Vertical dynamic impedance of pile groups considering topographic effects

In this study, the theoretical equations for vertical impedance for single piles are deduced based on the Hamilton's principle. The reasonable method for calculating the pile-to-pile interaction is proposed considering the vibration difference with respect to the propagation direction. Finally, the impedance of pile groups is solved by combining the deformation coordination condition and mechanical equilibrium of piles and cap. The parameter studies are carried out to investigate the topography effects on the dynamic impedance of pile groups in sloping ground with various pile slenderness ratios, pile-soil modulus ratios and pile spacings. The results show that the interaction factor and pile group impedance fluctuate a lot with frequency. The extent of topography effects depends on frequency and can be significant at specific frequencies. The difference between the impedances for the pile groups in sloping ground and the horizontal ground increases as the slope angle pile length, and soil stiffness increase, which indicates that neglecting the topography effects may bring considerable error to the dynamic impedance of pile groups in slopes.