A nonlinear shaft-plate coupled load transfer model for axially loaded helical piles

A nonlinear shaft-plate coupled load transfer model is proposed for axially compressed helical piles. The novelty of the model lies in treating the helix plate as a discrete internal bearing interface embedded within a continuous shaft load transfer system, so that the axial-force jump, displacement compatibility, and nonlinear resistance mobilization are solved simultaneously within a single boundary value problem. Hyperbolic load–displacement relations are adopted for both the distributed shaft resistance and the localized plate bearing, with the initial stiffness parameters k s0 and K b0 derived from the same elastic continuum solution to ensure internal consistency within a unified framework. Displacement compatibility and axial force jump at each plate location complete the nonlinear boundary value problem, which is solved through an iterative finite-difference scheme updating equivalent secant stiffness until convergence on both plate load and displacement field. The pile head response, axial force distribution, shaft friction mobilization, plate bearing ratio, and interface stiffness degradation are obtained. Parametric studies reveal that pile geometry, helix embedment depth, and soil stiffness gradient collectively govern the nonlinear load transfer characteristics. Within the investigated parameter range, increasing load promotes a progressive redistribution of axial resistance from the shaft toward the helix plate. The extent of this transition depends on the relative shaft-plate strength and stiffness, rather than being a fixed response mode. Both shaft friction mobilization and interface stiffness degradation exhibit a spatially non-monotonic distribution, peaking in a primary transfer zone above the helix plate and diminishing below. This depth-zoning pattern is induced by plate-mediated load diversion and is absent in conventional straight piles.