VERTICAL VIBRATION AMPLIFICATION OF A SATURATED FRACTIONAL DERIVATIVE TYPE VISCOELASTIC SOIL LAYER

The soil skeleton is treated as a viscoelastic medium with a fractional derivative constitutive relation. By utilizing the Biot’s theory, the influences of the viscosity of soil skeleton and the thickness of soil layer for a saturated soil layer on the vertical vibration amplification coefficient are investigated in the frequency domain. By decoupling dynamic control equations and bounding the boundary conditions, the analytical expressions of the displacement, stress and pore water pressure for the saturated classic elastic, saturated fractional derivative viscoelastic soil and saturated classic viscoelastic soil are obtained. On the basis, the vertical vibration amplification of the soil layer is analyzed for different physical and geometrical parameters of the soil. It is shown that the vertical vibration amplification of the saturated classic elastic, fractional derivative viscoelastic saturated soil and saturated classic viscoelastic soil are different for the different thickness of soil layers;the material parameters of the fractional derivative model have great influences on the vertical vibration amplification coefficient.