Kinematic response of end-bearing pile groups subjected to vertically incident P-waves

The kinematic response of end-bearing pile groups in an elastic half-space under vertically incident P-waves is investigated in this paper. The soil and the pile groups are considered as continuum elastic elements to formulate the asymmetrical scattered waves resulting from individual piles. General expressions for the vertical scattered displacements in the soil and piles are obtained using the method of separation of variables. Graf's addition theorem is modified to consider the scattered waves resulting from the individual pile pairs in different local polar coordinates. The boundary-valued problems are formulated as an infinite series of linear algebraic systems with unknown coefficients by considering the continuities along the soil-pile interfaces. Truncating numbers are selected to ensure the convergence and accuracy of the proposed method. Parametric studies are conducted to investigate the pile-to-pile interactions under vertically incident P-waves. Numerical results reveal that the pile separations and the pile numbers significantly affect the pile-to-pile interaction of pile groups. Pile group effects are distinct for different pile group arrangements. Dynamic concentrations are observed in the soil layers when the separations and the non-dimensional wavelengths match.