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Considering the non-linear creep characteristics of clays, the modified unified hardening (UH) relation is employed to reflect the visco-elastic-plastic deformation of soft soils. Simultaneously, Swartzendruber's flow in the form of a continuous function is captured to describe pore water flow through pores during consolidation. Thus, an upgraded one-dimensional (1-D) non-linear rheological consolidation (NRC) system of clays has been established, and its solutions are conducted using the finite volume method (FVM). Through comparisons against the theoretical solutions and laboratory test results, the effectiveness of the numerical algorithm and applicability of the modified UH relation is verified. Then, the effects of model parameters on non-linear rheological consolidation behavior were studied. The results indicate that ignoring the time effect of secondary consolidation coefficient overestimates the overall consolidation and settlement proceeding, and considering the viscous effect of the soils led to an unanticipated increase in excess pore-water pressure (EPP) at the initial loading period. Meanwhile, the rising EPP becomes more pronounced with the increase of the initial over-consolidated parameter, flow parameter, and soil thickness or the decrease of overlying load. Additionally, FVM and finite difference method (FDM) solutions, as well as the application scope of Darcy's law in the NRC system, are discussed. [ABSTRACT FROM AUTHOR]