The way to achieve satisfactory performance of a machine foundation is to limit its dynamic amplitude to a few micrometers. In using piles for the foundation, the interaction of the pile with the surrounding soils under vibratory loading will modify the pile stiffness and generate damping. This study presents the results of a three-dimensional finite element model of a soil-pile system with viscous boundaries to determine the dynamic stiffness and damping generated by soil-pile interaction for a vertical pile subjected to a vertical harmonic loading at the pile head. The pile was embedded in a linearly elastic, homogeneous soil layer with constant material damping. 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, ao, soil-properties, pile properties, and length and axial load on the pile head.;Pile foundations are generally constructed in groups. A three by three group of piles rigidly capped were used in this study. Three different pile spacings were used, two times, four times and six times the pile diameter. Both the dynamic stiffness and damping were determined for the whole group. The group effect on the stiffness and damping was determined by group stiffness and damping efficiency factor. The efficiency factor was found to be frequency dependent, could attain values above unity, and was very sensitive to the soil shear modulus. The distribution of forces among the pile group was also determined.
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