Research on the Effects of New Duckbill-Type Casing Boots’ Penetration Parameters on the Smear Zone in Soft Soil

The smearing effect during drainage board installation in soft soil foundation repairs can reduce permeability and compromise the surrounding soil’s structure, limiting the foundation’s consolidation efficiency. This study introduces a novel duckbill-type casing pile shoe with an axisymmetric geometric structure to address issues related to the stability and coating control of conventional pile shoes. A Coupled Euler–Lagrange (CEL) method is employed to develop a three-dimensional model for large-deformation penetration. Additionally, a new analytical framework for the pile shoe insertion and coating mechanism is established by modifying the circular hole expansion theory based on axial symmetry assumptions. This research systematically explores the effects of pile shoe groove curvature, penetration rate, and soil types on the smear zone’s extent. The findings indicate that the circumferential shear effect in the near-field soil intensifies with an increased penetration rate, leading to the expansion of both strong and weak smear zones. When the groove curvature is between 90° and 135°, the smear zone changes from a concentrated to a dispersed pattern, reducing local stress concentration. The extent of the smear zone is also influenced by soil types: ordinary clay exhibits the smallest smear zone, while silty clay demonstrates the greatest. The enhanced circular-hole axisymmetric expansion model shows excellent agreement with the CEL simulation results, confirming its effectiveness when soil strength factors and pile shoe geometry are taken into account. The results provide a theoretical foundation and numerical assistance for the design of pile shoe structures, anticipation of smearing effects, and optimization of drainage board construction in soft soil foundations.