Dynamic response of a spherical cavity in viscoelastic fractional derivative type saturated soil

Based on the Biot's consolidation theory, the dynamic response of a spherical cavity in viscoelastic fractional derivative type saturated soil is investigated in the frequency domain. The stress and strain constitutive relation of the soil skeleton is described by the fractional derivative type viscoelastic model. By utilizing a stress coefficient depending on the porosity of soil, the values of the inner water pressure in lining and in pore water are determined, respectively. Based on the continuity conditions at the interface between the soil and the lining, the steady-state dynamic response of the spherical cavity in fractional derivative type viscoelastic saturated soil subjected to the inner water pressure is obtained. The influences of physical parameters on the response amplitudes are studied, and it is revealed that their influences on the system response are remarkable by the viscosity of soil, the characteristics of materials and the relative permeabilities of the pore flexible lining and saturated soil.