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Considering the nonlinear rheological properties of saturated clay, the modified unified hardening (UH) constitutive relation was introduced to describe the nonlinear rheological deformation. Meanwhile, Swartzendruber's flow law was used to simulate the non-Darcian flow of pore water in the progress of rheological consolidation. Consequently, a nonlinear rheological consolidation model (NRCM), for one-dimensional consolidation, that simultaneously incorporates nonlinear stress-strain-time relationship, Swartzendruber's flow, self-weight stress, and variable permeability coefficient has been developed here. The finite volume method (FVM) was utilized to solve the NRCM system, and its effectiveness was verified by comparing with the existing consolidation data. The parametric analysis results indicate that the soil's nonlinear rheological effect induced the excess pore water pressure (EPWP)'s accumulation in the initial loading. This phenomenon became more significant when considering the self-weight stress or as the initial overconsolidated parameter, soil thickness, and seepage parameter increased. In contrast, it weakened with the increase of external loading. Additionally, considering the self-weight stress slowed down the whole dissipation of EPWP in the initial period of loading. Nevertheless, it accelerated the nonlinear consolidation process in the middle and late loading stages.

To further investigate the rheological consolidation mechanism of soft soil ground with vertical drains, the fractional-derivative Merchant model (FDMM) is introduced to describe the viscoelastic behavior of saturated clay around the vertical drains, and the flow model with the non-Newtonian index is employed to describe the non-Darcian flow in the process of rheological consolidation. Accordingly, the governing partial differential equation of the ideal sand-drained ground with coupled radial-vertical flow is obtained under the assumption that the vertical strains develop freely. Then, the numerical solution to the consolidation system is conducted using the implicit finite difference method. The validity of this method is verified by comparing the results of Barron’s consolidation theory. Furthermore, the effects of the parameters of non-Darcian flow and FDMM on the rheological consolidation of ground with vertical drains are illustrated and discussed.