This paper presents the results of a parametric study investigating the axisymmetric consolidation of a semi-infinite transversely isotropic saturated clay subjected to a time-varying circular pressure at the ground surface. Based on Biot’s governing consolidation equations for transversely isotropic clay, the general solutions have been previously derived by applying the Laplace–Hankel transform technique. A numerical inverting procedure was then used to study the consolidation behavior in the time domain for three loading cases, that is, instantaneous constant, ramp, and cyclical sinusoidal loadings. The obtained numerical results demonstrate that the pore pressure dissipation of the clay under the aforementioned time-varying loadings exhibits different characteristics that require special attention. Under ramp loading, the non-dimensional construction time factor, View the MathML source, significantly influences pore pressure dissipation, while under cyclical loading, pore water pressure changes may lag behind or exceed the period of the cycle, depending on the parameters that characterize the properties of the transversely anisotropic soil. Moreover, the change of soil surface settlement always lags behind the loading period under cyclical loading, which generates a negative pore water pressure.