Dynamic analysis for horizontal vibration of piles in layered Pasternak soils considering secondary ground waves

To comprehensively investigate the effects of secondary ground waves (SGWs) induced by the vibration of receiver piles (RPs) in layered soils on the pile-pile horizontal vibration (PPHV), a simplified mechanical model for frequency-domain analysis of PPHV is proposed. This proposed model is based on layered Pasternak soils and elastic Euler-Bernoulli beam theory, incorporating the effects of axial loads and SGW. Firstly, the horizontal displacements (HDs) and the internal forces of the source pile (SP) are obtained using the differential transformation method combined with the continuity boundary conditions (BCs) at the pile-soil interface. Secondly, considering the influence of the vibration of the SP on the RP, a horizontal vibration analysis model for the RP is established, followed by the derivation of an analytical solution for the horizontal dynamic response (HDR). Furthermore, to consider the influence of SGWs induced by the vibration of the RP on the HDR of the SP, an improved analytical solution for the HDR of the RP is obtained. Finally, based on the definition of the dynamic interaction factor, the pile-pile horizontal dynamic interaction factor (PPHDIF) is derived and its rationality is validated by comparisons with existing solutions. Parametric analyses are performed to explore the effects of soil shear deformation, pile-soil modulus ratio, and axial loads on the PPHDIF. The results provide theoretical guidance and references for the dynamic design of pile groups in engineering practice.