Analytical solution for dynamic interaction of end-bearing pile groups subjected to vertical dynamic loads

An analytical model for pile-soil-vertical coupled vibration of the pile considering the scattering effects of the passive pile is proposed based on the classical plane strain assumption. The governing equation for the soil is solved to obtain the expressions for the vertical displacement and resistance of the soil and the attenuation function of the soil displacement. Based on rigorous pile-soil interaction, the pile-interaction factor of the pile considering the scattering effects of the passive pile is obtained by solving the displacement of the active pile under vertical excitation and the displacement of the passive pile caused by the vibration of the active pile, as well as the displacement of the active pile caused by the scattering waves of the passive pile. Based on the modified pile-pile interaction factor, a stiffness-matrix is then established to derive the vertical dynamic responses of the pile groups by considering the scattering effects of the passive pile. Then the analytical solution for the vertical dynamic impedance of the pile groups is derived by incorporating the property of pile cap and the superposition principle. Finally, some arithmetical cases are presented to conduct the numerical analysis. It is found that the degenerated solution for the present solution agrees well with the existing one. The scattering effects cannot be ignored for the pile groups with small pile spacing. The pile spacing and slenderness ratio have considerable effects on the pile-interaction factor of the pile and the vertical dynamic impedance of the pile groups.