Regarding the soil skeleton as a viscoelastic medium with fractional derivative constitutive relation

the governing equations of the steady state vibration of the saturated fractional derivative viscoelastic soil embedded a spherical cavity are established based on the Biot’s theory. The analytical expressions of the displacements

stresses and pore water pressure of the saturated fractional derivative viscoelastic soil with a spherical cavity are obtained with the introduction help of potential functions in case of spherical symmetry. The influences of the parameters of fractional derivative model and saturated soil on the vibration characteristics of the soil are examined; and the numerical results show that the fluid compressibility has a great influence on the dynamic characteristics; while the influences of the soil skeleton compressibility and fluid-solid coupling coefficient are trivial. The influence of the fractional derivative order on the dynamic behavior of the soil depends on the values of material parameter ratio. Furthermore

the dynamic responses of the saturated soil with undrained boundary condition are greater than those with the drained boundary condition.