Analytical solution of horizontal SV wave response considering pile shear deformation and soil free-field shear stress

Abstract

An analytical solution is developed to investigate the horizontal SV wave responses of end-bearing pile considering shear deformation of Timoshenko beam and soil free-field shear stress. Firstly, the beam used is a Timoshenko beam that is more in line with the actual engineering project, in which taken into account the additional deflection caused by the bending and shear deformation of the pile. Meanwhile, the conditional transformation method is used to transform the coupled equation controlled by the two independent variables of displacement and rotation angle in the beam model into the decoupled governing equation. Then, the impedance of the soil to the pile under horizontal SV wave is obtained based on the fixed bottom and free top boundaries of the soil, and the continuous boundary conditions of the pile-soil interface. Furthermore, the closed solution of the problem is obtained according to the relationship of the governing equation of Timoshenko beam, the interaction between pile and soil, and the fixed bottom and free top boundaries of the end-bearing pile. In addition, the free vibration and forced vibration of the present solution are compared with the commercial finite element software ABAQUS and the existing analytical solutions of Euler beam to verify the rationality of the present analytical solution. Finally, the influence of soil free-field shear stress and pile shear deformation are emphatically analyzed. The results have certain guiding significance for engineering structure design.