Contact stiffness in granular porous materials: Comparison between theory and experiment

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Abstract
Propagation of acoustic waves in earth materials is controlled to a large extent by the properties of the solid frame of the material. In sedimentary materials, interactions at the grain contacts provide a key to understanding the frame properties. In this note, a recent theoretical model by Digby (1981) for acoustic velocities in dry, disordered sphere packs is discussed and applied to experimental data. Central to the model are the normal and tangential stiffnesses at the contacts between grains. We have inverted Digby’s results to give equations for the contact stiffnesses in terms of the measured velocities. These equations have been applied to experimental data from the literature for both unconsolidated glass beads and Berea sandstone at various confining pressures. Taken literally, these results indicate that interactions at real grain contacts are not well described by conventional Hertz‐Mindlin contacts or by modified Digby contacts. Alternatively, the results indicate that the theory requires modifications such as additional contact interactions or distributions of grain sizes, coordination numbers, or contact stiffnesses.