The prediction of time-dependent behavior of axial capacity for jacked piles are essential for coastal pile engineering. This study develops a numerical model to simulate the entire process of pile installation, soil consolidation, and loading, incorporating soil-pile interaction effects on excess pore pressure and effective stress distribution in the surrounding soil, which influence the bearing performance of jacked piles in saturated clay. The well consistency between the predictions from the presented approach and the experimental measurement data validate the applicability of the proposed model. The mechanism of set-up effects on the pile axial capacity is elucidated through the evolution of excess pore pressure. A parametric study is performed to assess the influence of the permeability coefficient (k) and length-to-diameter (L/De) ratio on the axial capacity of jacked piles. The findings demonstrate that the proposed model accurately predicts the set-up effects of jacked piles. Specifically, the permeability coefficient primarily impacts the rate of capacity increase, while the axial capacity exhibits a significant rise with an increase in L/De. The derived empirical formula can reasonably guide the design of the axial bearing capacity of piles in saturated clay.