The time-dependent response of a deep rigid anchor in a viscoelastic medium

Abstract

The problem of axially symmetric loading of a spheroidal rigid inclusion embedded in bonded contact with an isotropic linear viscoelastic infinite medium is investigated. This particular problem is of interest in connection with the analysis of the time-dependent anchorage efficiency of deep ground anchors and rock anchors embedded in soil and rock media susceptible to creep. The solution to the spheroidal rigid anchor problem pertaining to a linear viscoelastic medium is facilitated by the application of the Laplace transform-based correspondence principle. The transformed viscoelasticity problem is then solved by the use of Boussinesq's three-function approach developed for the solution of three-dimensional problems in classical elasticity. For the purposes of illustration, the particular viscoelastic material behavior is restricted to one which exhibits a dilatational response which is elastic and a deviatoric response which is that of a standard linear solid. Explicit analytical results are presented for anchors of both prolate and oblate spheroidal shapes which are subjected to either loads or displacements which vary as step functions of time. Numerical results are presented for cases where the rigid anchor embedded in typical geological materials is subjected to a step function of displacement. These results illustrate the manner in which the tension in the anchor rod can be influenced by the creep of the geological material in the vicinity of the anchor region.