Torsional response of pile partially embedded in fractional-order viscoelastic unsaturated transversely isotropic soil

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 three-phase 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 fractional-order 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.