An implicit two-phase material point method for simulating pile penetration in soft soils

This study proposes a robust implicit two-phase material point method for single-pile penetration in soft soils. The method combines GIMP-based stress smoothing and VMS stabilization of the volumetric content within an implicit framework. It strictly preserves the physical U–W block structure, with the Darcy resistance acting only in the fluid momentum equation. Contact is enforced by an augmented Lagrangian scheme that uses displacement as the only primary variable and employs a consistent tangent. Together with an axisymmetric formulation, it delivers stable large-deformation solutions with frictional slip. The method is verified by Terzaghi consolidation and flexible strip-footing benchmarks. Pressure and settlement responses show no checkerboards and no boundary ringing. The approach is then compared against an existing ALE-based penetration case. The results show excess pore-water pressure peaking at the pile tip, a negative-pressure zone beneath the tip, an expanding displacement wedge with depth, and resistance–depth curves consistent with the literature. Mesh sensitivity indicates that a near-field element size of 0.2D is close to the 0.05D reference, whereas 0.4D is overly stiff. The framework achieves large time steps with Newton convergence under low-permeability, nearly undrained conditions. It provides reliable predictions of the penetration process and short-term recovery of axial capacity.