Dynamic Torsional Response of Pile in Fractional-Order Viscoelastic Unsaturated Transversely Isotropic Soil With Imperfect Contact

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.