A Unified Winkler Model for Vertical and Lateral Dynamic Analysis of Tapered Piles in Layered Soils in the Frequency Domain

Tapered piles are a new type of pile foundation known for their simple construction and high bearing capacity, commonly used in railway, highway, or building foundation treatment. This study proposes a unified dynamic Winkler model for vertical and lateral vibration response of tapered piles in the frequency domain using the impedance function transfer matrix method. The computational expressions are obtained for the different springs and damping of tapered piles with different dimensions using the elastodynamic theoretical of rigid embedded foundations, and the dynamic interaction mechanisms of vertical and lateral vibrations between tapered piles and soil are analyzed. The rationality of the simplified model is validated by comparison with existing literature and finite element simulation results. Finally, an example is provided to discuss the influences of the dimensional parameters of the pile and soil properties on vertical, lateral, and rocking dynamic impedance. The analytical findings demonstrate that the lateral and rocking dynamic impedances of tapered piles undergo a substantially greater enhancement relative to their vertical counterpart as the taper angle is progressively enlarged, assuming the pile volume remains constant. The dynamic impedance of tapered piles under vertical and lateral vibration in upper hard and lower weak soil layers, or upper weak and lower hard soil layers, are both greater than those in a homogeneous foundation. Specifically, the vertical dynamic stiffness of tapered piles in double-layered soils is approximately twice that of homogeneous soil. The rocking dynamic stiffness of the pile is significantly influenced by the soil properties around the pile foundation, whereas the soil properties have little impact on the rocking damping coefficient. Overall, the vertical dynamic characteristics are less influenced by the geometric features of the upper part of the tapered pile, while the lateral dynamic characteristics are significantly affected by these features. The lateral dynamic impedance of the tapered pile increases with the diameter of the upper part of the pile. Furthermore, the vertical, lateral, and rocking dynamic impedance of the pile can be effectively improved by enhancing the soil properties around its upper section. These results can provide theoretical references for the engineering practice.