An Analytical Model for Long‐Term Settlement of Pile‐Soil Systems Considering Fractional‐Order Viscoelasticity and Soil Damage

Abstract

Accurate prediction of the long‐term settlement of pile foundations remains challenging because the viscoelastic characteristics and damage behavior of foundation soils are not adequately considered in conventional settlement models. To address this issue, a fractional‐order viscoelastic damage creep model is developed by incorporating nonlinear damage variables into the fractional‐order Merchant model. Based on fractional calculus and the elastic‐viscoelastic correspondence principle, the Mindlin displacement solution is derived for a viscoelastic damaged foundation subjected to vertical loading. The pile settlement is decomposed into pile‐soil coordinated deformation and axial compression of the pile shaft, and a settlement calculation model for the pile‐soil system is established using the superposition principle. A self‐developed testing device is employed to characterize the pile–soil interface mechanical behavior and validate the proposed model. The results show that the damage factor significantly affects both the initial settlement rate and final settlement, whereas the fractional order governs the time‐dependent evolution of settlement. The calculated results agree well with the experimental observations, demonstrating that the proposed model can effectively describe the long‐term settlement behavior of the pile‐soil system.