Softening effect and fluidization have been explored and identified as general phenomena of granular materials in the presence of vibrations. In the framework of statistical mechanics, we propose a statistical model to predict the softening effect, finding that the softening effect can be simply described by two parameters, the average potential energy of grain-contacts and the correction factor accounting for the graincontact orientation. The average potential energy is strongly dependent on the effective pressure applied on the granular system, and a power-law scaling with effective pressure is observed experimentally as well as theoretically based on the Hertz contact theory. Laboratory observations both on the compressive modulus and the shear modulus of the tested granular materials show consistence with our theoretical predictions, which provide a direct verification on our proposed model. A fluidization model is further implemented based on the proposed statistical model, which is also supported by the experimental observations. A quantitative analysis regarding the vibration amplitude as well as the vibration frequency further verifies the model of effective viscosity of the granular system in the presence of vibrations.
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