Torsional vibration of a pipe pile in unsaturated cross-anisotropic soil based on the fractional viscoelastic model

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.