Long-Term Deformation Analysis for a Vertical Concentrated Force Acting in the Interior of Fractional Derivative Viscoelastic Soils

Abstract

This paper gives a set of time-dependent displacement solutions for the case of a vertical concentrated force acting in the interior of fractional derivative viscoelastic soils. First, a three-dimensional fractional derivative viscoelastic model is introduced to describe the creep behavior of soils. Then based on the well-known Mindlin's elastic solutions and the correspondence principle from static elasticity to quasi-static viscoelasticity, the proposed precise solutions are systematically obtained in the Laplace transform domain. Subsequently, the proposed displacement solutions are validated against three previously published solutions, and all of the comparisons show a good agreement. Finally, parametric study and discussion are given, to analyze in detail the influence of parameters on the solutions. It is indicated that the displacements for fractional derivative viscoelastic models are smaller in the early stage and larger in the later stage than those for conventional viscoelastic models, and the proposed displacement solutions are more general.