To achieve the satisfactory performance of a machine foundation, the dynamic amplitude should be limited to a few micrometres. In using piles for the foundation, the interaction of the pile with the surrounding soils under vibratory loading will modify the pile stiffness and will generate damping. The results of a three-dimensional, finite element model of a soil-pile system with viscous boundaries were used to determine the dynamic stiffness and damping generated by soil-pile interactions for a single vertical pile subjected to a vertical harmonic loading at the pile head. The pile was embedded in a linearly elastic, homogeneous soil layer with material damping of the hysteretic type. A parametric study was undertaken to investigate the influence of the major factors of the soil-pile system that affect the vertical vibration characteristics of the pile response. These were found to include the dimensionless frequency, soil properties, pile properties, and length and axial load on the pile head. Equations were developed to determine the range of such influence. Two general equations that include all of these parameters and can be used to approximate the stiffness and damping of the pile were developed so that a finite element analysis does not have to be made in every case.
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