This study offers a comprehensive and advanced understanding of the torsional response of piles partially embedded in fractional-order viscoelastic unsaturated transversely isotropic soils, accurately capturing the true viscoelastic properties and particle orientation of the soil as formed during deposition. Based on Biot's threephase porous media wave equations and considering the coupling effects between the immiscible fluids (water and air) in the pores, the dynamic governing equations for fractional-order viscoelastic unsaturated transversely isotropic soil are established. The soil vibration displacement is solved using the method of separation of variables. In the frequency domain, employing the transfer matrix method and considering the continuity and boundary conditions of the pile-soil system for both the embedded and exposed portions, the analytical solution for the torsional complex impedance at the pile head of a partially embedded single pile in fractionalorder viscoelastic unsaturated transversely isotropic soil is derived. Furthermore, a semi-analytical solution for the pile head response in the time domain under half-sine pulse excitation is obtained through inverse Fourier transform and convolution theorem. Numerical examples are presented to investigate the effects of the parameters of the fractional-order viscoelastic constitutive model and the pile-soil parameters on the torsional complex impedance at the pile head.

An analytical solution for investigating the torsional dynamic response of a pipe pile in unsaturated poroelastic transversely isotropic soil under time-harmonic load is proposed. By employing the Biot's type three-phase porous media model and the three-dimensional continuum theory, taking into account the transversely isotropic characteristics of the soil skeleton, as well as the viscosity and inertial coupling between different phases, distinct dynamic governing equations are derived for the soils surrounding and inside the pipe pile. By considering the boundary and continuity conditions at the interface between the pipe pile and the soils surrounding and inside the pipe pile in the frequency domain, a mathematical expression is derived to describe the torsional dynamic behavior of the pipe pile. A parametric study aimed to investigate how the anisotropy of the soils surrounding and inside the pipe pile (soil plug) impacts its torsional complex impedance, twist angle, and torque was conducted. The parametric study also considered variations in saturation, pile lengths, porosity, the height of the soil plug and excitation frequencies to explore the effects of these parameters on the torsional behavior of the pipe pile.