interstitial air could be neglected., 24The hole diameter (D) was sufficiently large that the grains would flow even in the absence ofThe vessel was supported by four aluminum posts connected to an electromagnetic shaker controlled by two feedback accelerometers mounted on the rim of the vessel. The vessel was vibrated sinusoidally (y vessel = Asinωt) at a desired frequency, f = ω/2π, and a peak acceleration, Γ = Aω 2 /g, which we normalize to the gravitational acceleration, g = 9.81 m/s 2 .Grains flowing out from the container landed in a stationary collector suspended below the vessel. The collector was attached to an electronic balance, allowing us to record the mass of the effluent as a function of time, m(t), and thus determine the time-averaged flux from the hole, Φ(t) = dm/dt. The mass of glass spheres in the shaking vessel was such that there were between 20 and 90 grain layers in the container while data were acquired. The flux was found to be almost independent of mass in the shaker for the range of masses used in the experiments (variation of less than 10%). The frequencies used in our experiment ranged from 6 Hz to 400 Hz with Γ ranging from 1.25 to 10. The range of the vibration parameters was limited by the maximum amplitude of the shaker ( ~ 12 mm). The acquisition time for each measurement was 120 seconds (720 -48000 cycles), and each of the flux values reported below was taken as an average of at least five measurements (error bars represent the standard deviation of the measurements). All data were acqui...