CNCS Graduate Certificate Recipient

Robert R. Hartley

Thesis Title: Evolving Force Networks in Deforming Granular Material

Ph.D. Final Defense Date:  March 31, 2003

Ph.D. Dissertation Committee:

Robert P. Behringer (Chair)
Daniel J. Gauthier
Anna L. Lin
Joshua E.S. Socolar
Stephen W. Teitsworth

Abstract:

This thesis presents two related experimental studies of evolving force networks in granular materials subject to slow shear.  The first uses an annulus with a fixed outer boundary and movable inner boundary (the source of shear).  Particles that have previously undergone plastic deformation experience slow collective rearrangements of the internal force network over long time scales.  This is consistent with an observed increase in the mean stress with shear rate, $\Omega$: force chains generated by shearing cannot completely relax on the time scales over which new chains are formed, an effect exacerbated by increasing $\Omega$.  Ensembles of particles that have undergone elastic deformation (like moderate compression) show no such rate dependence.  Distributions of stress close to a critical packing fraction, $\gamma_c$ (below which the stress network disappears), collapse onto a single exponential curve when rescaled by the mean stress, but do not collapse far from $\gamma_c$.  Finally, dense sheared systems become statistically stationary 100 times faster compared to packing fractions close to $\gamma_c$.

In the second set of experiments, the particles are confined to a vertical hopper with a movable floor.  For static ensembles, distributions of the stress deep within the hopper are described by a power-law with exponent $-1.343\pm0.008$ for small stresses (in agreement with an exponent of -4/3 predicted by models of static avanlanches), but are exponentially distributed for large stresses. The observed saturation of the stress with depth is poorly described by the Janssen model.  When the floor is raised, the stress within the hopper builds up (within one particle diameter) to a mean saturated value of stress, $\sigma_{sat}$.  The $rms$ fluctuations are much greater at the edges, while $\sigma_{sat}$ is greater in the interior bulk.  Unlike the experiments with the annulus, these experiments seem to be rate-independent: measurements of the stress for granules previously compressed and subjected to shear show no change (within experimental resolution) over long times.  Particle motion is facilitated by the 1--2\% dilation of the granular material, and once dilated, convection-like motion is observed.