Frequency domain analysis of torsional vibration of single pile in orthotropic viscoelastic layered foundation

The present paper establishes a theoretical analytical framework based on a three-parameter solid model (standard linear solid model) for the torsional vibration of a single pile in an orthotropic viscoelastic layered foundation. The three-dimensional partial differential form of the pile-soil coupling equations is reduced to a set of axisymmetric frequency-domain ordinary differential equations by introducing Hankel integral transformations. In order to construct a layered transfer matrix model that accounts for viscoelastic energy dissipation, the following steps are taken. Firstly, transverse anisotropic soil constitutive relations and interlayer continuity conditions are combined. An explicit frequency-domain solution for the torsional complex stiffness at the pile top was derived. The study systematically analysed the effects of soil anisotropy coefficients, viscoelastic parameters, and soil layer distribution on the system’s dynamic response. The present study proposes a theoretical framework for the design of pile foundations in complex soil conditions, with particular reference to torsional loading.