Analysis of Torsional Vibration of Single Pile in Orthotropic Layered Soil

To address the difficulty in obtaining analytical solutions for the torsional vibration response of pile foundations in orthotropic layered soil foundations subjected to torsional excitation at the pile top, this study investigates a layered recursive algorithm based on the Hankel transform. An integral transformation method is employed to reduce the dimensionality of the coupled pile–soil torsional vibration equations, converting the three-dimensional system of partial differential equations into a set of ordinary differential equations. Combining the constitutive properties of transversely anisotropic strata with interlayer contact conditions, a transfer matrix model is established. Employing inverse transformation coupled with the Gauss–Kronrod integration method, an explicit frequency-domain solution for the torsional dynamic impedance at the pile top is derived. The research findings indicate that the anisotropy coefficient of the foundation significantly influences both the real and imaginary parts of the impedance magnitude. The sequence of soil layer distribution and the bonding state at interfaces jointly affect the nonlinear transmission characteristics of torque along the pile shaft.