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

An analytical model for the "pile-soil-pile" horizontal interaction in pile groups that accounts for the scattering effect of the receiver pile is presented in this study based on the plane strain model, to modify the calculating theory for closely-spaced and large-diameter pile groups embedded in single-phase soils. The displacement and horizontal dynamic resistance of the surrounding soil are analytically obtained by decoupling the governing equations of the soil. After that, the displacement of the source pile caused by the applied horizontal load, the displacement of the receiver pile caused by the incident wave and the displacement of the source pile caused by the scattering wave are respectively derived by considering the "incident wave-receiver pile interaction" and the "scattering wave-source pile interaction". Following that, a new-defined scattering factor for horizontally vibrating groups is proposed to modify the reported "pile-pile" interaction factor. Then, this modified interaction factor is used to establish the calculating matrix for the pile groups subjected to horizontal dynamic loads, and to further derive the corresponding dynamic complex impedance accounting for the scattering effect of the receiver pile. It is found through some arithmetical cases that the pile spacing, pile diameter and surrounding soil's shear modulus dominate the scattering effect; the scattering effect is frequency-dependent, transitioning from a load-bearing favorable case to a load-bearing unfavorable case with the increase of the vibration frequency; the critical frequency governing the transition between the favorable and the unfavorable state of the scattering effect is dependent on pile spacing, pile diameter, the direction of the applied load and the shear modulus of the soil.