Nonlinear Large-Strain Consolidation of Vertical Drains with Coupled Radial–Vertical Flow Considering Hansbo’s Flow and Smearing Effects

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 Ic 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/re) exceeds 10, the effect of vertical flow becomes negligible, and the consolidation behavior can be reasonably approximated using a radial-flow-only model.