Analytical Solutions for Plane Strain Consolidation of Layered Unsaturated–Saturated Ground With Vertical Drains: Role of Lateral Semi‐Permeable Boundaries

ABSTRACT The coexistence of saturated and unsaturated soil layers is common for soil subgrade improvement by a combination of prefabricated vertical drains (PVDs) and surcharge preloading. In such scenarios, the smear effect of PVDs and the layered hydraulic properties significantly influence the time‐dependent settlement. Under plane strain conditions, this paper analytically investigates the consolidation behavior of a composite subgrade consisting of a two‐phase (air‐water) flow unsaturated layer and a single‐phase (water) flow saturated layer, with PVDs installed on both lateral sides. By integrating classic consolidation theories for saturated and unsaturated porous media, and featuring the smear effect induced by PVDs using lateral semi‐permeable boundary conditions, Laplace‐domain analytical formulas for excess pore‐air pressure, excess pore‐water pressure, and surface settlement are derived. The proposed solutions are validated against the special cases of a homogeneous single soil ground with lateral semi‐permeable boundaries. A convergence study indicates that truncating 40 terms in the infinite series achieves a good trade‐off between accuracy and efficiency. This paper, with the present solution, conducts parametric investigations to examine how the lateral boundary parameter, PVD spacing, and hydraulic anisotropy affect the consolidation behavior. The results show that when the unsaturated layer has lower hydraulic conductivity than the saturated layer, the lateral semi‐permeable boundary condition significantly influences the pore‐water‐dominated consolidation stage across all examined PVD spacings and anisotropy ratios. This finding indicates that mitigating the smear effect is consistently beneficial for accelerating the consolidation of unsaturated–saturated soil composite strata across all examined PVD spacings and permeability anisotropy ratios.