Oscillated densely packed granular media immersed in a fluid

A densely packed bed of granular material immersed in a fluid is cyclically agitated. The fluid may be compressible due to a small amount of gas trapped in the pores. From the general two-phase equations the oscillatory motion characteristics are determined. A penetration depth of the order of magnitude of a few particle diameters is found. Secular cycle-averaged effects are investigated and two are identified: a particle pressure due to irreversible processes and collisions during the oscillation, which is linear in the velocity amplitude and a quadratic effect that arises due to non-zero correlations between the fluctuations in solids volume fraction and those in velocity, displacement and pore pressure. Orders of magnitude and time constants of both these secular effects are established. The analysis shows that the secular effects manifest themselves in a few cycles of the vibration. From constitutive estimates the influence on mean intergranular stress and interstitial pore pressure is obtained. It is found that the quadratic effect hardly affects the intergranular stress, but has a substantial influence on the pore pressure, which is reduced. The linear particle pressure effectively decreases the magnitude of the compressive intergranular stress. Linear and quadratic effects have markedly different frequency dependencies. A comparison with experiment on this point is reported. Applications are vibrated filtration and agitated magma chambers that contain sediment. For the latter the theory explains the formation of gas bubbles associated with rapid fluid pressure reduction during earthquake loading.