The fractional order derivative Kelvin constitutive model is used to describe the rheological characteristics of saturated soils. With continuous drainage boundary

the Laplace transform is used to derive the analytical solutions of the one-dimensional consolidation of soil in the transformed domain. Then the corresponding semi-analytical solutions of the effective stress and the settlement are obtained through inverse Laplace transform based on Crump’s method. The rationality of the proposed solutions is validated by reducing the presented solutions based on continuous drainage boundary to those based on the Terzaghi drainage boundary. Finally

the effects of relevant parameters on consolidation behavior of soil are investigated by the obtained solutions. The results show that the interface parameter reflects the permeability of the drainage boundary

which has an obvious effect on the dissipation rate of the excess pore water pressure in soil. The viscosity coefficient greatly affects the settlement development in the later stage of consolidation

and the larger the viscosity coefficient is

the slower the settlement development is. When ? is not zero

a smaller fractional order α indicates a stronger viscosity

a longer consolidation process and a slower development of secondary consolidation.