Static Stiffness of Unbounded Soil by Finite-Element Method

Abstract

To calculate the static-stiffness matrix of the unbounded soil for use in a time-domain analysis of soil-structure interaction, the consistent infinitesimal finite-element cell method is developed. Its derivation is based on the finite-element formulation and on similarity. The discretization is only performed on the structure-soil interface, yielding a reduction of the spatial dimension by 1. The procedure is exact in the radial direction and exact in the finite-element sense in the circumferential directions. In contrast to the boundary-element procedure, the consistent infinitesimal finite-element cell method does not require a fundamental solution and incorporates interfaces extending from the structure-soil interface to infinity compatible with similarity without any additional computational effort. A general anisotropic material can be processed. Applications of the consistent infinitesimal finite-element cell method to problems of increasing complexity ranging from a spherical cavity with uniform pressure to a tunnel in inhomogeneous transversely isotropic unbounded rock show excellent accuracy.