A bounding surface-based cyclic t–z model for axially loaded piles in clays

Prolonged axial cyclic loading leads to degradation in both the strength and stiffness of the pile –soil interface. Therefore, developing computational models that can reasonably predict the axial cyclic behavior of pile foundations is essential. This paper presents a novel cyclic t–z model formulated within a single bounding surface plasticity framework. The model incorporates a newly developed elastoplastic interface stiffness interpolation function to capture the evolution of interface stiffness under cyclic loading. By integrating an interface strength degradation function correlated with accumulated vertical plastic displacement, the model effectively captures the progressive degradation of interfacial strength during cyclic loading. The proposed t–z model is numerically implemented in MATLAB and validated through simulations of published interface shear tests. It is subsequently embedded into ABAQUS via a user-defined element subroutine to create a nonlinear spring element. The model demonstrates strong predictive capability for both monotonic and cyclic axial responses of pile foundations. With a relatively small set of parameters, it effectively simulates the evolution of axial force along the pile shaft and captures key characteristics of the pile head response, including hysteresis, nonlinearity, and accumulated displacement.