Dynamic torsional response of an end bearing pile in transversely isotropic saturated soil

The dynamic response of an end bearing pile embedded in transversely isotropic saturated soil and subjected to a time-harmonic torsional loading is investigated. Based on the dynamic wave equations of saturated soil and the stress–strain relationships of transversely isotropic medium, the dynamic governing equations of the transversely isotropic saturated soil are derived in cylindrical coordinates and the pile is modeled using one-dimensional elastic theory. At first, the torsional response of the soil layer is solved by using the separation of variables technique. Then by utilizing the boundary and continuity conditions of the pile–soil system, the dynamic response of the pile is obtained in a closed form in the frequency domain. By virtue of inverse Fourier transform and convolution theorem, a quasi-analytical solution for the velocity response of a pile subjected to a semi-sine wave exciting torque is obtained in the time domain. Finally, a parametric study has been undertaken to investigate the influence of the soil anisotropy on the torsional vibration characteristics of the pile, and the results obtained are presented in this paper.