A novel theoretical model is proposed to investigate the torsional response of a pile in fractional-order viscoelastic unsaturated transversely isotropic soil with imperfect contact. This model employs Biot's framework for three-phase porous media along with the theory of fractional derivatives. Unlike previous models that assume continuous displacement at the pile-soil interface, this study uses the Kelvin model to simulate relative slippage between pile-soil contact surfaces (imperfect contact). Incorporating fractional-order viscoelastic and transversely isotropic models to describe the stress-strain relationship, comprehensive dynamic governing equations are derived. Using the separation of variables method, inverse Fourier transform, and convolution theory, analytical solutions for the frequency domain response and semi-analytical solutions for the time domain response of the pile head under semi-sine pulse excitation are obtained. Using numerical examples, the effects of model parameters in the fractional-order viscoelastic constitutive model, pile-soil relative slip and continuity model, and soil anisotropy on the torsional complex impedance, twist angle, and torque are presented.

This study integrates cross-anisotropic and viscoelastic properties into the solid skeleton of unsaturated soils, conceptualized as a three-phase medium comprising solid, water, and air, in order to explore the torsional response of pipe pile. The stress-strain relationships are characterized using cross-anisotropic and fractional derivative models, resulting in more accurate torsional dynamic equations for the soils surrounding and inside the pipe pile. The torsional governing equations are solved in the frequency domain by applying the separation of variables and leveraging properties of fractional derivatives, while considering boundary continuity conditions and trigonometric orthogonality to derive the pipe pile's torsional complex impedance. The time-domain response to a half-sine excitation load is determined using inverse Fourier transforms and the convolution theorem. After validating the computational model, numerical analyses are conducted to explore the effects of model and geometric parameters on the complex stiffness, twist angle, and torque at the pipe pile head.