Analysis of vertical vibrations of a pile in saturated soil described by fractional derivative model

As we know, the soil has viscoelastic characteristic, the control equations of saturated soil described by fractional derivative model are established based on the theories of porous media and theories of fractional derivatives, in which the soil is regarded as porous medium filled with water; and the stress-strain relationship is described by fractional derivative viscoelastic model for considering the viscoelastic properties of soil skeleton. The vertical coupled vibration of a pile in a saturated soil described by fractional derivative model is investigated by introducing the potential functions and separation of variables method under the three-dimensional axisymmetric condition; and the influences of the model parameters on the vertical vibration of a pile in saturated soil is analyzed. The results indicate that the control equations of the saturated soil described by fractional derivative model has a wider application; and the model parameters has great influences on the vertical vibration of a pile in saturated soil.