Measurement of the mechanical properties of granular packs by wavelength-scanning interferometry

A wavelength scanning interferometer has been constructed to observe both the normal and in-plane displacements particle by particle at the base of a model granular pack. The pack comprised 25,000 of steel beads supported by a thick glass substrate and subjected to local disturbing forces on its upper surface. The system allows measurement of normal displacements of the beads to a precision of ca. 0.1 nm, thereby providing highly accurate determination of contact forces whilst minimizing artefacts due to substrate and grain compliance. The probability distribution of the normalized contact force was found to be approximately independent of the applied load on the upper surface of the granular pack and has an exponential tail. The probability distribution of the normalized response force and lateral displacement have similar power law tails. The interactions between contact forces and lateral displacements suggest that significant internal rearrangement occurs in the granular pack as the load is increased, and particle displacement plays an important role in the mechanics of the granular material.