The nonlinear flow law and soil boundaries greatly affect the dissipation process of soil consolidation. Thus, to study the impact of nonlinear flow under impeded drainage boundaries, the classical non-Darcian flow model described by non-Newtonian index was introduced. The numerical solutions are derived in detail by the finite difference method (FDM) for one-dimensional (1-D) consolidation incorporating the impeded boundaries, and the computer program is compiled. Then, comparing two analytical solutions based on Darcy’s law and a numerical case of Forchheimeer’s flow, the validity of the present method was verified. The numerical results indicate that there is a critical depth phenomenon for the non-Darcian flow incorporating impeded drainage boundaries. The excess pore water pressure of the soil below the critical depth dissipates more slowly than that of Darcy’s law, whereas the pore pressure of the soil above the critical depth dissipates more quickly than that of Darcy’s law. Moreover, considering that the non-Darcian flow with the non-Newtonian index will still delay the overall consolidation rate of the soft ground, the greater the nondimensional parameter I₀ is, the more obvious the lagging phenomenon of the overall dissipation of pore pressure is.

While early ideal consolidation theories for vertical drains focused primarily on radial flow, numerous coupled radial–vertical seepage models have since been developed to better capture complex flow behavior in practice. To overcome this limitation, a nonlinear large-strain consolidation model for vertical drains with coupled radial-vertical flow is proposed, explicitly incorporating Hansbo’s non-Darcy flow, smear effects, and soil nonlinearity. The finite difference method is then employed to obtain numerical solutions, and the reliability of the proposed numerical scheme is verified by degenerating the model to the radial consolidation case and comparing the results with the corresponding analytical solution. The results indicate that consolidation develops fastest when the permeability coefficient within the smear zone follows a parabolic distribution. Increasing the Hansbo’s flow parameter m and threshold hydraulic gradient parameter I₁ markedly slows down the consolidation process, while the contribution of vertical flow is primarily confined to the early stage. In addition, larger soil nonlinearity parameters I_c and α amplify the influence of radial–vertical coupled flow. Parametric analysis further shows that when the ratio of soil layer thickness to the radius of the influence zone (H/r_e) exceeds 10, the effect of vertical flow becomes negligible, and the consolidation behavior can be reasonably approximated using a radial-flow-only model.

The vacuum preloading method effectively strengthens soft soil foundations with vertical drainage, which produces a smear effect when laying sand drains. Meanwhile, the seepage of pore water and soil deformation during consolidation exhibit nonlinear characteristics. Therefore, based on Gibson’s 1D large-strain consolidation theory, this paper developed a more generalized large-strain radical consolidation model of sand-drained soft foundations under free-strain assumptions. In this system, the double logarithmic compression permeability relationships for soft soils with large-strain properties, the variation in the radical permeability coefficient in the smear zone, and the effect of the non-Darcy flow were all included. Then, the partial differential control equations were numerically solved by the finite difference method and validated with existing radical consolidation test results and derived analytical solutions. Finally, the influences of relevant model parameters on consolidation are discussed. The analysis shows that the greater the maximum dimensionless vacuum negative pressure P₀, the faster the consolidation rate of sand-drained foundations. Meanwhile, the decrease in the negative pressure transfer coefficient k₁ will result in a decreasing final settlement amount. Moreover, the consolidation rate of sand-drained foundations is slower considering the non-Darcy flow, but the final settlement is unaffected.