Torsional dynamic response of an end-bearing pile in homogeneous unsaturated transversely isotropic soil

Considering the soil skeleton to be statically transversely isotropic, the viscous and inertial coupling among three phases, along with the capillary pressure, the torsional dynamic response of an end-bearing pile in homogeneous unsaturated transversely isotropic soil under time-harmonic torsional load is investigated. The separation of variables method is employed to derive the torsional dynamic governing equations of unsaturated transversely isotropic soil in a cylindrical coordinate system, and pile is modeled as a 1D elastic theory. By combining the boundary conditions of the pile and soil, as well as the continuity conditions at the pile-soil interface, further employing the inverse Fourier transform and convolution theorem, fundamental analytical solutions for the torsional behavior of the pile are derived in both the frequency domain and time domain. Comparisons between the proposed solution and the two existing solutions indicate that the presented model exhibits stronger applicability, as it can simultaneously transition to both saturated transversely isotropic soil and unsaturated isotropic soil. Eventually, a parametric study is conducted to examine the influence of soil anisotropy, degree of saturation, pile-soil shear modulus ratio and pile length on the torsional dynamic response of end-bearing pile.