STEADY STATE RESPONSE OF ONE-DIMENSION LIQUID-SATURATED POROUS MEDIUM USING FRACTIONAL DERIVATIVE VISCOELASTIC MODEL

The stress-strain relationship of a solid skeleton is described by a fractional derivative Kelvin viscoelastic model, and the mathematic model and equations of motion of the steady state response of one-dimension liquid-saturated porous medium are established, in which the saturated porous material is modeled as a two phase system composed of an incompressible solid phase and an incompressible fluid phase, and the displacements both of the solid phase and fluid phase in one dimension liquid saturated porous medium described by fractional derivative viscoelastic model are obtained. The influence of fractional order on the steady state response is analyzed by a numerical example. The result indicates that the displacements both of solid phase and fluid phase will decrease to zero with the increase of frequency, and the displacements both of solid phase and fluid phase increase with the increase of fractional order at lower frequencies.