Infinite Elements for Ground Freezing Problems

Abstract

In the analysis of artificial ground freezing problems, one encounters the domains of interest extending to infinity. A conventional finite element method deals with these problems by extending the mesh to some considerable distance away from the zone of interest and applying a fixed boundary condition there. This method requires a large number of nodal points in modeling the remote region where the perturbation in the variable of interest is virtually zero. Consequently, the cost of numerical analysis increases. The purpose here is to show how the infinite boundary can be treated within the finite element method by developing infinite elements that can be incorporated into standard finite element programs. The proposed method results in appreciable savings in the computer storage and cost of the analysis. The infinite elements employed possess semi‐infinite domain with properly selected decaying shape functions.