Vertical Vibration Amplification of a Saturated Fractional Derivative Type Viscoelastic Soil Layer

Abstract

Regarding the soil skeleton as viscoelastic medium with fractional derivative constitutive behavior, the influences of the soil skeleton viscosity and the soil layer thickness of saturated fractional derivative viscoelastic soil layer on the vertical vibration amplification coefficient is studied in the frequency domain by using the theory of Biot and one dimensional wave. The analytical expressions of the displacement, stress and pore water pressure of saturated soil layer are obtained by decoupling dynamic control equations and bounding the soil layer boundary conditions. The influences of physical and geometrical parameters of the saturated soil on vertical vibration amplification are investigated, and it is revealed that the vertical vibration amplification of the saturated classic elastic, fractional derivative type viscoelastic saturated soil and saturated classic viscoelastic soil are different when the soil layer thickness are changed; the material parameters of the fractional derivative model have great influences on the vertical vibration amplification coefficient.