Ultrasound wave propagation in glass-bead packing under isotropic compression and uniaxial shear

The axial-stress dependence of sound wave velocity in granular packing is experimentally investigated with tri-axial and uni-axial devices. Preparing samples by repetitive loadings and unloadings in a range of 20 kPa-1000 kPa, we find that the axial-stress dependence of sound wave velocity approaches the Hertz scaling with an exponent of 1/6 for large axial stresses (> 400 kPa). Weak deviation from the Hertz scaling is seen at low stresses. Repetitive axial loadings slightly reduce this deviation, and sound velocities increase nonlinearly approaching some saturated values. Velocities for uni-axial case are found slightly to be bigger than those for tri-axial isotropic compression case. These effects are discussed in the frameworks of granular solid hydrodynamics (GSH) and effective medium theory (EMT), which indicate that they cannot be explained with density nor Janssen ratio only. Dissipation occurring during wave propagation may be a non-negligible factor.