Vertical Dynamic Impedance for Piles in Radially Weakened Soil

The effects of surrounding soil degradation on the performance of piles during their operational phase remain inadequately understood within dynamic context. This study presents an energy-based methodology for estimating the dynamic impedance of a single pile situated in radially weakened soil. To achieve this, the surrounding soil is segmented into discrete annular zones, wherein soil deformation is modeled as a function of a series of decay functions corresponding to the pile shaft displacement. Hamilton's energy principle and the method of variations are employed to derive the governing equations. To enhance computational efficiency, fixed-point iteration utilizing Steffensen's technique is implemented. Additionally, a novel radial distribution model based on Bessel functions is introduced to more accurately reflect the changes in soil properties observed in experimental investigations. The study examines the effects of three distinct types of radial distributions of soil shear modulus on pile stiffness and damping characteristics. The findings indicate that the proposed approach improves low-frequency prediction by reducing the impact of boundary wave reflections. It is also found that the depth of soil degradation significantly influences pile impedance, particularly in the case of short piles embedded in soft soil.