Abstract: Based on Biot's porous medium theory, a fractional order Kelvin model is used to describe the rheological effect of soil skeleton. The spatiotemporal analytical functions of slope, triangular, and trapezoidal loads are introduced to construct a three-dimensional axisymmetric consolidation model of saturated clay foundation under time-varying loads. The Hankel–Laplace coupled transform and tensor operation are used to derive the analytical solution of the control equation in the transformation domain, and then numerical inversion is used to obtain the spatiotemporal domain solution. Through numerical analysis, the rheological consolidation behavior and parameter influence law of saturated clay foundation under time-varying load were studied. The results indicate that the rheological properties of the soil skeleton have an inhibitory effect on pore water permeability, slowing down the settlement rate of the soil during the primary consolidation stage, accelerating the settlement rate during the secondary consolidation stage, and increasing the long-term settlement amount. During the unloading stage, the soil undergoes deformation and recovery, and the elastic expansion of the soil skeleton generates negative pore pressure. The stronger the rheological properties of the soil skeleton, the smaller the amount of deformation recovery, and the smaller the negative pore pressure generated. The type of load and loading path mainly affect the changes in displacement and pore pressure over time during the consolidation process, while the rheological properties of the soil skeleton affect the long-term settlement of the soil.