Semianalytical Solution for Long-Term Settlement of a Single Pile Embedded in Fractional Derivative Viscoelastic Soils

This paper proposes a semianalytical solution to analyze the long-term settlement of a single pile embedded in fractional derivative viscoelastic soils under time-dependent loading. In this paper, a three-dimensional (3D) fractional derivative viscoelastic model will be introduced to describe the rheological behavior of soils around the pile. Based on the shear deformation compatibility between the pile and soils, the semianalytical solution will be strictly derived using the correspondence principle and the Laplace transform technique. Three well-documented cases will be used to verify the correctness and reliability of the proposed semianalytical solution, all of which show a very close agreement. Furthermore, worked examples that include instantaneous and ramp loadings will be carried out to capture the influence of six dimensionless parameters, that is, a, b, c, d, κ, and α, on the long-term settlement of a single pile. The results indicate that: the dimensionless settlement for fractional derivative viscoelastic models is larger in the early stage and smaller in the later stage than those for conventional viscoelastic models; the dimensionless settlement capacity of the pile is controlled by the parameters a and d, and the dimensionless settlement rate is controlled by the parameters b and α, which means the selection of these four parameters has a great influence on the long-term settlement; and the parameter c causes little variation in the results.